SURFEX SCIENTIFIC
DOCUMENTATION
P. Le Moigne
February 23, 2018

2

EDITOR : Patrick Le MoigneContributing authors :2018
C. Albergel (1) , A. Boone (1) , S. Belamari (1) , B. Decharme (1) , M. Dumont (4) ,P. Le Moigne (1) , V. Masson (1)2012
A. Boone (1) , S. Belamari (1) , E. Brun (1) , J.-C. Calvet (1) , B. Decharme (1) , H. Giordani (1) ,S. Lafont (1) , P. Le Moigne (1) , S. Morin (4) , V. Vionnet (1)2009
A. Boone (1) , J.-C. Calvet (1) , B. Decharme (1) , S. Faroux (1) , A.-L. Gibelin (1) , C. Lebeaupin (2) ,P. Le Moigne (1) , J.-F. Mahfouf (1) , E. Martin (1) , V. Masson (1) , D. Mironov (3) , J. Noilhan (1) ,P. Tulet (1) , B. Van Den Hurk (4)(1): CNRM-UMR3589, Météo-France/CNRS, Toulouse, France: Laboratoire de Météorologique Dynamique, Ecole Polytechnique, Palaiseau, France(3): German Weather Service, Offenbach am Main, Germany(4): CNRM-UMR3589, Météo-France/CNRS, Grenoble, France(5): KNMI, The Netherlands(2)

Dissemination Level : public

SURFEX v8.1 - Issue no 3 - 2018

3
ISSUE No
1
2

3

V5.0
V7.2

V8.0
and
V8.1

DATE
May 2009
March 2012

PAGES
1 - 211
1 - 235

DESCRIPTION OF CHANGE
Original
Description of Crocus, Isba-CC, Teb-Veg
Bibliography references by chapter

February 2018

1 - 304

Description of MEB, TARTES,
Revision of ISBA-ES, ISBA-DF
Revision of TEB+VEG
Revision of water surfaces

SURFEX v8.1 - Issue no 3 - 2018

4

SURFEXI SURFACE PROCESSES SCHEME

11

1 Introduction: a brief description of the SURFEX system

13

2 Water surfaces
2.1 Simple parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Free water surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Sea ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Sea surface turbulent fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Bulk equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Direct parameterization: Louis (1979) . . . . . . . . . . . . . . . . . . . .
2.2.2.1 Roughness lengths . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2.2 Parameters and derived Richardson’s numbers . . . . . . . . . . .
2.2.2.3 Exchange coefficient for the wind (CD ) . . . . . . . . . . . . . .
2.2.2.4 Exchange coefficient for the temperature / humidity (CH =CE ) . .
2.2.3 Iterative parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3.1 The MR98 parameterization . . . . . . . . . . . . . . . . . . . .
2.2.3.2 The COARE 3.0 parameterization . . . . . . . . . . . . . . . . .
2.2.3.3 The ECUME parameterization . . . . . . . . . . . . . . . . . . .
2.2.3.4 Stability functions used in the iterative parameterizations . . . . .
2.2.3.5 Additional refinements included in the iterative parameterizations .
2.3 Coupling with a 1D TKE oceanic model . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Coupling objectifs and principles . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Description of the 1D oceanic model in TKE equation . . . . . . . . . . .
Prognostic equations for T, S, u and v . . . . . . . . . . . . . . . . . . . .
Prognostic equation for turbulent kinetic energy . . . . . . . . . . . . . . .
Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Inland Water: Lake Model FLake . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 The Water Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameterization of the Temperature Profile and the Heat Budget . . . . . .
The skin temperature module . . . . . . . . . . . . . . . . . . . . . . . . .
The Mixed-Layer Depth . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 The Water–Bottom Sediment Interaction . . . . . . . . . . . . . . . . . .
2.4.4 Ice and Snow Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.5 Empirical Relations and Model Constants . . . . . . . . . . . . . . . . . .
2.4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17
18
18
18
19
19
22
22
22
23
24
25
25
26
28
32
32
35
35
36
36
37
38
40
40
43
43
44
45
48
48
52
55

SURFEX v8.1 - Issue no 3 - 2018

5

3 Urban and artificial areas
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Modelling cities in atmospheric models . . . . . . . . . . . . . . . . . . .
3.1.2 Objectives of the Town Energy Balance scheme . . . . . . . . . . . . . . .
3.1.3 Overview of the Town Energy Balance scheme . . . . . . . . . . . . . . .
3.1.4 TEB patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.5 Town geometry description . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.6 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Basics of the Town Energy Budget scheme . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Temperature evolution equations . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Longwave budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diffuse solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Direct solar radiation for averaged directions . . . . . . . . . . . . . . . .
Direct solar radiation for a given canyon direction . . . . . . . . . . . . . .
Solar radiation reflectionsi . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Anthropogenic fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Turbulent fluxes for momentum . . . . . . . . . . . . . . . . . . . . . . .
Treatment of the urban roughness sublayer . . . . . . . . . . . . . . . . .
The drag approach with the Surface Boundary Layer scheme . . . . . . . .
The roughness length approach . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 Turbulent fluxes for heat and moisture . . . . . . . . . . . . . . . . . . . .
Considerations on the turbulent transfer of heat and moisture . . . . . . . .
Exchange coefficients between surfaces and atmosphere . . . . . . . . . .
Heat fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.7 Water reservoirs evolution . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.8 Snow effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.9 Atmospheric quantities inside the canyon . . . . . . . . . . . . . . . . . .
In the case of the Surface Boundary Layer scheme . . . . . . . . . . . . .
Wind inside the Canyon . . . . . . . . . . . . . . . . . . . . . . . . . . .
Canyon temperature and humidity . . . . . . . . . . . . . . . . . . . . . .
3.2.10 Averaged fluxes at town scale . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Urban vegetation: gardens and greenroofs . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Philosophy of vegetation in TEB . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Gardens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Greenroofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Irrigation and watering . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 The Building Energy Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Buildings description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Buildings energy budgets . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Inside solar irradiation, sheltering . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Domestic Heating and Air conditioning . . . . . . . . . . . . . . . . . . .
3.4.5 Waste heat emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.6 Ventilation and infiltration . . . . . . . . . . . . . . . . . . . . . . . . . .
SURFEX v8.1 - Issue no 3 - 2018

63
64
64
65
65
66
66
68
69
70
71
73
73
73
74
75
75
76
76
76
76
77
77
77
78
79
80
81
81
81
82
82
84
84
84
85
87
89
89
90
90
91
91
92

6

3.5

3.6

Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mechanical Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Natural Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.7 Solar panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Surface Boundary Layer module, when applied in TEB . . . . . . . . . . . . .
3.5.1 Drag by buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Mixing length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Miscellaneous indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Thermal comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mean radiant temperature . . . . . . . . . . . . . . . . . . . . . . . . . .
Universal Thermal Climate Index . . . . . . . . . . . . . . . . . . . . . .

92
92
92
93
95
95
95
97
97
97
98

4 Soil and vegetation
105
4.1 ISBA surface scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.1 Surface snow fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.2 Force restore approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Treatment of the soil heat content . . . . . . . . . . . . . . . . . . . . . . 108
Treatment of the soil water . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Treatment of soil ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.1.3 Diffusive approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Surface and soil heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . 117
Liquid Soil Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Soil water phase changes: freeze-thaw . . . . . . . . . . . . . . . . . . . . 133
4.1.4 Soil organic carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.1.5 Treatment of the intercepted water . . . . . . . . . . . . . . . . . . . . . . 138
4.1.6 Spatial variability of precipitation intensities . . . . . . . . . . . . . . . . 139
4.1.7 Treatment of the snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
One-layer snow scheme option . . . . . . . . . . . . . . . . . . . . . . . . 141
Multi-layer snow scheme options . . . . . . . . . . . . . . . . . . . . . . 142
Additional features of the Crocus scheme . . . . . . . . . . . . . . . . . . 145
4.1.8 The surface fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.1.9 ISBA-Multi-Energy-Budget (MEB) Explicit Vegetation . . . . . . . . . . . 153
Snow Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Energy Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Turbulent fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Radiative fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Heat Conduction fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Aerodynamic Resistances . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Ground resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Water Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Snow Interception within the canopy . . . . . . . . . . . . . . . . . . . . . 172
Rain Interception within the canopy . . . . . . . . . . . . . . . . . . . . . 174
Halstead Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
SURFEX v8.1 - Issue no 3 - 2018

7

4.2

4.3

Forest Litter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Energy and Mass conservation . . . . . . . . . . . . . . . . . . . . . . . . 178
4.1.10 Summary of Useful Parameters . . . . . . . . . . . . . . . . . . . . . . . 180
4.1.11 Appendix A: Continuous formulation of the soil secondary parameters . . . 181
4.1.12 Appendix B: Gaussian formulation for the C1 coefficient . . . . . . . . . . 182
4.1.13 Appendix C: ISBA-MEB Numerical Solution . . . . . . . . . . . . . . . . 183
Discretization of surface energy budgets . . . . . . . . . . . . . . . . . . . 183
Atmospheric temperature and specific humidity . . . . . . . . . . . . . . . 184
Canopy air temperature and specific humidity . . . . . . . . . . . . . . . . 185
Sub-surface temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Net Longwave radiation flux derrivatives . . . . . . . . . . . . . . . . . . 187
Halstead coefficient maximum . . . . . . . . . . . . . . . . . . . . . . . . 189
Surface stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Summary: Final solution of the implicitly coupled equations . . . . . . . . 190
ISBA-A-gs surface scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
4.2.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Background information . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Photosynthesis Model (no water stress) . . . . . . . . . . . . . . . . . . . 193
Soil moisture stress parameterization . . . . . . . . . . . . . . . . . . . . 196
From leaf to canopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Biomass evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
CO2 fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
4.2.2 Vegetation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
4.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Soil moisture stress parameterization . . . . . . . . . . . . . . . . . . . . 208
Temperature response of gm for C3 plants . . . . . . . . . . . . . . . . . . 208
Radiative transfer within the vegetation . . . . . . . . . . . . . . . . . . . 208
Representation of crops . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Representation of nitrogen dilution . . . . . . . . . . . . . . . . . . . . . 210
Annex 1: Description of the Fortran routine used to calculate the CO2 flux 210
The ISBA-CC model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
4.3.2 Allocation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Evolution of the biomass compartments . . . . . . . . . . . . . . . . . . . 211
Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Decline term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
4.3.3 Coupling with the soil organic matter scheme . . . . . . . . . . . . . . . . 216
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Supply of litter compartments . . . . . . . . . . . . . . . . . . . . . . . . 218
SURFEX v8.1 - Issue no 3 - 2018

8

4.3.4
4.3.5

Decomposition of the soil organic matter . . . . . . . . . . . . . . . . . . 219
Carbon fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Description of a simulation with ISBA-CC . . . . . . . . . . . . . . . . . 223
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

5 Surface boundary layer scheme
237
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
5.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
5.2.1 Atmospheric equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
5.2.2 Atmospheric equations modified by canopy obstacles . . . . . . . . . . . . 240
5.2.3 Implementation of the SBL equations into a surface scheme . . . . . . . . 241
5.2.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
5.2.5 Turbulence scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
5.3 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
5.4 Appendix: Vertical and temporal discretization . . . . . . . . . . . . . . . . . . 246
5.4.1 Vertical discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.4.2 Temporal discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.4.3 Implicit coupling with the atmospheric model . . . . . . . . . . . . . . . . 246
6 Chemistry and aerosols
251
6.1 Dust aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
6.1.1 Implementation in the Externalized surface . . . . . . . . . . . . . . . . . 252
6.1.2 Features of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Emission process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Parameterization of the friction velocity . . . . . . . . . . . . . . . . . . . 253
Friction velocity threshold . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Influence of soil moisture on friction velocity threshold . . . . . . . . . . . 254
Aerodynamical roughness height . . . . . . . . . . . . . . . . . . . . . . . 255
Surface flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Mass flux repartition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
6.2 Sea Salt emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
6.3 Dry deposition of gaseous species . . . . . . . . . . . . . . . . . . . . . . . . . . 256
6.3.1 Resistances for dry deposition . . . . . . . . . . . . . . . . . . . . . . . . 256
6.3.2 Dry deposition velocity formulation . . . . . . . . . . . . . . . . . . . . . 264
6.4 Dry deposition of aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
6.5 Biogenic VOC fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

II LAND COVER: ECOCLIMAP

271

7 Introduction273

8 Ecoclimap characteristics
277
8.1 Surface parameters definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
8.2 Aggregation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
SURFEX v8.1 - Issue no 3 - 2018

9

8.3

Writing of parameters in a latex file . . . . . . . . . . . . . . . . . . . . . . . . . 278

9 Ecoclimap-II realization
285
9.1 The Ecoclimap-II map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
9.1.1 The initial map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
9.1.2 NDVI satellite data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
9.1.3 The automatic classification process . . . . . . . . . . . . . . . . . . . . . 287
9.1.4 To the resulting map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
9.1.5 Short description of covers . . . . . . . . . . . . . . . . . . . . . . . . . . 289
9.2 Translation of covers in tiles and vegetation types . . . . . . . . . . . . . . . . . . 290
9.3 Initialization of LAI profiles and other parameters . . . . . . . . . . . . . . . . . . 291
9.3.1 Initialization of heights of trees, ground depths, irrigation and town parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
9.3.2 Initialization of LAI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
LAI by cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Disaggregation of LAI by vegtype inside covers . . . . . . . . . . . . . . . 292
9.4 Study of the discontinuity at the limits of the domain . . . . . . . . . . . . . . . . 293
10 Validation elements for Ecoclimap-II

295

11 Conclusion

297

III LAND SURFACE ANALYSIS

299

12 Surface Offline Data Assimilation
301
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
12.2 Source code - creation of the binary . . . . . . . . . . . . . . . . . . . . . . . . . 301
12.3 Optimal Interpolation soil moisture analysis . . . . . . . . . . . . . . . . . . . . . 301
12.4 Extended Kalman Filter soil moisture and vegetation analysis . . . . . . . . . . . . 302
12.5 Ensemble Kalman Filter soil moisture and vegetation analysis . . . . . . . . . . . 303

SURFEX v8.1 - Issue no 3 - 2018

10

SURFEX v8.1 - Issue no 3 - 2018

Part ISURFACE PROCESSES SCHEME

11

Chapter 1

Introduction: a brief description of the
SURFEX system
Surface modelling in numerical weather prediction has always held an important place in the activities of
the Centre National de Recherches Météorologiques (CNRM hereafter). In the late 80’s, Isba (Noilhan and
Planton (1989); Mahfouf and Noilhan (1996)), a soil vegetation atmosphere transfer scheme (Interaction
between Soil Biosphere and Atmosphere) has been developed and it aimed to better simulate the exchangesof energy and water between the land surface and the atmosphere just above. Isba model has been designed
to be simple and efficient in order to be put into operations at Météo-France. Isba scheme computes theexchanges of energy and water between the continuum soil-vegetation-snow and the atmosphere above.
In its genuine version, the evapotranspiration of the vegetation is controlled by a resistance like proposed
by Jarvis (1976) . A more recent version of the model named Isba-A-gs (Calvet et al. (1998)) accounts
for a simplified photosynthesis model where the evaporation is controlled by the aperture of the stomates,
the component of the leaves that regulates the balance between the transpiration and the assimilation of
CO2. Nowadays, Isba land surface scheme is used in the French operational and research forecast models.
Thanks to the efforts made by the research community at CNRM, French numerical weather prediction
models have always been at the forefront of research in terms of surface modelling. More recently, themodelling of urban areas has began to be of great interest in the research community. In 2000, TEB (Town
Energy Balance) model, specially designed to represent the exchanges between a town and the atmosphere
has enabled advanced studies in this direction (Masson (2000)). The TEB model is based on the canyon
concept, where a town is represented with a roof, a road and two facing walls with characteristics playing
a key role in the town energy budget. More especially, the ability, of the canyon to trap a fraction of theincoming solar and infrared radiation is taken into account in the model. A special effort has been made thislast years to externalize the surface scheme from the embedded surface-atmosphere Meso-NH model. The
main idea was to gather all the developments and improvements made in surface schemes in order to makethem available for as many people as possible. Not only physical parameterizations have been externalized,
but also the preparation of specific surface parameters needed by physical schemes and the initializationof all state variables of the different models: SURFEX (stands for surface externalisée) system was born.
Moreover, the surface representation has been improved and thus Surfex system has been enhanced with thespecific treatment for water surfaces. Indeed, up to now, the exchanges of energy between water surfaces
and the atmosphere were treated in a very simple way, while now a physically based model have been
introduced to build a more complex but accurate surface model, available for all atmospheric models. There
are two possibilities to compute fluxes over marine surfaces. The simplest one consists in using Charnock’s
approach to compute the roughness length and fluxes with a constant water surface temperature. Secondly,13

14
a one-dimensional ocean mixing layer model has been introduced (Lebeaupin (2007)) in order to simulate
more accurately the sea surface temperature (SST hereafter) and the fluxes at the sea/air interface. Thismodel based on Gaspar (1990) , will be very helpful especially at meso-scale to better represent diurnal
cycle of SST. At meso-scale, a good representation of lakes is of great interest especially for Northerncountries. In order to improve the treatment of lake areas, the simple but robust Flake model (Mironov(2010)) has been implemented within Surfex system. It allows to have an evolving lake surface temperature
and a good description of the energy exchanges within water.

Figure 1.1: Description of the exchanges between an atmospheric model sending meteorological and radiative fields to the surface and Surfex composed of a set of physical models that compute tiled variables F∗
covering a fraction f∗ of a unitary grid box and an interface where the averaged variables F are sent back to
the atmosphere

In Surfex, the exchanges between the surface and the atmosphere are realized by mean of a standardized
interface (Polcher et al. (1998); Best et al. (2004)) that proposes a generalized coupling between the atmosphere and surface. During a model time step, each surface grid box receives the upper air temperature,
specific humidity, horizontal wind components, pressure, total precipitation, long-wave radiation, shortwave direct and diffuse radiations and possibly concentrations of chemical species and dust. In return,Surfex computes averaged fluxes for momentum, sensible and latent heat and possibly chemical species anddust fluxes and then sends these quantities back to the atmosphere with the addition of radiative terms likesurface temperature, surface direct and diffuse albedo and also surface emissivity.
All this information is then used as lower boundary conditions for the atmospheric radiation and turbulent
schemes. In Surfex, each grid box is made of four adjacent surfaces: one for nature, one for urban areas,
one for sea or ocean and one for lake. The coverage of each of these surfaces is known through the global
ECOCLIMAP database (Masson et al. (2003)) , which combines land cover maps and satellite information.
The Surfex fluxes are the average of the fluxes computed over nature, town, sea/ocean or lake, weighted bytheir respective fraction.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

15

Bibliography[1] M. J. Best, A. Beljaars, J. Polcher, and P. Viterbo. A proposed structure for coupling tiled surfaces
with the planetary boundary layer. J. Hydrometeorol., 5(6):1271–1278, December 2004.
[2] J. C. Calvet, J. Noilhan, J. L. Roujean, P. Bessemoulin, M. Cabelguenne, A. Olioso, and J. P. Wigneron.
An interactive vegetation svat model tested against data from six contrasting sites. Agric. and For.
Meteorol., 92(2):73–95, July 1998.
[3] P. Gaspar, Y. Grégoris, and J.-M. Lefevre. A simple eddy kinetic energy model for simulations of theoceanic vertical mixing: Tests at station papa and long-term upper ocean study site. J. Geophys. Res.,
95(C9):16179–16193, 1990.
[4] P. G. Jarvis. The interpretation in the variations of leaf water potential and stomatal conductance foundin canopies in the field. Philos. Trans. R. Soc. London, B. 273:593–610, 1976.
[5] C. Lebeaupin. Etude du couplage océan-atmosphère associé aux épisodes de pluies intenses en régionméditerranéenne. PhD thesis, University Paul Sabatier, Toulouse, France, 2007.
[6] J. F. Mahfouf and J. Noilhan. Inclusion of gravitational drainage in a land surface scheme based on theforce-restore method. J. Appl. Meteorol., 35(6):987–992, June 1996.
[7] V. Masson. A physically-based scheme for the urban energy budget in atmospheric models. Bound.Layer Meteorol., 94(3):357–397, March 2000.
[8] V. Masson, J.-L. Champeaux, F. Chauvin, C. Meriguet, and R. Lacaze. A global database of land
surface parameters at 1-km resolution in meteorological and climate models. J. Clim., 16(9):1261–
1282, 2003.
[9] D. Mironov, E. Heise, E. Kourzeneva, B. Ritter, N. Schneider, and A. Terzhevik. Implementation of
the lake parameterisation scheme flake into the numerical weather prediction model cosmo. Boreal
Env. Res., 15:218–230, 2010.
[10] J. Noilhan and S. Planton. A simple parameterization of land surface processes for meteorologicalmodels. Mon. Weather Rev., 117(3):536–549, 1989.
[11] J. Polcher, B. McAvaney, P. Viterbo, M. A. Gaertner, A. Hahmann, J. F. Mahfouf, J. Noilhan,
T. Phillips, A. Pitman, C. A. Schlosser, J. P. Schulz, B. Timbal, D. Verseghy, and Y. Xue. A proposal for a general interface between land surface schemes and general circulation models. Glob. andPlanet. Change, 19(1-4):261–276, December 1998.

SURFEX v8.1 - Issue no 3 - 2018

16

SURFEX v8.1 - Issue no 3 - 2018

Chapter 2

Water surfaces
Contents
2.1

2.2

Simple parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.1

Free water surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1.2

Sea ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Sea surface turbulent fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1

Bulk equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.2

Direct parameterization: Louis (1979) . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2.1 Roughness lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2.2 Parameters and derived Richardson’s numbers . . . . . . . . . . . . . . . 22
2.2.2.3 Exchange coefficient for the wind (CD ) . . . . . . . . . . . . . . . . . . 23
2.2.2.4 Exchange coefficient for the temperature / humidity (CH =CE ) . . . . . . 24

2.2.3

Iterative parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3.1 The MR98 parameterization . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.3.2 The COARE 3.0 parameterization . . . . . . . . . . . . . . . . . . . . . 26
2.2.3.3 The ECUME parameterization . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.3.4 Stability functions used in the iterative parameterizations . . . . . . . . . 32
2.2.3.5 Additional refinements included in the iterative parameterizations . . . . . 32

2.3

Coupling with a 1D TKE oceanic model . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1

Coupling objectifs and principles . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3.2

Description of the 1D oceanic model in TKE equation . . . . . . . . . . . . . . . 36
Prognostic equations for T, S, u and v . . . . . . . . . . . . . . . . . . . . . . . . 36
Prognostic equation for turbulent kinetic energy . . . . . . . . . . . . . . . . . . . 37
Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4

Inland Water: Lake Model FLake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.1

Equation of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.4.2

The Water Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Parameterization of the Temperature Profile and the Heat Budget . . . . . . . . . . 43
The skin temperature module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
The Mixed-Layer Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.4.3

The Water–Bottom Sediment Interaction . . . . . . . . . . . . . . . . . . . . . . 48

17

18
2.4.4

Ice and Snow Cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.4.5

Empirical Relations and Model Constants . . . . . . . . . . . . . . . . . . . . . . 52

2.4.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.1 Simple parameterization
2.1.1 Free water surfaces
For ocean surfaces and over inland waters, all the prognostic variables are kept constant.
The surface fluxes are calculated using Eqs. 4.182, 4.183, 4.185 and Eqs. 4.205, 4.206, 4.207 of Isba, taking
the relative humidity of the ocean hu = 1, and veg = psn = 0. The roughness length is given by Charnock’s
relation:u2
z0sea = 0.015 ∗
g

(2.1)

2.1.2 Sea ice
Sea ice is detected in the model when sea surface temperature (SST) is two degrees below 0◦ C (i.e.
271.15 K). In this case, in order to avoid an overestimation of the evaporation flux, the calculations are
performed with the roughness length of flat snow surfaces:
z0ice = 10−3 m(2.2)

In the same manner, the sea ice albedo is set equal to the fresh snow albedo instead of the free water albedo.
This leads to a much brighter surface. This has no effect on the sea ice cover (since there is no evolutionof the sea surface parameters), but modifies the lower boundary shortwave flux input for the atmosphericradiative scheme.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

19

2.2 Sea surface turbulent fluxes
In this section, we introduce the various sea surface fluxes parameterizations available in the SURFEX
surface scheme, namely the direct parameterization of Louis (1979) and four iterative parameterizations:
the MR98 (Mondon and Redelsperger, 1998), the COARE3.0 (Fairall et al., 2003) and the two versions of
the ECUME (Belamari, 2005) parameterizations.

2.2.1 Bulk equations
Air-sea turbulent fluxes, i.e. the stress or momentum flux τsea, the sensible heat flux Hsea and the latent
heat flux LEsea are given by: |~τ |sea = ρa (w′ u′ )s(2.3)
Hsea = ρa cpa (w′ θ ′ )s LE = ρ L (w′ q ′ )
s
sea
a v

where w′ , u′ , θ ′ and q ′ stand for the fluctuations of the vertical speed, horizontal wind, potential temperatureand specific humidity. s index stands for sea surface variables whereas a index stands for atmosphericvariables at the “measurement’s height” (actually at the lowest level of the model). Lv is the latent heat ofseawater vaporization at sea surface, and cpa is the specific heat of moist air.
For this surface layer, four characteristic length scales can be derived from these surface fluxes, following
the Monin and Obukhov (1954) theory, namely:• the friction velocity u∗ such as:u∗ 2 = −(w′ u′ )s(2.4)• the temperature characteristic length scale θ∗ :
θ∗ = −(w′ θ ′ )s
u∗

(2.5)

q∗ = −(w′ q ′ )s
u∗

(2.6)

• the humidity characteristic length scale q∗ :• and last, the Monin-Obukhov length L:
L=

−u3
 ∗ 
κ θgv w′ θv ′

(2.7)

s

κ denotes the dimensionless von Kármán constant. θv is the virtual potential temperature:θv = θa (1.0 + 0.61 qa )(2.8)

Using the corresponding characteristic length scale θv ∗ defined as:
θv∗ = −

(w′ θv ′ )su∗leads to another formulation of the Monin-Obukhov length L: 2 
θv
u∗
L=
κ.g
θv ∗
SURFEX v8.1 - Issue no 3 - 2018

(2.9)

(2.10)

20
where θv∗ may be computed as:
θv ∗ = θ∗ (1.0 + 0.61 qa ) + 0.61(θa q∗ )(2.11)

New formulations of the air-sea turbulent fluxes can then be derived using these characteristic length scales:
2 |~τ |sea = −ρa u∗(2.12)
Hsea = −ρa cpa u∗ θ∗ LE = −ρ L u qseaa v ∗ ∗

In bulk parameterizations, transfer coefficients for the wind, potential temperature and specific humidity(hereafter referred to as CD , CH , and CE for drag, heat and evaporation) are introduced in order to be able
to compute the air-sea turbulent fluxes from mean meteorological gradients in the atmospheric boundary
layer:
2

 |~τ |sea = −ρa CD .U(2.13)
Hsea = −ρa cpa CH .U.(θa − θs ) LE = −ρ L C .U.(q − q )
sea
a v E
a
s

if the atmospheric convention is chosen, i.e. when fluxes are defined positive in case of energy benefit for
the atmosphere. Such transfer coefficients can be written as:
CX =−w′ x′
U ∆x(2.14)

where ∆x is the vertical gradient of the meteorological variable x (= u, θ or q) between the ocean surface
and the atmospheric lowest level, and U denotes the mean value of the relative wind. Using equations 2.12
and 2.13 leads to other formulations of these transfer coefficients as functions of the scaling parameters u∗ ,θ∗ and q∗ :


u∗ 2

 CD = U
θ∗CH = U (θua∗−θ(2.15)s) C = u∗ q ∗E
U (qa −qs )Transfer coefficients can also be expressed as functions of the atmospheric stratification and first atmospheric level height z. By applying the Buckingham theorem to the air flow in the surface layer, one may
indeed obtain, in neutral conditions, a relationship between the vertical gradient of the mean flow U and thecorresponding characteristic length scale u∗ :
∂U
u∗
=
∂z
κz

(2.16)

This vertical logarithmic profile obtained for neutral conditions can then be extended to any atmosphericconditions by introducing a function ϕm in order to take into account the stratification of the atmosphere:
z
∂U
u∗
(2.17)
=
× ϕm
∂z
κz
L
Integrating equation 2.17 allows then to express the vertical gradient of U , and in a similar way the verticalgradients of the potential temperature θ and specific humidity q as functions of the corresponding characteristic length scales u∗ , θ∗ and q∗ :
h  

i
z
z
u∗

−
ψ
ln
U
=
m

κ
z0
L



h  
i
(2.18)
θa − θs = θκ∗ ln zz0 − ψh Lz
t



i
h



 q − q = q∗ ln z − ψ z 
a

s

κ

z0q

q

L

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

21

or conversely the characteristic length scales u∗ , θ∗ and q∗ as functions of the vertical gradients in the real
atmosphere ∆u, ∆θ and ∆q:u∗ =  zκ.∆uln z −ψm (ζ)


0



 θ =  κ.∆θ
∗
(2.19)
ln zz −ψh (ζ)
0t





 κ.∆q q∗ = ln z −ψq (ζ)
z0qψm , ψh and ψq are stability functions depending on the Monin-Obukhov stability parameter ζ=z/L.
z0 , z0t and z0q stand for the roughness lengths for the wind, potential temperature and specific humidity,
respectively. The dynamical roughness length z0 is generally computed thanks to the relationship of Smith(1988):
 
 2
ν
u∗
(2.20)+βz0 = αgu∗where α is the Charnock parameter (as detailed hereafter, α may be a constant coefficient or may includes
a wind dependency), β is a constant coefficient, and ν is the air kinematic viscosity.
Combining equations 2.15 and 2.18 then leads to new formulations for the exchange coefficients: CD = FM (z, z0 , ζ) × CDn
CH = FH (z, z0 , z0t , ζ) × CHn
CE = FQ (z, z0 , z0q , ζ) × CEn

where FM , FH and FQ are stability functions:

"
#−2


ψ
(ζ)

FM (z, z0 , ζ)
= 1 − m z 


ln z


0



−1

"
#−1 




FH (z, z0 , z0t , ζ) = 1 − ψm (ζ)× 1 − ψh (ζ) 
z
ln
ln zz

z0

0t



−1


#−1
"




ψ (ζ)
ψ

m (ζ)


× 1 − q   FQ (z, z0 , z0q , ζ) = 1 − ln zz
ln z0(2.22)

z0q

and where CDn , CHn and CEn stand for the neutral exchange coefficients (i.e. for ζ=0):
2

CDn = h κz i2


ln z


0



 C =
κ2

  
Hn
ln zz ln zz
0
0t




2

κ

 CE n =    ln z ln z
z0(2.21)(2.23)

z0q

In the following sections, we will see that each parameterization uses its own closure hypothesis derived
either from a theoretical method or from experimentation to determine the exchange coefficients. These
parameterizations also differ in the calculation of the roughness lengths and/or of the neutral transfer coefficients, in the stability functions used to take into account the atmospheric stratification, as well as in
the representation of various processes including seawater salinity effect on evaporation, wind gusts, waves
effects, and sea spray (Brunke et al., 2003).
SURFEX v8.1 - Issue no 3 - 201822

2.2.2 Direct parameterization: Louis (1979)
In the SURFEX surface scheme, the parameterization of Louis (1979) may be used through the choice of
CSEA FLUX='DIRECT' in the NAM SEAFLUXn namelist. In this parameterization (for which two versions
are available as detailed hereafter), the exchange coefficients at the air-sea interface are computed from theirvalues in neutral conditions using stability functions depending on the Richardson number Ri that is definedas the ratio between the potential and kinetic energy of the surface layer:g.z θva − θvsRi = 2(2.24)
U
θv
where g is the gravity and θv is the mean virtual potential temperature of the atmospheric layer.
No specific computation is made for the humidity, as the corresponding exchange coefficient and roughness
length are set to be equal to those of the potential temperature, i.e.:(
CE = CH(2.25)
z0q = z0t (hereafter referred to as z0H )2.2.2.1 Roughness lengths
The dynamical and heat roughness lengths z0 and z0H are estimated with a distinction between the free sea
water and the sea ice by a temperature criterion with a threshold at -2◦ C (Tab. 2.1):→ in sea ice case, roughness lengths are the same than for the snow,→ over free seawater, roughness lengths are reduced to the relationship of Charnock (1955), i.e. α = 0.015
and β = 0 in equation 2.20.
For T ≤ −2◦ CWindz0seaice = z0snow = 10−3

Heat

z0Hseaice = z0Hsnow = 10−4◦
For T > −2
 C

u2∗
g 2 
z0H = 0.015 ug∗

z0 = 0.015

Table 2.1: Roughness lengths (in meters) in the parameterization of Louis (1979).

2.2.2.2 Parameters and derived Richardson’s numbers
In the formulations of the exchange coefficients for the wind (CD , Table 2.2) and temperature / humidity(CH =CE , Table 2.3), b, d and k are constant parameters:


 b=5
(2.26)d=5
 k=1

RiSD and RiSH are modified Richardson’s numbers:
Ri
RiSD = 1+γ.Ri

andRiSH =

Ri

1(1+γ.δRi) δwith γ=(XUSURIC×XUSURICL). XUSURIC and XUSURICL are critical Richardson’s numbers:(
XUSURIC = 1
XUSURICL = 4(2.27)(2.28)

δ is a constant depending on the value of a third critical Richardson’s number XUSURID: δ=1 if
XUSURID=0, else δ=3. Note that usually δ=3 as default value for XUSURID is 0.035.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

23

2.2.2.3 Exchange coefficient for the wind (CD )Primitive formulation
LDRAG COEF ARP='.FALSE.'
22

CDn = h κz i2

Neutralln(Ri=0)

StableCD =CDn = h  κ z i2
ln 1+ z

z0

 1

Ri
1+2b √1+d.Ri

!

CD n

(Ri > 0)
Unstable(Ri < 0)

New formulation
LDRAG COEF ARP='.TRUE.'CD = 


1

1+2b r
2b.Ri
CD = 1 − 1+2b.CM .X
PM ∗ .C
∗

X =

 

0

Dn

√

R

RiSD
1+ d RiSD
k



( )








  CD

n

CD n



X = 1 + zz0
R = 1 + zz0 (−Ri)

zz0

R = −Ri

CM ∗ and P M ∗ are 3rd order polynomials in ln(z0 /z0H ):
h 
h 
i
i2
h 
i3
CM ∗ = cm0 + cm1 ln zz00
+ cm2 ln zz00
+ cm3 ln zz00
H

cm0 = +6.8741, cm1 = +2.6933
cm2 = -0.3601, cm3 = +0.0154

HH

cm0 = +7.5,
cm1 = +2.39037
cm2 = -0.28583, cm3 = +0.01074

h 
h 
h 
i
i2
i3
PM ∗ = pm0 + pm1 ln zz00
+ pm2 ln zz00
+ pm3 ln zz00H

pm0 = +0.5233, pm1 = -0.0815
pm2 = +0.0135, pm3 = -0.0010

HH

pm0 = +0.0,
pm1 = -0.07028
pm2 = +0.01023, pm3 = -0.00067

Table 2.2: Exchange coefficient for the wind in the parameterization of Louis (1979).
Note that, in the new formulation, if the same roughness length is used for both the potential temperature/specific humidity and the wind (z0 = z0H , corresponding to LDZ0H='.FALSE.'), then:(CM ∗ = 7.5(2.29)P M ∗ = 0.0
and the formulation of the exchange coefficient for the wind then reduces in unstable conditions to:CD = 
1 −


2b.Ri
 CD nr
1 + 15b.CDn
1 + zz0 (−Ri)

SURFEX v8.1 - Issue no 3 - 2018(2.30)

24
2.2.2.4 Exchange coefficient for the temperature / humidity (CH =CE )Primitive formulation
LDRAG COEF ARP='.FALSE.'
NeutralCHn =New formulation
LDRAG COEF ARP='.TRUE.'

2

κ

  
ln zz ln z z
0

CHn =

0H

2

κ


 
ln 1+ zz ln 1+ z z00H(Ri=0)
Stable(Ri > 0)
Unstable(Ri < 0)

CH =



1
√
1+3b.Ri 1+d.Ri



CHn

CH =



1
√
1+3b.RiSH 1+dk.RiSHCH = 1 − 1+3b.CH .X3b.Ri
PH ∗
.C
∗

XH =



z
z0H



H

Hn

√

RH





CHn

CHn



XH = 1 + z0zH
RH = 1 + z0z (−Ri)

RH = −RiH

CH ∗ and P H ∗ are 3rd order polynomials in ln(z0 /z0H ):
h 
h 
i
i2
h 
i3
CH ∗ = ch0 + ch1 ln zz00
+ ch2 ln zz00
+ ch3 ln zz00H

ch0 = +3.2165, ch1 = +4.3431
ch2 = +0.5360, ch3 = -0.0781

HH

ch0 = +5.0,
ch1 = +4.51268
ch2 = +0.34012, ch3 = -0.05330

h 
h 
i
i2
h 
i3
PH ∗ = ph0 + ph1 ln zz00
+ ph2 ln zz00
+ ph3 ln zz00H

ph0 = +0.5802, ph1 = -0.1571
ph2 = +0.0327, ph3 = -0.0026

HH

ph0 = +0.0,
ph1 = -0.09421
ph2 = +0.01463, ph3 = -0.00099

Table 2.3: Exchange coefficient for the temperature / humidity in the parameterization of Louis (1979).

Note that, in the new formulation, if the same roughness length is used for both the potential temperature/specific humidity and the wind (z0 = z0H , corresponding to LDZ0H='.FALSE.'), then:(CH ∗ = 5.0(2.31)
P H ∗ = 0.0
and the formulation of the exchange coefficient for the potential temperature / specific humidity then reduces
in unstable conditions to:CH = 
1 −


3b.Ri
 CHn
r


1 + 15b.CHn
1 + z0z (−Ri)
H

SURFEX v8.1 - Issue no 3 - 2018(2.32)

CHAPTER 2. WATER SURFACES

25

2.2.3 Iterative parameterizations
Bulk equations can also be solved with iterative methods to compute the Monin-Obukhov characteristic
length scales from which the turbulent air-sea fluxes are derived. Among these iterative methods, the algorithm of Liu et al. (1979) known as the LKB algorithm is the most used and was in particular a base forseveral parameterizations developments such as the COARE (Fairall et al., 1996b, 2003), MR98 (Mondon
and Redelsperger, 1998) and ECUME (Belamari 2005) parameterizations. Such iterative algorithms either
use a number of iterations fixed a priori (e.g. MR98, COARE3.0 and ECUME), or rely on a convergencecriterion depending on the parameterization (e.g. ECUME6).
Note that the iterative parameterizations available in the SURFEX surface scheme use similar stability functions (the Businger functions with different numerical values, Table 2.6). All of them also may include
additional refinements such as a salinity correction for the saturated vapor pressure, the computation of awind subgrid correction, sensible heat flux and wind stress corrections due to the rainfall, or Webb effect asdetailed in section 2.2.3.5.
2.2.3.1 The MR98 parameterization
In SURFEX, the MR98 parameterization (Mondon and Redelsperger, 1998) may be used through the choiceof CSEA FLUX='ITERAT' in the NAM SEAFLUXn namelist.
This parameterization is in fact a declination of the COARE algorithm with different numerical values for
the Businger stability functions and in the gustiness correction computation.
A first preliminary step insures the initialization of all the required variables, with namely:
1. the computation of the vertical gradients of the wind, potential temperature and specific humidity: ∆u = U(2.33)∆θ = θa − θs ∆q = q − qas

2. the estimation of the Monin-Obukhov characteristic length scales:u∗ = 0.04 × ∆u θ = 0.04 × ∆θ∗ q∗ = 0.04 × ∆qθv∗ = θ∗ (1.0 + 0.61 qa ) + 0.61(q∗ θa )(2.34)The second step then consists in an iterative loop with a fixed number of iterations (IITERMAX=10) in
order to update:
1. the Monin-Obukhov length L (following equation 2.10) and stability parameter ζ:ζ = MAX ( Lz ; −20 000) if θv∗ ≥ 10−6 , else ζ = 0.
2. the stability functions ψm and ψh as ψq is supposed to be equal to ψh (section 2.2.3.4)
3. the dynamical roughness length z0 following the formulation of Smith (1988) with α=0.011 and
β=0.11 in equation 2.20, and with the air kinematic viscosity ν computed as a function of the airtemperature Ta at the first atmospheric level: ν = 1.318 10−5 + 9.282 10−8 Ta (with Ta in Kelvin)
SURFEX v8.1 - Issue no 3 - 201826
4. the roughness lengths for the potential temperature and specific humidity z0t and z0q using formulations depending on the value of u∗ (Table 2.4)
5. and last, the characteristic length scales u∗ , θ∗ and q∗ derived from equations 2.19.
At the end of the iterative loop, air-sea turbulent fluxes are then computed following equations 2.12.

Potential temperatureSpecific humidity−1
For u∗≤ 0.23
 m.s  2z0t = 0.015 ug∗ + 0.18 uν∗ 2
 
z0q = 0.0205 ug∗ + 0.294 uν∗For u∗ > 0.23m.s−1νz0t = 0.14 u∗ −0.2
+ 7.10−6νz0q = 0.20 u∗ −0.2
+ 9.10−6

Table 2.4: Roughness lengths for the temperature (z0t ) and humidity (z0q ) in the MR98 parameterization.

2.2.3.2 The COARE 3.0 parameterization
The COARE (Coupled Ocean-Atmosphere Response Experiment) algorithm was initially developed during
the TOGA (Tropical Ocean and Global Atmosphere) experiment. Several versions were then produced,
among them the 2.5b version (Fairall et al., 1996b) which was successfully used during several measurement campaigns in several locations overall the globe. Taking into account air-sea interaction data fromthe NOAA/ETL dataset and from the HEXMAX data reanalysis, the validation of this algorithm had been
extended leading to the last version 3.0 of the COARE algorithm (Fairall et al., 2003) that is available in the
SURFEX surface scheme (Lebeaupin Brossier et al., 2009) through the choice of CSEA FLUX='COARE3'
in the NAM SEAFLUXn namelist.
As in MR98, the COARE 3.0 algorithm begins with a first preliminary step that insures the initializationof all the required variables, namely:
1. the vertical gradients of the wind, potential temperature and specific humidity (∆u, ∆θ and ∆q)
2. the dynamical roughness length z0 computed following the relationship of Smith (1988) using inequation 2.20 a constant value for the Charnock parameter (α=0.011), with β=0.11, with the air
kinematic viscosity ν computed following Andrea (1989):
ν = 1.326 10−5 1 + 6.542 10−3 ta + 8.301 10−6 ta 2 − 4.84 10−9 ta 3

(2.35)

where ta stands for the air temperature (in ◦ C), and with the initial value of the friction velocity u∗
estimated as a function of the wind vertical gradient between the sea surface and 10 meters height inneutral conditions (u∗ = 0.035 × ∆u10n )3. the roughness lengths for temperature and humidity z0t and z0q (derived from the dynamical one)
4. the characteristic length scales u∗ , θ∗ and q∗ using equations 2.19 in which the Monin-Obukhov
stability parameter ζ is computed as a function of a bulk Richardson number Ri b (Grachev and Fairall,1997):

i−1
h

Ri b

if Ri b < 0 (unstable conditions) ζ = C.Ri b 1 + Ri
bc
(2.36)ih ζ = C.Ri 1 + 3 Ri b −1 if Ri ≥ 0 (stable conditions)bb
C
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES
with:

27

i
h

g.z ∆θ+0.61 Ta ∆q

Ri
=
−
2
b

Ta
∆u



−1
Ri bc = −z 0.004 × zBL × βgust 3




H
C = κCCD(2.37)

Ri bc stands for the saturation value of Ri b . zBL and βgust are the same parameters as those used in
the computation of the wind subgrid correction wg (section 2.2.3.5): zBL is the atmospheric boundary layer depth (fixed to 600 meters), βgust is a gustiness factor (βgust =1.2 following results fromthe TOGA-COARE experiment). CH and CD are the temperature and wind exchange coefficients,
respectively. This computation of ζ from Ri b leads to a better background of the stability parameter, and allows to reduce the iterations number of the iterative loop (NITERMAX=1 if ζ > 50, else
NITERMAX=3).
As a second step, the iterative loop then insures the computation of:
1. the dynamical roughness length z0 using:• either the relationship of Smith (1988) with β=0.11 in equation 2.20 and with a wind dependency
introduced for the Charnock parameter (Hare et al., 1999):

−1
−1

 α = 0.011
 if 0 m.s ≤ U ≤ 10 m.s

U −10
if 10 m.s−1 < U ≤ 18 m.s−1(2.38)
α = 0.011 + (0.018 − 0.011) 18−10−1
α = 0.018
if 18 m.s < U• or more elaborated formulations that take into account the gravity waves’ effects on roughness:
Oost et al., 2002

z0 =

50
2π



Lwv

Taylor and Yelland, 2001 z0 = 1200 Hwv
with:





u∗
Cwv
Hwv
Lwv

4.5

+ 0.11

4.5+ 0.11



ν
u∗





ν
u∗




g

 Cwv = 2π (0.729 U )g
Lwv = 2π(0.729 U )2

Hwv = 0.018 U 2 × (1 + 0.015 U )(2.39)(2.40)

2. the roughness lengths for temperature and humidity z0t and z0q that are directly derived from z0 :
0.6 !
ν
−4−5(2.41)
z0t = z0q = MIN 1.15 10 , 5.5 10
z0 u∗
3. the Monin-Obukhov stability parameter ζ=z/L with L computed as: 2 u∗Ta (1.0 + 0.61 qa )L=κ.gθ∗ (1.0 + 0.61 qa ) + 0.61(Ta q∗ )(2.42)(you may note the difference with respect to the exact formulation of L given by equation 2.10)
4. the stability functions ψm and ψh as ψq is supposed to be equal to ψh (section 2.2.3.4)
5. and last, the characteristic length scales u∗ , θ∗ and q∗ using equations 2.19.
SURFEX v8.1 - Issue no 3 - 2018

28
At the end of the iterative loop, the final values of the characteristic length scales are then used to derive:• the exchange coefficients CD , CH and CE (from equations 2.15),• the air-sea turbulent fluxes τsea , Hsea and LE sea (from equations 2.12),• and last, the dynamical roughness length z0 computed using a subgrid formulation derived from thatof Smith (1988) but aiming to take into account the subgrid effects through a modified second term:
 2


u∗
CD
z0 = α(2.43)+βgCD nwhere α is the wind dependent Charnock parameter defined as in equations 2.38, β=10−5 , and CDn
is the wind neutral exchange coefficient computed following equation 2.23. The roughness lengths
for temperature and humidity are then directly obtained as z0t = z0q = z0 .

2.2.3.3 The ECUME parameterization
The ECUME (Exchange Coefficients from Unified Multi-campaigns Estimates) parameterization is a bulk
iterative parameterization developed at CNRM in order to obtain an optimized parameterization covering a wide range of atmospheric and oceanic conditions. Two versions of this last iterative parameterization are in fact available in the SURFEX surface scheme and may be used through the choice of
CSEA FLUX='ECUME' or CSEA FLUX='ECUME6' in the NAM SEAFLUXn namelist. Both of them rely
on in-situ air-sea fluxes measurements performed during several cruises (Table 2.5). As these cruises cover
only low to moderate wind conditions (Weill et al., 2003), additional specific results obtained for very strong
winds (Powell et al., 2003 ; Donelan et al., 2004 ; French et al., 2007 ; Drennan et al., 2007) were also usedin order to take into account the saturation and even decrease of the exchange coefficients for wind speeds
higher than 33 ms−1 .
Experiment
SEMAPHORE (Eymard et al., 1996)
CATCH (Eymard et al., 1999)
FETCH (Hauser et al., 2003)
EQUALANT (Gouriou et al., 2001)
POMME (Mémery et al., 2005)
EGEE/AMMA (Bourras et al., 2009)used in ECUME
⋆
⋆
⋆
⋆
⋆

used in ECUME6

⋆
⋆
⋆
⋆

Table 2.5: Air-sea fluxes measurements campaigns used in ECUME / ECUME6 parameterizations.
The key difference between the two parameterizations is that the original one (ECUME, see Belamari, 2005
for more details) provides formulations of the neutral exchange coefficients at 10m (drag coefficient CD10n ,heat coefficient CH10n and evaporation coefficient CE10n ) as functions of the neutral vertical wind gradient
between the sea surface and 10m-height ∆u10n (Figure 2.1, left part) while the new one (ECUME6) provides
formulations of derived parameters for the wind Pu10n , potential temperature Pθ10n and specific humidity
Pq10n (Figure 2.1, right part), defined as:



CD10n


√
× ∆u10n Pu10n = CD10n C(2.44)
Pθ10n = √CH10n× ∆u10n
D10n






CE


× ∆u10n Pq10n = √C 10n
D10n

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

29

2

1

0

0

10

20

30
u10n (m/s)

40

Pt10n

CH10n * 1000

0

10

20

30
u10n (m/s)

40

3

ECUME
ECUME6150

ECUME6

2

1

0

10

20

30
u10n (m/s)

40

3

0

50

Pq10n

1

0

10

20

30
u10n (m/s)

40

3

ECUME
ECUME6

2

0

2

0

50

2

0

ECUME61

3

CE10n * 1000

3

ECUME
ECUME6
Pu10n

CD10n * 1000

350

ECUME6

2

1

0

10

20

30
u10n (m/s)

40

50

0

0

10

20

30
u10n (m/s)

40

50

Figure 2.1: Left: Neutral coefficients at 10 meters CD10n , CH10n and CE10n in the ECUME (solid line) and
derived from the ECUME6 (dashed line) formulations. Right: Neutral parameters at 10 meters Pu10n , Pθ10n
and Pq10n in the ECUME6 formulation.

SURFEX v8.1 - Issue no 3 - 2018

30
The definition of these new parameters was motivated by the wide dispersion of the scatterplots providing
the observed neutral exchange coefficients as a function of the neutral wind at 10 meters, in contrast to
those of these new parameters.
As in the two other iterative parameterizations, the ECUME and ECUME6 algorithms begin with a firstpreliminary step that insures the initialization of all the required variables, namely:
1. the vertical gradients of the wind, potential temperature and specific humidity at the air-sea interface(∆u, ∆θ and ∆q)
2. the corresponding neutral vertical gradients: ∆u10n = ∆u∆θ10n = ∆θ × d0 ∆q
10n = ∆qwith:(

d0 = 1.2 + 6.3 10−3 MAX (∆u − 10 , 0) in ECUME
d0 = 1.0
in ECUME6

In ECUME6, an initial guess is also made for the characteristic length scales as initial values of u∗ , θ∗ andq∗ are required by the convergence criterion: u∗ = 0.04 ∆uθ∗ = 0.04 ∆θ q = 0.04 ∆q∗

As a second step, the iterative loop then insures the computation of:

1. the neutral exchange coefficients/parameters as functions of the neutral vertical wind gradient between
the sea surface and 10m-height ∆u10n :Momentum
Heat
Moisture

ECUME
Neutral coefficient
CD10n = fu (∆u10n )CH10n = fθ (∆u10n )CE10n = fq (∆u10n )ECUME6
Neutral parameter
Pu10n = gu (∆u10n )Pθ10n = gθ (∆u10n )Pq10n = gq (∆u10n )2. the characteristic length scales u∗ , θ∗ and q∗ derived from the previous coefficients/parameters:

Momentum
Heat
Moisture

ECUME
ECUME6
Scaling parameterspu∗ = CD10n.∆u10nu∗ = Pu10n


C
∆θ10n
θ∗ = √CH10n.∆θ10n θ∗ = Pθ10n ∆u10n D10n 


CE10n
∆q10n
q∗ = √C.∆q10n q∗ = Pq10n ∆u
10n
D10n

3. the stability parameter ζ=z/L constrained to be in the range [-200.0;0.25], using for the MoninObukhov length L the same approximate formulation as in COARE3.0 (equation 2.42)
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

31

4. the stability functions ψm and ψh as ψq is supposed to be equal to ψh (section 2.2.3.4)
5. and last, the neutral vertical gradients:




z
∆u10n = ∆u − uκ∗ ln 10− ψm (ζ)






z
− ψh (ζ)∆θ10n = ∆θ − θκ∗ ln 10






z
∆q10n = ∆q − qκ∗ ln 10− ψq (ζ)

At the end of the iterative loop, the final values of the characteristic length scales are then used to derive:• the exchange coefficients CD , CH and CE (from equations 2.15),• the air-sea turbulent fluxes τsea , Hsea and LE sea (from equations 2.13 in ECUME and 2.12 in ECUME6),• and last, the roughness lengths:– in ECUME, the dynamical roughness length z0 is computed in a single way using the subgrid
formulation (equation 2.43) with β=10−5– in ECUME6, the dynamical roughness length z0 may be computed in three different ways depending on the choice of a dedicated parameter (KZ0):−5* using the subgrid formulation with β=10 in equation 2.43 if KZ0=0* using the relationship of Smith (1988) with β=0.11 in equation 2.20 if KZ0=1* from the characteristic length scale u∗ , using a formulation derived from equation 2.19 if
KZ0=2:
−1∆u(2.45)+ ψm (ζ)
z0 = z exp κu∗Note that if the dynamical roughness length z0 is computed using the subgrid formulation or the relationship of Smith (1988), the Charnock parameter α may be either constant if CCHARNOCK='OLD'(then α=0.021) or wind dependent as in COARE3.0 (equation 2.38) if CCHARNOCK='NEW'.
The ECUME and ECUME6 parameterizations include other specific points:
1. No waves effects are taken into account in these parameterizations.
2. A stochastic perturbation may be applied to the air-sea turbulent fluxes (logical OPERTFLUX) in bothparameterizations.
3. In ECUME, the number of iterations is prescribed (fixed to 10), while in ECUME6 a convergencecriterion is used: the iterative loop is stopped when the difference between the scale parameters of
two successive iterations is inferior to a prescribed threshold (10−6 ms−1 for u∗ , 10−6 K for θ∗ and10−9 kg/kg for q∗ ). Note that an important effort was done for the ECUME6 algorithm in order toensure the convergence in maximum 10 iterations whatever the meteo-oceanic conditions (Belamari,2005).
4. In ECUME, a correction may be applied to the neutral coefficient for humidity (default is XICHCE=0):CE10n = CE10n (1 − XICHCE ) + CH10n (XICHCE )with

SURFEX v8.1 - Issue no 3 - 2018

0.0 ≤ XICHCE ≤ 1.0

32
2.2.3.4 Stability functions used in the iterative parameterizations
The stability functions ψm and ψh used in the four iterative parameterizations to correct the wind, potential
temperature and specific humidity logarithmic profiles in the boundary layer according to the atmosphericstratification are all modified Businger’s functions as detailed hereafter. ECUME* stands for both ECUME
and ECUME6, and ψ∗ represents either ψm or ψh depending on the considered parameter.
You may note that in unstable conditions the stability functions result from two contributions: a Kansas
part to represent the classical unstability, and a Convective part to take into account the free convection,with a weight f depending on the Monin-Obukhov stability parameter ζ. In the MR98 parameterization, adifferent formulation is used for the weight f but we do not mention it here as the resulting formulation of
the stability functions including the two contributions is rigorously equivalent.
Wind
Stable(ζ ≥ 0)MR98
ECUME*
COARE3.0

Potential temperatureψ∗ (ζ) = −4.7 ζψ∗ (ζ)
 = −7.0iζhψ∗ (ζ) = − 1 + ζ + 32 ζ−14.28+ 8.525
exp(Γ)

with Γ = MIN (50, 0.35ζ)ψ∗ (ζ) = (1 − f )ψ∗K + f ψ∗Cζ2with f = 1+ζ
2

Unstable(ζ < 0)ψmK = 2. ln

Kansas

1+x
2



+ ln



−2. arctan(x) + π2
MR98
ECUME*
COARE3.0ψ∗C = 32 ln

Convective
MR98
ECUME*
COARE3.0



1+x2
2



2

ψhK = 2. ln( 1+x
2 )

with:
1
x = (1 − 16 ζ) 4
1
x = (1 − 16 ζ) 4
1
x = (1 − 15 ζ) 4

1+y+y 2
3



−



√
√
+ √π3
3. arctan 1+2y
3

with:
1
y = (1 − 12.87 ζ) 3
1
y = (1 − 12.87 ζ) 3
1
1
y = (1 − 10.15 ζ) 3
y = (1 − 34.15 ζ) 3

Table 2.6: Stability functions used in the iterative parameterizations.

2.2.3.5 Additional refinements included in the iterative parameterizations
Each of the four iterative parameterizations may include some refinements as detailed in Table 2.7.
1. Salinity correction: A reduction of 2% may be applied to the saturated vapor pressure Psat usedin the computation of the specific humidity at the sea surface qs in order to take into account the
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

33

decreasing of Psat due to seawater salinity (Kraus, 1972):
qs = qs (Psat )withPsat = 0.98 × Psat (Ts )(2.46)

2. Explicit dependency to sea surface salinity: In ECUME6, if the sea surface salinity (SSS) field
is available in the SURFEX surface scheme, an explicit dependency to the SSS may be used in thecomputation of both the saturated vapor pressure Psat from which the specific humidity at the sea
surface qs is derived (Sharqawy et al., 2010), and the latent heat of seawater vaporization Lv :(qs = qs (Psat ) with Psat = Psat (Ts , SSS)
Lv = Lv (SSS )3. Wind subgrid correction: The relative wind - and therefore the wind gradient - may be increased bya subgrid correction (wg ) introduced in order to take into account the gustiness impact:q1∆u = U 2 + wg 2
with
wg = βgust (BF .zBL ) 3(2.47)
zBL is the atmospheric boundary layer depth (in meters), βgust is a constant coefficient, and BF is thesurface buoyancy flux:
BF = −g.u∗ .F
If BF ≤0, the wind correction wg is set to a minimal value wgmin .
4. Wind stress correction and Heat flux correction due to rainfall: As rainfall tends to increase thesurface drag and to cool the ocean, two additional contributions τr (Fairall et al., 1996b) and Hr(Gosnell et al., 1995) may be computed in order to correct the surface wind stress and sensible heat
flux, respectively:(τr = −γ R × U(2.48)
Hr = R cplw αc (Ts − Ta ) 1 + B1
R denotes the precipitation rate (in kg.s−1 .m−2 ). cplw is the rain specific heat including a dependency
to the rain temperature (supposed to be equal to that of the air). αc is a dimensionless parameter called
the wet-bulb factor:
Lr dv dqsat −1(2.49)
αc = 1 +cpd dhdTwhere Lr is the latent heat of rain vaporization (in J.kg−1 ), cpd is the specific heat of dry air (inJ.K−1 .kg−1 ), dv and dh are the diffusivities for water vapor (Pruppacher and Klett, 1978) and heat,
respectively. The slope of the saturated specific humidity at atmospheric level qsat (θa ) as a functionof the temperature is derived from the Clausius-Clapeyron relation:


dqsat
Lr qsat (θa )=λdTRv Ta 2
B is the Bowen ratio:
B=µ



cpd
Lr



Ts − Taqs − qa

5. Webb correction: This small correction may be applied to the latent heat flux in order to take into
account the air density variations when the humidity varies under the evaporation action:
LEWebb = ρa Lv w qa
SURFEX v8.1 - Issue no 3 - 2018

34
where Lv is the latent heat of seawater vaporization at sea surface, and w is the mean value of thevertical speed perturbations:u∗ θ ∗
w′ θ ′′′= − 1.61 u∗ q∗ + (1 + 1.61 qa )w = 1.61 w q + (1 + 1.61 qa )Ta
TaSalinity correction
Explicit dependency
to sea surface salinity

Wind subgrid
correction

Wind stress correction
due to rainfall

MR98
Yes
No

COARE3.0
Yes
No

ECUME
Yes
No

ECUME6
Yes
Yes [1]

Yes with:
wgmin =0.0 ms−1
βgust =0.6
zBL =650 m
F = θθvv∗

Yes [2] with:wgmin =0.2 ms−1
βgust =1.2
zBL =600 m
a q∗ )
F = θ∗ +0.61(TTa

Yes [2] with:wgmin =0.0 ms−1
βgust =1.2
zBL =600 m
a −Ta )q∗
F = θv ∗ −0.61(θ
Ta

No

No

Yes [3] with
γ=0.85
Yes with:
λ=1µ=1

Yes [3] with
γ=1.0
Yes with:
v
λ= R
Rd
dh
µ = dvYes [3] with
γ=0.85
Yes with:
λ=1µ = ddhv

No
Heat flux correction
due to rainfall[1] If the sea surface salinity field is available in the SURFEX surface scheme.
Else, only the standard “Salinity correction” is applied.
[2] Logical LPWG in the NAM SEAFLUXn namelist.
[3] Logical LPRECIP in the NAM SEAFLUXn namelist.
Table 2.7: Additional refinements available (or not) in the iterative parameterizations.
Note that:
1. In the various formulations of the surface buoyancy flux BF , θv is the air virtual potential temperature(equation 2.8), θv∗ is the associated characteristic length scale given by equation 2.11, θa and Ta are
the air potential temperature and air temperature, respectively. This leads to different formulations in
COARE3.0 and ECUME when compared to the (exact) one used in MR98.
2. In the heat flux correction due to rainfall, λ and µ should be equal to 1 to be fully consistent with
Gosnell et al. (1995).

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

35

2.3 Coupling with a 1D TKE oceanic model
2.3.1 Coupling objectifs and principles
The main objective of the coupling is to improve the fine scale air-sea exchanges modelling in the SURFEX
surface scheme. To better represent the fine scale air-sea interactions, it is necessary to take into account theoceanic dynamics and the thermal content evolution (Lebeaupin et al. (2007, 2009)) .
The coupled system’s principle consists in modelling a seawater column under each grid point containing afraction of sea and limited by the bottom (Figure 2.2). The ocean model used is the uni-dimensional model
described by Gaspar et al. (1990) [see section 2.3.2] which allows to represent the oceanic vertical mixing
according to a parameterization of turbulence from Bougeault and Lacarrère (1989) adapted to ocean. By
the turbulent vertical mixing modelling, the 1D ocean model allows to represent the heat, water and momentum exchanges from the superficial oceanic layers in direct interaction with the atmosphere and subjected
to radiative effects, to the deepest layers. The turbulent vertical mixing is based on a parameterization of
the second-order turbulent moments expressed as a function of the turbulent kinetic energy (Gaspar et al.
, 1990). In this formulation, the vertical mixing coefficients are based on the calculation of two turbulent
length scales representing upward and downward conversions of turbulent kinetic energy (TKE) into potential energy (Gaspar et al. , 1990). By allowing a response to high frequencies in the surface forcing,the scheme improved the representation of the vertical mixed layer structure, sea surface temperature andupper-layer current (Blanke and Delecluse, 1993 ). However, this parameterization fails to properly simu-

Figure 2.2: The high-resolution ocean-atmosphere coupled system between (MESO-NH) SURFEX and the
1D oceanic model.
SURFEX v8.1 - Issue no 3 - 201836
late the mixing in strongly stable layers in the upper thermocline (Largeet al. , 1994 ; Kantha and Clayson,
1994 ). Consequently, a parameterization of the diapycnal mixing (Large et al. , 1994) was introduced into
Gaspar’s turbulence parameterization model in order to take into account the effects of the vertical mixing occurring in the thermocline (Josse, 1999 ). This non local source of mixing, mainly due to internal
wave breaking and current shear between the mixed layer and upper thermocline, impacts the temperature,salinity, momentum and turbulent kinetic energy inside the mixed layer particularly during restratification
periods. This parameterization was widely used, for instance to study successfully the diurnal cycle in the
Equatorial Atlantic (Wade et al. , 2011 ), the Equatorial Atlantic cold tongue (Giordani et al. , 2011 ), theproduction of modal waters in the North-East Atlantic (Giordani et al. , 2005b ) or to derive surface heat flux
corrections (Caniaux et al. , 2005b ). Note that horizontal and vertical advections can be easily prescribedin the 1D-mixing model to perform realistic simulations in heterogeneous situations.

2.3.2 Description of the 1D oceanic model in TKE equation
The 1D model includes a prognostic equation for the turbulent kinetic energy (e) with a 1.5 order closure.
The other prognostic variables are the temperature (T), the salinity (S), and the current [~u = (u, v)].
Prognostic equations for T, S, u and v
Each of the prognostic variables (α) is decomposed in a mean value (α) and a perturbation around this meanvalue (α′ ), so α = α + α′ . For each seawater column, T, S, u and v evolve under the turbulent verticalmixing effect. This mixing depends of air-sea interface fluxes.
The conservative equations are:
Fsol ∂I(z)∂T∂T ′ w ′∂t = ρ0 cp ∂z − ∂z





∂S ′ w ′∂S(2.50)∂t = − ∂z






′ ′
 ∂~u
= −f ~k × ~u − ∂~u w∂t∂zwhere w is the vertical velocity, ρ0 is a reference density, cp is the specific heat, f is the Coriolis parameter.
~k is the unit vertical along the vertical, Fsol is the solar radiation received by the surface, and I(z) is thesolar radiation fraction reaching the depth z (I(z) function decreases exponentially with depth).
The conditions at the top of the model (z=0) are:
Fnsol
H+LE+Fir′ ′ −T w (0) = ρ0 cp =
ρ0 cp





−S ′ w′ (0) = E−P(2.51)
ρ0 cp






 −~u′ w′ (0) = ~τ
ρ0 cp

Fluxes are positive here downwards.

Finally, the forcing variables to give to the oceanic model are:• the solar radiation Fsol
• the infra-red radiation Fir• the evaporation rate E proportional to the latent heat flux E = LEL
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

37• the sensible heat flux H• the zonal and meridional stress components ~τ = (τu , τv )• the precipitation rate P
Fnsol is defined as the sum of the sensible H, the latent heat flux LE and the infra-red radiation Fir and isnamed non-solar flux.
The closure relationships are given by:
−T ′ w′ = Kh ∂T

∂z





(2.52)−S ′ w′ = Ks ∂S
∂z






 −~u′ w′ = K ∂~um ∂z

The K∗ are diffusivity coefficients linked to the turbulent kinetic energy by:

Km
≃ Km
P rt
where ck is a constant to determine; lk is a mixing length and P rt is the Prandlt’s number.
1

K = ck lk e 2 = Kh = Ks =(2.53)

Prognostic equation for turbulent kinetic energy
The equation for TKE e = 12 (u′2 + v ′2 + w′2 ) is given by:


∂~u
∂
∂e
p′ w ′′′ew +=−+ b′ w ′ − ǫ− u~′ w′ ×
∂t
∂z
ρ0
∂z

(2.54)

30
where p is pressure; ǫ = cǫ lǫ e 2 is dissipation; b = g ρ−ρρ0 is the buoyancy. The seawater density is diagnosed
from temperature and salinity:ρ = ρ0 + (T − Tref ) × [−0.19494 − 0.49038(T − Tref )] + 0.77475(S − Sref )where Tref = 13.5 C, Sref = 32.6 psu and ρ0 = 1024.458 kg/m3 .
The vertical TKE flux is parameterized:p′ w ′∂e′′− ew += Ke
ρ0∂z(2.55)

with1

Ke = cǫ lǫ e 2(2.56)The Bougeault and Lacarrère mixing length are:1

lǫ = (lu ld ) 2(2.57)

lk = min(lu , ld ) pour k = h, s and m(2.58)

lu and ld (for “up” and “down”) are estimated as the upwards and downwards distances for which the kinetic
energy is transformed in potential energy:
Z z+lug[ρ(z) − ρ(z ′ )]dz ′e(z) =(2.59)
ρ0 z
Z z−ldge(z) =(2.60)[ρ(z) − ρ(z ′ )]dz ′ρ0 z
SURFEX v8.1 - Issue no 3 - 2018

38
Discretization
The temporal integration scheme is a semi-implicit scheme for T and S. For the horizontal current ~u =(u, v), the integration scheme is implicit/semi-implicit.
The discretization is here described in detail for the temperature. The same could be done for the salinity,
the TKE and the current in complex notation (~u → u + iv, i2 = −1).
The equation
Fsol ∂I(z)
∂
∂T
∂T
=
−
−K
∂t
ρ0 cp ∂z∂z∂z
is decomposed as:t+1
T t+1 − Tkt+1
T t+1 − Tk−1
Tkt+1 − Tkt
Fsol ∂I(z)1=+[K(k + 1) k+1− K(k) k](2.61)∆t
ρ0 cp ∂z∆z2 (k)∆z1 (k)∆z1 (k)






1
K(k + 1) − K(k)K(k + 1)
1 t Fsol ∂I
K(k)
t+1
t+1
t+1
+
T +
+ Tk
+ Tk+1 −=Tk−1 −∆z1 ∆z2∆t∆z1 ∆z2∆z1 ∆z2∆t k ρ0 cp ∂z

In a matricial writing following the vertical levels (k):1Fsol ∂I(z)[M] T t+1 =]Tt + [∆t
ρ0 cp ∂z(2.62)




.
.
0
 .

.
.
0


 0 β α γ

0


k
k
k
[M] = 
 − − − − − − − 
0 . . . 
0 . .
αk =

(2.63)

1
K(k + 1) − K(k)+∆t∆z1 ∆z2βk = −
γk = −

K(k)∆z1 ∆z2

K(k + 1)∆z1 ∆z2[M] is a tri-diagonal matrix to invers.
The vertical grid must be a z-coordinates grid as described by Fig. 2.3.
To take into account the bathymetry effects on the oceanic vertical mixing, we introduced a bathymetryindex (as the sea-land mask) which is worth 0 for free sea and 1 for levels under the sea-bed. For the verticallevels which have a bathymetry index equal to 1, we impose the prognostic variables values equal to the last
free-sea level values. The 1D model thus does not carry out any energy transfer towards or coming from thebottom. Only the energy contained in the higher free levels is taken into account.
We also introduced a diagnosis of mixed layer depth. The mixed layer base is diagnosed with an arbitrary
criterion on the density profile: we assume that the thermocline corresponds to the vertical level for which
the seawater density is superior to a 0.02 kg m−3 variations compared to the density for a reference level(taken at 5m depth).
Finally, the oceanic model must be initialized in temperature, salinity and current either from an oceanic
analysis or from climatologies.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

39

Figure 2.3: Vertical grid description of the 1D oceanic model from Gaspar et al. (1990) .

SURFEX v8.1 - Issue no 3 - 201840

2.4 Inland Water: Lake Model FLakeIn this section, a lake model (parameterisation scheme) capable of predicting the temperature structure oflakes of various depth on time scales from a few hours to many years is presented. A detailed descriptionof the model, termed FLake, is given in Mironov (2010). FLake is an integral (bulk) model. It is based ona two-layer parametric representation of the evolving temperature profile within the water column and on
the integral energy budget for these layers. The structure of the stratified layer between the upper mixed
layer and the basin bottom, the lake thermocline, is described using the concept of self-similarity (assumed
shape) of the temperature-depth curve. The same concept is used to describe the temperature structure of thethermally-active upper layer of bottom sediments and of the ice and snow cover. An entrainment equation
for the depth of a convectively-mixed layer and a relaxation-type equation for the depth of a wind-mixed
layer in stable and neutral stratification are developed on the basis of the turbulence kinetic energy (TKE)
equation integrated over the mixed layer. Both mixing regimes are treated with due regard for the volumetriccharacter of solar radiation heating. Simple thermodynamic arguments are invoked to develop the evolution
equations for the ice and snow depths. The system of ordinary differential equations for the time-dependent
prognostic quantities that characterise the evolving temperature profile, see Figs. 2.4 and 2.5, is closedwith algebraic (or transcendental) equations for diagnostic quantities, such as the heat flux through the lakebottom and the equilibrium mixed-layer depth in stable or neutral stratification.
The resulting lake model is computationally very efficient but still incorporates much of the essential
physics.
Within FLake, the lake water is treated as a Boussinesq fluid, i.e. the water density is taken to be constant equal to the reference density except when it enters the buoyancy term in the TKE equation and theexpression for the buoyancy frequency.
The other thermodynamic parameters are considered constant except for the snow density and the snow heat
conductivity.

2.4.1 Equation of StateWe utilise the quadratic equation of state of the fresh water,ρw = ρr
1
2
1 − aT (θ − θr ) ,2(2.64)

where ρw is the water density, ρr = 999.98 ≈ 1.0 · 103 kg·m−3 is the maximum density of the fresh
water at the temperature θr = 277.13 K, and aT = 1.6509 · 10−5 K−2 is an empirical coefficient (Farmer
and Carmack (1981)). Equation (2.64) is the simplest equation of state that accounts for the fact that thetemperature of maximum density of the fresh water exceeds its freezing point θf = 273.15 K. According
to Eq. (2.64), the thermal expansion coefficient αT and the buoyancy parameter β depend on the watertemperature,β(θ) = gαT (θ) = gaT (θ − θr ),where g = 9.81 m·s−2 is the acceleration due to gravity.
SURFEX v8.1 - Issue no 3 - 2018(2.65)

CHAPTER 2. WATER SURFACES

41

θb(t)

θs(t)

h(t)

D
H(t)
(a)
L

θ (t)
H

θ

L

Figure 2.4: Schematic representation of the temperature profile in the mixed layer, in the thermocline, and in the thermally active layer of bottom sediments. The evolving temperature profileis specified by several time-dependent quantities. These are the mixed-layer temperature θs (t)and its depth h(t), the temperature θb (t) at the water-bottom sediment interface, the shape factorCθ (t) with respect to the temperature profile in the thermocline, the temperature θH (t) at thelower boundary of the upper layer of bottom sediments penetrated by the thermal wave, and thedepth H(t) of that layer. The temperature θL at the outer edge z = L of the thermally active
layer of bottom sediments is constant.

SURFEX v8.1 - Issue no 3 - 2018

42

θ (t)
S

θ (t) θ (t) θ (t)Isb−HI(t)−HS(t)Snow−H (t)
I

Ice

h(t)
Water

θ (t)
H

D

Sediment

H(t)

(b)
θ

L

L

Figure 2.5: Apart from θs (t), h(t), θb (t), Cθ (t), θH (t), and H(t) (see Fig. 2.4), four additional
quantities are computed in case the lake is covered by ice and snow. These are the temperatureθS (t) at the air-snow interface, the temperature θI (t) at the snow-ice interface, the snow depth
HS (t), and the ice depth HI (t).

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

43

2.4.2 The Water Temperature
Parameterization of the Temperature Profile and the Heat Budget
We adopt the following two-layer parameterization of the vertical temperature profile:(θs
at 0 ≤ z ≤ hθ=θs − (θs − θb )Φθ (ζ)
at h ≤ z ≤ D,

(2.66)

where Φθ≡(θs − θ) / (θs − θb ) is a dimensionless function of dimensionless depthζ ≡ (z − h) / (D − h). The thermocline extends from the mixed-layer outer edge z = h to thebasin bottom z = D. Hereinafter the arguments of functions dependent on time and depth are not indicated(cf. Figs. 2.4 and 2.5 ).
RD
According to Eq. (2.66), h, D, θs , θb , and the mean temperature of the water column, θ ≡ D −1 0 θdz, arerelated throughθ = θs − Cθ (1 − h/D)(θs − θb ),(2.67)
where
Cθ =

Z 1

Φθ (ζ)dζ

(2.68)

0is the shape factor.
The parameterization of the temperature profile (2.66) should satisfy the heat transfer equation∂∂(ρcθ) = − (Q + I),∂t∂z(2.69)

where Q is the vertical turbulent heat flux, and I is the heat flux due to solar radiation.
Integrating Eq. (2.69) over z from 0 to D yields the equation of the total heat budget,
D

1
dθ
=
[Qs + Is − Qb − I(D)] ,
dt
ρw cw

(2.70)

where cw is the specific heat of water, Qs and Is are the values of Q and I, respectively, at the lake surface,and Qb is the heat flux through the lake bottom. The radiation heat flux Is that penetrates into the water isthe surface value of the incident solar radiation flux from the atmosphere multiplied by 1 − αw , αw being
the albedo of the water surface with respect to solar radiation. The surface flux Qs is a sum of the sensible
and latent heat fluxes and the net heat flux due to long-wave radiation at the air-water interface.
Integrating Eq. (2.69) over z from 0 to h yields the equation of the heat budget in the mixed layer,
h

dθs
1
=
[Qs + Is − Qh − I(h)] ,
dt
ρw cw

(2.71)

where Qh is the heat flux at the bottom of the mixed layer.
Given the surface fluxes Qs and Is (these are delivered by the driving atmospheric model or are known fromobservations), and the decay law for the flux of solar radiation , Eqs. (2.67), (2.70) and (2.71) contain seven
unknowns, namely, h, θ, θs , θb , Qh , Qb and Cθ . The mixed layer depth, the bottom heat flux and the shapefactor are considered in what follows. One more relation is required. Following Filyushkin and Miropolsky(1981), Tamsalu et al. (1997) and Tamsalu and Myrberg (1998), we assume that in case of the mixed layer
deepening, dh/dt > 0, the profile of the vertical turbulent heat flux in the thermocline can be represented ina self-similar form. That is
Q = Qh − (Qh − Qb )ΦQ (ζ)

at h ≤ z ≤ D,

SURFEX v8.1 - Issue no 3 - 2018(2.72)

44
where the shape function ΦQ satisfies the boundary conditions ΦQ (0) = 0 and ΦQ (1) = 1. Equation (2.72)
is suggested by the travelling wave-type solution to the heat transfer equation. If the mixed layer and thethermocline develop on the background of a deep stably or neutrally stratified quiescent layer (this situationis encountered in the ocean and in the atmosphere), the travelling wave-type solution shows that both thetemperature profile and the profile of the turbulent heat flux are described by the same shape function, i.e.
Φθ (ζ) = ΦQ (ζ). In lakes, the thermocline usually extends from the bottom of the mixed layer down to thebasin bottom (except for very deep lakes). In this case, the travelling wave-type solution to the heat transfer
equation also suggests self-similar profiles of the temperature and of the heat flux, however the relation
between the shape functions Φθ (ζ) and ΦQ (ζ) is different. The issue is considered in Mironov (2008).
Integrating Eq. (2.69) with due regard for Eqs. (2.66) and (2.72) over z ′ from h to z > h, then integrating
the resulting expression over z from h to D, we obtain

where


1
dθs
d 
(D − h)2−Cθθ (D − h)2 (θs − θb ) =
2
dt
dt


Z D
1
I(z)dz ,CQ (D − h)(Qh − Qb ) + (D − h)I(h) −
ρw cw
h
CQ =

Z 1

(2.73)ΦQ (ζ)dζ

(2.74)

Z ζ′(2.75)

0is the shape factor with respect to the heat flux, and
Cθθ =

Z 1
0

dζ

Φθ (ζ ′ )dζ ′0is the dimensionless parameter. The analysis in Mironov (2008) suggests that CQ = 2Cθθ /Cθ .
In case of the mixed-layer stationary state or retreat, dh/dt ≤ 0, Eq. (2.72) is not justified. Then, the bottom
temperature is assumed to be “frozen”,dθb= 0.
(2.76)
dt
If h = D, then θb = θs = θ and the mean temperature is computed from Eq. (2.70).
The skin temperature module
The objective of introducing a skin temperature was to simulate a surface temperature representative of theenergy budget at the lake surface, where the total derivative of temperature is in balance with the diffusionof the temperature plus a heat source, due to the divergence of the net radiation flux at the surface. In thisoptional module, the thickness of the skin layer is assumed to be constant and equal to 1 mm. During amodel time step, this new surface temperature is then used to compute the new surface heat fluxes in theatmosphere, the new thickness of the mixed layer and the new thermocline profile.
The 1D heat transfer of heat in the lake writes:dθ= κw ∇θ + F(2.77)
dt
Where θ is the water temperature, ρw and cw the water density and heat capacity respectively, κw is thewater heat transfer conductivity and F a source term.
ρw cw

For a lake, F can be simplified into the divergence of the solar radiation I neglecting the divergence of the
longwave radiation, which is a common assumption. At the continuum scale, decomposing an instantaneous
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

45

field into an average plus a fluctuation and applying the Reynolds averaging operator to eq. 2.77 allows
expressing the tendency of temperature. In the vicinity of the viscous layer, the turbulent term is negligible
when compared to the diffusion term. If, on top of that, an assumption of horizontal homogeneity is applied
to a steady state, eq. 2.77 can be transformed into leads to:κw∂ 2 θ ∂I=0+∂z 2 ∂z(2.78)

where I, the solar radiation that penetrates the water up to depth z follows a Beer-Lambert decay law
depending depth z and the extinction coefficient of radiation in the water ǫ.
Equation 2.78 can be integrated between the surface and the depth h to give the expression of the skintemperature θskin as a function of Qs , Is , θs and depth h:h
1 − e−ǫhθskin = θs +Q s + Is 1 −κwǫh

(2.79)

Details of the computation can be found in Le Moigne et al. (2016).
The Mixed-Layer Depth
Convective deepening of the mixed layer is described by the entrainment equation. This equation is conveniently formulated in terms of the dependence of the so-called entrainment ratio A on one or the otherstratification parameter. The entrainment ratio is a measure of the entrainment efficiency. It is commonly
defined as a negative of the ratio of the heat flux due to entrainment at the bottom of the mixed layer, Qh ,to an appropriate heat flux scale, Q∗ . In case of convection driven by the surface flux, where the forcing is
confined to the boundary, the surface heat flux Qs serves as an appropriate flux scale. This leads to the nowclassical Deardorff (1970a, 1970b) convective scaling, where h and |hβQs /(ρw cw )|1/3 serve as the scalesof length and velocity, respectively.
The Deardorff scaling is unsuitable for convective flows affected by the solar radiation heating that is notconfined to the boundary but is distributed over the water column. If the mixed-layer temperature exceeds
the temperature of maximum density, convective motions are driven by surface cooling, whereas radiation
heating tends to stabilise the water column, arresting the mixed layer deepening (Soloviev (1979); Mironov
and Karlin (1989)). Such regime of convection is encountered in the oceanic upper layer (e.g. Kraus andRooth (1961), Soloviev and Vershinskii (1982), Price et al. (1986) and in fresh-water lakes (e.g. Imberger(1985)). If the mixed-layer temperature is below that of maximum density, volumetric radiation heating
leads to de-stabilisation of the water column and thereby drives convective motions. Such regime of convection is encountered in fresh-water lakes in spring. Convective mixing often occurs under the ice, when
the snow cover overlying the ice vanishes and solar radiation penetrates down through the ice (e.g. Farmer(1975), Mironov and Terzhevik (2000), Mironov et al. (2002), Jonas et al. (2003)).
In order to account for the vertically distributed character of the radiation heating, we make use of a generalised convective heat flux scale
Z hQ∗ = Qs + Is + I(h) − 2h−1
I(z)dz,(2.80)0and define the convective velocity scale and the entrainment ratio asw∗ = [−hβ(θs )Q∗ /(ρw cw )]1/3 ,A = −Qh /Q∗ ,SURFEX v8.1 - Issue no 3 - 2018(2.81)

46
respectively. In order to specify A, we employ the entrainment equation in the formA+

Cc2 dh= Cc1 ,w∗ dt

(2.82)

where Cc1 and Cc2 are dimensionless constants (the estimates of these and other empirical constants of themodel are discussed in Section 2.4.5 and summarised in the Appendix). The second term on the l.h.s. of
Eq. (2.82) is the spin-up correction term introduced by Zilitinkevich (1975). This term prevents an unduly
fast growth of h when the mixed layer is shallow. If the spin-up term is small, Eq. (2.82) reduces to a simple
relation A = Cc1 that proved to be a sufficiently accurate approximation for a large variety of geophysicaland laboratory convective flows Zilitinkevich (1991).
Equations (2.80), (2.81) and (2.82) should be used to compute the mixed-layer depth when the buoyancy
flux B∗ = β(θs )Q∗ /(ρw cw ) is negative. The quantity −hB∗ ≡ w∗3 is a measure of the generation rate of
the turbulence kinetic energy in a layer of depth h by the buoyancy forces (see a discussion in Mironov etal. (2002)). A negative B∗ indicates that the TKE is generated through convective instability. Otherwise,
the TKE is lost to work against the gravity. This occurs when the density stratification is stable. A different
formulation for the mixed-layer depth is then required.
Mironov et al. (1991) used a diagnostic equation to determine the wind-mixed layer depth in stable andneutral stratification. That is, h was assumed to adjust to external forcing on a time scale that does not exceed
the model time step. This assumption is fair if seasonal changes of temperature and mixing conditions are
considered and the model time step is typically one day. The assumption is likely to be too crude to consider
diurnal variations. To this end, We utilise a relaxation-type rate equation for the depth of a stably or neutrally
stratified wind-mixed layer. It readshe − hdh=.
(2.83)dttrh
Here, he is the equilibrium mixed-layer depth, and trh is the relaxation time scale given by
trh =

he
,
Crh u∗(2.84)

where u∗ = |τs /ρw cw |1/2 is the surface friction velocity, τs being the surface stress, and Crh is a dimensionless constant. A rate equation (2.83) with the relaxation time scale proportional to the reciprocal of
the Coriolis parameter [that is a particular case of Eq. (2.84) with he specified through Eq. (2.85)] wasfavourably tested by Zilitinkevich et al. (2002) and Zilitinkevich and Baklanov (2002) against data fromatmospheric measurements and was recommended for practical use.
In order to specify he , we make use of a multi-limit formulation for the equilibrium depth of a stably or
neutrally stratified boundary layer proposed by Zilitinkevich and Mironov (1996). Based on the analysis of
the TKE budget, these authors proposed a generalised equation for the equilibrium boundary-layer depththat accounts for the combined effects of rotation, surface buoyancy flux and static stability at the boundarylayer outer edge [Eq. (30) in op. cit.]. That equation reduces to the equations proposed earlier by Rossby andMontgomery (1935), Kitaigorodskii (1960) and Kitaigorodskii and Joffre (1988) in the limiting cases of atruly neutral rotating boundary layer, the surface-flux-dominated boundary layer, and the imposed-stabilitydominated boundary layer, respectively. It also incorporates the Zilitinkevich (1972) and the Pollard et al.
(1973) equations that describe the intermediate regimes, where the effects of rotations and stratification
essentially interfere and are roughly equally important. We adopt a simplified version of the Zilitinkevichand Mironov (1996) equation [Eq. (26) in op. cit.] that does not incorporate the Zilitinkevich (1972) and the
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

47

Pollard et al. (1973) scales. It reads


f he
Cn u∗

2

+

he
N he
+
= 1,
Cs L Ci u∗(2.85)

where f = 2Ω sin φ is the Coriolis parameter, Ω = 7.29 · 10−5 s−1 is the angular velocity of the earth’s
rotation, φ is the geographical latitude, L is the Obukhov length, N is the buoyancy frequency below themixed layer, and Cn , Cs and Ci are dimensionless constants. A generalised formulation for the Obukhov
length is used, L = u3∗ /(βQ∗ /ρw cw ), that accounts for the vertically distributed character of the solar
radiation heating (note that the von Kármán constant is not included into the definition of L). A meanh
i1/2RDsquare buoyancy frequency in the thermocline, N = (D − h)−1 h N 2 dz
, is used as an estimate of
N in Eq. (2.85).
One further comment is in order. Zilitinkevich et al. (2002) reconsidered the problem of the equilibrium
stable boundary-layer depth. They concluded that the Zilitinkevich (1972) scale, |u∗ L/f |1/2 , and the Pollard et al. (1973) scale, u∗ /|N f |1/2 , are the appropriate depth scales for the boundary layers dominated by
the surface buoyancy flux and by the static stability at the boundary-layer outer edge, respectively. In otherwords, he depends on the Coriolis parameter no matter how strong the static stability. This is different from
Eq. (2.85) where the limiting scales are L and u∗ /N , respectively. The problem was further examined by
Mironov and Fedorovich (2010). They showed that the above scales are particular cases of more general
power-law formulations, namely, h/L ∝ (|f |L/u∗ )−p and hN/u∗ ∝ (|f |/N )−q for the boundary layers
dominated by the surface buoyancy flux and by the static stability at the boundary-layer outer edge, respectively. The Zilitinkevich (1972) and Pollard et al. (1973) scales are recovered with p = 1/2 and q = 1/2,
whereas the Kitaigorodskii (1960) and Kitaigorodskii and Joffre (1988) are recovered with p = 0 and q = 0.
Scaling arguments are not sufficient to fix the exponents p and q. They should be evaluated on the basis ofexperimental data. Available data from observations and from large-eddy simulations are uncertain. They
do not make it possible to evaluate p and q to sufficient accuracy and to conclusively decide between thealternative formulations for the boundary-layer depth. Leaving the evaluation of p and q for future studies,
we utilise Eq. (2.85). This simple interpolation formula is consistent with the complexity of the present lake
model and is expected to be a sufficiently accurate approximation for most practical purposes.
One more limitation on the equilibrium mixed-layer depth should be taken into account. Consider thesituation where the mixed-layer temperature exceeds the temperature of maximum density, the surface flux
Qs is negative, whereas the heat flux scale Q∗ given by Eq. (2.80) is positive (this can take place if −Qs /Is <1). A positive Q∗ indicates the the mixed layer of depth h is statically stable. A negative Qs , however,indicates that convective instability should take place, leading to the development of a convectively mixed
layer whose deepening is arrested by the solar radiation heating. The equilibrium depth hc of such mixed
layer is given by (see e.g. Mironov and Karlin (1989))Q∗ (hc ) = Qs + Is + I(hc ) − 2h−1c

Z hc

I(z)dz = 0.

(2.86)

0This regime of convection is encountered on calm sunny days. If the wind suddenly ceases, Eq. (2.85)
predicts a very shallow stably-stratified equilibrium mixed layer to which the mixed layer of depth h > heshould relax. In fact, however, the mixed layer would relax towards a convectively mixed layer whose
equilibrium depth is given by Eq. (2.86). In order to account for this constraint, we require that he ≥ hc if
Q∗ (h) > 0 and θs > θr .
SURFEX v8.1 - Issue no 3 - 2018

48

2.4.3 The Water–Bottom Sediment Interaction
Parameterization of the Temperature Profile and the Heat Budget We adopt the following two-layer
parametric representation, of the evolving temperature profile in the thermally active layer of bottom sediments proposed by Golosov et al. (1998):(
θb − [θb − θH ] ΦB1 (ζB1 )at D ≤ z ≤ H
θ=(2.87)
θH − [θH − θL ] ΦB2 (ζB2 )at H ≤ z ≤ L,
Where, θL is the (constant) temperature at the outer edge z = L of the thermally active layer of thesediments, θH is the temperature at the depth H where the vertical temperature gradient is zero, andΦB1 ≡ (θb − θ)/(θb − θH ) and ΦB2 ≡ (θH − θ)/(θH − θL ) are dimensionless functions of dimensionlessdepths ζB1 ≡ (z − D)/(H − D) and ζB2 ≡ (z − H)/(L − H), respectively.
The parameterization (2.87) should satisfy the heat transfer equation (2.69), where the heat flux Q is due tomolecular heat conduction and the bottom sediments are opaque to radiation. Integrating Eq. (2.69) over z
from z = D to z = H with due regard for Eq. (2.87), we obtainddH
1[(H − D)θb − CB1 (H − D)(θb − θH )] − θH=
[Qb + I(D)] ,
dt
dt
ρw cw

(2.88)

where the heat flux at z = H is zero by virtue of the zero temperature gradient there.
Integrating Eq. (2.69) over z from z = H to z = L, we obtaindHd[(L − H)θH − CB2 (L − H)(θH − θL )] + θH
= 0,
dt
dt
where the heat flux at z = L (the geothermal heat flux) is neglected.
The shape factors CB1 and CB2 are given by
Z 1
Z 1
ΦB2 (ζB2 )dζB2 .
ΦB1 (ζB1 )dζB1 ,
CB2 =
CB1 =
0

(2.89)(2.90)

0

Heat Flux through the Bottom The bottom heat flux Qb is due to molecular heat conduction through theuppermost layer of bottom sediments. It can be estimated as the product of the negative of the temperature
gradient at z = D + 0 and the molecular heat conductivity. The uppermost layer of bottom sediments issaturated with water. Its water content typically exceeds 90% and its physical properties, including the heat
conductivity, are very close to the properties of the lake water. Then, the heat flux through the lake bottom
is given byθH − θb ′Qb = −κwΦ (0),(2.91)
H − D B1
where κw is the molecular heat conductivity of water. This relation closes the problem.
It should be stressed that Eqs. (2.88), (2.89) and (2.91) do not contain the molecular heat conductivity ofbottom sediments, a quantity that is rarely known to a satisfactory degree of precision. It is through theuse of the integral (bulk) approach, based on the parameterization (2.87) of the temperature profile, that themolecular heat conductivity of bottom sediments is no longer needed.

2.4.4 Ice and Snow CoverIn this section, a two-layer thermodynamic (no rheology) model of the ice and snow cover is described. It
is based on a self-similar parametric representation of the temperature profile within ice and snow and on
the integral heat budgets of the ice and snow layers. The approach is, therefore, conceptually similar to
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

49

the approach used above to describe the temperature structure of the mixed layer, of the lake thermocline,
and of the thermally active layer of bottom sediments. Notice that the assumption about the shape of thetemperature profile within the ice, the simplest of which is the linear profile, is either explicit or implicit ina number of ice models developed to date. A model of ice growth based on a linear temperature distribution
was proposed by Stefan as early as 1891.
Parameterization of the Temperature Profile and the Heat Budget We adopt the following parametricrepresentation of the evolving temperature profile within ice and snow:(θf − [θf − θI ]ΦI (ζI )at −HI ≤ z ≤ 0
θ=(2.92)
θI − [θI − θS ]ΦS (ζS )at −[HI + HS ] ≤ z ≤ −HI .
Here, z is the vertical co-ordinate (positive downward) with the origin at the ice-water interface, HI is
the ice thickness, HS is the thickness of snow overlaying the ice, θf is the fresh-water freezing point, θIis the temperature at the snow-ice interface, and θS is the temperature at the air-snow interface. Noticethat the freezing point of salt water is a decreasing function of salinity. A model that accounts for thisdependence and is applicable to the ice over salt lakes or seas is presented by Mironov and Ritter (2004).
Dimensionless universal functions ΦI ≡ (θf − θ)/(θf − θI ) and ΦS ≡ (θI − θ)/(θI − θS ) of dimensionlessdepths ζI ≡ −z/HI and ζS ≡ −(z + HI )/HS , respectively, satisfy the boundary conditions ΦI (0) = 0,
ΦI (1) = 1, ΦS (0) = 0, and ΦS (1) = 1.
According to Eq. (2.92), the heat fluxes through the ice, QI , and through the snow, QS , due to molecularheat conduction are given by
QI = −κiθf − θI dΦI,
HI dζIQS = −κsθI − θS dΦS,
HS dζS(2.93)

where κi and κs are the heat conductivities of ice and snow, respectively.
The parameterization of the temperature profile (2.92) should satisfy the heat transfer equation (2.69). Integrating Eq. (2.69) over z from the air-snow interface z = −(HI + HS ) to just above the ice-water interfacez = −0 with due regard for the parameterization (2.92), we obtain the equation of the heat budget of thesnow-ice cover,dd{ρi ci HI [θf − CI (θf − θI )] + ρs cs HS [θI − CS (θI − θS )]} − ρs cs θS (HI + HS ) =dt
dt
Qs + Is − I(0) + κiθf − θI ′ΦI (0).
HI(2.94)

Here, ρi and ρs are the densities of ice and of snow, respectively, ci and cs are specific heats of these media,
and Qs and Is are the values of Q and I, respectively, at the air-snow or, if snow is absent, at the air-ice
interface. The radiation heat flux Is that penetrates into the interior of snow-ice cover is the surface value ofthe incident solar radiation flux from the atmosphere multiplied by 1 − αi , αi being the albedo of the ice orsnow surface with respect to solar radiation. The dimensionless parameters CI and CS , the shape factors,
are given by
Z 1
Z 1
ΦS (ζS )dζS .
(2.95)
ΦI (ζI )dζI ,
CS =
CI =
0

0

The heat flux at the snow-ice interface is assumed to be continuous, that is−κiθf − θI ′θI − θS ′ΦI (1) = −κsΦS (0).
HI
HS
SURFEX v8.1 - Issue no 3 - 2018(2.96)

50
Equations (2.94) and (2.96) serve to determine temperatures at the air-snow and at the snow-ice interfaces,
when these temperatures are below the freezing point, i.e. when no melting at the snow surface (ice surface,when snow is absent) takes place. During the snow (ice) melting from above, the temperatures θS and θI
remain equal to the freezing point θf , and the heat fluxes QS and QI are zero.
Snow and Ice Thickness The equations governing the evolution of the snow thickness and of the ice
thickness are derived from the heat transfer equation (2.69) that incorporates an additional term on its righthand side, namely, the term fM (z)Lf dM/dt that describes the rate of heat release/consumption due toaccretion/melting of snow and ice. Here, M is the mass of snow or ice per unit area, Lf is the latent heat
R H +Hof fusion, and fM (z) is a function that satisfies the normalization conditions HII S fM (z)dz = 1 and
R HI
0 fM (z)dz = 1 for snow and ice, respectively.
The accumulation of snow is not computed within the ice-snow model. The rate of snow accumulation isassumed to be a known time-dependent quantity that is provided by the atmospheric model or is known
from observations. Then, the evolution of the snow thickness during the snow accumulation and no melting
is computed fromdρs HSdMS=,(2.97)
dt
dt awhere MS = ρs HS is the snow mass per unit area, and (dMS /dt)a is the (given) rate of snow accumulation.
When the temperature θI at the upper surface of the ice is below the freezing point θf , the heat conduction
through the ice causes the ice growth. This growth is accompanied by a release of heat at the lower surface of
the ice that occurs at a rate Lf dMI /dt, where MI = ρi HI is the ice mass per unit area. The normalization
function fM is equal to zero throughout the snow-ice cover except at the ice-water interface where fM =δ(0), δ(z) being the Dirac delta function. Integrating Eq. (2.69) from z = −0 to z = +0 with due regard
for this heat release yields the equation for the ice thickness. It reads
Lfθf − θI ′dρi HI= Qw + κi
ΦI (0),
dt
HI(2.98)

where Qw is the heat flux in the near-surface water layer just beneath the ice. If the r.h.s. of Eq. (2.98) is
negative, i.e. the negative of the heat flux in the water, Qw , exceeds the negative of the heat flux in the ice,
QI |z=0 , ice ablation takes place.
As the atmosphere heats the snow surface, the surface temperature eventually reaches the freezing point andthe snow and ice melting sets in. This process is accompanied by a consumption of heat at rates Lf dρs HS /dt
and Lf dρi HI /dt for snow and ice, respectively. Notice that the exact form of the normalization function
fM is not required by virtue of the normalization conditions considered above. Integrating Eq. (2.69) fromz = −(HI + HS ) − 0 to z = −HI with due regard for the heat loss due to snow melting and adding the(given) rate of snow accumulation yields the equation for the snow thickness,dMSdρs HSdρs= −(Qs + Is ) + I(−HI ) + Lf.
(2.99)Lf+ cs θf HS
dt
dt a
dt
Integrating Eq. (2.69) from z = −HI to z = +0 with due regard for the heat loss due to ice melting yields
the equation for the ice thickness,
Lfdρi HI= Qw + I(0) − I(−HI ).
dt

If the ice melts out earlier than snow, the snow depth is instantaneously set to zero.
SURFEX v8.1 - Issue no 3 - 2018(2.100)CHAPTER 2. WATER SURFACES

51

The Temperature Profile beneath the Ice The simplest assumption is to keep the temperature profile
unchanged over the entire period of ice cover. This assumption is fair for deep lakes, where the heat flux
through the bottom is negligibly small. In shallow lakes, this assumption may lead to an underestimationof the mean temperature. The heat accumulated in the thermally active upper layer of bottom sediments
during spring and summer is returned back to the water column during winter, leading to an increase of thewater temperature under the ice. The water temperature under the ice can also increase due to heating by
solar radiation penetrating down through the ice. The thermodynamic regimes encountered in ice-coveredlakes are many and varied. Their detailed description requires a set of sophisticated parameterizations.
The use of such parameterizations in the framework of the present lake model is, however, hardly justified.
The point is that it is the snow (ice) surface temperature that communicates information to the atmosphere,
the water temperature is not directly felt by the atmospheric surface layer. It is, therefore, not vital that thetemperature regimes in ice-covered lakes be described in great detail. Only their most salient features shouldbe accounted for, first of all, the heat budget of the water column.
When the lake is ice-covered, the temperature at the ice-water interface is fixed at the freezing point θs = θf .
In case the bottom temperature is less than the temperature of maximum density, θb < θr , the mixed-layer
depth and the shape factor are kept unchanged, dh/dt = 0 and dCθ /dt = 0, the mean temperature θ iscomputed from Eq. (2.70) and the bottom temperature θb is computed from Eq. (2.67). If the entire watercolumn appears to be mixed at the moment of freezing, i.e. h = D and θs = θ = θb , the mixed layer depth
is reset to zero, h = 0, and the shape factor is set to its minimum value, Cθ = 0.5 (see Section 2.4.5).
The heat flux from water to ice is estimated from
Qw = −κw

θb − θs,D(2.101)

if h = 0, and Qw = 0 otherwise. Notice that the estimate of Qw given by Eq. (2.101) and the shapefactor Cθ = 0.5 correspond to a linear temperature profile over the entire water column. A linear profile isencountered in ice-covered shallow lakes when θb < θr and the heat flux is from the bottom sediments tothe lake water.
As the bottom temperature reaches the temperature of maximum density, convection due to bottom heatingsets in. To describe this regime of convection in detail, a convectively mixed layer whose temperature isclose to θr , and a thin layer adjacent to the bottom, where the temperature decreases sharply from θb > θr
to θr , should be thoroughly considered. We neglect these peculiarities of convection due to bottom heating
and adopt a simpler model where the bottom temperature is fixed at the temperature of maximum density,θb = θr . The mean temperature θ is computed from Eq. (2.70). If h > 0, the shape factor Cθ is kept
unchanged, and the mixed-layer depth is computed from Eq. (2.67). As the mixed-layer depth approaches
zero, Eq. (2.67) is used to compute the shape factor Cθ that in this regime would increase towards its
maximum value Cθmax . The heat flux from water to ice is estimated from
Qw = −κwθb − θsmax 1, Φ′θ (0) ,D(2.102)

if h = 0, and Qw = 0 otherwise.
One more regime of convection is often encountered in ice-covered lakes. In late spring, the snow overlying
the ice vanishes and solar radiation penetrates down through the ice. As the mixed-layer temperature is below that of maximum density, the volumetric radiation heating leads to de-stabilisation of the water column
and thereby drives convective motions. Such regime of convection was analysed by Farmer (1975), Mironov
and Terzhevik (2000), Mironov et al. (2002), and Jonas et al. (2003), among others. A parameterization of
convection due to solar heating (e.g. a parameterization based on a bulk model developed by Mironov et al.
(2002)) can, in principle, be incorporated into the present model. We do not do so, however, considering
SURFEX v8.1 - Issue no 3 - 2018

52
that the major effect of convection beneath the ice is to redistribute heat in the vertical and that it takes placeover a limited period of time.

2.4.5 Empirical Relations and Model Constants
The Shape Functions
We adopt the following polynomial approximation of the shape function Φθ (ζ) with respect to the temperature profile in the thermocline:




40
20
5 10
2
3
Φθ =
Cθ −
− Cθ ζ 4 .
(2.103)
ζ + (18 − 30Cθ ) ζ + (20Cθ − 12) ζ +33
3
3
The shape factor Cθ is computed from
C max − CθmindCθ
= sign(dh/dt) θ
,
dt
trc

Cθmin ≤ Cθ ≤ Cθmax ,(2.104)

where trc is the relaxation time scale, and sign is the signum function, sign(x)=−1 if x ≤ 0 and sign(x)=1
if x > 0. The minimum and maximum values of the shape factor are set to Cθmin = 0.5 and Cθmax =0.8. During the mixed-layer deepening, dh/dt > 0, the temperature profile evolves towards the limiting
curve, characterised by a maximum value of the shape factor, Cθmax = 0.8, and the maximum value ofthe dimensionless temperature gradient at the upper boundary of the thermocline, Φ′θ (0) = 4. During themixed-layer stationary state or retreat, dh/dt ≤ 0, the temperature profile evolves towards the other limiting
curve, characterised by a minimum value of the shape factor, Cθmin = 0.5, and the zero temperature gradientat the upper boundary of the thermocline, Φ′θ (0) = 0. Notice that Cθmin = 0.5 is consistent with a linear
temperature profile that is assumed to occur under the ice when the bottom temperature is less than thetemperature of maximum density (see Section 2.4.4).
According to Eq. (2.103), the dimensionless parameter Cθθ defined through Eq. (2.75) is given by
Cθθ =

7
11
Cθ − .
1845(2.105)

The relaxation time trc is estimated from the following arguments. The time trc is basically the time of theevolution of the temperature profile in the thermocline from one limiting curve to the other, following thechange of sign in dh/dt. Then, a reasonable scale for trc is the thermal diffusion time through the thermocline, that is a square of the thermocline thickness, (D − h)2 , over a characteristic eddy temperature conduch
i1/2
RD
tivity, KH∗ . Using a mean-square buoyancy frequency in the thermocline, N = (D − h)−1 h N 2 dz,
as an estimate of N and assuming that the TKE in the thermocline scales either on the convective velocityw∗ , Eq. (2.81), or on the surface friction velocity u∗ , we propose (see Mironov (2008) for details)trc =(D − h)2 N,
Crc u2T

uT = max(w∗ , u∗ ),(2.106)

where Crc is a dimensionless constant estimated at 0.003 (this value may be altered as new information
becomes available).
We adopt the following polynomial approximations of the shape functions ΦB1 (ζB1 ) and ΦB2 (ζB2 ) withrespect to the temperature profile in bottom sediments (cf. Golosov et al. (1998)):2
ΦB1 = 2ζB1 − ζB1,234
ΦB2 = 6ζB2
− 8ζB2+ 3ζB2.

(2.107)

which are the simplest polynomials that satisfy a minimum set of constraints. The conditions ΦB1 (0) =ΦB2 (0) = 0 and ΦB1 (1) = ΦB2 (1) = 1 follow from the definition of ζB1 , ζB2 , ΦB1 , and ΦB2 . The
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

53

conditions Φ′B1 (1) = Φ′B2 (0) = Φ′B2 (1) = 0 provide a zero temperature gradient at the depths z = H andz = L, and the condition Φ′′B2 (1) = 0 follows from the requirement that the temperature θL at the outer edgez = L of the thermally active layer of the sediments is constant in time. The shape factors that correspondto Eq. (2.107) are CB1 = 2/3 and CB2 = 3/5.
As a zero-order approximation, the simplest linear temperature profile within snow and ice can be assumed,ΦS (ζS ) = ζS and ΦI (ζI ) = ζI . This gives CS = CI = 1/2. Although a linear profile is a good approximation for thin ice, it is likely to result in a too thick ice in cold regions, where the ice growth takes place overa long period, and in a too high thermal inertia of thick ice. A slightly more sophisticated approximation
was developed by Mironov and Ritter (2004) who assumed that the ice thickness is limited by a certain
maximum value HImax and that the rate of ice growth approaches zero as HI approaches HImax (the snow
layer over the ice was not considered). They proposed






HI
HI
HI
2
ΦI = 1 − max ζI + (2 − Φ∗I ) max ζI + (Φ∗I − 1) max ζI3 ,(2.108)HI
HI
HI
where Φ∗I is a dimensionless constant. The shape factor that corresponds to Eq. (2.108) is
CI =

1
HI
1
− (1 + Φ∗I ) max .
2 12
HI(2.109)The physical meaning of the above expressions can be elucidated as follows. The relation Φ′I (0) =1 − HI /HImax that follows from Eq. (2.108) ensures that the ice growth is quenched as the ice thickness
approaches its maximum value. Equation (2.109) suggests that the shape factor CI decreases with increasing ice thickness. A smaller CI means a smaller relative thermal inertia of the ice layer of thickness HI [theabsolute thermal inertia is measured by the term CI HI that enters the l.h.s. of Eq. (2.94)]. This is plausible
as it is mostly the upper part of thick ice, not the entire ice layer, that effectively responds to external forcing.
For use in the global numerical weather prediction model GME of the German Weather Service, Mironov
and Ritter (2004) proposed an estimate of HImax = 3 m. This value is typical of the central Arctic in winter.
The allowable values of Φ∗I lie in the range between −1 and 5. Φ∗I > 5 yields an unphysical negativevalue of CI as the ice thickness approaches HImax . Φ∗I < −1 gives CI that increases with increasing HI .
There is no formal proof that this may not occur, but it is very unlikely. A reasonable estimate is Φ∗I = 2.
With this estimate CI is halved as HI increases from 0 to HImax . Notice that the linear temperature profile
is recovered as HI /HImax ≪ 1, i.e. when the ice is thin.
It should be stressed that, although the shape functions are useful in that they provide a continuous temperature profile trough the snow, ice, water and bottom sediments, their exact shapes are not required in thepresent model. It is not Φθ (ζ), ΦB1 (ζB1 ), ΦB2 (ζB2 ), ΦS (ζS ) and ΦI (ζI ) per se, but the shape factors Cθ ,CB1 , CB2 , CS and CI , and the dimensionless gradients Φ′θ (0), Φ′B1 (0), Φ′S (0), Φ′I (0) and Φ′I (1), that enter
the model equations. The estimates of these parameters are summarised in Table 2.8.
Constants in the Equations for the Mixed-Layer Depth The estimates of Cc1 = 0.2 and Cc2 = 0.8 in
Eq. (2.82) were recommended by Zilitinkevich (1991). They were obtained using laboratory, atmosphericand oceanic data. Apart from being commonly used in mixed-layer models of penetrative convection driven
by the surface buoyancy flux, these values were successfully used by Mironov and Karlin (1989) to simulate
day-time convection in the upper ocean that is driven by surface cooling but inhibited by radiation heating,and by Mironov and Terzhevik (2000) and Mironov et al. (2002) to simulate spring convection in ice-coveredlakes where convective motions are driven by volumetric radiation heating of the water at temperature below
the temperature of maximum density (Mironov et al. (2002) used Cc2 = 1.0). A slightly modified estimate
SURFEX v8.1 - Issue no 3 - 2018

54
of Cc1 = 0.17 was obtained by Fedorovich et al. (2004) from large-eddy simulation data. We adopt theestimates of Cc1 = 0.17 and Cc2 = 1.0 for use in the equation of convective entrainment.
For use in Eq. (2.85) for the equilibrium mixed-layer depth in stable or neutral stratification, we adopt
the estimates of Cn = 0.5, Cs = 10 and Ci = 20 obtained by Zilitinkevich and Mironov (1996). The
estimates of Cs and Ci are based on a limited amount of data and may need to be slightly altered as new(and better) data become available. The estimate of Cn was corroborated by the results from further studies(Zilitinkevich and Esau, 2002) and is reliable.
The estimates of the dimensionless constant Crh in the relaxation-type rate equation for the depth of a stablyor neutrally stratified wind-mixed layer, Eqs. (2.83) and (2.84), are not abundant. Kim (1976) and Deardorff(1983) recommended that the value of Crh = 0.28 be used to describe entrainment into a homogeneous
fluid. The same value was used by Zeman (1979), and a slightly lower value of Crh = 0.26 by Zilitinkevich
et al. (1979). The rate equations given by Khakimov (1976) and Zilitinkevich et al. (2002) use the reciprocalof the Coriolis parameter as the relaxation time scale. Their rate equations suggest the values of Crh = 0.45
and Crh = 0.5, respectively. A similar form of the rate equation was proposed earlier by Deardorff (1971)
who used a much lower value of Crh = 0.025. We adopt an estimate of Crh = 0.03 suggested by thesensitivity experiments with the present lake model (keeping in mind that this value may need to be altered).
The estimates of dimensionless constants in the equations for the mixed-layer depth are summarised inTable 2.8.
Thermodynamic Parameters The exponential approximation of the decay law for the flux of solar radiation is commonly used in applications. It reads
I(t, z) = Is (t)nX

ak exp[−γk (z + HS + HI )],(2.110)k=1

where Is is the surface value of the solar radiation heat flux multiplied by 1 − α, α being the albedo of
the water, ice or snow surface with respect to solar radiation, n is the number of wavelength bands, ak are
fractions of the total radiation flux for different wavelength bands, and γk (z) are attenuation coefficientsfor different bands. The attenuation coefficients are piece-wise constant functions of height, i.e. they havedifferent values for water, ice and snow but remain depth-constant within these media. The optical characteristics of water are lake-specific and should be estimated in every particular case. Rough estimates of akand γk for ice and snow are given by Launiainen and Cheng (1998).
The lake model includes a number of thermodynamic parameters. They are summarised in Table 2.9. Thesethermodynamic parameters can be considered constant except for the snow density and the snow heat conductivity that depend, among other things, on the snow thickness and the snow age. As a first approximation,
the following empirical formulations (Heise et al. (2003)) can be used that relate ρs and κs to the snow thickness:on,ρs = min ρmax
, |1 − HS Γρs /ρw |−1 ρminss

(2.111)= 400 kg·m−3 are minimum and maximum values, respectively, of= 100 kg·m−3 and ρmax
where ρminss
the snow density, and Γρs = 200 kg·m−4 is an empirical parameter, andκs = min κmax
, κmin+ HS Γκs ρs /ρw ,ss(2.112)= 1.5 J·m−1 ·s−1 ·K−1 are minimum and maximum values,= 0.2 J·m−1 ·s−1 ·K−1 and κmax
where κminssrespectively, of the snow heat conductivity, and Γκs = 1.3 J·m−2 ·s−1 ·K−1 is an empirical parameter.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 2. WATER SURFACES

55

2.4.6 Conclusions
A lake model suitable to predict the vertical temperature structure in lakes of various depths on time scales
from a few hours to many years is developed. The model, termed FLake, is based on a two-layer parametricrepresentation of the evolving temperature profile and on the integral budget of energy for the layers inquestion. The structure of the stratified layer between the upper mixed layer and the basin bottom, thelake thermocline, is described using the concept of self-similarity (assumed shape) of the temperature-depth
curve. The same concept is used to describe the temperature structure of the thermally active upper layerof bottom sediments and of the ice and snow cover. An entrainment equation is used to compute the depthof a convectively-mixed layer. A relaxation-type equation is used to compute the wind-mixed layer depth
in stable and neutral stratification, where a multi-limit formulation for the equilibrium mixed-layer depth
accounts for the effects of the earth’s rotation, of the surface buoyancy flux, and of the static stability in thethermocline. Both mixing regimes are treated with due regard for the volumetric character of solar radiation
heating. Simple thermodynamic arguments are invoked to develop the evolution equations for the ice andsnow depths. Using the integral (bulk) approach, the problem of solving partial differential equations (indepth and time) for the temperature and turbulence quantities is reduced to solving ordinary differential
equations for the time-dependent parameters that specify the evolving temperature profile. The result is acomputationally efficient lake model that incorporates much of the essential physics.
It must be emphasised that the empirical constants and parameters of FLake are not application-specific.
That is, once they have been estimated using independent empirical and numerical data, they should not
be re-evaluated when the model is applied to a particular lake. There are, of course, lake-specific externalparameters, such as depth to the bottom and optical characteristics of water, but these are not part of themodel physics. In this way FLake does not require “re-tuning”, a procedure that may improve an agreementwith a limited amount of data and is sometimes justified. This procedure should, however, be considered
as a bad practice and must be avoided whenever possible as it greatly reduces the predictive capacity of aphysical model (Randall and Wielicki, 1997).
Apart from the depth to the bottom and the optical characteristics of lake water, the only lake-specificparameters are the depth L of the thermally active layer of bottom sediments and the temperature θL at that
depth. These parameters should be estimated only once for each lake, using observational data or empirical
recipes (e.g. Fang and Stefan (1998)). In a similar way, the temperature at the bottom of the thermally active
soil layer and the depth of that layer are estimated once and then used in an NWP model as two-dimensional
external-parameter arrays.
The proposed lake model is intended for use, first of all, in NWP and climate models as a module (parameterization scheme) to predict the lake surface temperature. Apart from NWP and climate modelling, practicalapplications where simple bulk models are favoured over more accurate but more sophisticated models (e.g.
second-order turbulence closures) include modelling aquatic ecosystems. For ecosystem modelling, a sophisticated physical module is most often not required because of insufficient knowledge of chemistry andbiology.

SURFEX v8.1 - Issue no 3 - 2018

56
Appendix. A Summary of Model Parameters

Table 2.8: Empirical Constants and Parameters
Constant/
Parameter
Cc1
Cc2
Cn
Cs
Ci
Crh
Crc
Cθ
Cθmin
Cθmax
Cθθ
CQ
CB1
CB2
CI
CS
Φ′θ (0)Φ′B1 (0)Φ′I (0)Φ′I (1)
Φ′S (0)Φ∗I
HImax

Recommended Value/
Computed from
0.17
1.0
0.5
10
20
0.03
0.003
Eq. (2.104)
0.5
0.8
Eq. (2.105)
2Cθθ /Cθ
2/3
3/5
1/2
1/2
Eqs. (2.103) and (2.104)
2
1
1
1
2
3m

Comments

Optionally Eq. (2.109)

Optionally Eq. (2.108)
Optionally Eq. (2.108)

SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

57

Table 2.9: Thermodynamic Parameters
Notation

Parameter

Dimensionsgθr

Acceleration due to gravity
Temperature of maximum densityof fresh water
Fresh water freezing point
Coefficient in the fresh-waterequation of state
Density of fresh water
Maximum density of fresh water
Density of ice
Density of snow
Latent heat of fusion
Specific heat of waterSpecific heat of ice
Specific heat of snow
Molecular heat conductivity of water
Molecular heat conductivity of ice
Molecular heat conductivity of snow

m·s−2
K

θf
aT
ρw
ρr
ρi
ρs
Lf
cw
ci
cs
κw
κi
κs

Estimate/
Computed from
9.81
277.13KK−2

273.151.6509 · 10−5

kg·m−3kg·m−3kg·m−3kg·m−3
J·kg−1
J·kg−1 ·K−1
J·kg−1 ·K−1
J·kg−1 ·K−1
J·m−1 ·s−1 ·K−1
J·m−1 ·s−1 ·K−1
J·m−1 ·s−1 ·K−1

Eq. (2.64)
1.0 · 103
9.1 · 102
Eq. (2.111)
3.3 · 105
4.2 · 103
2.1 · 103
2.1 · 103
5.46 · 10−1
2.29
Eq. (2.112)

Bibliography[1] S. Belamari. Report on uncertainty estimates of an optimal bulk formulation for surface turbulent
fluxes. Technical report, Marine EnviRonment and Security for the European Area - Integrated Project(MERSEA IP), Deliverable D4.1.2, 29p, 2005.
[2] B. Blanke and P. Delecluse. Variability of the tropical atlantic ocean simulated by a general circulation
model with two different mixed-layer physics. Journal of Physical Oceanography, 23:1363–1388,
1993.
[3] P. Bougeault and P. Lacarrère. Parameterization of orography-induced turbulence in a mesobeta scalemodel. Mon. Wea. Rev., 117:1872–1890, 1989.
[4] M. A. Brunke, C. W. Fairall, X. Zeng, L. Eymard, and J. A. Curry. Which bulk aerodynamic algorithms
are least problematic in computing ocean surface turbulent fluxes? J. Clim., 16:619–636, 2003.
[5] G. Caniaux, S. Belamari, H. Giordani, and A. Paci. A one Year Sea Surface Heat Budget in the
North Eastern Atlantic Basin during the POMME Experiment : Part II : Flux Correction. Journal ofGeophysical Research, 110:15pp, 2005.
[6] H. Charnock. Wind stress on a water surface. Q. J. R. Meteorol. Soc., 81(350):639–640, 1955.
[7] J. W. Deardorff. Convective velocity and temperature scales for unstable planetary bound-ary layer
and for rayleigh convection. J. Atmos. Sci., 29:1211–1212, 1970.
SURFEX v8.1 - Issue no 3 - 2018

58
[8] J. W. Deardorff. Preliminary results from numerical integration of the unstable planetary boundary
layers. J. Atmos. Sci., 27:1209–1211, 1970.
[9] J. W. Deardorff. Rate of growth of the nocturnal boundary layer. In Symposium on Air Pollution,
Turbulence and Diffusion, Las Cruces, N. M., NCAR ms. No. 71-246, 1971.
[10] J. W. Deardorff. A multi-limit mixed-layer entrainment formulation. J. Phys. Oceanogr., 13:988–1002,
1983.
[11] C. W. Fairall, E. F. Bradley, J. E. Hare, A. A. Grachev, and Edson J. B. Bulk parameterization of airsea
fluxes: Updates and verification for the coare algorithm. J. Clim., 16:571–591, 2003.
[12] C.W. Fairall, E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young. Bulk parameterization of
air-sea fluxes for tropical ocean-global atmosphere coupled-ocean atmosphere response experiment. J.
Geophys. Res., 101:3747–3764, 1996.
[13] X. Fang and H. G. Stefan. Temperature variability in lake sediments. Water Resour. Res., 34:717–729,
1998.
[14] D. M. Farmer. Penetrative convection in the absence of mean shear. Q. J. R. Meteorol. Soc., 101:869–
891, 1975.
[15] D. M. Farmer and E. C. Carmack. Wind mixing and restratification in a lake near the temperature of
maximum density. J. Phys. Oceanogr., 11:1516–1533, 1981.
[16] E. Fedorovich, R. Conzemius, and D. Mironov. Convective entrainment into a shear-free, lineraly
stratified atmosphere: bulk models reevaluated through large eddy simulations. J. Atmos. Sci., 61:281–
295, 2004.
[17] B. N. Filyushkin and Y. Z. Miropolskij. Seasonal variability of the upper thermocline and selfsimilarity of temperature profiles. Okeanol., 21:416–424, 1981.
[18] P. Gaspar, Y. Grégoris, and J.-M. Lefevre. A simple eddy kinetic energy model for simulations of theoceanic vertical mixing: Tests at station papa and long-term upper ocean study site. J. Geophys. Res.,
95(C9):16179–16193, 1990.
[19] H. Giordani and G. Caniaux. Diagnosing Vertical Motion in the Equatorial Atlantic. Ocean Dynamics,
61(12):1995–2018, 2011.
[20] H. Giordani, G. Caniaux, L. Prieur, A. Paci, and S. Giraud. A One Year Mesoscale Simulation of theNortheast Atlantic : Mixed Layer Heat and Mass Budgets during the POMME Experiment. Journal ofGeophysical Research, 110(C07S08):19pp, 2005.
[21] I. Zverev Golosov, S. and A. Terzhevik. Modelling thermal structure and heat interaction between awater column and bottom sediments. Technical report, Report No. 3220 [LUTVDG/(TVVR-3220) 141(1998)], Dept. of Water Resources Engineering, Inst. of Technology, Univ. of Lund, Lund, Sweden,
41 p, 1998.
[22] A. A. Grachev and C. W. Fairall. Dependence of the monin-obukhov stability parameter on the bulk
richardson number over the ocean. J. Appl. Meteorol., 36:406–414, 1997.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

59[23] J. E. Hare, P. O. G. Persson, C. W. Fairall, and J. B. Edson. Behavior of charnocks relationship forhigh wind conditions. In 13th Symp. on Boundary Layers and Turbulence, Amer. Meteor. Soc., Dallas,
TX, 252-255, 1999.
[24] E. Heise, M. Lange, B. Ritter, and R. Schrodin. Improvement and validation of the multilayer
soil model. Technical report, COSMO Newsletter, No. 3, Consortium for Small-Scale Modelling,
Deutscher Wetterdienst, Offenbach am Main, Germany, 198-203, 2003.
[25] J. Imberger. The diurnal mixed layer. Limnol. Oceanogr., 30:737–770, 1985.
[26] T. Jonas, A. Y. Terzhevik, D. V. Mironov, and A. Wuest. Investigation of radiatively-driven convection
in an ice covered lake using temperature microstructure technique. J. Geophys. Res., 108(14):1–18,
2003.
[27] P. Josse, G. Caniaux, H. Giordani, and S. Planton. Intercomparaison of oceanic and atmospheric forced
and coupled mesoscale simulations. Part I: Surface fluxes. Annales Geophysicae, 17:566–576, 1999.
[28] L.H. Kantha and C.A. Clayson. An improved mixed layer model for geosphysical applications. Journalof Geophysical Research, 99(C12):25235–25266, 1994.
[29] I. R. Khakimov. The wind profile in the neutrally stratified atmospheric boundary layer. Izv. Akad.
Nauk SSSR. Fizika Atmosfery i Okeana, 12:628–630, 1976.
[30] J.-W. Kim. A generalized bulk model of the oceanic mixed layer. J. Phys. Oceanogr., 6:686–695,
1976.
[31] S. A. Kitaigorodskii. On the computation of the thickness of the wind-mixing layer in the ocean. Izv.
AN SSSR. Ser. geofiz., 3:425–431, 1960.
[32] S. A. Kitaigorodskii and S. M. Joffre. In search of simple scaling for the heights of the stratified
atmospheric boundary layer. Tellus, 40A:419–433, 1988.
[33] and Rooth C. Kraus, E. B. Temperature and steady state vertical heat flux in the ocean surface layers.
Tellus, 19:231–238, 1961.
[34] E. B. Kraus. Atmosphere-ocean interactions. Oxford University press, London, 1972.
[35] W.G. Large, J.C. McWilliams, and S. Doney. Ocean vertical mixing : a review and a model withnonlocal boundary layer parameterization. Reviews of Geophysics, 32(4):363–403, 1994.
[36] J. Launiainen and B. Cheng. Modelling of ice thermodynamics in natural water bodies. Cold. Reg.
Sci. Technol., 27:153–178, 1998.
[37] P. Le Moigne, J. Colin, and B. Decharme. Impact of lake surface temperatures simulated by the flake
scheme in the cnrm-cm5 climate model. Tellus A, 68, 2016.
[38] C. Lebaupin-Brossier, V. Ducrocq, and H. Giordani. Two-way one-dimensional high-resolution airsea
coupled modelling applied to mediterranean heavy rain events. Q. J. R. Meteorol. Soc., 135:187–204,
2009.
[39] D. Mironov and E. Fedorovich. On the limiting effect of the earth’s rotation on the depth of a stably
stratified boundary layer. Q. J. R. Meteorol. Soc., 136:1473–1480, 2010.
SURFEX v8.1 - Issue no 3 - 201860[40] D. Mironov and B. Ritter. A new sea ice model for gme. Technical report, Technical Note, Deutscher
Wetterdienst, Offenbach am Main, Germany, 12 p, 2004.
[41] D. Mironov, A. Terzhevik, G. Kirillin, T. Jonas, J. Malm, and D. Farmer. Radiatively driven convection
in ice-covered lakes: Observations, scaling, and a mixed layer model. J. Geophys. Res., 107(7):1–16,
2002.
[42] D. V. Mironov. Parameterization of lakes in numerical weather prediction. description of a lake model.
Technical report, COSMO Technical Report, No. 11, Deutscher Wetterdienst, Offenbach am Main,
Germany, 41 pp, 2008.
[43] D. V. Mironov, S. D. Golosov, S. S. Zilitinkevich, K. D. Kreiman, and A. Yu. Terzhevik. Modelling
Air-Lake Interaction. Physical Background, chapter Seasonal changes of temperature and mixing conditions in a lake, pages 74–90. Springer-Verlag, Berlin, etc., 1991.
[44] D. V. Mironov and L. N. Karlin. Penetrative convection due to surface cooling with vertically distributed heating. Dokl. Akad. Nauk SSSR., 309:1336–1340, 1989.
[45] D. V. Mironov and A. Yu. Terzhevik. Spring convection in ice-covered fresh-water lakes. Izv. Akad.
Nauk SSSR. Fizika Atmosfery i Okeana, 36:627–634, 2000.
[46] S. Mondon and J.-L. Redelsperger. Study of a fair weather boundary layer in toga-coare: Parameterization of surface fluxes in large-scale and regional models for light wind conditions. Bound.-Layer
Meteorol., 88:4776, 1998.
[47] R. T. Pollard, P. B. Rhines, and R. O. R. Y. Thompson. The deepening of the wind-mixed layer.
Geophys. Fluid Dyn., 3:381–404, 1973.
[48] J. F. Price, R. A. Weller, and R. Pinkel. Diurnal cycling: observations and models of the upper ocean
response to diurnal heating. J. Geophys. Res., 91:8411–8427, 1986.
[49] D. A. Randall and B. A. Wielicki. Measurements, models, and hypotheses in the atmospheric sciences.
Bull. Amer. Met. Soc, 78:399–406, 1997.
[50] C. G. Rossby and R. B. Montgomery. The layer of frictional influence in wind and ocean currents.
Pap. Phys. Oceanogr. Meteorol., 3:1–101, 1935.
[51] S. D. Smith. Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of windspeed and temperature. J. Geophys. Res., 93:15467–15472, 1988.
[52] A. V. Soloviev. lsquothin thermal structure of the ocean surface layer in the polymode-77 region,
izvestiya. Atmos. Oceanic Phys., 15:750–754, 1979.
[53] A. V. Soloviev and N. V. Vershinskii. The vertical structure of the thin surface layer of the ocean underconditions of low wind speed. Deep-Sea Res., 29:1437–1449, 1982.
[54] P. Mlkki Tamsalu, R. and K. Myrberg. Self-similarity concept in marine system modelling. Geophysica, 2:51–68, 1997.
[55] R. Tamsalu and K. Myrberg. A theoretical and experimental study of the self-similarity concept.
Technical report, Report series of the Finnish Institute of Marine Research, 1998.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

61[56] M. Wade, G. Caniaux, Y. DuPenhoat, M. Dengler, H. Giordani, and R. Hummels. A one-dimensionalmodeling study of the diurnal cycle in the equatorial atlantic at the PIRATA buoys during the EGEE-3
campaign. Ocean Dynamics, 61(1):1–20, 2011.
[57] O. Zeman. Parameterization of the dynamics of stable boundary layers and nocturnal jets. J. Atmos.
Sci., 36:792–804, 1979.
[58] S. Zilitinkevich and A. Baklanov. Calculation of the height of the stable boundary layer in practicalapplications. Bound.-Layer Meteorol., 105:389–409, 2002.
[59] S. Zilitinkevich, A. Baklanov, J. Rost, A.-S. Smedman, V. Lykosov, and P. Calanca. Diagnostic andprognostic equations for the depth of the stably stratified ekman boundary layer. Q. J. R. Meteorol.
Soc., 128:25–46, 2002.
[60] S. S. Zilitinkevich. On the determination of the height of the ekman boundary layer. Bound.-Layer
Meteorol., 3:141–145, 1972.
[61] S. S. Zilitinkevich. Comments on a model for the dynamics of the inversion above a convective boundary layer. J. Atmos. Sci., 32:991–992, 1975.
[62] S. S. Zilitinkevich, D. V. Chalikov, and Yu. D. Resnyansky. Modelling the oceanic upper layer.
Oceanologica Acta, 2:219–240, 1979.
[63] S. S. Zilitinkevich and D. V. Mironov. A multi-limit formulation for the equilibrium depth of a stably
stratified boundary layer. Bound.-Layer Meteorol., 81:325–351, 1996.
[64] S.S. Zilitinkevich. Turbulent Penetrative Convection. Avebury Technical, Aldershot, 1991.

SURFEX v8.1 - Issue no 3 - 2018

62

SURFEX v8.1 - Issue no 3 - 2018

Chapter 3

Urban and artificial areas
Contents
3.1

3.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.1

Modelling cities in atmospheric models . . . . . . . . . . . . . . . . . . . . . . . 64

3.1.2

Objectives of the Town Energy Balance scheme . . . . . . . . . . . . . . . . . . . 65

3.1.3

Overview of the Town Energy Balance scheme . . . . . . . . . . . . . . . . . . . 65

3.1.4

TEB patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.1.5

Town geometry description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.1.6

Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Basics of the Town Energy Budget scheme . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.1

Temperature evolution equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.2.2

Longwave budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.2.3

Solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Diffuse solar radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Direct solar radiation for averaged directions . . . . . . . . . . . . . . . . . . . . 73
Direct solar radiation for a given canyon direction . . . . . . . . . . . . . . . . . . 74
Solar radiation reflectionsi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.2.4

Anthropogenic fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.2.5

Turbulent fluxes for momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Treatment of the urban roughness sublayer . . . . . . . . . . . . . . . . . . . . . 76
The drag approach with the Surface Boundary Layer scheme . . . . . . . . . . . . 76
The roughness length approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.2.6

Turbulent fluxes for heat and moisture . . . . . . . . . . . . . . . . . . . . . . . . 77
Considerations on the turbulent transfer of heat and moisture . . . . . . . . . . . . 77
Exchange coefficients between surfaces and atmosphere . . . . . . . . . . . . . . 77
Heat fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.2.7

Water reservoirs evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.2.8

Snow effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.2.9

Atmospheric quantities inside the canyon . . . . . . . . . . . . . . . . . . . . . . 81
In the case of the Surface Boundary Layer scheme . . . . . . . . . . . . . . . . . 81
Wind inside the Canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

63

64
Canyon temperature and humidity . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.10 Averaged fluxes at town scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3

3.4

Urban vegetation: gardens and greenroofs . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3.1

Philosophy of vegetation in TEB . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.3.2

Gardens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.3.3

Greenroofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.3.4

Irrigation and watering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

The Building Energy Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.4.1

Buildings description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.4.2

Buildings energy budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.4.3

Inside solar irradiation, sheltering . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.4.4

Domestic Heating and Air conditioning . . . . . . . . . . . . . . . . . . . . . . . 91

3.4.5

Waste heat emissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.4.6

Ventilation and infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Mechanical Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Natural Ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.4.7
3.5

3.6

Solar panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

The Surface Boundary Layer module, when applied in TEB . . . . . . . . . . . . . . 95
3.5.1

Drag by buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.5.2

Mixing length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Miscellaneous indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.6.1

Thermal comfort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Mean radiant temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Universal Thermal Climate Index . . . . . . . . . . . . . . . . . . . . . . . . . . 98

3.1 Introduction
3.1.1 Modelling cities in atmospheric models
Due to the complexity and diversity of towns around the world, conclusions drawn from experimental studies
on the interaction between the atmosphere and urbanized areas most of the time are limited either to aparticular site or physical processes. To overcome this problem, numerical studies are aimed to simulate
the urban climatology or energy budget. However, they still follow some simplified approaches. Buildingresolving models - i.e. models in which individual building shapes are described - allow, from a long timeago, the detailed examination of some processes (radiative effects see for e.g. Terjung et al. (1980), or windchanneling), but because of computational cost, applications are limited to local urbanization and comfort
studies. Even now, the use of such models is limited to the neighbourhood scale (typically 1km2 or less).
Performing a coupling between the urban surface and the atmosphere in atmospheric models requires adifferent approach, that allows to simulate the effects of cities at a larger scale. Before year 2000, and still inmost climate models and numerous numerical weather prediction models, the most common way to do thiswas (ans is) to use a vegetation-atmosphere transfer model whose parameters have been modified (Seaman etal. (1989), Menut (1997)), as opposed to an urban model. Cities are then modeled as bare soil or a concrete
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

65

plate. The roughness length is often large (one to a few meters, see Wieringa (1993) or Petersen (1997)).
The soil moisture availability (or the soil depth) is reduced, so that the Bowen ratio is shifted towards highvalues (large sensible heat flux).
However, these approaches do not allow to represent accurately most of the physical processes in cities,
and their consequences, such as the urban heat island at night. This is why several models were developedsince year 2000, based on a simplified geometrical representation of the buiildings: the ’urban canyon’.
The ’canyon’ model, from Oke and colleagues was developed during the seventies, and is dedicated tourban streets: a road is bordered by two facing building walls. such an approach allows to capture the most
pertinent processes: radiative trapping inside the canyon, impact on flow, higher surface in contact with theatmosphere available for heat storage., imperviousness of the buildings and roads, etc...
The first two models of this type are TEB (Masson 2000) and BEP (Martilli et al. 2002). Several othermodels following this philosophy were developed in the ten next years (see reviews in Masson 2006 andMartilli 2007). Up to 25 urban models participated to a recent intercomparison exercice (Grimmond et al.
2010, 2011). The conclusions of this study was that either simple models (as LUMPS, using statistical
relationships based on urban fluxes observations) or the most ’complex’ ones, with the most physics in it,
performed the better to reproduce the energy balance. However, simpler models are not able to simulatediagnostic quantities, such as air temperatre, energy consumption of buildings, etc, that more complex
models, such as TEB (included in SURFEX), can do. This limits their range of use. Furthermore, anotherconclusion was that it was necessary to improve the representation of vegetation.

3.1.2 Objectives of the Town Energy Balance scheme
The TEB model is aimed to simulate the turbulent fluxes into the atmosphere at the surface of a mesoscaleatmospheric model which is covered by buildings, roads, or any artificial material. It should parameterizeboth the urban surface and the roughness sublayer, so that the atmospheric model only ’sees’ a constant flux
layer as its lower boundary.
It must be considered as a part of the surface parameterization of the atmospheric model. The fluxes should
be computed for each land occupation type by the appropriate scheme, and then averaged in the atmosphericmodel grid mesh, with respect to the proportion occupied by each type. For example, a partition shouldbe: (1) sea; (2) inland water; (3) natural and cultivated terrestrial surface; (4) towns. The following fluxes
are calculated: latent and sensible heat fluxes (W m−2 ), upward radiative fluxes (W m−2 ) and momentum
fluxes (m2 s−2 ). Many other indicators can be computed, especially to estimate local urban climate, energy
consumption, water runoff, thermal comfort, ...

3.1.3 Overview of the Town Energy Balance scheme
The physics treated by the TEB (Town Energy Balance, Masson 2000) scheme is relatively complete. Dueto the complex shape of the city surface, the urban energy budget is split into different parts: a minimum of
three surface energy budgets are considered: one for the roofs, roads, and walls. One second wall energy
budget is added if walls are treated separately to take into account orientation effetcs. Up to two energy
budgets are added for snow when it is present on roofs or roads. Some of the physics were derived fromthe literature (long wave radiation or thermal conduction through the surfaces), since they are classicallyassumed to estimate temperatures in conditions without feedback towards the atmosphere (during nights
with calm wind). However, most parts of the physics need an original approach (short wave radiation,
SURFEX v8.1 - Issue no 3 - 2018

66
thermodynamical and anthropogenic flux treatment, rain and snow), since they occur when interaction withthe atmosphere is strong.
The representation of urban vegetation has been improved in the recent years, with gardens and greenroofs.
A Building Energy Module (BEM) is also implemented in order to represents the energetics inside thebuildings. This allows to simulate indicators such as energy consumption of domestic ehating and air
conditioning.

3.1.4 TEB patches
Cities are very heterogeneous. Therefore, averaged urban characteristics in a grid mesh may be considered
as a broad approximation in regards of certain scientific objectives. From the point of view of the couplingof the urban surface to the atmosphere, an averaged description of the urban fabric in each grid mesh can beconsidered sufficient, since only the energy fluxes towards the atmosphere are needed (and they are mostly
governed by the atmospheric forcing and the overall view of the urban fabric, such as building density, wall
density, mean building height, etc...).
However, in order to simulate the details in some applications, such as for example to estimate the humancomfort in perpendicular roads, or to represent the energetics of different buildings in the grid mesh, one
may need to have several computations of TEB in the same grid mesh. For example, one could performa simulation for 2 canyons with perpendicular roads. This is possible, by using patches for TEB. While
such patches are often used for the natural part of the grid, especially for climate simulation, this is not thecase for TEB. However, if needed, the possibility to activate patches for TEB is implemented in SURFEX.
Per default, only road directions change when using several patches (4 roads at 45 from each other whenusing 4 patches for example). When using several patches, the user needs to define what are the differences
between the patches (e.g. patches with different building heights, with different building materials, etc...).
The description of the physics of the model in the subsequent sections are all done for only one patch, but
are valid if you use several patches as well.

3.1.5 Town geometry description
Numerous fine-scale studies on building climatology exist. In those, several individual buildings are usuallypresent in order to study their radiative interaction, the wind channeling effects, or the building insulation.
The canyon concept, developed by city climatologists (e.g. Oke (1987)), uses such a framework: it considers
a single road, bordered by facing buildings. In these studies, models are, at best, forced by atmospheric data(radiation, wind above the roofs) but are not in interaction with it.
The TEB model is aimed to parameterize town-atmosphere dynamic and thermodynamic interactions. It isapplicable for mesoscale atmospheric models (a grid mesh larger than a hundred meters typically). Then,
spatial averaging of the town characteristics as well as its effect on the atmosphere, are necessary. The
individual shapes of each building are no longer taken into account. The TEB geometry is based on thecanyon hypothesis. However, a single canyon would be too restrictive at the considered horizontal scale.
We therefore use the following original city representation:
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

67

Figure 3.1: Overall implementation of gardens in TEB a) original version without garden; b) with gardens
1. the buildings have the same height and width (in the model mesh). The roof level is at the surface
level of the atmospheric model.
2. buildings are located along identical roads, the length of which is considered far greater than theirwidth. The space contained between two facing buildings is defined as a canyon.
3. any road orientation is possible. At that point, two options are possible:(a) only the information on the main road orientation is kept in each grid mesh. This option induces
to simulate two wall energy balances instead of one, because of shading effects. However, it canbe pertinent to estimate canyon micro-climate and human comfort for a specific road direction.
(b) all directions exist with the same probability. This hypothesis allows the computation of averaged forcing for road and wall surfaces. In other words, when the canyon orientation appears in
a formula (with respect to the sun or the wind direction), it is averaged over 360◦ . In this way,
no discretization is performed on the orientation.
The parameters for the morphological description of the city, and the surface temperatures, are given below.
The urban vegetation on ground (gardens, small parks, etc...) can be either simulated outside the city, as isdone by the large majority of the Urban Canopy Models, or, for more realism, inside the canyon. This has
been implemented by Lemonsu et al. (2012), and allows the physical interactions between the buildings andthe vegetation(e.g. shadows). More details will be provided in section 3.5.
• fbld the fraction of buildings (as seen from bird’s view) relative to the urban surface, Troof (ot TR ) the
surface temperature of roofs. The roof surfaces can be composed of several subsurfaces:
SURFEX v8.1 - Issue no 3 - 2018

68
– structural roof
– green roof
– solar panel (that can shelter both structural and green roofs)• froad (or fr ) the fraction of impervious surfaces relative to the urban surface, Troad ’or Tr ) the surface
temperature of these impervious surfaces.
• fgarden the fraction of gardens relative to the urban surface (is equal to zero when the urban vegetation
is not treated within TEB in the SURFEX grid mesh), and Tgarden the surface temperature of gardens(including all effects influencing it, as the presence of snow mantel on vegetation).
• h/w the ratio between building’s height h and (idealized) modelled canyon width w (that can take into
account vegetation if gardens are simulated), Tf acadeA and Tf acadeB the temperature of both facades
A and B. The facades include structural walls and windows (the latter are present only if the Building
energy Module is used):– Twin the surface temperature of windows (supposed identical whatever the wall, A or B), fwin
is the fraction of windows relative to the surface of facade.
– TwallA and TwallB the surface temperature of each wall, (1 − fwin ) is the surface of structuralwall relative to the surface of the facade.
Note that a parameter is not easy to estimate: the h/w canyon aspect ratio. It can be computed following
many different hypotheses, for example from 3D buildings databases. Because the more important physicalprocesses leading to the Urban Heat Island phenomena are directly linked to the surface of walls (storage
term and convection term), and because the surface of wall is an indicator that is relatively straightforward
to compute, the h/w aspect ratio is computed following:
1 Rwall−hor
2 1 − fbld
where Rwall−hor is the ratio of wall to horizontal (town) surface.
h/w =3.1.6 Summary of the chapter
The following sections successively present:• the basics of TEB, for impervious surfaces only
• the representation of urban vegetation: gardens and greenroofs• the Building Energy Module• the Surface Boundary Layer module (cf chapter 5), when applied in TEB• miscellaneous indicators• the description of the architectural characteristics of the building
A list of the most important input parameters and of the prognostic variables of the scheme are given in
Appendix fot heis chapter in Tables 3.2 and 3.3. Only the most importants features are described. For
further details, the reader is invited to read the referenced papers.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

69

3.2 Basics of the Town Energy Budget scheme
In this section, the focus will be done to describe the processes of the simplest version of the model(without gardens, building energy module). However, some of the processes, especially those exchanging
with the different type of surfaces (as the radiative exchanges), need to take into account the more detailed
parameterizations when they are used. In order to avoid redundancy in the description of these processes,
the equations with all the terms will be presented.
δ snow R

δR
TR

1

TR

TR

Wsnow R

WR

2

TR

3

T

T

w

i bld

Tr

δr
Wr

δ snow r
Wsnow r

Tr

Tw

Tr

3

Tw

Tr

2

Tw

1
2
3

zero flux conditon

1

Figure 3.2: Canyon geometry in the TEB scheme (without gardens, building’s energy module, greenroofs),and its prognostic variables.
The TEB model does not use one urban surface temperature (representative of the entire urban cover),but three (or four) surface temperatures, representative of roofs, roads and walls (1 generic wall, or 2
separate facing walls in case of oriented road). There are two reasons for that:• urban climatologists generally consider complex (non-flat) geometry cases, in particular the ’canyon’geometry. In order to be consistent with their findings, the TEB model uses a complex surface consisting of multiple explicit energy budgets.
• one spatially-averaged surface temperature is often used in soil-vegetation schemes, in order to compute the turbulent fluxes towards the atmosphere following the Monin-Obukhov similarity theory.
However, over towns, the use of only one surface temperature is debatable, because it has been observed that the Monin-Obukhov similarity theory does not apply for temperature in the urban roughness sublayer.
The second point will be adressed in more detail in section 3.2.6. The parameters of the scheme depend
directly on building shapes and construction materials. This makes the TEB scheme easy to initialize,
without the need for any atmospheric data for parameter tuning. Construction material characteristics canbe found in the literature (e.g. see Oke (1988)), or defined locally depending on the building’s type, use anddate of construction (see section ??).
Because the two walls of the canyon behave identically (in term of representation of the processes), except
for direct solar radiation (one wall is under sunlight, the other in shadows), longwave radiation, and wind
SURFEX v8.1 - Issue no 3 - 2018

70
exposition (leeward and windward), all the presentation of the processes hereafter are done for only one
wall, with the index w. Specific effects of road direction on the processes will be specifically mentioned:
the quantities related to the walls (A and B indicating the two facing walls) will there be noted wA and wB ,instead of simply w.
These hypotheses, as well as the formulations chosen for the physics (see hereafter), allow the developmentof a relatively simple scheme from the geometric point of view, but taking into account most of the physicalprocesses.

3.2.1 Temperature evolution equations
As discussed above, the urban surface is very inhomogeneous with respect to shape and building materials.
Urban climatologists need at least four surfaces to describe it: the roof, the road, and two facing walls. The
problem considered here (the evaluation of the turbulent and radiative fluxes from the urban cover to theatmosphere) allows the treatment of only three types of surfaces (roof, road, wall), while keeping enoughaccuracy to correctly represent the different terms of the surface energy budget. This is why the TEB model
uses several surface temperatures, TR , Tr and TwA (and TwB eventually) representative of roofs, roads andwalls, respectively.
Furthermore, in order to treat the conduction fluxes to or from the building interiors (roof, wall) or the
ground (road), each surface type is discretized into several layers (Figure 3.2). Per convention, the layer
with subscript 1 is the one in contact with the air (hereafter ’surface layer’).
The equations describing the evolution of the temperatures of the layers (representative of the middle of thelayer) are based on energy budget considerations.
The prognostic equations for the surface layers of the roof, wall (either A or B) and road respectively, read:

CR1

∂TR1
= (1 − δsnowR )∂t+δsnowR

∂Tw1
=
∂t
∂Tr1
=
Cr 1
∂t

Cw 1

(1 − δsnowr )+δsnowr

These equations can be written in a generic way:

C⋆1


1
∗
SR
+ L∗R − HR − LER − GR1,2
dR1

1
GRsnow,1 − GR1,2
dR1

1
∗
Sw
+ L∗w − Hw − Gw1,2
dw1
1
Sr∗ + L∗r − Hr − LEr − Gr1,2
dr1

1
Grsnow,1 − Gr1,2
dr1



1
1
∂T⋆1
S⋆∗ + L∗⋆ − H⋆ − LE⋆ − G⋆1,2 + δsnow⋆
G⋆snow,1 − G⋆1,2= (1 − δsnow⋆ )
∂t
d⋆1
d⋆1

(3.1)

Where, the subscript ⋆ stands either for R , r or w , describing roof, road and wall variables (only roof androad for water variables) respectively. This convention is used in the rest of this paper.
T⋆k is the temperature of the kith layer of the considered surface (in the above equations, k = 1). C⋆krepresents the heat capacity, λk the thermal conductivity and d⋆k the layer thickness.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

71

The fluxes S⋆∗ , L∗⋆ , H⋆ , LE⋆ , G⋆1,2 and G⋆snow,1 stand for net solar radiation, net infra-red radiation, sensible heat flux, latent heat flux, and conduction heat flux between surface layer and the underlying layer,
conduction heat fluxes between the base of the snow mantel and the surface, respectively. δsnow⋆ is thesnow fraction on the surface (which is zero on the walls).
It is assumed that the surface layer of each surface is sufficiently thin such that the layer averaged temperature can be used to evaluate the radiative and turbulent surface fluxes. This means that the surface
temperatures T⋆ are computed as:T⋆ = T⋆1
For the sake of clarity, the 1 subscript will be removed in the next sections.
The other layer temperatures evolve according to a simple heat conduction equation. For the kith layer:
C⋆k


1
∂T⋆k
=
G⋆k−1,k − G⋆k,k+1
∂t
d⋆k

(3.2)

In these equations, the conduction flux between layers k and k + 1 reads (for k < n where n is the numberof layers):T⋆ − T⋆k+1
G⋆k,k+1 = λk,k+1 1 k(3.3)
2 (d⋆k + d⋆k+1 )with
λk,k+1 =d⋆k + d⋆k+1(d⋆k /λk ) + (d⋆k+1 /λk+1 )(3.4)

The lower boundary conditions for the roofs and walls are given by the building internal temperature, theroad one being represented as a zero flux lower boundary. The fluxes between the nth layer (the inner layer)
and the underlying material are then:GRn,n+1
Gwn,n+1
Grn,n+1

TRn − Tibld
1
2 (dRn )Tw − Tibld= λn 1n
2 (dwn )
= 0

= λn

(3.5)
(3.6)
(3.7)

Due to large temperature gradients which can exist, and because of the multi-layer structure of the walls
or the roofs, it is recommended that at least 5 layers are used to represent each surface. This is done
automatically by the model per default, that computes layers for the conduction equation within the roofs
and walls with fine layers outside and inside, and, for the road, finer layers in contact to the atmosphere.
Note that these computation layers are different from the information given to describe the materials thatcompose the building. There any number of layer and any thickness can be given (for example one layer ofconcrete of 30cm and one insulation layer of 5cm).

3.2.2 Longwave budget
Initially, in the historic version of the model (Masson 2000), the trapping of long-wave radiation by thecanyon surfaces was computed with one re-emission taken into account (from the Johnson et al. (1991)
formulation). However, with the separation of walls (with road orientation) and the addition of additional
components to the urban system with the gardens and the windows (for the Building Energy Module), the
SURFEX v8.1 - Issue no 3 - 2018

72
number of surfaces exchanging with other surfaces increased a lot. An approximate linear version of the
longwave exchanges between any two surfaces is now used. Such an approximation is classicaly used inbuildings energetics codes. The approximation is good when emissivities are high (typically larger than0.9), which is the case for most surfaces, except for metal ones.
The net Longwave budget for surface S1 due to the exchange of energy between surfaces S1 and S2 is now
simulated as :LS1 from S2 = 4σǫS1 ǫS2 ΨS1 S2

3
1(TS1 + TS2 ) (TS2 − TS1 )
2

(3.8)

Where ǫS∗ are the emissivities of each surface, σ is the Stefan constant, TS∗ the temperature of each surface,and ΨS1 S2 the view factor under which surface S1 sees surface S2 . For the exchanges with the sky, a sky
temperature is defined from the incoming downwards longwave radiation, L↓ , assuming (formally) an1emissivity of 1, Tsky = L↓ /σ 4 .

The view factors are needed. They are computed for the TEB geometry (an infinite canyon) according to
Noilhan (1981):
Ψr = [(h/w)2 + 1]1/2 − h/w
1
Ψw ={h/w + 1 − [(h/w)2 + 1]1/2 }/(h/w)
2(3.9)(3.10)

These factors represent the fraction of sky seen from the road and one wall respectively, compared to thesky fraction that a flat horizontal surface would see without obstruction. The sky-factor for the roof isthen equal to 1. If the buildings are very low, Ψr tends to 1 and Ψw to 0.5 (one wall then sees one half ofthe sky). In this case, longwave radiative fluxes from the roads will be undisturbed by the walls. On thecontrary, if the buildings are very tall, both sky factors tend to zero, and radiative exchanges will mostly
occur between the walls, and less energy will escape towards the sky.
The net longwave radiation absorbed by the snow-free road and wall surfaces is given by the following
equations.
L∗r =
+
+
+
L∗wA =
+
+
+
+
+

4σǫr
4σǫr ǫw
4σǫr ǫw
4σǫr ǫw
4σǫw
4σǫr ǫw
4σǫrsnow ǫw
4σǫr ǫw
4σǫ2w
4σǫ2w

Ψr
1
2 (1 − Ψr )(1 − fwin )1
2 (1 − Ψr )(1 − fwin )(1 − Ψr )fwin
Ψw
Ψw δroad (1 − δsnowr )Ψw δroad δsnowr
Ψw δgarden(1 − 2Ψw )(1 − fwin )(1 − 2Ψw )fwin

3
1
2 (Tsky + Tr )
3
1
2 (TwA + Tr ) 31
2 (TwB + Tr ) 31
2 (Twin + Tr ) 
3
1
2 (Tsky + TwA)3
1
2 (Tr + TwA )31
2 (Trsnow + TwA ) 
31
2 (Tgarden + TwA )3
1
2 (TwB + TwA ) 
31
2 (Twin + TwA )(Tsky − Tr )(TwA − Tr )(TwB − Tr )(Twin − Tr )(Tsky − TwA )(Tr − TwA )(Trsnow − TwA )(Tgarden − TwA )(TwB − TwA )(Twin − TwA )By inverting the snow-covered and snow-free road characteristics in Eq. 3.11, the longwave radiative
budget on top of snow mantel can be defined. To find the longwave balance of wall B, one inverts A and B
indices. δroad = froad /(froad + fgarden ) and δgarden = fgarden /(froad + fgarden ) are the fractions of road
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

73

and garden relative to the canyon surface, respectively.
To deduce Eqs 3.11, we used the fact that if Ψr represents the contribution of the sky to the road viewing,
then (1 − Ψr ) is the contribution of the two walls. For the budget of one wall, the sky-view factor is Ψw ,the road view factor is Ψw (per symmetry), and the facing wall view factor is (1 − 2Ψw ).

3.2.3 Solar radiation
Diffuse solar radiation
Diffuse solar radiation S⋆↓ is supposed to reach each surface according to the sky view factors of eachsurface S⋆↓ = Ψ⋆ S ↓ . A part of this energy is reflected, depending on the albedo of each surface α⋆ . The reflected energy can then be again absorbed by the other surfaces, and so on. This is described in section 3.2.3.

Direct solar radiation for averaged directions
Because of shadow effects, special computations are required to estimate the solar flux received either by
the walls or the roads.
Let S ⇓ be the direct solar radiation received by an horizontal surface at the first atmospheric model level.
The roof surface receives this amount of radiation.
Let θ be the angle between the sun direction and the canyon axis, and λ be the solar zenith angle(from zenith). Let us first consider a road perpendicular to the sun direction (θ = π2 , Figure 3.3).
λ0 = arctan(w/h) is defined as the zenith angle for which the sun begins to illuminate the road. It can benoted that whatever the sun position, one of the two walls is in shadow, the other one is (partially) in light.
The mean direct solar fluxes received by both walls and by the road, for a street direction perpendicular tothe sun, are:π⇓Sw(θ = ) =2(πSr⇓ (θ = ) =
2

(

1w ⇓
2 hS
1
⇓
2 tan(λ)Sif λ > λ0
if λ < λ00if λ > λ0 ⇓h1 − w tan(λ) S if λ < λ0

In order to take into account the other canyon orientations, one should replace w by w/sin(θ) in the above
expressions, and then multiply the wall fluxes by sin(θ). Then let θ0 be the critical canyon orientation forwhich the road is no longer in the light (or for which the radiation is minimum if the sun is high enough),
i.e.:



w 1
θ0 = arcsin min;1
h tan(λ)
Averaging a flux with respect to the canyon orientation is performed with two integrations, one between
θ = 0 and θ = θ0 , and the other one between θ = θ0 and θ = π2 . The direct solar fluxes for walls, roads androofs then read:
SURFEX v8.1 - Issue no 3 - 2018

74
S

S
λ

λ

l

l
h

λ0

h

w

w

road perpendicular to sun direction

road perpendicular to sun direction

Sun low over the horizon λ > λ 0

Sun high over the horizon λ < λ 0Figure 3.3: Solar radiation input for a road perpendicular to the sun azimuth. In the TEB scheme, thecontribution of all the other road directions are averaged with this one.

Sr⇓ =

S⇓

⇓
Sgarden
= Sr⇓
⇓
Sw
= S⇓
⇓
⇓
Swin
= Sw
⇓
=
SR



2θ0
2h
−
tan(λ) (1 − cos(θ0 ))ππw

(3.11)(3.12)



w
h



1 θ0
−
2
π



+

1
tan(λ) (1 − cos(θ0 ))π



(3.13)(3.14)

S⇓(3.15)⇓
Note that from the previous equations, one can check the conservation relation Sr⇓ + 2 wh Sw= S ⇓.

Direct solar radiation for a given canyon direction
When the road direction is taken into account, the amount of energy received is not the same for both walls.
One is shaded (per convention here it will be wall B, but it depends in the model of the azimuthal position of
the sun relative to the axis of the road), and the other one is under sunlight (at least partially). The formulae
for the direct solar energy received are then (see Lemonsu et al. 2012 for details) :

Sr⇓ =

S⇓

⇓
Sgarden=Sr⇓"

max 0 , 1 −hw tan(λ)

sin|θsun − θcan |#(3.16)(3.17)

w
−Sr⇓
h

⇓
=
Sw
A

S⇓

⇓
Sw
=
B

0

(3.19)

⇓
Swin
=

⇓
⇓
1
2 (SwA + SwB )(3.20)SURFEX v8.1 - Issue no 3 - 2018(3.18)

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

75

Solar radiation reflectionsi
The scattered solar radiation received by the surfaces (S⋆↓ ) is directly deduced from the sky-view factors. Because of the canyon shape and the possible high albedo of the surfaces (white paint, snow),the shortwave radiative budget is computed by resolving a geometric system for an infinite number ofreflections. The reflections are assumed to be isotropic: there is no specular reflection in this model.
Details of the following calculations are given in Appendix A for the simpler case with averaged canyon direction (no difference between wall A and B). The complete demonstration is given in Lemonsu et al. 2012.
The total solar radiation absorbed by each of the surface types is given by :Ar (∞)=

Asnowr (∞)=

Ag (∞)=AwA (∞)=AwB (∞)=hi(1 − αr ) Sr⇓ + Sr↓ + (1 − Ψr )W∞hi(1 − αsnowr ) Sr⇓ + Sr↓ + (1 − Ψr )W∞hi(1 − αg ) Sr⇓ + Sr↓ + (1 − Ψr )W∞

1 ⇓
↓
⇓
↓
(1 − αw ) (Sw
+ Sw
+ Sw
+ Sw
) + α̃ground Ψw (Sr⇓ + Sr↓ )
A
A
B
B
2
+α̃ground Ψw (1 − Ψr )W∞ + (1 − 2Ψw )W∞ ]
#
"
 ⇓

↓
⇓
↓
SwA + Sw− Sw
− Sw
α̃f ac (1 − 2Ψw )A
B
B+ (1 − αw ) 1 +1 + α̃f ac (1 − 2Ψw )
2

1 ⇓
↓
⇓
↓
(1 − αw ) (Sw
+ Sw
+ Sw
+ Sw
) + α̃ground Ψw (Sr⇓ + Sr↓ )
A
A
B
B
2
+α̃ground Ψw (1 − Ψr )W∞ + (1 − 2Ψw )W∞ ]
#
"
 ⇓

↓
⇓
↓
SwA + Sw− Sw
− Sw
α̃f ac (1 − 2Ψw )A
B
B− (1 − αw ) 1 +1 + α̃f ac (1 − 2Ψw )
2

with

W∞

=

⇓
↓
⇓
↓
α̃f ac (Sw
+ Sw
+ Sw
+ Sw
)/2 + α̃f ac Ψw α̃ground (Sr⇓ + Sr↓ )AAB
B
1 − α̃ground α̃f ac Ψw (1 − Ψr ) − α̃f ac (1 − 2Ψw )Where α̃f ac = fwin αwin + (1 − fwin )αw and α̃ground = δroad ((1 − δsnowr )αroad + δsnowr αsnowr ) +δgarden αgarden are the agregated albedo of the facade (wall+window) and canyon ground (road+garden),
respectively.
Solar energy reaching the windows Awin is then given by the averaged value of energy received by walls
A and B (by formally replacing (A − αw ) by (1 − αwin ) in the formula). Note that all this energy will
not be absorbed by the window, since part of it will reach the interior of the building (see the BEM section
fori reaching the garden is deduced from the one absorbed by the roadh details). Similarly, the solar energy⇓↓
Sgarden + Sgarden + (1 − Ψr )W∞ .

3.2.4 Anthropogenic fluxes
Due to human activity, heat and moisture are released towards the atmosphere. The two main sources comefrom domestic heating and from combustion.
Domestic heating is explicitly resolved by assuming a constant minimal internal temperature, whatever
the external temperature. The default value is 290.15 K. The heat is then released towards the wall/roof
SURFEX v8.1 - Issue no 3 - 2018

76
surfaces and then towards the atmosphere through the conduction flux formulation.
The combustion source is split into two contributions in the TEB model: traffic and industry. For each, theheat and moisture fluxes, averaged on the town surface (Htraf f ic and LEtraf f ic , Hindustry and LEindustry ),are specified by the user (from available information on the town activity).
However, these fluxes do not directly modify the surface energy budgets since they are released into the air.
The traffic related fluxes will modify the canyon air budget (they are incorporated in Equation 3.25, see
next section). The industry fluxes are assumed to influence the atmosphere directly.

3.2.5 Turbulent fluxes for momentum
Treatment of the urban roughness sublayer
In this section, the method to compute the turbulent fluxes between the surfaces and the atmosphericmodel will be presented. The resolution of the atmospheric model is far too low to be able to represent theurban roughness sublayer motions, as it applies to the mesoscale. The atmospheric models do not usually
parameterize the exchange processes in this layer: it is done by the surface scheme. If the first atmosphericlevel is outside the roughness sublayer, the traditional surface layer formulations can be used to computethe turbulent fluxes. The problem is that the roughness sublayer can have a substantial extension over anurban surface (several tens of meters), and the first level of the atmospheric model (often a couple of tens ofmeters) is often within it.
It is therefore necessary to have a closer look to the parameterization of the fluxes. Feigenwinter et al. (1999)
conducted measurements on a 50m height mast in the city of Basel (Switzerland). The authors found that themechanical properties in the roughness sublayer (such as profiles of velocity variances, non-dimensionalized
velocity variances and spectra of wind components) behave similarly to rural surface layers. Furthermore,they concluded that these quantities are quite well parameterized within the Monin-Obukhov similarity
theory, if local Monin-Obukhov length is applied.
Following their results, the TEB scheme computes the momentum fluxes for the entire urban (or suburban) cover.
The momentum fluxes can be computed using two main approaches:
The drag approach with the Surface Boundary Layer scheme
In this case, the wind, temperature, moisture and turbulent kinetic energy profiles are defined within andabove the canyon. The friction is not explicitly calculated by a single formulation, but simulated but theeffect of the drag force of the buildings (see section 3.5) for more details.
The roughness length approach
More classicaly, when the SBL scheme is not used, a roughness length formulation taking into accountstability coefficients is used. The stability coefficients that are available in TEB are:• Brutsaert (1982)• Mascart et al. (1995)• Kondo et al. (2007)
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

77

We recommend to use the Kondo et al. (2007) formulation, that was derived specifically for urban areas.
The momentum fluxes are computed for the entire urban surface. However, one difficulty lies in the determination of the roughness length to use in urban areas. Wieringa (1993) reviewed some experimental roughness length estimations for rather homogeneously built-up areas. Dense low building roughness lengths
were found between 0.4 and 0.7m, and those for regularly-built towns ranged from 0.7 to 1.5m. In these experiments, they are approximately equal to 1/10 of the houses or building heights. Bottema (1997) presents
a model computing roughness lengths from building shapes and relative positions (normal or staggered).
He found the modeled z0town to be in agreement with the available measurements. Sensitivity experimentsof his model show that the ratio z0town /h ranges from 0.05 to 0.1 (except for very sparsely built areas).
Therefore, as a first approximation, the roughness length in the TEB model is set equal to:z0town = h/10
(with an arbitrary limit of 5m), but it can be specified independently, either from in-situ measurements ormore complicated formulations (see for example the review of Grimmond (1999)).

3.2.6 Turbulent fluxes for heat and moisture
Considerations on the turbulent transfer of heat and moisture
In contrast, Feigenwinter et al. (1999) found that the temperature characteristics, and in particular the turbulent heat flux, cannot be satisfactorily reproduced by the Monin-Obukhov similitude framework. They
attribute this discrepancy to ’thermal inhomogeneity and/or different source areas’. The use of one uniquesurface exchanging heat with the atmosphere (the classical surface layer approach) becomes debatable.
The approach of the TEB scheme is to suppose that there are two major sources of heat from the artificial
cover towards the atmosphere, leading to two turbulent heat fluxes. These two different surfaces are
the roofs on the one hand, and the canyon systems on the other hand (see Figure 3.4). The two flux
contributions are averaged relative to their horizontal areas: this is a way to represent the mixing in theurban roughness sublayer.
Both for roof and roads, one will also explicitly suppose that the transfer coefficient for turbulent heat andmoisture fluxes are identical (but different than for momentum). Very few direct measurements of turbulent
moisture fluxes exist in the literature to validate or invalidate this hypothesis.
Exchange coefficients between surfaces and atmosphereAll heat and moisture fluxes are computed using exchange coefficient, based on aerodynamical resistances(or conductances), and the difference between the surface temperature of the considered surface (roof, road,wall) and the air temperature (either above roof or in the canyon).
The horizontal surfaces use formulations that take into account vertical atmospheric stability effects. While
this is is questionable for roofs (where air turbulence even at proximity of the surface is strongly influenced
by the buildings shape, this is probably pertinent for roads. The three possible formulations to compute theaerodynamical resistances RESR and RESr are:• Brutsaert (1982)
SURFEX v8.1 - Issue no 3 - 2018

78
• Mascart et al. (1995)• Kondo et al. (2007)
Between these three, we recommend Kondo et al. (2007), that was specifically developed for cities. Please
note that there is also another possible option for roofs (see below).
These formulations are used either for roads (with roughness length of 5cm) or roofs (with roughness lengthof 15cm, as observed by Sturrock et al. (1977)). However, the flow inside the canyon being often highly
turbulent even for low wind speeds. One takes into account in the wind estimation inside the canyon for theexchange coefficients formulation. Both the mean wind (Ucan , see below for its estimation) and a turbulent
1/3

g
Q0 h
) are then used, combined as an ’effective’
scale due to local canyon convection (w∗ = Tcanp
2 + (u + w )2 , Where u + w is the turbulent wind and Q encompasses
canyon wind equal to : Ucan
∗
∗
∗
∗
0
both road and wall turbulent heat fluxes.
When the SBL scheme is not used, one also need to compute the heat and moisture fluxes between thecanyon air and the atmosphere above. This is done using the same formulations as above (leading to theestimation of canyon resistance, noted REStop ), but using the roughness lentgh for the whole urban fabric(the same as for the momentum formulation), instead of the surface roughness lengths.
For walls, two formulations are available. The first one is the Rowley et al. (1930) and Rowley et al. (1932)
aerodynamic formulations. They were obtained from in-situ measurements. These formulae are also usedin the canyon circulation model of Mills (1993). It writes:
RESw = Cpd ρa (11.8 + 4.2Ucan )−1(3.21)For buildings, a recent development in the model was to introduce a formulation of
the exchanges coefficients directly dereived from state-of-the-art codes in Building energetics (energy+), by Pigeon et al. (2014).
This is the DOE-2 option (description in
http://apps1.eere.energy.gov/buildings/energyplus/pdfs/engineeringreference.pdf). It takes into account thewindward and leeward effects on exchange coefficients. Those coefficient lead to coefficient generally 2.5
times smaller than the other formulations.
The DOE-2 option can then be chosen for roof RESR and wall RESw exchange coefficients, in place ofthe stability fgunction and Rowley formulations, respectively.
All possible options are summarized in Table 3.1.

Heat fluxes
The effect on temperature and specific humidity of the difference in height between the atmospheric level
and the roof level is corrected using the Exner function Π = (p/p0)Rd /Cpd , where p is the pressure (psand pa are the surface pressure and the first level pressure in the atmospheric model respectively), p0 is areference pressure (equal to 100000 Pa), and Rd the gas constant for dry air. One defines:Tˆa =Ta Πs /Πaqˆa = qa qsat (Tˆa , ps )/qsat (Ta , pa )SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

Brutsaert (1982)
Mascart (1995)
Kondo et al. (2007)
Rowley (1930)
DOE-2

roofs

roads

X (z0 =15cm)
X (z0 =15cm)
X (z0 =15cm)

X (z0 =5cm)
X (z0 =5cm)
X (z0 =5cm)

79
walls

windows(if BEM)

X
X

X

canyon air and above(if not SBL scheme)
X (z0town )X (z0town )X (z0town )X

Table 3.1: Possible options for exchanges coefficients
The heat and moisture turbulent fluxes between roof and atmosphere read:HR = Cpd ρa (Tˆa − Tcan )/RESR

LER =

Lv ρa

(qˆa − qcan )/RESR

where ρa is the air density at first atmospheric level, and Cpd the heat capacity of dry air.
The heat fluxes between the canyon surfaces and the canyon air read:
Hr = Cpd ρa (Tr − Tcan )/RESr

Hw = Cpd ρa (Tw − Tcan )/RESw

LEr =

Lv ρa

LEw =

0

δr (qsat (Tr , ps ) − qcan )/RESr

The turbulent heat fluxes between the canyon air and the atmosphere are computed from the temperature andhumidity inside the canyon. The fluxes between surfaces and canyon air follow an empirical formulation.
The air characteristics inside the canyon are deduced from the continuity between the fluxes coming from thesurfaces and the flux with the atmosphere (inspired by the vegetation canopy scheme of Deardorff (1978)).
The heat fluxes are used in the energy budget conservation equations involving the surface temperatures.
This is why a precise approach has been chosen, specific to each surface. Figure 3.4 displays a summary of
the TEB options.
Above the canyon, the fluxes are estimated from classical surface boundary layer laws. However in theseformulae, the air characteristics in the canyon (Tcan and qcan ) are used instead of the surface characteristics.

Htop = Cpd ρa (Tˆa − Tcan )/REStop

LEtop =

Lv ρa(qˆa − qcan )/REStop

3.2.7 Water reservoirs evolution
Liquid or solid precipitation intercepted by urban surfaces is rarely addressed in the literature, except for
sewer system and hydrological considerations. An exception is Grimmond et al. (1991b), however, inwhich the model used was initially dedicated to forest studies, and is limited to the water budget, computedfrom the Penman Monteith equation. They added anthropogenic water sources and used the Grimmond etal. (1991a) heat storage flux formulation.

SURFEX v8.1 - Issue no 3 - 2018

80
Thanks to the presence of the surface temperatures in the TEB scheme, the saturation specific humidity, andthen the turbulent latent heat flux can be computed more easily (see section 3.2.6).
The liquid precipitation is intercepted by both roofs and roads. There is runoff from roofs and roads to thesewer system. Roads and roofs can be covered by a certain amount of water, parameterized by the variables
Wr and WR , respectively. These surfaces are impervious. Then, instead of defining a relative humidity,
it is more judicious to treat the fraction of surface covered by the water, δwaterr and δwaterR . This part issaturated (fractional water pools), while the other part is assumed to be dry. Water evaporates when the air
humidity is not saturated until all water has disappeared from the impervious surface.
2
The snow-free fraction of the surface occupied by liquid water is computed as: δwater⋆ = (W⋆ /W⋆max ) 3 ,(Noilhan and Planton (1989)), where W⋆max is the maximum water amount on the surface.
Furthermore, urban dew is taken into account (in case of negative latent heat flux), as its occurrence canhave significant effects, as pointed out by Richards (1998). It requires a special treatment: when conditions
are present for dew to occur (air humidity larger than the surface saturation humidity), the surface isconsidered wet (δwater∗ = 1). This allows then a (negative) latent heat flux, which can fill the interception
reservoirs. These treatments are deduced from those for the foliage interception reservoirs in vegetation
schemes (Deardorff (1978), Noilhan and Planton (1989)).
Addition of an anthropogenic water source was not retained in TEB, because it does not compute evaporation over gardens or parks. Irrigation water input should be taken into account through the vegetation
scheme dedicated to these natural surfaces. However, anthropogenic fluxes of water vapor directly into the
air exist in the scheme (see section 3.2.6), in order to represent factory release for example.
Finally, the water-reservoir evolution equation is (for roof or road):∂W⋆= R − LE⋆ /Lv∂t(W⋆ < W⋆max )(3.22)

where R is the rain rate (kg m−2 s−1 ) and Lv is the latent heat of vaporization.
The reservoirs are of small capacity (the water in excess is lost as runoff). They are set equal toWRmax =Wrmax =1 kg m−2 , which is well in the range of values explored by Grimmond and Oke (1991).
The total depletion of the reservoirs by evaporation requires, in general, a few hours for daytime conditions.
Additionnaly, the water during rainfall is supposed to fall at the temperature of the air. Therefore, because
there is no specific energy budget for the water reservoirs, the rainfall water is supposed to instantaneously
take the temperature of the surface (roof or road). This induces an immediate sensible heat flux (contrary to
the future latent heat flux that will be caused by evaporation). This heat flux, that is immediatly incorporated
into the corresponding surface layer (roof or road) heat budget, is equal to :Hrain⋆ = Cwater R(Ta − T⋆ )(3.23)

where Cwater is the heat capacity of water, supposed equal to 4218 J kg−1 K −1 .

3.2.8 Snow effects
Snow is intercepted by roofs and roads. A snow scheme is implemented on each surface type. Snow density,
albedo, temperature and thickness of water equivalent depth are parameterized. Radiation, sensible heat flux,
sublimation, conduction and melting are taken into account.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

81

The evolution rate of snow albedo is enhanced (and its minimum value lowered) in order to represent car
pollution (dirty snow). A time-dependent drainage term is included to take into account snow-plow work (ifany).
The snow fraction on roof or road surfaces is set equal to a function of the snow interception reservoir(Wsnow∗ ): δsnow∗ = (Wsnow∗ )/(Wsnow∗ + Wsnow∗ max ). The parameter Wsnow∗ max is set equal to 1 kg
m−2 . The snow has an effect on:• the energy budget of the surfaces (as part of the downward flux comes from the base of the snow),• the heat fluxes from the road towards the canyon or from the roof towards the atmosphere,• the radiative calculations for the canyon surfaces, because of the snow albedo, emissivity and temperature.

3.2.9 Atmospheric quantities inside the canyon
In order to compute the momentum and energy fluxes of the different surfaces, one needs to know the airtemperature, humidity and wind speed in the canyon and above the surfaces. Depending if the Surface
Boundary Layer scheme is active or not, there are two ways to estimate these.

In the case of the Surface Boundary Layer scheme
In this case, the wind, temperature and humidity profiles are known. For the roof fluxes computations, one
uses the atmospheric quantities at the first SBL layer above the roof. For the road fluxes computations, one
uses the atmospheric quantities at the first SBL layer, typically 50cm above ground. For the wall fluxes
computations, one uses the atmospheric quantities at middle height of the canyon, interpolated from the
SBL levels.

Wind inside the Canyon
In the absence of the SBL scheme (and associated profiles), one needs to estimate the wind, air temperatureand humidity at mid height of the canyon, in order to compute the road and wall fluxes. Roof fluxes are
directly computed using the information at forcing level.
The horizontal wind speed, Ucan , is estimated at half the height of the canyon. First, the horizontal windspeed at the top of the canyon is deduced from the logarithmic law above it (Figure 3.4, right side), and thedisplacement height is equal to two thirds of the building height from road surface (i.e. at h/3 under the roof
level - which is the zero height of the atmospheric model -, a classical assumption for plant canopies). Furthermore, in order to consider all canyon orientations, and since only the along canyon wind is considered,an integration over 360◦ is performed. At canyon top, this gives:


h/3
ln
z0
2
 town  ||U~a ||Utop =
π ln ∆z+h/3
z0townwhere ∆z is the height of the first atmospheric model level above the roofs.
SURFEX v8.1 - Issue no 3 - 201882
To calculate Ucan , a vertical profile of the wind inside the canyon is assumed. An exponential form is chosen(as is done in vegetation canopies, cf e.g. Arya (1988)). Such a profile applied at half-height gives:
Ucan = Utop exp(−N/2)
N must be determined. Rotach (1995) finds from his case study (h/w = 1), that Ucan ∼ 0.75Utop . Studies
in corn fields (h/w ∼ 4), which could be assimilated to narrow streets, give Ucan ∼ 0.4Utop (Arya 1988).
Therefore, the parameter N = 0.5h/w should be pertinent.
Then:



 ln h/3
z02
1h town  ||U~a ||(3.24)
Ucan = exp −π
4 w ln ∆z+h/3
z0
town

Canyon temperature and humidity
These quantities can be considered as output of a meteorological forecast. They are computed diagnostically: the equilibrium between thermodynamic fluxes for the canyon air is assumed to be valid at each time
step. The anthropogenic flux due to traffic is also taken into account. Note that in this formula, Htraf f ic ,representative of the whole urban surface, has been scaled to the road surface.

Htop = δr (1 − δsnowr )Hr + δr δsnowr Hsnowr + δgarden Hgarden+Htraf f ic 1−f1 bld+

2h[(1 − fwin)Hw + fwi
w

LEtop = δr (1 − δsnowr )LEr + δr δsnowr LEsnowr + δgarden LEgarden +LEtraf f ic 1−f1 bld
Then
Tcan =


Htraf f ic
Hgarden
Hwin
Tˆa
Tw
Tr
2h
+
+
f
(1
−
f
)
δr (1 − δsnowr ) RES
win
win
w
RESw
Cp ρa + REStop + Cp ρa (1−fbld ) + δgarden Cp ρa + δr δs
r
d

d

d

1
1
1
δr (1 − δsnowr ) RES+ 2h
w (1 − fwin ) RESw + REStopr(3.27)

andδ

qcan =qLE(T ,p )

r s
qˆa
f ic
sat
+ RES
+ Lv ρatraf
δr (1 − δsnowr ) waterrRES(1−fbld ) + δgardenr
topLEgarden+ δr δsnowr LELrvsnow
Lv ρa
ρa

waterr1
δr (1 − δsnowr ) δRES
+ RES
r
top

(3.28)

3.2.10 Averaged fluxes at town scale
As mentioned above, the averaging operation performed to obtain the turbulent fluxes at town scale is in
itself a way to solve the problem of the roughness sublayer: it mimics the mixing of the different sources ofturbulent heat fluxes, and then produces fluxes which are representative of the upper part of the surface
layer, above the roughness sublayer. The energy fluxes released by the industrial activities is also added at
this stage.
The total heat fluxes from the artificial material areas towards the atmosphere are then:

Htown = fbld HR + (1 − fbld )Htop + Hindustry

LEtown = fbld LER + (1 − fbld )LEtop + LEindustry
SURFEX v8.1 - Issue no 3 - 2018(3.29)(3.30)

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

Ta

83

qa
industry

log
RES R

RES topT R δR δsnow R

traffic

Tw

z

T can
q can

h/3
0town

Ucan

RESw

exp

RES r

T r δ r δ snow r
Aerodynamical resistanceswind profile

Figure 3.4: Scheme options for: (a) aerodynamic resistances; (b) wind profile within and above the canyon.
In order to have the total turbulent fluxes H, LE from the surface towards the atmospheric model, thesefluxes should be averaged with those computed by the vegetation scheme for the other land surfaces (cityparks, gardens, fields, forest, bare soil...) and those from water covered surfaces (rivers, lakes, sea...).

SURFEX v8.1 - Issue no 3 - 201884

3.3 Urban vegetation: gardens and greenroofs
3.3.1 Philosophy of vegetation in TEB
Cities are not only composed of impervious surfaces. Urban vegetation plays an important role, of course
in suburban areas, where gardens are often mixed within buildings and houses, but also in dense urban
centers, with parks, street trees, and vegetated courtyard or small gardens. Vegetation in cities give to a lotof ecosystemic services, such as:• climatic effects: reduction of urban heat, runoff management• absorption of CO2• biodiversity enhancement (both vegetal and animal)• recreative locations• prefered location for soft travel modes• improvement of wellbeing and health, reduction of stress• real estate improvement• etc...
While of course it is not the aim of TEB to simulate all these effetcs, the importance of urban vegetation on
micro-climate lead to simulate its role more precisely. However, the overall ecosystemic services of urban
vegetation show why in most urban planning strategies, and especially in relation with adaptation to climatechange, the question of vegetation is of prime importance.
This is why in TEB we have developed the representation of urban vegetation, for garden (and groundvegetation in general) and greenroofs. The strategy was not to develop from scratch an urban vegetation
model, but to couple TEB with ISBA, that is used in SURFEX for natural continental covers. This enable
to capitalize on all the developments done in ISBA on the physics and biologics of plants. For example, thisallows to simulate the CO2 flux due to soil and plant respiration and photosynthesis.
This means that ISBA can, for each grid point, be called several times independently: for the natural part of
the grid mesh, for the garden, and for the greenroofs. Each occurrence of ISBA will have its own descriptive
variables and prognostic variables (e.g. the soil moisture will be different in natural cover, on the greenroofs
and in the garden).

3.3.2 Gardens
The main change is first the definition of the town fraction. This now includes the urban vegetationthat interacts with the nearby buildings. This encompasses street trees, gardens, small parcks and green
corridors. However, large parks, where most of the vegetation is far from the buildings and do not directlyinteract with them (no shadows for example), should still be included in the nature part of the grid mesh.
The town part now contains the building fraction, the urban vegetation fraction, and the impervious surfaces(as roads, parkings) fraction (the sum of all three being equal to 1). The first impact to incorporate thevegetation within the town part of the grid mesh is that allows to more accurately described the urban
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

85

morphology. Indeed, the vegetation being included within the canyon, the space being the buildings islarger, and more coherent with the reality. This, in itself, modifies the simulation of all the processes alreadypresented for the version of TEB without gardens (that most often depend on geometry).
The other impacts are physical: the buildings send shadows on the gardens. This changes the solar radiation
received by the vegetation. The infra-red radiation is also increased, due to the interactions with the walls.
The vegetation also is sensitive to the canyon microclimate and influence it in return. All these effects aretaken into account. All details are given in Lemonsu et al. (2012).
1. First, radiative exchanges are computed between all the canyon surfaces, including now the vegetation, both for solar (still with an infinite number of reflections)(see section 3.7), and infra-red (withthe approximation of net exchanges between one surface and all of those that are seen by it, see section 3.2.2). These radiative information is using the albedo, surface temperature and emissivity of thegarden. Those quantities are estimated from previous time-step of the garden ISBA model.
2. Then the solar and infrared radiation received by the garden (taking into account shadowing andradiative trapping by the canyon) are sent to ISBA, with all the other meteorological information (airtemperature, humidity, wind, pressure, rainfall, snowfall) representative of the canyon. Please notehere that the atmospheric data is estimated, not from the forcing level that is above the buildings, butfrom the middle of the canyon if no SBL scheme is used, or at first SBL level (typically 0.5m) if hte
SBL scheme is used.
3. ISBA computes the energy fluxes. Note here that all the physics of ISBA are available. For example,
snow mantel in garden is simulated by the snow scheme chosen in ISBA. The reader should refer tothe chapter describing the ISBA model for a description of all the processes in the model.
4. Finally the turbulent and fluxes are sent back to the canyon, at the bottom of the canyon. These fluxes
are averaged with the fluxes coming from the road, and then influence the rest of the canyon as theroad fluxes do in the version of the model without gardens do.

3.3.3 Greenroofs
The need to prepare cities for climate change adaptation requests the urban modeller community to implement sustainable adaptation strategies within their models to be tested against specific city morphologies
and scenarios. Greening city roofs is part of these strategies. In this context, the greenroof module for
TEB (town energy balance) has been developed to model the interactions between buildings and greenroof
system at the scale of the city. This module, which combines the ISBA model (Interaction between Soil
Biosphere and Atmosphere) and TEB, allows for one to describe an extensive greenroof composed offour functional layers (vegetation grasses or sedums; substrate; retention/drainage layers; and artificial
roof layers) and to model vegetation-atmosphere fluxes of heat, water and momentum, as well as thehydrological fluxes throughout the substrate and the drainage layers, and the thermal fluxes throughout thenatural and artificial layers of the greenroof. TEB-greenroof is therefore be able to represent the impact ofclimate forcings on the functioning of greenroof vegetation and, conversely, the influence of the greenroof
on the local climate.
The greenroof also modifies strongly the roof energy balance, since the surface energy budget is replacedby the conduction flux at the base of the greenroof retention/drainage layer. This impacts the buildings
energetics a lot when the BEM module is active. The greenroof acts as a supplementary insulation layer in
SURFEX v8.1 - Issue no 3 - 2018

86

Figure 3.5: Overall algorithm of greenroof and gardens in TEB

addition to the effect of cooling due to the increased evaporation.
As established previously, the heat and water transfers involved in the natural layers of greenroofs(atmosphere, vegetation, and substrate and hydrological control layers) are similar to those of perfectly
natural surfaces. They can therefore be simulated, as is the case in the models previously examined, by astandard soil and vegetation model, provided that it is calibrated to reflect the peculiar characteristics ofthe soil-forming materials used for the construction of greenroofs. Therefore, the strategy proposed andultimately retained for the inclusion of greenroofs within TEB is to use a soil and vegetation model thatcan not only be calibrated for a specific soil but would also have the ability to overcome the limitationsof existing models. The ideal model should allow for a coupled modelling of greenroof hydrological andenergetic performances, employ sufficiently detailed parameterizations to describe the physical processes
involved (including evapotranspiration and soil water flows), and at the same time have spatial resolutions(i.e. time calculations) suitable for modelling applications at city scale.
From a physical point of view, the main change in TEB induced by the implementation of greenroofs is themodification of the surface flux condition at the top of the roof. Instead of being computed from the surface
energy balance (with the interaction of radiation, sensible and latent turbulent heat fluxes and conduction),
the energy tranfer boundary condition of the top layer of the roof is replaced by a heat conduction flux (deMunck et al. 2013):
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

GN −R = λN −R (TNn − TR1 )87(3.31)

TNn and −TR1 re, respectively, the temperatures of the deepest sub-layer of the natural roof and the top layerof the artificial roof. λN −R is the interfacial thermal conductivity between the two layers, approximatedusing the characteristics of the bottom layer of the greenroof.
The equation evolution of the top layer roof temperature (presented previously in section 3.2.1) is thenmodified as :
CR1



 1
∂TR1
∗
+ L∗R − HR − LER − GR1,2 + δsnowR GRsnow,1 − GR1,2= (1 − fgreenroof ) (1 − δsnowR ) SR∂tdR
1
+fgreenroof(GN −R − GR1,2 )dR1Due to the presence of waterproofing membranes, no hydrological coupling is required between thesoilvegetation model and the building model, and the excess water and the water that percolates leaves thesystem and are collated as the green roof outlet drainage. This will allow for connection to urban drainage
systems when these are developed within a future version of TEB.
The multi-soil-layer diffusion version of ISBA is used to simulate the greenroofs substrate. For standard
applications of ISBA to natural soils, the thermal characteristics for dry soil and the hydrological characteristics are deduced from empirical formulations, called pedotransfer functions, which connect thesecharacteristics to the user-input soil texture properties (sand and clay fractions, Decharme et al., 2011).
But the pedotransfer functions derived for natural soils are not really adapted to the soil-forming materials
constituting the substrate or the drainage layers of a greenroof. Consequently, whenever possible, it is better
to directly define greenroof-specific thermal and hydrological characteristics. However, when thermal
characteristics for greenroof materials are available, hydrological characteristics are not only hard to findbut also consist in lab measurements which do not reflect in situ conditions such as soil compaction or
root presence/growth. Indeed, root growth results in the formation of soil microstructures, which modifies
the intrinsic soil hydrological behaviour. De Munck et al. (2013) proposes to use pedotransfer parameters
based on organic matter. The best calibration ensemble obtained in this study for the drainage layer whose
texture, porosity and hydrological behaviour are complex displays hydrological characteristics which are
all typical of the behaviour of organic matter (peat): high porosity and saturated hydraulic conductivity.
Such characteristics are therefore recommended for extensive greenroofs. Intensive greenroofs, that arecomposed of trees with a deeper soil structure (typically 1m), can be represented by the classical values of
ISBA soils.

3.3.4 Irrigation and watering
Irrigation of gardens is somehow a common practice. Under most of climates during the hot season,
it is also necessary to irrigate the vegetation on greenroofs in order to avoid the drying of the plants.
Furthermore, road watering is also considered as a possibility to avoid extreme heat during heat waves.
Such a practice is indeed several centuries old in Japan, known as Uchimizu.
In TEB watering of gardens, greenroofs and roads is possible. This allows to take into accounts some aspects
linked to water management and adaptation of cities to climate. This is done with the following approach,for each three types of surfaces (separately). The user provides maps or data for:
SURFEX v8.1 - Issue no 3 - 2018

88
• the first and last month when watering occurs (both are included in the watering period). First monthcan be later in the calendar than the end day (for summer in the southern hemisphere for example).
• the begining (included) and end (excluded) hour of the watering period each day. The begining hour
can be later than the end one from a clock point of view (for nighttime watering for example).
• the total amount of water per 24h per square meter that will be used during the watering.
The amount of water (kg/m2 /24h) will be equaly distributed during the defined period within the day, if
the present month is a month of watering. Note that, for the same total amount of water during the day, thiswill induce larger instantaneaous flows if the period of watering is short and smaller flows if the period islong. For roads, the water is added to the road water reservoir Wr . For greenroofs and gardens, the water isdirectly added in the first layer of the soil in ISBA (not added to the rainfall). This simulated ground based
irrigation systems, and avoid the interception of water by the trees and low plant leaves.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

89

Figure 3.6: Diagram of a building and an urban canyon. The main physical processes included in BEMTEB are represented: heat storage in building and urban construction materials, internal heat gains, solar
heat fluxes, waste heat from HVAC systems, etc. The diagram also represents the multi-layer version of the
TEB scheme and the possibility of coupling it with an atmospheric mesoscale model.

3.4 The Building Energy Module
The energy consumption of heating, ventilation and air-conditioning (HVAC) systems in buildings has
become an important factor in the design and analysis of urban areas. HVAC systems are responsible forwaste heat emissions that can contribute (among other causes) to the increase in air temperature observedin urban areas with respect to their undeveloped rural surroundings. This increase in air temperature incities, a phenomenon known as the urban heat island (UHI) effect, can affect the energy consumption of
HVAC systems and the waste heat emissions associated with them. The use of HVAC systems is expected
to increase in the following years as a consequence of global-scale and urban-scale climate warming;
therefore, urban climate models, such as the Town Energy Balance (TEB) scheme (Masson, 2000), has been
improved in order to represent future scenarios of climate conditions and energy consumption in urban areas.
Bueno et al. (2012) and Pigeon et al. (2014) implemented a Buidling Energy Module (BEM) in TEB. The
reader is invited to refer to these articles for more details.

3.4.1 Buildings description
The BEM implemented in TEB considers a single thermal zone, a generic thermal mass to represent thethermal inertia of the indoor materials, the heat gains resulting from transmitted solar radiation and theinternal sources of heat, infiltration and ventilation. The heat conduction through the envelope of thebuilding is calculated using a finite difference method individually for each surface (roof, wall and floor).
An overview of all the processes simulated with the BEM implemented in TEB are displayed in figure 3.6.

SURFEX v8.1 - Issue no 3 - 201890

3.4.2 Buildings energy budgets
BEM uses a heat balance method to calculate indoor thermal conditions and building energy demand.
An energy balance is applied to each indoor surface (si: wall, window, floor, roof, and internal mass),
accounting for conduction, convection, and radiation heat component. The convection and radiation terms
are calculated from a standard heat transfer coefficient formulation, Q = h∆T .
The longwave radiative exchanges between all the surfaces in the interior of the building are computed using
the same type of approximation as for outdoor exchanges:
2

LS1 from S2 = 4σǫ FS1 S2

3
1(TS1 + TS2 ) (TS2 − TS1 )
2(3.32)

where FS1 S2 is the configuration factor between surfaces 1 and 2, and where the emissivity ǫ of internalsurfaces has been supposed to be equal for all surfaces (and set by default to 0.9). All the expressions of theconfiguration factors are given in Bueno et al. (2012).
The convection terms between each internal surface si and the indoor air are computed as:
Qcv = hcv (Tsi − Ti )(3.33)

where Tsi and Ti are the surface and indoor air temperatures respectively. The convective heat transfer
coefficient has the following values: hcv = 3.076W m−2 K −1 for a vertical surface (walls, internalmass); hcv = 0.948W m−2 K −1 for a horizontal surface with reduced convection (floor surface with
Tsi = Tf loor1 < Ti and ceiling surface with Tsi = Troofk > Ti ) ; and hcv = 4.040W m−2 K −1 for ahorizontal surface with enhanced convection.
The energy budget of internal air is also simulated (see below).

3.4.3 Inside solar irradiation, sheltering
Window effects have been introduced in the outdoor energy balance of the TEB model. The external surfaces of windows participate in the outdoor energy balance in the same manner as other urban surfaces(walls, road, garden, etc.). Window surfaces are semi-transparent and therefore have three optical properties (albedo, absorptivity, and transmittance). Two coupled surface energy balances are solved to calculate
the internal and external surface temperatures of windows. Each surface energy balance accounts for theconvective and radiative heat fluxes reaching the surface and the steady-state heat conduction through thewindow. Building energy models usually consider the dependence of the solar heat transmitted throughwindows on the angle of incidence of the sun. However, simulations with EnergyPlus for different window orientations show that for an average-oriented canyon, the solar transmittance of windows (τwin ) canbe approximated by a uniform value of 0.75 times the solar heat gain coefficient (SHGC). The SHGC canbe found in window catalogues and represents the fraction of incoming solar radiation that participates in
the indoor energy balance. Using the solar energy reaching the window (cf section 3.2.3), the solar heattransmitted through windows is then calculated as:
Sindoor = Awin τwin fwin
SURFEX v8.1 - Issue no 3 - 2018(3.34)

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

91

The solar absorptivity of windows is calculated as a function of the U-factor and the SHGC (Pigeon et al. 2014), by using the equations proposed in EnergyPlus documentation (description in
http://apps1.eere.energy.gov/buildings/energyplus/pdfs/engineeringreference.pdf). The U-factor can also befound in window catalogues and measures the window conductance, including the convective and longwave
heat transfer coefficients at both sides of the window. The window albedo is calculated so that the three
optical properties (albedo, absorptivity, and transmittance) sum to unity. As seen above, the model uses anarea-averaged facade albedo to calculate solar reflections by weighting the albedo of walls and windows
with the glazing ratio of buildings.
It is also possible to simulate shelters on the window, and the periods during which shelters are on. BEM
also includes a simplified model to account for window shadowing devices. If the solar radiation reaching
the window is above a predefined threshold, the model considers that shades are placed outside and in frontof the windows. These shades are characterized by a predefined transmittance. The model reduces the solar
radiation reaching the windows by changing its optical properties. The solar radiation that is not reflected,
absorbed, or transmitted by the windows is assumed to be converted into a sensible heat flux towards theurban canyon.

3.4.4 Domestic Heating and Air conditioning
To calculate the dynamic evolution of indoor air temperature between a cooling and a heating thermal set
point, BEM solves a sensible heat balance at the indoor air. The sensible heat balance is composed of theconvective heat fluxes from indoor surfaces, the convective fraction of internal heat gains, the infiltration
sensible heat flux, and the sensible heat flux supplied by the HVAC system.

dTi X=
Asi hcv,si (Tsi − T i)+ Qig (1− frd )(1− flat )+ V̇inf ρCp (Tcan − Ti )+ ṁsys Cp (Tsys − Ti )dt
si
(3.35)
where Ti is the indoor air temperature; Vbld ,ρ and cp are the volume, density and specific heat of the indoor
air, respectively; Asi is the area of the indoor surface of each type (wall, window, floor, roof, and internalmass); Qig represents the internal heat gains; flat is the latent fraction of internal heat gains; frd is theradiant fraction of sensible internal heat gains; V̇inf is the infiltration air flowrate; Tcan is the outdoor air
temperature; and ṁsys and Tsys are the mass flowrate and temperature of the air supplied by the HVAC
system.
Vbld ρCp

3.4.5 Waste heat emissions
The waste heat released into the environment by a cooling system is given by :Qwaste,cool = Qexch,cool + QHV AC,cool
where Qexch,cool = ṁsys Cp (Tsys − Ti ) is the thermal energy exchanged between the cooling system andthe indoor air, and QHV AC,cool is the energy consumption of the cooling system (e.g. electricity). The
user can specify the sensible-latent split of the waste heat produced by the cooling system, depending onwhether the system is air-condensed, water-condensed, or both. The user can also define which fraction of
SURFEX v8.1 - Issue no 3 - 2018

92
this waste heat/humidity is released into the canyon (e.g. for individual air-conditionning systems locatedon each balcony) or above roofs (for centralized systems).
For the heating system, the waste heat flux is related to the energy contained in the combustion gases and isgiven by:
Qwaste,heat = QHV AC,heat − Qexch,heat
where QHV AC,heat is the energy consumption of the heating system (e.g. gas).

3.4.6 Ventilation and infiltration
The flow rate V̇inf in equation 3.35 describes the amount of air exchanged between indoor and outdoor.
This exchange of air lead to modification of heat and moisture inside but also outside. For example, heatedbuildings will heat the outside air through conduction trhough the walls and roofs but also directly by airtransfers. Those air transferts have three potential sources: inflitration, ventilation, natural ventilation.
All these three processes can be simulated in TEB. Note that all are optional, but infiltration is per defaut
activated, while the two others are not.

Infiltration
Infiltration refers to the flow of air induced voluntary, e.g. by slits in walls and windows, or involuntary,
due to cracks and defaults of the structure of the building. The infiltration flow rate V̇inf is typically of theorder of 0.5 vol/h (where vol refers to the volume of air in the building).

Mechanical Ventilation
Mechanical ventilation is related to systems that force the exchange of air between indoor and outdoor. This
allows for example to evacuate humidity from bathrooms or kitchens. This type of equipment is common
in recent buildings and houses. The formulation is the same as for infiltration, but with an exchange ratethat can be larger. Double-flow mechanical ventilation can also reduce the heat loss during the exchange of
air between indoor and outdoor (this is parameterized using a smaller ventilation coefficient).

Natural Ventilation
People can open windows and doors. This leads to natural ventilation. This can be done for example for
aeration, to go inside or outside, or for ventilation of the building, e.g. to reduce the indoor temperature
if it is cooler outside. The latter process is parameterized in TEB. Contrary to inflitration and mechnaicalventilation, the flowrate in the case of natural ventilation is dependent of the external meteorological conditions. This flow will be larger if the wind is stronger, or if the temperature difference between indoor andoutdoor air is larger. The formulations for the natural ventilation coefficient is given in Bueno et al. 2012, as
well as the hypotheses done on the behaviour of people on the condition of opening and closing of windows.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

93

Figure 3.7: Schematic diagram of the energy balance of the solar panel and its impact on radiation received
by the roof (dashed arrows: solar fluxes; plain arrows: long-waves fluxes; dotted arrow: sensible heat

3.4.7 Solar panels
Solar panels can be simulated on the roofs (Masson et al. 2014). An additional energy balance is thencomputed for the solar panel, taking into account solar radiation (from above and reflected upwards), longwave radiation (received both from above and below, and emitted/reflected both upwards and downwards),
convection and energy production. No heat storage is taken into account, the solar panel being supposed
thin enough. The presence of solar panels also impacts the underlying surfaces: structural roof andgrennroof. solar panels modifiy their energy balance, by sheltering the solar radiation (in an amount equal
to their surface coverage fpanel ), and modify the longwave balance.
For downwards longwave emission, solar panel is supposed of emissivity 1 and at air temperature. For the
upwards longwave emitted terms, the solar panel temperature takes into account air temperature and solar
irradiance (that itself uses an empirical coefficient F T = 1.1 to take simulates the geometrical effect of thetilting of the solar panel towards the sun). Default value for emissivity of solar panels is 0.9.

Tpanel = Ta + kT × F T (SW⇓ + SW↓ )(3.36)

Two types of solar panels can be simulated:• thermal panels, for hot water production• photovoltaic panels, for electricity production
Thermal panels are more efficient than photovoltaic panels (efficientcy coefficient of 0.6 instead of 0.14,
per default). However, thermal panels are more complicated to install, and only a limited amount of solar
panels is necessary for warming water, depending on the need in hot water. In TEB, thermal panels aresupposed to be installed on residential buildings only (note that this requires to have an information on thefraction of residential buildings in the grid mesh). It is then necessary to define what proportion of theroof area is required for thermal panels, and how much area remains available for PV panels. In residentialbuildings, one supposes that the density is typically 1 occupant per 30m2 of floor area. Furthermore, 1m2
SURFEX v8.1 - Issue no 3 - 201894of thermal panel is needed per capita. This means 1m2 of panel per 30m2 of floor area. For single story
accommodation, 1/30 of the roof is then equipped with thermal panels, and (fpanel 1/30) by PV panels. If
the building has two stories, thermal panels will occupy 2/30 of the roof area, and so on. So if Nf loor is thenumber of floors of the building (variable calculated in TEB), the proportions of thermal panels (fther panel )and and photovoltaic panels (fphot panel ) are calculated as :fther panel = min(Nf loor /30; fpanel )fphot panel =fpanel − fther panel

All details on the production of energy by both types of panels is given in Masson et al. (2014). The energy
produced by the solar panels, that influences its energy balance, is computed as:

Eprod = (fther panel Ether prod + fphot panel Ephot prod )/fpanel(W/m2 of solar panel)

And finally, the sensible heat flux Hpanel that is not easy to parameterize, is found as the residual of thesolar panel energy balance.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

95

3.5 The Surface Boundary Layer module, when applied in TEB
The TEB-SBL (for Surface Boundary Layer) version of TEB has been recently developed in order toimprove prediction of the meteorological fields inside the street canyon (Hamdi et al. (2008), Masson et al.
(2009)). It resolves the surface boundary layer inside and above urban canopy by introducing a drag force
approach - based on Yamada (1982) for vegetation canopies - in order to take into account the influence ofbuildings on the local atmospheric characteristics.

3.5.1 Drag by buildings
The equations for momentum, turbulent kinetic energy, air temperature, and specific humidity follow thesame general expression (here for momentum):∂U∂U= FU +∂t∂t T EB(3.37)

According to Martilli (2002) , the momentum equation includes, besides the general forcing term FU , a contribution from the area-average effect of the subgrid urban elements that is partitionned into a contribution
from vertical surfaces (buildings and walls) and a contribution from horizontal surfaces (roofs and roads).
For the present version of TEB-Veg that only takes into account low vegetation, the garden contribution is
included in the horizontal term:
H∂USH= −Cd U 2
∂t T EB
Vair(3.38)

where Cd is the drag coefficient, SH the horizontal surface area of roofs, roads, and gardens, and Vair thevolume of air in the urban grid cell. The drag coefficient is equal to (the π term coming from averaging of
the drag coefficient along all wind directions) :Cd = 0.4/π(3.39)For temperature (T) and humidity (q), the contributions from gardens are taken into account through thesensible and latent heat fluxes:∂T∂t T EB=∂q∂t T EB=Q HR + Q Hr + Q Hg
SH
Q H w SV+ρCp
Vair
ρCp Vair
Q ER + Q Er + Q Eg
SH
ρ
Vair


(3.40)(3.41)

with QHR , QHr , and QHg the sensible heat fluxes for roofs, roads, and gardens (same for the latent heatflux), QHw the sensible heat fluxes for walls, and SV the vertical surface area of walls.

3.5.2 Mixing length
Vertical turbulent exchanges within the canyon (and also above the canyon) are parameterized with the
turbulent scheme of Cuxart et al. (2000). This scheme uses an equation for the turbulent kinetic energy, andis closed with a mixing length. Hamdi et al. (2008) use a constant mixing length within the canyon, equal
to the building height. Here, we improve this representation following the works of Santiago and Martilli(2010) , that used fluid dynamics models to explicitly simulate the motions within the canyon to derive a
vertical profile of the mixing length.
SURFEX v8.1 - Issue no 3 - 2018

96

The mixing length (L) is parameterized as :
L
C
L
C

=

min [ 2.24(h − d) , z ]for=max [ 2.24(h − d) , z − d ]

for

z
< 1.
h
z
> 1.5
h

(3.42)(3.43)

with a continuous linear transition between the top of the canopy layer and the base of the inertial sublayer,
and where the displacement height d is also parameterized following Santiago and Martilli (2010):
d = max3h , λ0.13hf4



(3.44)

Here z is the height above ground, h is the building height, λf is the frontal area density, that is derived
from other TEB geometric parameters assuming no prefered direction of buildings with respect to the winddirection (λf = [ wh fbld ]/ π2 , with w being the road width and fbld the building fraction). C is dependant on
the turbulence scheme constants and of the atmospheric stability, using Monin-Obukhov stability functions(Redelsperger (2001)). Note that near the surface, one limits the mixing length to reproduce the effect of
the surface on the turbulent eddies.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

97

3.6 Miscellaneous indicators
3.6.1 Thermal comfort
A lot of indices (more than 50!) exist to evaluate the thermal comfort of human beings. This is the scienceof bioclimatology. The COST action 730 recently proposed a new index: the Universal Thermal Climate
Index (UTCI) (http://www.utci.org/). This is the index that is estimated in TEB to represent the thermal
comfort of people. This index takes into account effects of wind, temperature, humidity and radiation.
It makes implicit hypotheses on the activity and clothing of the person for which the UTCI is estimated.
Therefore, this index should be understood as an index relative to a typical person, but the actual sensationof people may of course be different. The UTCI provide a temperature value, that can be compared to atemperature scale to infer the amount of comfort or cool or heat discomfort.
In TEB, we calculate the UTCI for :• outdoor condition, in sunlight• outdoor condition, in shade• indoor condition (pertinent only without AC system in summer)
Mean radiant temperature
To calculate the UTCI, one must first estimate radiant temperature. This is done using the radiative terms
computed by TEB. For outdoor computations, one first estimate the view factors of ground, facades and sky
for a human body (of mean height hhuman = 1.7m):

Fhuman−f ac =Fhuman−ground =Fhuman−sky =q2h2human + w4 +q22
h2 + w4 − w/2 − (h − hhuman )2 + w4 /(2hhuman )
#
"
r
2
1
w
w
+1
2 2hhuman + 1 −2hhumanq

1 − Fhuman−f ac − Fhuman−groundwhere w is the canyon width, computed from input TEB parameters as:
w = 2h(1 − fbld )/Rwall−hor
The radiation received by the human body, from solar diffuse and infra-red radiation (so for a person inshade), is estimated as:hiRADbody,shade = (1 − αbody )/ǫbody
Fhuman−sky S ↓ + Fhuman−f ac Sf ac + Fhuman−f ac Sgroundhi+ Fhuman−sky L↓ + Fhuman−f ac Lf ac + Fhuman−f ac Lground(3.45)

where αbody = 0.3 is the albedo of human body, ǫbody = 0.97 the emissivity of human body, and Sf ac ,Sground the solar radiation reflected by facades and ground (garden and road together) respectively, and
Lf ac , Lground the longwave radiation emitted/reflected by facades and ground, respectively.

SURFEX v8.1 - Issue no 3 - 2018

98
For the evaluation of the UTCI in sunlight, the amount of solar radiation received by the human bodyis added. This is done taking into account the solar elevation angle (deduced from the zenithal angle asγ = π2 − λ), because the human being is supposed standing in upright position.


⇓
Sbody
= S ⇓ × 0.308cos γ(1 − γ 2 /14.744)⇓
RADbody,sun = RADbody,shade + Sbody(1 − αbody )/ǫbody

And finally the mean radiant temperature, either in shade or sun, is equal to :1

Tmrt = (RADbody,⋆ /σ) 4(3.46)

Universal Thermal Climate Index
Then, the UTCI indices are computed using an approximated form of a complete human body energybalance model. This approximated form is a polynomial formulae, taking into account air temperature at 2
meters (◦ C), vapor pressure at 2 meters (hpa), wind at 10m (ms−1 ), and mean radiant temperature (◦ C).
For indoor index computations, the radiative temperature is computed using the radiation emitted by eachinterior surface, the wind is supposed equal to 0.5ms−1 .
For outdoor index computations, the mean radiant temperature is computed according to the above shade or
sunlight formulae. If the SBL scheme is not used, the wind is taken at 10m above roofs level or at forcing
level, and the temperature and humidity are equal to the canyon air temperature and humidity. If the SBL
scheme is used, the wind is equal interpolated 10m above the ground (road and garden) from the SBL
layers, and the temperature and humidity are equal to the air temperature and humidity 2m above groundlevel.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 3. URBAN AND ARTIFICIAL AREAS

symbolgeometric parameters
atown
fbld
fgarden1 − fbld - fgarden
fwin
1 − fwinfgreenroofhh/w
z0townradiative parameters
αR , αr , αwǫR , ǫr , ǫw
αgarden , αwinǫgarden , ǫwinthermal parametersdRk , drk , dwk
λRk , λrk , λwk
CRk , Crk , Cwk
Uwin

99

designation of symbol

unit

fractional area occupied by artificial material
fractional artificial area occupied by buildings
fractional artificial area occupied by urban vegetation
fractional artificial area occupied by roads
fractional area occupied by windows relative to the whole facade surface
fractional area occupied by structural walls relative to the whole facade surface
fractional area occupied by greenroofs relative to the roof surfacebuilding heightcanyon aspect ratio
dynamic roughness length for the building/canyon systemmmroof, road and wall albedosroof, road and wall emissivities
garden and window albedos
garden and window emissivities-

thickness of the kth roof, road or wall layer
thermal conductivity of the kth roof, road or wall layer
heat capacity of the kth roof, road or wall layer
U-factor of windowsm
W m−1 K−1
J m−1 K−1-

Table 3.2: Parameters of the TEB scheme. Note that atown is not strictly a parameter of the TEB scheme,
but is used to average the output TEB fluxes with those computed for the vegetation and water portions of
the grid mesh. Note also that some surfaces between the buildings, such as gardens or parks for example,
are not treated by the TEB model, but modify the canyon width, w.

SURFEX v8.1 - Issue no 3 - 2018

100

symbolprognostic variables
TRk , Trk , Twk
WR , Wr
Twink
Tmassk , Tf loork
Tibld
Wsnow R , Wsnow r
Tsnow R , Tsnow rρsnow R , ρsnow r
αsnow R , αsnow r
diagnostic variables
Tcan
qcan
Ucan
αtown
Tstowninput energy fluxes
L↓
S↓
S⇓!——————————————————————————- Htraf f ic
LEtraf f ic
Hindustry
LEindustry
other energy input
Theat targetbld
Tcool targetbld
output energy fluxes∗∗SR, Sr∗ , Sw∗∗
LR , Lr , L∗w
HR , Hr , Hw
LER , LEr , LEw
GRk,k+1 , Grk,k+1 , Gwk,k+1
Htown
LEtowndesignation of symbol
temperature of the kth roof, road or wall layerroof and road water interception reservoir
window temperaturestemperature of the kth internal mass or floor layer
building interior air temperatureroof and road snow interception reservoir
roof and road snow temperatureroof and road snow density
roof and road snow albedo
canyon air temperaturecanyon air specific humidity
along canyon horizontal wind
town effective albedo
town area averaged radiative surface temperature
downward infra-red radiation on an horizontal surface
downward diffuse solar radiation on an horizontal surface
downward direct solar radiation on an horizontal surface
anthropogenic sensible heat flux released in the canyon
anthropogenic latent heat flux released in the canyon
anthropogenic sensible heat flux released by industries
anthropogenic latent heat flux released by industries
domestic heating target for interior air temperature
air-conditioning target for interior air temperature

net solar radiation budget for roofs, roads and walls
net infra-red radiation budget for roofs, roads and walls
turbulent sensible heat flux for roofs, roads and walls
turbulent latent heat flux for roofs, roads and walls
conduction heat flux between kth and k + 1th roof, road or wall
town averaged turbulent sensible heat flux
town averaged turbulent latent heat flux

Table 3.3: Energy fluxes and variables in the TEB scheme

SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

101

Bibliography[1] S.P. Arya. Introduction to Micrometeorology. Academic Press, Inc., 1988.
[2] M. Bottema. Roughness modelling in relation to pollutant dispersion. Atmos. Environ., 31(18):3059–
3075, 1997.
[3] B. Bueno, G. Pigeon, L. K. Norford, K. Zibouche, and C. Marchadier. Development and evaluation of abuilding energy model integrated in the teb scheme. Geoscientific Model Development, 5(2):433–448,
2012.
[4] P. Bougeault Cuxart, J. and J.-L. Redelsperger. A turbulence scheme allowing for mesoscale andlarge-eddy simulations. Q. J. R. Meteorol. Soc., 116:1–30, 2000.
[5] C. De Munck, Lemonsu A., Bouzouidja R., Masson V., and Claverie R. The greenroof module (v7.3)
for modelling green roof hydrological and energetic performances within teb. Geoscientific Model
Development, 6:1941–1960, 2013.
[6] J. Deardorff. Efficient prediction of ground temperature and moisture with inclusion of a layer ofvegetation. J. Geophys. Res., 83:1889–1903, 1978.
[7] B. Decharme, A. Boone, C. Delire, and J. Noilhan. Local evaluation of the interaction between soil
biosphere atmosphere soil multilayer diffusion scheme using four pedotransfer functions. J. Geophys.
Res., 116(D20), October 2011.
[8] C. Feigenwinter, R. Vogt, and E. Parlow. Vertical structure of selected turbulence characteristics above
an urban canopy. Theor. Appl. Climatol., 62:5163, 1999.
[9] C. S. B. Grimmond, M. Blackett, M. J. Best, J.-J. Baik, S. E. Belcher, J. Beringer, S. I. Bohnenstengel, I. Calmet, F. Chen, A. Coutts, A. Dandou, K. Fortuniak, M. L. Gouvea, R. Hamdi, M. Hendry,
M. Kanda, T. Kawai, Y. Kawamoto, H. Kondo, E. S. Krayenhoff, S.-H. Lee, T. Loridan, A. Martilli, V. Masson, S. Miao, K. Oleson, R. Ooka, G. Pigeon, A. Porson, Y.-H. Ryu, F. Salamanca, G.J.
Steeneveld, M. Tombrou, J. A. Voogt, D. T. Young, and N. Zhang. Initial results from phase 2 of theinternational urban energy balance model comparison. Int. J. Clim., 31(2):244–272, 2011.
[10] C. S. B. Grimmond, M. Blackett, M. J. Best, J. Barlow, J-J. Baik, S. E. Belcher, S. I. Bohnenstengel, I. Calmet, F. Chen, A. Dandou, K. Fortuniak, M. L. Gouvea, R. Hamdi, M. Hendry,
T. Kawai, Y. Kawamoto, H. Kondo, E. S. Krayenhoff, S-H. Lee, T. Loridan, A. Martilli, V. Masson,
S. Miao, K. Oleson, G. Pigeon, A. Porson, Y-H. Ryu, F. Salamanca, L. Shashua-Bar, G-J. Steeneveld,
M. Tombrou, J. Voogt, D. Young, and N. Zhang. The international urban energy balance models comparison project: First results from phase 1. J. Appl. Meteorol. Climatol., 49(6):1268–1292, February
2010.
[11] C.S.B. Grimmond and 38:12621292 1999b Oke, T.R. Aerodynamic Properties of urban areas derived
from Analysis of Surface form. J. Appl. Meteorol. Aerodynamic properties of urban areas derived
from analysis of surface form. J. Appl. Meteorol., 38:1262–1292, 1999.
[12] C.S.B. Grimmond and T.R. Oke. An evapotranspiration-interception model for urban areas. Water
Resour. Res., 27:1739–1755, 1991.
SURFEX v8.1 - Issue no 3 - 2018

102
[13] R. Hamdi and V. Masson. Inclusion of a drag approach in the town energy balance (teb) scheme:
Offline 1d evaluation in a street canyon. J. Appl. Meteorol. Climatol., 47(10):2627–2644, October
2008.
[14] G.T. Johnson, T.R. Oke, T.J. Lyons, D.G. Steyn, I.D. Watson, and J.A. Voogt. Simulation of surface
urban heat islands under ideal conditions at night. part i: theory and tests against field data. Bound.Layer Meteorol., 56:275–294, 1991.
[15] A. Lemonsu, V. Masson, L. Shashua-Bar, E. Erell, and D. Pearlmutter. Inclusion of vegetation in
the town energy balance model for modeling urban green areas. Geoscientific Model Development
Discussions, 5(2):1295–1340, 2012.
[16] Alberto Martilli. Numerical study of urban impact on boundary layer structure: Sensitivity to windspeed, urban morphology, and rural soil moisture. J. Appl. Meteorol., 41(12):1247–1266, December
2002.
[17] Alberto Martilli. Current research and future challenges in urban mesoscale modelling. International
Journal of Climatology, 27(14):1909–1918, 2007.
[18] P. Mascart, J. Noilhan, and H. Giordani. A modified parameterization of flux-profile relationships
in the surface layer using different roughness length values for heat and momentum. Bound.-Layer
Meteorol., 72:331–344, 1995.
[19] V. Masson. A physically-based scheme for the urban energy budget in atmospheric models. Bound.Layer Meteorol., 94(3):357–397, March 2000.
[20] V. Masson. Urban surface modeling and the meso-scale impact of cities. Theor. and Appl. Clim.,
84:35–45, 2006. 10.1007/s00704-005-0142-3.
[21] V. Masson, Bonhomme M., Salagnac J.-L., Briottet X., and Lemonsu A. Solar panels reduce bothglobal warming and urban heat island. Front. Environ. Sci, 2(14):1–10, 2014.
[22] Valéry Masson and Yann Seity. Including atmospheric layers in vegetation and urban offline surface
schemes. J. Appl. Meteor. Climatol., 48(7):1377–1397, July 2009.
[23] L. Menut. Etude expérimentale et théorique de la couche limite Atmosphérique en agglomération
parisienne (experimental and theoretical study of the ABL in Paris area). PhD thesis, University
Pierre et Marie Curie, Paris, France, 1997.
[24] J. Noilhan. A model for the net total radiation flux at the surfaces of a building. Build. and Environ.,16(4):259–266, 1981.
[25] J. Noilhan and S. Planton. A simple parameterization of land surface processes for meteorologicalmodels. Mon. Weather Rev., 117(3):536–549, 1989.
[26] T. R. Oke. Boundary Layer Climates. Methuen, London and New York, 1987. 435 pp.
[27] T. R. Oke. The urban energy balance. Prog. Phys. Geogr., 12:471–508, 1988.
[28] R.L. Petersen. A wind tunnel evaluation of methods for estimating surface roughness length at industrial facilities. Atmos. Environ., 31(1):45–57, 1997.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

103[29] G. Pigeon, Zibouche K., Bueno B., Le Bras J., and Masson V. Evaluation of building energy simulations with the teb model against energyplus for a set of representative buildings in paris. Energy and
Buildings, 76:1–14, 2014.
[30] J.-L. Redelsperger, F. Mahe, and P. Carlotti. A simple and general subgrid model suitable both forsurface layer and free-stream turbulence. Bound.-Layer Meteorol., 101:375–408, 2001.
[31] K. Richards and T.R. Oke. Dew in urban environments. In IInd AMS Urban Environment Symposium,
1998.
[32] Algren A.B. Rowley, F.B. and Blackshaw. Surface conductances as affected by air velocity, temperature and character of surface. ASHRAE Trans., 36:429–446, 1930.
[33] F.B. Rowley and W.A. Eckley. Surface coefficients as affected by wind direction. ASHRAE Trans.,
38:33–46, 1932.
[34] J. Santiago and A. Martilli. A dynamic urban canopy parameterization for mesoscale models based oncomputational fluid dynamics reynolds-averaged navierstokes microscale simulations. Bound.-Layer
Meteorol., 137:417–439, 2010. 10.1007/s10546-010-9538-4.
[35] N.L. Seaman, F. Ludwig, E.G. Donall, T.T. Warner, and C.M. Bhumralkar. Numerical studies of urban
planetary boundary-layer structure under realistic synoptic conditions. J. Appl. Meteorol., 28:760781,
1989.
[36] N.S. Sturrock and R.J. Cole. The convective heat exchange at the external surface of buildings. Build.
and Environ., 12:207–214, 1977.
[37] W.H. Terjung and P.A. ORourke. Influences of physical structures on urban energy budgets. Bound.Layer Meteorol., 19:421–439, 1980.
[38] Brutsaert W. Evaporation into the atmosphere: Theory, History and Applications. D. Reidel, Hingham
Mass., 1982.
[39] J. Wieringa. Representative roughness parameters for homogeneous terrain. Bound.-Layer Meteorol.,
63:323–363, 1993.
[40] Tetsuji Yamada. Journal of the Meteorological Society of Japan, 60:439–454, 1982.

SURFEX v8.1 - Issue no 3 - 2018

104

SURFEX v8.1 - Issue no 3 - 2018

Chapter 4

Soil and vegetation
Contents
4.1

ISBA surface scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.1

Surface snow fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.1.2

Force restore approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Treatment of the soil heat content . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Treatment of the soil water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Treatment of soil ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.1.3

Diffusive approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Surface and soil heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Liquid Soil Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Soil water phase changes: freeze-thaw . . . . . . . . . . . . . . . . . . . . . . . . 133

4.1.4

Soil organic carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4.1.5

Treatment of the intercepted water . . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.1.6

Spatial variability of precipitation intensities . . . . . . . . . . . . . . . . . . . . 139

4.1.7

Treatment of the snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
One-layer snow scheme option . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Multi-layer snow scheme options . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Additional features of the Crocus scheme . . . . . . . . . . . . . . . . . . . . . . 145

4.1.8

The surface fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4.1.9

ISBA-Multi-Energy-Budget (MEB) Explicit Vegetation . . . . . . . . . . . . . . . 153
Snow Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Energy Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Turbulent fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Radiative fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Heat Conduction fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Aerodynamic Resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Ground resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Water Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Snow Interception within the canopy . . . . . . . . . . . . . . . . . . . . . . . . . 172

105

106
Rain Interception within the canopy . . . . . . . . . . . . . . . . . . . . . . . . . 174
Halstead Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Forest Litter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Energy and Mass conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
4.1.10 Summary of Useful Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.1.11 Appendix A: Continuous formulation of the soil secondary parameters . . . . . . . 181
4.1.12 Appendix B: Gaussian formulation for the C1 coefficient . . . . . . . . . . . . . . 182
4.1.13 Appendix C: ISBA-MEB Numerical Solution . . . . . . . . . . . . . . . . . . . . 183
Discretization of surface energy budgets . . . . . . . . . . . . . . . . . . . . . . . 183
Atmospheric temperature and specific humidity . . . . . . . . . . . . . . . . . . . 184
Canopy air temperature and specific humidity . . . . . . . . . . . . . . . . . . . . 185
Sub-surface temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Net Longwave radiation flux derrivatives . . . . . . . . . . . . . . . . . . . . . . 187
Halstead coefficient maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Surface stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Summary: Final solution of the implicitly coupled equations . . . . . . . . . . . . 190
4.2

ISBA-A-gs surface scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
4.2.1

The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Background information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Photosynthesis Model (no water stress) . . . . . . . . . . . . . . . . . . . . . . . 193
Soil moisture stress parameterization . . . . . . . . . . . . . . . . . . . . . . . . 196
From leaf to canopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Biomass evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
CO2 fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

4.2.2

Vegetation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

4.2.3

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Soil moisture stress parameterization . . . . . . . . . . . . . . . . . . . . . . . . 208
Temperature response of gm for C3 plants . . . . . . . . . . . . . . . . . . . . . . 208
Radiative transfer within the vegetation . . . . . . . . . . . . . . . . . . . . . . . 208
Representation of crops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Representation of nitrogen dilution . . . . . . . . . . . . . . . . . . . . . . . . . 210
Annex 1: Description of the Fortran routine used to calculate the CO2 flux . . . . 210

4.3

The ISBA-CC model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
4.3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

4.3.2

Allocation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
Evolution of the biomass compartments . . . . . . . . . . . . . . . . . . . . . . . 211
Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Decline term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

107

Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
4.3.3

Coupling with the soil organic matter scheme . . . . . . . . . . . . . . . . . . . . 216
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Supply of litter compartments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Decomposition of the soil organic matter . . . . . . . . . . . . . . . . . . . . . . 219
Carbon fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

4.3.4

Description of a simulation with ISBA-CC . . . . . . . . . . . . . . . . . . . . . 223

4.3.5

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

4.1 ISBA surface scheme
4.1.1 Surface snow fractions
Snow is known to have a significant impact on heat conduction fluxes owing to its relatively high insulating
properties. In addition, it can significantly reduce turbulent transfer owing to reduced surface roughness, andit has a relatively large surface albedo thereby impacting the surface net radiation budget. Thus, for spatiallydistributed (parcel, meso, regional and/or global scales), the parameterization of its areal coverage turns out
to be a critical aspect of land surface model (LSM) representation of snowpack-atmosphere interactions andsub-surface soil and hydrological processes. For example, the areal snow cover fraction for each patch of
the ISBA land surface model has an impact on the total upwelling radiative and turbulent fluxes, in addition
to soil freezing (depth and intensity), and snow melt rates. In ISBA (like many other land surface models),
the total snow fraction for a given surface is comprised of several component fractions which are describedherein.
First, the snow fraction over vegetation is computed frompsnv =hs
hs + wsv z0(4.1)

where z0 is the surface roughness length (including the effects of snow cover, soil, vegetation...). hs (m) is
the single-layer total snow depth. It is defined as
hs = Ws /ρs(4.2)

where ρs (kg m−3 ) is the average single-layer snowpack density and Ws (kg m−2 ) is the single-layer bulk
snow water equivalent (or SW E). The empirical parameter wsv is a coefficient set to 5 (default). The snow
cover fraction for the bareground portion of the patch is given bypsng =Ws(Ws + Wcrn )(4.3)

The critical snow water equivalent is defined as Wcrn = 10 kg m−2 .
Note that the formulation for psng is slightly different for the multi-layer snow schemes. In this case, it isdefined aspsng = min (1, Dn /Dng )(4.4)
where Dn is the total depth for a multi-layer snow scheme option and Dng (m) a ground snow depth threshold set to 0.01 m. Note that Dn is analogous to hs , but different symbols are used to distinguish between the
single-layer snow-scheme bulk depth, hs , and the total depth, Dn , as a sum of multiple layer thicknesses forthe multi-layer snow scheme options.
SURFEX v8.1 - Issue no 3 - 2018

108
The total snow cover fraction, psn is computed as the sum between the bare ground snow covered fraction,psng , and the fraction of vegetation covered by snow, psnv , weighted by the vegetation fraction of the patches
covered by vegetation, veg as
psn = (1 − veg)psng + veg psnv
(4.5)
veg is specified for each vegetation patch: it is equal to 0.0 for bare soil, 0.95 for grassland/tundra as well
as for temperate and boreal forests, and varies exponentially according to the leaf area index (LAI) for
crop types. As a final note, a recent explicit canopy vegetation (bulk-layer) option (called the multi-energy
budget or ISBA-MEB option) has been added to ISBA. In this parameterization, neither veg or psnv areused (thus for MEB, psn = psng ): thus MEB has a much lower dependence on the empirical snow fraction
parameterization. In addition, vegetation can be buried (for sufficiently deep snowpacks) in the verticalsense for MEB: see Section 4.1.9 for details.

4.1.2 Force restore approach
Treatment of the soil heat content
The prognostic equations for the surface temperature Ts and its mean value T2 over one day τ , are obtained
from the force-restore method proposed by Bhumralkar (1975) and Blackadar (1976):∂Ts
2π= CT (Rn − H − LE) −(Ts − T2 )
∂t
τ
1
∂T2
= (Ts − T2 )
∂t
τ

(4.6)
(4.7)

where H and LE are the sensible and latent heat fluxes, and Rn is the net radiation at the surface. The
surface temperature Ts evolves due to both the diurnal forcing by the heat flux G = Rn − H − LE and a
restoring term towards its mean value T2 . In contrast, the mean temperature T2 only varies according to aslower relaxation towards Ts .
The coefficient CT is expressed by(1 − veg)(1 − psng ) veg(1 − psnv ) psn
+
+
(4.8)
CT = 1/
Cg
Cv
Cs
where veg is the fraction of vegetation, Cg is the ground heat capacity, Cs is the snow heat capacity, and Cv
is the vegetation heat capacity. The snow cover fraction for the bare-ground portion of the patch is computedfrom Eq. 4.3. The partitioning of the grid into bare soil, vegetation, and snow areas, is indicated in Fig.(4.1).
The heat capacities of the ground and snow canopies are respectively given by
Cg = Cgsat (wsat /w2 )b/2log10

Cg ≤ 1.5 × 10−5



(4.9)

where Ggsat (K m2 J−1 ) is the heat capacity at saturation, and wsat the volumetric moisture content of thesoil at saturation; and1/2
π(4.10)
Cs = 2λs cs τwhere λs = λi × ρs 1.88 ; cs = ci (ρs /ρi ): λi is the ice conductivity; ci is the heat capacity of ice; and ρi isthe relative density of ice (Douville, 1994; Douville et al. 1995).

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

109

Ev
Es

Vegetation

Eg

Snow

1-psnv

psnv

psng

veg

1-psng
1-veg

Figure 4.1: Partitioning of the grid

After an intermediate surface temperature Ts ∗ is evaluated from Eq. (4.6), the cooling due to the melting ofsnow is considered following
Ts + = Ts ∗ − CT Lf Mlt ∆t(4.11)

where Lf is the latent of fusion, ∆t is the timestep, and the melting rate of snow isTn − T0(Mlt ≥ 0)
Mlt = psn
Cs Lf ∆t(4.12)

andTn = (1 − veg)Ts ∗ + veg T2(4.13)

Similarly, the intermediate mean temperature T2 ∗ is also modified due to the melting/freezing of water inthe soil layer occurring for temperatures (Boone et al. 2000). The resulting mean temperature isT2 + = T2 ∗ + (∆w2 )f rozen Lf Cg df(4.14)([1 − (T2 ∗ − 268.16) /5] [w2 (t) − w2 (t − ∆t)](∆w2 )f rozen =0T2 ≥ 0 or T2 ≤ Tf − 5(4.15)

withwhere df = 0.15 m is an estimated average of the penetration of the diurnal wave into the soil. Only themean temperature T2 is modified by this factor. The surface temperature Ts , however, indirectly feels thiseffect through the relaxation term in Eq. 4.6. Finally, Note that the single-bulk snow layer hydrology is
described in Section 4.1.7.
Treatment of the soil water
Equations for wg and w2 are derived from the force-restore method applied by Deardorff (1977) to theground soil moisture:
∂wg
C1
C2
=
(wg − wgeq )(Pg − Eg ) −
∂t
ρw d1
τ
∂w2
1
C3
=
max [0, (w2 − wf c )](Pg − Eg − Etr ) −
∂t
ρw d2
d2 τ
SURFEX v8.1 - Issue no 3 - 2018(0 ≤ wg ≤ wsat )(4.16)(0 ≤ w2 ≤ wsat )(4.17)

110
where Pg is the flux of liquid water reaching the soil surface (including the melting), Eg is the evaporation
at the soil surface, Etr is the transpiration rate, ρw is the density of liquid water, and d1 is an arbitrarynormalization depth of 1 centimeter. In the present formulation, all the liquid water from the flux Pg goes
into the reservoirs wg and w2 , even when snow covers fractions of the ground and vegetation. The first termon the right hand side of Eq. (12) represents the influence of surface atmospheric fluxes when the contribution of the water extraction by the roots is neglected. The coefficients C1 and C2 , and the equilibrium
surface volumetric moisture wgeq , have been calibrated for different soil textures and moistures (Noilhan
and Planton (1989)).
The expression for C1 differs depending on the moisture content of the soil. For wet soils (i.e., wg ≥ wwilt ),this coefficient is expressed as

C1 = C1sat



wsat
wg

b/2+1(4.18)For very dry soils (i.e., wg < wwilt ), the vapor phase transfer needs to be considered in order to reproduce
the physics of water exchange. These transfers are parameterized as a function of the wilting point wwilt , thesoil water content wg , and the surface temperature Ts , using the Gaussian expression (Braud et al. (1993),
Giordani (1993)

(wg − wmax )2
C1 = C1max exp −2σ 2



(4.19)

where wmax , C1max , and σ are, respectively, the abscissa of the maximum, the mode, and the standard
deviation of the Gaussian functions (see Appendix 4.1.12). The other coefficient, C2 , and the equilibrium
water content, wgeq , are given by
C2
wgeq




w2
= C2ref
wsat − w2 + 0.01

 "
 #

w2 8p
w2 p
1−
= w2 − a wsat
wsat
wsat

(4.20)(4.21)For the w2 evolution, Eq. (13) represents the water budget over the soil layer of depth d2 . The drainage,
which is proportional to the water amount exceeding the field capacity (i.e., w2 − wf c ), is considered in thesecond term of the equation (see Mahfouf and Noilhan (1996)). The coefficient C3 does not depend on w2
but simply on the soil texture (see Appendix 4.1.11). Similarly, run-off occurs when wg or w2 exceeds thesaturation value wsat or when a sub-grid runoff scheme is used. Coefficients C1sat , C1max , C2ref and p are
made dependent on the soil texture (Noilhan and Mahfouf (1996))

Root zone soil layer option In the standard two-soil layer version of ISBA, it is not possible to distinguishthe root zone and the total soil water reservoirs. With the three-layer version, the deepest soil layer may
provide water to the root zone through capillary rises only, and the available water content for transpiration
is defined as (wsat − wsat ) × d2 .

The bulk soil layer (referred to as w2 in the previous sections) is divided into a root-zone layer (with a depthd2 ) and base-flow layer (with a thickness defined as d3 −d2 ). The governing equations for the time evolution
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

111

of soil moisture for the two sub-surface soil layers are written following Boone et al. (1999) as
1
C3
C4
∂w2
=
(Pg − Eg − Etr ) −max [0, (w2 − wf c )] −(w2 − w3 )
∂t
ρw d2
d2 τ
τ
(
)
∂w3
C3
d2
C4
=
max [0, (w2 − wf c )] +(w2 − w3 )∂t
(d3 − d2 ) d2 ττC3−max [0, (w3 − wf c )](d3 − d2 ) τ(4.22)(4.23)

where both w2 and w3 are ≤ wsat . C4 represents the vertical diffusion coefficient and it is defined as
C4 = C4 ref w 2,3 C4b(4.24)

where w2,3 represents the interpolated volumetric water content representative of the values at the layerinterface (d2 ). The C4 ref and C4b coefficients are defined using the soil sand and clay contents, consistent
with the other model parameters (see the section on model coefficients). In addition, the C4 ref coefficientis scaled as a function of grid geometry. The equations are integrated in time using a fully implicit method.
Exponential profile of the saturated hydraulic conductivity In this version, the soil column assumes
an exponential profile of the saturated hydraulic conductivity, ksat , with soil depth (Decharme et al. 2006).
This parameterization depends only on two parameters, which represent the rate of decline of the ksat profileand the depth where ksat reaches its so-called ”compacted” value.
ksat (z) = ksat,c exp [−f (z − dc )](4.25)

where z (m) is the depth of the soil profile, f (m−1 ) is the exponential profile decay factor and dc (m) thecompacted depth where ksat reaches its compacted value, ksat,c given by Clapp and Hornberger (1978). In
the standard approach, f varies with soil properties (texture and/or rooting depth) but can not exceed 2 m−1
and dc assumes to be equal to rooting depth d2 . Sensitivity tests to these parameters and a detailed discussion
about this parameterization can be found in Decharme et al. (2006). The main hypothesis is that roots andorganic matter favor the development of macropores and enhance the water movement near the soil surface,
and that soil compaction is an obstacle for vertical water transfer in the deeper soil. This exponential soil
profile increases the saturated hydraulic conductivity at the surface by approximately a factor 10, and its
mean value increases in the root zone and decreases in the deep layer in comparison with the values given
by Clapp and Horneberger (1978). In ISBA, all hydraulic force-restore coefficients (C1, C2, C3 and C4)
are re-formulated to take into account this ksat profile.
Treatment of runoff in the ISBA initial version Run-off occurs when w2 exceeds the saturation value
wsat . In its standard version, ISBA simulates surface runoff through the saturation excess mechanism (alsoknown as Dune mechanism), therefore, runoff is only produced when the soil is saturated (i.e. w2 exceeds
the saturation value wsat ). Note that if w3 exceeds the saturation, the excess water is added to the drainage
term.
When the scale of variability of runoff production is smaller than the typical scale of the grid scale (whichis common in most applications), the soil almost never saturates and the runoff production is very low, eventhough, in reality, a fraction of the cell is saturated and does produce surface runoff.
In order to account for subgrid scale runoff, three parametrisations are available and are described hereafter.
SURFEX v8.1 - Issue no 3 - 2018

112
The variable Infiltration Capacity (VIC) scheme. This subgrid parametrisation was introduced by Habets et al. (1999) following the approach of the Variable Infiltration Capacity (VIC) scheme, described inWood et al. (1998) and Dumenil and Todini (1992) and inspired from the Nanjing model Zhao (1992). In
this scheme it is considered that the infiltration capacity (the maximum depth of water that can be stored in
the soil column) varies non-linearly within the grid cell. The fraction of the grid cell that is saturated is afunction of some soil parameters (the soil water content at saturation, the wilting point and the root depth),
the soil water content of the root zone (w2 ) and a new parameter, called b, which represents the shape of theheterogeneity distribution of effective soil moisture capacity. (Note, b is not to be confused with b, which isused to compute the exponent of the soil pedotransfer functions).
This approach is summarized in Fig. 4.2. A grid cell is assumed to be composed of an infinity of elementary
reservoirs, whose infiltration capacity continuously varies from 0 and a maximum value im . The mean watercontent (wg2 ) is the sum of the water content of all the reservoirs.
i is the water content of the non saturated elementary reservoirs (all reservoirs with a water content below iare saturated). A(i) is the saturated fraction of the cell. In case of precipitation (P ), all reservoirs with an
infiltration capacity lower than i + P will be filled, and then produce runoff. The runoff is the sum of thecontribution of the elementary reservoirs.
In this scheme, the infiltration capacity is given by :


i
h
1
i0 b
b
(4.26)
i = im 1 − (1 − A(i)) ⇐⇒ A(i) = 1 − 1 −imFigure 4.2: Simplified scheme of the VIC subgrid runoff. Left : principles. Right : variation of the saturated
proportion of the grid cell for several values of the soil water content and of the parameter b in the VIC
model. In Isba, the saturated fraction of the grid is computed between wwilt and wsat .
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

113

where A(i) is the fraction of the grid cell whose the infiltration capacity is lower than i (0 ≤ A(i) ≤ 1),
im is the maximum infiltration capacity of the grid cell, and b is the curvature parameter, which controls the
distribution function A : the runoff is high when b is high, and low when b is small.
In the grid cell, the runoff is given by :
"


 #
Z i+P
i b+1
im
i + P b+1
− 1−
(4.27)Qr =A(i)di = P +
1−
b+1
im
im
i
For a water content w2 , the saturated fraction of the grid cell ( A(w2 )) is given by:

w2
A(w2 ) = 1 − 1 −
wsat

 b

b+1

(4.28)

After preliminary testing of this parameterization on the Adour watershed, Habets et al. (1999) found thatthe parameterization generated too much runoff in summer for dry soil conditions. To avoid this problem, athreshold was introduced in the soil wetness, wc,min , below which runoff was not produced. This threshold
was set to be the wilting point (wc,min = wwilt ). Note that this threshold is somewhat arbitrary in termsof it’s relationship to surface runoff. For example, a recent study using ISBA has shown that for a tropicalcatchment the relationship with wilting point is weak and a larger threshold value of wc,min produces optimal
results (Getirana et al., 2014). So, wc,min = wwilt should be used by default, but a different value could be
best for a given catchment or climate (Note, currently = wwilt is hard-coded).
The discretized form of Qr used within the model can be written as(w2 − wc,min ) 1/(1+b)
1
Rt ∆t
−
(4.29a)Qr crit = 1 −(wsat − wc,min )ρw zr (1 + b) (wsat − wc,min )
)
(
ρw zr
(4.29b)(wsat − w2 ) − (wsat − wc,min ) [max (0, Qr crit )]1+b
Q r = Rt −∆twith the constraints:
Qr = 0if(Qr < 0)or

(w2 ≤ wc,min )(4.30)

where Rt (m s1 ) is the through-fall rate (sum of canopy drip, precipitation and snow-melt).
TOPMODEL approach TOPMODEL (TOPography based MODEL) attempted to combine the important distributed effects of channel network topology and dynamic contributing areas for runoff generation(Beven and Kirkby (1979), Silvapalan et al. (1987)). This formalism takes into account topographic heterogeneities explicitly by using the spatial distribution of the topographic indices, λi (m), in each grid-celldefined as follows:
λi = ln (ai / tan βi )(4.31)
where ai (m) is the drainage area per unit of contour of a local pixel, i, and tan βi approximates the local hydraulic gradient where βi is the local surface slope. If the pixel has a large drainage area and a low
local slope, its topographic index will be large and thus, its ability to be saturated will be high. Then,
this topographic index can be related to a local water deficit, and using the spatial distribution of the topographic indices over the grid cell, a saturated fraction, fsat , inversely proportional to the grid cell mean
deficit, Dt (m), can be defined. The ”coupling” between TOPMODEL and ISBA was proposed by Habets and Saulnier (2001) and generalized by Decharme et al. (2006). The active layer used for the ISBATOPMODEL coupling is the rooting layer, and not the total soil column. TOPMODEL describes generally
SURFEX v8.1 - Issue no 3 - 2018

114
the evolution of a water storage deficit near the soil surface that reacts quasi-instantaneously following rainy
events (Beven and Kirkby, 1979). In that case, the root zone appears to be a reasonable compromise in
ISBA. So, the relation between the grid cell mean deficit and the soil moisture computed by ISBA is simply
expressed as:
0 ≤ Dt = (wsat − w2 ) × d2 ≤ d0
(4.32)
where d2 (m) is the rooting depth and d0 (m) the maximum deficit computed as the difference between thesaturation, ws at, and the wilting point, ww ilt :d0 = (wsat − wwilt ) × d2

(4.33)

So for a given rooting soil moisture, w2 , a mean deficit, Dt , is calculated and it is therefore possible todetermine the saturated fraction of the grid-cell. The runoff, Qtop , is thus simply given by: Qtop = Pg × fsat
where Pg is the throughfall rain rate. For w2 lower than the wilting point, the mean deficit is a maximum,
Dt = d0 , fsat = 0 and no surface runoff occurs. Note that, the spatial distribution of the topographic index
in each grid-cell can be computed with the three- parameter gamma distribution introduced by Silvapalan
et al. (1987). The three parameters are derived from the mean, standard deviation, and skewness of theactual distribution that can be done by the HYDRO1K dataset at a 1 km resolution or another database. This
TOPMODEL approach has been intensively validated both at the regional and global scale (Decharme et al.
(2006), Decharme and Douville (2006 and 2007)).
Horton runoff approach. The Horton runoff occurs for a rainfall intensity that exceeds the effective
maximum infiltration capacity. This infiltration excess mechanism tends to dominate the overland flow
production in most desert or semiarid regions where short rainfall events can be very intense, but also where
the absence of vegetation and other organic matter prevents the development of a porous soil structure
through which water can move easily. The development of a thin crust at the soil surface can also inhibit the
infiltration (arid or frozen soil). So the Horton runoff, Qhort , is calculated using two infiltration functions
following Decharme and Douville (2006):
Qhort = (1 − δf ) × max (0, Sm + Pg − Iunf ) + δf max (0, Sm + Pg − If )(4.34)

where Sm is snowmelt, Pg the throughfall rain rate, Iunf and If the infiltration functions over unfrozen
and frozen soil, and δf the fraction of the frozen soil. These functions depend on root zone soil moisture
conditions as well as on soil hydraulic properties. When the Horton runoff (being estimated only on the
non-saturated fraction of the grid) is activated with the VIC or the TOPMODEL runoff, the surface runoff
is given by :(4.35)
Qs = Qtop or vic + (1 − fsat ) Qhort
Treatment of drainage The gravitational drainage when w > wf c is given by the following equations(Mahfouf and Noilhan, 1996; Boone et al. 1999) :
K2 =
K3 =

C3 d3
τ d2 max[0, (w2 − wf c )]C3 d3
τ d3 −d2 max[0, (w3 − wf c )](4.36)(4.37)

where τ is a characteristic time (one day). C3 is the force-restore parameter which account for the speed
at which the humidity profile is restored to the field capacity. This parameter depends on the hydraulicproperties of the soil (Noilhan and Mahfouf, 1996). In ISBA, it can be described by an empirical equationand depends on the proportion of clay in the grid cell.
−1.043C3 = 5.327 · Xclay

SURFEX v8.1 - Issue no 3 - 2018(4.38)

CHAPTER 4. SOIL AND VEGETATION

115

Treatment of soil ice
The inclusion of soil freezing necessitates the addition of so-called phase change to the thermal and hydrological transfer equations. In addition, a freezing/drying wetting/thawing analogy is used to model changes
in the force-restore coefficients so that they must also be modified accordingly. Terms which have been
added to the baseline ISBA scheme are underlined in this section, while terms which are modified are denoted using an ∗ superscript. Additional details related to soil freezing scheme can be found in Boone et al.
(2000) and Boone (2000).
The basic prognostic equations including soil ice are expressed as
i
h
2π
∂Ts
= CT ∗ Rn − H − LE ∗ − Lf (Ms − Fg w ) −(Ts − T2 ) ,(4.39)∂tτ
1∂T2(4.40)=(Ts − T2 ) + CG ∗ Lf F2 w ,
∂t
τ
i
∂wg
1 h ∗
C2 ∗
C1 (Pg − Eg l + Ms ) − Fg w −=(wg − wg eq ∗ )(4.41)∂td1 ρw
τ(wmin ≤ wg ≤ wsat − wg f ) ,(4.42)
∂w2
1(4.43)=
Pg − Eg l − Etr ∗ + Ms − F2 w − C3 τ max(0 , w2 − wfc ∗ )∂t
dp ρw(wmin ≤ w2 ≤ wsat − w2 f ) ,(4.44)∂wg f
1=(Fg w − Eg f )(0 ≤ wg f ≤ wsat − wmin ) ,(4.45)
∂t
d1 ρw
∂w2 f
1
=
F2 w
(0 ≤ w2 f ≤ wsat − wmin ) .
(4.46)∂t(d2 − d1 ) ρw

where wg f and w2 f represent the volumetric soil ice content (m3 m−3 ) in the surface and deep-soil reservoirs, respectively. The phase change mass and heat sink (source) terms (F ; kg m−2 s−1 ) are expressedas
Fg w = (1 − psng ) (Fg f − Fg m ) ,F2 w = (1 − psng ) (F2 f − F2 m ) ,(4.47)(4.48)

where the m and f subscripts represent melting and freezing, respectively. The freezing and melting phasechange terms are formulated using simple relationships based on the potential energy available for phasechange. They are expressed for the surface soil layer as
Fg f= (1/τi ) min [Ks ǫs f max(0, T0 − Ts )/CI Lf , ρw d1 (wg − wmin )] ,Fg m = (1/τi ) min [Ks ǫs m max(0, Ts − T0 )/CI Lf , ρw d1 wg f ] ,(4.49)(4.50)

and for the deep soil layer as
F2 f= (δ2 f /τi ) min [ǫ2 f max(0, T0 − T2 )/CI Lf , ρw (d2 − d1 ) (w2 − wmin )] ,F2 m = (1/τi ) min [ǫ2 m max(0, T2 − T0 )/CI Lf , ρw (d2 − d1 ) w2 f ] .

(4.51)(4.52)

The characteristic time scale for freezing is represented by τi (s). The phase change efficiency coefficients,
ǫ, introduce a dependence on the water mass available for phase changes which are expressed as the ratio of
the liquid volumetric water content to the total soil porosity for freezing, and the ratio of ice content to theporosity for melting. The ice thermal inertia coefficient is defined as CI = 2(π/λi Ci ρi τ )1/2 (J m−2 K−1 ).
The insulating effect of vegetation is modeled using a coefficient defined as



veg
LAI
Ks = 1 −1−,(4.53)K2
K3
SURFEX v8.1 - Issue no 3 - 2018

116
where the dimensionless coefficients have the values K2 = 5.0 and K3 = 30.0 (Giard and Bazile (2000)).
The most direct effect of vegetation cover is to slow the rate of phase changes for more dense vegetation
cover as energy not used for phase change is assumed to cool/warm the vegetative portion of the lumped
soil-vegetation layer.
The deep-soil phase change (freezing) term is multiplied by a factor (δ2 f ) which essentially limits ice
production during prolonged cold periods. It is defined as 0 if zf ≥ zf max wherezf max = 4/ (CG ∗ cg )and the actual depth of ice in the soil is defined as
w2 fzf = d2
w2 f + w2(4.54)(0 ≤ zf < d2 )(4.55)

Ice is assumed to become part of the solid soil matrix. This is accomplished by defining the modified
porosity (eg. Johnsson and Lundin (1991)) as
wsat ∗ = wsat − wj f

(4.56)

where j corresponds to the surface (g) or sub-surface (2) soil water reservoirs. This, in turn, is used tomodify the force-restore coefficients (see Boone et al. , 2000, for more details).
As a final note, more recently an option to this simple method to compute the phase changes has been added
based on the Gibbs-free energy approach. It is especially adapted for the DuFfusion (DF) version of ISBA
(see Section 4.1.3), but it can also be used with the FR approach. See Section 4.1.3 for more details. But thesoil ice modification to the porosity etc. remains as described in this Section for both phase change options.

4.1.3 Diffusive approach
Governing Equations
The governing equations for the heat and mass transfer from the surface down through the soil column forthe snow-free case are expressed as (Boone et al. 2000; Decharme et al. 2011):
ch

∂Tg
∂t
∂wl
∂t
∂wi
∂t

=
=
=

∂G
+Φ
∂z
∂F
Φ
Sl
−
−
−
∂z
Lf ρw
ρw
Φ
Si
−
Lf ρw
ρw

(4.57)(wmin ≤ wl ≤ wsat − wi )(4.58)(0 ≤ wi ≤ wsat − wmin )(4.59)

Eq. (4.57) is the vertical component of the heat transfer equation: heat flow is induced along the thermal
gradient and due to convection, ch is the total heat capacity (J m−3 K−1 ): it is represented by a lumped heat
capacity in the surface layer, and by the soil heat capacity (cg ) in the sub-surface layers. λ is the thermal
conductivity (W m−1 K−1 ), F is the vertical flow rate of water (m s−1 ), Tg is the composite soil-vegetation
temperature (K) at the surface and the soil temperature only for sub-surface layers, Φ (J m−3 s−1 ) is a latent
heat source/sink resulting from phase transformation of soil water, and the soil depth, z (m), is increasing
downward.
wl and wi in Eq.s (4.58) and (4.344) represent the volumetric liquid water and liquid water equivalent ice
contents of the soil (m3 m−3 ), respectively. They are related to the total volumetric water content (m3 m−3 )throughw = wl + wi .
(4.60)SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

117

In Eq. (4.58), Sl (evapotranspiration, lateral inflow) and Si (sublimation) represent external sources/sinks(kg m−3 s−1), of the liquid and ice liquid equivalent soil water, respectively, Lf is the latent heat of fusion(3.337 ×105 J kg−1 ), and ρw is the density of liquid water (1000 kg m−3 ). The total soil porosity is wsat
(m3 m−3 ), and wmin is a minimum liquid water threshold (0.001 m3 m−3 ).
The phase change terms on the right-hand sides of Eq.s (4.58) and (4.344) represent a mass transfer between
the solid and liquid phases of the soil water. The continuity equation for the total soil volumetric watercontent is obtained by adding Eq.s (4.58) and (4.344) and then substituting Eq. (4.60) into the resulting
expression to have
∂w
∂F
1
= −
−
(Si + Sl )
∂t
∂z
ρw

(wmin ≤ w ≤ wsat )(4.61)

Surface and soil heat transfer
Heat flow is along the thermal gradient, so that the soil heat flux (W m−2 ) can be expressed as
G=λ

∂T
∂z

(4.62)The soil thermal conductivity and heat capacity are expression as functions of soil properties and moisture.
The parameterizations are described below.
Calculation of the thermal properties The thermal heat capacity and thermal conductivity are parameterized as functions of the soil moisture and texture by most SVAT schemes. SVAT schemes which participatedin PILPS-phase2c predicted, in general, ground heat fluxes poorly, which is most likely related to thermal
conductivity parameterization Liang et al. (1996). ISBA uses the formulations from McCumber and Pielke(1981 : MP81) together with parameter values from Clapp and Hornberger (1978) to evaluate the heat
capacity and thermal conductivity (Noilhan and Planton, 1989), but it is known that thermal conductivity
estimates using the MP81 model tend to be too large for wet conditions (nearing saturation) while underestimating thermal conductivity for dry soils. Also, there is no consideration of frozen soils in this formulation.
There are several alternatives to using the MP81 model for thermal conductivity, and one such method isthat discussed in Peters-Lidard et al. (1998). The layer-averaged soil heat capacity can be written as
cg j = (1 − wsat )Csoil ρsoil + wl j cw + wi j ci

(4.63)

where ci and cw are the heat capacities of ice and liquid water, (J K−1 m−3 ). Csoil is the specific heat of thesoil (J kg−1 K −1 ) and ρsoil represents the soil dry density. The specific heat (Csoil ) value of 733 J kg−1 K−1
for soil minerals/quartz from Peters-Lidard et al. (1998) is used. where ρsoil represents the unit weight ofthe solids (2700 kg m3 ). The heat capacity of air in the soil is neglected in Eq. (4.63).
For fine soils or coarse frozen soils, the method of Johansen (1975) was shown by Farouki (1986) to be
the most accurate relative to other commonly used methods for calculating thermal conductivity. Following Peters-Lidard et al. (1998), the thermal conductivity is calculated as the weighted sum of the dry andsaturated thermal conductivities from (Johansen, 1975)
λ = Ke λsat + (1 − Ke ) λdry

(4.64)

where Ke is the non-dimensional Kersten number.
The dry thermal conductivity is defined as
λdry =

0.135ρsoil + 64.7
ρsolids − 0.947ρsoil

SURFEX v8.1 - Issue no 3 - 2018(4.65)

118
where λdry is in W m−1 K −1 . For crushed rock,λdry = 0.039 wsat −2.2

(4.66)The saturated thermal conductivity is written as
λsat = λsoil (1−wsat ) λi (wsat −χu ) λw χu(4.67)

where χu represents the unfrozen volume fraction of the soil. It is defined asχu = wsat (wl /w)(0 ≤ χu ≤ wsat )(4.68)In Eq. (4.67), λi represents the thermal conductivity of ice (2.2 W m−1 K), λw represents the thermal
conductivity of water (0.57 W m−1 K), and the thermal conductivity of solids is written as
λsoil = λq q λo 1−q(4.69)The quartz content (0 ≤ q ≤ 1) is non-dimensional. It is fit as a function of sand (following the method of
Noilhan and Lacarrère (1995) using the data from PL98:
q = 0.038 + 0.0095 Xsand(4.70)

where the fraction of the soil comprised by sand is represented by Xsand (%). The relation is shown graphically in Fig. (4.3). The thermal conductivity of quartz is represented as λq (7.7 W m−1 K), and the thermal
conductivity of other minerals is represented as λo (W m−1 K) where(
2 q > 0.2
λo =(4.71)
3 q ≤ 0.2
The Kersten number is written as(
0.7 log 10 θ + 1.0 θ > 0.05 (coarse)
Ke =log10 θ + 1.0
θ > 0.10 (fine)(4.72)

Ke = θ

(4.73)

and for frozen soils it iswhere θ is the degree of saturation (w/wsat ) of the soil layer. Because use of Eq. (4.73) can result in a large
jump in Ke as a soil begins to freeze, the following expression is used for partially frozen fine soils:
Ke = (wl /w) (log10 θ + 1.0) + (wi /w)θ(4.74)The same weighting scheme in Eq. (4.74) can be used for coarse soils as well.
Numerical discretization of the soil heat equation The governing equations for heat transfer within thesoil discretized in Ng layers are described using the classical one-dimensional Fourier law and are written
as:∂Tg, j= Gj−1 − Gj + ∆zj Φj∂t∂Tg, jλj−1
λj∆zj cg j=(Tg, j−1 − Tg, j ) −(Tg, j − Tg, j+1 ) + ∆zj Φj∂t∆z̃j−1∆z̃j∆zj cg j

SURFEX v8.1 - Issue no 3 - 2018

∀ = 2, Ng(4.75a)(4.75b)CHAPTER 4. SOIL AND VEGETATION

119

1.0

q=0.0378 + 0.0095 Xsand
0.8

q

0.6

Data
1:1
Linear fit

0.4

0.2

0.0
0.0

20.0

40.0
60.0
Xsand (%)

80.0

100.0

Figure 4.3: The relation between quartz content (q) and sand fraction (Xsand ) of the soil (%). The relationship between quartz and sand content is described by Eq. (4.70). The data are plotted using the values of q
from Peters-Lidard et al. (1998) and the sand fraction from Cosby et al. (1984).

where the heat conduction flux (W m−2 ) is therefore defined asGj =λj(Tg, j − Tg, j+1 )∆z̃j(4.76)∆zj (m) is the thickness of the layer j, ∆z̃j = (∆zj + ∆zj+1 ) /2 is the thickness (m) between two consecutive layer mid-points or nodes, CG is the soil thermal inertia at the surface (J m−1 kg−2 ), cg j is the totalsoil heat capacity(J m−3 K−1 ), and λj (W m−1 K−1 ) is the inverse-weighted arithmetic mean of the soil
thermal conductivity at the interface between two consecutive nodes expressed as:
λj =∆zj + ∆zj+1.
(∆zj+1 /λj+1 ) + (∆zj /λj )(4.77)

In general, the contribution of convective heating to the local soil temperature change is relatively small
and can be neglected. Vapor transfer effects have been incorporated and are currently being tested: they
are not outlined here. The model grid configuration is shown in Fig. 4.4. The shaded region at the surface
represents a vegetation/biomass/litter layer. The prognostic variables (Tg, j , wl , and wi ) are shown (water
store variables will be discussed in subsequent sections).
Boundary conditions Upper boundary condition: To be consistent with the ISBA-FR surface energy
budget, the surface temperature evolves according to the heat storage in the soil/vegetation composite and to
the thermal gradient between the surface (the same fine superficial layer than for ISBA-FR) and the second
SURFEX v8.1 - Issue no 3 - 2018

120

G0

F0

z0

T 1 wl 1 wi 1
G 1 F1∆ zj

z1

T j wl j wi j
G j Fjzj

T N wl N wi N

G N FNzN

Figure 4.4: The model grid configuration: soil prognostic variables temperature (Tg, j ), liquid volumetricwater content (wl j ) and volumetric ice content (wi j ) are layer mean quantities. The soil heat (Gj ) andliquid water fluxes (Fj ) are evaluated at each level, zj . The surface energy budget is evaluated defining
Ts = Tg, 1 . The shaded region at the surface represents a vegetation/biomass/litter. The soil depth, z, isincreasing downward (away from the atmosphere).

layer (Boone et al. ,2000). Accordingly, the surface temperature is defined as
1 ∂Tg,1
C G λ1= G0 + ∆z1 Φ1 −(Tg,1 − Tg,2 )CT ∂t
CT ∆z̃1∂Tg,1
λ1= CT (Rn − H − LE + ∆z1 Φ1 ) − CG
(Tg,1 − Tg,2 )∂t∆z̃1(4.78a)(4.78b)where the flux between the atmosphere and the surface is represented by G0 (W m−2 ). This definition of
the prognostic equation for Tg,1 is similar to that presented by Bhumralkar (1975) and Blackadar (1979).
It is the same as the standard Force-Restore method of Noilhan and Planton (1989) if G1 is expressed as a
restore term. The thermal inertia coefficient for the composite surface layer is expressed asCT =1(veg/CV ) + [(1 − veg)/CG ]SURFEX v8.1 - Issue no 3 - 2018(4.79)

CHAPTER 4. SOIL AND VEGETATION

121

where veg represents the vegetation cover fraction. The thermal inertia for the vegetation (CV ) can be caseor species dependent. By default, it is computed as
CV =1CV,ref + cw Wr(4.80)

where Wr (kg m−2 ) is the vegetation interception reservoir water storage and Cv,ref (J K−1 m−2 ) thereference or baseline vegetation heat capacity (defined by the user or ECOCLIMAP) set by default to 1×104
J K−1 m−2 for low vegetation and 2 × 104 J K−1 m−2 for forests. The soil thermal inertia (J K−1 m−2 ) isdefined as1
CG =(4.81)
cg,1 ∆z1
where cg,1 is the heat capacity of the first soil layer (J K−1 m−3 : Eq. 4.63). The uppermost soil thickness,∆z1 , must be chosen to be sufficiently thin in order to be consistent with the daily surface temperature
cycle (i.e., 0.01 m by default). In the limit when there is no vegetation (i.e., veg = 0), the thermal inertia
coefficient collapses into 1/CT = ∆z1 cg so that Eq. 4.78a takes on exactly the same form as the sub-surface
soil temperature equations.
Lower boundary condition: The average temperature for the lowest layer is written using Eq.(4.75a) as∂TN(GN −1 − GN )=∂t
cg N ∆zN(4.82)

where the heat flux from below zN is assumed to be negligible, resulting in a zero-flux lower boundary
condition (i.e. GN = 0). Note that in order for this assumption to be valid, zN must be sufficiently large(deep). The annual temperature wave penetration depth is, in general, on the order of several meters (eg.,Figs 4.5 and 4.6), so that zN must be at least this deep in oder to accurately model the soil temperature
profile at time scales of an annual cycle or more. An alternate method to increasing the soil depth is tospecify the lower boundary flux using an annual mean soil temperature and an appropriate scaling depth(Lynch-Stieglitz, 1994). This depth can be estimated as the annual wave penetration depth [see Eq. (4.86)].
The only drawback is that the mean annual soil temperature and the annual wave penetration depth must
be known a priori. The advantages are that less model layers can be used (a lower total model depth)
thereby reducing computational expense and memory/storage requirements, and the soil temperature profileis “constrained” to some extent by observational data. Currently in the model, there is an option to apply aprescribed T ∗ (either as a constant or varying in time) at zN
GN = λN[TN − T ∗ (z = zN )](zN + zN −1 ) /2

(4.83)

But note that GN = 0 is the default. Recently the soil depth has been extended for thermal computations inorder to ensure that this approximation is reasonable: see Decharme et al. (2016) for details.
Vertical grid The soil model grid levels do not necessarily have constant spacing. The assumption thatthe vertical temperature gradients are largest near the surface and smaller deeper in the soil indicates that thegrid spacing can increase with increasing soil depth. It is of interest to specify the first grid level to be thinenough to resolve the diurnal temperature wave. An estimate of this depth is calculated using conductivity
calculated by Eq. (4.64) for thawed soils with the relation for wave penetration depth from Dickinson (1988):
zd =



λ1 τ
cg 1 π1/2

SURFEX v8.1 - Issue no 3 - 2018(4.84)

122
Since the diurnal wave penetration depth (zd ) is a function of soil moisture and texture, an average or
maximum value could also be used to a good approximation: this value might represent the zd depth forthe average soil moisture etc. The diurnal wave penetration depths computed using Eq. (4.84) are shown in
Fig. (4.6). The depth zd is plotted as a function of the normalized volumetric water content defined as
wnorm =

w − wwilt
wsat − wwilt(0 ≤ wnorm ≤ 1)

(4.85)The zd depth usually ranges from 12-18 cm for most soils across their nominal range of soil moisture: values
in the range from 12-15 cm could be used for most general cases. It is of interest to compare the methodof Johansen to the method of McCumber and Pielke (1981) which is used by many surface vegetation
atmosphere transfer (SVAT) schemes including ISBA (Noilhan and Planton, 1989). The zd values computed
using the method of McCumber and Pielke (1981) together with the soil classification and hydrologicalparameter values For the force-restore method used by ISBA, this variability in zd is accounted for as there
are no fixed soil depths which effect the diurnal cycle. But when using a fixed grid geometry, as is the casefor the diffusion method outlined here, zd calculated from the method of Johansen is more consistent witha fixed grid geometry. These depths represent the depth to which the diurnal wave is felt: but to represent
the diurnal cycle of the soil surface or soil-vegetation composite surface accurately in terms of phase andamplitude, the uppermost layer should be considerably thinner: in ISBA the uppermost thickness is chosen
as a compromise between thickness, numerical stability (time step) and processes (both hydrological andthermal): see below for more details.
0.25

0.23

Sand
Loam
Clay

Diurnal Wave Penetration Depth (m)

0.20

0.17

0.15

0.12

0.10

0.08

0.05
0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Volumetric Water Content (m3/m3)

1.0

Figure 4.5: The diurnal temperature wave penetration depths (zd ) for the 11 soil classes from Clapp andHornberger (1978). Depths are plotted as a function of normalized soil water content [Eq. (4.85)]. Thermal
conductivity is calculated using the method of McCumber and Pielke (1981) together with soil hydraulicparameter values from Clapp and Hornberger (1978). Soil depths are in m.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

123
3.98

0.21

0.19

3.60

0.17

3.22

0.15

2.85

0.13

2.47

0.11
0.0

Annual Wave Penetration Depth (m)Diurnal Wave Penetration Depth (m)

Sand
Loam
Clay

2.09
0.2
0.4
0.6
0.8
Normalized Volumetric Water Content

1.0

Figure 4.6: The diurnal and annual soil temperature wave penetration depths (zd ) for the 11 soil classes fromClapp and Hornberger (1978). Depths are plotted as a function of normalized soil water content [Eq. (4.85)].
Thermal conductivity is calculated using the method of Johansen (1975) as presented by Peters-Lidard etal. (1998). Soil depths are in m: zd should be used as a guild-line for determining the maximum uppermost
soil layer depth, z1 , and the minimum total soil depth, zN .

The depth of the lower limit of the soil-temperature model domain depends upon the time scale: if annual
cycles are to be properly handled, the lower boundary depth zN can be determined using Eq. (4.84) asza =λ 365 τcg π

1/2

(4.86)

where za denotes the annual wave penetration depth. Note that cg and λ should be evaluated using an
estimate of the total soil column mean water content. The annual wave penetration depths computed using
Eq. (4.86) are shown in Fig. (4.6). The depth za (labeled on the right side of the figure) is plotted asa function of the normalized volumetric water content. Thus for multi-year simulations, the depths forthermal computations should extend to a depth proportional to the time period considered (thus deeper thanthose shown in Fig. 4.6).
The heat transfer within the soil is computed using 14 layers up to a depth of 12 m, which corresponds tothe lower boundary condition of the soil temperature. Conversely, the hydrological depth varies from 0.2 to
8 m according to the land cover. As shown in Fig. 4.7, if the hydrological lower boundary condition is equal
to 1 m for bare soil, the soil moisture is solved within the first eight layers, whereas soil temperatures arecomputed over all layers. The simulation of freezing and thawing processes is thus facilitated by the consistency between hydrologic and thermal nodes. Because the soil thermal properties require the water and ice
content to be known for each layer, the total soil water profile is extrapolated under the hydrological lower
boundary condition of the soil to each underlying temperature node, assuming a hydrostatic equilibrium soil
moisture profile and the presence of a possible deep water table. The partitioning between liquid water andice content is then computed using the relationship between the matric potential and the temperature based
SURFEX v8.1 - Issue no 3 - 2018

124
on Fuchs et al. (1978): see Eq. 4.126. Note that for permafrost regions (shown in the rightmost columnof Fig. 4.7), the liquid and solid water prognostic equations extend to the base of the soil in order to moreaccurately compute the evolution of the permafrost, especially for deeper soil layers.
Finally, the thicknesses of the current 14 layers have been arranged to minimize numerical errors in solving
energy and water diffusion equations, especially in the first meter of soil (Decharme et al. 2011). Notethat the thermal and/or hydrological lower boundary conditions of the soil, as well as the thickness and thenumber of layers, can be modulated by the user.
Numerical solution of the soil temperature equation
Eq. (4.75a) can be written using an implicit time scheme as
Tj n = Tj n−1 +Neglecting the phase transformation term,



∆t 
(1 − ϕ) Gj−1 n−1 − Gj n−1 + ϕ (Gj−1 n − Gj n )cg j ∆zj(4.87)

where ϕ = 1 (backward difference) is currently used for the soil temperature profile (ϕ = 1/2 corresponds
to the Crank-Nicolson scheme). Using either scheme, the linear set of diffusion equations can be castin tridiagonal form and solved with relative ease. Although the Crank-Nicolson scheme is more accurate(second order), the surface energy budget equation is solved in ISBA using the backward difference scheme,
so for consistency this scheme is used to evaluate the diffusion term in Eq. (4.75a).

Figure 4.7: The ISBA-DF soil grid configurations. Prognostic variable nodes (for liquid water, wg , soil ice,
wgf and temperature, Tg ) are located at the center of each of the layers. There are 14 layers used for thermal
computations, and the same default grid thicknesses are used everywhere (note this can be modified by theuser). Hydrological grids are enclosed by the solid black lines: thus the soil water prognostic equations do
not extend as deeply as the thermal computations except for areas/grid cells with permafrost. See Decharme
et al. (2013) for more details.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION125

The superscripts n − 1 and n represent the values at the beginning and end of the time step, ∆t, respectively.
The solution method is shown in Appendix B. Once the new temperature profile has been determined, phasechanges are evaluated and the profile is updated. The phase change method is described in section 4.

Liquid Soil Water
The vertical soil water flux from Eq. (4.58) is derived assuming soil water transfer arises due to pressure
gradients and a background drainage, and it is expressed as
F = −kDνψ ∂ψ
∂(ψ + z) −∂z
ρw ∂z(4.88)

where F is the vertical soil water flux (m s−1 ), k is the hydraulic conductivity (m s−1 ), ψ is the soil matricpotential (m), and z is the soil depth (m). The first term on the right hand side of Eq. 4.88 represents Darcy’s
law for liquid water transfer. The second term represents the water flux due to vapor transfer. The isothermal
vapor conductivity Dνψ (kg m−2 s−1 ) is a function of soil texture, water content and temperature following
Braud et al. (1993), except for some slight modifications due to the inclusion of soil ice outlined here.
This representation of the fluxes results in the so-called “mixed-form” of the Richard’s equation. It permits
the use of a heterogenous soil texture profile (by considering the gradient of matric potential which iscontinuous as opposed to soil water content which is not necessarily continuous when the soil propertiesvary).
Finally, when soil ice is present, Eq. 4.88 is modified as
F = −k



∂ψ
℘
−z
∂z



−

℘ Dνψ ∂ψρw ∂z

(4.89)

where the non-dimensional coefficient ℘ has been introduced which acts to limit vertical diffusion in thepresence of a freezing front (see Eq. 4.96).

Flux parameterization
form as:The vertical soil water flux term [Eq. (4.88)] can be expressed in more compact
F = −η

∂ψ−k∂z(4.90)

where η (m2 s−1 ) represents the effective diffusion coefficient. It is expressed asDνψη=℘ k +
ρw

(4.91)

The first term on the RHS of Eq. 4.90 is the diffusion term and usually is positive (directed upward), theexceptions possibly being during precipitation, snowmelt or perhaps soil thaw events. The second term on
the RHS of Eq. (4.90) represents total drainage and is always directed (positive) downward. During strong
infiltration events (rainfall, snowmelt etc...) generally k dominates the (downward) water flux. Note that if
vapor diffusion is neglected and the soil is not frozen, the vertical flux given by Eq. (4.88) collapses into thestandard Darcy flux expression for liquid water movement:
F = −k∂(ψ + z)∂z

SURFEX v8.1 - Issue no 3 - 2018(4.92)

126
Soil Freezing As a soil freezes, ice is assumed to become part of the soil matrix thereby reducing theliquid water holding capacity of the soil. The degree of saturation of the soil by liquid water is expressed asΘ =wl
w − wi=wsat − wiwsat l(0 ≤ Θ ≤ 1)

(4.93)

where wsat l represents the soil liquid water holding capacity. The porosity is decreased in the presence ofsoil ice as it is assumed ice becomes part of the soil matrix (see Boone et al. (2000) for more information).
The hydraulic conductivity and soil water potential are related to the liquid volumetric soil water content
through the relations (Clapp and Hornberger, 1978):k = ksat Θ2b+3(4.94)

ψ = ψsat Θ−b(4.95)

where b is an empirical parameter, ksat is the hydraulic conductivity at saturation, ψsat is the water potential
at saturation and wsat is the soil porosity. In recent years, several SVATs (eg. VISA: Yang and Niu, 2003)
have adopted the idea that the saturated hydraulic conductivity decreases exponentially with increasing soil
depth (Beven and Kirby, 1979). This can be handled by ISBA-DF since Richard’s equation is expressed in
mixed-form (i.e. a heterogeneous profile of ksat can be specified).
Soil ice has the effect of decreasing the hydraulic conductivity relative to a thawed soil with the same totalsoil moisture. The ice impedance coefficient is represented by ℘. It is calculated following Johnsson andLundin (1991):℘ = 10−a℘ wi /w(4.96)
where the coefficient a℘ is currently assigned a value of 6 proposed by Lundin (1990). This coefficient
prevents an overestimation of the upward liquid water flux to the freezing front. Note that the model israther sensitive to this parameter, and a calibration might be required to obtain optimal agreement withobservations. The dependence of ℘ on ice content ratio (wi /w) is shown in Fig. 4.8. Note that the effect of
this coefficient is currently under investigation, and that alternate formulations (such as dependence on soil
temperature rather than soil ice) will also be explored.
Vapor diffusion

The isothermal vapor conductivity can be expressed asDνψ = Dν∂ρν∂ψ

(4.97)

where ρν represents the water vapor density in the air-filled pore space of the soil, and Dν represents aneffective molecular diffusivity (Milly (1982)). It can be written following Braud et al. (1993) asDν = Dνa αν fνap(p − pν )(4.98)

where the tortuosity is αν = 0.66, and the atmospheric and soil vapor pressures are represented by p andpν , respectively. The function fνa is defined as([wsat − (wl + wi )] [1 + (wl + wi ) / (wsat − wk )] if (w > wk )
fνa =
wsat
if (w ≤ wk )where wk is a parameter which defines the point corresponding to the loss of continuity of the liquid phasein the soil pores (0.05 m3 m−3 for the current study). The function fνa is related to the available pore space
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

127

1.0

Eice = 1
Eice = 2
Eice = 3
Eice = 4
Eice = 5
Eice = 6

Ice Flux Impedence Coefficient

0.8

0.6

0.4

0.2

0.0
0.0

0.2

0.4
0.6
Ice Fraction

0.8

1.0

Figure 4.8: The dependence on the water flux impedance factor (℘) on soil ice fraction (wi /w) for various
values of a℘ (denoted as “Eice” in the figure). This coefficient is multiplied by the vertical soil water flux,
and as such can strongly modulate vertical flow of liquid water and subsequent freezing.

for vapor, or volumetric air content (wsat − wl − wi ). The molecular diffusivity coefficient for water vapor
is given as   n ν
p0TDνa = cν(4.99)
p
Tf

where cν = 2.17 × 10−5 m2 s−1 , nν = 1.88, and p0 = 106 Pa. It is assumed that the soil water vapor is inequilibrium with the liquid, and that the air is saturated with respect to the ice present in the soil so that thevapor density can be expressed asρν = ρν sat (T )χsat hν + (1 − χsat ) ρν sat i min(T, Tf )where the humidity is given byhν = exp
The soil ice factor is defined as



ψg
Rν T



χsat = (wsat − wi ) /wsat(4.100)(4.101)(4.102)

Taking the derivative of ρν with respect to ψ and substituting the resulting expression and Eq. (4.98) into
Eq. (4.97) using the ideal gas law for water vapor results inDνψ =αν p Dνa fνa χsat g pν sat hν(p − pν )(Rν T )2

(4.103)The diffusion coefficient (dν ) is shown in Fig. (4.9) for four soil textures over the entire range of soil wetness(wl /wsat ) assuming a constant temperature and pressure of 300 K and 101325 Pa, respectively. It is largest,
SURFEX v8.1 - Issue no 3 - 2018

128
1e−08

Silty Clay Loam
Clay
Loam
Sand

8e−09

dv (m2/s)

6e−09

Pres=101325 Pa

4e−09

2e−09

0e+00
0.0

0.2

0.4

0.6

0.8

1.0

Wetness

Figure 4.9: Soil vapor diffusion coefficient (dν ) for four soil textures assuming constant soil temperatureand pressure.

in general, for the most coarse textured soils approximately at or below the soil permanent wilting pointvalue. A comparison between the vapor diffusion and the hydraulic conductivity are shown in Fig. (4.10).
This shows that vapor diffusion comprises the most significant contribution to the net diffusion process overa soil water range around the wilting point. In the ISBA force-restore method, this vapor phase transfer
is parameterized within the coefficient C1 for dry soil (Braud et al. (1993) and Giordani (1996)). As a
final note, strictly speaking, vapor diffusion involves latent heating effects which couples the mass and heat
eqiuations very tightly over a certain range of temperature and soil moisture. But currently in ISBA, theeffect of vapor diffusion is simply modeled by increasing the effective diffusivity of liquid transfer as afirst order approach (thus, mass is conserved and energy is unchanged) since historically, the goal was tomaintain baresoil evaporation under dry but sufficiently hot surface conditions. Future work could consist
in adding the latent heating effect.
Layer averaging Integrating Eq. (4.58) downward into the soil to obtain the prognostic equation for thelayer-average volumetric liquid water content for each j layer givesZ −zj−1Z −zj−1 Z −zj−1∂FΦ∂wldz = −dz −dz(4.104)
Sl −
∂t
∂z
Lf ρw
−zj
−zj
−zj
where
wl j =1∆zj

Z −zj−1

wl dz(4.105)−zj

wl j is the layer averaged volumetric liquid water content (j = 1, ..., N ).
Carrying out the integration in Eq. 4.104 using Eq. 4.105 yields
∆zj

wl j
∆zj Φj= F−F− Qj −
∂t
Lf ρw
−zj
−zj−1
SURFEX v8.1 - Issue no 3 - 2018(4.106)

CHAPTER 4. SOIL AND VEGETATION

129

0

10

Sand Dν ψ
Sand kLoam Dν ψ
Loam k−5

Conductivity (m/s)

10

Clay

Dν ψ

Clay

k

−10

10

−15

10

−20

10

0.0

0.2

0.4
0.6
Soil Wetness

0.8

1.0

Figure 4.10: The total hydraulic conductivity contributions from liquid water (k) and vapor (Dνψ ) for threesoil textures as a function of soil wetness. The soil temperature and surface atmospheric pressure haveconstant values of 285 K and 105 Pa, respectively.

where
Qj = ∆zj Sj
is in kg m−2 s−1. The flux across a model level (zj ) is written asψj+1 − ψjF= Fj = η j− kj(∆zj + ∆zj+1 ) /2
−zj


Dνψ,j
η j = ℘j k j +ρw(4.107)(4.108a)(4.108b)where kj and Dνψ,j (both in m s−1 ) represent the geometric means over two consecutive nodes of the soil
hydraulic conductivity and isothermal vapor conductivity values, respectively. The inter-facial hydraulicconductivity is defined asqkj =kj (ψj ) × kj+1 (ψj+1 )(4.109)The choice of an appropriate intra-block approximation for unsaturated hydraulic conductivity has been
pointed out as critical in the numerical solution of unsaturated flow by many studies. As discussed in
Decharme et al. (2011)/nociteDecharme2011, many studies have demonstrated that the geometric mean
generates little weighting error, improves the simulated infiltration front, and is generally applicable in all
situations.
A graphic representation of the interpolation method is shown for two contiguous soil layers with different
textures (and therefore, different soil hydraulic properties) in Fig. 4.11.
Boundary Conditions
SURFEX v8.1 - Issue no 3 - 2018

130

zj−1
∆ zj

kj

zj

_

kj

zj
∆ zj+1 zj+1
zj+1

k j+1
Xclay jXsand jXclay j+1
Xsand j+1

Figure 4.11: The interfacial hydraulic conductivity. kj represents the hydraulic conductivity centered at zj ,˜ j = (∆zj + ∆zj+1 ) /2.
and ∆zLower Boundary The lower boundary condition is modeled as gravitational drainage (vertical diffusion isneglected). The mean water content of the lowest layer is used to evaluate the flux so that from Eq. (4.108a)
one can write
FN = −kN(4.110)The diffusion term (i.e. capillary rise across the lower model boundary) can be significant, however, when
the water table is near zN . An option exists for utilizing this information using a simple expression consistent
with the vertical flux formulation used for the other model layers. In this case, FN is modified to be
FN





ψN − ψsat= − kN fwtd
+ 1 + (1 − fwtd )∆zwtd∆zwtd = min (zN , zwtd ) − (zN + zN −1 ) /2

(4.111)(4.112)where fwtd is the gird-cell fraction where capillary rise occurs. It can be 1 at the local scale or depend on
topography at larger scales. Indeed, only a fraction of the grid cell corresponding to the flat valleys andalluvial plains should be affected by water capillary rises. This fraction must reflect the subgrid topographical heterogeneity inside each grid cell, which can be significant, for example, when considering the coarse
resolution of the climate models. A grid cell with steeper topography would be affected by upward capillary fluxes over a small fraction of the grid cell, unlike those characterized by relatively flatter terrain. See
Vergnes et al. (2014) for more details.
Upper Boundary The upper boundary condition represents infiltration. By default, the soil infiltration I
is equal to the potential (supply limited) infiltration rate, i.e. I = Rt . This case is specially relevant for
local scale studies. The soil-water infiltration is put preferentially in the first layer. If this first layer can notcontain this amount of water, the remaining is forced into the next layer and so forth (downward).
An Horton runoff option exists that computes the soil infiltration via a Green and Ampt (1911) approach(Decharme et al. 2013). This approach, based on Darcys law, includes the hydrodynamic parameters of
the soil and determines the infiltration capacity of soil over the time. It represents the soil infiltration as a
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

131

wetting front in which the hydraulic gradient is uniform. In ISBA-DF, the analytical form of the GreenAmpt approach is used to determine the maximum amount of water that infiltrates the soil to a depth close
to 0.1 m (the thickness generally used for relatively large time steps). The infiltration capacity, Ic (kg m−2s−1 ), is therefore parameterized as:



nic 
ρw X
ψsat − ψi+ 1 ∆zi℘i ksat,i(4.113)
Ic =
znic
∆zi
i=1

where znic (m) represents the depth of the layer nic that is the nearest 0.1 m, and ∆zi (m) is the thicknessof each of the i layers. Finally, the soil-water infiltration in ISBA-DF can be computed by comparing thisinfiltration capacity with the flux of water reaching the soil:
I = min (Rt , Ic )(4.114)

All of the excess water (i.e. defined as Rt − I when it is > 0) is treated as a Horton surface runoff flux
whereas the soil infiltration is treated as a moisture source term.
For non-local scale applications, an alternate form of generating surface runoff is needed. In this case,infiltration is computed as:
I = min(Rt − Qr , Ic )(4.115)
It can also be computed via a variable infiltration capacity (VIC: Dumenil and Todoni, 1992) sub-grid surface
runoff scheme used in ISBA (Habets et al. 1999). In this scheme, Qr represents sub-grid surface runoff fromsaturated regions within the computational unit/cell (See Eq.s 4.26-4.28 for the theoretical background). It
is computed using a similar form as that for the Force-Restore approach (Eq.s 4.29a-4.30):




Rt ∆t
1
(w r − w c,min ) 1/(1+b)−(4.116a)Qr crit = 1 −(wsat − wc,min )ρw zr (1 + b) (w sat − wc,min )
(
)
ρw zr
1+b
Q r = Rt −(wsat − w r ) − (wsat − w c,min ) [max (0, Qr crit )](4.116b)∆twith the constraints (as in Eq. 4.30, but using a layer averaged wc,min ):Qr = 0if(Qr < 0)or

(w r ≤ w c,min )(4.117)Note that currently, wc,min = wwilt by default until further studies can be done. Qr is evaluated using the
average total soil moisture, w r , integrated from the surface down to a characteristic depth, zr . It is defined
as
P

Nr
∆z
w
j j + wNr +1 max (0, zr − zNr )j=1
P(zr ≤ zN )(4.118)
wr =
Nr
+
max
(0,
z
−
z
)
∆z
r
Nr
j
j=1

where Nr is the total number of soil layers for which zr ≥ zj (i.e. the depth is greater than or equal to thelower boundary of the soil layer j). Note that the porosity and wilting point volumetric water contents arealso averaged over zr using the same operator. This depth should be at least several tens of centimeters thick(Liang et al. 1996).
It should also be noted that several authors use a form of Darcy’s law assuming the soil right at the surface
is saturated as the maximum potential infiltration rate (Mahrt and Pan, 1984; Abramopoulos et al. 1988).
This, however, has a very minimal impact on the infiltration (compared to the above equations) for the timeand space scales considered in typical ISBA applications, and the linearization of such a term can posesome numerical problems (the linearized surface flux can actually exceed the amount of water available for
infiltration under some rare circumstances).
SURFEX v8.1 - Issue no 3 - 2018

132
The equation for liquid water transfer is solved using:̺j (wl j n − wl j n−1 ) = (1 − ϕ) Fj n−1 − Fj−1 n−1 + ϕ (Fj n − Fj−1 n ) − Qj n

Solution method(4.119)where ̺j = ∆zj /∆t, and n indicates the value at the end of the time step, ∆t. The Crank-Nicolson
time scheme is currently used to integrate the equations in time (i.e., ϕ = 1/2). The flux terms can belinearized or an iterative solution method can be used. The linearization method is obviously more attractive
for numerical weather prediction applications as it consumes less CPUs, and for this method, an uppermost
layer of several cm thickness can safely be used for typical GCM (upper limit for ∆t) time steps (Bonan,
1996). Note that updates in mass owing to phase changes (Φ) are evaluated in a subsequent computation(see section 4).
Soil moisture sink term The sink term is composed of soil water losses/gains due to evapotranspiration/condensation and gains due to lateral inflow or so-called soil water excess. The production/reduction ofsoil ice decreases/increases the liquid soil water content while leaving the total soil water content unchanged.
Evapotranspiration Bare soil evaporation, Eg , is extracted from the uppermost soil layer only. Transpiration, Etr , can be extracted from multiple layers. A normalized root-zone fraction is specified for each soil
layer, and is zero for layers below the root zone. Normalized transpiration weights are then calculated basedon the specified vertical root zone fraction and the thickness of each model soil layer:Υj ∆zjξ j = PN
j=1 Υj ∆zj(0 ≤ ξj ≤ 1)

(4.120)P
where ξj represents the transpiration weight. Note that N
j=1 ξj = 1 unless there are no roots, in which caseξj = 0. Υj represents the root fraction:NX
Υj = 1 .
(4.121)jThis parameter is not well known for many regions and transpiration from SVAT models can be highly
sensitive to the vertical root zone distribution (Desborough (1997)): this study suggests the use of a uniform
distribution. A uniform root zone distribution can be specified by setting Υj constant within the root zone
soil layer(s), or a simple exponential function dependent on plant cover can be specified (Jackson et al.
(1996)). In ISBA, the effect of water stress on transpiration is modeled using a normalized soil moisturefactor (Noilhan and Planton, 1989; Calvet et al. 1998):
wl j − wwilt j
wn j =(ǫ ≤ wn j ≤ 1)
(4.122)(wf c j − wwilt j )where wwilt is the wilting point volumetric water content, and ǫ is a small numerical value (≈ 10−3 ).
From Eq. (4.122), soil ice in the root zone can hinder plant evaporation even if atmospheric conditions are
conducive to transpiration and the total soil water content is above field capacity since freezing produces aneffective soil drying (reducing the liquid part).
The factor in Eq. (4.122) is applied to the stomatal conductance so that transpiration can proceed at an
unstressed rate relative the soil water for moisture values above field capacity, and is negligible for soils
drier than wilting point. The layer-averaged water stress factor, which is applied to the net transpiration, iscalculated as Pan and Mahrt (1987)
NX
ξj wn j(4.123)
wn =j=1

The above coefficients are simply used to partition the transpiration among the various root-zone soil layers.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

133

Soil moisture excess When the increase over a given time period in observed total soil water content
exceeds that of precipitation less evapotranspiration, a laterally induced source (negative sink) is assumed
to occur (Calvet et al. (1998)). This can be due to lateral inflow of water (most likely) or capillary risefrom below the observation depth. Since vertical diffusion across the base of the model is assumed to be
negligible, this source is parameterized as lateral inflow. The vertical distribution is assumed to be linear
down to the depth of the soil moisture observations:δυ j ∆zjυj = PN
j=1 δυ j ∆zj(4.124)

where υj represents the normalized soil water excess coefficient, and δυ j is a delta function which is either 1
or 0 depending on whether or not excess inflow is occurring in layer j. For applications where soil moistureexcess is not available, this source is set to zero.
Liquid water sink

The external soil water source/sink term [Eq. (4.107)] is expressed as
wn j
Etr + δg j Eg L − υj Xs .
Qj = ξ jwn(4.125)

Xs represents the soil water excess (lateral inflow). Eg L is the evaporation from the bare soil surface(uppermost layer), and δg j is a delta function which is unity only the uppermost soil layer (δg 1 = 1), andis zero for all the other soil layers. The uppermost layer is prescribed to be thin in order to capture thedaily cycle in bare-soil evaporation. The root zone fraction in this layer, Υ1 , is usually set to zero. The
transpiration, bare-soil evaporation and water excess terms are in units of kg m−2 s−1 .
Soil water phase changes: freeze-thaw
Soil ice [Eq. (4.344)] increases when there is energy available for ice production, while decreases are due
to melting and sublimation. In order to avoid a more computationally intensive iterative solution procedure[between Eq.s (4.57)-(4.344)], the soil temperature is first calculated using Eq. (4.87), then the phase change
term (Φj ) is evaluated. The temperature for a given layer at time n will then be adjusted at the end of thetime step such that Tj n → Tf if melting or freezing occurs (where Tf is the freezing point temperature).
The method presented in Boone et al. (2000) and in Boone (2000) for ISBA-DF has been modified owing
to research involving PILPS-2e (Bowling et al. (2003)) with ISBA (Habets et al. 2002). In original test simulations involving ISBA-DF using the PILPS-2e experimental design and forcing, it was found that nearly
all of the near surface water froze, and this caused some unrealistic conditions (although no observations
are available to verify this). Boone et al. (2000) treated NWP-time-scale events, and soil freezing was not
as extensive as in the PILPS-2e domain. Thus, it was decided to adopt an approach which determines a
maximum liquid water content as a function of temperature using the Gibbs free energy method. See forexample Cox et al. (1999), Cherkauer and Lettenmaier (1999) and Koren et al. (1999) for examples of thismethod used in SVATs. Many examples exist in soil-science literature: see Boone (2000) for references.
The main difference between this method and the one presented in Boone et al. (2000) is that not all of theavailable liquid water is frozen. The method outlined herein represents a near seamless model change in thatit does not augment CPU’s significantly, and it requires no additional parameters. It has been documented
by Decharme et al. (2016).
The relation between the soil water potential and temperature for sub-freezing conditions is from Fuchs etal. (1978):
Lf (T − Tf )(4.126)ψ∗ =gT
SURFEX v8.1 - Issue no 3 - 2018

134
The potential ψ ∗ can be substituted in the expression for the soil matric potential in order to obtain the
maximum unfrozen (liquid) water content at a given soil temperature, T . Currently for ISBA, this is the
Brooks and Corey (1966) model as modified by Clapp and Hornberger (1978), so that ∗ −1/bψ(4.127)wl max = wsat
ψsatDuring phase changes, the total soil water content (w = wl + wi ) for each soil layer is conserved, so that,for example, as a soil freezes, the liquid water content will decrease owing to a corresponding increase insoil ice content (wi ). This concept can be used to establish the maximum temperature at which soil ice ispresent (again using the Gibbs free energy concept) as
Tmax =

Lf Tf(Lf − g ψ)

(4.128)where the soil liquid water potential is defined as a function of the liquid water content using the relationshipfrom Clapp and Hornberger (1978) [Eq. (4.95)]. The maximum unfrozen fraction (wl max /wsat ) and wl max
as a function of temperature depression are shown in Fig. (4.12). for three soil textures. Note that a larger
percentage of liquid water can freeze for more coarse textured soils and that relatively dry soils might havevery cold temperatures before any freezing takes place.
1.0

0.5

Unfrozen Fraction (−)

0.8

Water Content (m3 m−3)

Sand
Loam
Clay

0.6

0.4

0.2

0.0

0

2

4

6

Tf−T (K)

8

10

0.4

0.3

0.2

0.1

0.0

0

2

4

6

8

10

Tf−T (K)

Figure 4.12: The maximum unfrozen fraction (wl max /wsat ) and wl max as a function of temperature depression for three soil textures. The corresponding porosity values (wsat ) are shown in the right panel (thickhorizontal lines) as a reference.

The phase change term is parameterized in a manner similar to that presented in Boone (2000), Boone etal. (2000) and Giard and Bazile (2000), but with the available thermal energy evaluated using the difference
Tmax − T as opposed to Tf − T , and the available liquid water for freezing being defined using wl − wl max
as opposed to wl − wl min . The freezing and melting terms are, respectively:
Φf j = min [Ks ǫf max (0, Tmax j − Tj ) ci , Lf ρw max (0, wl j − wl max j )] /τiΦm j =min [Ks ǫm max (0, Tj − Tmax j ) ci , Lf ρw wi j ] /τi(4.129)where ci is the heat capacity of ice (1.883 ×106 J K−1 m−3 ). A parameter which represents the characteristic
time scale for phase changes is represented by τi (Giard and Bazile, 2000). It can be determined throughcalibration, possibly (eventually) be related to soil texture. A constant value of 3300 s−1 is currently used.
The expressions for the phase change efficiencies (ǫf and ǫm ) are parameterized as functions of liquid soil
water for freezing and soil ice for melting (similar to the method used by Cogley et al. (1990) and Pitman et
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION
al. (1991):
ǫj =

(

135

wl j / (wsat − wi j ) if (Tj ≤ Tf )wi j / (wsat − wmin ) if (Tj > Tf )The principle of using such coefficients is that it is assumed that when the grid box average liquid soil
moisture is relatively large, more energy is used for freezing the soil compared to a more dry average soil
with the same available energy (for freezing). It is also a rudimentary method for modeling sub-grid freezing
effects. The same basic idea holds for soil ice melting.
The surface insulation coefficient, Ks , is modeled following Giard and Bazile (2000) and is written (here in
non-dimensional form) as



LAI
veg
1−
(0 < Ks ≤ 1)
(4.130)Ks = 1 −K2
K3
where the values from Giard and Bazile (2000) are used: K2 = 5 and K3 = 30 m2 m−2 . For relatively
dense vegetation covers (i.e., large LAI and veg), more energy is used to heat or cool the vegetation whileless is used to freeze/thaw the soil water/ice (compared to a surface with less vegetation).
The total phase change is then simply expressed as the difference between the freezing and melting components, although note that one or the other is always zero:Φj = Φf j − Φm j

(4.131)

Using the above model, the phase changes tend to follow the so-called soil specific freezing characteristic
curve from Fuchs et al. (1978), although there can be considerable scatter about this line owing to ǫ < 1 andKs < 1, and ice can be present at significantly above-freezing layer-average temperatures. In the limit as ǫand Ks become unity, the scatter is greatly reduced, and the presence of ice at above-freezing temperatures
is also greatly reduced.
An example of the application of the above model to a cold climate is shown in Fig. (4.13). The forcing andparameters are from Goose Bay, Canada (Ross Brown, personal communication). The relationship between
simulated soil temperature and liquid water content for all 5 soil layers using the model as presented herein isshown in the upper panel, and the relationship for which ǫ and Ks have been set to zero is shown in the lower
panel. Each point represents at value at a 30-minute time step for which either Tj ≤ Tf or wi j ≥ 0.001 m3
m−3 .
Soil ice and the overall soil water content are decreased due to sublimation. This term is expressed as
Si = ∆z1 Eg I,

(4.132)where Eg I represents the liquid water equivalent loss of soil ice from the bare soil (uppermost) model layer(kg m−2 s−1 ).
The temperature and soil water profiles are updated at the end of the time step, ∆t, using the calculated
phase change term together with:
∆t Φj
ch j
∆t Φj
wL j n′ = wL j n −
Lf ρw
∆t
Φj
wI j n′ = wI j n +Lf ρw
Tj n′ = Tj n +(4.133)(4.134)(4.135)Additional final minor adjustments are made as needed to prevent supersaturation of a layer, etc. The
modification of the soil hydrological parameters owing to freezing is described in Section 4.1.2.
SURFEX v8.1 - Issue no 3 - 2018

136
Soil freezing characteristic curve
1.000

unfrozen fraction (−)

0.800

0.600

0.400

0.200

0.000
1.000

unfrozen fraction (−)

0.800

0.600

0.400

0.200

0.000
0.00

2.00

4.00
6.00
Tf − T (K)

8.00

10.00

Figure 4.13: The simulated unfrozen liquid water fraction (wl / (wi + wl )) as a function of temperature
depression (Tf − T ) for five soil model layers. The forcing are from Goose Bay, Canada. The parameters ǫand Ks have been set to one in the lower panel.

4.1.4 Soil organic carbon
The physical properties of soil organic carbon (or peat soil) play a significant role for understanding the waterand energy budgets of the land surface in northern regions. North-Eurasian soils are very rich in organiccarbon because the low soil temperatures in this region inhibit decomposition of dead plant material that
accumulates over time, thereby forming peat deposits. Soil organic carbon exhibits very different hydraulicand thermal properties than mineral soil (Boelter 1969; Letts et al. 2000). It is characterized by a very highporosity, a weak hydraulic suction, and a sharp vertical hydraulic conductivity profile from high values atthe surface to very low values at the subsurface. This generally induces a relatively wet soil with a shallow
water table (Letts et al. 2000). Its low thermal conductivity and its relatively high heat capacity act as an
insulator for soil temperature that prevents the soil from significant warming during the summer (Bonan andShugart 1989; Lawrence and Slater 2008). Over permafrost regions, the hydraulic and thermal properties
of soil organic carbon partly control the soil depth reached by the 0 C isotherm which, in turn, defines the
thickness of the active layer during summer (Paquin and Sushama, 2015). However, using the multi-layer
version of ISBA over cold regions, winter top soil temperatures tend to be underestimated (Wang et al.
2016) while during summer they are generally too warm. It is partly due to the fact that ISBA only accounts
for mineral soil properties while many studies pointed out that the specific properties of soil organic carbon
are required to simulate realistic soil thermal regime over cold regions (Nicolsky et al. 2007; Beringer et al.
2001; Lawrence and Slater, 2008; Lawrence et al. 2008; Dankers et al. 2011).
An optional parameterization of the organic carbon effect on hydraulic and thermal soil properties has been
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

137

added by Decharme et al. (2016). The parameterization is based on the pedotransfer function of Boelter(1969) and inspired by works of Letts et al. (2000) and Lawrence and Slater(2008). The pedotransfer
functions of Boelter (1969) link the soil water retention at different pressure levels to the fiber content of apeat soil. Letts et al. (2000) describe the vertical profile of hydraulic properties such as soil matric potential
and hydraulic conductivity at saturation for a typical organic soil. The hydraulic properties change sharply
from the near surface where peat is weakly decomposed (fibric soil) to the sub-surface with moderately andwell decomposed peat (hemic and sapric soils respectively). Lawrence and Slater (2008) proposed a linear
combination of such soil organic properties with the standard mineral soil properties.
In ISBA-DF, before averaging soil organic with mineral properties, a typical peat soil profile is computedfor the model soil grid using a power function for each hydraulic property, αpeat , found in Table 4.1. For
each soil layer i, this function is described as:
αpeat (i) = αf ibric z(i)ββ =(4.136)ln (αsapric /αf ibric )ln (dsapric /df ibric )(4.137)

where z (m) is the depth of the considered soil grid node, αf ibric and αsapric are the fibric and sapric
parameter values, respectively (Table 4.1). df ibric (m) is the depth arbitrarily set to 0.01 m where the profile

fSOC

wsat

ksat

Peat
MineralCombined

2
2,

-1

2

mm.day

10

1

1

0,

01
0,

-3

9

75

6
3

m .m

0,

0,

0,

45
0,

3
0,
2
0,
1
0,
0

(-)

10

Figure 4.14: Parameterization of the effect of soil organic carbon (SOC) on soil hydraulic and thermal
properties. The soil organic carbon density profile, ρsoc , is given by Eq. 4.139 using a top soil organiccarbon content of 10 kg m−2 , a sub soil content of 15 kg m−2 , and via a simple linear interpolation ateach soil grid nodes that conserves the total soil carbon mass. The fraction of the soil that is organic, fsoc ,in each layer is determined assuming a simple relationship between this last soil organic carbon density
profile and an idealized peat soil density profile (Eq.4.142). Examples for the soil porosity, wsat , the soil
saturated hydraulic conductivity, ksat , and the soil heat capacity, c, are given. Dotted lines represent verticalhomogeneous mineral soil properties, dashed lines the idealized peat soil properties, and plain lines theresulting combined soil properties using averaging method summed-up in Table 4.1.
SURFEX v8.1 - Issue no 3 - 2018

138
starts to depart from fibric values, and dsapric (m) the depth of 1 m where the soil properties reach the sapric
values according to Letts et al. (2000).
To determine the organic fraction of soil, the density profile of the soil carbon must be
known for the entire soil grid.
Using the the Harmonized World Soil Database (HWSD;
http://webarchive.iiasa.ac.at/Research/LUC/External-World-soil-database/HTML/), the soil carbon densities in the first 0.3 m, ρtop (kg m−3 ), and the remaining 0.7 m below, ρsub (kg m−3 ), are known:
Stop
∆dtop
Ssub
ρsub =∆dsub
ρtop =(4.138a)(4.138b)where Stop and Ssub (kg m−2 ) are the topsoil and subsoil organic carbon contents respectively, ∆dtop and∆dsub (m) represent the thicknesses of each observed soil horizon (0.3 and 0.7 m, respectively). We extrapolate the density below 1 m from this observed near-surface profile (Eq. 4.138). The extrapolation assumes
that the carbon profile decreases sharply with soil depth according to a power function. The shape of thisfunction is given by the observed profile if the topsoil organic carbon density is superior to the subsoil density. Otherwise, the density of soil carbon below a 1 m depth, ρdeep (kg m−3 ), is taken equal to the subsoil
density:
#
 "
β

∆ddeepStop + Ssub
−1
(4.139)ρdeep = (1 − δ) ρsub + δ∆ddeep − ∆dtop − ∆dsub∆dtop + ∆dsub
where

and
β=

(
0 ∀ ρtop ≤ ρsub
δ =1 ∀ ρtop > ρsub(4.140)ln [Stop / (Stop + Ssub )]ln [∆dtop / (∆dtop + ∆dsub )](4.141)

Finally, the soil carbon density profile, ρsoc (kg m−3 ), over the entire soil grid is computed using these threesoil horizons and a simple linear interpolation at each grid node that conserves the total soil carbon mass
(Fig. 4.14). The fraction of the soil that is organic, fsoc , in each layer is determined assuming this simple
relationship:ρsoc (i)(4.142)
fsoc (i) =[1 − wsat,peat (i)] ρom

where ρom is the pure organic matter density equal to 1300 kg m−3 (Farouki, 1986) and wsat,peat the porosityof the peat soil profile computed using Eq. 4.136 and Table 4.1. As in Lawrence and Slater (2008), thisfraction is used to combine the standard mineral soil properties with soil organic properties using weighted
arithmetic or geometric averages, depending on the parameter (Table 4.1). An example of this method isshown in Fig. 4.14 for soil porosity, soil saturated hydraulic conductivity and soil heat capacity.

4.1.5 Treatment of the intercepted water
Rainfall and dew intercepted by the foliage feed a reservoir of water content Wr . This amount of water
evaporates in the air at a potential rate from the fraction δ of the foliage covered with a film of water, as theremaining part (1 − δ) of the leaves transpires. The fraction of the vegetation covered with water is defined
as
2/3

ωrv WrWr+(4.143)δv = (1 − ωrv )Wr,max(1 + arv LAI) Wr,max − arv Wr
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

139

Table 4.1: The peat soil hydraulic and thermal parameter values used in ISBA for fibric and sapric soil.
wsat (m3 m−3 ) is the porosity, wf c (m3 m−3 ) the water content at field capacity specified as matric potential
at -0.1 bar for peat soil, wwilt (m3 m−3 ) the water content at wilting point (matric potential of -15 bar),b the dimensionless shape parameter of the soil-water retention curve, ψsat (m) the soil matric potential,
ksat (m s−1 ) the soil hydraulic conductivity at saturation, c (J m−3 K−1 ) the soil heat capacity of organic
matter, λs (W m−1 K−1 ) the thermal conductivity of soil matrix, and λdry (W m−1 K−1 ) the dry soil thermal
conductivity. For pedotransfer functions of Boelter (1969), the fiber content in fibric soil is assumed to beequal to 76.8 against 21.8 in sapric soil in order to reach soil porosity values close to those of Letts et al.
(2000). The method for averaging mineral soil properties with peat soil values using the fraction of soil thatis organic is also given for each parameter.
αpeat

Fibric soil

Sapric soil

Source

wsat
wf c
wwilt
b
ψsat
ksat
c
λs
λdry

0.93000.36900.07302.7000-0.0103
2.8×10−4
2.5×10−6
0.25000.05000.84500.71900.222012.0000-0.0101
1.0×10−7
2.5×10−6
0.25000.0500

Letts et al. (2000) and Boelter (1969)
PTF from Boelter (1969)
TF from Boelter (1969)
Letts et al. (2000)
Letts et al. (2000)
Letts et al. (2000)
Farouki (1986)
Farouki (1986)
Farouki (1986)

Mineral/Peat average
Arithmetic
Arithmetic
Arithmetic
Arithmetic
Arithmetic
Geometric
Arithmetic
Geometric
Geometric

Delire et al. (1997) used the first term on the RHS of Eq. 4.143 for relatively low vegetation (Deardorff,
1978) and the second term for tall vegetation (Manzi and Planton, 1994). A weighting function is usedwhich introduces the vegetation height dependence using the roughness length as a proxy from
ωrv = 2 z0v − 1(0 ≤ ωrv ≤ 1)

(4.144)

where the current value for the dimensionless coefficient is arv = 2.
Following Deardorff (1978), we set∂Wr= vegP − (Ev − Etr ) − Rr ; 0 ≤ Wr ≤ Wrmax(4.145)∂twhere P is the precipitation rate at the top of the vegetation, Ev is the evaporation from the vegetation
including the transpiration Etr and the direct evaporation Er when positive, and the dew flux when negative(in this case Etr = 0), and Rr is the runoff of the interception reservoir. This runoff occurs when Wr
exceeds a maximum value Wrmax depending upon the density of the canopy, i.e., roughly proportional tovegLAI. According to Dickinson (1984), we use the simple equation:
Wrmax = cwrmax veg LAI(4.146)

Generally speaking, cwrmax = 0.2 kg m−2 , although it can be modified slightly for certain vegetation cover.

4.1.6 Spatial variability of precipitation intensities
With this option, the main assumption is that, generally, the rainfall intensity is not distributed homogeneously over an entire grid cell. As a first-order approximation, the sub- grid variability in liquid precipitation, Pi , can be given by an exponential probability density distribution, f (Pi ):f (Pi ) =µ −µ Pie P
PSURFEX v8.1 - Issue no 3 - 2018(4.147)

140
where P represent the mean rainfall rate over the grid cell and µ a fraction of the grid cell affected byrainfall. µ is calculated using the results of Fan et al. (1996), who showed an exponential relationshipbetween the fractional coverage of precipitation and rainfall rate, based on their analyses of over 2 years
radar observations and rain gauge measurements over the Arkansas-Red river basin in the southern plains of
the United States. This relationship is:µ = 1 − e−βP
(4.148)where β is a parameter which depends on grid resolution, dx :β = 0.2 + 0.5e−0.001dx(4.149)dx represents represents lengths of square grid cells ranging from 40 km to 500 km. In consequence, theµ parameter is fixed to 1 at high resolution (≤ 10km). This Spatial variability of precipitation intensities
induces a new expression for the runoff from the interception reservoir, Wr :Wr = P × eµ(Wr −Wrmax )P ∆t(4.150)The second consequence is that the Horton runoff, Qhort , is calculated by integrating the difference between
the local rainfall and the local maximum infiltration capacity, Ii , as follows:
Z ∞Qhort = µ(Pi − Ii ) f (Pi )dPi
(4.151)
Ii

Another assumption is made on the spatial heterogeneity of the local maximum infiltration capacity. Its
spatial distribution can also be approximated by an exponential probability density distribution:g(Ii ) =1 − Iie I
I(4.152)where I is the mean maximum infiltration rate over the grid cell. As previously said, I is calculated for
unfrozen and frozen soil conditions. So Eq.4.151 , without snowmelt, can be noted as :Z ∞Z ∞
Qhort = µ(1 − δf )(Pi − Iunf,i )f (Pi )g(Iunf,i )dPi dIunf,i0I

Z ∞ Z ∞ unf,i+ µδf(Pi − If,i )f (Pi )g(If,i )dPi dIf,i0(4.153)If,iAfter some mathematical developments, the Horton runoff in presence of rainfall and snowmelt, Sm , isgiven following Decharme and Douville (2006):!
P
Qhort = (1 − δf )+ max(0, Sm − Iunf )1 + Iunf Pµ!
P+δf(4.154)+ max(0, Sm − If ) dPi dIf,i
1 + If Pµ4.1.7 Treatment of the snow
ISBA features several schemes to handle snow on the ground, which are described below. They range fromsingle-layer schemes with a minimal number of prognostic variables and highly simplified treatment of snow
thermodynamics, to state-of-the-art multi-layer snowpack schemes (Explicit Snow -ES- and Crocus). Table
4.2 provides an summary of the available snowpack schemes and the corresponding scientific references.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION
Single-layer
Multi-layer
Multi-layer

D95
Explicit-Snow (ES)
Crocus141
Douville et al. (1995a,1995b)
Boone (2000); Boone and Etchevers (2001)
Brun et al. (1989,1992); Vionnet et al. (2012)

Table 4.2: Summary of the snowpack schemes available in ISBA
One-layer snow scheme option
The evolution of the equivalent water content of the snow reservoir is given by∂Ws= Ps − Es − Mlt∂t(4.155)where Ps is the precipitation of snow, and Es is the sublimation from the snow surface.
The presence of snow covering the ground and vegetation can greatly influence the energy and mass transfers
between the land surface and the atmosphere. Notably, a snow layer modifies the radiative balance at thesurface by increasing the albedo. To consider this effect, the albedo of snow αs is treated as a new prognostic
variable. Depending if the snow is melting or not, αs decreases exponentially or linearly with time.
If there is no melting (i.e., Mlt = 0):αs (t) = αs (t − ∆t) − τa∆t Ps ∆t+(αsmax − αsmin )τWcrn(αsmin ≤ αs ≤ αsmax )(4.156)

where τa = 0.008 is the linear rate of decrease per day, αsmin = 0.50 and αsmax = 0.85 are the minimum
and maximum values of the snow albedo.
If there is melting (i.e., Mlt > 0):∆t+ αsminαs (t) = [αs (t − ∆t) − αsmin ] exp −τfτ(4.157)Ps ∆t+(αsmax − αsmin )(αsmin ≤ αs ≤ αsmax )Wcrn
where τf = 0.24 is the exponential decrease rate per day. Of course, the snow albedo increases as snowfalls
occur, as shown by the second terms of Eqs. 4.156-4.157.
The average albedo of a model grid-area is expressed as
αt = (1 − psn )α + psn αs(4.158)Similarly, the average emissivity ǫt is also influenced by the snow coverage:
ǫt = (1 − psn )ǫ + psn ǫs(4.159)where ǫs = 1.0 is the emissivity of the snow. Thus, the overall albedo and emissivity of the ground forinfrared radiation is enhanced by snow.
Because of the significant variability of thermal properties related with the snow compactness, the snow density, ρs , is also considered as a prognostic variable. Based on Verseghy (1991), ρs decreases exponentiallyat a rate of τf per day:


Ps ∆t
∆t
ρsmin
(ρsmin ≤ ρs ≤ ρsmax ) (4.160)+ρsmax +ρs (t) = [ρs (t − ∆t) − ρsmax ] exp −τfτWs
where ρsmin = 100 and ρsmax = 300 kg m−3 are the minimum and maximum snow densities.
SURFEX v8.1 - Issue no 3 - 2018

142
Multi-layer snow scheme options
Two multi-layer snow schemes options are available in ISBA, namely Explicit Snow (ES) and Crocus.
Explicit Snow (Boone and Etchevers, 2001; Decharme et al. 2016) is a so-called intermediate complexity
scheme which is representative of a class of snow models which use several layers and have simplified
physical parameterization schemes (Loth et al. 1993; Lynch-Stieglitz, 1994; Sun et al. 1999). In contrast,
Crocus features a detailed description of processes occurring within the snowpack (Brun et al. 1989; 1992;
Vionnet et al. 2012). Crocus was initially a stand-alone model, and it was recently coupled to ISBA buildingon the ES model structure. In what follows, the description applies to both ES and Crocus unless otherwise
stated.
Compared to the baseline ISBA snow scheme, the explicit multi-layered approach shared by ES and Crocus
resolves the large thermal and the density gradients which can exist in the snow cover, distinguishes thesurface energy budgets of the snow and non-snow covered portions of the surface, includes the effects ofliquid water storage in the snow cover, computes the absorption of incident radiation within the pack, andcalculates explicit heat conduction between the snow and the soil. Figure 4.15 provides an overview of theprocesses handled in the multi-layer snow schemes, coupled to the soil and vegetation components of ISBA.
The multi-layer snowpack schemes Crocus and ES are most consistently used together with ISBA-DF rather
than the force-restore soil schemes. In addtion, Crocus handles snow metamorphism, i.e. the physicaltransformations of snow grains through time, and interactively modifies the vertical discretization of thevertical grid of snow layers to optimize the representation of internal snow processes. In practice, Crocus isgenerally run with a larger total possible number of snow layers than ES. ES typically uses up to 12 snow
layers, while standard Crocus runs use up to 20 or 50 snow layers. The latter configuration is appropriate
when the focus is placed on the study of the properties of the snowpack itself (avalanche hazard prediction,snow physical properties, combined use of remote sensing).

Figure 4.15: Overview of the physical processes and prognostic variables used to characterize the snowpackin the multi-layer snowpack schemes options of ISBA (ES and Crocus). The major differences between the
ES and Crocus scheme is that ES does not treat snow metamorphism explicitly, and that the number of snow
layers is kept significantly lower than for Crocus (on the order of 3 typically, vs. up to 20 or 50 for Crocus.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

143

The conservation equation for the total snow cover mass is expressed as∂Ws= Ps + psn (P − Ps ) − Es − Esl − Qn ,∂t

(4.161)

where Esl represents evaporation of liquid water from the snow surface, and the product psn (P − Ps )represents the portion of the total rainfall that is intercepted by the snow surface while the remaining rainfall
is assumed to be intercepted by the snow-free soil and vegetation canopy. The snow-runoff rate, Qn , is therate at which liquid water leaves the base of the snow cover.
The snow state variables are the heat content (Hs ), the layer thickness (D), and the layer average density(ρs ). The temperature (Tsn ) and liquid water content (wsl ) are defined using the heat content. The use of the
Crocus scheme induces the definition of further variables, which describe the morphological properties ofsnow grains (d dendricity, s sphericity, gs grain size, h historical variable and A age of a given snow layer).
See Vionnet et al. (2012) for details.
The total snow depth, Ds (m) is defined as
Ds =

Ns
X

Di

(4.162)i=1

where a 12-layer configuration is currently used by default (i.e. Ns = 12). In ES and Crocus, the thicknessof the surface snow layer can be as low as 1 mm although it typically ranges on the order of 0.01 to 0.02 m.
The thickness of internal snow layers is on the order of a few cm typically, with a finer mesh towards theair/snow and ground/snow interface. See Vionnet et al. (2012) and Decharme et al. (2016) for details.
The evolution of snow density in each layer is due to snow compaction resulting from changes in snow
viscosity (Brun et al. 1989) and wind-induced densification of near surface snow layers (Brun et al. 1997).
This wind-driven compaction process is assumed to occur when wind velocity exceeds a threshold value that
depends on snow surface characteristics. This process is especially important for simulating the evolution of
the snow density over polar regions. In ES, additional changes arise from snowfall which generally reduce
the snow density and more details can be seen in Decharme et al. (2016). In Crocus, snowfall induces thecreation of a new snow layer at the surface ; mechanical settling is computed using a Newtonian formalism
where the viscosity depends mostly on the snow density and temperature but also on the snow type (seeVionnet et al. 2012, for details). When Crocus is used, the slope angle has an impact on the compaction
rate, since only the component of the weight perpendicular to the snow layering need be taken into account.
In practice, the acceleration of gravity (g = 9.80665 m s2 ) is then simply multiplied by cos(slopei ) where
slopei is the slope of the grid point i.
The snow heat content (J m−2 ) is defined as
Hs i = cs i Di (Tsn i − T0 ) − Lf ρw (ws i − wsl i ) ,(4.163)where ws is the total snow layer water equivalent depth (m), wsl is the snow layer liquid water content(m), and cs is the snow heat capacity (J m−3 K−1 ) (using the same definition as the baseline ISBA snow
scheme). The snow heat content is used in order to allow the presence of either cold (dry) snow which
has a temperature less than or equal to the freezing point or warm (wet) snow which is characterized by atemperature at the freezing point and contains water in liquid form. The snow temperature and liquid watercontent can then be defined as
Tsn i = Tf + (Hs i + Lf ρw ws i ) / (cs i Di ) ;wl i = 0

wsl i = ws i + (Hs i /Lf ρw ) ;Tsn i = Tf and wsl i ≤ wsl max i (4.165)

SURFEX v8.1 - Issue no 3 - 2018(4.164)

144
where wsl max i is the maximum liquid water holding capacity of a snow layer, which is based on empirical
relations. All water exceeding this flows into the layer below where it can do one or all of the following:
add to the liquid water content, refreeze, or continue flowing downward.
Snow heat flow is along the thermal gradient as any snow melt or percolated water within the snow cover isassumed to have zero heat content. The layer-averaged snow temperature equation (Ts i ) is expressed as∂Tsn i= Gs i−1 − Gs i + Rs i−1 − Rs i − Ss i ,(4.166)∂twhere Ss represents an energy sink/source term associated with phase changes between the liquid andsolid phases of water. Incoming short wave radiation (Rs ) transmission within the snowpack decreases
exponentially with increasing snow depth. At the surface, it is expressed as
cs i DiRs 0 = Rg (1 − αs )(4.167)

where the snow albedo is defined following Brun et al. (1992). In ES and Crocus the solar radiation ishandled using three separate spectral bands ([0.3-0.8], [0.8-1.5] and [1.5-2.8] µm). First of all, the albedo
is computed in each band, as a function of the snow properties in the first snowpack layer for ES and the
top 0.03 m of the snowpack for Crocus. In the UV and visible range ([0.3-0.8] µm), snow albedo depends
mostly on the amount of light absorbing impurities, but also on its micro-structure. The latter is represented
by the optical diameter of snow, dopt , which corresponds to the diameter of a collection of mono-dispersed
ice spheres possessing the same hemispherical albedo as the corresponding semi-infinite snow layer. The
impact of snow browning due to the deposition of light absorbing impurities is parametrized from the ageof the uppermost snow layer. In the near-infrared bands, the spectral albedo depends only on the optical
diameter of snow. The optical diameter of snow is currently empirically derived from the snow density andage for ES (Decharme et al. 2016) and the microstructure properties of the snow for Crocus (see below, andVionnet et al. 2012). Once the spectral albedo is calculated, in every spectral band the incoming radiation
is depleted according to the albedo value, and the remaining part penetrates the snowpack and is graduallyabsorbed in the snow layers assuming an exponential decay of radiation with depth. The solar flux, Qs , at a
depth z below the snow surface is expressed as follows:
)

(
3
i
X
X
(βk,j ∆zj )
(4.168)Qs = SW ↓ωk (1 − αk ) exp −
k=1

j=1

where SW ↓ represents the incoming solar radiation, αk the albedo and βk,j the absorption coefficient forthe spectral band k and layer j. In the current version, the incoming shortwave radiation Rs is split into threebands using empirical coefficients ωk equal to 0.71, 0.21 and 0.08 respectively for bands [0.3-0.8], [0.81.5] and [1.5-2.8] mm. Future developments will allow for forcing where incoming shortwave radiation ispartitioned into several bands. Finally, shortwave radiation excess for thin snow cover (transmitted throughthe snow) is added to the snow/ground heat flux.
The sub-surface heat (Gs ) flux terms are evaluated using simple diffusion. At the surface, this flux is
expressed as
Gs 0 = ǫs RA − σSB Tsn 1 4 − H (Tsn 1 ) − LE (Tsn 1 ) − cw psn (P − Ps ) (Tf − Tr ) , (4.169)

The last term on the right hand side of the above equation represents a latent heat source when rain witha temperature (Tr ) greater than T0 falls on the snow cover, where cw represents the heat capacity of water(4187 J kg−1 K−1 ). Rainfall is simply assumed to have a temperature which is the larger of the air temperature (Ta ) and the freezing point. The latent heat flux from the snow includes the liquid fraction weighted
contributions from the evaporation of liquid water and sublimation.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATIONThe ISBA surface soil/vegetation layer temperature is then coupled to the snow scheme using



2π
1 ∂Ts
4
= (1 − pn ) Rg (1 − α) + ǫt RA − σTs − H − LE −(Ts − T2 )
CT ∂t
CT τ

145

(4.170)+ pn (Gs N + Rs N )The net surface fluxes to/from the atmosphere are then calculated as the snow-cover fraction weighted sums
over the snow and non-snow covered surfaces. When either multi-layer option is used (ES or Crocus), thesingle-layer snowpack scheme in ISBA is used when the snow cover is relatively thin (arbitrarily defined as
0.05 m depth). When the snow depth exceeds this threshold, the snow mass and heat is transferred to thechosen multi-layer scheme. This prevents numerical difficulties for vanishingly thin snow packs.
Additional features of the Crocus scheme
Evolution of the vertical discretization of the finite-element grid
The dynamical evolution of the number and thicknesses of the numerical snow layers is a key and original
feature of Crocus, which aims at simulating the vertical layering of natural snowpacks in the best possible
way. The maximum number of numerical layers is an important user-defined set-up option. A minimumof 3 layers is imposed for solving the heat conduction through the snowpack but there is no limitationon the maximum number. As the maximum number of layers increases, the snowpack stratigraphy canbe simulated in more detail. According to the research or operational objectives, the user has to find theappropriate balance between the realism and the computational cost of the simulation. An important point
to mention is that the snowpack scheme dynamically manages a different vertical grid mesh, in terms of thenumber and the thickness of snow layers, for each grid point when it is run in parallel mode for a spatiallydistributed simulation ; this is a common case for snow/atmosphere coupled simulations or for distributed
stand-alone simulations.
The adjustment of the snowpack layering is achieved with a set of rules. The procedure is activated at the
beginning of each time step according to the following sequence:• for snowfall over a bare soil, the snowpack is built up from identical layers, in terms of thickness andstate variables. Their number depends on the amount of fresh snow and on the maximum number oflayers;• for snowfall over an existing snowpack, it is first attempted to incorporate the freshly fallen snow into
the existing top layer, provided its grain characteristics are similar and its thickness is smaller than afixed limit. The similarity between two adjacent layers is determined from the value of the sum of
their differences in terms of d, s and gs , each weighted with an appropriate coefficient. If the merging
is not possible, a new numerical layer is added to the preexisting layers. If the number of layers thenreaches its maximum, a search is carried out to identify two adjacent layers to be merged. This isdone by minimizing a criterion balancing the similarity between their respective grain characteristics
and their thicknesses;• for no snowfall, a check is carried out to see whether it is convenient to merge too thin snow layers
or to split thoses which are thick. This is achieved by comparing the present thickness profile toan idealized profile, which acts as an attractor for the vertical grid. This idealized thickness profile
depends on the current snow depth and on the user-defined maximal number of layers (see Figure 4.16
for an example). Merging two layers is only possible for those which are similar enough in terms ofgrain characteristics. Grid resizing affects only one layer per time step, with a priority given to the
SURFEX v8.1 - Issue no 3 - 2018

146
surface and bottom layers, in order to accurately solve the energy exchanges at the surface and at thesnow/soil interface;• for most time steps, no grid resizing is carried out, except that the thickness of each layer decreases
according to its compaction rate.
The consistency of the physical prognostic variables is maintained in case of grid resizing. A projectionis achieved from the former vertical grid to the new one. Mass, heat content and liquid water content areconserved. When a new numerical snow layer is built from several former layers, its grain characteristics arecalculated in order to conserve the averaged weighted optical grain size of the former layers. This insures astrong consistency in the evolution of surface albedo, even when frequent grid resizing occur at the surface
in case of frequent snowfalls or surface melting events.

Figure 4.16: Illustration of the optimal vertical grid of Crocus, which depends on total snow depth and on
the user-defined maximum number of snow layers.

Snow metamorphism
Snow metamorphism is implemented in the snowpack scheme Crocus through a set of quantitative laws
describing the evolution rate of the type and size of the snow grains in each layer (Brun et al. 1992). This
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

147

is carried out within the subroutine. A distinction is made between dendritic and non-dendritic snow. Snow
falls as dendritic snow and remains dendritic until d reaches 0. Snow then reaches the state of rounded
crystals, faceted crystals or belongs to an intermediate state. It is is then characterized by its sphericity (s),ranging from 0 to 1, and a grain size, gs , ranging from 0.3 to 0.4 mm. Such snow is defined as non-dendritic.
The metamorphism laws that govern the evolution of snow grain depend on temperature, the temperature
gradient, and include wet metamorphism. They are similar to the laws initially described by Brun et al.
(1992) and are mostly based on empirical fits to experimental data. The metamorphism laws that govern theevolution of snow grain are given in Table 4.3 and 4.4, respectively for dry and wet metamorphism. In thecase of temperature gradient metamorphism, fits to experimental data by Marbouty (1980) are used. In thiscase, the increase of grain size gs follows:δgs= f (T )h(ρ)g(G)Φ
δt(4.171)

where G is the absolute value of the temperature gradient (|δT /δz|) and f , g, h and Φ are dimensionlessfunctions varying from 0 to 1 given by:0
if T − Tfus < −40 K 0.011 × (T − T + 40)
if − 40 ≤ T − Tfus < −22 Kfusf=(4.172)
0.2 + 0.05 × (T − Tfus + 22) if − 22 ≤ T − Tfus < −6 K

1 − 0.05 × (T − Tfus )otherwise

where Tfus is temperature of the melting point for water (K), and h, g and Φ are given below:
Φ = 1.0417.10−9 m s−1
if ρ < 150 kg m−3
 1.
h=
1 − 0.004 × (ρ − 150) if 150 < ρ < 400 kg m−3 0.
otherwise0.
if G < 15 K m−1





0.01 × (G − 15)
if 15 ≤ G < 25 K m−1 0.1 + 0.037 × (G − 25)
if 25 ≤ G < 40 K m−1g=
0.65 + 0.02 × (G − 40)
if 40 ≤ G < 50 K m−1
0.85 + 0.0075 × (G − 50) if 50 ≤ G < 70 K m−11.
otherwise(4.173)(4.174)(4.175)In addition to this default metamorphism formulations, three other formulations of metamorphism can be
activated. The first one (C13) is similar to the default one but uses the optical diameter and the sphericity as
prognostic variables. The second one (T07) is based on the parameterizations from Taillandier et al. (2007)
and Domine et al. (2007) and the last one (F06) is based on the parameterizations from Flanner et al. (2006).For detail of these implementations please refer to Carmagnola et al. (2014) .
Snow radiative transfer scheme
In addition to the basic formation of solar energy absorption and snow albedo over three spectral bands
described above, a new option is available for solar radiative transfer calculation in the snowpack. The
radiative scheme is called TARTES Libois et al. (2013) (Two-streAm Radiative TransfEr in Snow model).
TARTES is a two-stream radiative transfer scheme based on an analytical formulation of radiative transfer
in snow (Kokhanovsky et al. (2004)). TARTES computes spectral solar absorption within each layer anddiagnoses spectral and broadband albedo. The default spectral resolution is 20 nm. The scheme uses spectral solar irradiance calculated from input broabdand data using a parameterization derived from SBDARTSURFEX v8.1 - Issue no 3 - 2018

148

Table 4.3: Metamorphism laws under dry conditions. G is the vertical temperature gradient (|δT /δz|), T thetemperature (K) and t is time expressed in days. f , g, h and Φ are empirical functions to predict depth-hoar
growth-rate from Marbouty (1980).

G ≤ 5 K.m−1
5 < G ≤ 15 K.m−1
G > 15 K.m−1

Non-dendritic snowδs
9 −6000/T
δt = 10 eδgs
δt = 0δs
8 −6000/T G0.4
δt = −2.10 eδgsδt = 0δs
8s
if s >0: δt = −2.10 e−6000/T G0.4 and δgδt = 0δgs
if s =0: δsδt = 0 and δt = f (T )h(ρ)g(G)Φ

Dendritic snowδd8 −6000/T
δt = −2.10 eδs
9 −6000/T
δt = 10 eδd
8 −6000/T G0.4
δt = −2.10 eδs
8 −6000/T G0.4
δt = −2.10 e

Table 4.4: Metamorphism laws in the presence of liquid water. θ is the mass liquid water content and t is
time expressed in days. v refers to the equivalent volume of snow grain and v0′ and v1′ are empirical constants
taken from Brun (1989).

0≤s<1
s=1

Non-dendritic snowδgs
δt = 0δs
1 3
δt = 16 θδsδt = 0δv′ 3′
δt = v0 + v1 θ

Dendritic snow
δd1 3
δt = − 16 θWliqwith θ = 100 ρD

1 3
δsδt = 16 θ(Ricchiazzi et al. (1998)) at Col de Porte site. The scientific documentation of TARTES is available at
http://lgge.osug.fr/ picard/tartes/.
TARTES simulates the effect of light absorbing impurities as an equivalent black-carbon content. To thisrespect, three options can be activated :• ”TA1”: no impurity• ”TA2”: snow impurity content constant to 100 ng g−1• ”TAR” : impurity content = 2*snow age ng g−1
Effects of wind
! As a 1D model, the continental surface scheme ISBA within SURFEX isNOT designed to handle explicitly wind-induced snow redistribution.
Indeed, grid points are treated independently from each other.
Nevertheless, the Crocus snowpack scheme includes parameterizations
that represent some effects of wind drift on the snowpack.
The compaction and the metamorphism of the surface layers during wind drift events are taken into accountin a simplified way, as described initially by Brun et al. (1997). A mobility index, MO , describes thepotential for snow erosion for a given snow layer and depends on the microstructural properties of snow (d,s and gs ):(0.34 (0.75d − 0.5s + 0.5) + 0.66F (ρ)
dendritic caseMO =(4.176)0.34 (−0.583gs − 0.833s + 0.833) + 0.66F (ρ) non-dendritic case
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

149

Table 4.5: Evolution rates of snow grain properties and density in layer i caused by snow drifiting. t is time
expressed in hours and τ represents the time characteristic for snow grains change under wind transport
given by Eq. 4.178.
Parameters
Grain properties
Snow density

Non-dendritic snow Dendritic snow
1−s
d
δs
δd
δt = τ
δt = 2τ
−4
δgs
δs
5.10
1−s
δt =
τ
δt = τ
ρmax −ρδρwith ρmax = 350 kg m−3δt =τwhere F (ρ) = [1.25 − 0.0042 (max(ρmin , ρ) − ρmin )] and ρmin = 50 kg m−3 . The expression for MO
in Eq. 4.176 combines the parameterization of Guyomarc’h and Merindol (1998) (first term) developed for
alpine snow with a term depending on snow density (F (ρ)). The purpose is to extend the use of MO to polarsnow which has a density generally larger than 330 kg m−3 (upper limit for application of Guyomarc’h andMerindol, 1998). Fresh snow (high values of d, low value of ρ) presents high values of mobility index which
tend to decrease with time due to sintering (increase of s) and compaction (increase of ρ). Guyomarc’h andMerindol (1998) combined the mobility index with wind speed, U , to compute a so-called ”driftability”
index, SI :SI = −2.868 exp(−0.085U ) + 1 + MO
(4.177)
Positive values of SI indicate that snow drifting can occur while SI = 0 gives the value of the threshold
wind speed for snow transport. During a drift event, blown snow particles in saltation break upon collision
with the snow surface and tend towards rounded grains (Clifton et al. (2006)). For a given snow layer i, atime characteristic for snow grain change under wind transport is computed:
τi =τ
Γi driftwhere Γi drift = max[0, SIi exp(−zi /0.1)](4.178)where τ is empirically set to 48 hours. The pseudo-depth in the snow pack, zi (in m, positive downwards),
takes into account previous hardening of snow layers j situated above the current layer i:Xzi =[Dj × (3.25 − SIj )](4.179)jTherefore, through the variable Γdrift, compaction and rounding rates in a snow layer depends on thegrain driftability and are propagated to the layers below with an exponential decay until it reaches a nontransportable layer (SI ≤0). Compaction and rounding rates are detailed in Table 4.5.
As an option and in case of snow drifting, Crocus computes the associated rate of sublimation according
to a parameterization developed by Gordon et al. (2006). This parameterization allows the estimation of
the sublimation rate in a column of blowing or drifting snow, combining existing parameterizations from
Schmidt et al. (1982), Bintanja et al. (1998) and Déry et al. (2001). The total sublimation rate of blowing
snow Qs depends on the near-surface meteorological conditions according to:
Qs = A(

T0 γ
U) Ut ρa qsi (1 − Rhi )( )BTa
Ut(4.180)where Ta is the air temperature (K), T0 a constant with a value of 273.16 K, U the wind speed, Ut thethreshold wind speed for snow transport, ρa the air density and Rhi the relative humidity with respect to ice.
qsi denotes the saturation specific humidity (kg/kg) at temperature Ta . γ, A and B are dimensionless parameters with values 4.0, 0.0018 and 3.6, respectively. Ut is the threshold wind speed for wind transportation,
SURFEX v8.1 - Issue no 3 - 2018

150
obtained by setting SI = 0. in equation (4.177):
Ut = −log ((MO + 1.)/2.868)
0.085(4.181)

Using this option, Crocus subtracts the corresponding mass from the snowpack surface at each modeltimestep.

4.1.8 The surface fluxes
Only one energy balance is considered for the whole system ground-vegetation-snow (when the 3-layer snow
scheme option is not in use). As a result, heat and mass transfers between the surface and the atmosphere
are related to the mean values Ts and wg .
The net radiation at the surface is the sum of the absorbed fractions of the incoming solar radiation RG andof the atmospheric infrared radiation RA , reduced by the emitted infrared radiation:
(4.182)
Rn = RG (1 − αt ) + ǫt RA − σSB Ts 4

where σSB is the Stefan-Boltzmann constant.
The turbulent fluxes are calculated by means of the classical aerodynamic formulas. For the sensible heatflux:
H = ρa cp CH Va (Ts − Ta )(4.183)where cp is the specific heat; ρa , Va , and Ta are, respectively, the air density, the wind speed, and thetemperature at the lowest atmospheric level; and CH , as discussed below, is the drag coefficient depending
upon the thermal stability of the atmosphere. The explicit snow scheme sensible heat flux is calculated using
the same formulation (but with Tsn ). The water vapor flux E is the sum of the evaporation of liquid waterfrom the soil surface (i.e., Eg l ), from the vegetation (i.e., Ev ), and sublimation from the snow and soil ice(i.e, Es and Eg f ):LE = LEg l + LEv + Li (Es + Eg f )(4.184)Eg l = (1 − veg)(1 − psng ) (1 − δi ) ρa CH Va (hu qsat (Ts ) − qa )(4.185)

Es = psn ρa CH Va (qsat (Ts ) − qa )(4.187)

Ev = veg(1 − psnv )ρa CH Va hv (qsat (Ts ) − qa )

Eg f

=

(1 − veg) (1 − psng ) δi ρa CH Va (hui qsat (Ts ) − qa )(4.186)(4.188)where L and Li are the specific heat of evaporation and sublimation, qsat (Ts ) is the saturated specifichumidity at the temperature Ts , and qa is the atmospheric specific humidity at the lowest atmospheric level.
The snow fractions psn and psnv are defined by Eq.s 4.5 and 4.1, respectively. The water vapor flux E fromthe explicit snow surface is expressed as
LE (Tsn 1 ) = LEsl + Li Es(4.189)Esl = δsn ρa CHs Va (qsat (Tsn 1 ) − qa )Es = (1 − δsn ) ρa CHs Va (qsat (Tsn 1 ) − qa )

δsn = wsl 1 /wsl max 1 ;(4.190)(4.191)0 ≤ δsn ≤ 1(4.192)where evaporation of liquid water is zero when Tsn 1 < T0 . The transfer coefficient (CHs ) is calculated overthe snow covered surface using the same formulation as CH .
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION151

The surface ice fraction is is used to partition the bare soil latent heat flux between evaporation and sublimation, and it is defined as
δi = wg f / (wg f + wg ) ;0 ≤ δi < 1 .

(4.193)

The relative humidity hu at the ground surface is related to the superficial soil moisture wg following
i

( h
wg
1
π
wg < wf c ∗
1
−
cos
2
wf c ∗(4.194)hu =1
wg ≥ wf c ∗where the field capacity with respect to the liquid water is defined using the modified soil porosity so that∗ /w
wf c ∗ = wf c wsat
sat . The humidity for the ice covered portion of the grid box is calculated in a similar
fashion as
i

( h
w f
1
π
wg f < wf c ∗∗1 − cos wfgc ∗∗2
hui =(4.195)1
wg f ≥ wf c ∗∗where wf c ∗∗ = wf c (wsat − wg )/wsat . In case of dew flux when qsat (Ts ) < qa , hu is also set to 1 (seeMahfouf and Noilhan (1991) for details). When the flux Ev is positive, the Halstead coefficient hv takes
into account the direct evaporation Er from the fraction δ of the foliage covered by intercepted water, as
well as the transpiration Etr of the remaining part of the leaves:hv =(1 − δ)Ra /(Ra + Rs ) + δδ
Er =veg(1 − psnv )[qsat (Ts ) − qa ]Ra1−δ
[qsat (Ts ) − qa ]Etr =veg(1 − psnv )Ra + Rs(4.196)(4.197)(4.198)When Ev is negative, the dew flux is supposed to occur at the potential rate, and hv is taken equal to 1.
The aerodynamic resistance is Ra = (CH Va )−1 . The surface resistance, Rs , depends upon both atmosphericfactors and available water in the soil; it is given by:
Rs =

Rsmin
F1 F2 F3 F4 LAI(4.199)with the limiting factors F1 , F2 , F3 , and F4 :f + Rsmin /Rsmax
1+f
w2 − wwilt
and 0 ≤ F2 ≤ 1=
wf c − wwilt= 1 − γ (qsat (Ts ) − qa )F1 =(4.200)F2(4.201)F3−3F4 = 1 − 1.6 × 10

2

(Ta − 298.15)(4.202)(4.203)where the dimensionless term f represents the incoming photosynthetically active radiation on the foliage,
normalized by a species-dependent threshold value:f = 0.55

RG 2
RGl LAI(4.204)Moreover, γ is a species-dependent parameter (see Jacquemin and Noilhan (1990)) and Rsmax is arbitrarily
set to 5000 sm−1 .
SURFEX v8.1 - Issue no 3 - 2018

152
The surface fluxes of heat, moisture, and momentum can be expressed as(w′ θ ′ )s =(w′ rv′ )s =Hρa cp Ta /θaEρa (1 − qa )(4.205)(4.206)|w′ V ′ |s = CD |Va |2 = u2∗(4.207)

where rv is the water vapor mixing ratio, w is the vertical motion, θa is the potential temperature at thelowest atmospheric level. The primes and overbars denote perturbation and average quantities.
For the drag coefficients CH and CD , the formulation of Louis (1979) was modified in order to consider
different roughness length values for heat z0 and momentum z0h (Mascart et al. (1995)):
CD = CDN Fm(4.208)CH = CDN Fh(4.209)

with
CDN =

k2
[ln (z/z0 )]2(4.210)where k is the Von Karmann constant. Also
Fm = 1 −
Fm =

10Ri
p
1 + Cm |Ri|
1

1 + √10Ri
1+5Ri

if Ri ≤ 0

(4.211)

if Ri > 0

(4.212)and# ln(z/z0 )15Rip×Fh = 1 −ln(z/z0h )1 + Ch |Ri|1ln(z/z0 )√Fh =×ln(z/z0h )1 + 15Ri 1 + 5Ri"

if Ri ≤ 0

(4.213)

if Ri > 0

(4.214)

where Ri is the gradient Richardson number. The coefficients Cm and Ch of the unstable case are given by
Cm = 10Cm ∗ CDN (z/z0 )pm
Ch(4.215)ln(z/z0 )= 15Ch ∗ CDN (z/z0h )ph ×
ln(z/z0h )

(4.216)∗ , C ∗ , p , and p are functions of the ratio µ = ln(z /z ) only:
where Cm
0 0h
h
h m

Ch∗ = 3.2165 + 4.3431 × µ + 0.5360 × µ2 − 0.0781 × µ3

(4.217)∗Cm= 6.8741 + 2.6933 × µ − 0.3601 × µ2 + 0.0154 × µ3

(4.218)3(4.219)pm = 0.5233 − 0.0815 × µ + 0.0135 × µ2 − 0.0010 × µ3

(4.220)2

ph = 0.5802 − 0.1571 × µ + 0.0327 × µ − 0.0026 × µ
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

153

4.1.9 ISBA-Multi-Energy-Budget (MEB) Explicit Vegetation
ISBA includes an option to represent forests (using the corresponding patches) using the Multi-EnergyBudget (ISBA-MEB) explicit vegetation scheme (Boone et al., 2017; Napoly et al., 2017) . MEB is basedon the classic two-source model for snow-free conditions which considers explicit energy budgets (for computing fluxes and effective surface temperatures) for the soil and the vegetation, and it has been extended toa three-source model in order to include an explicit representation of snowpack processes and their interactions with the ground and the vegetation. The vegetation canopy is represented using the so-called big-leaf
method which lumps the entire vegetation canopy into a single effective leaf for computing energy budgets and the associated fluxes of heat, moisture and momentum. One of the first examples of a two-source
model designed for atmospheric model studies is Deardorff (1978), and further refinements to the vegetation
canopy processes were added in the years that followed leading to fairly sophisticated schemes which aresimilar to those used today (e.g. Sellers et al., 1986) . The two-source big-leaf approach (e.g. Braud et al.,1995) has been used extensively within coupled regional and global scale land-atmosphere models (Xue etal., 1991; Sellers et al., 1996; Dickinson et al., 1998; Lawrence et al., 2011; Saluelsson et al., 2011) . Somekey features of MEB compared to the default ISBA treatment of forests are:• seperate ground (surface) and vegetation canopy energy budgets. This is in contrast to the single
composite soil-vegetation energy budget in ISBA. This permits the estimation of a more realistic
surface radiative temperature, and surface flux partitioning.
• a snow fraction which can gradually bury the vegetation vertically thereby transitioning the turbulence and radiative coupling from the snow to the canopy air space to that between the snow and theatmosphere. Note that this differs from the notion of the vegetation snow cover fraction, pnv , of the
ISBA composite scheme.
• the detailed solar radiation transfer scheme which is a multi-layer model that considers two spectral
bands, direct and diffuse flux components and the concept of sunlit and shaded leaves Carrer et al.
(2013). It is used when ISBA-Ags is active: for MEB it is always used.
• a detailed treatment of canopy snow interception and unloading processes and a coupling with the
ISBA physically-based multi-layer snow scheme.
• an explicit forest litter layer model (which also acts as the below-canopy surface energy budget when
litter covers the soil)• seperate ground surface and vegetation surface properties (roughness lengths, albedo, emissivity...).
Note that the composite surface notion of veg is dropped in MEB.
All of the energy budgets are numerically implicitly coupled with each other and with the atmosphere using
the coupling method adapted from Best et al. (2004) which was first proposed by Polcher et al. (1998) .
Currently, forests make up 8 patches for the 19-class option, and three for the 12-class option. ISBA-MEB(referred to hereafter simply as MEB) option can be activated for any number of the forest patches. By
default, MEB is coupled to the multi-layer soil (DF) (Boone et al., 2000; Decharme et al., 2011) , andsnow (ES) schemes (Boone et al., 2001; Decharme et al., 2016) . MEB can also be coupled to the simple 3layer soil Force-Restore (3-L) option (Boone et al., 1999) in order to be compatible with certain applications
which have historically used 3-L, but by default, it is coupled with DF since the objective is to move towards
a less conceptual (more explicit process-based) LSM.
SURFEX v8.1 - Issue no 3 - 2018

154
A schematic diagram for a maximum illustrating the various resistance pathways for the turbulent fluxes
for the three fully (implicitly) coupled surface energy budgets is shown in Fig. 4.17. The water budget
prognostic variables are also indicated. There are six aerodynamic resistance, Ra (m s−1 ), pathways which
are indicated in red and defined as being between; i) the non-snow buried vegetation canopy and the canopy
air, Ra vg−c , ii) the non-snow buried ground surface (soil or litter) and the canopy air, Ra g−c , iii) the snow
surface and the canopy air, Ra n−c , iv) the ground-based snow-covered part of the canopy and the canopy air,Ra vn−c , v) the canopy air with the overlying atmosphere, Ra c−a ), and vi) the ground-based snow surface(directly) with the overlying atmosphere, Ra n−a . Previous papers describing ISBA (Noilhan and Planton,
1989; Noilhan and Mahfouf, 1996) expressed heat fluxes using a dimensionless heat and mass exchange
coefficient, CH : however for the new MEB option, it is more convenient to express the different fluxes
using resistances (s m−1 ) which are related to the exchange coefficient as Ra = 1/ (Va CH ).
The surface energy budgets are formulated in terms of prognostic equations for the temperature evolutionof the bulk vegetation canopy, Tv , the snow-free ground surface (soil or litter), Tg , and the ground-based
snowpack, Tn (K). The prognostic hydrological variables are: the liquid soil volumetric water content, wg(m3 m−3 ), liquid water equivalent volumetric ice content, Wgf (m3 m−3 ), snow water equivalent (SWE),

Ta Va qa
Ran-c

Ran-a

Rac-a

Ravn-c
Wrn

Zhv
pαv
zhvh

Tn,1

Wn,1

Tn,k

Wn,k

k=2,Nn

zg

Tv Wr

qc
Ravg-c Tc Vc
Rag-c

wgf,1 wg,1 Tg,1
wgf,k wg,k Tg,kqg

k=2,Ngpng

1-png

Figure 4.17: A schematic representation of the turbulent aerodynamic resistance, Ra , pathways for ISBAMEB. The prognostic temperature, liquid water, and liquid water equivalent variables are shown. The
canopy air diagnostic variables are enclosed by the red-dashed circle. The ground-based snow pack is
indicated using turquoise, the vegetation canopy is shaded green, and ground layers are colored brown.
Atmospheric variables (lowest atmospheric model or observed reference level) are indicated using the asubscript. The ground snow fraction, png (note, this corresponds to psng in the text), and canopy-snowcover fraction, pnα , are indicated.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

155

Wn , vegetation canopy intercepted liquid water, Wr , and intercepted snow, Wrn (kg m−2 ). The diagnosed
variables which are determined implicitly during the simultaneous solution of the energy budgets are; thesurface specific humidity at saturation for each of the three energy budgets, q (kg kg−1 ), and the canopy
air specific humidity, qc , temperature, Tc and wind speed, Vc (m s−1 ). The surface snow cover fraction
area is represented by psng as in the (baresoil part of the) composite version of ISBA, while the fractionof the canopy buried by the ground-based snowpack is defined as pαn The snowpack has Nn layers, while
the number of soil layers is defined as Ng where k is the vertical index (increasing from 1 at the surface
downward). The ground and snowpack uppermost layer temperatures correspond to those used for thesurface energy budget (i.e. k = 1).
Snow Fractions
The fractional ground coverage by the snowpack, psng , is defined from Eq. 4.3. The suggested value for thecritical snow water equivalent (at which coverage is unity) for MEB is currently Wcrn = 1 (kg m−2 ). Notethat this is considerably lower than the previous value of 10 kg m−2 used in ISBA (Douville et al., 1995) ,but this value has been shown to improve the ground soil temperatures using an explicit snow scheme within
ISBA Brun et al. (2013).
Note that for MEB, the ISBA snow fraction over vegetation, psnv (Eq. 4.1), is not used since it is moreconsistent with a composite surface. The fraction of the vegetation canopy which is buried by ground-basedsnow which is deamed to be more consistent with a forest canopy structure is defined aspnα =(Dn − zhv,b )(zhv − zhv,b )(0 ≤ pnα ≤ 1)

(4.221)

where Dn is the total ground-based snowpack depth (m), and zhvb represents the base of the vegetation
canopy (m) (see Fig. 4.18) which is currently defined aszhvb = ahv (zhv − zhv,min )(zhvb ≥ 0)

(4.222)where ahv = 0.2 and the effective canopy base height is set to zhv,min = 2 (m) for forests. The foliage
distribution should be reconsidered in further development since literature suggests (e.g. Massman, 1982),
that the foliage is not symmetrically distributed in the crown but skewed upward.
Energy Budget
The coupled energy budget equations for a three-source model can be expressed for a single bulk canopy, aground-based snowpack and a underlying ground surface as∂Tv=Rn v − Hv − LEv + Lf Φv(4.223)∂t∂Tg,1= (1 − psng ) (Rn g − Hg − LEg ) + psng (Ggn + τn,Nn SWn n ) − Gg,1 + Lf Φg,1 (4.224)
Cg,1
∂t
∂Tn,1
Cn,1
=Rn n − Hn − LEn − τn,1 SWn n + ξn,1 − Gn,1 + Lf Φn,1
(4.225)∂tCv

where Tg,1 is the uppermost ground (surface soil or litter layer) temperature, Tn,1 is the surface snow temperature, and Tv is the bulk-canopy temperature (K). Note that the subscript 1 indicates the uppermost layeror the base of the layer (for fluxes) for the soil and snowpack. The ground-based snow fraction is definedas psng . Note that the terms of Eq. 4.224 are multiplied by psng to make them patch-relative (or grid-box
relative in the case of single-patch mode) since the snow can potentially cover only part of the patch. Within
SURFEX v8.1 - Issue no 3 - 2018

156
the snow module itself, the notion of psng is not used (the computations are snow-relative). But note thatwhen simultaneously solving the coupled equations Eq.s 4.223-4.225, Eq. 4.225 must be multiplied by psng
since snow only covers a fraction of the area to make the snow patch-relative: further details are given in
Section 4.1.13.
The phase change terms (freezing less melting: expressed in kg m−2 s−1 ) terms for the snow water equivalent intercepted by the vegetation canopy, the uppermost ground layer, and the uppermost snowpack layer
are represented by Φv , Φg,1 and Φn,1 , respectively. Lf represents the latent heat of fusion (J kg−1 ). The
computation of Φg,1 uses the Gibbs free-energy method (also note that Φg,1 = Φf,1 − Φm,1 : see Section 4.1.3), Φn,1 is based on available liquid for freezing or cold content for freezing (see Section 4.1.7) andΦv is described herein (see Eq. 4.339). Note that all of the phase change terms are computed as adjustments
to the surface temperatures (after the fluxes have been computed), therefore only the energy storage terms(and not the fluxes) are modified directly by phase changes for each model time step. The last term on the
RHS of Eq. 4.225, ξn,1 , represents the effective heating or cooling of a snowpack layer caused by exchanges
in enthalpy between the surface and sub-surface model layers when the vertical grid is reset (the snow model
grid layer thicknesses vary in time).
The surface ground, snow, and vegetation effective heat capacities, Cg,1 , Cv and Cn,1 (J m−2 K−1 ) aredefined, respectively, as
Cg,1 =∆zg,1 cg,1(4.226)

Cn,1 =Dn,1 cn,1

(4.228)

Cv =Cvb + Ci Wr,n + Cw Wr(4.227)

where Ci and Cw are the specific heat capacities for solid (2.106 × 103 J kg−1 K−1 ) and liquid water(4.218 × 103 J kg−1 K−1 ), respectively. The uppermost ground layer thickness is ∆zg,1 (m), and thecorresponding heat capacity of this layer is defined as cg 1 (J m−3 K−1 ). There are two options for modelingthe thermal properties of the uppermost ground layer. First, they (cg 1 and λg 1 ) can be defined using thedefault ISBA configuration for a soil layer with parameters based on soil texture properties which can also
incorporate the thermal effects of soil organics (Decharme et al., 2016): see Section 4.3.3. The second
option, which is the default when using MEB, is to model the uppermost ground layer as forest litter. This

a)

b)

c)

Rac−a
Ran−c
Ravg−cRac−aRan−c
Ravg−cRag−cRavn−c

Rag−c

psng

d)

Ran−a

Rac−a

Ran−a

Ran−a

Ravg−c

zhv
pnα
zhvb

Rag−c

psng

psng

psng

Figure 4.18: A schematic sketch illustrating the role of pnα , the fraction of the vegetation canopy which isburied by ground-based snow. In panel a), the snow is well below the canopy base, zhvb , resulting in pnα = 0
and the snow has no direct energy exchange with the atmosphere. In panel b), the canopy is partly buried
by snow (0 < pnα < 1) and the snow has energy exchanges with both the canopy air and the atmosphere.
In panel c), the canopy is fully buried by snow (pnα = 1) and the snow has energy exchange only with theatmosphere while the soil and canopy only exchange with the canopy air space (psng < 1). Finally, in paneld), both psng = 1 and pnα = 1, so that the only exchanges are between the snow and the atmosphere.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

157

means using values of c, λ and ∆z which correspond to litter to compute C in Eq. 4.226 (Napoly et al.,2017): see Section 4.1.9 for details.
The canopy is characterized by low heat capacity which means that its temperature responds fast to changes
in fluxes. Thus, to realistically simulate diurnal variations in 2-meter temperature this effect must be accounted for. Sellers et al. (1986) defined the value as being the heat capacity of 0.2 kg m−2 of water per
unit leaf area index (LAI: m2 m−2 ). This results in values on the order of 1 × 104 J m−2 K−1 for forest
canopies in general. For local scale simulations, Cvb can be defined based on observational data. In spatiallydistributed simulations (or when observational data is insufficient), Cvb = 0.2/CV,ref where the vegetation
thermal inertia, CV,ref is defined as a function of vegetation class by the SURFEX default physiographic
database ECOCLIMAP (Faroux et al. , 2013). Note that CV has been determined for the composite soilvegetation scheme, so the factor 0.2 is used to reduce this value to be more representative of vegetation andon the order of the value discussed by Sellers et al. (1986). Numerical tests have shown that using this value,
the canopy heat storage is on the order of 10 W m−2 at mid-day for a typical mid-latitude summer day for a
forest. The minimum vegetation heat capacity value is limited at 1× 104 (J m−2 K−1 ) in order to model, in arather simple fashion, the thermal inertia of stems, branches, trunks, etc. The contributions from interceptedsnow and rain are incorporated, where Wr,n and Wr (kg m−2 ) represent the equivalent liquid water content
of intercepted canopy snow and liquid water, respectively. The uppermost snow layer thickness is Dn,1(m), and the corresponding heat capacity is represented by cn,1 (see Section 4.1.7 for details on the explicit
snow scheme variables). The numerical solution of the surface energy budget, sub-surface soil and snow
temperatures, and the implicit numerical coupling with the atmosphere is described in Appendix 4.1.13.
Turbulent fluxes
In this section, the turbulent heat and water vapor fluxes in Eq.s 4.223-4.225 are described.
The MEB sensible heat fluxes are defined as(Tv − Tc )Ra v−c(Tg − Tc )Hg =ρaRa g−c(Tn − Ta )(Tn − Tc )+ pnα
Hn =ρa (1 − pnα )Ra n−cRa n−a(Tc − Ta )Hc =ρaR a c−a
(Tc − Ta )(Tn − Ta )H =ρa (1 − pnα psng )+ pnα psng
Ra c−aRa n−aHv =ρa(4.229)(4.230)(4.231)(4.232)(4.233)where ρa represents the lowest atmospheric layer average air density (kg m−3 ). The fluxes between the
canopy air space and the vegetation, Hv , the snow-free ground, Hg , and the ground-based snowpack, Hn ,appear in the surface energy budget equations (Eq.s4.223-4.225). The sensible heat flux from the groundbased snowpack (Eq. 4.231) is partitioned by the fraction of the vegetation which is buried by the groundbased snowpack, pnα , between an exchange between the canopy air space, and the overlying atmosphere(Eq. 4.221). The heat flux between the overlaying atmosphere and the canopy air space is represented by Hc ,and it is equivalent to the sum of the fluxes between the different energy budgets and the canopy air space.
The total flux exchange between the overlying atmosphere and the surface (as seen by the atmosphere) isdefined by H. It is comprised of two components: the heat exchange between the overlying atmosphereand the canopy air space and the part of the ground-based snowpack which is burying the vegetation. The
SURFEX v8.1 - Issue no 3 - 2018

158
ground-based snowpack heat flux, Hn (Eq. 4.231), can be split into a part which modulates the heat exchangewith the canopy air space, Hn−c and the other part which controls the exchanges directly with the overlying
atmosphere, Hn−a, defined as(Tn − Tc )Ra n−c(Tn − Ta )Hn−a =ρa
Ra n−aHn−c =ρa(4.234)(4.235)

Tc is diagnosed by imposing conservation of the heat fluxes between the surface and the canopy air (Asdescribed in Appendix 4.1.13). Using the definition in Eq. 4.235, the total sensible heat flux exchange withthe atmosphere (Eq. 4.233) can also be written in more compact form as
H = ρa [(1 − psng pnα ) Hc + psng pnα Hn−a ](4.236)

Finally, the final fluxes for the given patch are aggregated using psng and pnα .
The total canopy aerodynamic resistance is comprised of snow-buried, Ra vn−c , and non-snow buried,
Ra vg−c , resistances from(1 − psng ) −1
(1 − pnα ) psng+
(4.237)Ra v−c =Ra vn−c
Ra vg−c
The separation of the resistances is done to mainly account for differences in the roughness length between
the buried and non-covered parts of the vegetation canopy, so the primary effect of snow cover is to increase
the resistance relative to a snow-free surface assuming the same temperature gradient owing to a lower
surface roughness, thus Ra vn−c ≥ Ra vg−c . The formulation also provides a continuous transition to thecase of vanishing canopy turbulent fluxes as the canopy becomes entirely buried (as pnα → 1). In this case,the energy budget equations collapse into a simple coupling between the snow surface and the overlying
atmosphere, and the ground energy budget is simply consists in heat conduction between the ground surface
and the snowpack base. The formulations of the resistances between the different surfaces and the canopy
airspace and the overlying atmosphere are described in detail in Sect. 4.1.9. The canopy air temperature,
which is needed by different physics routines, is diagnosed by combining Eq. s4.229-4.233 and solving for
Tc and using Eq. 4.238 to determine Tc (see Eq. 4.401).
The thermodynamic variable (T : J kg−1 ) is linearly related to temperature as
Tx = Bx + Ax Tx(4.238)where x corresponds to one of the three surface temperatures, canopy air temperature, Tc , or the overlying
atmospheric temperature, Ta . The definitions of Ax and Bx depend on the atmospheric variable in the
turbulent diffusion scheme and are usually defined to cast T in the form of dry static energy, or potential
temperature and are determined by the atmospheric model in coupled mode. If potential temperature is usedas the thermodynamic variable in the coupled model diffusion scheme, then the thermodynamic variable
coefficients are defined as
Bx =0

Ax =Cp /Πs(x = v, g, n, c, a)(4.239)(x = v, g, n, c)(4.240)Aa =Cp /Πa
SURFEX v8.1 - Issue no 3 - 2018(4.241)CHAPTER 4. SOIL AND VEGETATION

159

where Π is the non-dimensional Exner function and Cp is the heat capacity of dry air (J kg−1 K−1 ). If theatmospheric variable being diffused is dry static energy thenBx =0

(x = v, g, n, c)

Ax =Cp(x = v, g, n, c, a)

Ba =g za

(4.242)(4.243)(4.244)

where za is the height (m) of the simulated or observed overlying atmospheric temperature, Ta and g is thegravitational constant. The choice of the atmospheric thermodynamic variable is transparent to ISBA-MEB(it is made within the surface-atmosphere coupler). The default (in offline mode and in in-line mode withcertain atmospheric models) is using Eq.s 4.239-4.241. Note that the method can be extended to use theactual air heat capacity (including water vapor) if a linearization of the heat capacity is used.
The MEB water vapor fluxes are expressed as(qsat v − qc )Ra v−c(qg − qc )Eg =ρaRa g−c(qsati n − qa )(qsati n − qc )+ pnα
En =ρa hsn (1 − pnα )Ra n−cRa n−a(qc − qa )Ec =ρaR a c−a(qsati n − qa )(qc − qa )+ pnα psng hsn
E =ρa (1 − pnα psng )Ra c−aRa n−aEv =ρa hsv(4.245)(4.246)(4.247)(4.248)(4.249)where, in an analogous fashion to the sensible heat flux, the vapor flux between the canopy air space andthe vegetation canopy, Ev , the snow-free ground, Eg , and the ground-based snowpack, En , correspondto the fluxes in the surface energy budgets (Eq.s 4.223-4.225). The vapor flux between the canopy air
and the overlying atmosphere is represented by Ec , and the total vapor flux exchanged with the overlying
atmosphere is defined as E. The specific humidity (kg kg−1 ) of the overlying atmosphere is represented by
qa , while qsat and qsati represent the specific humidity at saturation over liquid water and ice, respectively.
For the surface specific humidities at saturation, the convention qsat x = qsat (Tx ) is used. The canopy air
specific humidity, qc , is diagnosed assuming that Ec is balanced by the vapor fluxes between the canopy air
and each of the three surfaces considered (the methodology for diagnosing the canopy air thermal properties
is described in Appendix 4.1.13, Section 4.1.13). The effective ground specific humidity is defined as
qg = hsg qsat g + (1 + ha ) qc
where the so-called humidity factors are defined as
 
 
Ls
Lv
+ δgf hugf δi
hsg =δg hug (1 − δi )
L
L
 
 
Lv
Ls
ha =δg (1 − δi )+ δgf δi
L
L

(4.250)(4.251)(4.252)

The fraction of the surface layer which is frozen, δi , is simply defined as the ratio of the liquid waterequivalent ice content to the total water content (Eq. 4.193).
The latent heats of sublimation and vaporization are defined as Ls and Lv (J kg−1 ), respectively. The
average latent heat, L, is essentially a normalization factor which ranges between Ls and Lv as a function
SURFEX v8.1 - Issue no 3 - 2018

160
of snow cover and surface soil ice. It could be determined in a number of ways. This coefficient ensuresconservation of mass between the different surfaces and the atmosphere. One possible method is to diagnose
it by inverting the equation for LEc (multiplying Eq. 4.403 by L thereby eliminating it from the RHS of thisequation, and then solving for L), but the resulting equation is difficult to apply since the terms can be either
positive or negative, and division by a small number is possible. Here, a more smooth (in time) function is
proposed which accounts for each of the surfaces weighted by it’s respective fraction:aLs Ls + aLv Lv(4.253)L=
aLs + aLv
where
aLv = [σf LW (1 − pnv ) + (1 − psng ) (1 − δi )] (1 − psng pnα )aLs = [σf LW pnv + (1 − psng ) δi + psng ] (1 − psng pnα ) + psng pnα(4.254a)(4.254b)

In the limit as the snow totally buries the canopy vegetation, L → Ls . In contrast, for snow and surface ice
free conditions, L = Lv . σf LW is a normalized non-dimensional coefficient related to vegetation density(see Eq. 4.298).
The soil coefficient δg in Eq.s 4.251-4.252 is defined as
Ra g−cδg =δgcor(4.255)Ra g−c + Rg
where the soil resistance, Rg , is defined by Eq. 4.323. Note that the composite version of ISBA did notinclude an explicit soil resistance term, so this also represents a new addition to the model. This term
was found to further improve results for baresoil evaporation within MEB, and it’s inclusion is consistent
with other similar multi-source models (e.g. Xue et al., 1991). The delta function, δgcor , is a numericalcorrection term which is required owing to the linearization of qsat g and is unity unless both hug qsat g < qc
and qsat g > qc , in which case it is set to zero. The surface ground humidity factor is defined using thestandard ISBA formulation from Noilhan and Planton (1989). Note that it would be more accurate to use
qsati in place of qsat for the sublimation of the canopy-intercepted snow and the soil ice in Eq.s 4.245-4.246,
respectively, but this complicates the linearization and this has been neglected for now. The snow factor isdefined as hsn = Ls /L. This factor can be modified so that En includes both sublimation and evaporation(Boone and Etchevers, 2000), but the impact of including a liquid water flux has been found to be negligible
thus for simplicity, only sublimation is accounted for currently.
The leading coefficient for the canopy evapotranspiration is defined as
hsv = (1 − pnv ) hsvg (Lv /L) + pnv hsvn (Ls /L)(4.256)

where pnv is defined by Eq. 4.335). When part of the vegetation canopy is buried (i.e. pnα > 0), a different
roughness and LAI are felt by the canopy air space so that a new resistance is computed over the pnαcovered part of the canopy as is done for sensible heat flux. This is accounted for by definingRa v−cRa v−chvn + (1 − psng )hvg(4.257a)hsvg =psng (1 − pnα )Ra vn−c
Ra vg−cRa v−cRa v−c+ (1 − psng )(4.257b)hsvn =psng (1 − pnα )Ra vn−c
Ra vg−c

The so-called Halstead coefficients in Eq. 4.257a are defined as
Ra vg−chvg =(1 − δ) + δ
Ra vg−c + Rs
Ra vn−c(1 − δ) + δ ,hvn =Ra vn−c + Rsn
SURFEX v8.1 - Issue no 3 - 2018(4.258a)(4.258b)

CHAPTER 4. SOIL AND VEGETATION

161

The stomatal resistance, Rs , can be computed using either the so-called Jarvis method or the more physically
based ISBA-Ag-s method (the current default is AST: see Section 4.2.1). The stomatal resistance for thepartially snow-buried portion defined as
Rsn = Rs / [1 − min (pnα , 1 − Rs /Rs,max )](Rsn ≤ Rs,max )(4.259)so that the effect of coverage by the snowpack is to increase the canopy resistance. Note that when the
canopy is not partially or fully buried by ground based snowpack (pnα = 0) and does not contain any
intercepted snow (pnv = 0), the leading coefficient for the canopy evapotranspiration simplifies to the same
form as the Halstead coefficient from the composite version of ISBA (hv : Eq. 4.196) asRa vg−c(1 − δ) + δ(pnα = 0 and pnv = 0)(4.260)hsv =Ra vg−c + Rs
The fraction of the vegetation covered by water is δ and is described in Sect. 4.1.9.
The evapotranspiration from the vegetation canopy, Ev , is comprised of three components:
Ev = Etr + Er + Ern(4.261)

where the transpiration, evaporation from the canopy liquid water interception store and sublimation fromthe canopy snow interception store are represented by Etr , Er , and Ern , respectively. Using the definitions
in Eq.s 4.256-4.258b, the components of Ev can be expressed as 1
 psng (1 − pnα )1 − psng
Lv+(1 − pnv ) (1 − δ)
(4.262)
Etr = ρa(qsat v − qc )L
Ra vn−c + Rsn
Ra vg−c + Rs psng (1 − pnα )1 − psng
Lv+(1 − pnv ) δ(4.263)(qsat v − qc )Er = ρaL
Ra vn−c
Ra vg−c Lspsng (1 − pnα )1 − psng
Ern = ρa+pnv
(4.264)(qsat v − qc )L
Ra vn−c
Ra vg−c
The complex resistances (bracketed terms in Eq.s 4.262-4.264) arise owing to the inclusion of the effectsof burying the snow canopy by the ground based snowpack. If the ground-based snowpack is not sufficiently deep to bury any of the canopy (pnα = 0), then the bracketed term in Eq. 4.262 simplifies to
1/ (Ra vg−c + Rs ) (note that Ra vg−c = Ra v−c when pnα = 0 from Eq. 4.237), and likewise the bracketed
terms in Eq.s 4.263-4.264 simplify to 1/Ra vg−c . Finally, the partitioning between the vapor fluxes fromintercepted snow and the snow-free canopy reservoir and transpiration is done using pnv .
Using the definitions of qg from Eq. 4.250 together with those for the humidity factors, hsg and ha(Eq.s 4.251 and 4.252, respectively) and the soil coefficient, δg (Eq. 4.255), the bare soil evaporation, Eg ,components can be expressed as


 
δgcor
Lv
(1 − δi )(4.265)(hug qsat g − qc )Egl = ρaL
Ra g + Rg δgf corLs(hugf qsat g − qc )δi(4.266)
Egf = ρaL
Ra g + Rgf
where Eg = Egl + Egf . The delta function, δgf cor , is a numerical correction term which is required owing
to the linearization of qsat g and is unity unless both hugf qsat g < qc and qsat g > qc , in which case it is set
to zero. Note that the ground resistances, Rg and Rgf , are set to zero if the forest litter option is active (thedefault for forests).
SURFEX v8.1 - Issue no 3 - 2018

162
The ground-based snowpack sublimation, En (Eq. 4.247), can be partitioned into a vapor exchange with the
canopy air space, En−c and the overlying atmosphere, En−a , as qsati n − qcLs
(4.267)
En−c = ρaL
Ra n−c Lsqsati n − qa
En−a = ρa(4.268)L
Ra n−aThe corresponding latent heat fluxes can be determined by simply multiplying Eq. 4.262-4.266 by L. Finally,using the definition in Eq. 4.268, the total vapor exchange with the atmosphere (Eq. 4.249) can also be
written in more compact form as
E = ρa [(1 − psng pnα ) Ec + psng pnα En−a ](4.269)Radiative fluxes
The Rn terms in Eq.s 4.223-4.225 represent the surface net radiation terms (longwave and shortwave components):
Rn x = SWnet,x + LWnet,x(4.270)where x = n, g or v. The total net radiation of the surface is
Rn = Rn n + Rn g + Rn v = SW ↓ − SW ↑ + LW ↓ − LW ↑(4.271)

where the total down-welling solar (shortwave) and atmospheric (longwave) radiative fluxes (W m−2 ) at the
top of the canopy or snow surface (in the case snow is burying the vegetation) are represented by SW ↓ andLW ↓, respectively. The total upwelling (towards the atmosphere) shortwave and longwave radiative fluxes,
SW ↑ and LW ↑, respectively, are simply defined as the downward components less the total surface net
radiative fluxes (summed over the three surfaces). The effective total surface albedo and surface radiative
temperature (and emissivity) can then be diagnosed for coupling with the host atmospheric model. The τn
is defined as the solar radiation transmission at the base of a snowpack layer, so that τn,1 SWn n term in
Eq. 4.225 corresponds the amount of shortwave radiation which is not absorbed in the uppermost snowpack
layer. For sufficiently thin snowpack, solar energy penetrating the snow to the underlying ground surface
is expressed as τn,Nn SWn n , where Nn represents the number of modeled snowpack layers (for a deep
snowpack, this term becomes negligible).
The total land surface shortwave energy budget can be shown to satisfy
SW ↓= SWnet g + SWnet v + SWnet n + SW ↑(4.272)where SWnet g , SWnet v , SWnet n represent the net shortwave terms for the ground, vegetation canopy
and the ground-based snowpack. The effective surface albedo (which may be required by the atmosphericradiation scheme or for comparison with satellite-based data etc.) is diagnosed as
αs = SW ↑ /SW ↓(4.273)The distinction between the visible (VIS) and near-infrared (NIR) radiation components is important interms of interactions with the vegetation canopy. The shortwave radiation scheme in ISBA-MEB is describedby Carrer et al. (2013) (hereafter refered to as CEA13 in this section): it is the radiative scheme used for
ISBA-Ags applications for photosynthesis. Note that when using MEB, it is also used for energy budget
computations for increased consistency.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION163

The CEA13 scheme requires the vegetation and surface albedos for 2 spectral bands (visible, V IS, andnear-infrared, N IR) The V IS wavelengths range from approximately 0.3 to 0.7 ×10−6 m, and N IR wavelengths range from approximately 0.7 to 1.4 ×10−6 m. The vegetation albedos, αv,V IS , αv,N IR , and thebaresoil albedos, αg,V IS , αg,N IR , are provided by ECOCLIMAP or prescribed within the namelist file. For
MEB, the snow free surface is either baresoil or litter, which is assumed for now, to have the same albedo
as the soil. MEB is, by default, coupled to the ISBA-ES snow scheme which includes 3 spectral bands
for the snow albedo (V IS, N IR and U V ): the corresponding albedo values for each band are diagnosed
from the prognostic snow age variable as discussed in Decharme et al. (2016). Since CEA13 and therefore
MEB currently only considers 2 spectral bands for the soil and vegetation, the snow albedo components for
the V IS and N IR bands are used within MEB: this can be changed in the future as MEB is more or lesstransparent to this (it would mean updating the CEA13 scheme). The snow V IS band albedo is used as-is,while the snow N IR albedo is simply computed as
αn,N IR =(αn − ωV IS αn,V IS )
ωN IR

(4.274)

where αn is the all-wavelength snow albedo, and the usual spectral weights ωV IS = 0.48 and ωN IR =0.52 are used. The snow albedos are time-varying and are diagnosed at each time step based on a snow
age variable as discussed in Decharme et al. (2016). The effective surface albedo required by CEA13 isrepresented by the aggregatating the snow and baresoil albedo contributions weighted by the ground snow
cover fraction, psng . The effective surface albedo, αgn , components are then defined as
αgn,V IS = psng αn,V IS + (1 − psng ) αg,V IS

αgn,N IR = psng αn,N IR + (1 − psng ) αg,N IR(4.275)(4.276)

CEA13 computes the absortion of the shortwave radiation, SWnet , for the vegetation and soil as
SWnet,v = ωV IS SWnet,v,V IS + ωN IR SWnet,v,N IR(4.277)

SWnet,g = ωV IS SWnet,g,V IS + ωN IR SWnet,g,N IR(4.278)The multi-level transmission computations for direct and diffuse radiation are made, and the sum of theabsorbed radiaton is SWnet v . The details of these computations are given by Carrer et al. (2013).
The effective all-wavelength surface (below-canopy) albedo is defined as
αgn = ωV IS αgn,V IS + ωN IR αgn,N IR(4.279)which upon substitution of Eq.s 4.275-4.276. can also be expressed as
αgn = psng αn + (1 − psng ) αg

(4.280)where the all-wavelength albedo for the snow, αn , and the ground, αg , are computed using the same spectral
weighting. Note that the flooded fraction of the gridbox uses a ground-flooded zone composite energy
budget, so to consider water surfaces the effective snow-free ground would need to be modified to include
the surface water albedo: this will be done in future versions of SURFEX.
The net solar radiation at the surface assumes one reflection from the vegetation back to the ground or snow
surface and is defined as
SWnet n =psng SW ↓ Tr [1 − αn + αgn αv (1 − Tr )] (1 − τn,Nn )SWnet g = (1 − psng ) SW ↓ Tr [1 − αg + αgn αv (1 − Tr )] +psng SW ↓ Tr [1 − αn + αgn αv (1 − Tr )] τn,Nn
SURFEX v8.1 - Issue no 3 - 2018(4.281)(4.282)

164
where Tr (dimensionless: bound between 0 and 1) represents the fraction of the incoming radiation transmitted through the canopy from the multi-level vegetation radiative transfer scheme. It depends strongly on
the vegetation density via the pontentially snow-buried LAIn (see Eq. 4.299). At this point we define theenergy absorbed at the snow surface (see the surface energy budget equations: Eq.s 4.224-4.225) as
SWn n = SW ↓ Tr [1 − αn + αgn αv (1 − Tr )](4.283)Note that the total surface net shortwave energy is obtained by summing Eq.s 4.281 and 4.282 resulting in
simply
SWnet s = SWnet n + SWnet g = SW ↓ Tr 1 − αgn [1 − αv (1 − Tr )](4.284)
If we assume that none of the shortwave radiation arriving at the snow surface is transmitted to the ground(for sufficinetly deep snowpack, which is often the case), Eq.s 4.281-4.282 simply to
SWnet n =psng SW ↓ Tr [1 − αn + αgn αv (1 − Tr )] = psng SWn n

SWnet g = (1 − psng ) SW ↓ Tr [1 − αg + αgn αv (1 − Tr )](4.285)(4.286)Note that for snow-free conditions, SWnet n = 0, αgn = αg , and αv = αv , and so that
SWnet g = SW ↓ Tr 1 − αg [1 − αv (1 − Tr )](4.287)

LW ↓= LWnet g + LWnet v + LWnet n + LW ↑(4.288)so in this case, as LAI → 0, Tr → 1 so that SWnet g → SW ↓ (1 − αg ) thus the net radiation collapses
in the limit of vanishing vegetation to that of a baresoil patch. If the surface is totally snow covered andthe vegetation is totally buried by snow, then αgn = αn , and the ground net shortwave energy is simply
SWnet g = τn,Nn SW ↓ (1 − αn ) and the surface net shortwave energy is SWnet = SWnet n = SW ↓(1 − αn ) (1 − τn,1 ). Note that the total effective albedo (when averaged over daylight hours) is boundedby the maximum and minimum of the prescribed soil and vegetation and prognostic snow all-wavelength
albedos.
The effective canopy albedo, αv , represents the combined canopy vegetation, αv , and intercepted snow
albedos. Currently, however, we assume that αv = αv which is based on recommendations by (Pomeroy etal., 1996). They showed that multiple reflections and scattering of light from patches of intercepted snow
together with a high probability of reflected light reaching the underside of an overlying branch implied thattrees actually act like light traps. Thus, they concluded that intercepted snow had no significant influence on
the short-wave albedo or the net radiative exchange of Boreal conifer canopies.
In addition to baseline albedo values required by the radiative transfer model for each spectral band, themodel requires the direct and diffusive downwelling solar components. The diffuse fraction can be provided
by observations (offline mode) or a host atmospheric model. For the case when no diffuse information isprovided to the surface model, the diffuse fraction is computed using the method proposed by Erbs et al.
(1982).
The longwave radiation scheme is based on a representation of the vegetation canopy as a plane-parallel
surface. The total land surface longwave energy budget can be shown to satisfy

where LWnet g , LWnet v , LWnet n represent the net longwave terms for the ground, vegetation canopy andthe ground-based snowpack.
The model considers one reflection with three reflecting surfaces (ground, ground-based snowpack and thevegetation canopy: a schematic is shown in Fig. 4.19. The net longwave radiation for the under-story,
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

165

snowpack and vegetation canopy are therefore defined, respectively, as
LWnet g =Cg + Fg + Jg + Jn − Dg − Gg − Ig

(4.289a)

LWnet n =Cn + Fn + Kn + Kg − Dn − Gn − In(4.289b)

LWnet v =Ag + Dg + Gg + Ig + An + Dn + Gn + In
− Bg − Cg − Eg − Hg − 2Fg − Jg − Lg − Kg

(4.289c)− Bn − Cn − En − Hn − 2Fn − Jn − Ln − Kn

where the upwelling longwave radiation is computed from
LW ↑= LW ↓ −LWnet g − LWnet n − LWnet v(4.290)The effective surface radiative temperature (which may be required by the atmospheric radiation scheme orfor comparison with satellite-based data etc.) is diagnosed as
LW ↑ −LW ↓ (1 − ǫs ) 1/4
Trad =
ǫs σ(4.291)

where σ is the Stefan-Boltzmann constant, and ǫs represents the effective surface emissivity. In Eq. 4.291,
there are two knowns (LW fluxes) and two unknowns (Trad and ǫs ). Here we opt to pre-define ǫs in amanner which is consistent with the various surface contributions as
ǫs = psng ǫsn + (1 − psng ) ǫsg(4.292)The canopy-absorption weighted effective snow and ground emissivities are defined, respecitvely, asǫsn =σ n LW ǫv + (1 − σ n LW ) ǫn

(4.293)

ǫsg =σ g LW ǫv + (1 − σ g LW ) ǫg

A

B

Eg En

Hg F

Hn

(4.294)

Lg

Ln

Vegetation

Dg Dn

Gg

Gn

Cg Cn

Jg

Fg Fn
Snow

Soil

Snow

Kg
Ig

In

Jn
Kn

Snow

GroundFigure 4.19: Simple schematic for longwave radiation transfer for one reflection and up to three emitting
surfaces (in addition to the down-welling atmospheric flux). Hollow arrows indicate fluxes after one reflection.
SURFEX v8.1 - Issue no 3 - 2018

166
where ǫv , ǫg and ǫn represent the emissivities of the vegetation, snow-free ground and the ground-based
snowpack, respectively. The ground and vegetation emissivities are given by ECOCLIMAP for spatiallydistributed simulations, or they can be prescribed for local scale studies. The snow emissivity is currently
defined as ǫn = 0.99. The effect of longwave absorption through the non-snow buried part of the vegetation
canopy is included as
σ n LW = [1 − psng − pnα (1 − psng )] σLW + [psng + pnα (1 − psng )] σf LW
σ g LW = [1 − psng (1 − pnα )] σLW + psng (1 − pnα ) σf LW(4.295)(4.296)

where the canopy absorption is defined as
σLW = 1 − exp (−τLW LAI) = 1 − χv

(4.297)and τLW represents a longwave radiation transmission factor which can be species (or land classification)
dependent, and χv is defined as a vegetation view factor. The absorption over the under-story snow-covered
fraction of the grid box is modeled quite simply from Eq. 4.297 as
σf LW = 1 − exp [−τLW LAIn ](4.298)so that transmission is unity (no absorption or reflection by the canopy: σ LW = σf LW = 0) when pnα = 1(i.e. when the canopy has been buried by snow). LAIn is used to represent the LAI which has been reduced
owing to burial by the snowpack and is simply defined as:
LAIn = LAI (1 − pn α )(4.299)From Eq.s 4.292-4.296, it can be seen that when there is no snowpack (i.e. psng = 0 and pnα = 0),then the effective surface emissivity is simply an absorption-weighted soil-vegetation value defined as ǫs =σLW ǫv + (1 − σLW ) ǫg .

The complete expression for the vegetation canopy net longwave radiation with an infinite number of reflections can be expressed as a series expansion (e.g. Braud, 2000) as a function of the temperatures ofthe emitting surfaces (Tv , Tg,1 , Tn,1 ), their respective emissivities (ǫv , ǫg and ǫn ) and the canopy longwave
absorption function, σLW (Eq. 4.297). The MEB expressions are derived by explicitly expanding the series
and assuming one reflection from each emitting source, which is a good approximation since emissivities
are generally close to unity (fluxes from a single reflection are proportional to 1 − ǫx where x represents g,v or n, and ǫ is close to unity for most natural surfaces).

Snow is considered to be intercepted by the vegetation canopy and to accumulate on the ground below.
The canopy-intercepted snow is treated using a composite approach, so that the canopy temperature, Tv ,represents the effective temperature of the canopy-intercepted snow composite. The canopy emissivity istherefore simply defined as
ǫv = (1 − pnv ) ǫv + pnv ǫn(4.300)In order to facilitate the use of a distinct multi-layer snow process scheme, we split the fluxes between those
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

167

interacting with the snowpack and the snow-free ground. The expressions for the snow-free surface are
Ag =LW ↓ (1 − psng )(4.301a)

Bg =Ag σLW (1 − ǫv )(4.301b)

Dg =Cg (1 − ǫg )(4.301d)

Cg =Ag (1 − σLW )′Eg =Dg 1 − σLW′
Fg =σLWσ ǫv Tv4 (1 − psng )Gg =Fg (1 − ǫg )′Hg =Gg 1 − σLWIg =σ ǫg Tg4 (1 − psng )′Jg =Ig σLW(1 − ǫv ) 1 − p′sng′
Kg =Ig σLW(1 − ǫv ) p′sng
′Lg =Ig 1 − σLW
p′sng =psng (1 − pnα )(4.301c)(4.301e)(4.301f)(4.301g)(4.301h)(4.301i)(4.301j)(4.301k)(4.301l)(4.301m)

and the equations for the snow-covered under-story fraction are
An =LW ↓ psng

(4.302a)

Bn =An σf LW (1 − ǫv )(4.302b)

Dn =Cn (1 − ǫn )(4.302d)

Cn =An (1 − σf LW )′En =Dn 1 − σLW(4.302c)(4.302e)Fn =σ f LW σ ǫv Tv4 psng

(4.302f)

Gn =Fn (1 − ǫn )(4.302g)
′
Hn =Gn 1 − σLW
In =σ ǫn Tn4 psng′
Jn =In σLW(1 − ǫv ) 1 − p′′sng′
Kn =In σLW(1 − ǫv ) p′′sng′
Ln =In 1 − σLW
p′′sng =psng + pnα (1 − psng )(4.302h)(4.302i)(4.302j)(4.302k)(4.302l)(4.302m)

where the different terms are again indicated in Fig. 4.19. In MEB, the ground-based snowpack depth canincrease to the point that it buries the canopy, thus for both the snow-covered and snow free under-story
fractions a modified snow fraction is defined as′σLW= 1 − p′sng σLW + p′sng σf LW(4.303)

The factor, σf LW , over the understory snow-covered fraction of the grid box is modeled quite simply from
Eq. 4.298. The inclusion of the snow-buried canopy fraction in Eq.s 4.301m and 4.302m causes all of thevegetation transmission and below canopy fluxes to vanish as psng and pnα → 0 so that the only longwave
radiative exchanges occur between the atmosphere and the snowpack in this limit.
SURFEX v8.1 - Issue no 3 - 2018

168
Heat Conduction fluxes
The heat conduction fluxes in Eq.s 4.224-4.225 are modeled using Fourier’s Law (G = λ∂T /∂z) andhave been defined in previous sections (since MEB uses either the multilayer diffusive or 2 to 3 layer
Force-Restore hydrology/soil configurations, coupled to the explicit multilayer snow scheme ES). The main
potential difference between ISBA and ISBA-MEB is that the heat capacity and thermal conductivity forthe ground depend either on the thermal properties of the soil (possibly including organic content) or on thethermal properties of the forest litter in the uppermost layer (Napoly et al., 2017): this parameterization is
described in more detail in Section 4.1.9.
Aerodynamic Resistances
The resistances between the surface and the overlying atmosphere, Ra n−a and Ra c−a , are based on the values of CH computed from Eq. 4.209 between the overyling atmosphere and the snow surface, and between
the overyling atmosphere and the canopy air space, respectively, where CHx = (Va Ra x−a )−1 .
The aerodynamic resistance between the vegetation canopy and the surrounding airspace can be defined as∗ −1
Ra vg−c = (gav + gav)(4.304)The parameterization of the bulk canopy aerodynamic conductance, gav , between the canopy and the canopy
air is based on Choudhury and Monteith (1988). It is defined as
2 LAI aav  uhv 1/2
gav =[1 − exp(−φ′v /2)].
(4.305)φ′v
lw

where uhv represents the wind speed at the top of the canopy (m s−1 ), LAI is the leaf area index (m2 m−2 ),and the remaining parameters are defined in Table ??. The conductance accounting for the free convection
correction from Sellers et al. (1986) is expressed as" #LAI Tv − Tc 1/4∗(Tv ≥ Tc )(4.306)
gav =
890
lw

Note that this correction is only used for unstable conditions. The effect of snow burying the vegetation
impacts the aerodynamic resistance of the canopy is simply modeled by modifying the LAI to obtain LAIn
using Eq. 4.299. The LAIn is used in Eq. 4.304 to compute Ra vn−c , and this resistance is limited to 5000 s
m−1 as LAIn → 0.
The resistance between the ground and the canopy air space is defined as
Rag−c = Rag n /ψH(4.307)

where Rag n is the default resistance value for neutral conditions. The stability correction term, ψH , depends
on the canopy structural parameters, wind speed and temperature gradient between the surface and the
canopy air. The aerodynamic resistance is also based on Choudhury and Monteith (1988). It is assumed thatthe eddy diffusivity, K (m2 s−1 ), in the vegetation layer follows an exponential profile: z
K (z) = K (zhv ) exp φv 1 −(4.308)zhv
where zhv represents the canopy height. Integrating the reciprocal of the diffusivity defined in Eq. 4.308
from z0g to d + z0v yields
(
 

 
 )
z0g
zhv
d + z0v
exp φv 1 −(4.309)Rag n =
− exp φv 1 −φv K (zhv )zhv
zhv
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION169

The diffusivity at the canopy top is defined as
K (zhv ) = k u∗hv (zhv − d)(4.310)The von Karman constant, k, has a value of 0.4. The displacement height is defined as (Choudhury andMonteith, 1988)hid = 1.1 zhv ln 1 + (cd LAIf )1/4
(4.311)
where the leaf drag coefficient, cd , is defined from Sellers et al. (1996):



1.6
1
2
+ 0.45cd = 1.328(1 − χL )π
Re 1/2(4.312)

χL represents the Ross-Goudriaan leaf angle distribution function, which has been estimated according toMonteith (1975) (see Table 4.6), and Re is the Reynolds number defined as
Re =

ul lw
.
υ

(4.313)

The friction velocity at the top of the vegetation canopy is defined as
k uhv
ln [(zhv − d) /z0v ](4.314)uhv = fhv Va(4.315)u∗hv =
where the wind speed at the top of the canopy is

and Va represents the wind speed at the reference height, za , above the canopy. The canopy height is defined
based on vegetation class and climate within ECOCLIMAP as a primary parameter. It can also be definedusing an external dataset, such as from a satellite-derived product (as a function of space and time). The
vegetation roughness length for momentum is then computed as a secondary parameter as a function of thevegetation canopy height. The factor fhv (≤ 1) is a stability dependent adjustment factor taken from the
RCA LSM (Samuelsson et al., 2006; Samuelsson et al., 2011). They are defined as(√(Cv,N + Cv,S ) CD /k if Ri > 0√
fhv =(Cv,N + Cv,U ) CD /k if Ri ≤ 0
where the Richardson number, Ri , is defined in Eq. 4.321. The coefficients are defined as
(



)
k
Cv,N =ln 1 + φz exp √
−1
CDN


k
k
−√
Cv,S = − φz √
CDN
CD
(

)


k
k
−√
−1
Cv,U = − ln 1 + φz exp √CDN
CD(4.316)(4.317)(4.318)where the drag coefficient, CD , and the drag coefficient for neutral conditions, CDN , are computed between
the canopy air space and the free atmosphere above using the standard ISBA surface layer transfer functions(Eq. 4.208 and Eq. 4.210, respectively).
The dimensionless height scaling factor is defined asφz =(zhv − d)zr(φz ≤ 1)SURFEX v8.1 - Issue no 3 - 2018(4.319)

170
The reference height is defined as zr = za − d for simulations where the reference height is sufficiently
above the top of the vegetation canopy. This is usually the case for local scale studies using observation
data. When MEB is coupled to an atmospheric model, however, the lowest model level can be below the
canopy height, so for coupled model simulations zr = max (za , zhv − d + zmin ) where zmin = 2 (m).
Finally, the stability correction factor from Eq. 4.307 is defined asψH = (1 − ahv Ri )1/2==

1

1 + b Ri (1 + c Ri )
fz0

1/2



1+



Ri
Ri,crit(fz0 − 1)(Ri ≤ 0)(4.320a)(Ri > 0 and Ri ≤ Ri,crit )(4.320b)(Ri > Ri,crit)(4.320c)

1 + b Ri (1 + c Ri )1/2

where the Richardson number is defined asRi =−g zhv (Ts − Tc )Ts uhv 2(4.321)

Note that strictly speaking, the temperature factor in the denominator should be defined as (Ts + Tc ) /2, but
this has only a minor impact for our purposes. The so-called critical Richardson number, Ri,crit , is set to0.2. This parameter has been defined assuming that some turbulent exchange is likely always present (even
if intermittent), but it is recognized that eventually a more robust approach should be developed for very
stable surface layers. The expression for unstable conditions (Eq. 4.320a) is from Sellers et al. (1996) where
the structural parameter is defined as ahv = 9.
It is generally accepted that there is a need to improve the parameterization of the exchange coefficient for
extremely stable conditions typically encountered over snow (e.g.s Niu and Yang, 2004; Andreadis et al.,2009) . Since the goal here is not to develop a new parameterization, we simply modify the expression
for stable conditions by using the standard function from ISBA. The standard ISBA stability correction forstable conditions is given by Eq. 4.320c where b = 15 and c = 5. The factor which takes into accountdiffering roughness lengths for heat and momentum is defined asfz0 =ln (zhv /z0g )ln (zhv /z0gh )(4.322)where z0gh is the ground roughness length for scalars. The weighting function (i.e. ratio of Ri to Ri,crit ) in
Eq. 4.320b is used in order to avoid a discontinuity at Ri = 0 (the roughness length factor effect vanishes
at Ri = 0) in Eq. 4.320c. An example of Eq. 4.320c is shown in Fig. 4.20 using the z0g from Table ??, andfor z0gh /z0g of 0.1 and 1.0. Finally, the resistance between the ground-based snowpack, Ra n−c , and the
canopy air use the same expressions as for the aerodynamic resistance between the ground and the canopy
air outlined herein, but with the surface properties of the snowpack (namely the roughness length and snow
surface temperature).
Ground resistance
The soil resistance term is defined based on Sellers et al. (1992) as
Rg = exp [aRg − bRg (wg /w sat )] .

(4.323)The coefficients are aRg = 8.206 and bRg = 4.255, and the vertically averaged volumetric water content
and saturated volumetric water content are given by w g and w sat , respectively. The averaging is done from
one to several upper layers. Indeed, the inclusion of an explicit ground surface energy budget makes it
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

171

more conceptually straightforward to include a ground resistance compared to the original composite soilvegetation surface. The ground resistance is often used as a surrogate for an additional resistance arising
due to a forest litter layer, therefore the soil resistance is set to zero when the litter layer option is activated.
Finally, the coefficients aRg and bRg were determined from a case study for a specific location, and could
possibly be location dependent. But currently these values are used, in part, since the litter formulation isthe default configuration for MEB for forests as it generally gives better surface fluxes (Napoly et al., 2017).
Water Budget
The governing equations for (water) mass for the bulk canopy, and surface snow and ground layers are
written as∂Wr=Prv + max (0, −Etr ) − Er − Drv − Φv∂t∂Wr n=In − Un − Ern + Φv
∂t
∂Wn,1
psng
=Ps − In + Un + psng (Pr − Prv + Drv − Fnl,1 − En + Φn,1 + ξnl,1 )∂t∂wg,1ρw ∆zg,1= (Pr − Prv + Drv − Eg ) (1 − psng ) + psng Fnl,Nn − R0 − Fg,1 − Φg,1∂t
∂wgf,1ρw ∆zg,1=Φg,1 − Egf (1 − psng )∂t(4.324)(4.325)(4.326)(4.327)(4.328)3.5
z0/z0h=1z0/z0h=103.0

ψ H (-)

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

0.0
Ri (-)

0.5

Figure 4.20: Stability correction term is shown using the Sellers formulation for Ri ≤ 0 while the function
for stable conditions adapted from ISBA (Ri > 0) for two ratios of z0g /z0gh . The ground surface roughness
length is defined in Table 4.6.
SURFEX v8.1 - Issue no 3 - 2018

172

Table 4.6: Surface vegetation canopy turbulence parameters which are constant.
Symbol
aav
φ′v
lw
φv
z0g
χL
ul
υ

Definition

Unit

canopy conductance scale factor
attenuation coeff. for windleaf width
attenuation coeff. for mom.
roughness of soil surface
Ross-Goudriaan leaf angle dist.
Typical local wind speed
Kinematic viscos. of air

−1/2

ms
m
m
m s−1
m2 s−1

Value

Reference

Comment

0.01
3
0.02
2
0.007
0.12
1
0.15 × 10−4

Choudhury and Monteith (1988)
Choudhury and Monteith (1988)

Eq. 26
p 386

Choudhury and Monteith (1988)

p 386

Monteith (1975)
Sellers et al. (1996)

p 26
Eq. B7

where Wr and Wr n represent the vegetation canopy water stores: intercepted water, and the interceptedsnow and frozen water (all in kg m−2 ), respectively. Wn,1 represents the snow liquid water equivalent(SWE) for the uppermost snow layer of the multi-layer scheme. The soil liquid water and equivalent frozen
water equivalent volumetric water content are defined as wg and wgf , respectively (m3 m−3 ).
The interception reservoir, Wr , is modeled as single layer bucket, with losses represented by evaporation,
Er , and canopy drip, Drv , of liquid water which exceeds a maximum holding capacity (see Sect. 4.1.9
for details). Sources include condensation (negative Er and Etr ) and Prv which represents the intercepted
precipitation. The positive part of Etr is extracted from the sub-surface soil layers as a function of soil
moisture and a prescribed vertical root zone distribution. This equation is the same as that used in ISBA,
except for the addition of the phase change term, Φv (kg m−2 s−1 ). This term has been introduced owing to
the introduction of an explicit canopy snow interception reservoir, Wr n : the canopy snow and liquid water
reservoirs can exchange mass via this term which is modeled as melt less freezing. The remaining rainfall(Pr − Prv ) is partitioned between the snow-free and snow-covered ground surface, where Pr represents thetotal grid-cell rainfall rate. The canopy snow interception is more complex, and represents certain baseline
processes such as snow interception, In , and unloading, Un : see Sect. 4.1.9 for details.
The soil water and snow liquid water vertical fluxes at the base of the surface ground and snow are represented, respectively, by Fg,1 using Darcy’s Law and by Fnl,1 using a tipping-bucket scheme (kg m−2 s−1 ).
The liquid water flux at the base of the snowpack, Fnl,Nn , is directed downward into the soil and consistsin the liquid water in excess of the lowest model liquid water holding capacity. A description of the explicit snow and soil schemes are given in Sections 4.1.7 and 4.1.3, respectively. R0 is the so-called surface
runoff. It accounts for sub-grid heterogeneity of precipitation, soil moisture and for when potential infiltration exceeds a maximum rate: see Sections 4.1.6 and 4.1.2. The soil liquid water equivalent ice content
can have some losses owing to sublimation in the uppermost soil layer, Egf , but it mainly evolves owing tophase changes from soil water freeze-thaw, Φg . The remaining symbols in Eq.s 4.324-4.325 are defined anddescribed in Sections 4.1.9 and 4.1.9.
Snow Interception within the canopy
The intercepted snow mass budget is described by Eq. 4.325, while the energy budget is included as a partof the bulk canopy prognostic equation (Eq. 4.223). The positive mass contributions acting to increaseintercepted snow on canopy are snowfall interception, In , water on canopy that freezes, Φv < 0, andsublimation of water vapor to ice, Ern < 0. Unloading, Un , sublimation, Ern > 0, and snow melt, Φv > 0,
are the sinks. All of the terms are in kg m−2 s−1 . It is assumed that intercepted rain and snow can co-exist
on the canopy. The intercepted snow is assumed to have the same temperature as the canopy, Tv , thus there
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

173

is no advective heat exchange with the atmosphere which simplifies the equations. For simplicity, whenintercepted water on the canopy freezes, it is assumed to become part of the intercepted snow.
The parameterization of interception efficiency is based upon Hedstrom and Pomeroy (1998). It determines
how much snow is intercepted during the time step and is defined as
In,v,0 = (Wr∗n − Wr n ) [1 − exp (−kn,v Ps ∆t)](4.329)where Wr n ∗ is the maximum snow load allowed, Ps the frozen precipitation rate and kn,v a proportionality
factor. kn,v is a function of Wr n ∗ and the maximum plan area of the snow-leaf contact area per unit area ofground, Cn,vp :Cn,vp(4.330)kn,v =Wr n ∗For a closed canopy, Cn,vp would be equal to one, but for a partly open canopy it is described by the
relationship:
Cn,vc(4.331)
Cn,vp =
1 − Cn,vc uhv zhv / (wn Jn )where Cn,vc is the canopy coverage per unit area of ground which can be expressed as 1 − χv where χv isthe sky-view factor (see Eq. 4.297), and uhv represents the mean horizontal wind speed at the canopy top(Eq. 4.315) which corresponds to the height zhv (m). The characteristic vertical snow-flake velocity, wn , isset to 0.8 m s−1 (Isymov, 1971). Jn is set to 103 m which is assumed to represent the typical size of themean forested down wind distance.
For calm conditions and completely vertically falling snowflakes, Cn,vp = Cn,vc . For any existing wind,snow could be intercepted by the surrounding trees so that high wind speed increases interception efficiency.
Generally for open Boreal conifer canopies, Cn,vc < Cn,vp < 1. Under normal wind speed conditions (i.e.
wind speeds larger than 1 m s−1 ), Cn,vc (and Cn,vp ) values are usually close to unity.
The maximum allowed canopy snow load, Wr n ∗ , is a function of the maximum snow load per unit brancharea, Sn,v (kg m−2 ), and the leaf area index:
Wr n ∗ = Sn,v LAI
where Sn,v is defined as
Sn,v = Sn,v



46
0.27 +
ρn,v(4.332)(4.333)Sn,v = 6.3 kg m−2 Based on measurements, Schmidt and Gluns (1991) estimated average values of
6.6Sn,v = 6.3 kg m−2 for pine and 5.9 kg m−2 for spruce trees. Because the average value for this parameter only varies by about 10% across these two fairly common tree species, and ECOCLIMAP does not
currently make a clear distinction between these two forest classes, we currently use 6.3 as the default value
for all forest classes. ρn,v is the canopy snow density (kg m−3 ) defined by the relationship:ρn,v = 67.92 + 51.25 exp [(Tc − Tf ) /2.59](Tc ≤ Tc max )(4.334)

where Tc is the canopy air temperature and Tc max is the temperature corresponding to the maximum snow
density. Assuming a maximum snow density of 750 kg m−3 and solving Eq. 4.334 for canopy temperatureyields Tc max = 279.854 K. This gives values of Sn,v in the range 4-6 kg m−2 .
The water vapor flux between the intercepted canopy snow and the canopy air, Ern (Eq. 4.264), includes
the evaporative efficiency, pnv . This effect was first described by Nakai et al. (1999). In the ISBA-MEB
SURFEX v8.1 - Issue no 3 - 2018

174
parameterization, the formulation is slightly modified so that it approaches zero when there is no interceptedsnow load:
0.89 Snv 0.3
pnv =(4.335)
1 + exp [−4.7(Snv − 0.45)]

where Snv is the ratio of snow-covered area on the canopy to the total canopy area:
Snv =

Wr n
Wr n ∗(0 ≤ Snv ≤ 1)

(4.336)

A numerical test is performed to determine if the canopy snow becomes less than zero within one timestep due to sublimation. If this is true, then the required mass is removed from the underlying snowpack
so that the intercepted snow becomes exactly zero during the time-step to ensure a high degree of massconservation. Note that this adjustment is generally negligible.
The intercepted snow unloading, due to processes such as wind and branch bending, has to be estimated.
Hedstrom and Pomeroy (1998) suggest an experimentally verified exponential decay in load over time, t,
which is used in the parameterization;
Un,v = In,v,0 exp(−UnL t) = In,v,0 cnL(4.337)

where UnL is an unloading rate coefficient (s−1 ) and cnL the dimensionless unloading coefficient. Hedstrom and Pomeroy (1998) found that cnL = 0.678 was a good approximation which, with a time step of
15 minutes, gives UnL = −4.498 · 10−6 s−1 . A tuned value for the RCA-LSM from the Snow Model
Intercomparison Project phase 2 (SnowMIP2) experiments Rutter et al. (2009) is UnL = −3.4254 × 10−6
s−1 which has been adopted for MEB for now. All unloaded snow is assumed to fall to the ground where
it is added to the snow storage on forest ground. Further, corrections to compensate for changes in theoriginal LSM due to this new parameterization have been made for heat capacity, latent heat of vaporisation,
evapotranspiration, snow storages and fluxes of latent heat.
Finally, canopy snow will partly melt if the temperature rises above the melting point and become intercepted water, where the intercepted (liquid and frozen) water phase change is simply proportional to thetemperature:
Ci W r n
Ci Snv Wr∗nΦv =(Tf − Tv ) =(Tf − Tv )(4.338)
Lf τ Φ
Lf τ Φ
where Φv < 0 signifies melting. Tf represents the melting point temperature (273.15 K) and the characteristic phase change timescale is τΦ (s). If it is assumed that the available heating during the time step forphase change is proportional to canopy biomass via the LAI then Eq. 4.338 can be written (for both melt
and refreezing) as
Φv = Snv kΦv (Tf − Tv )(4.339)Note that if energy is available for melting, the phase change rate is limited by the amount of intercepted
snow, and likewise freezing is limited by the amount of intercepted liquid water. The melting of interceptedsnow within the canopy can be quite complex, thus currently the simple approach in Eq. 4.339 adopted
herein. The phase change coefficient was tuned to a value of kΦv = 5.56 × 10−6 kg m−2 s−1 K−1 for the
SNOWMIP2 experiments with the RCA-LSM. Currently, this value is the default for ISBA-MEB.
Rain Interception within the canopy
The rain intercepted by the vegetation is available for potential evaporation which means that it has a strong
influence on the fluxes of heat and consequently also on the surface temperature. The rate of change of
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

175

intercepted water on vegetation canopy is described by Eq. 4.324. The rate that water is intercepted by theover-story (which is not buried by the ground-based snow) is defined as
Prv = Pr (1 − χv ) (1 − png pαn )(4.340)where χv is a view factor indicating how much of the precipitation that should fall directly to the ground(see Eq. 4.297). The fractional coverage of water within the reservoir is given by Eq. 4.143. The over-story
canopy drip rate, Drv , is defined simply as the value of water in the reservoir which exceeds the maximum
holding capacity
Drv = max (0, Wrv − Wrv,max ) /∆t(4.341)
where the maximum liquid water holding capacity is defined from Eq. 4.146. Note that Eq. 4.324 is firstevaluated with Drv = 0, and then the canopy drip is computed as a residual. Thus, the final water amountis corrected by removing the canopy drip or through-fall. This water can then become a liquid water source
for the soil and the ground-based snowpack.
Halstead Coefficient
In the case of wet vegetation, the total plant evapotranspiration is partitioned between the evaporation of intercepted water, and transpiration via stomata by the so-called Halstead coefficient. In MEB, two such coefficients are used for the non-snow buried and buried parts of the vegetation canopy, hvg and hvn (Eq.s 4.258aand 4.258b, respectively). In MEB, the general form of the Halstead coefficient, as defined in Noilhan and
Planton (1989) by Eq. 4.196, is modified by introducing the factor kv to take into account the fact that saturated vegetation can transpire, i.e. when δv = 1 (Bringfelt et al., 2001). Thus for MEB, we define δ = kv δv .
The intercepted water forms full spheres just touching the vegetation surface when kv = 0 which allows
full transpiration from the whole leaf surface. In contrast, kv = 1 would represent a situation where a water
film covers the vegetation completely and no transpiration is allowed. To adhere to the interception model
as described above, where the intercepted water exists as droplets, we set the value of kv to 0.25. Note thatin the case of condensation, i.e. E < 0, hv = 1.
Without a limitation of hvg and hvn , the evaporative demand could exceed the available intercepted water
during a time step, especially for the canopy vegetation which experiences a relatively low aerodynamic
resistance. To avoid such a situation, a maximum value of the Halstead coefficient is imposed by calculatinga maximum value of the δv . See Appendix 4.1.13 for details.
Forest Litter
The ground surface in forest regions is generally covered by a litter layer consisting of dead leaves and or
needles, branches, fruit, and other organic material. Some LSMs have introduced parameterizations for litter(e.g.s Gonzalez-Sosa et al., 1999; Ogée and Brunet, 2002; Wilson et al., 2012) , but the approach can be very
different from one to another depending on their complexity. The main goal of this parameterization within
MEB is to account for the generally-accepted first-order energetic and hydrological effects of litter; this layer
is generally accepted to have a strong insulating effect owing to its particular thermal properties (leading toa relatively low thermal diffusivity), it causes a significant reduction of ground evaporation (capillary rise
into this layer is negligible), and it constitutes an interception reservoir for liquid water which can also lose
water by evaporation (Napoly et al., 2017).
Forest litter is represented using a single model layer which generally ranges in thickness from 0.01 to
0.10 m, and in the absence of ancillary data, the default value is 0.03 m. When this option is active, anadditional layer is added to the soil for the thermal and energy budget computations with litter-specific
SURFEX v8.1 - Issue no 3 - 2018

176
thermal properties. This means that the numerical solution method is identical to that in Appendix 4.1.13,
except that litter thermal properties used used for the litter in place of the uppermost soil properties, andthe soil grid is shoft down by 1 level (but keeping the same number of soil layers). In terms of hydrology,
an additional reservoir is added which uses a relatively simple bucket-type scheme with a litter-specificmaximum water storage capacity. The model physics and governing equations are reviewed herein.
Prognostic equations For the litter scheme, two new prognostic equations are added. Currently, it can
only be used with the DF soil scheme option (as the energy budget is solved as part of the soil tri-diagnoal
matrix). The energy budget for the snow-free litter layer can be expressed as:
Cl∂Tl= (Rnl − Hl − LEl ) (1 − psng ) + psng (Ggn + τn,Nn SWn,n ) − Gl + Lf Φl∂t(4.342)where Tl is the litter temperature (K), ∆zl (m) is the thickness of the litter layer, and Cl (J K−1 m−2 ) is theeffective heat capacity of the litter. Rn,l , Hl , LEl , Gl represent the net radiation, sensible heat flux, latent
heat flux and ground conduction flux from the litter layer, respectively. Note that when litter is present,
Rn,l , Hl , LEl correspond to the ground surface fluxes in Sections 4.1.9-4.1.9, and an additional soil layer isadded.
The liquid water content of the litter layer evolves following:∂Wl= (Pr − Prv + Drv − El ) (1 − psng ) + psng Fnl,N n − Dl − Φl∂t

(0 < Wl < Wl,max )(4.343)where El represents the litter evaporation rate, Dl is the drainage rate from the litter to the soil (all in
kg m−2 s−1 ). Thus when litter is present, Dl represents the potential infiltration rate for the soil (before
surface runoff is removed and the actual infiltration into the soil is computed). The remaining flux terms aredefined in Section 4.1.9. The maximum liquid water content in the litter reservoir is defined as Wl,max =wl,max ∆zl ρw (kg m−2 ). The default value for the maximum holding capacity of the litter layer, wl,max , is0.12 m3 m−3 (Putuhena and Cordery, 1996). The liquid water equivalent of ice contained in the litter layer
is governed by:∂Wlf= Φl − Elf(4.344)∂twhere Elf represents the sublimation of ice contained within the litter layer.
Phase Change The phase change rate, Φl (kg m−2 s−1 ), is defined as:
(


)

ρi Ci ∆zl (Tf − Tl )ρi Ci ∆zl (Tl − Tf )1
Φl =, Wlf + (1 − δf ) min, Wlδf minτi
Lf
Lf(4.345)where Lf represents the latent heat of fusion (J kg−1 ), ρi is the density of ice (here defined as 920 kg m−3 ),the freezing point temperature is Tf = 273.15 K, and Ci is the specific heat capacity of ice (2.106 × 103
J K−1 kg−1 ). The delta function δf = 1 if energy is available for melting (i.e. Tl − Tf > 0), otherwise
it is δf = 0. τi is a parameter which represents the characteristic time scale for phase changes: currently
the same value for soil is used for litter (see Section 4.1.2) The updated temperature is first computed from
Eq. 4.342 with Φl = 0, then the phase change is computed as an adjustment to Tl , Wl and Wlf as is done
for the soil.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

177

Energy Fluxes It is assumed that litter below the canopy is spatially homogeneous so that it intercepts allof the incoming radiation. Thus, the net radiation Rnl for the litter layer is the same that for the first soil
layer in MEB:
Rn,g = SWnet g + LWnet g(4.346)Note that currently, the soil emissivity and albedo values are used for the litter for spatially distributed
simulations pending the development of global datasets of these parameters for litter or the developmentof an appropriate model to estimate them. For local scale simulations, the values can be defined based on
observations.
The below-canopy sensible heat flux, Hl (W m−2 ), is computed the same way that for the top soil layer in
the ISBA model as:(Tl − Tc )(4.347)
Hl = ρaRag−cwhere the aerodynamic resistance between the ground and the canopy air space, Rag−c , is defined in
Eq. 4.307. Tl and Tc (J kg−1 ) are thermodynamic variables which are linearly related to temperature and it
is analogous in form to Eq. 4.230. The latent heat flux is partitioned between evaporation and sublimationin the litter layer:
LEl = (1 − plf ) LEl + plf LElf
(4.348)where plf is the fraction of frozen water in the litter layer and[hul qsat (Tl ) − qc ]Rag−c[hulf qsat (Tl ) − qc ]LElf =Ls ρa
Rag−c
LEl =Lv ρa(4.349a)(4.349b)where the specific humidity of the canopy air space is represented by qc . The specific humidity at saturation
over liquid water is represented by qsat (kg kg−1 ). Note, it would be more accurate to use the specific humidity at saturation over ice in Eq. 4.349b, but this complicates the linearization and this effect is neglected
for now (Boone et al., 2017). The surface humidity factors for liquid and frozen water are represented by
hul and hulf , respectively. They are computed as the relative humidity in an analogous fashion as for thesoil following Noihan and Planton (1989):



1
Wl
hul =
1 − cos π(4.350)2
Wl,max
Note that hulf is computed by replacing Wl and Wl,max by the values for the liquid water equivalent ice
content. The maximum liquid holding capacity is modified for ice following Boone et al. (2000).
Finally, the ground conduction flux (W m−2 ) between the litter layer and the underlying soil is computedas:Tl − Tg,1Gl =(4.351)(∆zl /λl ) + (∆zg,1 /λg,1 )where λl and λg,1 are the litter and first soil layer thermal conductivities respectively and ∆zg,1 is the
thickness of the first soil layer.
Water interception and fluxes The water intercepted by the litter layer corresponds to the sum of the rainpassing through the canopy, snow runoff (saturation excess from sufficiently large melt or rainfall), and thedrip from the canopy. Note that for simplicity, a gravitational drainage type formulation is not used for litter,but rather a tipping bucket following Ogée and Brunet (2002) as:
Dl = max (0, Wl − Wl,max )SURFEX v8.1 - Issue no 3 - 2018(4.352)

178
Thermal properties(1963) as:

The litter thermal conductivity, λl (W m−1 K−1 ), is computed according to De Vries
λl = 0.1 + 0.03

Wl
ρw ∆zl(4.353)The effective heat capacity of the litter, Cl (J m−2 K−1 ), is computed using
Cl = ∆zl ρld Cld + Wl Cw + Wlf Ci(4.354)

where the specific heat capacity of liquid water is Cw = 4.218 × 103 (J K−1 kg−1 ). The dry density of
the litter is defined as ρld . Ogée and Brunet (2002) used a value of dry litter density of 45 kg m−3 for apine forest. Meekins and McCarthy (2001) measured a litter density of 46 kg m−3 in a deciduous forest andKostel-Hughes et al. (1998) estimated values varying between 27 to 38 kg m−3 for oak forests. Currently
ECOCLIMAP doesn’t distinguish between different types of deciduous trees, thus by default, ρld is assigned
a value of 45 kg m−3 . As a proxy for the specific heat of litter, we use the specific heat capacity of organic
material from Farouki (1986) which is Cld = 1.926 × 103 J kg−1 K−1 . Currently, constant values for ρld
and Cld are used for spatially distributed applications or on the local scale, unless observational data are
available.
Energy and Mass conservation
The soil and snowpack prognostic temperature equations can be written in flux form for k = 1, Ng soil
layers and k = 1, Nn snow layers as∂Tg,k= Gg,k−1 − Gg,k + Lf Φg,k∂t∂Tn,k= Gn,k−1 − Gn,k + Lf Φn,k + ξn,k−1 − ξn,k + SWnet,n (τn,k−1 − τn,k )
Cn,k
∂t
Cg,k

(4.355)(4.356)

The total energy balance of the vegetation canopy-soil-snowpack system is conserved at each time step, ∆t,and can be obtained by summing the discrete time forms of Eq. 4.223, Eq. 4.355, and Eq. 4.356 for all soil,
snow and the single bulk vegetation layers yielding
Cv ∆Tv h+P Ng

k=1 Cg,k ∆Tg,k + psng

P Nn

k=1 Cn,k ∆Tn,k=∆t (1 − psng ) Gg,0 + psng (Gn,0 + τn,N n SWnet,n + Gn,0 ) + Rn v − Hv−c − LEv−c +

i
P Ng
P n
Φg,k + psng N
Lf Φv + k=1
Φ
k=1 n,k

(4.357)

where ∆Tx = Tx (t+∆t)−Tx (t). Note that Eq. 4.356 has been multiplied by psng to make it patch-relative.
The surface boundary conditions for Eq. 4.223 and Eq. 4.225 are, respectively,
Gg,0 = (1 − pn ) (Rn g − Hg − LEg ) + pn (Ggn + τn,Nn SWn n )(4.358)

τn,0 = 1(4.360)ξn,0 = 0(4.361)

Gn,0 = Rn n − Hn − LEn − Hn − LEn−N(4.359)Eq. 4.360 signifies that the net shortwave radiation at the surface enters the snowpack, and Eq. 4.361 represents the fact that energy changes owing to the time evolving snow grid can only arise in the surface
layer owing to exchanges with the sub-surface layer. Snowfall is assumed to have the same temperature
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION179

as the snowpack, thus a corresponding cooling/heating term does not appear in Eq. 4.359, although thecorresponding mass increase must appear in the snow water budget equation (see Sect. 4.1.9).
The lower boundary conditions for Eq. 4.355 and Eq. 4.356 are, respectively,
Gg,Ng = 0(4.362)

ξn,Nn = 0(4.363)

The appearance of the same discrete form for Φ in both the energy and mass budget equations ensuresenthalpy conservation. Owing to Eq.s 4.361 and 4.363, the total effective heating of the snowpack owing togrid adjustments is
Z DNn
ξn dDn = 0(4.364)0

where DN n represents the total snow depth. Thus this term only represents a contribution from contiguous
snow layers, not from a source external to the snowpack. The energy storage of the snow-soil-vegetation
system is balanced by the net surface radiative and turbulent fluxes and internal phase changes (solid andliquid phases of water substance).
The soil and snowpack prognostic mass equations can be written in flux form for k = 2, Ng w soil layers
and k = 1, Nn snow layers as∂Wn,k=png (Fnl,k−1 − Fnl,k − Φn,k + ξnl,k − ξnl,k−1 )∂t∂wg,k=Fg,k−1 − Fg,k − Φg,k − F2,k max (0, Etr )ρw ∆zg,1∂t∂wgf,kρw ∆zg,1
=Φg,k
∂t
png

(k = 2, Nn )(4.365)(k = 2, Ng w )(4.366)(k = 2, Ng w )(4.367)

The total grid-box water budget at each time step is obtained by summing the budget equations for thesurface layers (Eq.s 4.324-4.328) together with those for the sub-surface layers (Eq.s 4.365-4.367) to have
P Ng w
P Nn
∆W
+
ρ
+
p
∆Wr + ∆W
w
r
n
ng
n,
k
k=1
k=1 ∆zg, k (wg k + wgf k ) =h∆t Pr + Ps − R0 − Fg, Ngw − (1 − png ) Eg − Ev − png En(4.368)i
P Ng
P Nn− Φv − k=1 Φg,k − png k=1 Φn,k

where R0 can simply be a diagnostic or coupled with a river routing scheme. The soil water lower boundary
condition, Fg,Ngw represents the so-called base-flow or drainage leaving the lowest hydrological layer which
can then be transfered as input to a river routing scheme (see references above) or to a ground water scheme.
In such instances, it can be negative if an option to permit a ground water inflow is activated. The soil liquidwater and equivalent frozen water equivalent volumetric water content extend down to layer Ng w , where
Ng w ≤ Ng . Note that the vertical soil water transfer or evolution is not computed below zg (k = Ngw ),whereas heat transfer can be. In order to compute the thermal properties for deep soil temperature (thermal
conductivity and heat capacity for example), soil moisture estimates are needed: values from the soil are
extrapolated downward assuming hydrostatic equilibrium
Note that Eq. 4.365 is snow-relative, therefore this equation must be multiplied by the ground-based snow
fraction, png , to be grid box relative for coupling with the soil and vegetation water storage terms. The
lower boundary condition for liquid water flow, Fnl,Nn , is defined as the liquid water exceeding the lowest
maximum snow layer liquid water holding capacity. ξnl represents the internal mass changes of a snowpack
layer when the vertical grid is reset. When integrated over the entire snowpack depth, this term vanishes(analogous to Eq. 4.364 for the snowpack temperature equation). The coupling of MEB with the interactive
flooding scheme will be the subject of future work.
SURFEX v8.1 - Issue no 3 - 2018

180

4.1.10 Summary of Useful Parameters
The parameters have been chosen in order to characterize the main physical processes, while attempting to
reduce the number of independent variables. They can be divided into two categories: primary parametersneeding to be specified by spatial distribution, and secondary parameters which values can be associatedwith those of the primary parameters.
In the present state of the method, the primary parameters describe the nature of the land surface and its
vegetation coverage by means of only four numerical indices: the percentage of sand and clay in the soil,
the dominant vegetation type, and the land-sea mask.
The secondary parameters associated with the soil type are evaluated from the sand and clay composition of
the soil, according to the continuous formulation discussed in Giordani (1993) and Noilhan and Lacarrère(1995) (see Appendix). These parameters are:• the saturated volumetric moisture content wsat ;• the wilting point volumetric water content wwilt ;• the field capacity volumetric water content wf c ;• the slope b of the retention curve;• the soil thermal coefficient at saturation CGsat ;• the value of C1 at saturation (i.e., C1sat );• the reference value of C2 for w2 = 0.5wsat (i.e., C2ref );• the drainage coefficient C3 ;• the diffusion coefficients C4 ref and C4b ;• and the coefficients a, p for the wgeq formulation.
On the other hand, the parameters associated with the vegetation can either be derived from the dominant
vegetation type, or be specified from existing classification or observations. They are• the fraction of vegetation veg;
• the depth of the soil column d2 (or the root zone depth);• the depth of the soil column d3 (if third soil layer option in use);• the minimum surface resistance Rsmin ;• the leaf area index LAI;
• the heat capacity Cv of the vegetation;• the RGl and γ coefficients found in the formulation of the surface resistance Rs ;• and the roughness length for momentum z0 and for heat z0h .
Other necessary parameters are
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

181• the albedo α• the emissivity ǫ.
• and characteristic time scale for phase changes (currently constant) τi .

4.1.11 Appendix A: Continuous formulation of the soil secondary parameters
Following Giordani (1993), Noilhan and Lacarrère (1995), the sand and clay composition (i.e., SAN D and
CLAY ) are expressed in percentage.
The saturated volumetric water content (m3 m−3 ):wsat = (−1.08SAN D + 494.305) × 10−3

(4.369)The wilting point volumetric water content (m3 m−3 ):wwilt = 37.1342 × 10−3 (CLAY )0.5

(4.370)The field capacity volumetric water content (m3 m−3 ):wf c = 89.0467 × 10−3 (CLAY )0.3496(4.371)The slope of the retention curve:b = 0.137CLAY + 3.501(4.372)The soil thermal coefficient at saturation (Km2 J −1 ):CGsat = −1.557 × 10−2 SAN D − 1.441 × 10−2 CLAY + 4.7021(4.373)The value of C1 at saturation:
C1sat = (5.58CLAY + 84.88) × 10−2

(4.374)The value of C2 for w2 = 0.5wsat :C2ref = 13.815CLAY −0.954(4.375)C3 = 5.327CLAY −1.043(4.376)C4b = 5.14 + 0.115 CLAY

(4.377)The coefficient C3 :The coefficient C4b :The coefficient C4 ref :C4 ref

=

#
"
3
X

2(d3 − d2 )βj SAN D j + αj CLAY j
log10 −1 β0 +(d2 d3 2 )j=1(4.378)where the βj (j = 0, 3) coefficients are 4.42 × 10−0 , 4.88 × 10−3 , 5.93 × 10−4 and −6.09 × 10−6 . The
αj (j = 1, 3) coefficients are defined as −2.57 × 10−1 , 8.86 × 10−3 and −8.13 × 10−5 .
The coefficients for the wgeq formulation:a = 732.42 × 10−3 CLAY −0.539
p = 0.134CLAY + 3.4

SURFEX v8.1 - Issue no 3 - 2018(4.379)(4.380)

182

4.1.12 Appendix B: Gaussian formulation for the C1 coefficient
Following Giordani (1993) and Braud et al. (1993), for dry soils (i.e., wg < Wwilt ), the C1 coefficient in
Eq. (13) is approximated by the Gaussian distribution:(wg − wmax )2(4.381)C1 (w) = C1max exp −2σ 2
In this expression,
C1max = (1.19wwilt − 5.09) × 10−2 Ts + (−1.464wwilt + 17.86)(4.382)wmax = ηwwilt(4.383)

η = (−1.815 × 10−2 Ts + 6.41)wwilt + (6.5 × 10−3 Ts − 1.4)

(4.384)withand
σ2 = −

2Wmax

2ln C0.01
1max

SURFEX v8.1 - Issue no 3 - 2018(4.385)

CHAPTER 4. SOIL AND VEGETATION

183

4.1.13 Appendix C: ISBA-MEB Numerical Solution.
The numerical solution of the full set of coupled thermodynamic prognostic equations (ISBA-MEB surface
energy budget, ISBA sub-surface soil and snow, and atmospheric profile) is presented herein. The couplingis numerically implicit and heat and mass (and enthalpy) conservative (flux form equations are used).

Discretization of surface energy budgets
The surface energy budget equations (Eq.s 4.223-4.225) are integrated in time using the implicit backward
difference scheme. They can be written in discretized form as(Tv+ − Tv ) ∂LWnet v∂LWnet v  +Tg,1 − Tg,1=
Tv+ − Tv +
∆t
∂Tv
∂Tg,1


∂LWnet v++
Tn,1− Tn,1 + SWnet v + LWnet v∂Tn,1+ ϕv Av Tv+ − Ac Tc+∂qsat v++
+ hsv ϕv L qsat v +Tv − Tv − qc
∂Tv
 "

+

Tg,1
− Tg,1∂LWnet g  +∂LWnet g=
Tv+ − Tv +Tg,1 − Tg,1
Cg,1
∆t
∂Tv
∂Tg,1


∂LWnet g+Tn,1− Tn,1 + SWnet g + LWnet g
+
∂Tn,1

+ ϕg Ag Tg+ − Ac Tc+
(
)



∂qsat g
+ ϕg L hsg qsat g +Tg+ − Tg − ha qc+
∂Tg
#




+
+
+
∗
−
T
T
−
T
−
Λ
(1 − psng ) + psng Λg,n Tn,N
g,1
g,1
g,1
g,2
n
Cv

psng Cn,1



+
Tn,1
− Tn,1∆t

=(4.386)(4.387)(∂LWnet n  +∂LWnet n
Tv+ − Tv +Tg,1 − Tg,1
∂Tv
∂Tg,1

∂LWnet n  ++Tn,1 − Tn,1 + SWnet n + LWnet n∂Tn,1+ (1 − pnα ) ϕn−c An Tn+ − Ac Tc++ pnα ϕn−a Bn − Ba + An Tn+ − Aa Ta+∂qsati n++++ (1 − pnα ) ϕn−c Ls qsati n +Tn − Tc − qc
∂Tn



∂qsati n++++ pnα ϕn−a Ls qsati n +Tn − Ta − qa
∂Tn
)


+
+
− Λg,1 Tn,1 − Tn,2
psng
SURFEX v8.1 - Issue no 3 - 2018(4.388)

184
where Eq. 4.225 has been multiplied by psng to make it patch-relative for the combined solution of the three+budget equations. The qsat
x terms have been linearized with respect to Tx as∂qsat x ++qsat
Tx − Tx(4.389)x = qsat x +∂Txwhere again, x = n, 1, g, 1 or v. The longwave radiation terms are also linearized and the derivatives are
given by Eq. 4.413. The superscript + corresponds to the values of variables at time t + ∆t, while theabsence of a superscript indicates variables evaluated at time t. Note that we have defined ϕx = ρa /Ra x(kg m−2 s−1 ) for simplicity. The thermodynamic variable, Tx , in the sensible heat flux terms have been
expressed as a function of Tx using Eq. 4.238. Several of the Bx terms have canceled out in the sensible heat
flux terms in Eq.s 4.386-4.388 since they are defined such that Bc = Bv = Bg = Bn . Note that compared toEq.s 4.223-4.225, the phase change terms (Φx ) do not appear in Eq.s 4.386-4.388. This is because they areevaluated as an adjustment after the energy budget and the fluxes have been computed.
∗
represents a test temperature for the lowest snowpack layer. It is first computed using an
In Eq. 4.387, Tn,Nnimplicit calculation of the combined snow-soil layers to get a first estimate of the snow-ground heat conduction inter-facial flux when simultaneously solving the surface energy budgets. The final snow temperature+, is computed afterwards within the snow scheme: any difference between the resulting
in this layer, Tn,Nnconduction flux and the test-flux in Eq. 4.387 is added to the soil as a correction at the end of the time stepin order to conserve energy. In practice, this correction is generally small, especially since the snow fraction
goes to unity very rapidly (i.e. for a fairly thin snowpack since MEB only uses psng at the surface, and not
psnv ). Thus, in this general case, the difference between the test flux and the final flux arise only owing to∗is computed using an
updates to snow properties within the snow scheme during the time step. Since Tn,Nnimplicit solution method for the entire soil-snow continuum, it is also quite numerically stable. The use of atest flux permits a modular coupling between the snow scheme and the soil-vegetation parts of ISBA-MEB.
+
In order to solve Eq.s 4.386-4.388 for the three unknown surface energy budget temperatures, Tv+ , Tg,1
, and
+
+
+
+
+
+
+
Tn,1 , equations for the six additional unknowns, Ta , Tc , qa , qc , Tg,2 and Tn,2 , must be defined. They can++, and Tn,1
, and their derivations are presented in thebe expressed as linear equations in terms of Tv+ , Tg,1remaining sections of this Appendix.
Atmospheric temperature and specific humidity
The first step in solving the surface energy budget is to eliminate the lowest atmospheric energy and water
vapor variables from the snow surface energy budget equation. They will also be used to diagnose the final
flux exchanges between the canopy air space and overlying atmosphere.
The atmospheric turbulence scheme is generally expressed as a second order diffusion equation in the vertical (which is assumed herein) and it is discretized using the backward difference time scheme. Assuming afixed for zero (the general case) upper boundary condition at the top of the atmosphere, the diffusion equations for the generic variable φ can be cast as a linear function of the variable in the layer below following
Polcher et al. (1998) as+φ+
k = Bφ,k + Aφ,k φk+1

(k = 1, Na − 1)

(4.390)where Na represents the number of atmospheric model layers, k = 1 represents the uppermost layer with k
increasing with decreasing height above the surface, and the superscript + indicates the value of φ at timet + ∆t (at the end of the time step). The coefficients Aφ,k and Bφ,k are computed in a downward sweep
within the turbulence scheme. As shown by Best el al. (2004), the equation for the lowest atmosphericmodel layer can be expressed using a flux lower boundary condition as+φ+
Na = Bφ,Na + Aφ,Na Fφ,Na +1

SURFEX v8.1 - Issue no 3 - 2018(k = Na )(4.391)CHAPTER 4. SOIL AND VEGETATION

185+
where Fφ,Nis the implicit surface flux from one or multiple surface energy budgets. For explicit landa +1
atmosphere coupling or offline land-only applications, the coupling coefficients can be set to Aφ,Na = 0 and
Bφ,Na = φNa in the driving code.
From Eq. 4.391, the thermodynamic variable of the lowest atmospheric model variable at time t + ∆t isdefined as
TN+a = BT ,Na + AT ,Na H +(4.392)

Note that using Eq. 4.238, we can rewrite Eq. 4.392 in terms of air temperature as
Ta + = BTa + ATa H +(4.393)where BTa = (BT ,Na − Ba ) /Aa , ATa = AT ,Na /Aa , and Ta is shorthand for T (k = Na ). Substitution of
Eq. 4.233 for H in Eq. 4.393 and solving for Ta+ yields
Ta+ = BTa + ATa Tc+ + CTa Tn+(4.394)no
C =Aa 1 + ATa [ϕc−a (1 − psng pαn ) + psng pαn ϕn−a ](4.395a)where

ATa =ATa ϕc−a Ac (1 − psng pαn ) /Cnh
BTa = BTa − Ba + ATa (1 − psng pαn ) ϕc−a (Bc − Ba ) +iopsng pαn ϕn−a (Bc − Ba ) /C
CTa =ATa psng pαn ϕn−a Ac /C(4.395b)(4.395c)(4.395d)(4.395e)In analogous fashion to determining the air temperature, the specific humidity of the lowest atmosphericmodel variable at time t + ∆t is defined from Eq. 4.391 as
qa+ = Bq,a + Aq,a E +(4.396)

where again the subscript q, a represents the values of the coefficients A and B for the lowest atmosphericmodel layer (k = Na ). Substitution of Eq. 4.249 for E in Eq. 4.396 and solving for Ta+ yields+
qa+ = Bq,a + Aq,a qc+ + Cq,a qsatin(4.397)

where the coefficients are defined as
C =1 + Aq,a [(1 − psng pαn ) ϕc−a + ϕn−a hsn pαn psng ](4.398a)

Aq,a =Aq,a ϕc−a (1 − psng pαn ) /C

(4.398b)

Bq,a =Bq,a /C(4.398c)

Cq,a =Aq,a ϕn−a hsn pαn psng /C(4.398d)Canopy air temperature and specific humidity
In order to close the energy budgets, Tc+ and qc+ must be determined.
Assuming conservation of the heat flux between the different surfaces and the canopy air space, we have+
+ (1 − psng ) Hg+ + Hv+(1 − psng pnα ) Hc+ = psng (1 − pnα ) Hn−c

SURFEX v8.1 - Issue no 3 - 2018(4.399)

186
which can be expanded as
ϕc−a (1 − psng pαn ) ×h
Bc + Ac Tc+ − Ba − Aa Ta+ =Ac ϕg Tg+ − Tc+ (1 − psng ) + ϕv Tv+ − Tc+i
ϕn−c Tn+ − Tc+ psng (1 − pαn )(4.400)Note that the above conservation equation does not include the part of the snow sensible heat flux which isin direct contact with the atmosphere (Hn−a ) since it was already accounted for in the expression for Ta+
via Eq. 4.393. Eliminating Ta+ using Eq. 4.394 and solving for Tc+ yields
Tc+ = aT c + bT c Tv+ + cT c Tg+ + dT c Tn+(4.401)

with the coefficients
C =ϕc−a (1 − psng pαn ) (Ac − Aa AT a ) +(4.402a)Ac [ϕv + ϕg (1 − psng ) + ϕn−c psng (1 − pαn )]hiaT c = ϕc−a (1 − psng pαn ) (Ba − Bc + Aa BT a ) /C

(4.402b)bT c =Ac ϕv /C(4.402c)cT c =Ac ϕg (1 − psng ) /C

(4.402d)dT c = [Ac ϕn−c psng (1 − pαn ) + Aa CT a ϕc−a (1 − psng pαn )] /C(4.402e)

In an analogous fashion for canopy air temperature determination, assuming conservation of the vapor flux
between the different surfaces and the canopy air space,++ (1 − psng ) Eg+ + Ev+(1 − psng pnα ) Ec+ = psng (1 − pnα ) En−c(4.403)

which can be expanded using the definitions of the evaporative fluxes, Ex , from Eq.s 4.245-4.403 together
with the definitions of qg from Eq. 4.250 and qa+ from Eq. 4.397 as
ϕc−a (1 − psng pαn ) ×

 +

 h
+
+
+
+
+
qc (1 − Aq,a ) − Bq,a − Cq,a qsatin = ϕg hsg qsat g − ha qc (1 − psng ) + ϕv hsv qsat v − qc
i

+
+
−
q
p
(1
−
p
)
ϕn−c hsn qsati
sng
αn
c
n

(4.404)

Owing to the linearization of the qsat x terms about Tx , Eq. 4.404 can be solved for qc+ as a function of thesurface energy budget temperatures as
qc+ = aqc + bqc Tv+ + cqc Tg+ + dqc Tn+
SURFEX v8.1 - Issue no 3 - 2018(4.405)

CHAPTER 4. SOIL AND VEGETATION

187

where the coefficients are defined as
C =ϕc−a (1 − psng pnα ) (1 − Aq,a ) + ϕg hN (1 − psng )+ ϕv hsv + ϕn−c hsn psng (1 − pnα )n∂qsat v
aqc = (1 − psng pnα ) ϕc−a Bq,a + ϕv hsv qsat v −
Tv
∂Tv


∂qsat gTg (1 − psng )+ ϕg hsg qsat g −
∂Tg


o
∂qsati n+ ϕn−c hsn qsati n −Tn psng (1 − pnα ) /C∂Tn
∂qsat v
bqc =hsv ϕv/C∂Tv∂qsat g(1 − psng ) /C
cqc =hsg ϕg∂Tg∂qsati n
dqc =hsn ϕn−cpsng (1 − pnα ) /C
∂Tn

(4.406a)(4.406b)(4.406c)(4.406d)(4.406e)Sub-surface temperatures
The sub-surface conduction heat fluxes can be expressed in compact form as


+
+
−
T
=
Λ
T
G+
x,k
x,k+1
x,k
x,k

(4.407)++= Bg,k + Ag,k Tg,k−1Tg,k(4.408)where Λx,k represents the ratio of the inter-facial thermal conductivity to the thickness between the midpoints of contiguous layers (k and k + 1). Using the methodology described in Appendix ?? for the atmospheric diffusion scheme, the soil and snow heat diffusion equation (both using the form of Eq. 4.355) canbe defined in an analogous fashion as(k = 2, Ng )where the coefficients Bg,k and Ag,k are determined during the upward sweep (first step of the tridiagonal
solution) from the base of the soil to the sub-surface soil and snow layers as described by Richtmeyer and
Morton (1967). The resulting coefficients for the soil are defined as
C = (Cg k /∆t) + Λg k−1 + Λg k (1 − Ag k+1 )Bg i = [(Cg k /∆t) T g k + Λg k Bg k+1 ] /C
Ag k =Λg k−1 /C(4.409a)(2 ≤ k ≤ Ng − 1)

(4.409b)(4.409c)

The same form holds for the snow layers. The upward sweep is performed before the evaluation of the++energy budget, thus Eq. 4.408 is used to eliminate Tg,2and Tn,2from Eq.s 4.387 and 4.388, respectively. To
do this, the sub-surface implicit fluxes in Eq.s 4.224 and 4.225 can be expressed, respectively, asih+(4.410a)
T
(1
−
A
)
+
B
G+
=Λ
g,2
g,2
g,1
g,1
g,1
i
h
+
(4.410b)G+n,1 =Λn,1 Tn,1 (1 − An,2 ) + Bn,2
Net Longwave radiation flux derrivatives
The first order derivatives of the net longwave radiation terms are needed in order to solve the system of
linearized surface energy budget equations (Eq.s 4.386-4.388). The Taylor series expansion (neglecting
SURFEX v8.1 - Issue no 3 - 2018

188
higher order terms) is expressed as+
LWnet
i = LWnet i +

N
seb
X
j=1


∂Lnet i  +Tj − Tj∂Tj(i = 1, Nseb )(4.411)

where Nseb represents the number of surface energy budgets, and i and j represent the indexes for eachenergy budget. The superscript + represents the variable at time t + ∆t, while by default, no superscript
represents the value at time t. Eq. 4.411 therefore results in a Nseb x Nseb Jacobian matrix (3x3 for MEB).
The matrix coefficients are expressed as
∂Hg
∂Fg
∂Gn
∂Hn
∂Fn
∂LWnet v ∂Gg
=
−
−2
+
−
−2
∂Tv
∂Tv
∂Tv
∂Tv
∂Tv
∂Tv
∂Tv
∂Jg
∂Kg
∂Lg
∂LWnet v ∂Ig
=
−
−
−
∂Tg
∂Tg
∂Tg
∂Tg
∂Tg
∂LWnet v ∂In
∂Jn
∂Kn
∂Ln
=
−
−
−
∂Tn
∂Tn
∂Tn
∂Tn
∂Tn
∂Gg
∂LWnet g ∂Fg
=
−
∂Tv
∂Tv
∂Tv
∂Ig
∂LWnet g ∂Jg
=
−
∂Tg
∂Tg
∂Tg
∂LWnet g ∂Jn
=
∂Tn
∂Tn
∂Gn
∂LWnet n ∂Fn
=
−
∂Tv
∂Tv
∂Tv
∂LWnet n ∂Kg
=
∂Tg
∂Tg
∂LWnet n ∂Jn
∂In
=
−
∂Tn
∂Tn
∂Tn

(4.412a)(4.412b)(4.412c)(4.412d)(4.412e)(4.412f)(4.412g)(4.412h)(4.412i)

Using Eq. 4.289 to evaluate the derivatives we have
∂LWnet v
4= (Gg − Hg − 2Fg + Gn − Hn − 2Fn )∂Tv
Tv
4∂LWnet v= (Ig − Jg − Kg − Lg )∂Tg
Tg
∂LWnet v
4= (In − Jn − Kn − Ln )∂Tn
Tn
∂LWnet g
4= (Fg − Gg )∂Tv
Tv
4
∂LWnet g= (Jg − Ig )∂Tg
Tg
4
∂LWnet g
= Jn
∂Tn
Tn
∂LWnet n4= (Fn − Gn )∂Tv
Tv
4
∂LWnet n
= Kg
∂Tg
Tg
∂LWnet n
4= (Kn − In ) fLW n∂Tn
Tn
SURFEX v8.1 - Issue no 3 - 2018(4.413a)(4.413b)(4.413c)(4.413d)(4.413e)(4.413f)(4.413g)(4.413h)(4.413i)

CHAPTER 4. SOIL AND VEGETATION

189

so that from a coding perspective, the computation of the derivatives is trivial (using already computed
quantities). Note that Eq. 4.413i has been corrected relative to Boone et al. (2017) in that the first term on
the RHS should be Kn , not Jn . But note that in fact, this correction has almost no impact on the results
since this term is nearly two orders of magnitude smaller than the largest term of the net longwave snow
term. Also, note that the factor fLW n has been added to this derivative term. It is defined as
fLW n = min 1, max [0, Tgrad max − (Tn − Tv )] /Tgrad dif(Tn > Tv )(4.414)

The need for this factor is quite rare: for very thin snow combined with extremely cold conditions, very weak
LW ↓ forcing and strong temperature differences between a relatively warm snow surface and the overlying
atmosphere, the derrivative ∂LWnet n /∂Tn can pose problems (i.e. the assumption of a linear change in
LWnet n relative to Tn over the given time step is a poor approximation). Note that under these conditions,
Tv should be close to Tc , thus we used Tv as a proxy to compute the aforementioned temperature gradient.
Thus in these rare instances, this derivative is forced to vanish over some small temperature difference range:
Tgrad dif , when it exceeds the gradient Tgrad max − Tgrad dif . Also note that this (when this zerm is zero) has
no impact on numerical stability since the longwave linerization has no effect on this and has no impact on
results in the general sense (since it is temporary and the assumed gradieints are so large that they are rarely,
if ever during a run, encountered). For example, default values are Tgrad max = 60 K and Tgrad dif = 10 K,
thus it should be evoked rarely, if ever. Indeed, the linearization is needed simply to ensure better phasingof Trad for large model time steps.
Halstead coefficient maximum
A maximum Halstead coefficient is imposed by estimating which value of δv that is needed to just evaporate
any existing intercepted water, Wrv , given the conditions at the beginning of the time step. Assumingthat phase changes are small, and neglecting canopy drip and any condensation from transpiration, the timedifferenced prognostic equation for intercepted water on canopy vegetation (Eq. 4.324) can be approximatedas:
Wrv + − Wrv= (1 − χv )(1 − psng pαn )Pr − Er(4.415)∆t+ = 0), and substituting the fullAssuming that all existing water evaporates in one time step (i.e. Wrv
expression for Er (Eq. 4.263) into Eq. 4.415, the maximum value of δv can be determined as

δv,max =[(1 − χv ) (1 − psng pαn ) Pr + (Wrv /∆t)] (L/Lv )noρa (1 − pnv ) kv [psng (1 − pαn ) /Ravn−c ] + [(1 − psng ) /Ravg−c ] (qsat v − qc )(4.416)

Eq. 4.416 is an approximation since all of the variables on the RHS use conditions from the start of thetime step, however, this method has proven to greatly reduce the risk for occasional numerical artifacts(jumps) and the associated need for mass corrections (if net losses in mass exceed the updated test value forinterception storage).
Surface stresses
Using the same surface-atmosphere coupling methodology as for temperature and specific humidity, theu-wind component in the lowest atmospheric model layer can be expressed as+u+
a = Bu a + Au a τx

SURFEX v8.1 - Issue no 3 - 2018(4.417)

190
The surface u component momentum exchange with the atmosphere is expressed as
τx+ = −u+a [(1 − psng pnα ) ϕDc−a + pn pnα ϕDn−a ](4.418)where it includes stresses from the snow-buried and non-snow buried portions of the surface consistent withthe fluxes of heat and water vapor. For simplicity, we have defined
ϕDx = ρa Va CDx(4.419)and CD is the surface drag coefficient (Eq. 4.208). Eliminating τx+ from Eq. 4.418 using Eq. 4.419 gives
Bu a
1 + Au a ϕDcu+
a =(4.420)where for convenience we have defined the average drag coefficient as
ϕDc = (1 − psng pnα ) ϕDc−a + psng pnα ϕDn−a(4.421)

The net u-momentum flux from the surface to the canopy air space is expressed as
τx+ = −

Bu a ϕDc(1 + Au a ϕDc )(4.422)

Finally, the vector momentum flux in the atmosphere can be computed from the scalar friction velocity:
∗

u =



ϕDc Va+ρa1/2(4.423)+++where Va+ is the updated wind speed (computed from u+a and va ). Note that va and τy are computed in
the same manner, but using Bv a from the atmosphere (note that Av a = Au a ).

Summary: Final solution of the implicitly coupled equations
The fully implicit solution of the surface and atmospheric variables proceeds for each model time step asfollows:
1. Within the atmospheric model, perform the downward sweep of the tri-diagonal matrix within the
turbulent diffusion scheme of the atmospheric model to obtain the Aφ,k and Bφ,k coefficients foreach diffused variable (φ = T , q, u, and v) for each layer of the atmosphere (k = 1, Na ). Update
Aa and Ba , then pass these values along with the aforementioned coupling coefficients at the lowest
atmospheric model layer (i.e. AT,a , BT,a , Aq,a , Bq,a , Au,a , Bu,a , and Bv,a ) to the land surface model.
These coefficients are then used to eliminate Ta+ and qa+ from the implicit surface energy budget
equations (Eq.s 4.386-4.388).
2. Within the land surface model, perform the upward sweep of the tri-diagonal matrix within the soil
and snow layers to determine the An,k , Bn,k , Ag,k , and Bg,k , coefficients for the soil and snow layers(from soil layer Ng to layer 2, and again from soil layer Ng to layer 2 of the snow scheme). Notethat coefficients for layer 1 of the snow and soil schemes are not needed since they correspond to thelinearized surface energy budgets (next step).
3. Within the land surface model, the expressions for Ta+ (Eq. 4.394), qa+ (Eq. 4.397), Tc+ (Eq. 4.401),++(Eq. 4.410b) can now be substituted into the energy budget(Eq. 4.410a)and Tn,2
qc+ (Eq. 4.405), Tg,2++
, and Tn,1.
equations (Eq.s 4.386-4.388) which can then be readily solved for Tv+ , Tg,1
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

191+
4. Within the land surface model, perform back-substitution (using Tg,1
as the upper boundary condition)+
to obtain Tg,k for soil layers k = 2, Ng using Eq. 4.408.

5. Within the land surface model, call the explicit snow-process scheme to update the snow scheme+
temperature, Tn,k, and the snow mass variables for snow layers k = 2, Nn . The implicit snow surface++
fluxes, Rn,n , Hn and En+ , are used as the upper boundary condition along with the implicit soil+
temperature, Tg,1
, to compute the updated lower snowpack boundary condition (i.e. the snow-soil
inter-facial flux, Ggn ).
6. Within the land surface model, compute Va+ (See Section 4.1.13). Diagnose Ta+ , Tc +, qa+ and qc+(again, using the equations mentioned in Step 3) in order to compute the updated (implicit) fluxes.
The updated evapotranspiration (Eq.s 4.262-4.266) and snow melt water mass fluxes are used within
the hydrology schemes to update the different water storage variables for the soil and vegetation
canopy (Eq.s 4.324-4.328).
7. Within the atmospheric model, perform back-substitution (using H + , E + , τx+ and τy+ as the lower
boundary conditions: Eq. 4.391) to obtain updated profiles (or turbulent tendencies, depending on
the setup of the atmospheric model) of Tk , qk , uk and vk for atmospheric layers k = 1, Na . Finally,
the updated upwelling shortwave, SW ↑, and implicit longwave flux, LW ↑+ (or equivalently, the+effective emissivity and implicit longwave radiative temperature, Trad
) are returned to the atmosphericmodel as lower boundary conditions for the respective radiative schemes.
Alternately, in offline mode, Aφ,a = 0 and Bφ,a = φa in the driving routine in Step 1, and the solution
procedure ends at Step 6. Finally, if multiple patches and/or tiles are being used within the grid call ofinterest, the corresponding fractional-area weighted fluxes are passed to the atmospheric model in Step 7.

SURFEX v8.1 - Issue no 3 - 2018

192

4.2 ISBA-A-gs surface scheme
Not up-to-date, new version to be released by June 2018

4.2.1 The Model
Introduction
Météo-France is developing SURFEX (SURFace EXternalisée) to be used in operational NWP models, andoffline for applications in hydrology and vegetation monitoring (Martin et al. (2007)). SURFEX serves themerging of a number of land and ocean surface models. Over land, SURFEX includes ISBA-A-gs, a CO2
responsive land surface model able to simulate the diurnal cycle of carbon and water vapour fluxes (Calvet
et al. (1998), Calvet et al. (2004), Gibelin et al. (2006), Calvet et al. (2008)). This latter model accounts
for different feedbacks in response to changes in [CO2 ], photosynthesis enhancement and transpiration
reduction (fertilization and anti-transpirant effects, respectively). Daily values of Leaf Area Index (LAI)
and biomass can be produced by ISBA-A-gs.
ISBA-A-gs uses a CO2 responsive parameterization of photosynthesis based on the model of Goudriaan
et al. (1985) modified by Jacobs (1994) and Jacobs et al. (1996). This parameterization is less detailed
than that commonly used in most land surface models (Farquar et al. (1980)) for C3 plants and Collatz etal. (1992) for C4 plants), but it has the same formulation for C4 plants as for C3 plants differing only by
the input parameters. The model also includes an original representation of the soil moisture stress. Two
different types of drought responses are distinguished for both herbaceous vegetation (Calvet (2000)) andforests (Calvet et al. 2004), depending on the evolution of the water use efficiency (WUE) under moderatestress: WUE increases in the early soil water stress stages in the case of the drought-avoiding response,
whereas WUE decreases or remains stable in the case of the drought-tolerant response.
ISBA-A-gs calculates interactively the leaf biomass and the LAI (defined as the leaf area per unit groundarea), using a simple growth model (Calvet et al. 1998). The leaf biomass is supplied with the carbon
assimilated by photosynthesis, and decreased by a turnover and a respiration terms. LAI is inferred from theleaf biomass multiplied by the Specific Leaf Area ratio, which depends on the leaf nitrogen concentration(Calvet and Soussana (2001), Gibelin et al. 2006). Gibelin et al. (2006) showed that ISBA-A-gs simulates
realistic LAI at the global scale under various environmental conditions. The physics of ISBA-A-gs has
been implemented in SURFEX by CNRM. Meanwhile, the physics of ISBA-A-gs has been implemented in
the ECMWF land surface scheme TESSEL (Van den Hurk et al. (2000)) by KNMI. The A-gs extension of
TESSEL is called CTESSEL (Voogt et al. (2006), Lafont et al. (2006).
Background information
Vegetation patches SURFEX contains the ISBA-A-gs photosynthesis model, for which particular vegetation types need to be distinguished. In each grid box several vegetation types are present, with their own
water and energy budget, and their own roughness length. ISBA-A-gs has a reduced number of parameters
but is able to represent contrasting vegetation types. The model includes 7 vegetation types: 3 of them arehigh vegetation types: deciduous broadleaf forest, coniferous forest and evergreen broadleaf forest. The
other 4 are low-vegetation types: C3 grass, C4 grass, C3 crops and C4 crops. The C3 and C4 carbon fixation
mechanisms correspond to contrasting photosynthetic biochemical pathways. C3 plants represent the vast
majority of the Earths plant biomass. C4 plants consist mainly of tropical grasses and some of them arecultivated (maize, sorghum, millet, sugar cane).
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

193

Table 4.7: Options of ISBA-A-gs

OptionDrought response

AGS

Calvet et al. (1998)

LAI

Calvet et al. (1998)

AST

Avoiding or Tolerant
Calvet (2000), Calvet et al. (2004)
Avoiding or Tolerant
Calvet (2000), Calvet et al. (2004)
Avoiding or Tolerant
Calvet (2000), Calvet et al. (2004)

LST
NIT

Leaf Area Index
and leaf biomass
Not calculated(prescribed value is used)
Calculated(from photosynthesis)
Not calculated(prescribed value is used)
Calculated(from photosynthesis)
Calculated(from photosynthesis)

Above-ground biomass(non-woody)
Not calculated
Not calculated
Not calculated
Not calculated
Calculated(nitrogen dilution)

The canopy resistance in ISBA-A-gs is calculated in the routine COTWORES (or COTWORESTRESS forthe most recent version able to differentiate drought-avoiding from drought-tolerant biomes). The photosynthesis model is called from COTWORES (or COTWORESTRESS).

! The parameters of ISBA-A-gs cannot be aggregated/averaged. Spatial heterogeneity within agrid cell has to be represented by running the model several times (as many times as the number ofpatches found within the grid cell).
Options of ISBA-A-gs
namelist

Five options of ISBA-A-gs (Table 4.7) can be activated by using the NAM ISBA

! The use of the most recent drought response formulation (present in options AST, LST, NIT) is
recommended as it is based on meta-analyses of leaf-level observations and was validated
successfully at the field and at the global scale (see Rivalland et al. (2006), Gibelin et al. (2006, 2008) andCalvet et al. 2008).
This option is used in CTESSEL (Voogt et al. (2006).
Photosynthesis Model (no water stress)
The canopy resistance is calculated from the photosynthesis, which is the net CO2 assimilation (An ) of
the canopy. An is calculated as a function of different environmental factors based on the approach by
Goudriaan et al. (1985).
First, CO2 assimilation limited by the air CO2 concentration is determined via a saturation equation:∗
Am = Am,max [1 − exp {−gm
(Ci − Γ)/Am,max }](4.424)∗ is the mesophyll conductance (with no soil waterwhere Am,max is the maximum net CO2 assimilation, gm
stress), Ci is the CO2 concentration in the leaf and Γ is the CO2 concentration at which assimilation com-

SURFEX v8.1 - Issue no 3 - 2018

194
pensates respiration, called CO2 compensation concentration. Am,max depends on temperature via a Q10
function:Am,max (Ts ) =(T −25)/10

Am,max (25) × Q10s
[1 + exp {0.3(T1 − Ts )}] [1 + exp {0.3(Ts − T2 )}](4.425)where Am,max (25) is Am,max at 25°C, Q10 is fixed at 2.0, Ts is the skin temperature in °C and T1 and T2∗ , depends on
are reference temperature values (see Table 4.8). gm in unstressed soil moisture conditions, gm
temperature via the same Q10 function as Am,max . The dependence on temperature of Γ is described by:(T −25)/10

Γ(Ts ) = Γ(25) × Q10s
where Q10 is fixed at 1.5.

SURFEX v8.1 - Issue no 3 - 2018

(4.426)

CHAPTER 4. SOIL AND VEGETATION

195

Table 4.8: Values of model parameters at 25°C and of parameters in the temperature response functions (Tin °C)

Mechanism
C3

Parameter (X)ǫ0 [mg J −1 ]f0∗Γ [ppm]∗ [mm s−1 ]gm
Am,max [mg m−2 s−1 ]X(@25)
0.017
0.85
45
7.0
2.2

Q10
1.5
2.0
2.0

T1 [◦ ]
5
8

T2 [◦ ]
361
38

C4

ǫ0 [mg J −1 ]f0∗Γ [ppm]∗ [mm s−1 ]gm
Am,max [mg m−2 s−1 ]

0.014
0.50
2.8
17.5
1.7

1.5
2.0
2.0

13
13

36
38

As can be seen from Table 4.8, some parameters depend only on the photosynthesis mechanism (C3 /C4 ).
∗ , depend on the vegetation type (Table 4.11). The internal CO concentration C , is directly
Others, like gm
2iderived from the CO2 concentration in the air Cs . It is controlled by the air humidity via:
Ci = f Cs + (1 − f )Γ(4.427)andf = f0∗



Ds
1− ∗
Dmax



+ fmin



Ds
∗
Dmax



(4.428)∗is the maximum specific humidity deficit of the air tolerated by the vegetation (with no soil
where Dmax∗
water stress) and Ds is the actual deficit. If the deficit exceeds Dmax
, the plant closes its stomata. f0∗ is∗the value of f if there is no saturation deficit (with no soil water stress). Both the unstressed Dmax
and∗unstressed f0 are parameters that are vegetation type specific (Table 4.11). Depending on vegetation typeand stress strategy, soil moisture stress influences these values (see Section 4.2.1). fmin is given by:fmin =

gc∗
gc + gm(4.429)where gc is the cuticular conductance, its value depending on vegetation type (Table 4.11). The CO2 assimilation limited by CO2 concentration is further limited by radiation by:
(
 
 )
ǫ Ia
An = (Am + Rd ) 1 − exp −− Rd(4.430)Am + Rd
where Ia is the photosynthetically active radiation (PAR), ǫ is the initial quantum use efficiency and Rd isthe dark respiration. ǫ is given by:Ci − Γ
(4.431)ǫ = ǫ0Ci + 2Γ
1

see section 4.2.3

SURFEX v8.1 - Issue no 3 - 2018

196
where ǫ0 is the maximum quantum use efficiency (Table 4.8). Rd is parameterized simply as:
Rd = Am /9(4.432)The stomatal conductance to CO2 , gsc , is estimated using a flux-gradient relationship, modified to account∗ is given by:
for the effect of a specific humidity deficit on stomatal aperture. The first guess gsc

i
h

i
h
An +RdAn +Rd+R
1−An − Amin DD∗ sd
Am +RdAm +Rdmax∗(4.433)gsc=
Cs − Ci
where Amin represents the residual photosynthesis rate (at full light intensity) associated with cuticulartransfers when the stomata are closed because of a high specific humidity deficit. It is parameterized as:∗Amin = gm(Cmin − Γ)(4.434)∗):
where Cmin is the value of Ci at maximum specific humidity deficit (Ds = Dmax

Cmin =∗ Γ
gc Cs + gm∗
gc + gm(4.435)

Taking into account the ratio of diffusivity of water vapour and CO2 (=1.6), the first guess of the stomatal
conductance to water vapour is:
f irstgsf irst = 1.6gsc(4.436)The diffusion of CO2 interacts with that of water vapour. The first guess of the stomatal conductance to
CO2 , must be corrected for this interaction by:
f irstgsc = gsc
+E

Ma Cs + Ci
ρa Mv 2(Cs − Ci )(4.437)

where Ma and Mv are molecular masses of air and water vapour respectively, ρa is the air density and E isleaf transpiration based on the first guess of the stomatal conductance to water vapour:E = ρa gsf irst Ds(4.438)In order to refine the estimation of the stomatal conductances to CO2 and water vapour, a single iteration
over Eqs. 4.436, 4.438 and 4.437 is applied. Finally, the stomatal conductance to water vapour is given by:
gs = 1.6gsc + gc

(4.439)

Soil moisture stress parameterization
Initial version In the initial version of ISBA-A-gs (Calvet et al. 1998), the effect of soil moisture stress∗ by the normalized soil moisture. This quantity
was applied to the mesophyll conductance, by multiplying gm
is referred to by the function f2 :f2 =w̄ − wwilt
wf c − wwilt(4.440)∗was fixed at 45 g kg−1 . The value of f0 for C3 plants was 0.85 and for C4 plants 0.5.
In this version Dmax
The routine corresponding to the initial version is called COTWORES.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

197

Table 4.9: Differences between figure 4.21 and the model

Figure
Model

f2c
0.5
0.3

DmaxX
403
300

DmaxN
55
30

Improved representation of plant response to drought The initial parameterization is replaced by amore complex one, based on a meta-analysis of several herbaceous and woody vegetation types (Calvet,
2000; Calvet et al. 2004). The meta-analysis shows relationships between gm and Dmax for low vegetation
and between gm and f0 for high vegetation. Furthermore, it seems that plants react in two different ways tosoil moisture stress. There are plants that try to avoid stress, by reducing the evaporation via stomatal regulation, and/or growing during well-watered conditions. This stress strategy is typified as drought-avoiding(or defensive). Others apply another strategy in order to resist stress, by a more efficient root water-uptake
or a more rapid growing cycle. This stress strategy is typified as drought-tolerant (or offensive). Among
species within the 7 vegetation classes of ISBA-A-gs both strategies may occur. Therefore, it is not easy
to generalize the strategy for each class. It seems most likely that coniferous forests and C3 crops havea drought-avoiding strategy, whereas an drought-tolerant strategy is assigned to the other classes. In bothstress strategies, 2 regimes are distinguished. One with moderate stress, in which the normalized soil moisture f2 exceeds the critical value f2c . The other with severe stress, where f2 is less than f2c . The criticalvalue is fixed at 0.3 for global modelling. For local modelling this value may be adapted to available data.
Low vegetation Calvet (2000) discusses the soil moisture stress response by low vegetation types. In
unstressed conditions, the following relationship holds for low vegetation types:∗∗
C3 plants : ln(gm) = 2.381 − 0.6103 ln(Dmax)

C4 plants :

∗
∗
ln(gm
) = 5.323 − 0.8923 ln(Dmax)(4.441)(4.442)−1∗ in mms−1 and D ∗with gm
max in gkg .
The negative correlation between gm and Dmax indicates that plants that are sensitive to the air humidity(low Dmax value), compensate the early closing of the stomata by a high mesophyll conductance. On theother hand, plants that are less sensitive to the air humidity have a lower mesophyll conductance. Figure
4.21 shows the stress response for low vegetation types schematically. The symbol θ is equal to f2 . The
figure represents an example of a C3 plant with specific parameter values. Table 4.9 presents differences
between the example in the figure and the model values.
The starting point is the unstressed condition (θ=100%). First we follow the drought-avoiding strategy.
When stress sets in, Dmax decreases while gm increases until the critical soil moisture is reached. This is
described by:N∗N
Dmax = Dmax
+ (Dmax− Dmax)f2 − f2c
1 − f2c(4.443)This strategy leads to less evaporation, but keeps up the CO2 assimilation, thereby increasing the water use
X,efficiency. Under moderate stress Eq. 4.441 is still valid. Via this equation, the maximum value of gm , gm
SURFEX v8.1 - Issue no 3 - 2018

198

Figure 4.21: Responses of C3 herbaceous plants to soil moisture stress as represented in the ISBA-A-gs
model, through the relationship between the mesophyll conductance at 25 ◦ C, gm, and the maximum leafto-air saturation deficit, Dmax (adapted from Calvet (2000): drought-avoiding and drought-tolerant (redand blue arrows, respectively). The soil moisture stress is represented by the ratio of the Available soil
Water Content (AW C) to the maximum AW C (M axAW C). For moderate soil water stress (i.e. AW C >θC × M axAW C), the deviation of Dmax from its unstressed value towards its minimum (0.03 kg kg−1 )or maximum (0.30 kg kg−1 ) value (drought-avoiding and drought-tolerant, respectively), is proportional to
AW C, scaled between M axAW C and θC × M axAW C. The value of gm is driven by Dmax through alogarithmic equation (solid line): ln(gm) = 2.3810.6103 × ln(Dmax), with gm and Dmax in units of mms1 and g kg1 , respectively. For more pronounced soil water stress (i.e. AW C < θC × M axAW C), either
gm or Dmax (drought-avoiding and drought-tolerant, respectively), decrease from its value at AW C =θC × M axAW C to its minimum value, proportional to AW C/(θC × M axAW C). As an example, thevalues θC = 0.3 and unstressed gm = 1 mm.s−1 are used (Calvet et al. 2012).

follows from the value of DmaxN . If the stress goes below the critical value (severe stress), Dmax does notchange anymore, but gm drops with ongoing severity of stress:X
gm = gm

f2
f2c(4.444)

Now we follow the drought-tolerant strategy. When stress sets in, Dmax increases while gm decreases until
the critical soil moisture is reached. This is described by:
X∗
X
Dmax = Dmax
+ (Dmax− Dmax)f2 − f2c
1 − f2c(4.445)This strategy leads to more evaporation, thereby possibly decreasing the water use efficiency. If the stressgoes below the critical value (severe stress), gm does not change anymore, but Dmax drops with ongoingseverity of stress:
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

199

X
Dmax = Dmax

f2
f2c

(4.446)∗ via Eq. 4.441. f ∗ for C∗
follows from gm
For low vegetation types in the new parameterization, Dmax
30plants is fixed at 0.95 and for C4 plants at 0.6. The routine corresponding to the new version is called
COTWORESTRESS.

High vegetation Calvet et al. (2004) discuss the soil moisture stress response by high vegetation types. In
unstressed conditions, the following relationship holds for low vegetation types:∗ln(gm) = 4.7 − 7f0∗

(4.447)∗ in mm s−1 . The product g f controls A , since C is influenced by f . Therefore the negativewith gmm 0mi0
correlation between the two parameters makes that CO2 assimilation flux does not drop too much. Figure
4.22 shows the stress response for high vegetation types schematically. The starting point is the unstressed
condition (θ=100%). First we follow the drought-avoiding strategy. When stress sets in, f0 decreases while
gm keeps its unstressed value until the critical soil moisture is reached. This is described by:

f0 = f0∗ + (f0∗ − f0N )1 − f2
1 − f2c(4.448)where f0N is the value of f0 given by the relationship between gm and f0 under severe stress conditions,∗ :with gm = gm∗ln(gm
) = 2.8 − 7f0(4.449)This strategy leads to an increase of the water use efficiency. If the stress goes below the critical value(severe stress), f0 increases and gm decreases via:∗
gm = gm

f2
f2c(4.450)

Now we follow the drought-tolerant strategy. When stress sets in, f0 keeps its unstressed value while gm
decreases until the critical soil moisture is reached. This is described by:∗∗N
gm = gm
− (gm
− gm
)

1 − f2
1 − f2c(4.451)

N is the value of g given by Eq. 4.449 with f = f ∗ . This strategy leads to a decrease of the waterwhere gmm00
use efficiency. If the stress goes below the critical value (severe stress), f0 increases and gm decreases via:N
gm = gm

f2
f2c(4.452)∗ via Eq. 4.447. For D ∗For high vegetation types in the new parameterization, f0∗ follows from gm
max a∗
relationship with gm was developed based on results from Calvet et al. (2004):∗∗
Dmax= −37.97 ln(gm) + 150.4∗
in the case of forests.
This equation was used in Table 4.11 to determine Dmax

SURFEX v8.1 - Issue no 3 - 2018

(4.453)

200

Figure 4.22: Stress responses for high vegetation. Reproduced from Calvet et al. (2004)

From leaf to canopy
The photosynthesis model calculates the net CO2 assimilation at the leaf scale. For the upscaling to the
canopy, integration over the canopy is needed. It is assumed that variables Ts , Ds and Cs do not vary within
the canopy together with the model parameters. In SURFEX, wet leaves from the interception of rain or
leaves covered by snow do not assimilate CO2 . The tile-specific skin temperature Ts is calculated by solving
the surface energy balance for each tile. In COTWORES (and COTWORESTRESS), Ds at canopy levelis calculated from Ds at the reference atmospheric level from a simple flux-gradient relationship by using
the aerodynamic resistance ra and the water vapour flux of the previous time step. For Cs , this is done too,with the net CO2 flux. The incoming shortwave radiation is attenuated in the canopy. At the top of the
canopy, the incoming PAR is assumed to be 48% of the incoming shortwave radiation. The PAR extinction
is described by Roujean (1996). The PAR at height z in the canopy is given by:Ia (z) = [1 − K(z)] × Ia (h)(4.454)

where h is the height of the top of the canopy and K is the extinction coefficient given by:
K(z) = f (θs ) × Kdf (z) + [1 − f (θs )] × Kdr (z)(4.455)

Where Kdf (z) and Kdr (z) are the extinction coefficients of diffuse and direct light, respectively:
Kdf (z) = 1 − exp(−0.8bLAI(h − z)/h)
GbLAI(h − z)/hKdr (z) = 1 − exp −cos θs(4.456)(4.457)

where θs is the solar zenith angle and G is a parameter that describes the distribution of leaves (a sphericalangular distribution is assumed: G=0.5). f is the ratio of diffuse to total downward shortwave radiation at
the top of the canopy given by:
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

201

f (θs ) =0.25
0.25 + cos θs(4.458)b is the foliage scattering coefficient:√
1− 1−ω
√(4.459)b=1−
1+ 1−ω
where ω (=0.2) is the leaf single scattering albedo in the part of the solar spectrum corresponding to thePAR.
Assuming an homogeneous leaf vertical distribution, the integrated canopy net CO2 assimilation and conductance can be written as:
LAI
AnI =
h
gsI =

Z h

An dz

(4.460)Z h(4.461)

0

1
LAI
=
rs
h

gs dz

0

where rs is the canopy resistance. The integrations are parameterized with a three-point Gauss quadrature
method:AnI = LAI ×
gsI = LAI ×

3
X

Wi An (zi )(4.462)

Wi gs (zi )(4.463)

i=1

3
X
i=1

where zi and Wi are the Gauss levels and weights respectively. rs is used in the calculation of the exchangeof water vapour between the vegetation and the atmosphere.
Biomass evolution
The user may define whether the vegetation must be calculated interactively, or must follow from surface
climatology fields of LAI. This can be done via a flag (Table 4.7) in the namelist NAM ISBA (CPHOTO).
This section presents the calculations belonging to interactive vegetation.
With a dynamic representation of LAI, the model is able to account for interannual variability, droughts inparticular. The interactive LAI is based on biomass evolution due to photosynthetic activity. The biomass
module simulates growth and mortality of the vegetation. Throughout SURFEX, the vegetation biomass isexpressed in units of kg of dry matter per m2 .
Initial version In the initial version a single biomass reservoir B is considered (Calvet et al. 1998). It
represents the photosynthetic active biomass, including the leaves and also a proportion of the stem androots, which provide water for transpiration. Once a day (∆t = 1 day), at midnight, both growth and mortality
is calculated:
B(t + ∆t) = B(t) + ∆B + − ∆B −(4.464)

The growth is based on the accumulated net CO2 assimilation over the previous day:∆B + =

MC
AnI,day ∆t
PC MCO2SURFEX v8.1 - Issue no 3 - 2018(4.465)

202
where Pc is the proportion of carbon in the dry plant biomass, for which a constant value of 0.4 is chosen,
and MC and MCO2 are the molecular weights of carbon and CO2 (12 and 44 gmol−1 ). AnI,day is the daily
accumulated AnI . Mortality can be due to soil moisture stress, diseases and senescence but also to thetransportation of organic molecules from the active biomass to stocking and structural organs. It is given by
an exponential extinction of B characterized by a time-dependent effective life expectancy:



∆t
∆B − = B 1 − exp −τ(4.466)andτ (t) = τM

Anf m (t)An,max(4.467)

where τM is the maximum effective life expectancy, depending on vegetation type (Table 4.11), Anf m is the
maximum leaf An reached on the previous day and An,max is the optimum leaf An obtained when:Ds = 0 g kg−1
Ia (h) = 500 W m−2
Ts = 25°C for C3 plants and Ts = 35 °C for C4 plants.
In order to avoid extreme loss of biomass in periods when An is low, the following constraint on leaf spantime is imposed:
τM(4.468)
10The LAI is obtained from the biomass assuming a constant ratio, depending on vegetation type (Table 4.11):
τ≥B(4.469)LAI
One other vegetation parameter is needed, in order to enable vegetation to start assimilating CO2 after aperiod of unfavourable conditions: a LAI minimum value LAImin (Table 4.11). The routine of biomass
loss is called LAILOSS. The routine of biomass growth is called LAIGAIN.
αB =Version with nitrogen dilution
Theory In reality, αB depends on climate (temperature and CO2 concentration) and nitrogen fertilisation.
In order to account for plant morphology, the nitrogen dilution concept by Lemaire and Gastal (1997) is applied in the new version of biomass evolution. The plant N decline model is a well-established agronomical
law relating the plant N in non-limiting N-supply conditions to the accumulated aboveground dry matter.
The critical plant N is the value of N maximizing growth, and this value decreases for increasing biomass
accumulation following a negative power law. The basis of the model is that the metabolic component of
the plant biomass is related to total biomass through an allometric logarithmic law (Calvet and Soussana,2001). In ISBA-A-gs, the metabolic biomass component is identified as the active biomass, or leaf biomass.
The relationship between active biomass B and total, non-woody aboveground biomass BT is:
BT =



B
c

1/(1−a)(4.470)where a and c are constant parameters: c = 0.754, and a may vary with CO2 concentration, but for thesake of simplicity a constant value a = 0.38 is used (XCA 1x CO2 NIT). The total aboveground biomass
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

203

consists of the active biomass reservoir and the structural aboveground reservoir (Bs ), which can be considered as the ”living” structural biomass, like the stem. For forests, wood is a dead reservoir and does notcontribute to Bs . Within the nitrogen dilution model a relationship between the leaf area ratio LAR and theaboveground nitrogen concentration NT is applied:
LAR =

LAI
= eNT + fBT

(4.471)

where e and f are called plasticity parameters and are derived per vegetation type (Table 4.11). Eq. 4.471
can be used as a closure equation to estimate αB :αB =1eNa + f /(cBT−a )(4.472)where Na is the nitrogen concentration in the active biomass. It depends on vegetation type and on thenitrogen fertilisation. For further details and derivations see Calvet and Soussana (2001). In this way, αB
has become a model variable depending on BT . However, for global simulations, it is desirable to keep αB
as a constant parameter in order to let αB represent rather intrinsic plant characteristics denoting a biological
adaptation to average climate and growing conditions (Calvet and Soussana, 2001). For that purpose, Eq.
4.472 can only be solved by iteration. Moreover, LAR and NT data to derive the plasticity parameters byregression is lacking. However, data is available for leaves in the form of the specific leaf area SLA and thenitrogen content in leaves NL :
SLA =

LAI
= eNL + fBL(4.473)

Both the iteration issue and the availability of data to derive e and f give rise to modify the nitrogen dilution
module. Eq. 4.472 is simplified by considering αB as the ratio of the biomass of green leaves to LAI:
αB =

1
1
=
SLA
eNL + f(4.474)

It must be noted that NL may decrease for increasing CO2 concentration (Calvet et al. 2008) and section
4.2.3).
Biomass reservoirs The different biomass reservoirs are calculated using a simplified allocation scheme(Calvet and Soussana, 2001). Figure 4.23 presents the allocation scheme schematically. Next to B and Bs ,there is a belowground structural biomass reservoir Bs2 . The active biomass is calculated in the same way
as in the initial version (Eq. 40). The B-decline term (Eq. 4.466) is split into a mortality and storage term:∆B − = MB + SB

(4.475)In the growing phase (∆B + ≥ ∆B − ) the N decline equations can be applied. When the vegetation becomessenescent (∆B + < ∆B − ), the equations are no longer valid. Therefore a distinction between the two phases
is made.
In the growing phase, following the N decline equations, BT is derived from B using Eq. 4.470 and Bs is
the difference between the two terms. The mortality of Bs is assumed to be independent of photosynthesis
and is given by:
MBs = Bs∆t
1 − exp −τM

SURFEX v8.1 - Issue no 3 - 2018

(4.476)

204

Figure 4.23: Schematic representation of the simple biomass model. Nitrogen (N) and carbon fluxes are represented by dashed and solid lines, respectively. The three biomass (B) compartments are indicated together
with storage and mortality terms (S and M, respectively). Heterotrophic respiration (R) is represented bydotted lines. The mortality terms may be used as an input of a model of wood production and SOM. From:
Calvet and Soussana (2001)
The structural biomass also looses carbon through respiration. This term is estimated using the common
observation that maintenance respiration of non-active biomass is proportional to the biomass value, with a
Q10 temperature dependence:(T −25)/10

RBs = ηR Bs Q10s∆t(4.477)

where Ts is the skin temperature in °C, ηR is a respiration rate fixed at 1%day −1 and Q10 = 2.0. Finally,
the storage term SB is calculated as the residual of the structural biomass budget:
SB = ∆Bs − MBs − RBs(4.478)The mortality MB in Eq. 4.475 is obtained by difference. In situations where SB exceeds ∆B − (implyingthat MB < 0), an alternative formulation of B-decline is employed. It is assumed that there is no loss ofactive biomass outside the plant system during the considered time step, so MB = 0 and that the difference
in total aboveground biomass is the difference between the biomass gain due to daily net assimilation andthe mortality and respiration losses of structural biomass:∆BT = ∆B + − MBs − RBs
SURFEX v8.1 - Issue no 3 - 2018

(4.479)

CHAPTER 4. SOIL AND VEGETATION205

BT is derived from this difference and the value at the previous time step. B follows from BT via Eq. 4.470
and Bs is the difference between the two terms. A new value of the storage term SB is given by Eq. 4.478.
In the senescent phase, Bs evolves independently from B. SB is set to zero and the mortality and respiration
losses are directly applied to Bs :Bs = Bst−1 − MBs − RBs(4.480)The belowground structural biomass Bs2 is not treated by the plant N decline model. The mortality andrespiration losses of Bs2 are calculated using equations similar to Eqs. 4.476 and 4.477:
MBs2 = Bs2







(4.481)−25)/10∆t(4.482)∆t
1 − exp −τM(TRBs2 = ηR Bs2 Q10soil

where Tsoil is the temperature in °C of the soil layer in the force-restore version of ISBA. Note that bothRBs and RBs2 are calculated every time step and accumulated over one day. Bs2 is fed by two mechanisms.
First, when the storage term SB is negative (this may happen, e.g., when a cut is prescribed in the model),this quantity is redirected to Bs2 . Second, when the total aboveground plant biomass BT is lower than c1/a ,it is assumed that the mortality term MB becomes a storage term that increases Bs2 .
The routine corresponding to the nitro dilution version is called NITRO DECLINE.
The module can be coupled to a soil organic matter (SOM) model. The SOM is fed by the mortality
terms (Calvet and Soussana, 2001). Besides, the model still lacks a wood (dead biomass) reservoir. Those
extensions have been developed by Gibelin et al. (2008) (ISBA-CC, see Sect. 4.3).
Note: In the model, the biomass loss is calculated before the biomass gain. When NITRO DECLINE iscalled and values from the previous day are needed, those are the values of the previous day calculated in
NITRO DECLINE, so before the biomass growth due to photosynthesis (calculated in LAIGAIN) is added
to the biomass reservoir. In that case, LAILOSS is not called (in VEGETATION EVOL).
Respiration
Since the biomass model is not coupled to a soil model, soil respiration needs to be parameterized in anotherway. In ISBA-A-gs, a simple Q10 equation is used to represent the ecosystem respiration, but this method
lacks a representation of the effect of soil moisture on the soil respiration. The representation of all the respiration terms (including the heterotrophic respiration and its dependence on soil moisture) was developedby Gibelin et al. (2008) in ISBA-CC (see Sect. 4.3).
The CO2 ecosystem respiration is parameterised by a Q10 function, weighted by a soil moisture scaling
factor (Albergel et al. (2010)):(T−25)/10(4.483)f (wg ) = min(1, wg /wf c )(4.484)

RECO = RE25 · f (wg ) · Q10soil

where RE25 is the reference respiration at 25 ◦ C , Tsoil is the temperature in ◦ C of the root-zone soil layer(at a depth of about 20cm), wg is the surface soil moisture, corresponding to the first top cm of the soil, wf c
is the soil moisture at field capacity, and Q10 is fixed at 2.0.
SURFEX v8.1 - Issue no 3 - 2018

206

Table 4.10: Example of harvest estimates (t C ha−1 y −1 )Vegetation type
Deciduous
Coniferous
Evergreen
C3 grass
C4 grass
C3 crops
C4 crops

Harvest
3.2
2.3
3.2
2.3
3.2
2.3
3.2

RE25 has to be determined per vegetation type in each grid box, assuming equilibrium between multiannual CO2 assimilation by photosynthesis (or gross primary production, GP P , i.e. raw carbon uptake byphotosynthesis), harvest and ecosystem respiration:no(T−25)/10
GP Pacc − Harvestacc = RECOacc = RE25 f (wg ) · Q10soil

acc(4.485)where acc stands for accumulated over the multi-year period. For harvest, examples of yearly harvest
estimates per vegetation type are given in Table 4.10. Numbers are based on a 40% carbon content of dry
biomass.
Once RE25 is calibrated for each vegetation type within each grid box, it may be treated as a surface
climatology field, which is input to the model.

CO2 fluxes
The photosynthesis model is called from COTWORES (or COTWORESTRESS) for all present vegetation
tiles (Section 4.2.1).
The net ecosystem CO2 exchange (NEE) per vegetation type is given by:

N EE = GP P − RECO

(4.486)

Throughout SURFEX, the unit of the kinematic CO2 flux is kgCO2 kgAir −1 m s−1 (as opposed to dynamic
CO2 flux units of kgCO2 m−2 s−1 ).

4.2.2 Vegetation parameters
Gibelin et al. (2006) have proposed default values for the parameters of the new version of ISBA-A-gs (NIT
option). They are listed in Table 4.11 for 7 vegetation types.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

207∗ in mm s−1 , τ
Table 4.11: Values of ISBA-A-gs parameters for the ECOCLIMAP vegetation types (gm
M
−1
2
−2
∗
−1
∗
in days, LAImin in m m , Dmax in g kg , f0 dimensionless, gc in mm s , strategy of response to soil
moisture stress (drought-tolerant or drought-avoiding), θC dimensionless, e in m2 kg−1 %−1 , f in m2 kg−1 ,and Nl in %Vegetation type
Deciduous broadleaf
trees
Evergreen broadleaf
trees
Needle leaf trees
C3 crops
C4 crops
C3 natural herbaceous
C4 natural herbaceous

∗
gm
3

τM
230

LAImin
0.3

∗
Dmax
109

f0∗
0.51

gc
0.15

Strategytolerant

θC
0.3

e
4.83

f
2.53

Nl
2

2

365

1

124

0.57

0.15

tolerant

0.3

4.83

2.53

2.5

2
1
9
1
6

365
150
150
150
150

1
0.3
0.3
0.3
0.3

124
50
33
50
52

0.57
0.95
0.6
0.95
0.6

0
0.25
0.15
0.25
0.15

avoiding
avoiding
tolerant
tolerant
tolerant

0.3
0.3
0.3
0.3
0.3

4.85
3.79
7.68
5.56
7.68

-0.24
9.84
-4.33
6.73
-4.33

2.8
1.3
1.9
1.3
1.3

∗ , τ , LAI∗∗! In the code, gm
M
min , Dmax , f0 , gc , θC , e, f , Nl are named
GMES, SEFOLD, LAIMIN, DMAX, FZERO, GC, F2I, CE NITRO, CF NITRO,CNA NITRO, respectively.
GMES and GC are in units of m s−1 , SEFOLD in s, DMAX in kg kg−1∗
For herbaceous vegetation: f0∗ is prescribed in MODD CO2V PAR, Dmax
is derived
from the inversion of 4.441.
∗
are not prescribed in the code, they are derived fromIn the case of trees: f0∗ and Dmax
the inversion of Eqs 4.447 and 4.453, respectively.

4.2.3 Discussion
In this section, some issues are discussed that deserve attention for future code development.
Respiration
Ecosystem respiration is a major component of the net CO2 flux. ISBA-A-gs lacks a soil carbon reservoir
and a wood (dead biomass) reservoir. Moreover, roots are not explicitly represented. Those extensions (andthe associated respiration fluxes) are present in the ISBA-CC version, which has been coded into SURFEX(see Sect. 4.3). This provides possibilities for respiration calculations for each of the carbon reservoirs, thatmight replace the present respiration calibration. There is a strong need for direct respiration measurements
to validate the parameterization.
With respect to the present Q10 calibration of ecosystem respiration, soil moisture effects are not accountedfor. This hypothesis is not correct and a simple representation of the surface soil moisture effect on ecosystem respiration has to be introduced in SURFEX. Furthermore, the value of Q10 is fixed at 2, because it isgenerally used in literature about respiration. However, climate conditions may ask for a differentiation in
SURFEX v8.1 - Issue no 3 - 2018

208
the Q10 value.
Soil moisture stress parameterization
The soil moisture stress parameterization may depend on the way soil hydrology is represented. Since thesoil moisture content depends on the soil parameterization, which is different for ISBA-FR and ISBA-DF,
this may lead to divergent behaviour. The use of ISBA-A-gs with the ISBA-DF option has still to be tested.
Temperature response of gm for C3 plants
Table 4.8 presents for C3 plants a T2 of 36 °C for gm . However, in the beginning of the ISBA-A-gs development, this value was 28 °C (Calvet et al. 1998). This was changed during the development of new versions(e.g. Calvet, 2000). This implies that the temperature response of gm , which is a sensitive parameter forphotosynthesis, for C3 plants approaches the response for C4 plants, i.e. an optimal temperature for photosynthesis of 32 °C. This is certainly too high for boreal forests and grasslands adapted to cold climates (highlatitudes or mountainous areas). The T2 parameter will have to be adapted as a function of a climatology of
air temperature.
Radiative transfer within the vegetation
The radiative transfer equations and the quadrature method described in section 4.2.1 are based on many approximations (Calvet et al. 1998). In particular, the representation of (1) scattering of the photosynthetically
active radiation (PAR), (2) the interception of the diffuse radiation, within the canopy, may be oversimplified for regions/seasons with a lot of diffuse PAR (clouds, high solar zenith angles), especially for dense
canopies.
The radiative transfer influences (1) photosynthesis and the canopy conductance, (2) mortality. Moreover,
Calvet et al. (2008) have shown that the way light interception within the canopy is modelled may impact
the simulated plant response to climate change.
Tropical evergreen forests Simulations with ISBA-A-gs showed that An is underestimated in tropicalevergreen forest. This may cause an underestimation of net primary production (NPP) and an overestimationof the mortality of leaves. A solution must be found to improve photosynthesis and mortality. Mortality
depends on the optimum net CO2 assimilation (with 500 W m−2 PAR). For evergreen forests that have ahigh radiation extinction in the canopy, 500 W m−2 PAR may not be realistic under optimal conditions.
Therefore, mortality might be overestimated. This could be dealt with by either reducing the optimum PAR
or by considering a different mortality parameterization. Radiative transfer equations may also be improvedfor dense canopies in order to account better for diffuse radiation.
For the photosynthesis and canopy resistance, the vegetation parameter values in the photosynthesis model
may be reconsidered. Therefore, data sets of tropical evergreen forests are needed to calibrate parameterslike gm and Na .
Representation of mortality In NITRO DECLINE, a correction of mortality is introduced for dense
canopies. The effective life expectancy of the leaves (governing the exponential decline of B) is increased.
Indeed, Eq. 4.467 relates mortality to the factors acting on photosynthesis at the leaf level. The factors
accounted for by Eq. 4.467 include self shading since Anf m is the maximum average leaf net assimilation:
this quantity depends on LAI, which is employed to compute the extinction of solar radiation (see section
4.2.1). Preliminary tests of the nitrogen dilution option (NIT) showed that at very high values of LAI, the
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

209

self shading effect in Eq. 4.467 may trigger exaggerated values of mortality and, finally, underestimated values of biomass. Therefore, Eq. 4.467 was modified such as, for dense canopies, the leaf-level Anf m /An,max
ratio is replaced by a value representative of the canopy:
LAI Anf m /(X An,max ), where X represents the maximum value of the ratio between canopy- and leaflevel optimum net assimilation. The value of X denotes the relative advantage of a well-developed canopy
over a single horizontal leaf in terms of net assimilation of CO2 , in optimal conditions. This value wassearched for various models parameters such as LAI, and gm , by performing simulations over one annual
cycle at several latitudes. In each configuration, a value of LAI (always higher than 5 m2 m−2 ) maximising
the ratio between canopy- and leaf-level optimum net assimilation could be found. A logarithmic relationship between the optimal value of X and gm was obtained (X tends to decrease for increasing values of
gm ). This relationship depends on latitude because of the influence of maximum solar elevation on X (X islower at high latitudes). Finally, Eq. 4.467 was rewritten as:
τ (t) = τM

 0.321
Anf m (t)M ax 1, gm
LAI/LAIB
An,max(4.487)

where gm is expressed in units of mm s−1 , and LAIB represents a limit value of LAI depending on latitude(La ) as:LAIB = 5.76 − 0.64 tan (M in {kLa k , 73◦ })(4.488)The LAIB parameter ranges from 5.6 to 3.6, from equator to latitudes higher than 73◦ . For values of gm
close to 1 mm s−1 , it represents the maximum LAI value for which the leaf-level net assimilation may be
employed to represent mortality. Those equations were derived with the radiative transfer parameterisation
described in section 4.2.1 and may be different for another radiative transfer model.
Representation of crops
In ISBA-A-gs, crops are represented like natural vegetation. There is no particular description of the harvested elements like fruits and e.g. grain yield (cereals) is not directly simulated. Nevertheless, Calvet etal. (2008) show that the maximum above-ground biomass simulated by the model correlates with the crop
yield and that the model is able to simulate realistic time series of LAI values over one annual cycle, and torepresent the interannual variability.
Moreover, a simple representation of irrigation was implemented in SURFEX, and the possibility to simulate
crops sown at springtime.
Irrigation An irrigation amount of 30mm is added to the precipitation forcing each time the simulated
extractable soil moisture content (dimensionless) reaches a predefined threshold. This threshold decreases
from 0.70 for the first irrigation, to 0.55 for the second, 0.40 for the third, and 0.25 for the following ones
(Calvet et al. 2008). The threshold values are declared in MODD AGRI.
Emergence Whereas the LAI annual cycle of natural vegetation (leaf onset, senescence, regrowth) isdriven by climate conditions, crops are sown at dates chosen by the farmers. In ISBA-A-gs, crops sown at
wintertime (i.e. emerging at springtime like natural vegetation) like wheat, are simulated in the same way
as natural vegetation. The advantage of this is that no ancillary information is needed and that possible
regrowths after a drought period are simulated interactively with the climate.
On the other hand, crops developing at summertime cannot be simulated like natural vegetation. An emergence date has to be prescribed and before this date (MODD AGRI n), LAI is limited to a minimum value
SURFEX v8.1 - Issue no 3 - 2018

210
(e.g. 0.3 m2 m−2 ). An harvest date is not prescribed. It is considered that climatic conditions (drought,cold) permit to drive the senescence.
In order to prescribe emergence dates, future developments should couple SURFEX to existing crop calendars, at the global scale.
Representation of nitrogen dilution
The CO2 fertilization effect tends to increase the vegetation biomass but this effect is limited by nitrogen
dilution. In Calvet et al. (2008), nitrogen dilution is accounted for by parameterizing the change in leaf
nitrogen mass-based concentration NL in response to [CO2 ] rise. The sensitivity of leaf nitrogen concentration versus [CO2 ] is accounted for by using the meta-analysis of the literature carried out by Yin 2002
(Yi02). The meta-analysis of Yi02 indicates that, on average, a CO2 -doubling causes a 18% decrease in
NL , but that the NL response to CO2 is influenced by a number of factors. A change in [CO2 ], from [CO2 ]= C1 to [CO2 ] = C2 , produces a change in NL from NL1 to NL2 following:



  
NL2
C2
NL1
ln
= −a exp b −ln(4.489)
NL1
NLmax
C1
with a = 0.048 and NLmax =6.3 %. In the Yi02 study, C2 /C1 ranges from 0.53 to 3.2. The b parameter mayvary significantly from one vegetation type to another. For example, in median radiation and air temperature(Ta ) conditions, b = 1.48 for a fertilised crop, b = 2.56 for a deciduous forest, b = 1.81 for a coniferous forest
or natural grasslands. The values of b are given by:Ta(4.490)23
with DF = 1 for deciduous forests (0 for other biomes), and F ERT = 1 for fertilized ecosystems likecrops (0 for other biomes). P P F D is the average photosynthetically active solar radiation reaching the leaf
within the vegetation canopy (median value of 0.74 mmol m2 s1 , equivalent to a total solar radiation of 335
W m2 ). In this study, no solar radiation or temperature effect is associated with a change in [CO2 ] and the
median P P F D and Ta values of Yi02 are used in Eq. 4.490.
b = 0.75DF − 0.33F ERT + 1.1P P F D +Annex 1: Description of the Fortran routine used to calculate the CO2 flux
SUBROUTINE COTWORESTRESSThis routine is used at the time step of SURFEX (default offline value ∆t = 300 s).
1. The photosynthetically active radiation (PAR) is derived from the incident shortwave radiation. A
constant factor of 0.48 is used.
2. Drought-avoiding and drought-tolerant responses to soil moisture stress are simulated for herbaceous andfor woody plants (depending on the vegetation type of the considered patch). Namely, the photosynthesis
parameters are refreshed to be consistent with the root-zone soil moisture.
3. The CO2 compensation concentration of photosynthesis (ZGAMMT), the maximum photosynthesis(ZANMAX), and the mesophyll conductance (ZGMEST) are refreshed to be consistent with the leaf
temperature (i.e. surface temperature in a single-source configuration).
4. The leaf-to-air saturation deficit within the canopy (depends on leaf temperature and air humidity) is
refreshed (ZDSP).

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

211

5. The CO2 concentration within the canopy is refreshed (ZCSP).
6. Ecosystem respiration is refreshed (ZRSOIL).
7. The solar zenith angle is prescribed (PZENITH).
8. Integrated canopy values of photosynthesis (ZTPST), net assimilation (ZTAN), and leaf conductance(ZTGS) are obtained by a 3-point Gauss quadrature method (SIZE(PABC) is equal to 3 ; can be modified).
9. The PAR at each Gauss level is calculated by radiative transfer equations in SUBROUTINE CCETR. In
CCETR, the interception of direct and diffuse light is represented. The fraction of diffuse radiation (ZXFD)
depends on the solar zenith angle, only.
10. At each Gauss level within the canopy, the photosynthesis model (SUBROUTINE COTWO) is run.
11. The canopy resistance (PRS) is calculated, as well as the net ecosystem exchange of CO2 (PCO2FLUX).

4.3 The ISBA-CC model
4.3.1 Introduction
The ISBA-CC model is a new version of ISBA developped by Gibelin et al. (2008) with the aim of simulating
the terrestrial carbon cycle.
ISBA-CC is based on the ISBA-A-gs model (Calvet and Soussana, 2001). The latter simulates the grossphotosynthesis rate, the dark leaf respiration, and changes in leaf biomass. Also, ISBA-A-gs simulates theecosystem respiration using a Q10 parameterization based on soil temperature and surface soil moisture(Albergel et al. 2010). ISBA-CC and ISBA-A-gs share the same photosynthesis model (Jacobs et al. 1996),
and the same representation of the photosynthesis response to drought (Calvet (2000), Calvet et al. 2004)
and of the carbon allocation to the leaf biomass compartment (Calvet and Soussana, 2001). The added valueof ISBA-CC is a more detailed representation of (1) the ecosystem respiration, including its autotrophic andheterotrophic components, (2) the biomass compartments, including roots and wood (in the case of trees).
The heterotrophic respiration, produced by the decomposition of the soil organic matter, is represented
following the STOMATE carbon model included into the IPSL ORCHIDEE model (Krinner et al. (2005)).
The litter and the soil organic matter pools are simulated, together with the carbon fluxes from one carbon
pool to another, and with the respiration flux to the atmosphere.
The various litter pools are supplied by the fluxes of dead biomass. A specific carbon allocation scheme was
implemented in order to represent various biomass components, which were not accounted for by ISBAA-gs: an explicit representation of roots, and (in the case of trees) of the above-ground and below-groundwood. For all the biomass compartments, turnover and respiration terms are calculated. Also, ISBA-CC
simulates the autotrophic respiration, the net primary production (NPP), and the total biomass of the plant.

4.3.2 Allocation scheme
Evolution of the biomass compartments
The ISBA-CC allocation scheme simulates the various carbon reservoirs of the plant. Six biomass pools are
considered, in units of kg m−2 , including four above-ground pools and two below-ground pools:
SURFEX v8.1 - Issue no 3 - 2018

212

Figure 4.24: Schematic representation of the plant carbon reservoirs and fluxes in (a) ISBA-A-gs (Calvet
and Soussana, 2001), and in ISBA-CC for (b) herbaceous (c) and woody vegetation. The various biomass
reservoirs are prefixed by B. Input and output fluxes are indicated for each reservoir: allocation and storage(A and S, solid arrows), mortality (M, dashed arrows) and respiration (R, dotted arrows). The autotrophic
respiration is the sum of all the biomass respiration terms.

BL
leaf biomass,Bs,act active structural biomass, linked to BL through nitrogen dilution,
Bs,pas passive structural biomass,
Bs,bg
below ground structural biomass,
Bw,ag above ground woody biomass (for trees),
Bw,bg below ground woody biomass (for trees).
This new allocation scheme was based, as much as possible, on the structure of the ”NIT” option of ISBAA-gs, described in (Calvet and Soussana (2001). The BL and Bs,act compartments were not modified andcorrespond to the BL and Bs compartments of ISBA-A-gs. Therefore ISBA-CC and ISBA-A-gs simulate thesame values of LAI, as LAI is derived from the leaf biomass BL . Bs,pas is a buffer reservoir corresponding
to a fraction of the Bs2 compartment. It is used for the storage of the biomass released by Bs,act during
the senescence phase. Bs,bg represents non-woody roots. Bw,ag and Bw,bg correspond to above-ground andbelow-ground wood components, respectively. They are used for woody vegetation types (i.e. broadleaf
deciduous and evergreen forests, and coniferous forests).
Figure 4.24 shows the plant carbon reservoirs and fluxes simulated by ISBA-A-gs and by ISBA-CC.
The evolution of all the biomass reservoirs is calculated with a time step ∆t of 1 day, following the genericequation 4.491.
∆B = AB − DB − RB
SURFEX v8.1 - Issue no 3 - 2018(4.491)CHAPTER 4. SOIL AND VEGETATION213

A B biomass term is driven by an incoming allocation term AB , by a respiration carbon loss term RB , andby a turnover term DB , expressed in units of kg m−2 . These three terms are detailed below, for all thebiomass compartments.
Respiration
The autotrophic respiration results from the oxydation of organic molecules, as part of the plant metabolism.
Generally, two autotrophic respiration terms are considered: the growth respiration associated to the production of new plant tissues, and the maintenance respiration, corresponding to the existing biomass.
The respiration terms are calculated at the time step of the model dt and accumulated at the ∆t = 1daytime step.
The BL respiration term of ISBA-A-gs, Rd , is used in ISBA-CC, also. It is included in the leaf net assimilation term, which is the difference between photosynthesis and dark respiration Rd . Rd corresponds to thesum of the growth respiration and of the maintenance respiration of the leaves.
X

RBL =

10−6

dt

MC
RdC dtPc MCO2(4.492)P
where
dt = ∆t, Pc is the fraction of carbon of the dry biomass, assumed to be equal to 40%, MC andMCO2 are the molecular weights of carbon and CO2 (12 and 44 g mol−1 , respectively), and RdC is the dark
respiration rate integrated from the leaf to the canopy.
The Bs respiration term of ISBA-A-gs, is used in ISBA-CC for Bs,act .
RBs,act =X(T −25)/10

Bs,act ηR Q10s

dt

(4.493)dt= 0.01 g g −1 j −1 , corresponding to a B

where Q10 = 2, and ηRs,act biomass loss of 1 % per day through◦respiration, at a temperature of 25 C.
For the other structure biomass pools (Bs,pas and Bs,bg ), the linear response to temperature of the maintenance respiration proposed by Ruimy et al. (1996) is used:RBs,pas =X

Bs,pas R0 (1 + 0.16 Ts ) dt

(4.494)Bs,bg R0 (1 + 0.16 Tp ) dt

(4.495)dt

RBs,bg =X
dt

where R0 is the respiration value at 0 ◦ C, equal to 1.19 10−4 g g−1 j −1 (as proposed by Ruimy et al. (1996)
for the sapwood compartment), Ts is leaf temperature and Tp is soil temperature in units of ◦ C. This value
can be compared with the scaling factor of Bs,act at 0 ◦ C in equation 4.493: 2 10−3 g g−1 j −1 .
Bw,ag and Bw,bg represent the wood, and no respiration term is associated to these reservoirs.
Decline term
The decline term represents the various processes, other than respiration, able to trigger a biomass decrease.
It includes decreases due to mortality and reallocation to other plant elements. It is expressed simply, as
an exponential decrease of the biomass. The decline term of the biomass B is expressed by the genericequation:∆t

DB = B (1 − e− τ )SURFEX v8.1 - Issue no 3 - 2018(4.496)

214
where τ is a residence time (in days).
The residence time of all the non-woody reservoirs is determined using the τM parameter of the ISBA-A-gs
model (the maximum leaf span time). For the leaf biomass BL , the leaf span time τBL is calculated daily,
based on the photosynthesis efficiency (see Eq. 4.467). The residence time is τM for the Bs,act and Bs,bgbiomass compartments, and τM /4 for Bs,pas . For the woody biomass compartments, the span time τw isequal to 40 years for broadleaf deciduous forests, 50 years for the coniferous forests, and 30 years for thebroadleaf evergreen forests. For the sake of comparison, in the ORCHIDEE model (Krinner et al. 2005),
the residence time of the wood compartment depends on the climatic zones: 80 years for boreal forests, 40
years for temperate forests, and 30 years for the tropical forests.
− τ∆t

DBL

= BL (1 − eDBs,act= Bs,act (1 − eDBs,pas= Bs,pas (1 − eDBs,bg= Bs,bg (1 − e

DBw,agDBw,bg

BL

)

− τ∆t

M

)

− 4τ ∆t
M

− τ∆t

=

=

(
(

M

)
(4.497))0

for herbaceous species,− τ∆tBw,ag (1 − ew

0) for woody species.
for herbaceous species,− τ∆t

Bw,bg (1 − ew) for woody species.

Then, the decline term is broken down into storage and mortality terms, dedicated to the carbon allocation
to other biomass reservoirs, and to the litter, respectively.
DB = MB + SB

(4.498)

Allocation
Allocation of carbon to BL , ABL , is the same as in the ”NIT” option of ISBA-A-gs (Calvet and Soussana,2001). The leaf biomass is directly supplied by gross assimilation (photosynthesis). The latter includes thenet carbon assimilation (AnC ), and the dark respiration (RdC ) combining the leaf growth respiration and theleaf maintenance respiration. AnC may present negative values, for example at nighttime.
ABL =

X
dt

10−6

MC
(AnC + RdC ) dt
Pc MCO2(4.499)where Pc is the carbon fraction of the dry biomass, equal to 40%, MC and MCO2 are the molecular weights
of carbon and CO2 (12 and 44 g mol−1 , respectively), and AnC and RdC are the net assimilation rate ofcarbon and the dark respiration, integrated at the canopy level.
The other reservoirs are supplied through biomass translocation. A storage term SB is derived from thedecline term DB , depending on the reservoir and on the plant type. The following reservoirs can be used
to allocate carbon to other reservoirs: BL , Bs,act and Bs,pas for herbaceous plants; BL , Bs,act , Bs,pas andBs,bg for woody plants, as shown in figure 4.24). For the other reservoirs, the decline is entirely converted
into mortality: Bs,bg for herbaceous vegetation types ; Bw,ag and Bw,bg for woody vegetation types. Also,
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

215

allocation and mortality depend on the phase of plant growth: the growing phase corresponds to an increaseof the leaf biomass, i.e. to the net gain of carbon resulting from net assimilation values higher than the
decline term BL ; the senescence phase corresponds to a decrease of the leaf biomass. During the growing
phase, all the decline DB terms are converted to storage SB , whereas during the senescence phase, only afraction of the decline terms is reallocated, and the other fraction becomes a mortality term MB supplying
the litter.
During the growing phase, the storage terms are calculated as:
SBL
= DBL
SBs,act = DBs,act
SBs,pas = D(Bs,pas0SBs,bg =DBs,bgSBw,ag = 0
SBw,bg = 0

for herbaceous species,
for woody species(4.500)During the senescence phase,

SBL
SBs,act
SBs,pasSBs,bgSBw,agSBw,bgsi ABL − RBL ≤ 0
 0=
fA,BL (ABL − RBL ) si 0 < fA,BL (ABL − RBL ) ≤ fD,BL DBL f
si fA,BL (ABL − RBL ) > fD,BL DBL
D,BL DBL= fD,Bs,act DBs,act= f(D,Bs,pas DBs,pas=

0fD,Bs,bg DBs,bg(4.501)for herbaceous species,
for woody species;=0=0where fD,B is the biomass B decline fraction reallocated towards other compartments during the senescence.
fD,BL , fD,Bs,act , fD,Bs,pas and fD,Bs,bg are equal to 0.5. A number of tests showed that this value permits
realistic simulations of the biomass allocation to the various compartments. The senescence BL storage
rate, used to supply the Bs,bg compartment (see below), cannot be higher than a fraction of the net carbon
supply provided by photosynthesis (ABL − RBL ), and this fraction fA,BL is equal to 0.5.
Then, the storage terms are used to supply one or several reservoirs.
The supply of Bs,act follows Calvet and Soussana (2001). During the growing phase, Bs,act is derived from
BL using the nitrogen dilution law. It must be noted that during the growing phase, while the leaf biomass
increases, the model is able to simulate a decrease of Bs,act . This may happen when the growing phaseoccurs after a temporary senescence phase or after a cut. ABs,act is the supply term of Bs,act . This term is
calculated a posteriori as the sum of the changes in Bs,act , of the respiration terms RBs,act and of the decline
DBs,act . ABs,act corresponds to the decline of BL . During the senescence, Bs,act is not supplied any longer.
ABs,act =(∆Bs,act + DBs,act + RBs,act
0during the growing phase,during the senescence phase.

(4.502)

When Bs,act decreases while the leaf biomass increases, Bs,pas is supplied by the carbon lost by the Bs,act
reservoir. The Bs,pas buffer reservoir avoids the irreversible loss of Bs,act biomass through mortality.
During the senescence, Bs,pas is not supplied any longer.
SURFEX v8.1 - Issue no 3 - 2018

216



 0
ABs,pas =−ABs,act 0during the growing phase with ABs,act ≥ 0,
during the growing phase with ABs,act < 0,during the senescence phase.

(4.503)

During the growing phase, Bs,bg is supplied by the storage reservoirs: BL , Bs,act et Bs,pas . During thesenescence phase, Bs,bg is supplied by the leaf biomass storage reservoir, only.
ABs,bg = fS,BL ,Bs,bg SBL + fS,Bs,act,Bs,bg SBs,act + fS,Bs,pas ,Bs,bg SBs,pas(4.504)

During the growing phase, fS,BL ,Bs,bg is the remaining SBL fraction after the carbon allocation to Bs,act ,following the nitrogen dilution law (equation 4.502). This quantity is updated at the daily time step. During
the senescence phase, fS,BL ,Bs,bg = 1. fS,Bs,act,Bs,bg and fS,Bs,pas ,Bs,bg are constant. During the growing
phase, they are equal to 1 for herbaceous vegetation types and 0.3 for woody vegetation types, only, as theother fraction is allocated to the wood compartments (equations 4.505 and 4.506). During the senescencephase, they are equal to 0.
For woody vegetation types, the wood compartments are supplied by the storage of Bs,act and Bs,pas for
Bw,ag , and by the storage of Bs,bg for Bw,bg .
ABw,ag = (1 − fS,Bs,act ,Bs,bg ) SBs,act + (1 − fS,Bs,pas ,Bs,bg ) SBs,pas(4.505)

ABw,bg = SBs,bg(4.506)Mortality
The mortality of a biomass compartment results from high decline term values, higher than the storage
term (if any). The mortality is used to supply the above- and below-ground litter compartments of the soilorganic matter scheme. This definition of the mortality differs slightly from the definition used by Calvet andSoussana (2001), who allow the use of a fraction or the BL mortality to supply the below-ground reservoir
Bs2 . In the ISBA-CC model, this contribution supplies the storage term.
MB = DB − SB(4.507)4.3.3 Coupling with the soil organic matter scheme
In order to simulate the terrestrial carbon cycle in a more realistic way, the simple ecosystem respiration
equation used in ISBA-A-gs (Albergel et al. 2010) is replaced by the soil organic matter scheme used in
ORCHIDEE (Krinner et al. 2005).
Overview
The soil respiration scheme used in ISBA-CC is derived from the STOMATE (Saclay Toulouse Orsay Modelfor the Analysis of Terrestrial Ecosystems) carbon model included in the ORCHIDEE (ORganizing Carbon
and Hydrology in Dynamic EcosystEms) (Krinner et al. 2005) land surface model. The latter is an adaptationof one of the first versions of the CENTURY (Parton et al. (1987, 1988) model.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION217

CENTURY simulates the carbon flux and storage and their interactions with the water cycle and nutrient(nitrogen N, sulfur S, and phosphorus P) cycles, in the soil-plant system. It includes a plant growth module, together with a representation of the soil organic matter. Initially, CENTURY was designed for thesimulation of the crops and grasslands of the US Great Plains (Parton et al. 1987; 1988).
The current version of CENTURY differs from the older version used in STOMATE, but the main attributes
are the same (www.nrel.colostate.edu/projects/century/, last access January 2012). Also, CENTURY was
improved and validated for other vegetation types and other biomes (Parton et al. (1993), Peng et al. (1998)),
and has become a reference model in the international scientific community.
The model simulates several carbon pools of the soil, corresponding to different organic matter categories,
residence time, and location, together with the carbon fluxes from one pool to another.

Figure 4.25: Schematic representation of the heterotrophic respiration parameterization of ISBA-CC,
adapted from Parton et al. (1987). The soil carbon pools are indicated together with input mortality terms(dashed lines), fluxes of carbon exchanged between the pools (solid lines), and fluxes of mineralized carbon(dotted lines). The heterotrophic respiration is the sum of all the fluxes of mineralized carbon. The various
carbon pools are reported in Table 4.13.

Four litter categories are simulated: two surface litter compartments, supplied by the mortality fluxes of
the above-ground biomass, and two soil litter compartments, supplied by the mortality fluxes of the belowground biomass. For both above- and below-ground litter, two carbon reservoirs displaying contrasting
residence times are considered. The structural litter is made of the lignin and cellulose of the dead vegetation residues, with a residence time of 2 to 5 years. The metabolic litter is made of more labile organic
components, with a residence time of 0.1 to 1 year (Parton et al. 1988).
SURFEX v8.1 - Issue no 3 - 2018

218
Also, three soil organic matter pools are simulated. They are supplied by the organic matter flux producedby the litter compartments (figure 4.25). The active pool represents the soil microorganisms, together withthe decomposition products with a short residence time (2 to 4 years). The slow pool represents the soilorganic molecules/components characterized by a residence time ranging from 20 to 50 years. The passive
pool represents the soil organic molecules/components characterized by a residence time ranging from 800
to 1200 years (Parton et al. 1988). These simulated carbon pools do not represent distinct physical entities
but, rather, various chemical status of the soil organic matter. At a given soil depth, the soil may containseveral types of organic matter, at various decomposition stages. Decomposition is controlled by climaticconditions (soil moisture and soil temperature), by the physical properties of the soil (e.g. texture), and by
the chemical composition of the substrate (i.e. the carbon, nitrogen, lignin content of the residues). While
CENTURY simulates the nutrient (nitrogen N, sulfur S, and phosphorus P) cycles, and their interactions withthe carbon cycle (Parton et al. 1987; 1988), this capability was not implemented so far in either STOMATEor ISBA-CC.
Supply of litter compartments
The ISBA-CC allocation scheme, described in Sect. 4.3.2, provides a flux of dead vegetation residues fromthe various plant elements. These residues supply the litter compartments according to which plant element
is considered.
The residues of the above-(below-)ground biomass supply the above-(below-)ground litter compartments.
Also, the structural/metabolic litter compartments are supplied according to the lignin to nitrogen ratio of
the residues. The fraction allocated to the metabolic litter FM is:
FM = 0.85 − 0.018

LN(4.508)The other fraction FS is allocated to the structural litter:
FS = 1 − FM(4.509)Therefore, high L/N values tend to produce more structural litter.
In CENTURY, the lignin content of the biomass depends on the accumulated yearly precipitation, andthe nitrogen concentration of the biomass is calculated by the model. In STOMATE, the L/N values areconstant and result from the values of L/C and C/N . Table 4.12 shows the L/C, C/N , and L/N values
used by ISBA-CC (see Sect. 4.3.2), derived from those used by STOMATE. It must be noted that the C/N
could be derived, also, from the Pc /NL ratio.
Biomass Compartment
BL
Bs,actBs,pas
Bs,bg
Bw,ag
Bw,bg

L/C
0.22
0.35
0.35
0.35
0.35
0.35

C/N
40
40
40
40
40
40

L/N
8.8
14
14
14
14
14

Table 4.12: Lignin to carbon, carbon to nitrogen, and lignin to nitrogen ratio for all the biomass compartments of the ISBA-CC model.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

219

Decomposition of the soil organic matter
Changes in soil organic matter pools are represented as:
dCi= Kia Md Td Ci(4.510)dt
where Ci is the carbon content (in units of gC m−2 ) of the soil organic matter pool i (see Table 4.13),
Kia is the decomposition rate (in units of yr −1 ) of the soil organic matter pool i, Md is the response of
the decomposition to soil wetness (dimensionless, ranging between 0 and 1), and Td is the response of thedecomposition to soil temperature (dimensionless, ranging between 0 and 1).
Reservoir
Structural above-ground litter
Metabolic above-ground litter
Structural below-ground litter
Metabolic below-ground litter
Active carbon pool
Slow carbon pool
Passive carbon pool

Index
1
2
3
4
5
6
7

Table 4.13: Indices i of the soil carbon pools.
The decomposition rate Kia is derived from the maximum decomposition rate Ki , possibly modulated byphysical characteristics:
K1a = K1 exp(−3 Ls1 )K2a = K2
K3a = K3 exp(−3 Ls3 )K4a = K4
K5a = K5 (1 − 0.75(fsilt + fclay ))K6a = K6
K7a = K7

(4.511)

where Lsi is the fraction of lignin in the structural litter pools, fsilt and fclay are the fractions of silt and clayin the soil. High lignin fraction values tend to slow down the decomposition of the structural litter (smallvalues of Kia ). Similarly, fine-textured soils (high fractions of either silt or clay) tend to stabilize the organic
molecules and a lower decomposition rate of the active carbon pool is simulated. In ISBA-CC, the original
CENTURY expression for K5a , depending on (fsilt + fclay ), is used, while in STOMATE, the (fsilt + fclay )term is replaced by fclay .
Table 4.14 presents the equivalent residence time values Ki−1 (where Ki is the maximum decompositionrate) used in the initial version of CENTURY (Parton et al. 1987) and in STOMATE (Krinner et al. 2005),
for the various carbon pools of the soil. While in CENTURY the maximum decomposition rate Ki is 20%
smaller for the above-ground litter than for the below-ground litter, the same value is used for the two littercompartments in STOMATE. Moreover, the Ki value of the passive carbon pool is smaller in STOMATE
than in CENTURY. In ISBA-CC, the STOMATE values are used.
In CENTURY, the dependence of the decomposition on soil moisture is represented by a normalized factor,
Md , driven by the ratio of monthly precipitation to the potential evaporation rate. In STOMATE, the original
representation of Md was replaced by a function depending on soil moisture (Krinner et al. 2005). It must
SURFEX v8.1 - Issue no 3 - 2018

220
Reservoir
Structural above-ground litter
Metabolic above-ground litter
Structural below-ground litter
Metabolic below-ground litter
Active carbon pool
Slow carbon pool
Passive carbon pool

1/Ki
CENTURY
0.252
0.068
0.204
0.055
0.137
5.05
147.5

1/Ki
STOMATE
0.245
0.066
0.245
0.066
0.149
5.37
241.

Table 4.14: Values of the equivalent residence time Ki−1 (year) used in the initial version of CENTURY(Parton et al. 1987) and in STOMATE (Krinner et al. 2005).
be noted that while the minimum value of Md is 0 in (Krinner et al. 2005), the value actually used in the
ORCHIDEE code is 0.25:
Md = min(0.25, max 1, −1.1θ 2 + 2.4θ − 0.29)

where θ is a normalized soil moisture value ranging between 0 and 1:
w − wwilt)
θ = min 0, max(1,wf c − wwilt(4.512)(4.513)where w is either the surface or the root-zone soil moisture (see below), in units of m3 m−3 , wwilt is soil
moisture at wilting point (in units of m3 m−3 ), and wf c is soil moisture at field capacity (in units of m3 m−3 ).
In ISBA-CC, this equation was modified, in order to account for the drop in the decomposition rate for highsoil moisture values, ranging between wilting point and saturation values (equation 4.514). Indeed, whilewater is a limiting factor for microbial growth at moderate soil moisture values, above field capacity, an
increase in soil moisture content tends to slow down the exchanges of oxygen in the soil, down to anaerobic
conditions at saturation. In the latter situation, less CO2 is emitted through heterotrophic respiration. Following Probert et al. (1998) (the APSIM model), the modified equation allows a linear decrease of Md , from
1 to 0.5, when soil moisture increases from field capacity to saturation. Moreover, the minimum Md value(at low soil moisture values) is taken as 0.05. The latter is consistent with the group of models described by
Paul (2001).
For θ ≤ wf c ,For θ ≥ wf c ,Md = min(0.05, max(1, −1.1θ 2 + 2.4θ − 0.29))
Md = max(0.5, 1 − 0.5 θsat )(4.514)

where θsat is another soil moisture index defined as:θsat =

w − wf cwsat − wf c

(4.515)where wsat is the saturation soil moisture value.
The Md values used in STOMATE and ISBA-CC are shown by Fig. 4.26.
Since the soil organic matter model does not represent the profile carbon content of the soil, two soil moisturequantities are used in ISBA-CC: the surface soil moisture (a skin soil moisture corresponding to a thin soil
layer of about 1cm) and the root-zone soil moisture. For the litter reservoirs, w, wwilt , wf c and wsat
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

221

Figure 4.26: Normalized decomposition response function to soil moisture used in (left) STOMATEORCHIDEE and (right) ISBA-CC. The three vertical dashed lines indicate (from left to right) wwilt , wf c
and wsat .

correspond to the surface soil moisture. For the other reservoirs, w, wwilt , wf c and wsat correspond to theroot-zone soil moisture.
In CENTURY, the dependence of the decomposition on temperature is represented by a normalized factor,
Td , driven by the average monthly temperature, according to a bell curve (Parton et al. 1987).
In STOMATE, Td is defined as:
T −30

Td = 2( 10 )(4.516)

where T is soil temperature in units of ◦ C. This formulation is used in ISBA-CC, also.
The Td values used in STOMATE and ISBA-CC are shown by Fig. 4.27.
Since the soil organic matter model does not represent the profile carbon content of the soil, two soil temperature quantities are used in ISBA-CC: the surface temperature Ts and a deep soil temperature Tp . For thelitter reservoirs, T = Ts . For the other reservoirs, T = Tp .
Carbon fluxes
The decomposition of the organic matter contained in the soil carbon reservoir i, dCi /dt, triggers various
carbon fluxes (Fig. 4.25). A fraction of the decomposed organic matter fi,CO2 is mineralized through therespiration process and released as CO2 to the atmosphere. The other fraction is allocated to the other carbon
pools of the soil, based on their resistance to decomposition. The fraction of the decomposition flux fromreservoir i to reservoir j is fi,j , and:Xfi,j + fi,CO2 = 1(4.517)j

For the structural litter reservoirs, the decomposition supplies the respiration flux and the stabilisation ofcarbon into a soil organic matter carbon pool, either active or slow, depending on the lignin content of the
SURFEX v8.1 - Issue no 3 - 2018

222

Figure 4.27: Normalized decomposition response function to soil temperature used in both STOMATEORCHIDEE and ISBA-CC.

litter and on the nature of the litter (above-ground or below-ground). The lignin tends to reduce both themineralization and the decomposition of the plant residues.
For the above-ground structural litter, the fractions are defined as:

f1,5 = 0.55 (1 − L1 )f1,6 = 0.7 L1
f1,CO2 = 0.45 (1 − L1 ) + 0.3 L1(4.518)where L1 is the lignin fraction of the above-ground structural litter reservoir.
For the below-ground structural litter, the fractions are slightly different, in relation to a lower efficiency ofthe decomposition process to stabilize carbon into the active soil organic matter pool:

f3,5 = 0.45 (1 − L3 )f3,6 = 0.7 L3
f3,CO2 = 0.55 (1 − L3 ) + 0.3 L3(4.519)where L3 is the lignin fraction of the below-ground structural litter reservoir.
The decomposition of the metabolic litter reservoirs supplies the respiration flux and the stabilization ofcarbon into the active soil organic matter carbon pool. The fractions are the same for above-ground andbelow-ground reservoirs:
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 4. SOIL AND VEGETATION

223

f2,5 = 0.45
f2,CO2 = 0.55
(4.520)f4,5 = 0.45
f4,CO2 = 0.55
The decomposition of the active soil organic matter carbon pool supplies the respiration flux and the slow
and passive soil organic matter carbon pools, based on soil texture:
f5,6 = 1 − 0.004 − (0.85 − 0.68 (fsilt + fclay ))f5,7 = 0.004
f5,CO2 = 0.85 − 0.68 (fsilt + fclay )(4.521)

f6,5 = 0.42
f6,7 = 0.03
f6,CO2 = 0.55

(4.522)

The f5,6 and f5,CO2 terms are identical to those used in CENTURY. Note that in STOMATE, fclay is usedinstead of the (fsilt + fclay ) term.
The decomposition of the slow soil organic matter carbon pool supplies the respiration flux and the active
and passive soil organic matter carbon pools, based on soil texture:

Finally, the decomposition of the passive soil organic matter carbon pool supplies the respiration flux andthe active soil organic matter carbon pool.
f7,5 = 0.45
f7,CO2 = 0.55

(4.523)4.3.4 Description of a simulation with ISBA-CC
Not up-to-date, new version to be released by June 2018
ISBA-CC describes the evolution of several prognostic variables: the plant biomass reservoirs and the soilorganic matter reservoirs. Prescribing initial or equilibrium values of these reservoirs is not easy, at both
local and global scales. Indeed, accurate observations of these quantities are lacking. More often than not,the various biomass components are not measured separately, or do not correspond to the definition of themodelled compartments. Also, the soil carbon observations are sparse, and generally concern the first top
centimeters of the soil, rarely below 30cm, and barely ever below 1m.
In order to avoid drifts in the carbon reservoirs, spin-up simulations must be performed, until equilibrium
reservoir values are reached. Whereas the initial CENTURY model was designed to work at a monthly
scale, ISBA-CC accounts for the diurnal cycle and is coupled with a land surface model working at the halfhourly time scale or better. As the time scale for reaching equilibrium values is about a few hundred years
for wood and several thousand years for the passive soil carbon pool, the spin-up simulations concern very
long periods of time. Therefore, the spin-up simulations cannot involve the whole coupled model. Instead,the carbon reservoir spin-up is performed offline, in several steps described below.
1. A first spin-up simulation (a few years) is performed with ISBA-CC in order to initialize the soil
moisture reservoirs, together with the biomass reservoirs presenting a relatively high turnover such asleaves and the plant structural biomass. For the woody plant types, the wood allocation terms resulting
from this simulation are stored at a daily time step (see Section 4.3.2).
SURFEX v8.1 - Issue no 3 - 2018

224
2. An offline program produces the evolution of wood reservoirs, at a daily time step, until equilibrium
has been reached, using the allocation and decline terms. The latter depends on the amount of carbon
stored in the reservoir (Section 4.3.2), and as such must be recalculated every day.
3. A second ISBA-CC simulation is performed, in order to calculate and store daily surface and deep
soil temperature and soil moisture values. Also, the mortality fluxes of the plant biomass reservoirs
are obtained.
4. An offline program produces the evolution of the soil carbon reservoirs, at a monthly time step, until
equilibrium has been reached, using the mortality fluxes and the soil temperature and soil moisturevalues, based on the equations listed in Section 4.3.3. The equilibrium is reached after several thousand years. It must be noted that since the use of a monthly time step tends to filter out the variabilityof the surface soil moisture, the obtained equilibrium values may differ from those that would havebeen obtained using a daily time step.
5. Finally, a last ISBA-CC simulation permits the spin-up of the litter reservoirs and of the active soilorganic matter.
A major shortcoming of this equilibrium method is that on an annual or multi-annual basis, the litter supply and the gross primary production are counterbalanced by the heterotrophic respiration, and by the autotrophic respiration, respectively. Therefore, the average net carbon exchange and net primary production
present null values. This method does not permit the determination of long term land carbon sinks andsources. Performing more refined carbon budgets at a global scale is very difficult, as a perfect knowledgeof the initial values of the carbon reservoirs and of the land cover/land use history is needed, especially for
managed forests and for agricultural lands. However, the seasonal variability of the carbon fluxes can be
represented by this method, as well as the impact of extreme events (e.g. droughts). Also, the equilibrium
state can be used to initialize impact simulations related to the response of the terrestrial carbon cycle tolong term perturbations.
In practise, two SURFEX namelists (NAM ISBA and NAM PREP ISBA CARBON) have to be modified
before performing ISBA-CC runs. In NAM ISBA, CPHOTO = ’NCB’. In NAM PREP ISBA CARBON,
CRESPSL = ’CNT’. The former activates the 6 biomass pools, and the latter activates the soil heterotrophic
repiration and the soil organic matter pools. The different steps of spin-up have been coded in a script calledspinup CC.bsh, available on the SURFEX web site. This script automatically perfoms the namelist changes
and the simulation repetitions needed for the spin-up. This script can be used as a template and be adapted
for specifics needs. Please note that the spin-up procedure is designed for inputs and outputs in ASCII
format. In particular, the NetCDF, and FA formats cannot be used.

4.3.5 Conclusion
The ISBA-CC model is a new version of ISBA permitting the detailed simulation of the land-atmospherecarbon exchange. It results from the coupling between ISBA-A-gs (Calvet and Soussana, 2001) and theheterotrophic respiration parameterization used in ORCHIDEE (Krinner et al. 2005). This coupling has
required a number of developments.
The ISBA-A-gs allocation scheme was upgraded, in order to simulate all the plant biomass compartments,roots and wood in particular (Section 4.3.2). The principles of the initial allocation scheme, proposed by
Calvet and Soussana (2001), were extended to the new biomass reservoirs. All the plant respiration terms
are now calculated and their sum represents the autotrophic respiration. Also, the mortality of the biomass
elements is calculated, and supplies the heterotrophic respiration module. The latter is derived from the
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

225

parameterization used in ORCHIDEE (Krinner et al. 2005), based on the CENTURY model (Parton etal. 1987). It simulates several soil organic matter pools (above-ground and below-ground litter, and thedecomposed organic matter), the carbon fluxes between these pools, and the CO2 flux to the atmospheregenerated by the heterotrophic respiration (Section 4.3.3).
A few equations differ from the ORCHIDEE parameterization. The soil texture effect is based on theoriginal CENTURY formulation, i.e. using the silt and clay fraction sum (fsilt + fclay ) instead of themere clay fraction fclay in ORCHIDEE. Also, the decomposition response to soil moisture is based on thesaturation soil moisture value wsat , available in ISBA simulations. This permits the representation of thelower decomposition rates which are observed in anaerobic conditions.
The added value of ISBA-CC is the calculation of the two heterotrophic and autotrophic respiration terms,
allowing the simulation of the net primary production (NPP). The latter describes the net carbon flux absorbed by the vegetation. Also, wood compartments are simulated, and even if forest management processes
are not represented so far, forest biomass estimates can be used, to some extent, to validate the model simulations.
A complete ISBA-CC simulation has to be made in several steps, including three simulations separated byoffline spin-up simulations of (1) the plant biomass reservoirs, and (2) the soil carbon pools.
This method produces equilibrium simulations and does not permit the determination of long term landcarbon sinks and sources. However, the seasonal variability of the carbon fluxes can be represented by thismethod, as well as the impact of extreme events (e.g. droughts) and of climate change.

Bibliography[1] F. Abramopoulos, C. Rosenzweig, and B. Choudhury. Improved ground hydrology calculations for
global climate models (gcms): Soil water movement and evapotranspiration. J. Clim., 1:921–941,
1988.
[2] C. Albergel, J.-C. Calvet, J.-F. Mahfouf, C. Rüdiger, A. L. Barbu, S. Lafont, J.-L. Roujean, J. P.
Walker, M. Crapeau, and J.-P. Wigneron. Monitoring of water and carbon fluxes using a land data
assimilation system: a case study for southwestern france. Hydrol. and Earth Syst. Sci., 14(6):1109–
1124, 2010.
[3] K. M. Andreadis, P. Storck, and D. P. Lettenmaier. Modeling snow accumulation and ablation processes in forested environments. Water Resour. Res., 45(5), 2009. W05429.
[4] Decharme B., E. Martin, and S. Faroux. Reconciling soil thermal and hydrological lower boundary
conditions in land surface models. J. Geophys. Res., 118, 2013.
[5] M. J. Best, A. Beljaars, J. Polcher, and P. Viterbo. A proposed structure for coupling tiled surfaces
with the planetary boundary layer. J. Hydrometeorol., 5(6):1271–1278, December 2004.
[6] K. J. Beven and M. J. Kirkby. A physically based, variable contributing area model of basin hydrology/ un modèle base physique de zone d’appel variable de l’hydrologie du bassin versant. Hydrol. Sci.
Bull., 24(1):43–69, March 1979.
[7] Chandrakant M. Bhumralkar. Numerical experiments on the computation of ground surface temperature in an atmospheric general circulation model. J. Appl. Meteor., 14(7):1246–1258, October
1975.
SURFEX v8.1 - Issue no 3 - 2018

226
[8] R. Bintanja and M.R. Van den Broeke. The surface energy balance of antarctic snow and blue ice. J.
Appl. Meteor., 34(4):902–926, 1995.
[9] A.-K. Blackadar. Modeling the nocturnal boundary layer. In Third Symp. on Atmospheric Turbulence,
Diffusion and Air Quality , Boston, Amer. Meteor. Soc., pages 46–49, 1976.
[10] D. H. Boelter. Physical properties of peats as related to degree of decomposition. Soil Science Societyof America Journal, 33:606–609, 1969.
[11] G. B. Bonan. A land surface model (lsm version 1.0) for ecological, hydrological, and atmosphericstudies: technical description and user’s guide. Technical report, National Center for AtmosphericResearch, Boulder, CO, Tech. Note TN-417+STR, 150 p, 1996.
[12] G. B. Bonan and Shugart H. H. Environmental-factors and ecological processes in boreal forests.
Annu Rev Ecol Syst, 20:128, 1989.
[13] A. Boone. Modelisation des processus hydrologiques dans le schema de surface ISBA: Inclusiond’un reservoir hydrologique, du gel et modelisation de la neige. PhD thesis, University Paul Sabatier,Toulouse, France, 2000.
[14] A. Boone, J. C. Calvet, and J. Noilhan. Inclusion of a third soil layer in a land surface scheme using
the force-restore method. J. Appl. Meteorol., 38(11):1611–1630, November 1999.
[15] A. Boone and P. Etchevers. An intercomparison of three snow schemes of varying complexity coupled
to the same land surface model: Local-scale evaluation at an alpine site. J. Hydrometeorol., 2(4):374–
394, 2001.
[16] A. Boone, V. Masson, T. Meyers, and J. Noilhan. The influence of the inclusion of soil freezing on
simulations by a soil-vegetation-atmosphere transfer scheme. J. Appl. Meteorol., 39(9):1544–1569,
September 2000.
[17] A. Boone, P. Samuelsson, S. Gollvik, A. Napoly, L. Jarlan, E. Brun, and B. Decharme. The interactions between soil-biosphere-atmosphere (isba) land surface model multi-energy balance (meb)option in surfex - part 1: Model description. Geosci. Model Dev., 30:1–30, 2017.
[18] L.C. Bowling, D.P. Lettenmaier, B. Nijssen, L.P. Graham, D.B. Clark, M. El Maayar, R. Essery, Goers, Y. S., Gusev, F. Habets, B. van den Hurk, J. Jin, D. Kahan, D. Lohmann, X. Ma, S. Mahanama,
D. Mocko, O. Nasonova, G. Niu, P. Samuelsson, A.B. Shmakin, K. Takata, D. Verseghy, P. Viterbo,
Y. Xia, Y. Xue, and Z.L. Yang. Simulation of high-latitude hydrological processes in the torne kalix
basin: Pilps phase 2(e): 1. experiment description and summary intercomparisons. Global and Planetary Change, 38:1–30, 2003.
[19] I. Braud. Sispat user’s manual. Model Documentation, September 2000 3.0, LTHE, LTHE, BP 53,
38041 Grenoble Cédex 9, France, 2000.
[20] I. Braud, A. C. Dantas-Antonino, M. Vauclin, J.L. Thony, and P. Ruelle. A simple soil plant atmosphere transfer model (sispat), development and field verification. J. Hydrol., 166:213–250, 1995.
[21] I. Braud, J. Noilhan, P. Bessemoulin, P. Mascart, R. Haverkamp, and M. Vauclin. Bare-ground surface
heat and water exchanges under dry conditions: Observations and parameterization. Bound.-Layer
Meteorol., 66(1):173–200, 1993.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

227[22] B. Bringfelt, J. Räisänen, S. Gollvik, G. Lindström, L. P. Graham, and A. Ullerstig. The land surface treatment for the Rossby Centre regional atmosphere climate model - version 2. Reports ofMeteorology and Climatology 98, SMHI, SE-601 76 Norrköping, Sweden, 2001.
[23] R. H. Brooks and A. T. Corey. Properties of porous media affecting fluid flow. J. Irrig. Drain. Am.
Soc. Civil Eng., 17:187–208, 1966.
[24] E. Brun, P. David, M. Sudul, and G. Brunot. A numerical model to simulate snow-cover stratigraphy
for operational avalanche forecasting. J. Glaciol., 38:13–22, 1992.
[25] E. Brun, E. Martin, V. Simon, C. Gendre, and C. Coléou. An energy and mass model of snow coversuitable for operational avalanche forecasting. J. Glaciol., 35(121):333–342, 1989.
[26] E. Brun, V. Vionnet, B. Decharme, Y. Peings, R. Valette, A. Boone, F. Karbou, and S. Morin. Simulation of northern eurasian local snow depth, mass and density using a detailed snowpack model andmeteorological reanalyses. J. Hydrometeorol., 14:203–219, 2013.
[27] J. C. Calvet, A. L. Gibelin, J. L. Roujean, E. Martin, P. Le Moigne, H. Douville, and J. Noilhan.
Past and future scenarios of the effect of carbon dioxide on plant growth and transpiration for threevegetation types of southwestern france. Atmos. Chem. and Phys., 8(2):397–406, 2008.
[28] J.-C. Calvet, S. Lafont, E. Cloppet, F. Souverain, V. Badeau, and C. Le Bas. Use of agricultural
statistics to verify the interannual variability in land surface models: a case study over france withisba-a-gs. Geosci. Model Dev., 5(1):37–54, 2012.
[29] J. C. Calvet and J. Noilhan. From near-surface to root-zone soil moisture using year-round data. J.
Hydrometeorol., 1(5):393–411, October 2000.
[30] J. C. Calvet, J. Noilhan, and P. Bessemoulin. Retrieving the root-zone soil moisture from surface
soil moisture or temperature estimates: A feasibility study based on field measurements. J. Appl.
Meteorol., 37(4):371–386, April 1998.
[31] J. C. Calvet, J. Noilhan, J. L. Roujean, P. Bessemoulin, M. Cabelguenne, A. Olioso, and J. P.
Wigneron. An interactive vegetation svat model tested against data from six contrasting sites. Agric.
and For. Meteorol., 92(2):73–95, July 1998.
[32] J. C. Calvet, V. Rivalland, C. Picon-Cochard, and J. M. Guehl. Modelling forest transpiration and co2
fluxes - response to soil moisture stress. Agric. and For. Meteorol., 124(3-4):143–156, August 2004.
[33] J. C. Calvet and J. F. Soussana. Modelling co2-enrichment effects using an interactive vegetation svat
scheme. Agric. and For. Meteorol., 108(2):129–152, June 2001.
[34] C. M. Carmagnola, S. Morin, M. Lafaysse, F. Domine, B. Lesaffre, Y. Lejeune, G. Picard, and L. Arnaud. Implementation and evaluation of prognostic representations of the optical diameter of snow
in the surfex/isba-crocus detailed snowpack model. The Cryosphere, 8(2):417–437, 2014.
[35] D. Carrer, J.-L. Roujean, S. Lafont, J.-C. Calvet, A. Boone, B. Decharme, C. Delire, and J.-P.
Gastellu-Etchegorry. A canopy radiative transfer scheme with explicit fapar for the interactive vegetation model isba-a-gs: Impact on carbon fluxes. J. Geophys. Res., 188:888–903, 2013.
[36] K. A. Cherkauer and D. P. Lettenmaier. Hydrologic effects of frozen soils in the upper mississippi
river basin. J. Geophys. Res., 104(D16):19599–19610, 1999.
SURFEX v8.1 - Issue no 3 - 2018

228[37] B. J. Choudhury and J. L. Monteith. A four-layer model for the heat budget of homogeneous land
surfaces. Q. J. Roy. Meteor. Soc., 114:373–398, 1988.
[38] R. B. Clapp and G. M. Hornberger. Empirical equations for some soil hydraulic properties. Water
Resour. Res., 14(4):601–604, 1978.
[39] A. Clifton, J.D. Ruedi, and M. Lehning. Snow saltation threshold measurements in a drifting-snow
wind tunnel. J. Glaciol., 52(179):585–596, 2006.
[40] A. J. Pitman Cogley, J. G. and A. Henderson-Sellers. A land surface for large scale climate models,tech. note 90-1. Technical report, Trent Univ., Peterborough, Ont., 1990.
[41] GJ Collatz, M Ribas-Carbo, and JA Berry. Coupled photosynthesis-stomatal conductance model forleaves of c4 plants. Funct. Plant Biol., 19(5):519–538, January 1992.
[42] B. J. Cosby, G. M. Hornberger, R. B. Clapp, and T. R. Ginn. A statistical exploration of the relationships of soil moisture characteristics to the physical properties of soils. Water Resour. Res.,
20:682–690, 1984.
[43] P. M. Cox, R. A. Betts, C. B. Bunton, R. L. H. Essery, P. R. Rowntree, and J. Smith. The impact
of new land surface physics on the gcm simulation of climate and climate sensitivity. Clim. Dyn.,
15:183–203, 1999.
[44] R. Dankers, Burke E. J., and J. Price. Simulation of permafrost and seasonal thaw depth in the jules
land surface scheme. Cryosphere, 5:773–790, 2011.
[45] J. Deardorff. Efficient prediction of ground temperature and moisture with inclusion of a layer ofvegetation. J. Geophys. Res., 83:1889–1903, 1978.
[46] J. W. Deardorff. A parameterization of ground-surface moisture content for use in atmospheric prediction models. J. Appl. Meteor., 16(11):1182–1185, November 1977.
[47] B. Decharme, A. Boone, C. Delire, and J. Noilhan. Local evaluation of the interaction between soil
biosphere atmosphere soil multilayer diffusion scheme using four pedotransfer functions. J. Geophys.
Res., 116(D20), October 2011.
[48] B. Decharme, E. Brun, A. Boone, C. Delire, P. Le Moigne, and S. Morin. Impacts of snowpack
properties and soil organic carbon content on characteristics and soil temperature profiles simulatedby the isba land surface model. Cryosphere, 10:853–877, 2016.
[49] B. Decharme and H. Douville. Introduction of a sub-grid hydrology in the isba land surface model.
Clim. Dyn., 26(1):65–78, January 2006.
[50] B. Decharme and H. Douville. Global validation of the isba sub-grid hydrology. Clim. Dyn.,
29(1):21–37, July 2007.
[51] B. Decharme, H. Douville, A. Boone, F. Habets, and J. Noilhan. Impact of an exponential profile ofsaturated hydraulic conductivity within the isba lsm: Simulations over the rhone basin. J. Hydrometeorol., 7(1):61–80, February 2006.
[52] C. Delire, J. C. Calvet, J. Noilhan, I. Wright, A. Manzi, and C. Nobre. Physical properties of amazonian soils: A modeling study using the anglo-brazilian amazonian climate observation study data. J.
Geophys. Res.-Atmos., 102(D25):30119–30133, December 1997.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

229[53] S.J. Déry and MK Yau. Large-scale mass balance effects of blowing snow and surface sublimation.
J. Geophys. Res., 107(D23):4679, 2002.
[54] C. E. Desborough. The impact of root-weighting on the response of transpiration to moisture stressin a land surface scheme. Mon. Weather Rev., 125:1920–1930, 1997.
[55] R. E. Dickinson, M. Shaikh, R. Bryant, and L. Graumlich. Interactive canopies for a climate model.
J. Clim., 11:2823–2836, 1998.
[56] Florent Domine, A-S Taillandier, and William R Simpson. A parameterization of the specific surface
area of seasonal snow for field use and for models of snowpack evolution. Journal of GeophysicalResearch: Earth Surface, 112(F2), 2007.
[57] H Douville. Développement et validation locale d’une nouvelle paramétrisation du manteau neigeux.
Technical report, Note de travail de GMGEC, N36, Météo-France, 1994.
[58] H. Douville, J. F. Royer, and J. F. Mahfouf. A new snow parameterization for the meteo-france
climate model .1. validation in stand-alone experiments. Clim. Dyn., 12(1):21–35, November 1995.
[59] H. Douville, J. F. Royer, and J. F. Mahfouf. A new snow parameterization for the meteo-france
climate model .2. validation in a 3-d gcm experiment. Clim. Dyn., 12(1):37–52, November 1995.
[60] H. Dumenil and E. Todoni. A rainfall-runoff scheme for use in the hamburg climate model. Adv.
Theor. Hydrol., 9:129–157, 1992.
[61] D. G. Erbs, S. A. Klein, and J. A. Duffie. Estimation of the diffuse radiation fraction for hourly, daily
and monthly average global radiation. Sol. Energy, 28:293–304, 1982.
[62] Y. Fan, ML. Wood, E.and Baeck, and JA. Smith. The fractional coverage of rainfall over a grid:
Analyses of nexrad data over the southern plains. Water Resour. Res., 32:2787–2802, 1996.
[63] O.T. Farouki. Thermal Properties of Soils, volume 11. Series on Rock and Soil Mechanics, Trans.
Tech., 1986.
[64] Kaptu Tchuent A. T. Roujean J.-L. Masson V. Martin E. Faroux, S. and P. Le Moigne. Ecoclimapii/europe : a twofold database of ecosystems and surface parameters at 1 km resolution based onsatellite information for use in land surface, meteorological and climate models. GEOSCIENTIFIC
MODEL DEVELOPMENT, 6(2):563–582.
[65] G. D. Farquhar, S. von Caemmerer, and J. A. Berry. A biochemical model of photosynthetic co2
assimilation in leaves of c3 species. Planta, 149:78–90, 1980.
[66] Mark G Flanner and Charles S Zender. Linking snowpack microphysics and albedo evolution. Journal of Geophysical Research: Atmospheres, 111(D12), 2006.
[67] M. Fuchs, G. S. Campbell, and R. I. Papendick. An analysis of sensible and latent heat flow in apartially frozen unsaturated soil. Soil Sci. Soc. Am. J., 42:379–385, 1978.
[68] A.C.V. Getirana, A. Boone, and C. Peugeot. Evaluating lsm-based water budgets over a west africanbasin assisted with a river routing scheme. J. Hydrometeor., 15:2331–2346, 2014.
[69] D. Giard and E. Bazile. Implementation of a new assimilation scheme for soil and surface variables
in a global nwp model. Mon. Weather Rev., 128(4):997–1015, April 2000.
SURFEX v8.1 - Issue no 3 - 2018

230[70] A. L. Gibelin, J. C. Calvet, J. L. Roujean, L. Jarlan, and S. O. Los. Ability of the land surface modelisba-a-gs to simulate leaf area index at the global scale: Comparison with satellites products. J.
Geophys. Res.-Atmos., 111(D18):D18102, September 2006.
[71] A.-L. Gibelin, J.-C. Calvet, and N. Viovy. Modelling energy and co2 fluxes with an interactive
vegetation land surface model-evaluation at high and middle latitudes. Agric. and For. Meteorol.,148(10):1611–1628, 2008.
[72] H. Giordani. Expériences de validation unidimensionnelles du schéma de surface np89 aux normesarpège sur trois sites de la campagne efeda 91. Technical report, Note de travail 24 GMME/MétéoFrance, 1993.
[73] H. Giordani, J. Noilhan, P. Lacarrere, P. Bessemoulin, and P. Mascart. Modelling the surface processes and the atmospheric boundary layer for semi-arid conditions. Agric. and For. Meteorol.,
80:263–287, 1996.
[74] E. Gonzalez-Sosa, I. Braud, J.-L. Thony, M. Vauclin, P. Bessemoulin, and J.-C. Calvet. Modellingheat and water exchanges of fallow land covered with plant-residue mulch. Agr. For. Meteorol.,97(3):151–169, 1999.
[75] M Gordon, K. Simon, and P. Taylor. On snow depth predictions with the canadian land surface scheme
including a parametrization of blowing snow sublimation. Atmos.-Ocean, CMOS, 44:239–255, 2006.
[76] J. Goudriaan, van Laar, H.H., H. van Keulen, and W. Louwerse. Photosynthesis, CO2 and plant
production, pages 107–122. Plenum Press, New York, Series A, 86, 1985.
[77] G. Guyomarc’h and L. Merindol. Validation of an application for forecasting blowing snow. Ann.
Glaciol., 26:138–143, 1998.
[78] F. Habets, P. Etchevers, C. Golaz, E. Leblois, E. Ledoux, E. Martin, J. Noilhan, and C. Ottle.
Simulation of the water budget and the river flows of the rhone basin. J. Geophys. Res.-Atmos.,
104(D24):31145–31172, December 1999.
[79] F. Habets and G.-M. Saulnier. Subgrid runoff parameterization. Phys. and Chem. of the Earth, Part
B: Hydrol., Ocean. and Atmos., 26 (5-6):455–459, 2001.
[80] N. R. Hedstrom and J. W. Pomeroy. Measurements and modelling of snow interception in the boreal
forest. Hydrol. Process., 12:1611–1625, 1998.
[81] N. Isymov. An approach to the prediction of snow loads. Technical report, Faulty of Engineering
Science, The Univ. of Western Ontario, London, 1971. 442 pp.
[82] R. B. Jackson, J. Canadell, J. R. Ehleringer, H. A. Mooney, O. E. Sala, and E. D. Schulze. A global
analysis of root distributions for terrestrial biomes. Oecologia, 108(3):389–411, 1996.
[83] C. M. J. Jacobs. Direct impact of CO2 enrichment on regional transpiration. PhD thesis, Agricultural
University, Wageningen, The Netherlands, 1994.
[84] C.M.J. Jacobs, B.M.M. van den Hurk, and H.A.R. de Bruin. Stomatal behaviour and photosynthetic
rate of unstressed grapevines in semi-arid conditions. Agric. and For. Meteorol., 80(24):111–134,
July 1996.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

231[85] B. Jacquemin and J. Noilhan. Validation of a land surface parameterization using the hapex-mobilhy
data set. Bound.-Layer Meteorol., 52:93–134, 1990.
[86] O. Johansen. Thermal conductivity of soils. PhD thesis, University of Trondheim, Norway, 1975.
[87] H. Johnsson and L.-C. Lundin. Surface runoff and soil water percolation as affected by snow and soil
frost. J. Hydrol., 122(14):141–159, January 1991.
[88] Alexander A Kokhanovsky and Eleonora P Zege.
43(7):1589–1602, 2004.

Scattering optics of snow.

Applied Optics,[89] V. Koren, J. Schaake, K. Mitchell, Q.-Y. Duan, F. Chen, and J. M. Baker. A parameterization of snowpack and frozen ground intended for ncap weather and climate models. J. Geophys. Res., 104:19569–
19585, 1999.
[90] F. Kostel-Hughes, T. P. Young, and M. M. Carreiro. Forest leaf litter quantity and seedling occurrencealong an urban-rural gradient. Urban Ecosys., 2:263–278, 1998.
[91] G. Krinner, Nicolas Viovy, Nathalie de Noblet-Ducoudré, Jérme Ogée, Jan Polcher, Pierre Friedlingstein, Philippe Ciais, Stephen Sitch, and I. Colin Prentice. A dynamic global vegetation model forstudies of the coupled atmosphere-biosphere system. Glob. Biogeochem. Cycles, 19(1):1015–, February 2005.
[92] S. Lafont, A. Beljaars, M. Voogt, L. Jarlan, P. Viterbo, B. van den Hurk, and J.-C. Calvet. Comparisonof c-tessel co2 fluxes with transcom co2 fluxes. In Proc. Second Recent Advances in Quantitative
Remote Sensing II, Torrent (Valencia), Spain, 474-477, 2006.
[93] D. Lawrence and A. Slater. Incorporating organic soil into a global climate model. Clim. Dyn.,
30:145160, 2008.
[94] D. M. Lawrence, A.G. Slater, V. E. Romanovsky, and D. J. Nicolsky. The sensitivity of a model
projection of near-surface permafrost degradation to soil column depth and inclusion of soil organic
mater. J. Geophys. Res., 113, 2008.
[95] David Lawrence, Keith W. Oleson, Mark G. Flanner, Peter E. Thorton, Sean C. Swenson, Peter J.
Lawrence, Xubin Zeng, Zong-Liang Yang, Samuel Levis, Koichi Skaguchi, Gordan B. Bonan, andAndrew G. Slater. Parameterization improvements and functional and structural advances in version
4 of the community land model. J. Adv. Model. Earth Syst., 3:27p., 2011.
[96] G. Lemaire and F. Gastal. N uptake and distribution in plant canopies, pages 3–43. Springer, Berlin,
1997.
[97] M. G. Letts, N. T. Roulet, N. T. Comer, M. R. Skarupa, and D. L. Verseghy. Parametrization ofpeatland hydraulic properties for the canadian land surface scheme. Atmos Ocean, 38:141160, 2000.
[98] E. Wood Liang, Xu and D. Lettenmaier. Surface soil moisture parameterization of the vic-2l model:
Evaluation and modification. Glob. and Planet. Change, 13:195–206, 1996.
[99] Q Libois, G Picard, JL France, L Arnaud, M Dumont, CM Carmagnola, and MD King. Influence ofgrain shape on light penetration in snow. The Cryosphere, 7(6):1803–1818, 2013.
SURFEX v8.1 - Issue no 3 - 2018

232
[100] B. Loth, H.-F. Graf, and J. M. Oberhuber. Snow cover model for global climate simulations. J.
Geophys. Res., 98(D6):10451–10464, 1993.
[101] J.-F. Louis. A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Lay. Meteorol.,
17:187–202, 1979.
[102] L.-C. Lundin. Hydraulic properties in an operational model of frozen soil. J. Hydrol., 118:289–310,
1990.
[103] M. Lynch-Stieglitz. The development and validation of a simple snow model for the giss gcm. J.
Clim., 7(12):1842–1855, December 1994.
[104] J.-F. Mahfouf and J. Noilhan. Comparative study of various formulations of evaporation from baresoil using in situ data. J. Appl. Meteorol., 9:1354–1365, 1991.
[105] J. F. Mahfouf and J. Noilhan. Inclusion of gravitational drainage in a land surface scheme based on
the force-restore method. J. Appl. Meteorol., 35(6):987–992, June 1996.
[106] L. Mahrt and H. Pan. A two-layer model of soil hydrology. Bound.-Layer Meteorol., 29:1–20, 1984.
[107] A. O. Manzi and S. Planton. Implementation of the isba parameterization scheme for land surface
processes in a gcm-an annual cycle experiment. J. Hydrol., 155:353–387, 1994.
[108] D. Marbouty. An experimental study of temperature-gradient metamorphism. J. Glaciol., 26:303–
312, 1980.
[109] E. Martin, P. Le Moigne, and V. Masson. Le code de surface externalisée surfex de météo- france. In
Ateliers de Modélisation de lAtmosphère, 2007.
[110] P. Mascart, J. Noilhan, and H. Giordani. A modified parameterization of flux-profile relationships
in the surface layer using different roughness length values for heat and momentum. Bound.-Layer
Meteorol., 72:331–344, 1995.
[111] W. J Massman. Foliage distribution in old-growth coniferous tree canopies. Canadian Journal ofForest Research, 12(1):10–17, 1982.
[112] M. C. McCumber and R. A. Pielke. Simulation of the effects of surface fluxes of heat and moisture
in a mesoscale numerical model. J. Geophys. Res., 86 (C10):9929–9938, 1981.
[113] J. F. Meekins and B. C. McCarthy. Effect of environmental variation on the invasive success of anonindigenous forest herb. Ecol. Appl., 11(5):1336–1348, 2001.
[114] P. C. D. Milly. Moisture and heat transport in hysteretic, inhomogeneous porous media: a matrichead-based formulation and a numerical model. Water Resour. Res., 18 (3):489–498, 1982.
[115] J. L. Monteith, editor. Vegetation and the atmosphere, volume 1. Academic Press, 1975.
[116] Y. Nakai, T. Sakamoto, T. Terajima, K. Kitamura, and T. Shirai. The effect of canopy-snow on theenergy balance above a coniferous forest. Hydrol. Process., 13:2371–2382, 1999.
[117] A. Napoly, A. Boone, P. Samuelsson, S. Gollvik, E. Martin, R. Seferian, D. Carrer, B. Decharme, andL. Jarlan. The interactions between soil-biosphere-atmosphere (isba) land surface model multi-energybalance (meb) option in surfex - part 2: Model evaluation for local scale forest sites.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

233[118] D. J. Nicolsky, V. E. Romanovsky, V. A. Alexeev, and D. M. Lawrence. Improved modeling of
permafrost dynamics in alaska with clm3. Geophys Res Lett, 34, 2007.
[119] G.-Y. Niu and Z.-L. Yang. Effects of vegetation canopy processes on snow surface energy and massbalances. J. Geophys. Res., 109(D23), 2004. D23111.
[120] J. Noilhan and P. Lacarrère. Gcm grid-scale evaporation from mesoscale modeling.
8(2):206–223, 1995.

J. Clim.,[121] J. Noilhan and J. F. Mahfouf. The isba land surface parameterisation scheme. Glob. and Planet.
Change, 13(1-4):145–159, June 1996.
[122] J. Noilhan and S. Planton. A simple parameterization of land surface processes for meteorologicalmodels. Mon. Weather Rev., 117(3):536–549, 1989.
[123] J. Ogée and Y. Brunet. A forest floor model for heat and moisture including a litter layer. J. Hydrol.,255(1):212–233, 2002.
[124] H. Pan and L. Mahrt. Interaction between soil hydrology and boundary layer development. Bound.Layer Meteorol., 38:185–202, 1987.
[125] J.-P. Paquin and L. Sushama. On the arctic near-surface permafrost and climate sensitivities to soil
and snow model formulations in climate models. Clim. Dyn., 44:203228.
[126] W.J. Parton, D.S. Schimel, C.V. Cole, and D.S. Ojima. Analysis of factors controlling soil organic
matter levels in great plains grasslands. Soil Sci. Soc. Am. J., 51:1173–1179, 1987.
[127] W.J. Parton, J.M.O. Scurlock, D.S. Ojima, T.G. Gilmanov, R.J. Scholes, D.S. Schimel, T. Kirchner,
J.-C. Menaut, T. Seastedt, E. Garcia Moya, A. Kamnalrut, and J.I. Kinyamario. Observations andmodeling of biomass and soil organic matter dynamics for the grassland bioma worldwide. Glob.
Biogeochem. Cycles, 7:785–809, 1993.
[128] W.J. Parton, J.W.B. Stewart, and C.V. Cole. Dynamics of c, n, p and s in grassland soils: a model.
Biogeochem., 5:109–131, 1988.
[129] K. Paul. Temperature and moisture effects on decomposition. In M. Kirschbaum and R. Mueller,
editors, Net ecosystem exchange, pages 95–102. CRC for greenhouse accounting, 18-20 April 2001.
[130] C. Peng, M.J. Apps, D.T. Price, I.A. Nadler, and D.H. Halliwell. Simulating carbon dynamics along
the boreal forest transect case study (bftcs) in central canada: 1, model testing. Glob. Biogeochem.
Cycles, 12:381–392, 1998.
[131] C. D. Peters-Lidard, E. Blackburn, X. Liang, and E. F. Wood. The effect of soil thermal conductivity
parameterization on surface energy fluxes and temperatures. J. Atmos. Sci., 55(7):1209–1224, April
1998.
[132] A. J. Pitman, Z.-L. Yang, J. G. Cogley, and A. Henderson-Sellers. Description of bare essentials
of surface transfer for the bureau of meteorology research centre agcm. Technical report, BMRC
Research Report No. 32, 1991.
SURFEX v8.1 - Issue no 3 - 2018

234[133] J. Polcher, B. McAvaney, P. Viterbo, M. A. Gaertner, A. Hahmann, J. F. Mahfouf, J. Noilhan,
T. Phillips, A. Pitman, C. A. Schlosser, J. P. Schulz, B. Timbal, D. Verseghy, and Y. Xue. A proposal for a general interface between land surface schemes and general circulation models. Glob. andPlanet. Change, 19(1-4):261–276, December 1998.
[134] J. W. Pomeroy and K. Dion. Winter radiation extinction and reflection in a boreal pine canopy:
measurements and modelling. Hydrol. Process., 10:1591–1608, 1996.
[135] M.E. Probert, J.P. Dimers, B.A. Keating, R.C. Dalal, and W.M. Strong. Apsim’s water and nitrogen
modules and simulation of the dynamics of water and nitrogen in fallow systems. Agric. Syst., 56:1–
28, 1998.
[136] William M Putuhena and Ian Cordery. Estimation of interception capacity of the forest floor. J.
Hydrol., 180(1):283–299, 1996.
[137] Paul Ricchiazzi, Shiren Yang, Catherine Gautier, and David Sowle. Sbdart: A research and teachingsoftware tool for plane-parallel radiative transfer in the earth’s atmosphere. Bulletin of the American
Meteorological Society, 79(10):2101, 1998.
[138] R. Richtmeyer and K. Morton. Difference method for initial values problems. Interscience Publishers,
second edition, 1967.
[139] V. Rivalland, J.-C. Calvet, P. Berbigier, Y. Brunet, and A. Granier. Transpiration and co2 fluxes of apine forest: modelling the undergrowth effect. Ann. Geophys., 23:291–304, 2006.
[140] J.-L. Roujean. A tractable physical model of shortwave radiation interception by vegetative canopies.
J. Geophys. Res., 101D5:9523–9532, 1996.
[141] A. Ruimy, L. Kergoat, C. Field, and B. Saugier. The use of co2 flux measurements in models of the
global terrestrial carbon budget. Global Change Biology, 2(3):287–296, 1996.
[142] N. Rutter, R. Essery, J. Pomeroy, N. Altimir, K. Andreadis, I. Baker, A. Barr, P. Bartlett, A. Boone,
H. Deng, H. Douville, E. Dutra, K. Elder, C. Ellis, X. Feng, A. Gelfan, A. Goodbody, Y. Gusev,
D. Gustafsson, R. Hellstrom, Y. Hirabayashi, T. Hirota, T. Jonas, V. Koren, A. Kuragina, D. Lettenmaier, W.-P. Li, C. Luce, E. Martin, O. Nasonova, J. Pumpanen, R. D. Pyles, P. Samuelsson,
M. Sandells, G. Schadler, A. Shmakin, T. G. Smirnova, M. Stahli, R. St ckli, U. Strasser, H. Su,
K. Suzuki, K. Takata, K. Tanaka, E. Thompson, T. Vesala, P. Viterbo, A. Wiltshire, K. Xia, Y. Xue,
, and T. Yamazaki. Evaluation of forest snow processes models (SnowMIP2). J. Geophys. Res.,
114(D6):18, 2009.
[143] P. Samuelsson, S. Gollvik, and A. Ullerstig. The land-surface scheme of the rossby centre regional atmospheric climate model (rca3). Report in Meteorology 122, SMHI, SE-60176 Norrköping, Sweden,
2006.
[144] P. Samuelsson, C. Jones, U. Willén, A. Ullerstig, S. Gollvik, U. Hansson, C. Jansson, E. Kjellström,
G. Nikulin, and K. Wyser. The rossby centre regional climate model rca3: Model description andperformance. Tellus A, 63:1–3, 2011.
[145] R. A. Schmidt and D. R. Gluns. Snowfall interception on branches of three conifer species. Can. J.
For. Res., 21:1262–1269, 1991.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

235[146] R.A. Schmidt. Vertical profiles of wind speed, snow concentration, and humidity in blowing snow.
Bound.-Layer Meteorol., 23(2):223–246, 1982.
[147] P. J. Sellers, M. D. Heiser, and F. G. Hall. Relations between surface conductance and spectral
vegetation indices at intermediate (100 m2 to 15 km2 ) length scales. J. Geophys. Res., 97:19033–
19059, 1992.
[148] P. J. Sellers, Y. Mintz, Y. C. Sud, and A. Dalcher. A simple biosphere model (SiB) for use within
general ciculation models. J. Atmos. Sci., 43:505–531, 1986.
[149] P. J. Sellers, D. A. Randall, G. J. Collatz, J. A. Berry, C. B. Field, D. A. Dazlich, C. Zhang, G. D.
Collelo, and L. Bounoua. A revised land surface parameterization (SiB2) for atmospheric GCMs.
Part I: Model formulation. J. Climate, 9:676–705, 1996.
[150] Beven K.J. Silvapalan, M. and E.F. Wood. On hydrologic similarity: 2. a scaled model of storm
runoff production. Water Resour. Res., 23:2266–2278, 1987.
[151] S. Sun, J. Jin, and Y. Xue. A simple snow-atmosphere-soil transfer (sast) model. J. Geophys. Res.,
104:19587–19579, 1999.
[152] Anne-Sophie Taillandier, Florent Domine, William R Simpson, Matthew Sturm, and Thomas A Douglas. Rate of decrease of the specific surface area of dry snow: Isothermal and temperature gradientconditions. Journal of Geophysical Research: Earth Surface, 112(F3), 2007.
[153] B. J. J. M. Van den Hurk, P. Viterbo, A. C. M. Beljaars, and A. K. Betts. Offine validation of theera40 surface scheme, ecmwf techmemo. 295, 42 p. Technical report, ECMWF, Reading, 2000.
[154] J.-P. Vergnes, Decharme B., and Habets F. Introduction of groundwater capillary rises using
subgrid spatial variability of topography into the isba land surface model. J. Geophys. Res.,
119:11,06511,086, 2014.
[155] D. L. Verseghy. Class: A canadian land surface scheme for gcms. i. soil model. Int. J. Clim.,
11(2):111–133, 1991.
[156] V. Vionnet, E. Brun, S. Morin, A. Boone, S. Faroux, P. Le Moigne, E. Martin, and J.-M. Willemet.
The detailed snowpack scheme crocus and its implementation in surfex v7.2. Geoscientific Model
Development, 5(3):773–791, 2012.
[157] M. Voogt, B.J.J.M. van den Hurk, and C. Jacobs. The ecmwf land surface scheme extended witha photosynthesis and lai module tested for a coniferous site, knmi publication: Wr-06-02, 22 pp.
Technical report, KNMI, De Bilt, The Netherlands, 2006.
[158] D. A. De Vries. Thermal properties of soils. Physics of plant environment, 1963.
[159] W. Wang, A. Rinke, J. C. Moore, D. Ji, X. Cui, S. Peng, D. M. Lawrence, A. D. McGuire, E. J. Burke,
X. Chen, B. Decharme, C. Koven, A. MacDougall, K. Saito, W. Zhang, Alkama, R., T. J. Bohn,
P. Ciais, C. Delire, I. Gouttevin, T. Hajima, G. Krinner, D. P. Lettenmaier, P. A. Miller, B. Smith,
T. Sueyoshi, and A. B. Sherstiukov. Evaluation of airsoil temperature relationships simulated by land
surface models during winter across the permafrost region. Cryosphere, 10:1721–1737, 2016.
SURFEX v8.1 - Issue no 3 - 2018

236[160] T. B. Wilson, T. P. Meyers, J. Kochendorfer, M. C. Anderson, and M. Heuer. The effect of soil surface
litter residue on energy and carbon fluxes in a deciduous forest. Agr. For. Meteorol., 161:134–147,
2012.
[161] E. F. Wood, D. P. Lettenmaier, X. Liang, D. Lohmann, A. Boone, S. Chang, F. Chen, Y. J. Dai,R. E. Dickinson, Q. Y. Duan, M. Ek, Y. M. Gusev, F. Habets, P. Irannejad, R. Koster, K. E. Mitchel,O. N. Nasonova, J. Noilhan, J. Schaake, A. Schlosser, Y. P. Shao, A. B. Shmakin, D. Verseghy,
K. Warrach, P. Wetzel, Y. K. Xue, Z. L. Yang, and Q. C. Zeng. The project for intercomparisonof land-surface parameterization schemes (pilps) phase 2(c) red-arkansas river basin experiment: 1.
experiment description and summary intercomparisons. Glob. and Planet. Change, 19(1-4):115–135,
December 1998.
[162] Y. Xue, P. J. Sellers, J. L. Kinter, and J. Shukla. A simplified Biosphere Model for Global Climate
Studies. J. Climate, 4:345–364, 1991.
[163] Z.-L. Yang and G.-Y. Niu. The versatile integrator of surface atmospheric processes (visa): Part 1.
model description. Glob. Planet. Change, 38:175–189, 2003.
[164] R. J. Zhao. The xinanjiang model applied in china. J. Hydrol., 134:317–381, 1992.

SURFEX v8.1 - Issue no 3 - 2018

Chapter 5

Surface boundary layer scheme
Contents
5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

5.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
5.2.1

Atmospheric equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

5.2.2

Atmospheric equations modified by canopy obstacles . . . . . . . . . . . . . . . . 240

5.2.3

Implementation of the SBL equations into a surface scheme . . . . . . . . . . . . 241

5.2.4

Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

5.2.5

Turbulence scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

5.3

conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

5.4

Appendix: Vertical and temporal discretization . . . . . . . . . . . . . . . . . . . . . . 246
5.4.1

Vertical discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

5.4.2

Temporal discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

5.4.3

Implicit coupling with the atmospheric model . . . . . . . . . . . . . . . . . . . . 246

5.1 Introduction
Surface atmosphere exchanges, mainly momentum, water and heat surface fluxes, drive the boundary layer
evolution, and influence the formation of low level clouds and more generally the synoptic flows and climate system. The modelling of these fluxes is performed by specific surface schemes: Soil-VegetationAtmosphere Transfer (SVATs) schemes for vegetation (Chen et al. (1997) review the vegetation schemes
used in the intercomparison exercice on Cabauw grass site), urban schemes for cities (see a review in Masson (2006)), or schemes dedicated to sea or ice surfaces. The degree of complexity of these schemes iswide. The simplest models are bucket models (e.g. Manabe (1969), Robock et al. (1995)), with only one
water reservoir in the soil. Next are the so-called big leaf models (Deardorff (1978), Noilhan and Planton(1989) with only one surface energy balance and no canopy. The more detailed schemes have several layers
in the soil, several energy budgets (low vegetations, snow and tree canopy) and photosynthesis production tosimulate the carbon cycle (see Simon et al. (2005)). The same degree of variability exists in the complexityof the physical processes described in urban schemes (see Masson (2006)).
However, the present paper will not discuss on the complexity of the physical and physiological processesof the soil or plants in these schemes. The topic of this paper is to discuss the coupling of surface schemes
237

238
to atmospheric models. Independantly of the complexity of the processes, two coupling methods are usuallyused (fig 5.1):• single-layer coupled schemes: these surface schemes are forced by only one atmospheric layer (i.e.
the lowest atmospheric layer of an atmospheric model, as in fig 5.1b). The surface schemes respondto atmospheric variables at this level (temperature, wind, humidity, incoming radiation, etc...) andthey produce averaged upwards turbulent fluxes and radiative quantities (albedo, emissivity, surface
temperature). Note that this level is physically supposed to be high enough above the surface to be in
the inertial sublayer (or constant flux layer), most schemes using Monin-Obukhov theory to parameterize turbulent fluxes. These exchanges have been normalized in the Assistance for Land-surface
Modelling activities (ALMA) norm (see Best et al. (2004) and Polcher et al. (1998)).
Because of the simplicity of this type of coupling, these surface schemes can be used off-line (e.g.
forced directly by observations), so that they can be used for a wide range of applications (e.g. hydrology). All schemes presented in the offline intercomparison by Chen et al. (1997) are single-layer
schemes. These schemes can have a separate modelling of the soil and of the canopy, but the coupling with the atmosphere is always done at a forcing level above the canopy. The link between theforcing level and the soil/canopy to compute energy fluxes is usually done using systems of aerodynamical/stomatal resistances (as in Deardorff (1978)), that may depend on many factors, such as plantstress or atmospheric stability.
• multi-layer coupled schemes: these schemes are coupled with several atmospheric levels (fig 5.1c).
They interact not by surface fluxes (except for the lowest level), but directly throughout the prognostic
variables equations of the atmospheric model at each level. For example, drag forces by the obstacles(trees or buildings) will slow the wind and increase the turbulence, heat (water) fluxes by these obstacles will produce differential heating (moistening) between the levels. Xinmin et al. (1999) use sucha scheme coupled inline to a planetary boundary layer model to study the influence of the tree density
in a forest on the air characteristic within the canopy at day and at night. Recently Simon et al. (2005)
built a multilayer scheme to describe precisely the water and carbon dioxyde fluxes inside the Amazonian forest. For building canopies, Martilli et al. (2002), Coceal and Belcher (2005) and Kondo etal. (2005) are example of multi-layer schemes. The drawback of this high resolution description of
the atmospheric processes is an intimate coupling of the surface scheme and the atmospheric model.
Furthermore, because atmospheric layers are thin near the surface (depth of the order of 1m) to finely
describe the air profile in the Surface Boundary Layer (SBL), the time step of the atmospheric model
must usually be much smaller in order to insure numerical stability.
Such schemes are used when one wants to describe very finely the interaction between the atmosphereand the surface features. For example, low vegetation and soil will interact with air temperature near
the surface (say 1m), while tree leaves exchange temperature and humidity with higher level air (withother temperature, humidity). This therefore allows a priori a better simulation of the physical andphysiological processes. Another interest of these schemes is the direct simulation of air characteristics down to the surface itself, allowing several specific applications (wind stress in forest ridges, airtemperature profile between buildings, etc...).
The objective of this paper is to implement into single-layer schemes the fine description of air profiles
near the ground of the multi-layer schemes. That way, the single-layer schemes will gain the explicit physical representation of the surface boundary layer thanks to additionnal air layers, and still be coupled toatmospheric models through only one layer.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 5. SURFACE BOUNDARY LAYER SCHEME
a)forcind level

b)

239

c)

lowest atm.
levellowest atm.
level"single-layer" surface
scheme forced off-line"single-layer" surface scheme
coupled to an atmospheric model"multi-layer" surface scheme
coupled to an atmosphericmodel

Figure 5.1: Schematic view of surface scheme coupling: a) single-layer surface scheme forced offline. b)single-layer surface scheme forced by an atmospheric model. c) multi-layer scheme forced by an atmospheric model. Dotted arrows show the interactions between surface and coupling/atm. forcing: (a) with theforcing level, (b) the lowest atm level and (c) with all levels intersecting the canopy.

5.2 Theory
5.2.1 Atmospheric equations
The atmosphere can be described by dynamical (3 wind components) and thermodynamical variables(heat content or temperature, water vapor, possibly other water phases quantities). In this study, only thePlanetary Boundary Layer was considered, neglecting mean vertical velocity and horizontal turbulent
fluxes. The Boussinesq hypothesis is applied for the sake of simplicity. However, the following derivation
can be generalized to more complex equation systems. Only the theory is described in the main part of thepaper. The numerics for implementation and coupling in models are discussed in the last section.
Using mean horizontal wind components (U , V ), potential temperature (θ) and water vapor specific humidity (q), without water phase changes, the equations describing the atmosphere evolution can be written
as:


∂U
∂u′ w′
∂U
∂U


=
−U
−
−
V
+f
V
−f
V
g

∂t

∂x
∂y | {z }∂z }| {z } | {z


|
{z
} Cor

P res.


T
urb
Adv



∂v ′ w′
∂V
∂V

∂V


−V
−f Ug −
+f U
= −U

∂t

∂x
∂y | {z }| {z }

| ∂z
{z }

|
{z
} Cor

P res.
T
urb
Adv
(5.1)
′ θ′
∂w
∂θ
∂θ

∂θ


−
+
Q̇
=
−U
−
V

∂t

|{z}
∂x
∂y

{z }
| ∂z

{z
}
|

Diab.

T urb

Adv



∂w′ q ′
∂q
∂q


 ∂q
−
=
−U
−
V

∂t

∂x
∂y

| ∂z
{z }

{z
}
|

Adv

T urb

∂p
∂p
and Vg = − f1ρ ∂y
are the geostrophic wind components, u′ w′ , v ′ w′ , w′ θ ′ and w′ q ′ arewhere Ug = − f1ρ ∂x

the turbulent fluxes, and Q̇ represents the diabatic sources of heat (e.g. radiative tendency).

In addition, a Turbulent Kinetic Energy (TKE, noted e = 12 (u′2 + v ′2 + w′2 )) equation can be used to
SURFEX v8.1 - Issue no 3 - 2018

240
describe the turbulence in some atmospheric models:
∂e
∂e
∂e
∂U
∂V
−u′ w′+= −U−V− v ′ w′
∂t
∂x
∂y |
∂z {z
∂z}
{z
}
|
Adv

Dyn.P rod.

g ′ ′
w θv
|θ {z }−

T herm.P rod.

∂w′ e
− |{z}
ǫ
{z }
| ∂z
T urb

(5.2)

Diss.

where Right Hand Side terms stand for advection of TKE, dynamical production, thermal production,
turbulent transport of TKE and dissipation respectively.

5.2.2 Atmospheric equations modified by canopy obstacles
The above equations refer to air parcels that do not interact with any obstacles. Near the surface, when
one wants to take into account the influence of obstacles on the flow, these equations must be modified.
In atmospheric models, this is done by adding additional terms for each variable, representing the average
effect of these obstacles on the air contained in the grid mesh. One should note here that ideally, the volumeof the obstacles (trees, buildings) contained into the grid mesh should be removed from the volume of air of
the grid mesh. However, this significantly complexifies a lot the atmospheric model, and the approximation
to keep the air volume constant even in the presence of obstacles is normally done. This simplification is
also chosen here. Then, obstacles impact on the flow is parameterized as:
 ∂U

∂t


 ∂V
∂t

∂θ

∂t


 ∂q
∂t

and

=
=
=
=

Adv +Cor+P res. +T urb(U )Adv +Cor+P res. +T urb(V )Adv +Diab.
+T urb(θ)
Adv+T urb(q)+Dragu+Dragv+ ∂θ∂t canopy+ ∂q∂t canopy∂e∂e= Adv + Dyn.P rod. + T herm.P rod. + T urb + Diss. +∂t∂t canopy

(5.3)

(5.4)

where,• Dragu and Dragv are the drag forces (due to pressure forces against the obstacles) that slow the flow,• ∂θ∂t canopy is the heating/cooling rate due to the heat release/uptake by the surfaces of the canopy obstacles in the grid mesh,• ∂q∂t canopy is the moistening/drying impact of these obstacles,• and ∂e∂t canopy represents the TKE production due to wake around and behind obstacles as well as the
additionnal dissipation due to leaves-induced small-scale turbulence.
The prescription of these terms due to the obstacle impact on the flow are parameterized differently for each
multi-level surface scheme, and this is not described in detail here. Parameterizations for dynamical variables are often similar for forest canopies. Wind drag is usually parameterized as the opposite of the square√of the wind, as in Shaw and Schumann (1992) or Patton et al. (2001): Dragu = −Cd a(z)U U 2 + V 2 and√Dragv = −Cd a(z)V U 2 + V 2 , where Cd is a drag coefficient and a(z) is the leaf area density at height z(this parameter can be derived from Leaf Area Index and vegetation height, assuming a normalized verticalprofile of leaves distribution in the canopy). The TKE production/destruction term can be parameterized
as the sum of two effects: wake production by the leaves (parameterized as proportionnal to the cubic
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 5. SURFACE BOUNDARY LAYER SCHEME

241

3

2
2 2
power of wind: ∂e∂t canopy ∝ Cd (U + V ) as in Kanda and Hino (1994)) and the energy loss due to fastdissipation of small scale motions (leaves are of a much smaller scale than the grid mesh). The latter term√2
2
is often parameterized as proportionnal to the product of wind by TKE ( ∂e∂t canopy ∝ −Cd e U + V as
in Kanda and Hino (1994), Shen and Leclerc (1997), Patton et al. (2003)). Because of the high degreeof complexity of the processes involved (and hence of possibles simplifications), parameterizations fortemperature and humidity exchanges are much more variables. For example, Sun et al. (2006) parameterize
heating effects simply as a function of radiation vertical divergence, while more complex vegetation
models, as in Park and Hattori (2004), solve leaves temperature and use it to estimate at each atmosphericlayer the heat and water vapor exchanges between the forest canopy and the air: ∂θ∂t canopy ∝ a(z)(θl − θ)and ∂q∂t canopy ∝ a(z)(qsat (θl ) − q), where θl is the leaves potential temperature and qsat is humidity atsaturation (proportionnality coefficients depend on physiological processes of the plant).

For urban canopies, the same drag approach is chosen in general for the effect on wind, and only the wakeproduction term is kept for TKE (because turbulent eddies are large behind buildings, so their dissipation
is not as fast as those produced by leaves). Heat exchanges are however more complex and detailled (seeMasson (2006) for a review), as radiative trapping and shadows, different building heights, and sometimes
even road trees are taken into account in state-of-the-art urban models. An exemple of urban canopy
parameterization is given in Hamdi and Masson (2008).
As stated above, these additional terms allow a fine description of the mean variable profiles in theatmospheric model in the SBL (e.g. wind and temperature profile as a function of stability, wind speed inforest canopy, etc...) and of the flow statistics (non constant flux layer inside the canopy for example).

5.2.3 Implementation of the SBL equations into a surface scheme
The objective of this paper is to provide a way to implement such a description of the SBL with a lot of
atmospheric layers directly into the surface scheme. Such a scheme could be used offline (figure 5.2a)or coupled to an atmospheric model (figure 5.2b). As seen by comparing with figure 5.2c, the verticalresolution is the same as with a multi-layer model. The problem is that the computation of most of the termsof the equations (advection, pressure forces, diabatic heating) requires the atmospheric model dynamics
and physical parameterizations.
The set of equation (5.3) is rewritten by separating the processes as (i) ’large scale forcing’ (LS, that aresolved by the atmospheric model), (ii) the turbulence and (iii) the canopy effects:
 ∂U

∂t


 ∂V

=
=
=
=

∂t

∂θ

∂t


 ∂q
∂t

LS(U )
LS(V )LS(θ)LS(q)+T urb(U )+T urb(V )+T urb(θ)+T urb(q)+Dragu+Dragv+ ∂θ∂t canopy+ ∂q∂t canopy(5.5)

The TKE equation remains the same:∂e∂e= Adv(e) + Dyn.P rod. + T herm.P rod. + T urb + Diss. +∂t∂t canopy(5.6)

To represent the SBL into the single-layer surface scheme, one considers prognostic atmospheric layers,
between the surface and the forcing level of the surface scheme (that is the level that is coupled to the
SURFEX v8.1 - Issue no 3 - 2018

242
a)

SBL levelb)forcing levelc)lowest atm.
SBL level
level

SBL level
SBL level
SBL level

SBL level
SBL level
SBL level"single-layer" surface scheme+ Surface Boundary Layer scheme
forced offline"single-layer" surface scheme+ Surface Boundary Layer scheme
coupled to an atmospheric model

lowest atm.
level"multi-layer" surface scheme
coupled to an atmosphericmodel

Figure 5.2: Schematic view of the coupling between surface scheme and SBL scheme : a) single-layer
surface scheme with SBL scheme forced offline. b) single-layer surface scheme with SBL scheme forcedby an atmospheric model. c) multi-layer scheme coupling (as c) in figure 5.1). Dotted arrows show theinteractions between surface and SBL scheme (a and b). Upper SBL level is at same height as atmosphericforcing level.
atmosphere). Each of these layers is represented by the wind speed, the potential temperature, the humidity
and the Turbulent kinetic energy (all these variables being prognostically computed). They satisfy the set of
equations (12.7). In order to solve them, the following assumptions are made:• The mean wind direction does not vary in the SBL (Rotation due to Coriolis inside the SBL is neglected).
• The advection of TKE is negligible. This assumption is not valid for horizontal scales (and gridmeshes) of the order of a few times the canopy height, as equilibrium with forcing condition above is
not reached (Belcher et al. (2003), Coceal and Belcher (2005)), but it is valid for larger scales.
• The turbulent transport of TKE (w′ e) is negligible near the ground and in the SBL. This assumption
is fairly valid, this term being generally important only higher in the BL .
• Above the canopy, the turbulent fluxes are uniform with height (constant flux layer).
• The Large Scale forcing terms (LS(U ), LS(V ), LS(θ), LS(q)) are supposed to be uniform withheight in the SBL. It is assumed, for example, that advection and pressure forces are driven by synoptic flow or by the mesoscale BL flow (e.g. sea breeze). Diabatic effects on temperature are also
supposed to be uniform.
Then, the equations can be solved if the turbulent terms in the SBL (see subsection (5.2.5)), the canopy
terms (depending on each surface scheme physics), and the (uniform with height) large scale forcing are
known or parameterized.
Writing the equations at the forcing level (z = za ), which is supposed to be above the canopy (all canopy
terms are set to zero) and therefore in the constant flux layer (the turbulent fluxes are supposed to be uniform,
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 5. SURFACE BOUNDARY LAYER SCHEME

243

so that the divergences of turbulent fluxes are small), large scale terms can be estimated from the temporal
evolution of the variables at the forcing level:∂U∂t (z = za ) ∂V (z = z )
a
∂t
∂θ

(z
=
z
)
a
 ∂t

 ∂q
∂t (z = za )

=
=
=
=

LS(U )
LS(V )
LS(θ)
LS(q)

(5.7)

In reality, the constant flux layer hypothesis supposes not a constant turbulent flux but a small variationof the turbulent flux compared to its value. The small decrease/increase of the turbulent flux can lead totendencies of the mean variables. However, this small variation is generally relatively uniform in the wholeboundary layer (e.g. uniform heating of the convective boundary layer). This impact of the fluxes at thescale of the whole BL is included in the LS terms.

5.2.4 Boundary conditions
Finally, one obtains (using only one wind component, as the wind does not veer with height in the SBL):
 ∂U

 ∂t
And




∂θ
∂t
∂q
∂t

=
=
=

∂U
∂t (z = za )∂θ∂t (z = za )∂q∂t (z = za )+T urb(U ) +Dragu+T urb(θ) + ∂θ∂t canopy+T urb(q) + ∂q∂t canopy∂e∂e= Dyn.P rod. + T herm.P rod. + Diss. +∂t∂t canopy

(5.8)

(5.9)

The surface condition for the wind equation is given by the turbulent flux at the surface u′ w′ (z = 0). The
value at the top of the SBL scheme is given by wind at forcing level: U = U (z = za ).
The surface condition for the potential temperature equation is given by the turbulent flux at the surface
w′ θ ′ (z = 0). The value at the top is given by the temperature at forcing level: θ = θ(z = za ).
The surface condition for the humidity equation is given by the turbulent flux at the surface w′ q ′ (z = 0).
The value at the top is given by humidity at forcing level: q = q(z = za ).
The turbulent fluxes at the surface are computed by the surface scheme, using the atmospheric variables ofthe lowest level of the SBL (and not at the usual forcing level at za ). The exact formulation depends on
the surface scheme used. For example, a lot of (1 layer) surface schemes use to compute the surface heat(vapor) flux a formulation with exchange coefficients Ch (including a dependancy with stability), surface
and air temperatures (humidity) (w′ θ ′ (z = 0) = Ch (θs − θa )). With the SBL scheme, θa is the temperature
at first SBL level, and the stability in the lowest layer in near neutral (because of the proximity to the ground-we used 50cm as first layer-).
There is no need of boundary condition for the TKE at the surface or at the forcing level, as no verticalgradient of TKE is used. The only term that needs special computation near the surface is the Dynamical
production term, as it uses a vertical gradient of mean wind.

SURFEX v8.1 - Issue no 3 - 2018

244

5.2.5 Turbulence scheme
One turbulence scheme is of course needed in the SBL. A TKE turbulence scheme, developed by Cuxart
et al. (2000), is chosen here. The mixing length is computed as in Redelsperger et al. (2001). Mixing anddissipative length scales are not equal, in order to represent accurately the dissipation modification due tothe -1 power law of the turbulence in the SBL. Other turbulence schemes may be used.
A summary of the turbulence scheme is given below:√u′ w′ = −Cu l e ∂U

∂z

√ ∂θ



w′ θ ′ = −Cθ l e ∂z


√ ∂q
 ′ ′
w q = −Cq l e ∂z

g ′ ′
∂U

∂e

+
wθ
= −u′ w′


∂t

∂z}
θ {z }v{z||
Dyn.P rod.

T herm.P rod.

3e 2 ∂e− Cǫ+lǫ ∂t canopy| {z }(5.10)

Diss.

with Cu = 0.126, Cθ = Cq = 0.143, Cǫ = 0.845 (from Cheng et al. (2002) constants values for pressure
correlations terms and using Cuxart et al. (2000) derivation). The mixing and dissipative lengths, l and lǫ
respectively, are equal to (from Redelsperger et al. (2001), α = 2.42) :

√
−1
2

 l = κz/[ αCu φm (z/LM O )φe (z/LM O )](5.11)
lǫ = lα2 Cǫ /Cu /(1 − 1.9z/LM O )ifz/LMO < 0
 l = lα2 C /C /(1 − 0.3pz/L )if
z/LMO > 0MOǫǫuWhere LM O is the Monin-Obukhov length, φu and φe the Monin-Obukhov stability functions for momentum and TKE.

5.3 conclusion
A formulation allowing to include prognostic atmospheric layers in offline surface schemes is derived fromatmospheric equations. The interest of this approach is to use the advanced physical description of the SBLcanopy interactions that was available only in complex coupled multi-layer surface schemes. The coupling
only occurs at the bottom level of the atmospheric model that should be coupled above the surface+SBL
scheme. Variables that must be exchanged are: incoming radiation and forcing level air characteristics
towards the surface scheme, upward radiative and turbulent fluxes from it. The air layers prognosticallysimulated with the SBL scheme take into account:• The term that is related to large-scale forcing (e.g. advection). The detail of this term is not known by
the SBL scheme. The evolution of the air characteristics at the forcing level is supposed to take into
account all these large-scale forcing terms.
• The turbulent exchanges in the SBL (including in the canopy, if any). They will modify verticalprofiles in the SBL. For example, the logarithmic profile of wind is directly induced by these turbulent
fluxes, and is well reproduced by the SBL scheme.
• The drag and canopy forcing terms. These are computed for each layer, due to the interaction between
air and the canopy. These exchanges have to be modeled by the surface scheme to which the SBL
scheme is coupled. In the present paper, for forests, it takes into account the dynamical terms: dragand impact on Tke.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 5. SURFACE BOUNDARY LAYER SCHEME

245

The possible applications of a SBL scheme included in surface schemes can be:• a more physical determination of standard 2m variables and 10m wind. It can be seen as a drastic
increase of the vertical resolution of the atmospheric models near the ground, without the drawback
of a smaller time step (that would be necessary to resolve the advection on a very fine grid). Furthermore, because the additional air layers are not handled by the atmospheric model, the SBL scheme(associated to a surface single-layer scheme) is easy to couple with Numerial Weather Prediction or
research atmospheric models.
• a better description of the turbulent exchanges and the stability in the SBL, including over complex
terrain, for low-level flow and dispersion studies near the surface. As future applications, the dispersion processes in presence of canopy (e.g. chemistry vertical diffusion in urban areas) could then be
more accurately simulated.
• the inclusion of the detailed physics of the multi-layer schemes (e.g. the interactions of forest or urban
canopy with atmospheric layers in the SBL) into single-layer schemes.

SURFEX v8.1 - Issue no 3 - 2018

246

5.4 Appendix: Vertical and temporal discretization
5.4.1 Vertical discretization
The vertical grid for the SBL scheme is a staggered grid (figure 5.3). Historical variables (U , θ, q, e) are∂q
defined on ’full’ levels. The temporal evolution terms due to canopy obstacles (Dragu , ∂θ∂t canopy , ∂t canopy ,∂e∂t canopy ) are also located on these full levels.

The turbulent fluxes computed by the SBL scheme arecomputed on the ’flux’ levels, staggered between the full levels. The height of full levels is exactly at
middle height between half levels. Note that the grid can be (and is most of the time) stretched, with ahigher resolution near the ground. The ground is the first flux level (to be consistent with the boundary
condition provided: the surface turbulent fluxes). The atmospheric forcing level is the upper full level (tobe consistent with the upper boundary condition).

5.4.2 Temporal discretization
For any variable X (U , θ, q or e), the evolution equation can be written as:∂F ( ∂X
∂X
∂X
∂z )
=
(z = za ) −+ F or(X)∂t∂t∂z(5.12)

where F is the turbulent flux for X = [U, θ, q], and F or contains canopy forcing terms ( ∂X∂t canopy for
X = [U, θ, q, e]) and other RHS forces for X = [e]. Note that the turbulent flux terms F depend formallyon the vertical derivative of the variable ( ∂X∂z ) while canopy forces and RHS TKE forces depend on thevariable itself (X).
In order to satisfy the stability of the SBL scheme at large time-steps, an implicit solving is performed. If thecoupling at the atmospheric level is explicit, the atmospheric forcing is not modified in the current time-stepby the SBL and surface schemes (i.e. ∂X∂t (z = za ) does not change during the SBL solving). Of course,
the atmosphere will further evolve in response to the turbulent SBL fluxes (through the atmospheric model
turbulence parameterization). In these conditons, the SBL implicit solving writes:− X+ − X−∂X −∂F − ∂ ∂F∂F or −∂X + ∂X −∂z=(z = za )−− ∂X ×−+F or − +×(X + −X − ) (5.13)
∆t
∂t
∂z
∂z
∂z
∂X
∂ ∂z
Where ∆t is the time step, − subscript stands for previous time-step variable (known), and + subscript
for the future time-step variable (which one seeks to calculate). Such an implicit scheme leads to a linear
system linking all variables at each level to those from the levels below and above (due to the verticalgradient at instant + ). This system is tridiagonal, and easy to solve numerically.

5.4.3 Implicit coupling with the atmospheric model
It may be necessary in some atmospheric models (essentially due to very long time steps - half an hour- andthe turbulence scheme used in the atmospheric model) to couple implicitly the surface (including the SBL
−
+
]/∆t.
−X(z=zscheme here) and the atmosphere. First RHS term in Equation 5.13 is now equal to [X(z=za)a)+
The atmospheric variable at time is modified by the surface flux at the forcing level. It is formalized by
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

247

+
+
+ B (where A and B are known). Therefore, Equation 5.13, in= A × F(z=zBest et al. (2004) : X(z=za)a)
case of implicit coupling with the atmosphere, writes:
X + −X −
=
∆t





−
+
B−X(z=za )−−A∂X −+ ∂(∂F+ ∆t× F(z=z(z = za ) × ∂X∂X∆t∂z (z = za ) − ∂z (z = za )
a)
)
∂z


−
−
∂ ∂F
∂X +
or −
∂X −
∂z
− ∂F
×
+ F or(X)− + ∂F−−
× (X + − X − )
∂X
∂z
∂z
∂z
∂X
∂



∂z

(5.14)
This is still a linear system involving variables at future time step at all levels of the SBL scheme, but this+system is no longer tridiagonal, because the term ∂X∂z (z = za ) (i.e. at upper SBL level) influences directly
the variable X + at each level. However, such a system is still resolvable, showing the generality of the SBL
scheme method proposed here.

Bibliography[1] S. E. Belcher, N. Jerram, and J. C. R. Hunt. Adjustment of a turbulent boundary layer to a canopy ofroughness elements. J. Fluid Mech., 488:369–398, 2003.
[2] M. J. Best, A. Beljaars, J. Polcher, and P. Viterbo. A proposed structure for coupling tiled surfaces
with the planetary boundary layer. J. Hydrometeorol., 5(6):1271–1278, December 2004.
[3] T. H. Chen, A. Henderson-Sellers, P. C. D. Milly, A. J. Pitman, A. C. M. Beljaars, J. Polcher,
F. Abramopoulos, A. Boone, S. Chang, F. Chen, Y. Dai, C. E. Desborough, R. E. Dickinson, L. Dmenil,
M. Ek, J. R. Garratt, N. Gedney, Y. M. Gusev, J. Kim, R. Koster, E. A. Kowalczyk, K. Laval, J. Lean,
D. Lettenmaier, X. Liang, J.-F. Mahfouf, H.-T. Mengelkamp, K. Mitchell, O. N. Nasonova, J. Noilhan,
A. Robock, C. Rosenzweig, J. Schaake, C. A. Schlosser, J.-P. Schulz, Y. Shao, A. B. Shmakin, D. L.
Verseghy, P. Wetzel, E. F. Wood, Y. Xue, Z.-L. Yang, and Q. Zeng. Cabauw experimental results fromthe project for intercomparison of land-surface parameterization schemes. J. Clim., 10(6):1194–1215,
June 1997.
[4] V. Canuto Cheng, Y. and A. Howard. An improved model for the turbulent pbl. J. Atmos. Sci.,
59:1550–1565, 2002.
[5] O. Coceal and S. E. Belcher. A canopy model of mean winds through urban areas. Quart. J. Roy.
Meteor. Soc., 130:1349–1372, 2005.
[6] P. Bougeault Cuxart, J. and J.-L. Redelsperger. A turbulence scheme allowing for mesoscale andlarge-eddy simulations. Q. J. R. Meteorol. Soc., 116:1–30, 2000.
[7] J. Deardorff. Efficient prediction of ground temperature and moisture with inclusion of a layer ofvegetation. J. Geophys. Res., 83:1889–1903, 1978.
[8] R. Hamdi and V. Masson. Inclusion of a drag approach in the town energy balance (teb) scheme:
Offline 1d evaluation in a street canyon. J. Appl. Meteorol. Climatol., 47(10):2627–2644, October
2008.
[9] M. Kanda and M. Hino. Organized structures in developing turbulent flow within and above a plant
canopy, using a large eddy simulation. Bound.-Layer Meteorol., 68:237–257, 1994.
SURFEX v8.1 - Issue no 3 - 2018248
[10] Hiroaki Kondo, Yutaka Genchi, Yukihiro Kikegawa, Yukitaka Ohashi, Hiroshi Yoshikado, and Hiroshi
Komiyama. Development of a multi-layer urban canopy model for the analysis of energy consumption
in a big city: Structure of the urban canopy model and its basic performance. Bound.-Layer Meteorol.,
116:395–421, 2005. 10.1007/s10546-005-0905-5.
[11] S. Manabe. Climate and the ocean circulation 1. the atmospheric circulation and the hydrology of theearths surface. Mon. Weather Rev., 97:739–774, 1969.
[12] Alberto Martilli. Numerical study of urban impact on boundary layer structure: Sensitivity to windspeed, urban morphology, and rural soil moisture. J. Appl. Meteorol., 41(12):1247–1266, December
2002.
[13] V. Masson. Urban surface modeling and the meso-scale impact of cities. Theor. and Appl. Clim.,
84:35–45, 2006. 10.1007/s00704-005-0142-3.
[14] J. Noilhan and S. Planton. A simple parameterization of land surface processes for meteorologicalmodels. Mon. Weather Rev., 117(3):536–549, 1989.
[15] H. Park and S. Hattori. Modeling scalar and heat sources, sinks, and fluxes within a forest canopy
during and after rainfall events. J. Geophys. Res., 109:D14 301, 2004.
[16] E. G. Patton, K. J. Davis, M. C. Barth, and P. P. Sullivan. Decaying scalars emitted by a forest canopy- a numerical study. Bound.-Layer Meteorol., 100:91–129, 2001.
[17] E. G. Patton, P. P. Sullivan, and C.-H. Moeng. The influence of a forest canopy on topdown andbottom-up diffusion in the planetary boundary layer. Q. J. R. Meteorol. Soc., 129:1415–1434, 2003.
[18] J. Polcher, B. McAvaney, P. Viterbo, M. A. Gaertner, A. Hahmann, J. F. Mahfouf, J. Noilhan,
T. Phillips, A. Pitman, C. A. Schlosser, J. P. Schulz, B. Timbal, D. Verseghy, and Y. Xue. A proposal for a general interface between land surface schemes and general circulation models. Glob. andPlanet. Change, 19(1-4):261–276, December 1998.
[19] J.-L. Redelsperger, F. Mahe, and P. Carlotti. A simple and general subgrid model suitable both forsurface layer and free-stream turbulence. Bound.-Layer Meteorol., 101:375–408, 2001.
[20] A. Robock, K. Y. Vinikov, C. A. Schlosser, N. A. Speranskaya, and Y. Xue. Use of midlatitude soil
moisture and meteorological observations to validate soil moisture simulations with biosphere andbucket models. J. Clim., 8:15–35, 1995.
[21] R. Shaw and U. Schumann. Large-eddy simulation of turbulent flow above and within a forest. Bound.Layer Meteorol., 61:119–131, 1992.
[22] S. Shen and M. Y. Leclerc. Modelling the turbulence structure in the canopy layer. Agric. and For.
Meteorol., 87:1–84, 1997.
[23] E. Simon, F. X. Meixner, L. Ganzeveld, and J. Kesselmeier. Coupled carbon-water exchange of theamazon rain forest, i. model description, parameterization and sensitivity analysis. Biogeosciences,2(3):231–253, 2005.
[24] H. Sun, T. L. Clarka, R. B. Stulla, and Black T. A. Two-dimensional simulation of airflow and carbon
dioxide transport over a forested mountain part i: Interactions between thermally-forced circulations.
Agric. and For. Meteorol., 140:338–351, 2006.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

249[25] Z. Xinmin, Z. Ming, S. Bingkai, and W. Hanjie. Study on a boundary-layer numerical model withinclusion of heterogeneous multi-layer vegetation. Adv. in Atmos. Sci., 16:431–442, 1999.

SURFEX v8.1 - Issue no 3 - 2018

250

forcing levelzf, k+1
U,θ,q,e,l,lε

w’u’, w’θ’, w’q’

z, k

zf, k

Figure 5.3: Schematic view of the vertical discretization for the SBL scheme. Plain lines are full levels.
Dotted lines are flux levels.

SURFEX v8.1 - Issue no 3 - 2018

Chapter 6

Chemistry and aerosols
Contents
6.1

Dust aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
6.1.1

Implementation in the Externalized surface . . . . . . . . . . . . . . . . . . . . . 252

6.1.2

Features of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Emission process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Parameterization of the friction velocity . . . . . . . . . . . . . . . . . . . . . . . 253
Friction velocity threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Influence of soil moisture on friction velocity threshold . . . . . . . . . . . . . . . 254
Aerodynamical roughness height . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Surface flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Mass flux repartition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

6.2

Sea Salt emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

6.3

Dry deposition of gaseous species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
6.3.1

Resistances for dry deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

6.3.2

Dry deposition velocity formulation . . . . . . . . . . . . . . . . . . . . . . . . . 264

6.4

Dry deposition of aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

6.5

Biogenic VOC fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

6.1 Dust aerosols
Dust is mobilized from dry desert surfaces when the wind friction speed reaches a threshold wind friction
speed of approximately 0.2 m/s. Dust is an important aerosol with annual global emissions ranging from1000 to 3000 T g yr −1 and average global load around 10-30 T g (Zender et al. (2004)).
Dust is mobilized by two related processes called saltation and sandblasting. Saltation is the horizonal
movement of soil grains in a turbulent near surface layer. Sandblasting is the release of fine dust when thesaltating grains hit the surface. Several papers document these two processes. (Marticorena and Bergametti(1995) and references therein describe the physics of saltations, and Shao et al. (1993) describe the physics
of sandblasting.
251

252

6.1.1 Implementation in the Externalized surface
The dust fluxes are calculated using the Dust Entrainment And Deposition (DEAD) model (Zender et al.
(2003)). This model is based on Marticorena and Bergametti (1995). The dust fluxes are calculated consistently with the ISBA soil surface scheme. Table 6.1 gives an overview of the main input to the dust
production model.

PARAMETER
wind friction speed
Soil moisture
Vegetation fraction
Surface roughness
Surface texture

Table 6.1: ISBA variables used by the dust module
EFFECT ON DUST EMISSION
REFERENCE
Increase emissions
Inhibit emissions
Inhibit emissions
Inhibit emissions
Soil sizes > 50µm
increase saltation flux

Marticorena and Bergametti (1995)
Fecan et al. (1999)
Marticorena and Bergametti (1995)
Laurent et al. (2005)
Iversen and White (1982)

6.1.2 Features of the model
Emission process
The production of desert aerosols follows in fact the sandblasting process following the bombing of theaggregates present at the surface by particles in saltation (Figure 6.1). These processes depend on bothweather conditions and surface states. Indeed, the kinetic energy of the grains caused by saltation is used inshocks induced by these particles, when they fall to the ground to release and eject fine particles constituting
aggregates (Gillette and Goodwin (1974), Gomes et al. (1990)). The resistance to wrenching, concerns soil
properties like the gravity force and the inter-particle forces. Moreover, emission of aerosols is a thresholdphenomenon: it occurs only when the wind friction force exerted on soil grains becomes greater than theforces that maintain them to the ground. When this threshold is exceeded, the soil grains start moving
horizontally. The smallest particles can be suspended in the atmosphere and constitute the desert aerosol.
The production intensity of fine particles thus depends on the ratio between the transfered kinetic energy
flow and the cohesion forces of the particles forming the aggregates.

Figure 6.1: illustration of the two main processes involved in the emission of aerosols desert (saltation andsandblasting) when the erosion threshold is exceeded.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 6. CHEMISTRY AND AEROSOLS

253

Once the particle is injected into the atmosphere, the forces to which it is subjected will control its suspension. It is generally accepted, given the balance of forces, that only particles with a diameter less than about
20 µm can be transported (Nickling (1994)). Those fine particles, named aerosols, constitute the main partof the vertical flow of desert aerosol (F ). This vertical flow is defined as the mass of particles crossing perunit of time a unitary surface parallel to the surface.
Parameterization of the friction velocity
Wind is the driving force in the aerosols desert generating process. The ground surface opposes the air flow
and slows the air mass at its base. The surface wind is very sensitive to changes in surface characteristics at
small scale. These changes may be due, for example, to the presence of vegetation or rocks. In the first few
meters of the atmosphere, a surface boundary layer (CLS) develops, in which the horizontal component of
the wind speed has a vertical gradient whose intensity depends on the ability of the soil surface to slow theflow (Figure 6.2). For a laminar flow over a horizontal surface, the shear constraint (τ ) exerted by the windon the surface is connected to the vertical gradient of the wind speed (U ) by:
τ =µ

∂U
∂Z

(6.1)

Where is the air dynamic viscosity coefficient and Z the height above the ground.

Figure 6.2: Representation of the effect of soil on the airflow and of the shear stress τ exerted by the flowon the ground.

The shear constraint can also be expressed in terms of friction wind speed U∗ , which is usually the physicalquantity used to quantify friction forces exerted by wind on a surface:τ = ρa U∗(6.2)

Where ρa is the air density. Under conditions of thermal neutrality, U∗ can be determined from the windspeed U at a height z from the ground and the height of aerodynamic roughness (Z0 ) using a wind speed
logarithmic profile (Priestley (1959):
U (Z) =

z
U∗
ln( )
κ
Z0

SURFEX v8.1 - Issue no 3 - 2018

(6.3)

254
Where κ = 0.4 is the Von Karman constant.
Physically, Z0 reflects the length scale of the sink of air momentum induced by the surface roughness. Morespecifically, Z0 represents quantitatively the effect of erodible elements (soil grains) or non-erodible ones(rocks or vegetation) on the transfer of wind energy to the surface.
Friction velocity threshold
The resistance of the surface on the motion is represented by the friction velocity threshold U∗t . Indeed, thefriction velocity threshold U∗t controls both the frequency and the intensity of emissions of aerosols desert,
so it is important to parameterize carefully U∗t and give special attention to obtain the quantities it depends
on. The erosion threshold is mainly computed from the soil grains diameter Dp , the surface roughness(Rug) and the soil moisture (w). The friction velocity threshold is expressed as:U∗t = U∗t (Dp ) · F (Rug) · F (w)(6.4)

U∗t (Dp ): depends on the friction speed with the diameter of soil grains. F (Rug) and F (w): weighting
functions of the influence of roughness and soil moisture. Under idealized conditions, ie for a smooth surface
and a loose and dry soil, the friction velocity threshold U∗t (Dp ) can be determined using the formulation ofMarticorena and Bergametti (1995), which consists in adjusting an empirical expression as a function of theparticle diameter. Under standard atmospheric conditions (ρa = 0.00123g · cm−3 , ρp = 2.65g · cm−3 ), thefriction velocity threshold U∗t (Dp ) is given by:
0.129K, 0.03 ≤ Re∗t ≤ 10
0.5
1.928Re∗t 0.092
U∗t (Dp ) = 0.129K [1 − 0.0858 exp (−0.0617 (Re∗t − 10))] , Re∗t > 10U∗t (Dp ) =

(6.5)
(6.6)

Where Re∗t = U∗t Dp /ν is the Reynolds number threshold (ν = 0.157 cm2 s−1 : kinematic viscosity)
and: K =ρp gDpρa

0.5
0.5 
1 + ρ 0.006
gD 2.5pp

The optimal diameter of the particle is equal to 75 µm.
Influence of soil moisture on friction velocity threshold
The presence of interstitial water between soil grains has the effect of increasing the cohesion of the soil,
thus increasing the friction velocity threshold. This increase is integrated in the module DEAD from theparameterization developed by Fecan et al. (1999). The proposed equation, expresses the threshlod increase,
under wet conditions U∗tw compared to that in dry conditions.

hU∗tw = U∗t′U∗tw = U∗t 1 + 1.21(w − w )0.68

f or w < w
i0.5

f or w > w

′
′

(6.7)
(6.8)

With: w: mass soil moisture (% mass water / mass dry soil). And soil moisture threshold is given by:′

w = 0.17(%clay) + 0.14(%clay)2
SURFEX v8.1 - Issue no 3 - 2018

(6.9)

CHAPTER 6. CHEMISTRY AND AEROSOLS

255

Aerodynamical roughness height
The effects of the internal boundary layer (IBL) on friction velocity threshold, due to the presence of stones,
is set in DEAD scheme by Marticorena and Bergametti (1995). The energy distribution is defined in this parameterization as the ratio between the IBL shear friction and the total shear friction of the surface boundary
layer (SBL). This ration is given by:
fef f (Z0 , Z0s ) = 1 − ln(Z0 /Z0s )/ ln(0.35(10/Z0s )0.8 )(6.10)

Z0s = 33.3 × 10−6 m: roughness length of the smooth surface
Z0 = 100.0 × 10−6 m: roughness length of the erodible surface
The friction velocity threshold is expressed as:U∗t (Dp , Z0 , Z0s ) =U∗t (Dp )fef f (Z0 , Z0s )(6.11)

Surface flux
The horizontal saltation flux (G) is calculated in module DEAD through the White (1979) relationship :



U∗t
U∗t
ρ 3
1+
G = c · U∗ 1 −g
U∗U∗(6.12)

With c = 2.61. The ratio between the vertical flux and the horizontal flux is a function of clay content. For
contents between 0 and 20%, this ratio is :F
= 100 exp [(13.4(%clay) − 6) × ln(10) ](6.13)G
In the DEAD module, the fraction of clay is considered constant and is equal to 20%. The final vertical flux
is averaged by a pre-determined factor equals to 0.0021 and by the sand fraction.
α=

Mass flux repartition
Upon Alfaro and Gomes (2001) the mass flux is partitioning on the different modes upon the surface friction
velocity. More the collision energy is strong more the dust aggregates can be separates into small particles.
In surfex, two possibilities are offered. Users can fix the partitioning or the mass flux on the differents modes
considered, or compute automatically this partitioning upon the ISBA friction velocity. In this latter case,
Alfaro and Gomes (2001) gives the following partitionning:• u* less than 0.32 m.s−1 , all particles are emitted in the coarse mode.
• u* at 0.42 m.s−1 , 63 % of the mass flux is in the bigger coarse mode (D=14.2 µm) , 36 % in thelower coarse mode (D=6.7 µm), and 1 % in the accumulation mode (D=1.5 µ m)
• u* at 0.50 m.s−1 , 49 % of the mass flux is in the bigger coarse mode (D=14.2 µm) , 43 % in thelower coarse mode (D=6.7 µm), and 8 % in the accumulation mode (D=1.5 µ m)
• u* at 0.66 m.s−1 , 9 % of the mass flux is in the bigger coarse mode (D=14.2 µm) , 76 % in the lower
coarse mode (D=6.7 µm), and 15 % in the accumulation mode (D=1.5 µ m)
Between these friction velocities values, the mass flux partitioning is linearly interpolated.
SURFEX v8.1 - Issue no 3 - 2018

256

6.2 Sea Salt emission
Sea salt aerosols are produced as film and jet droplets when bubbles, entrained in the water by breaking
waves, disrupt the sea surface (Blanchard, 1983), and at winds speeds exceeding about 9 m.s−1 , by direct
disruption of the wave tops (spume droplets) (Monahan et al. (1983)).
Sea Salt emission are parameterized upon the formulation of Vignati et al. (2001) (effective source function)
or upon a lookup table defined by Schulz et al. (2004). Vignati et al. (2001) gives a formulation of particles
emission upon the wind at 10 meters as:• F (R = 0.2µm) = 100.09U10m +0.283 particles.cm−2 .s−1
• F (R = 2µm) = 100.0422U10m +0.288 particles.cm−2 .s−1
• F (R = 12µm) = 100.069U10m −3.5 particles.cm−2 .s−1

6.3 Dry deposition of gaseous species
The removal of gases from the atmosphere by turbulent transfer and uptake at the surface is defined as
dry deposition. This process enables some chemically reactive gases to be efficiently removed from theFc,atmosphere. Dry deposition is usually parametrized through a deposition velocity vd , defined by vd = − c(z)where Fc is the flux of the considered compound (Fc is assumed constant over the considered range ofheights) and c(z) is the concentration at height z (molecules/cm3 ). vd depends on many variables suchas wind speed, temperature, radiation, the considered species and the surface conditions. It is commonlydescribed through a resistance analogy often called ”Big-Leaf” Model (e.g. Wesely and Hicks (1977)).
vd (z) =1
Ra + Rb + Rc

where Ra is the aerodynamic resistance, which is a function of the turbulence in the boundary layer, Rb thequasi-laminar resistance partially controlled by molecular diffusion, and Rc the surface resistance, which
combines all the transfer pathways playing a role in the uptake of trace gases by the surface.
Meso-NH surface for dry deposition
As shown fig. 6.3, earth surface is divided into four major parts. On those surfaces calculation of specificparameters are done (friction velocities, surface resistances, ...). The earth splitting is done as follows :town horizontal fraction Masson (2000), inland water and sea surfaces (differents because of their surface
temperature) and nature fractions. Nature surface is cut into 9 cover type, which can be reorganized by’patches’ (1 to 9). One ’patch’ contains one or several cover types (user choice). These cover types areconnected with the Wesely classes of vegetation for the surface resistance data parameters (see table 6.2).

6.3.1 Resistances for dry deposition
Aerodynamic resistance Ra
Ra determines the rate of transport of gases between a given level in the atmosphere and the height ofthe effective surface sink. It is usually calculated as the bulk aerodynamic resistance to the transfer ofmomentum : Ra (zR ) = CD1VA , where CD is the drag coefficient for momentum (see for example Weselyand Hicks (1977); Sheih et al. (1979); Walcek et al. (1996)) and VA the wind speed (in the following,
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 6. CHEMISTRY AND AEROSOLS

257

Figure 6.3: Schematic resistances for dry deposition module in accordance with the surface state. Ra
represents the aerodynamic resistance, Rb the quasi-laminar resistance and Rc the surface resistance.
the parameters which are already used or calculated in the MESO-NH subroutines will be noted in boldcharacters). The reference height zR is taken as the lowest atmospheric level in the ISBA scheme.
An alternate way is to use the ISBA calculation of Ra , Ra (zR ) = CH1VA which determines the transfer ofwater vapor. CH is then the drag coefficient depending upon the thermal stability of the atmosphere.
Heat drag coefficients are calculated in WATER FLUX for inland water and sea, in URBAN for artificial
land (town) and in ISBA for the other nature cover types or patch. So there is one Ra different for eachdifferent coefficient.
This formulation of Ra requires an additional term to the quasi-laminar resistance described below.

Quasi-laminar resistance Rb
The component Rb is associated with transfer through the quasi-laminar layer in contact with the surface.
Rb quantifies the way in which pollutant or heat transfer differ from momentum transfer in the immediate
vicinity of the surface (this is due to the effects of molecular diffusion and the difference of roughness
lengths found for momentum and mass transfer). Rb depends on both turbulence characteristics and themolecular diffusion of the considered gas. Transport of a gas through the quasi-laminar layer by molecular
diffusion depends on the thickness of the layer, the concentration gradient over the layer and on a diffusion
constant, which in turn depends on the radius of the gas molecule and on the temperature. The complexityof vegetation generally limits the accuracy with which the magnitude of this mechanism can be estimated in
SURFEX v8.1 - Issue no 3 - 2018

258
Meso-NH nature cover typeC3 cultures types(low)C4 cultures types(hight)
forest and trees
grasslandno vegetation (smooth)no vegetation (rocks)
permanent snow and ice
irrigated crops
irrigated parks gardens or peat bogs

Wesely correspondence class(2) Agricultural land
(2) Agricultural land
(4) Deciduous and (5) coniferous forest(3) Range land
(8) Baren land, mostly desert(11) Rocky open areas with low-growing shrubs
No correspondence(9) None forested wetland(6) Mixed forest including weet landand (9) none forest wetland

Table 6.2: Meso-NH vegetative cover type and Wesely connected class for dry deposition calculation

the field. This resistance can be conveniently written as:
Rb =

z0
1
log( )∗
kuzc

k is the Von Karman constant and u∗ the friction velocity. zc is the roughness length for the pollutant underinvestigation (Baldocchi et al. (1987)).
According to Hicks et al. (1987), Garrat and Hicks (1973) Rb can be approximated for vegetation and fibrousroughness elements by :2 Sc 2/3
Rb =( )ku∗ P rSc and P r are the Schmidt and Prandtl numbers respectively. P r = 0.72 and Sc = Dνi , with ν the kinematic
viscosity of air (0.15 cm2 s−1 , 20o C, p = 1 atm) and Di the molecular diffusivity of gas i (see table 6.3 forsome of these constants). For snow, ice, water and bare soil, Rb can be calculated by (Ganzeveld andLelieveld (1995)):
1 Sc 2/3
Rb =( )ku∗ P rThis formulation is used for all Meso-NH grid fraction cover with no vegetation (Leaf Area Index = 0), that
include artificial land, water and sea.
p4
< u′ w′ >xx 2 + < v′ w′ >xx 2 . Where
Definition of friction velocity in MNH is given by : u∗ =< u′ w′ >xx and < v ′ w′ >xx represents surface fluxes of horizontal momentum in x and y directions (xxfor sea, water, town and nature patch). Molecular diffusivity species/air can be obtain by the knowledge of
H2 O/air diffusivity. The coefficient of diffusivity is given by the general formula as:
0.376kT
D = vl/3 = N (MCste)0.5
with l mean free path, v mean molecular velocity, k Boltzmann constant, T temperature, N concentration,
M molecular mass. So we use for computing molecular diffusivity:
D(gaz) = D(H2 O)
with

M (H2 O)M (gaz)0.5

D(H2 O) = 2.22e − 5 + 1.2510−7 (T + 273)f or193K < T < 0K
D(H2 O) = 2.22e − 5 + 1.4610−7 (T + 273)f or273K < T < 323K
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 6. CHEMISTRY AND AEROSOLS

259

However, these formulations of Rb remain still controversial. Recent results from fields studies indicate thatthey are not in agreement with experimentally derived results, at least for the transfer of HNO3 over wheat(Muller et al. (1993)). At last, velocity dry deposition is not very sensitive of the choosen definition of Rb(Ganzeveld and Lelieveld (1995)).
Surface Resistance Rc
The surface resistance is the most difficult of the three resistances to describe. Rc values can be obtained
from theoretical considerations based for instance on solubility and equilibrium; calculations in combination
with simulation of vegetation specific processes, such as accumulation, transfer process through stomata,mesophyll, cuticles, etc . . . (Baldocchi et al. (1987), Wesely (1989)). The values of Rc are based on measurements of Vd . By determining Ra and Rb from the meteorological measurements, Rc is calculated as theresidual resistance. The calculated Rc are then related to surface conditions, time of day, etc . . . in order toobtain parametrizations of Rc .

Vegetative surface resistance

Stomatal

In-canopy
transport

Rc

Externalleaf uptake
Mesophyll

Soil

Figure 6.4: Surface resistance schematic for vegetation.
Rc is a function of the canopy stomatal resistance Rstom and mesophyll resistance Rm , the canopy cuticle
or external leaf resistance Rext , the soil resistance Rsoil and in-canopy resistance Rinc , and the resistance tosurface waters or moorland pools, Rwat , Rsea (Erisman and Baldocchi (1994)). In turn, these resistances areaffected by leaf area index, stomatal physiology, soil and external leaf surface, pH presence and chemistryof liquid drops and films. In summary, Rc should be calculated as Erisman and Baldocchi (1994) :• Vegetative surfaces : Rc =



1
1
1
Rstom +Rm + Rinc +Rsoil + Rext

• Water surfaces : Rc = Rwat

−1

• Sea surfaces : Rc = Rsea
• Bare soil (no vegetation) : Rc = Rno• Rock surfaces : Rc = Rrock• Snow/ice cover : Rc = Rsnow• Artificial land : Rc = Rtown
SURFEX v8.1 - Issue no 3 - 2018

260
Stomatal and mesophyll resistance Rstom and Rm
The stomatal resistance for water vapor is calculated in the ISBA subroutines as
Rstom =Rsmin,
F1 F2 F3 F4 LAI

where LAI is the leaf area index computed by patch, and F1 , F2 , F3 , F4 are limiting factors depending onradiation, wetness of soil and temperature. In order to describe the stomatal resistance for another gas, theISBA Rstom for water vapor should be corrected as followed :Rstom,x = Rstom ×

DH2 O
,
Dx

DH2 O and Dx are the diffusion coefficients of H2 O and x respectively (Wesely (1989)).
There is not much knowledge on the mesophyll resistance for different gases and the conditions which
determine its value. For some gases, such as SO2 O3 and NH3 , Rm is experimentally found near zero values(Erisman and Baldocchi (1994)). This is in agreement with the parametrization suggested by Wesely (1989)
for the calculation of the mesophyll resistance :Rmx = (

H∗
+ 100f0 )−1
3000

In this expression, H ∗ is the Henry’s law constant for the considered gas, f0 a reactivity factor which
determines the rate of reduction of the substance. Two parallel pathways are thus assumed, one for highly
reactive gases, the other one for soluble substances. Table 6.3 lists H ∗ and f0 for some species (Baer and
Nester (1992)).
External leaf uptake Rext
The external leaf uptake can act as an effective sink, especially for soluble gases at wet surfaces. The resistance of the outer surfaces in the upper canopy (leaf cuticular resistance in healthy vegetation) is computedby Wesely (1989), for a dry surface to any gas (x), as :Rext.x.dry = Rext (10−5 H ∗ + f0 )−1
In this expression, Rext is given by land category and season in table 6.4, the constants (H ∗ , f0 ) can befound in table 6.3.
The following equation is supposed to give an analytic expression of Rext in accordance with Wesely table
6.4, and including seasonal variations through the leaf area index LAI :Rext = 6000 − 4000 tanh(1.6(LAI − 1.6))
These results had been compared with Wesely table in accordance with Méso-NH (ISBA) data of LAI (seefig. 6.3.1 ).
In case of dew or rain, and according to the same author and Walmsley and Wesely (1996), the equation
should be replaced by :Rext.x.wet = [1/(3Rext.x.dry ) + (10−7 H ∗ + f0 /RextOzone ]−1
with
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 6. CHEMISTRY AND AEROSOLS

Species
Sulfur dioxide
Nitric oxide
Nitrogen dioxide
Nitric acid
Ozone
Hydrogen peroxide
Formaldehyde
Aldehydes
Organic acids
Organic peroxide
Peroxyacetic acid
Peroxyacetyl nitrate
Other alkanes
EthaneEthenePropeneButene and other olefins
TolueneXyleneReactivity factor
0
0
0.1
0
1.
0
0
0
0
0.25
0.5
0.1
0
0
0
0
0
0
0

261

Henry’s law (M/atm)
1.6(1 + 2.1 10−2 /H+)
1.9 10−3
10−2
5.8 106 /H+
1.5 10−2
1.8 105
3.26 10−476
1.45 10−4
665
1635
3.6
1. 10−3
1.9 10−3
4.9 10−3
4.7 10−3
1.3 10−3
0.15
0.1

Table 6.3: Reactivity factor and Henry’s law constants for different chemical species

Figure 6.5: Rext fonction of LAI (from Wesely table)

SURFEX v8.1 - Issue no 3 - 2018

262
1
2
3
4
5
Midsummer with lush vegetation
9999 2000 2000 2000 2000
Autumn with unharvested cropland9999 9000 9000 9000 4000
Late autumn after frost, no snow
9999 9999 9000 9000 4000
Winter9999 9999 9999 9999 6000
Spring9999 4000 4000 4000 2000

6

7

8

9

10

11

2000

9999

9999

2500

2000

4000

8000

9999

9999

9000

9000

9000

8000

9999

9999

9000

9000

9000

9000

9999

9999

9000

9000

9000

3000

9999

9999

4000

4000

8000

Table 6.4: Input resistances for calculation of external leaf resistance (Wesely,1989) : (1)urban land, (2)agricultural land, (3)range land, (4)deciduous forest, (5)coniferous forest, (6)mixed forest including wetland,(7)water, (8)barren land, mostly desert, (9)nonforested wetland, (10)mixed agricultural and range land,(11)rocky-open areas with low-growing shrubs• Rain :RextOzone = (1/(3Rext ) + 1/1000)−1• Dew :
RextOzone = (1/(3Rext ) + 1/3000)−1
To apply the same comput for each species we approximate in case of wet soil these formulas by using
RextOzone as 3000 s/m .
These formulas should be corrected when surface temperature decreases below -2o C by adding the value
1000 exp(−T − 4), in order to take into acccount the lesser uptake by surfaces when cold.
In-canopy transport Rinc
Deposition to soils under vegetation can be relatively important. Meyers and Baldocchi (1988) found that
20% - 30% of SO2 was deposited in summer to the soil under a deciduous forest. This transport is due tolarge-scale intermittent eddies through the vegetation. The corresponding resistance has been parametrized
by Erisman and Baldocchi (1994) using data of VanPul and Jacobs (1994) as :Rinc =b LAI hu∗b is an empirical constant estimated at 14 m−1 . LAI = LAI patch is the leaf area index given by
patches computed in the GROUND PARAMn files and h is the vegetation height which can be calculated
as four times the vegetation roughness length (formula of Kondo and Yamazawa (1986), assuming a dense
vegetation canopy with similar height).
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 6. CHEMISTRY AND AEROSOLS

263

Soil resitances for surfaces with no vegetation and those under vegetation
Table 6.5 presents a review of soil resistances for SO2 and O3 for clay, sand, snow and it is completed withtable 6.6, Wesely value for all other vegetation types, town and rock.
For other gases, the resistance can be computed following Wesely (1989) :Rsoilx = (

f0
H∗
+
)−1
5
10 RsoilSO2
RsoilO3

According to the same author, this formula should be corrected when surface temperature decreases below-2o C by adding the value :Rsoilx = Rsoilx + 1000 exp(−T − 4)
For no vegetation cover soil surface composition (sand, clay) is considered. If it is covered by snow, thisformlation will be update by using table 6.5.
Rsandx = (

H∗
f0
+
)−1
105 RsandSO2
RsandO3

Rclayx = (Rsnowx = (

f0
H∗
+
)−1
5
10 RclaySO2
RclayO3

H∗
f0
+
)−1
5
10 RsnowSO2
RsnowO3

In this context Rno.x for bare ground (no veg.) without snow is the weighted average of Rsandx and Rclayx
as:αclay −1
αsand+)
Rno.x = (Rsandx Rclayx
withαsand : percentage of sand in the ground
αclay : percentage of clay in the ground
For all the other type of soil, resistance is calculated with table 6.6 as :
H∗
f0
+
)−1
5
10 RrockSO2
RrockO3
H∗
f0
( 5
+
)−1
10 RtownSO2
RtownO3
H∗
f0 −1
( 5
+
)
10 Rc3SO2
Rc3O3
f0 −1
H∗
+
)
( 5
10 Rc4SO2
Rc4O3
f0
H∗
+
)−1
( 5
10 RtreeSO2
RtreeO3
H∗
f0
( 5
+
)−1
10 RgrassSO2
RgrassO3
H∗
f0 −1
( 5
+
)
10 RirrSO2
RirrO3
f0
H∗
+
)−1
( 5
10 RparkSO2
RparkO3

Rrockx = (Rtownx =Rc3x =
Rc4x =
Rtreex =Rgrassx =Rirrx =
Rparkx =SURFEX v8.1 - Issue no 3 - 2018

264
Type of soil
snow

SO2
540 at T <-1o C
70(2-T) at -1 < T < 1
1000
1000

sand
clay

O3
2000
200
100

Table 6.5: Soil resistance
MNH cover typec3
c4
tree grass
Soil resistance for SO2
150 150 500 350
Soil resistance for O3
150 150 200 200

no

rock

snow/ice

irr

park

town

1000

400

no data

0

100

400

400

200

no data

1000

700

300

Table 6.6: Soil resistance for MNH-C decomposition from Wesely table (quasi constant during the year).
Values for “snow/ice” and “no” (no veg.) are not used see table 6.5.

Surfaces resistances for sea and water
For deposition over water surface bodies, the surface resistance can be calculated from the expression recommended by Sehmel (1980) that incorporates wind speed and and air/water partitioning coefficient, rather
than from Wesely’s tabulated values for water bodies. The surface resistance over water is:
Rwaterx =2, 54.10−4= Rcwaterx
H ∗ Twateru∗

Rseax =

2, 54.10−4= Rcseax
H ∗ Tsea u∗

6.3.2 Dry deposition velocity formulation
Artificial land resistance
Rglobaltown = Ratown + Rbtown + Rctown
Sea and water resistance
Rglobalwater = Rawater + Rbwater + Rcwater

Rglobalsea = Rasea + Rbsea + Rcsea
Nature final resistance
Rglobalnature=nvegtype
X 
i=1

αi
j
patch
Ra
+ Rbjpatch + Rci

SURFEX v8.1 - Issue no 3 - 2018

−1

CHAPTER 6. CHEMISTRY AND AEROSOLS

265

with
f
i 7−→ f (i) = jpatch like i ∈ [1, nvegtype], f (i) = jpatch ∈ [1, npatch ≤ nvegtype]
and αi fraction of cover type (9 types)
Dry deposition velocity
Final dry deposition formulation:
vdrydeposition =αwaterαsea
αtownmax
αnature+++Rglobalwater
Rglobalsea Rglobaltown Rglobalnature

where

αwater: fraction of water
αsea: fraction of sea
αtownmax : fraction of town increased
αsea: fraction of nature
Fraction of town has to be increased in order to take account of the non negligible dry deposition on verticalsurfaces in artificial area. The increase is done as follows :αtownmax = αtown (1 + 2 H
L αbld ) with :αtown horizontal fraction of town
H building height
L building caracteristic width
αbld fraction of buildings in artificial areas (only)

Figure 6.6: town parameters in MNH (modd gr field) to increase fraction of town

6.4 Dry deposition of aerosols
Brownian diffusivity and sedimentation velocity
Dry deposition and sedimentation of aerosols are driven by the Brownian diffusivity:


kT
Cc
Dp =
6πνρair rp
SURFEX v8.1 - Issue no 3 - 2018(6.14)

266
and by the gravitational velocity:
Vg =



2g
9ν



ρp,i
ρair



rp2



Cc

(6.15)

where k is the Bolzmann constant, T the ambient temperature, ν the air kinematic velocity, ρair the air
density, g the gravitational acceleration, ρp,i the aerosol density of mode i, and Cc = 1 + 1.246 λrair
thepgliding coefficient. These expressions need to be averaged on the kth moment and mode i as:Z ∞1
Xrpk ni (ln rp )d(ln rp )X̂ =Mk,i −∞
where X represents either Dp or vg . After integration, we obtain for Brownian diffusivity:





−2k + 1 2
−4k + 4 2D̂pk,i = D̃pg,i exp
ln σg,i + 1.246Kng exp
ln σg,i22with D̃pg,i = 6πνρkT
air Rg,iand for gravitational velocity:





2k + 4 2
4k + 4 2ln σg,i + 1.246Kng exp
ln σg,iVˆg pk,i = V˜g pg,i exp
222gρp,i 2
with V˜gpg,i = 9νρairRg,i(6.16)(6.17)(6.18)

Dry deposition
According to Seinfeld and Pandis (1997) and using the resistance concept of Wesely (1989), aerosol dry
deposition velocity for the kth moment and mode i is:v̂dk,i = (ra + r̂dk,i + ra r̂dk,i Vˆgpk,i )−1 + Vˆg pk,i(6.19)

where surface resistance r̂dk,i is given byr̂dk,i =ˆˆ −2/3+ 10−3/Stk,i )
(Sc
k,i



w2
1 + 0.24 2∗
u∗



u∗

−1

(6.20)

ˆ k,i = ν/D̂p and St
ˆ k,i = (u2 /gν)v̂d . One canSchmidt and Stokes number are respectively equal to Sc
∗
k,i
k,i
observe that the friction velocity u∗ and the convective velocity w∗ depend on meteorological and surface
conditions.

6.5 Biogenic VOC fluxes
Biogenic fluxes are parameterize on-line in the surfex code. For a model grid-cell, biogenic fluxes ofisoprene and monoterpenes are calculated according to the classical Guenthers approach (Guenther et al.
(1994, 1995)), using the general formulation :Fxcell =X

νn X.EPx,n X.ECFx,n(6.21)

N

Where Fxcell (in g.m-2.h-1) is the grid-cell averaged biogenic fluxes in which x refers either to isopreneor monoterpenes. νn represents the surface fractions occupied by N sub-grid emitting ecosystems (forests,
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

267

shrublands, crops, etc). The related emission potential, EPx,n , (in µg.m−2 .h−1 ), accounts for the emission capacity of the underlying nth ecosystem under fixed climatic conditions. According to Guenthers
approach, EPiso is standardized to a surface vegetation temperature Ts of 303 K and a photosynthetically
active radiation (par) of 1000 µE.m−2 .s−1 , whereas EPmono is generally standardized only for Ts =303 K.
The temporal evolution of fluxes is given by environmental correction factors ECFx,n calculated from thecanopy micro-climates of the N underlying ecosystems. This formulation assumes a simple homogeneousvertical leaf distribution in ecosystem canopies. Over France, emission potential have been pre calculated
by GIS treatment of land cover data base (Corine Land Cover), forest composition data for the main tree
species (Inventaire forestier national) and species emission factors collected in the literature. The resulting
emission potential maps are given at a resolution of 2km and are then interpolated on the MNH grid (during
the prepPGD). The environmental correction factor, which accounts for radiation and vegetation temperature variation effects on emissions is calculated using the surface energy budget (calculated by ISBA) and asimple in canopy radiation transfer scheme (similar as ISBA-Ags) for each of the ecosystem (Forest, shrublands, etc) contained in the model grid cells (cf PATCH approach). More details on the method can be foundin Solmon et al. (2004).

Bibliography[1] S. Alfaro and L. Gomes. Modeling mineral aerosol production by wind erosion: Emission intensities
and aerosol size distributions in source areas. J. Geophys. Res., 106(D16):18075–18084, 2001.
[2] Dennis D. Baldocchi, Bruce B. Hicks, and Pamela Camara. A canopy stomatal resistance model forgaseous deposition to vegetated surfaces. Atmos. Environ., 21(1):91–101, 1987.
[3] J. Erisman and D. Baldocchi. Modelling dry deposition of so2. Tellus, 46B:159–171, 1994.
[4] B. Marticorena Fecan, F. and G. Bergametti. Parameterization due to the increase of the aeolian erosion
threshold wind friction velocity due to soil moisture for arid and semi-arid areas. Ann. Geophys.,
17:149–157, 1999.
[5] L. Ganzeveld and J. Lelieveld. Dry deposition parametrization in a chemistry general circulation modeland its influence on the distribution of reactive trace gases. J. Geophys. Res., 100:20999–21012, 1995.
[6] J. Garrat and B. B. Hicks. Momentum, heat and water vapor transfer to and from natural and artificial
surfaces. Quart. J. Roy. Meteor. Soc., 99:680–687, 1973.
[7] D. A. Gillette and P. A. Goodwin. Microscale transport of sand-sized soil aggregates eroded by wind.
J. Geophys. Res., 79:4080–4084, 1974.
[8] L. Gomes, G. Bergametti, G. Coudé-Gaussen, and P. Rognon. Submicron desert dusts: A sandblastingprocess. J. Geophys. Res., 95:13927–13935, 1990.
[9] Alex Guenther, C. Nicholas Hewitt, David Erickson, Ray Fall, Chris Geron, Tom Graedel, Peter
Harley, Lee Klinger, Manuel Lerdau, W. A. Mckay, Tom Pierce, Bob Scholes, Rainer Steinbrecher,Raja Tallamraju, John Taylor, and Pat Zimmerman. A global model of natural volatile organic compound emissions. J. Geophys. Res., 100(D5):8873–8892, 1995.
[10] Wildermuth M. Guenther, A. Zimmerman P. Natural volatile organic-compound emission rate estimates for u.s. woodland landscapes. Atmos. Environ., 28(6):1197–1210, 1994.
SURFEX v8.1 - Issue no 3 - 2018268
[11] B. Hicks, D. Badolcchi, T. Meyers, R. Hoskers, and D. Matt. A preliminary multiple resistance routine
for deriving dry deposition velocities from measured quantities. Water Air Soil Pollu., 36:311–330,
1987.
[12] J. Iversen and B. White. Saltation threshold on earth, mars and venus. Sedimentol., 29:111–119, 1982.
[13] J. Kondo and H. Yamazawa. Measurement of snow surface emissivity. Bound. Layer. Meteor., 34:415–
416, 1986.
[14] B. Laurent, B. Marticorena, G. Bergametti, P. Chazette, F. Maignan, and C. Schmechtig. Simulation of
the mineral dust emission frequencies from desert areas of china and mongolia using an aerodynamic
roughness length map derived from polder/adeos 1 surface products. J. Geophys. Res., 110:D18S04,
2005.
[15] B. Marticorena and G. Bergametti. Modeling the atmospheric dust cycle: 1. design of a soil-derived
dust emission scheme. J. Geophys. Res., 100(D8):16415–16430, 1995.
[16] V. Masson. A physically-based scheme for the urban energy budget in atmospheric models. Bound.Layer Meteorol., 94(3):357–397, March 2000.
[17] E. C. Monahan, C. W. Fairall, K. L. Davidson, and P. J. Boyle. Observed inter-relations between 10 m
winds, ocean whitecaps and marine aerosols. Q. J. R. Meteorol. Soc., 109:379–392, 1983.
[18] H. Muller, F. Meixner, G. Kramm, D. Fowler, G. J. Dollard, and M. Possanzini. Determination of hno3
deposition by modified bowen ratio and aerodynamic profile techniques. Tellus, 45B:346–367, 1993.
[19] S.A. Nickling, W.G. & Wolfe. The morphology and origin of nabkhas, region of mopti, mali, west
africa. J. Arid Environ., 28:13–30, 1974.
[20] C. H. B. Priestley. Turbulent Transfer in the Lower Atmosphere. The University of Chicago Press,
Chicago, IL, 130 pp., 1959.
[21] M. Schulz, G. de Leeuw, and Y. Balkanski. chapter Sea-salt aerosol source functions and emissions,pages 333–359. Kluwer Academic Publishers, 2004.
[22] J. H. Seinfeld and S. N. Pandis. Atmospheric Chemistry and Physics: Air Pollution to Climate. Wiley,
1997.
[23] Y. Shao, M. R. Raupach, and P. A. Findlater. Effect of saltation bombardment on the entrainment of
dust by wind. J. Geophys. Res., 98(D7):12719–12726, 1993.
[24] M. Wesely Sheih, C. and B. Hicks. Estimated dry deposition velocities of sulfur over the eastern unitedstates and surrounding regions. Atmos. Environ., 13:1361–1368, 1979.
[25] Fabien Solmon, Claire Sarrat, Dominique Sera, Pierre Tulet, and Robert Rosset. Isoprene and monoterpenes biogenic emissions in france: modeling and impact during a regional pollution episode. Atmos.
Environ., 38(23):3853–3865, July 2004.
[26] W. A. J. Van Pul and A. F. G. Jacobs. The conductance of a maize crop and the underlying soil toozone under various environmental conditions. Bound.-Layer. Meteorol., 63:83–99, 1994.
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

269[27] Elisabetta Vignati, Gerrit de Leeuw, and Ruwim Berkowicz. Modeling coastal aerosol transport andeffects of surf-produced aerosols on processes in the marine atmospheric boundary layer. J. Geophys.
Res., 106(D17):20225–20238, 2001.
[28] C. Walcek, R. Brost, J. Chang, and M. Wesely. So2, sulfate and hno3 deposition velocities computed
using regional landuse and meteorological data. Atmos. Environ., 20:949–964, 1996.
[29] J. Walmsley and M. Wesely. Modification of coded parametrizations of surface resistances to gaseous
dry deposition. Atmos. Environ., 30:1181–1188, 1996.
[30] M. Wesely. Parametrizations of surface resistance to gaseous dry deposition in regional scale, numerical models. Atmos. Environ., 23:1293–1304, 1989.
[31] M. L. Wesely and B. B. Hicks. Some factors that affect the deposition rates of sulfur dioxide andsimilar gases on vegetation. J. Air. Poll. Control Assoc., 27:1110–1116, 1977.
[32] B. R. White. Soil transport by winds on mars. J. Geophys. Res., 84:4643–4651, 1979.
[33] C. S. Zender, R. L. Miller, and I. Tegen. Quantifying mineral dust mass budgets: Terminology, constraints, and current estimates. Eos Trans. AGU, 85(48):509–512, 2004.
[34] H. Bian Zender, C. and D. Newman. The mineral dust entrainment and deposition (dead) model:
Description and global dust distribution. J. Geophys. Res., 108(D14):4416, 2003.

SURFEX v8.1 - Issue no 3 - 2018

270

SURFEX v8.1 - Issue no 3 - 2018

Part IILAND COVER: ECOCLIMAP

271

Chapter 7

Introduction
Ecoclimap is a global database of land surface parameters at 1-km resolution. It is intented to be used toinitialize the soil-vegetation-atmosphere transfer schemes (SVATs) in meteorological and climate models.
A first version was developed in 2003 (Masson et al. (2003)). A second version was developed in 2008 on
Europe and is implemented into Surfex. Ecoclimap is designed to satisfy both the Surfex ”tile” approach:each grid box is made of four adjacent surfaces for nature (NAT), urban areas (TWN), sea or ocean (SEA)
and lake (WAT), and the Isba ”vegetation types” structure (see tab. 7.1).

ISBA vegetation type (vegtype)bare soilbare rockpermanent snow
deciduous broadleaved
needleleaved
evergreen broadleaved
C3 crops
C4 crops
irrigated crops
temperate grassland
tropical grassland
wetlands, parks and gardens

abbreviation
NO
ROCK
SNOW
TREE
CONI
EVER
C3
C4
IRR
GRAS
TROG
PARK

Table 7.1: The 12 ISBA vegetation types
It consists first of a global land cover map at 1/120°resolution that is directly read by Surfex. This map
proposes a set of classes (or covers) which represent homogeneous ecosystems. Secondly, Surfex interpretsthese covers in terms of tiles and vegetation types. Land surface parameters (see tab. 7.2 and tab. 7.3 forthe list of parameters) depend on tiles, vegetation types and on covers for some of them. A mechanismof aggregation is used to compute the surface parameters for each grid point, according to the horizontal
resolution, by combining land covers defined over the 4 tiles and represented by a fraction of the 12
vegetation types (table 7.1) obtained from the 1km resolution land cover map.
In the first version of Ecoclimap, two hundred and fifteen ecosystems were obtained by combining existing
273

274
land cover and climate maps, in addition to using Advanced Very High Resolution Radiometer (AVHRR)
satellite data. Then, all surface parameters were derived for each of these ecosystems using lookup tables
with the annual cycle of the leaf area index (LAI) being constrained by the AVHRR information. The
second version uses more recent existing land cover maps. Moreover, ecosystems are now built through an
automatic classification process applied on normalized difference vegetation index (NDVI) seven-years timeseries from SPOT/VEGETATION satellite data, more precise than AVHRR. Existing land cover maps give
starting classes which are split in clusters by the classification process. Then, surface parameters are still
derived using lookup tables but the annual cycle of the LAI stems from MODIS satellite data. It’s possible
to run Surfex with LAI values averaged on available years or to choose one particular year.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 7. INTRODUCTION

275

surface parameterleaf area index
height of trees
first soil depth
root depth
total soil depth
town roughness length
albedo of roofs,
roads,
walls
emissivity of roofs,
roads,
walls
heat capacity of roofs,
roads,
walls (*3 layers)
thermal conductivity of roofs,
roads,
walls (*3 layers)
width of roofs,
roads,
walls (*3 layers)buildings heightbuilding shapebuilding fraction
canyons shapeanthropogenic sensible heat fluxes
due to traffic,
due to factory
anthropogenic latent heat fluxes
due to traffic,
due to factory
seeding datereaping datewater supply quantity
flag for irrigation
vegetation fraction
dynamical vegetation
roughness length
emissivity
ratio of z0 for momentum and heatabbreviation
LAI
HT
DG1
ROOT DEPTH / DG2
GROUND DEPTH / DG3
Z0 TOWNALB ROOF,
ALB ROAD,
ALB WALL
EMIS ROOF,
EMIS ROAD,
EMIS WALL
HC ROOF*3,
HC ROAD*3,
HC WALL*3
TC ROOF*3,
TC ROAD*3,
TC WALL*3
D ROOF*3,
D ROAD*3,
D WALL*3
BLD HEIGHTWALL O HORBLDCAN HW RATIO

associated tile
nature (monthly)
naturenaturenaturenature
town
town

town

town

town

town

town
town
town
town
town

H TRAFIC,
H INDUSTRY
town
LE TRAFIC,LE INDUSTRY
SEED
REAP
WATSUP
IRRIG
VEG
Z0

naturenaturenaturenaturenature (monthly)
nature (monthly)EMIS
Z0 O Z0H

nature (monthly)
natureTable 7.2: Surface parameters given by Ecoclimap (1/2)

SURFEX v8.1 - Issue no 3 - 2018

276

surface parameternear infrared albedo
visible albedo
UV albedo
minimum stomatal resistancecoefficient for the calculationof the surface stomatal resistancecoefficient for maximum water interception
storage on capacity on the vegetation
maximum solar radiation usable in photosynthesis
vegetation thermal intertia coefficientmesophyll conductanceecosystem respiration parametercuticular conductancecritical normalized soil watercontent for stress parameterisation
ratio d(biomass)/d(LAI)
maximum air saturation deficit
tolerated by vegetation
vegetation response type to water
stress (true: defensive false: offensive)
e-folding time for senescenceminimum LAI
leaf area ratio sensitivity
to nitrogen concentration
lethal minimum value ofleaf area ratio
nitrogen concentrationof active biomassroot extinction
ponderation coefficient between
root fractions formulations
coefficient for SO2 deposition
coefficient for O3 deposition
cumulative root fraction
biomass/LAI ratio from nitrogendeclin theory

abbreviation
ALBNIR VEG
ALBVIS VEGALBUV VEG
RSMIN
GAMMA

associated tile
naturenaturenaturenaturenatureWRMAX CFnatureRGL
CV
GMES, GMES ST
RE25
GC, GC ST
F2I

naturenaturenature (AGS)
nature (AGS)
nature (AGS)
nature (AGS)BSLAI, BSLAI ST
DMAX, DMAX ST

nature (AGS)
nature (AGS)

STRESS

nature (AGS)SEFOLD, SEFOLD STLAIMINCE NITRO

nature (AGS)
nature (AGS)
nature (AGS)

CF NITRO

nature (AGS)CNA NITRO

nature (AGS)

ROOT EXTINCTIONROOT LIN

naturenatureSOILRC SO2SOILRC O3
CUM ROOT FRAC
BSL INIT NITRO

naturenaturenaturenatureTable 7.3: Surface parameters given by Ecoclimap (2/2)

SURFEX v8.1 - Issue no 3 - 2018

Chapter 8

Ecoclimap characteristics
8.1 Surface parameters definition
Parameters listed in tab. 7.2 and 7.3 are initialized:• by cover and vegetation types for LAI, HT, DG (3 layers), SEED, REAP, WATSUP, IRRIG. Indeed,
these parameters are not only a feature of a given vegetation type but also of regional considerations;• by vegetation type for other natural parameters. They are thus viewed as depending on the vegetation
type only and not on the location;• by cover for town parameters: the ”town” tile is not subdivided in types like the ”nature” tile.
Some of the natural parameters receive immediate values whereas others are calculated from some of theformer. Tab. 8.1 and tab. 8.2 give modes of obtaining of the natural parameters (lines), by vegetation type(columns). Report to tab. 7.1 to get the meaning of abbreviations of parameters names.
Tab 8.3 delivers values for urban parameters, by type of class. Types of Ecoclimap urban classes come fromthe Corine Land Cover (CLC) classification that is considered in the two versions of Ecoclimap (see tab. 8.4
for the correspondence).
All these values and formulas date from Ecoclimap-I and come from previous studies. Part of them are
mentionned and detailed in Masson et al. (2003), other can be found in literature.

8.2 Aggregation method
The aggregation of parameters assumes two aspects:• the aggregation in ”patchs” of several vegetation types;• the geographic aggregation linked to the spatial resolution.
Indeed, the Surfex user can choose to work with a number of 1 to 12 patchs of vegetation types. Tab. 8.5
gives the combinations of vegetation types according to the retained number of patches: numbers associated to vegetation types (columns) correspond to patchs to which they are attached, depending on the total
number of patches (lines and left column). The Surfex user also chooses his own spatial resolution whose
maximum is this of Ecoclimap: 1/120°. When the chosen resolution is coarser, parameters by grid pointtake aggregated values from the 1-km ones.
277

278
The common method for these two kinds of aggregation is nearly linear, apart from the fact that some particular averages are applied to several parameters (see tab. 8.6 for more details) : contributions of every
vegetation type to each gridpoint and each patch are weighted and added, next the total value in one point
and one patch is brought back to the total number of contributions, that is the total weight, providing thewanted average value of the parameter. As seen in tab. 8.7, weights vary with parameters, depending on thesurface on which they make sense.

8.3 Writing of parameters in a latex file
Distribution of classes among tiles and vegetation types, also values of surface parameters are described ina tex file called class cover data.tex. It can be compiled to get a ps or pdf file that recapitulates all thesevalues in different arrays.

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 8. ECOCLIMAP CHARACTERISTICS
parameter
LAI
HT
DG1
DG2
DG3
SEED
REAP
WATSUP
IRRIG
VEG
GREEN
Z0
EMIS
Z0 O Z0H
ALBNIR VEG
ALBVIS VEGALBUV VEG
RSMIN
GAMMA
WRMAXCF
RGL
CV
GMES
GMES ST
RE25
GC
GC ST
F2I
BSLAI
BSLAI STDMAXDMAX ST
STRESSSEFOLDSEFOLD ST
LAIMINCE NITRO
CF NITRO
CNA NITROROOT EXTINCTIONROOT LIN
SOILRC SO2SOILRC O3
CUM ROOT FRAC
BSL INIT NITRO

NO

279

ROCK

SNOW TREECONI
EVER
from satellite data by cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation type
0.
0.95
0.95
0.99
−0.5∗LAI0.
M IN (1 − e, 0.95) 0.99
0.1
1.
0.01
HT
HT
HT
V EG ∗ 0.97 + (1 − V EG) ∗ 0.94 1.
V EG ∗ 0.97 + (1 − V EG) ∗ 0.94
10.
0.3
0.3
0.3
0.25
0.15
0.21
0.1
0.1
0.1
0.05
0.05
0.05
0.06
0.06
0.06
0.525
0.0425
0.038
40.
40.
40.
150.
150.
250.
0.
0.
0.
0.04
0.04
0.04
0.2
0.2
0.2
0.1
0.1
0.1
100.
100.
100.
30.
30.
30.
−5
−5
−5
−5
−5
2E
2E
2E
1E
1E
1E −5
0.02
0.02
0.02
0.001
0.001
0.001
0.003
0.003
0.003
0.003
0.002
0.002
3E −7
3E −7
3E −7
3E −7
1E −7
3E −7
0.00025 0.00025
0.00025 0.00015
0.
0.000150.00015 0.00015
0.00015 0.00015
0.
0.00015
0.3
0.3
0.3
0.3
0.3
0.3
0.36
0.36
0.36
0.25
0.25
0.25
0.08
0.08
0.08
0.125
0.50
0.25
0.1
0.1
0.1
0.1
0.1
0.1
0.05
0.05
0.05
0.109
0.124
0.124
1.
1.
1.
0.
1.
0.
90.*XDAY
365.*XDAY
150.*XDAY
230*XDAY
365.*XDAY
0.3
0.3
0.3
0.3
1.
1.
7.68
7.68
7.68
4.83
4.85
4.83
-4.33
-4.33
-4.33
2.53
-0.24
2.53
1.3
1.3
1.3
2.
2.8
2.5
0.961
0.961
0.961
0.966
0.943
0.962
0.05
0.05
0.05
0.05
0.05
0.05
1000.
400.
100.
500.
500.
200.
400.
200.
3500.
200.
200.
500.
DG∗100.

(1−ROOT EXT.)
DG, 1.) + (1 − ROOT LIN ) ∗ (1−ROOT
ROOT LIN ∗ M IN ( DG2
EXT.)DG2∗100.

1./(CEIT RO
A N IT RO + CF N IT RO)
SURFEX
v8.1N- Issue
no+
3 -CN
2018

Table 8.1: Lookup tables for Ecoclimap natural parameters, by vegetation type (1/2)

280
parameter
LAI
HT
DG1
DG2
DG3
SEED
REAP
WATSUP
IRRIG
VEG
GREEN
Z0
EMIS
Z0 O Z0H
ALBNIR VEG
ALBVIS VEGALBUV VEG
RSMIN
GAMMA
WRMAXCF
RGL
CV
GMES
GMES ST
RE25
GC
GC ST
F2I
BSLAI
BSLAI STDMAXDMAX ST
STRESSSEFOLDSEFOLD ST
LAIMINCE NITRO
CF NITRO
CNA NITROROOT EXTINCTIONROOT LIN
SOILRC SO2SOILRC O3
CUM ROOT FRAC
BSL INIT NITRO

C3

C4
IRR
GRAS
TROG PARK
from satellite data by cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation typeby cover and vegetation type−0.6∗LAI
1−e
0.95
0.95
0.95
−0.6∗LAI−0.6∗LAI
1−e
M IN (1 − e, 0.95)(LAI−3.5)/1.3(LAI−3.5)/1.3
M IN (1., e) M IN (2.5, e)
LAI/6
V EG ∗ 0.97 + (1 − V EG) ∗ 0.94
10.
0.3
0.3
0.3
0.3
0.3
0.3
0.1
0.1
0.1
0.1
0.1
0.1
0.06
0.06
0.045
0.08
0.125
0.045
40.
120.
40.
40.
120.
40.
0.
0.
0.
0.
0.
0.
0.2
0.2
0.2
0.2
0.2
0.2
100.
100.
100.
100.
100.
100.
−5
−5
−5
−5
−5
2E
2E
2E
2E
2E
2E −5
0.003
0.003
0.003
0.02
0.02
0.02
0.001
0.009
0.009
0.001
0.006
0.006
3E −7
2.5E −7 3E −7
3E −7
3E −7
3E −7
0.000250.00025 0.00025
0.00025 0.00025 0.00025
0.000250.00015 0.00015
0.00025 0.00015 0.00025
0.3
0.3
0.3
0.3
0.3
0.3
0.06
0.06
0.06
0.36
0.36
0.36
0.06
0.06
0.06
0.08
0.08
0.08
0.1
0.1
0.1
0.1
0.1
0.1
0.05
0.033
0.033
0.05
0.052
0.05
1.
0.
1.
0.
0.
0.
60.*XDAY
90.*XDAY
150.*XDAY
0.3
0.3
0.3
0.3
0.3
0.3
3.79
7.68
7.68
5.56
7.68
5.56
9.84
-4.33
-4.33
6.73
-4.33
6.73
1.3
1.9
1.9
1.3
1.3
1.3
0.961
0.972
0.961
0.943
0.972
0.943
0.05
0.05
0.05
0.05
0.5
0.5
150.
150.
0.001
350.
350.
100.
150.
150.
1000.
200.
200.
700.
DG∗100.

(1−ROOT EXT.)
DG, 1.) + (1 − ROOT LIN ) ∗ (1−ROOT
ROOT LIN ∗ M IN ( DG2
EXT.)DG2∗100.

1./(CEROno+
A N IT RO + CF N IT RO)
SURFEX
v8.1N- IT
Issue
3 -CN
2018

Table 8.2: Lookup tables for Ecoclimap natural parameters, by vegetation type (2/2)

CHAPTER 8. ECOCLIMAP CHARACTERISTICS
parameter
ALB ROOF
ALB ROAD
ALB WALL
EMIS ROOF
EMIS ROAD
EMIS WALL
HC ROOF(1)HC ROOF(2)HC ROOF(3)HC ROAD(1)HC ROAD(2)HC ROAD(3)HC WALL(1)HC WALL(2)HC WALL(3)TC ROOF(1)TC ROOF(2)TC ROOF(3)TC ROAD(1)TC ROAD(2)TC ROAD(3)TC WALL(1)TC WALL(2)TC WALL(3)D ROOF(1)D ROOF(2)D ROOF(3)D ROAD(1)D ROAD(2)D ROAD(3)D WALL(1)D WALL(2)D WALL(3)Z0 TOWNBLD HEIGHTWALL O HORBLDCAN HW RATIOH TRAFIC
H INDUSTRY
LE TRAFICLE INDUSTRY

151

152

155

3.
30.
1.
0.5

1.
10.
0.5
0.5

2.
20.
0.5
0.5

20
10.
0.
0.

10.
5.
0.
0.

10.
20.
0.
0.

281
156

157 158
0.15
0.25
0.08
0.90
0.94
0.85
2.11E 6
0.28E 6
0.29E 6
1.94E 6
1.28E 6
1.28E 6
1.55E 6
1.55E 6
0.29E 6
1.51
0.08
0.05
0.74540.25130.25130.93380.9338
0.05
0.05
0.4
0.1
0.05
0.1
1.
0.02
0.125
0.05
0.5 2.
0.01
5.
20. 10.
0.5 1.
0.5
0.1 0.5 0.1
O HOR
0.5 ∗ W ALL
1−BLD
30. 10. 10.
0.
20. 0.
0.
0.
0.
0.
0.
0.

159

160

161

0.1
5.
0.5
0.1

0.5
5.
0.5
0.1

1.
10.
1.
0.5

0.
0.
0.
0.

0.
0.
0.
0.

0.
0.
0.
0.

Table 8.3: Lookup tables for Ecoclimap urban parameters, by cover
SURFEX v8.1 - Issue no 3 - 2018

282
cover namedense urban
suburbanindustries and commercial areas
road and rail networks
port facilities
airportmineral extraction and construction sites
urban parks
sport facilities

cover(s) number(s)151152,153,154,7
155
156
157
158
159
160
161

Table 8.4: Ecoclimap covers numbers for urban classes
patchs
1
2
3
4
5
6
7
8
9
10
11
12

NO
1
1
1
1
1
1
1
1
1
1
1
1

ROCK
1
1
1
1
1
1
1
1
1
1
2
2

SNOW
1
1
1
1
1
1
2
2
2
2
3
3

TREE
1
2
2
2
2
2
3
3
3
3
4
4

CONI
1
2
2
2
2
2
3
3
4
4
5
5

EVER
1
2
2
2
2
2
3
3
3
5
6
6

C3
1
1
3
3
3
3
4
4
5
6
7
7

C4
1
1
3
3
3
3
4
5
6
7
8
8

IRR
1
1
3
3
4
4
5
6
7
8
9
9

GRAS
1
1
3
4
5
5
6
7
8
9
10
10

TROG
1
1
3
4
5
5
6
7
8
9
10
11

PARK
1
1
3
4
4
6
7
8
9
10
11
12

Table 8.5: Combinations of vegetation types according to the retained number of patchs in Surfex
averaging type
ARI
INV

name
arithmetic
inverseadded element
X
1./X

averaging
Σ/Γ
Γ/Σ

CDN

inverse ofsquarelogarithm

DZ ∗ e−MAJ

dominant
date

1./LN (DZ/X)2
with DZ height of thefirst model mass level if
available and 20m otherwiseno addition: the mostfrequently occurrent
date is selected

none

√

affected parameters
every but...
RSMIN, CV, HC ROOF,
HC ROAD, HC WALL
Γ/ΣZ0, Z0 TOWN

SEED, REAP

Table 8.6: Averaging types and associated parameters in Ecoclimap. X is a single value of the parameter toaverage; Σ represents the total of the added weighted elements; Γ represents the total weight of the added
weighted elements.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 8. ECOCLIMAP CHARACTERISTICS

type of weight
ALL

name
all

value
1.

NAT

naturefraction of tile ”nature”(* fraction of added vegtype)

TRE

tree

LAI

LAI

VEG

fraction ofvegetation

TWN
BLD

town
building

fraction of tile ”nature”* (either) fraction of vegtype TREE*(or) fraction of vegtype CONI*(or) fraction of vegtype EVER
(non-zero only for trees vegtypes)
fraction of tile ”nature”* fraction of added vegtype* associated LAI value
fraction of tile ”nature”* fraction of added vegtype* associated VEG value
fraction of tile ”town”
fraction of tile ”town”* fraction of building BLD

STRstreetfraction of tile ”town”* (1.-fraction of building BLD)

283

associated parameters
fractions of tiles
NAT,TWN,SEA,WAT
fractions of vegtypes,
VEG, Z0, Z0 O Z0H, EMIS,
DG, CUM ROOT FRAC, RE25
HT, DMAX ST, DMAX

RSMIN

all remaining
natural parameters
every town parameter but...
ALB ROOF, EMIS ROOF, HC ROOF,
TC ROOF, D ROOF, ALB WALL,
EMIS WALL, HC WALL, TC WALL,
D WALL, WALL O HORALB ROAD, EMIS ROAD,
HC ROAD, TC ROAD,
D ROAD

Table 8.7: Weighting functions and associated parameters in Ecoclimap. Parenthesis indications in the”value” column refer to what happens in case of calculation defined by patch, ie for all natural parameters
but neither for the fractions of tiles and vegetation types nor for the town parameters.

SURFEX v8.1 - Issue no 3 - 2018

284

SURFEX v8.1 - Issue no 3 - 2018

Chapter 9

Ecoclimap-II realization
Ecoclimap-II has been developed on a European field. Its limits are 11W and 62E in longitude and 25N and
75N in latitude.

9.1 The Ecoclimap-II map
9.1.1 The initial map
Existing land cover maps taken into account in this development are:
• Global Land Cover 2000 (GLC2000)1 ;• Corine Land Cover 2000 (CLC2000)2 ;GLC2000 was built from daily SPOT/VEGETATION satellite data for year 2000 (dataset VEGA2000). The
spatial resolution is 1/112° (corresponding to ∼1.1km) and the projection is latlon. Several regional maps
and a global map of 23 classes exist. The latter global map is taken as a basis and classes from available
regional maps are added when relevant.
Then, CLC2000 covers only a part of the domain (political Europe) and includes 44 classes. It was realizedby photo-interpretation of SPOT and LANDSAT satellite images. The projection is Lambert’s azimuthal
equivalent and the resolution is 100m. In order to fit Ecoclimap, Corine data are reprojected and broughtback to the same resolution. In these conditions, the Corine class number attributed to the pixel at 1-km
resolution is this of the most numerous class into the pixel. It’s decided to introduce majority classes atmore than 70% in the map under construction. It happens that 55% of Corine pixels are kept by this way.
So-obtained Corine pixels have priority on GLC information because their contents is better known andsupposed to characterize more homogeneous ecosystems.
The resulting map comprises classes from several origins and potentially complementary: their headings
and geographic distribution give indications to melt some of them. After a couple of such combinations,a 76-covers map (called C76 from now on) is finally obtained on the considered area. This map is thereference used for the further classification process. It’s thus a mix of GLC2000 and CLC2000.
12

http://www-gvm.jrc.it/glc2000
http://www.ifen.fr, http://www.eea.eu.int

285

286

Figure 9.1: Example of NDVI profiles: rough (dotted), masked (dashed), smoothed (solid). (A technicalerror led to NDVI values overestimated of 0.09 but it has no impact on classification which is relative).

9.1.2 NDVI satellite data
NDVI is deduced from B2 (red) and B3 (near infrared) satellite normalized reflectances (ratios of the reflected over the incoming radiation in each spectral band) according to the formula:
N DV I =B3 − B2
B3 + B2(1)

This rate usually ranges from 0 to 1. Negative values indicate the presence of snow. Works have showna correlation between NDVI values and the vegetation photosynthesis activity. The LAI and NDVI annual
cycles are supposed to be correlated. In Ecoclimap-I, LAI profiles by cover were obtained from NDVI
through the formula:
LAI(t) = LAImin + (LAImax − LAImin ) ∗N DV I(t) − N DV Imin
N DV Imax − N DV Imin

(2)

LAImin and LAImax being set from in-situ measurements or empirically following ISBA simulations.
Then, LAI profiles by vegetation types (inside covers) are deduced from these LAI by cover thanks tosimple rules, mostly by changing extreme values of the cycle (LAImin and LAImax ) depending on thevegetation height in the formula (2), sometimes looking for ”pure” near ”mixte” covers and giving ”pure”
LAI to vegetation types in mixte covers. Note that for the NO, ROCK and SNOW vegetation types LAI
profiles are equal to zero.
In Ecoclimap-II, NDVI satellite data come from SPOT/VEGETATION3. They are decadal, at true 1-km
resolution, that is to say that, contrary to AVHRR, one pixel signal is theorically not contaminated by pixels
around. Data range from 1999, january to 2005, december.
They are delivered with a mask encoded on 8 bits: 2 bits represent the situations: clear sky, shadow, uncertain, cloud; 1 bit for snow and ice, 1 bit for the land sea mask, and the 4 last bits for the quality of the 43

http://free.vgt.vito.be/, http://www.spot.vegetation.com

SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 9. ECOCLIMAP-II REALIZATION

287

satellite radiometric bands. This mask is applied in order to keep clear sky pixels for which the quality ofbands B2 (red) and B3 (near infrared) is good. The land/sea/snow distinction is set by to the classification.
The plots of NDVI mean profiles for the covers of the C76 map show that data, even if cleared from aberrant
values by the mask, remain noisy. That’s why a smoothing is realized at the upper envelope of the roughcurve because highest values are supposed better because atmospheric parameters (clouds, water vapor,aerosols) are likely to attenuate the signal reflected to the satellite. Anyway the work on NDVI time series
is relative and the exact NDVI values don’t matter. The smoothing is based on a 4-degree polynomial. The
figure 9.1 shows effects of the mask and smoothing on the mean NDVI signal for a given class. The distance
between the rough and the smoothed curves is relative to this mean: the smoothing is done pixel by pixel,
filtering out low values entering the mean in the rough case.

9.1.3 The automatic classification process
The classification algorithm is k-means. It consists in reading the NDVI profiles of all pixels of one class,then of gathering closest profiles according to the Euclidian distance. Initial center-profiles of clusters are
randomly defined and successive iterations are performed: each pixel is linked to the most like-looking
center-profile; centers of clusters are recalculated; pixels are linked to the most like-looking center-profile
again, and so on. It’s thus necessary to fix from the beginning the number of wished clusters by class.
A first map is realized by setting high numbers of clusters by classes, then looking at NDVI profiles and geographic positions of the clusters, and setting new lower numbers of clusters, until a satisfying classification
is obtained. This first map comprises 464 classes and is called C464.
However, for practical purposes, this method poses several problems:• When each class of C76 is split into several clusters, the total number of classes increases very fast,
rendering reading, interpretation and processing hard;• it boils down to consider initial classes as frozen and separated each from one another, what can prove
false, notably with various initial maps;• the continuity of analysis is compromised and the quality of NDVI as classification criterion is hardto evaluate. Moreover, numbers of clusters have no option but being arbitrarily posed.
Owing to all these reasons, NDVI is no longer used as a secondary classification criterion: it’s admitted thatit can rival the initial C76 classes boundaries. Moreover, three quantities are now taken into account during
the NDVI classification:• the Euclidian distance between profiles (still);• the correlation between profiles, focusing on the shapes of profiles;
distance, outlining the shapes of profiles without ne• a criterion mixing the two precedents: euclidian
correlation2
glecting the distance between them.

The principle is to gather profiles using a threshold for one or the other of the latter criterions. Other
conditions come then into the picture:• the size of classes: for example, the threshold is looser for smaller classes, in order not to encourage
the formation of low pixels number classes;• the NDVI maximum: as NDVI is the expression of vegetation activity, it’s not relevant with lowvegetated areas, also low NDVI maximum areas;
SURFEX v8.1 - Issue no 3 - 2018288
• the cover type: water, town and bare soil pixels can’t be distinguished through the NDVI, they haveto conform the initial nomenclature.
Lastly, comparisons are conducted:• between profiles of clusters and classes they come from: if the cluster is closer to another class thanthe one it comes from, it can be linked to the former class;• families of classes are formed, then splited in a number of clusters equal to the number of classes
constituing them, through the automatic classification. Clusters obtained by this totally automaticmeans are compared to initial classes, in order to verify the robustness of the first method through it
consistency with the second one.
At each step, the geographic position, the contents of classes according to the initial nomenclature, NDVI
profiles and standard deviations are observed. These operations allow a better approach of the NDVI timeseries, adapting to the different types of covers and ensuring more mixing and flexibility than if initial
boudaries between classes were perfectly respected and if the strict k-means method was applied. At thispoint, the map under construction comprises 257 classes and is called C257.

9.1.4 To the resulting map
Several means are added to complete the new map realization:• C257 is compared with the map realized by purely respecting the classes boundaries, C464. Every class of each map is splited into 5 clusters through the automatic classification. The distance,
the correlation and the standard deviation between each cluster and its mother-class are calculated.
Maximum, minimum and median of these quantities are compared for C257 and C464. Results areequivalent whereas the total numbers of classes clearly vary between the two maps.
• C257 is compared to C76. C76 covers are grouped into 14 general types, close to ISBA vegetation
types. Then, each C257 class is divided in its contributions to the latter 14 types. Associated NDVI
profiles are plotted; geographic distribution of so-obtained clusters is also examined. These operations
aim at verifying that mixing of initial classes produce consistent and acceptable results.
First, given the high resemblance of NDVI profiles of some classes, pixels from a class corresponding
to a type (among the 14) that is neither its first nor its second prevailing are moved to a class where
the considered type prevails, provided that the resemblance between the two classes is sufficient (ondistance
NDVI profiles). The correlation
2 criterion is used with a threshold: the moving occurs if the criterion
is lower than 1., provided that the correlation is positive and higher than 0.9. This operation allows to
considerably reduce the distance between C76 and C257 in terms of nomenclature. It’s also verified
that geographically gathered parts of land are not contradictory. Results are satisfying. Lastly, on acase by case basis, couple of last reshapings are done. The C257 map becomes at this point C271
(with 271 classes).
• NDVI profiles are plotted for only part of the pixels of classes. They are plotted for french pixels
and on several specialized classes coming from CLC2000: vineyards, orchards, rice fields, olive
groves. The goal is to check that those pixels, often melted in larger classes, haven’t a very particularbehaviour that would have been flooded during the classification. This process leads to add still 2classes of vineyards. The final resulting map comprises 273 classes and is called C273.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 9. ECOCLIMAP-II REALIZATION

289

Figure 9.2: Ecoclimap-II C273 map on Europe (one color by class) (latlon projection)

To conclude, the Ecoclimap-II map comprises 273 classes (see fig. 9.2 for an illustration). The classification
process combines both an automatic k-means algorithm on NDVI seven-years time series from SPOT/VGT
and a more or less leaning constraint provided by an initial map built from existing land cover maps that are
CLC2000 and GLC2000. The nomenclature of this map serves to contain the automatic classification andavoid the emergence of incoherent classes.
Note also that the use of seven-years time series data induces that the inter-annual variability is taken into
account during the classification process.

9.1.5 Short description of covers
To summarize, it can be said that:• Distribution of forests over the domain is quite linear and progressive, either on the geographic or on
the NDVI profiles sides. The evolution follows a north-east to south-west axis.
• Crops are very regionalized, in areas with well-marked outlines; they doesn’t seem to follow a strictly
natural logic. Indeed, the human intervention plays a role for these kinds of covers.
• Distribution of shrubs and meadows is intermediate between forests and crops.
• Concerning bare land, snow, inland water and urban areas, resulting classes are very close to thoseof the initial map C76. Indeed, the NDVI classification doesn’t allow to discriminate such types of
SURFEX v8.1 - Issue no 3 - 2018

290
covers. However, the analysis of NDVI profiles is efficient to separate pure pixels from mixed ones,
and to classify areas functions of the vegetation part of mixed ones. Nevertheless, maintaining such
distinctions generates a very important amount of classes. That’s why only few of these nuances arereally integrated in C273, much with bare land and snow, just a little with inland water, not at all withurban areas. It could be interesting in the future to study the relevance of such distinctions.
Generally, ecosystems are rather homogeneous on large areas in the north continental, and very mixed in
the mediterranean perimeter.
For practical purposes, it can be noted that classes are numbered from 301 to 573; sea and oceans present in
the European domain take the number 1 from Ecoclimap-I.

9.2 Translation of covers in tiles and vegetation types
The next step is to define every new cover as a linear combination of the 4 tiles (types of surface) and the 12
vegetation types (inside the ”nature” tile). The available sources are following:• (a) Nomenclatures at 1-km resolution from CLC2000, GLC2000 (world, Europe, North Eurasia, Asia,
Africa), Ecoclimap-I, C76 (initial map for the classification, see 9.1.1);• (a)’ The nomenclature at 100m resolution from CLC2000;• (b) Agricultural statistics from Agreste on France, expressed in hectares, available department bydepartment, since 1989. They comprise details about the types of crops;• (c) a global map about the distribution of C4 vegetation, at 1-degree resolution, provided within theframework of ISLSCP2 and dating from 2003;• (d) estimates of farm produce by european state, from the FAO;
• (e) data on the maize production by european country in 2003, available on website Maı̈sadour, inthousands of hectares.
The method is then the following:• (a) each Ecoclimap-II cover is broken up among classes of considered other maps. Percentages ofrepresentation of the second in the first are listed and associated to the titles of the corresponding
nomenclatures. The total percentage of the Ecoclimap-II cover in the considered map is indicated (inthe case of Corine and GLC regional tiles, only a part of the domain is concerned).
• (b) For AGRESTE, department by department, quantities of forests, meadows, C3 crops, C4 crops,
permanent crops and other types of covers are calculated. Values are averaged on the 1999-2006 spellof time. Resulting curves are plotted and overlain with the associated Ecoclimap-II curves, functionsof the way of repartition of the covers in the 12 vegetation types.
• (c) The Ecoclimap-II C4 map is resampled at 1-degree resolution in order to compare with the
ISLSCP2 map.
• (d) (e) The FAO and Maı̈sadour estimates haven’t been exploited yet.
SURFEX v8.1 - Issue no 3 - 2018

CHAPTER 9. ECOCLIMAP-II REALIZATION

291

If the class is included in the CORINE area at more than 50%, the CORINE 100-m information is favoured,
instead of 1-km nomenclatures. Amounts of C4, C3, meadows, forests, permanent crops are calibrated
thanks to the AGRESTE curves, for well-represented classes on France. The ISLSCP2 map allows to givean idea about the C4 distribution outside France. Note that Agreste provides informations on irrigatedsurfaces that haven’t been exploited yet.

9.3 Initialization of LAI profiles and other parameters
In Ecoclimap, as seen in tab. 8.1 and tab. 8.2, several parameters are initialized at the cover level.

9.3.1 Initialization of heights of trees, ground depths, irrigation and town parameters
First of them, heights of trees are set by using Ecoclimap-I values and the compositions of Ecoclimap-II
covers into other nomenclatures (GLC, CLC, Ecoclimap-I). Concerning shrubs classes, a distinction is done
between meadows and low-level trees.
Then, the ground depths are set by using exclusively the Ecoclimap-I information, the only available.
These two last parameters would gain by benefiting from other sources of information.
Then, the vegetation type ”irrigated crops” is arbitrarily considered as composed of C4 crops only. In Surfex,
the modelling of irrigation passes by four parameters (cf tab. 7.2): SEED, REAP, WATSUP and IRRIG. In
Ecoclimap-I, by default these variables take constant values that are respectively: 10/05, 01/08, 30 and 1. In
Ecoclimap-II, these default values are kept and defined as soon as the ”irrigated crops” fraction is not null.
It would be worth leaning on these values and precise them according to the classes.
Lastly, town parameters don’t change in Ecoclimap-II: Ecoclimap urban classes are the same in the two
versions and come directly from the CLC nomenclature.

9.3.2 Initialization of LAI
The LAI (Leaf Area Index) is defined as the ratio of total upper leaf (or needle) surface of vegetation divided
by the surface area of the land on which the vegetation grows. The effective LAI seen by the satellite is not
the same as the in-situ LAI used by ISBA: the latter is measured on the whole thickness of the vegetation
whereas the satellite sees only the top of canopy and deduces the LAI by more or less performing algorithms.
It notably often causes saturations for high LAI.
LAI by coverTwo satellite LAI have been examined for Ecoclimap-II: CYCLOPES (SPOT/VEGETATION) and MODIS.
Algorithms leading from the satellite bands to the LAI are complex. Land cover maps are included, andthe 7 satellite bands (in the case of SPOT) are used. CYCLOPES data range from 2000, January to 2004,
December; MODIS data from 2000, March to 2006, December. As for the NDVI (see 9.1.2), a smoothingby pixel at the upper envelop of the LAI profiles is performed. This smoothing is debatable because it makes
average LAI values by class very higher than these of rough LAI.
MODIS LAI, CYCLOPES LAI and SPOT/VGT NDVI are plotted by cover so as to be compared. The
three products are quite correlated, but MODIS LAI values tend to be higher on forests. Given that MODIS
LAI time series are longer and that higher values on forests seem more realistic, MODIS LAI are kept for
Ecoclimap-II. Nonetheless, preconceptions relative to the smoothing could lead in the future to review thisLAI and its range of values in particular, all the more because tests of smoothing with varying parameters
give clearly different results.
SURFEX v8.1 - Issue no 3 - 2018

292
Moreover, there is a mask with MODIS data that distinguishes not classed data, built areas, wetlands andmarshes, permanent snow, ice and tundra, bare soil or sparse vegetation areas, inland water, missing data.
These masked values can be interpolated in the time series, excluded or replaced by zero during the smoothing. It happens that missing data are very numerous at the end of 2000 and 2001, particularly for northernand continental classes. That’s why, finally, LAI times series are kept only from 2002, January, in order not
to damage average on all years. It appears necessary to replace masked values because of snow, bare soil orwater by zero, since LAI are otherwise not realistic (what is seen during the disaggregation coming next).
On the contrary, missing and not classed values are interpolated in the limit of 4 successive decades, but
those which are not interpolated are ignored during the calculation of means by cover (acceptable insofar as
they are not predominant).
Disaggregation of LAI by vegtype inside covers

vegtype
CONI
TREE
EVER
GRAS
TROG
PARK
C3
C4
IRR
SNOW
NO
ROCK
total

90-100%
0
0
0
0
0
9
0
0
0
50
3
2
1

80-90%
6
2
0
1
0
2
1
0
3
0
2
0
2

70-80%
3
0
0
4
0
0
5
1
5
0
3
0
3

fraction of vegetation type60-70% 50-60% 40-50% 30-40%
1
3
2
4
0
1
2
3
0
0
0
0
2
7
10
14
0
0
0
0
0
2
0
2
9
9
5
9
1
0
1
0
3
0
2
3
0
0
0
0
4
6
8
6
0
0
0
1
2
4
4
6

20-30%
4
6
0
16
0
0
5
0
2
0
11
5
7

10-20%
13
26
0
17
0
3
13
2
2
0
22
7
15

Table 9.1: Percentages of classes (calculated functions of the total numbers of classes by vegetation type)concerned by the fraction (columns) of each of the 12 vegetation types (lines)
nb of vegtypes or tiles n
nb of classes (vegtypes)
nb de classes (tiles)

1
13
126

2
6
94

3
19
53

4
44
0

5
45
/

6
72
/

7
44
/

8
23
/

9
6
/

Table 9.2: Number of classes comprising n vegetation types (second line) or n tiles (third line)
Remains to determine LAI by vegtype inside covers from LAI by cover. Given the complexity of classes interms of vegetation types composition (see tab. 9.1 and tab. 9.2), an automatic LAI disaggregation techniqueis welcome. The principle of the applied method is the following:• LAI 5-years profiles by cover are averaged in order to obtain the annual mean cycles.
• LAI from vegetation types NO, ROCK and SNOW are supposed null and constant.
SURFEX v8.1 - Issue no 3 - 2018

0-10%
65
60
0
29
100
83
45
95
81
50
35
85
57

CHAPTER 9. ECOCLIMAP-II REALIZATION

293• In each class, the main vegetation type is put apart. For each of the minority vegetation types, the LAI
distance
profile the closest according to the correlation
2 criterion is searched, provided that it corresponds to aclass where this vegetation type is majority.
• The profile found is taken from the profile of the initial class, weighted by its representation fraction
into the class.
• One all minority vegetation types of the classes are thus processed, residual profiles of classes are
obtained. Divided by the inverse of the fraction of the majority vegetation type, they are admitted torepresent the pure majority profiles, in the classes.
• The whole operation is repeated, replacing initial classes profiles by the previously obtained pureprofiles.
• A new set of pure profiles results, for majority vegetation types of classes. Plotting shows that thethree profiles, initial (mixte), pure (first extimate), pure (second estimate) differ not much from one
another.
• Lastly, 5-years LAI profiles are built by propagating the error between years and the average on theobtained pure profiles.
This method presents two problems:• The seeking of approached classes only relies on profiles and not on the geographic localisation.
Associations of classes coming from totally different climate areas are so expectable.
• The technique of subtracting the secondary profiles to deduce the main profile might produce negative
LAI.
The first problem is corrected by introducing two climate maps (Firs on Europe, Koeppe et de Lond on therest of the world). In the algorithm above, climate proximity is now favoured with the seeking beginningin the most represented climate area, next the second, etc. The second problem is solved by excluding a
profile if its subtraction give negative values of LAI. If no suitable profile is found, this which gives the lessnegative values is linearly transformed in order to keep values just over zero.
This method presents the advantages that it relies only on the LAI profiles of covers, and doesn’t create
theoritical profiles. It’s fast and supple (the longer step is to verify the spatial coherence of the origins
of majority and minority profiles) and can be reprocessed in case of modifications of the distribution ofclasses among the 12 vegetation types. It ensures to diversify vegetation types profiles inside covers andguarantees the exact reconstitution of LAI covers profiles. However, it should be evaluated if the initialapproximation between the cover profile and the main vegetation type profile doesn’t produce too muchbias in the definition of supposed pure profiles. But before, MODIS LAI also need to be validated.

9.4 Study of the discontinuity at the limits of the domain
For practical purposes, if the work area overflows the Ecoclimap-II domain, C273 is completed at its edges
by Ecoclimap-I. First, north and major part of west of the domain, there is nearly only sea and ocean (apartfrom in New-Zemble, but the snow class Ecoclimap-II continues there in the snow class Ecoclimap-I). Southand a little west, the boundary is located in the Sahara desert. Except from a possible discontinuity between
SURFEX v8.1 - Issue no 3 - 2018

294
bare rock and bare soil, and between very sparse vegetated and desert areas, the impact is so minor. Remains
the East to study: from northern Russian tundra to Central Asia deserts, by Russian forests, it’s about quite
homogeneous areas organized with latitude, what already dulls the discontinuity.
Classes, LAI by class and by vegetation type and vegetation types fractions on both sides are compared.
Ecoclimap-II classes generally continue in Ecoclimap-I classes. LAI and fractions are often different, butthese discrepancies are rarely enormous.
It’s so chosen to begin tests with the straight discontinuity. Then, if the delimitation is too obvious, it will
be possible to contemplate a version with a smoothed (but artificial) delimitation.

SURFEX v8.1 - Issue no 3 - 2018

Chapter 10

Validation elements for Ecoclimap-II
Validation aspects relate to three fields:• Ecoclimap-II new map has already been quite examined during the processing, through comparisonswith other existing land cover maps (GLC, CLC, Ecoclimap-I - see 9.1.3 and 9.1.4). Other tests
could be performed, for example a comparison with GlobCover, a global land cover map for the year
2005-2006 using ENVISAT MERIS fine resolution (300m) data, developed by ESA (European Spatial
Agency) and distributed by Medias-France.
• Vegetation types fractions have been set in the light of existing land cover map nomenclatures. Other
comparisons have been realized with AGRESTE and ISLSCP2 to calibrate values, but also a posteriori
with Formosat on a square of 60km at the south-west of Toulouse, France. Formosat describes the land
cover, year by year, on this area; the resolution is 20m. This map is produced by the CESBIO1 . This
last comparison gives encouraging results but also reveals the difficulty of different sources to agree:
sources are sometimes contradictory, their charasterics and the geographic precision vary and are notnecessarily easy to compare. However, the progressive use of more recent sources should allow to stillrefine this definition. Concerning specialized vegetation types thar are C4 crops, tropical grassland,
irrigated crops, a lack of homogeneity inside the covers doesn’t allow to get precise fractions. It could
be interesting to make a potential new map with covers built by introducing entering informations
about such characteristics.
• Difficulties have been met to validate other parameters initialized at the cover level: heights of trees,
ground depths, LAI profiles and irrigation parameters. Indeed, complete and reliable sources aren’t
available. A prospect for the following is thus to find means of validating these quantites. Note againthat the organization by covers yields a constraint (especially for irrigation) whose reliance could also
be interrogated in the light of such new validating data.

1

Centre d’Etudes Spatiales de la BIOsphere (spatial study of the biosphere center)

295

296

SURFEX v8.1 - Issue no 3 - 2018

Chapter 11

Conclusion
Ecoclimap-II keeps the same general structure as Ecoclimap-I but several points have changed:• The new covers relie on a k-means automatic classification process and on recent existing land covermaps (GLC2000, CLC2000);• The vegetation types fractions and other cover-based parameters are consequently re-initialized, withhelp from several information sources (AGRESTE, ISLSCP2, land cover maps nomenclatures);• The LAI profiles by cover come from MODIS satellite data, they are smoothed pixel by pixel;• The LAI profiles by vegetation type inside covers are built through an original automatic disaggregation process in which only LAI profiles by cover step in;• LAI profiles are available for the average of 5 years (2002-2006) or for each of these years.
Except from these discrepancies, other surface parameters are still likewise obtained. The geographic andby patch aggregation also remains. Several comparisons with other products have already been done but
Ecoclimap-II now needs to be used in order to better qualify improvements and wastes in relation with thefirst version. Further evolution of the database is considered functions of users returns and of potential newly
available validation data.

Bibliography[1] V. Masson, J.-L. Champeaux, F. Chauvin, C. Meriguet, and R. Lacaze. A global database of land surface
parameters at 1-km resolution in meteorological and climate models. J. Clim., 16(9):1261–1282, 2003.

297

298

SURFEX v8.1 - Issue no 3 - 2018

Part IIILAND SURFACE ANALYSIS

299

Chapter 12

Surface Offline Data Assimilation
Contents
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
12.2 Source code - creation of the binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
12.3 Optimal Interpolation soil moisture analysis . . . . . . . . . . . . . . . . . . . . . . . 301
12.4 Extended Kalman Filter soil moisture and vegetation analysis . . . . . . . . . . . . . 302
12.5 Ensemble Kalman Filter soil moisture and vegetation analysis . . . . . . . . . . . . . 303

12.1 Introduction
SURFEX Offline Data Assimilation (SODA) is the first implementation of a unified assimilation in SURFEX. The present description is based on the offline version from SURFEX v.8. It is assumed that thisversion is currently running on your computer, if not, the first step is to install such version before trying to
use the SODA scheme. SODA permits the land surface analysis of screen level parameters, soil moistureand vegetation. The screen level analysis relies on a two-dimensional Optimal Interpolation (2D-OI). The
soil moisture and/or vegetation analysis rely either on a simplified Extended Kalman Filter or an Ensemble
Kalman Filter (EnKF).

12.2 Source code - creation of the binary
SODA is available under the directory $SURFEX EXPORT/src/ASSIM. Main file is soda.F90 that performs
the various steps of the assimilation : definition of initial perturbed states, reading of fields from SURFEX
outputs, writing of fields necessary for the analysis, and finally the surface analysis. The latter being executed by either assim nature isba oi.F90, assim nature isba ekf.F90 or assim nature isba enkf.F90.

12.3 Optimal Interpolation soil moisture analysis
Methodology
This soil analysis scheme is based on an local optimum interpolation technique as described in Mahfouf(1991), Giard and Bazile (2000). The analysis increments from the screen-level analysis (2-meter temperature, T2 m and relative humidity, RH2 m) are used to produce increments for the water content given by:
301

302

∆ws = αTs ∆T2m + αRH
s ∆RH2m(12.1)∆wp = αTp ∆T2m + αRH
p ∆RH2m(12.2)

andfor the superficial volumetric and mean volumetric water content, respectively. The coefficients αTp and αRHpdepend on soil texture, increasing as the standard range of variation of soil moisture δw = δwf c − δwwilt(soil water content at field capacity and wilting point, respectively).

12.4 Extended Kalman Filter soil moisture and vegetation analysis
Methodology
The EKF soil moisture analysis used in SODA is a point wise data assimilation scheme (Mahfouf et al.
(2009), Barbu et al. (2011, 2014) , Fairbairn et al. (2017), Albergel et al. (2017)). The analysis update
equation of the EKF is:xa (ti ) = xf (ti ) + Ki (y0 (ti ) − hi [xf ])(12.3)

The a, f and o subscripts stand for analysis, forecast and observation, respectively. x is the control vector
of dimension Nx , computed at time ti , that represents the prognostic equations of the LSM M .
yo is the observation vector of dimension Ny . The Kalman gain matrix Ki is computed at time ti as:
Ki = BH T (HBH T + R)−1

(12.4)

A non-linear observation operator h, enables the extraction of the model counterpart of the observations:y(ti ) = h(x)(12.5)

B and R are error covariance matrices characterising the forecast and observations vectors. The crosscorrelated terms represent covariances. The operator H (and its transpose H T ) from 12.4 is the Jacobianmatrix: the linearized version of the observation operator (defined as Ny rows and Nx columns) that transforms the model states into the observations space. A numerical estimation of each Jacobian element iscalculated by finite differences, by perturbing each component xj of the control vector x by a specificamount δxj resulting in a column of the matrix H for each integration m:Hmj =ym (x + δxj ) − ym
∂ym
≈
∂xj
δxj

(12.6)The background error covariance matrix undergoes an analogous forecast and analysis cycle:
Bf (ti ) = M (ti−1 )Ba (ti−1 )M T (ti−1 ) + Q(12.7)Ba (ti ) = (I − K(ti )H(ti ))Ba (ti )(12.8)In the forecast step (equation 12.7), the previous analysis, Ba (ti−1 ), is forecast forward in time by thetangent linear of the state forecast model M , and the forecast error covariance matrix Q, is added to accountfor errors in the model forecast, giving the background error matrix forecast Bf (ti ). The model state analysis
decreases the model error, and B is reduced by an analysis step (equation 12.8). The linearization of M is
SURFEX v8.1 - Issue no 3 - 2018

BIBLIOGRAPHY

303

obtained by the same finite difference method used for H. The control vector evolution from time ti to time
ti+1 is then controlled by the following equation:
xf (ti+1 ) = Mi [xa (ti )](12.9)

12.5 Ensemble Kalman Filter soil moisture and vegetation analysis
Although an EnKf analysis is available within SODA (Fairbairn et al. (2015)), it is still in consolidation
phase.

Bibliography[1] C. Albergel, S. Munier, D. J. Leroux, H. Dewaele, D. Fairbairn, A. L. Barbu, E. Gelati, W. Dorigo,
S. Faroux, C. Meurey, P. Le Moigne, B. Decharme, J.-F. Mahfouf, and J.-C. Calvet. Sequential assimilation of satellite-derived vegetation and soil moisture products using surfex v8.0: Ldas-mondeassessment over the euro-mediterranean area. Geoscientific Model Development, 10:3889–3912, 2017.
[2] A. L. Barbu, J.-C. Calvet, J.-F. Mahfouf, C. Albergel, , and S. Lafont. Assimilation of soil wetness
index and leaf area index into the isba-a-gs land surface model: grassland case study. Biogeosciences,8:1971–1986, 2011.
[3] A. L. Barbu, J.-C. Calvet, J.-F. Mahfouf, and S. Lafont. Integrating ascat surface soil moisture andgeov1 leaf area index into the surfex modelling platform: a land data assimilation application overfrance. Hydrol. Earth Syst. Sc., 18:173–192, 2014.
[4] D. Fairbairn, A. L. Barbu, J.-F. Mahfouf, J.-C. Calvet, and E. Gelati. Comparing the ensemble andextended kalman filters for in situ soil moisture assimilation with contrasting conditions. Hydrol. Earth
Syst. Sc., 19:4811–4830, 2015.
[5] D. Fairbairn, A. L. Barbu, A. Napoly, C. Albergel, J.-F. Mahfouf, and J.-C. Calvet. The effect of satellitederived surface soil moisture and leaf area index land data assimilation on streamflow simulations overfrance. Hydrol. Earth Syst. Sc., 21:2015–2033, 2017.
[6] D. Giard and E. Bazile. Implementation of a new assimilation scheme for soil and surface variables ina global nwp model. Mon. Wea. Rev., 128:997–1015, 2000.
[7] J.-F. Mahfouf. Analysis of soil moisture from near surface parameters: A feasibility study. Journal ofApplied Meteorology, 30:506–526, 1991.
[8] J.-F. Mahfouf, K. Bergaoui, C. Draper, F. Bouyssel, F. Taillefer, and L. Taseva. A comparison of two
off-line soil analysis schemes for assimilation of screen level observations. Journal of GeophysicalResearch: Atmospheres, 114(D08), 2009.

SURFEX v8.1 - Issue no 3 - 2018

304

SURFEX v8.1 - Issue no 3 - 2018