1 /-. 

r, - */! 1 

, /$- 

NASA Technical Memorandum 104606, Vol. 9 

d - ~ 

, -/ - 

Technical Report Series on 

Global Modeling and Data Assimilation 

Max J. Suarez, Editor 

Volume 9 

Energy and Water Balance Calculations 

in the Mosaic LSM 

Randal D. Koster and Max J. Suarez 

March 1996 

HYDROLOGICAL SCIENCES BRANCH 
NASA Technical Memorandum 104606, Vol. 9 

Technical Report Series on 

Global Modeling and Data Assimilation 

Max J. Suarez, Editor 

Goddard Space Flight Center 

Greenbelt, Maryland 

Volume 9 

Energy and Water Balance Calculations 

in the Mosaic LSM 

Randal D. Koster 

Max J. Suarez 

Goddard Space Flight Center 

Greenbelt, Maryland 

National Aeronautics and 

Space Administration 

Goddard Space Flight Center 

Greenbelt, Maryland 

1996 
This publication is available from the NASA Center for Aerospace Information, 

800 Elkridge Landing Road, Linthicum Heights, MD 21090-2934, (301) 621-0390. 

I I 
Abstract 

The Mosaic land surface model (LSM): which is designed for use with an atniospheric general circulation model (GCM), computes areally-averaged energy and wat,er 

fluxes from the land surface in response to meteorological forcing. The model allows 

explicit vegetation control over the computed surface energy and water balances, with 

environmental st,resses (high temperatures, dry soil: etc.) acting to increase canopy 

resistance and thus decrease transpiration. The scheme includes a canopy interception 

reservoir and three soil reservoirs: a thin layer near the surface, a middle layer that 

encompasses the remainder of the root zone, and a lower “recharge” layer for long term 

storage. Bare soil evaporation, transpiration, and interception loss occur in parallel, 

and runoff occurs both as overland flow during precipitation events and as groundwater 

drainage out of the recharge layer. A complete snow budget is included. The model 

was originally derived from the SIB model of Sellers et al. (1986) and still maintains 

certain SiB forniulationst particularly those for canopy resistance. 

The model accounts for subgrid variability in surface characteristics through the 

“mosaic” approach. A grid square area containing several different vegetation regimes is 

divided into relatively homogeneous sub-regions (“tiles” of the mosaic): each containing 

a single vegetation or bare soil type. Observed vegetation dist,ributions are used to 

determine the partitioning. A separate energy balance is calculated for each tile, and 

each tile maintains its own prognostic soil moisture contents and temperatures. 

This report provides thorough documentat,ion of the pararneterizations used within 

a single Mosaic LSM tile. The requirements for coupling to a GChif are also discussed. 

... 

111 
Contents 

List of Figures 

List of Tables 

1 Introduction 

2 Overview of Calculations 

vii 

ix 

1 

1 

3 Energy Balance: Solution Procedure 4 

3.1 Surface Energy Balance Equation ........................ 4 

3.2 Vapor Flux Equation ............................... 6 

3.3 Solution of Simultaneous Equations ....................... 7 

3.4 Correction for Snowmelt ............................. 8 

3.5 Energy Balance in the Deep Soil ........................ 9 

4 Energy Balance: Components 9 

4.1 Surface Reflectance ................................ 10 

4.2 Canopy Resistance ................................ 11 

4.2.1 Unstressed Canopy Resistance ..................... 11 

4.2.2 Environmental Stresses ......................... 13 

4.3 Resistance for Bare Soil Evaporation ...................... 16 

4.4 Canopy Interception and Snow; Effective Surface Resistance ......... 17 

4.5 Derivatives of Effective Surface Resistance ................... 19 

V 
4.6 Linearization of Longwave Radiation ...................... 

4.7 Linearization of Heat Flux to Deep Soil .................... 

5 Water Balance: Solution Procedure 

6 Water Balance: Components 

6.1 Canopy Int. crception Reservoir ......................... 

6.1.1 Interceptmion Reservoir Capacity ..................... 

6.1.2 Precipitation Loading .......................... 

6.2 Surface Rii~ioff arid Infilt. ration ......................... 

6.3 Evaporation Sink ................................. 

6.4 Groiindwatcr Diffusion .............................. 

6.5 Percolation to the Water Table ......................... 

6.6 Snow Budget. ................................... 

7 Connection to the GCM 

7.1 Version1 ..................................... 

7.2 Version2 ..................................... 

7.3 Version3 ..................................... 

Appendix 1: List of Symbols 

19 

20 

21 

22 

22 

22 

23 

27 

29 

30 

32 

33 

33 

34 

38 

38 

39 

Appendix 2: Tables of Parameter Values 

References 

vi 

45 

57 
List of Figures 

The e~iergy balance at the land surface. The shaded fluxes are computed 

within the Mosaic LSM; the others are provided by the GCM. ........ 

Schematic of the water balance calculat,ions performed by the Mosaic LSM. 

Temperat,ure st,ress fiiIict,ions (l/F(T)) froni SiB (solid lines) and the Mosaic 

LSM (dashed lines) for six vegetation types. .................. 

Demonstration of how differences in assumed fractional area coverage of 

storms can affect. the loading of the interception reservoir. .......... 

Demonstration that the neglect of temporal correlation in storm position can 

lead to higher interception storage. ....................... 

Areal fract,ions of the tile considered when computing interception of rainwater wit8h Version 1. ................................ 

Areal fractions of the tile considered when cornpiitsing interception of rainwater with Version 2. ................................ 

Subgrid dist,ribiition of soil moisture assiimcd for diffusion between top two 

soil layers. ..................................... 

Example of the construction of input arrays for the TILE subroutine. ... 

3 

4 

15 

23 

24 

25 

27 

32 

34 

vii 
List of Tables 

1 Heat storage and unstressed canopy resistance parameter values assigned 

to the eight fundamental surface types. A relevant equation is provided in 

parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

2 Parameter values related to environmental stress factors, for each of the eight 

fundamental surface types. A relevant equation is provided in parentheses. . 

3 Water balance parameter values assigned to the eight fundamental surface 

types. A relevant equation is provided in parentheses. AZ refers to the 

thickness of a soil layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

4 Reflectance parameters. A relevant equation is provided in parentheses. 

KS91 refers to Koster and Suarez [1991]. . . . . . . . . . . . . . . . . . . . . 

5 Seasonal variation of leaf area index, Lt (dimensionless). . . . . . . . . . . 

6 Seasonal variation of greenness fraction, fs (dimensionless). . . . . . . . . 

7 Seasonal variation of roughness length, zo (m). . . . . . . . . . . . . . . . 

8 Seasonal variation of csca. (dimensionless). . . . . . . . . . . . . . . . . . . . 

9 Seasonal variation of root length density, Dd (n~-~). . . . . . . . . . . . . . 

10 Seasonal variation of zero plane displacement height, d (m). . . . . . . . . . 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

... Vlll 
1 Introduction 

The land surface model (LSM) described by Koster and Suarez (1992a) (hereafter referred 

to as the Mosaic LSM) has been fully coupled to the Aries GCM at NASA/GSFC, and 

the coupled models have been used to address a number of climate-related problems. For 

example, Koster and Suarez (1994) examined how simulated mean climate is affected by 

various components of the land surface, specifically those components that differentiate a 

surface-vegetation-atmosphere-transfer (SVAT) LSM from a typical bucket LSM. Koster 

and Suarez (1995) used the models to isolate the contributions of land and ocean processes 

to interannual precipitation variability, and Scott et al. (1995) used them in an analysis of 

land surface control over precipitation persistence. The Mosaic LSM is also incorporated 

into current simulations of the atmosphere/ocean/land system by GSFC’s Coupled Climate 

Dynamics Group. 

Although the Mosaic LSM was originally an offshoot of the Simple Biosphere, or SiB, LSM 

(Sellers et al. 1986), it has sufficiently diverged from SiB to warrant separate documentation. 

The present report describes the framework of the Mosaic LSM calculations (Section 2) and 

presents its specific energy and water balance formulations (Sections 3-6). The report ends 

with a detailed discussion of the model’s coupling to the GCM (Section 7). 

Three different versions of the Mosaic LSM are described in this report: 

Version 1. This is the model version used by Koster and Suarez (1993, 1994, 1995). It is 

also the version used in PILPS, the Project for the Intercomparison of Land-surface 

Parameterization Schemes (Henderson-Sellers et al. 1993). 

Version 2. This model, which was used by Scott et al. (1995, 1996), includes an improved 

formulation of the canopy interception reservoir. 

Version 3. In addition to the improvements in Version 2, this model includes improved 

treatments of surface runoff and fractional snow cover, as well as a more comprehensive 

list of output variables. 

For the most part, the three versions use identical physical parameterizations. The discussions below will mention version numbers only to distinguish version-specific features of the 

model. 

2 Overview of Calculations 

The Mosaic LSM is named for its use of the “mosaic” strategy to account for subgrid 

heterogeneity in surface characteristics. Using vegetation maps, every surface grid cell in 

the GCM is subdivided into relatively homogeneous subregions, or “mosaic tiles”, each 

1 
tile containing a single veget(at,ion or bare soil type (Kost,er and Suarez 1992a). Energy 

and water balance calculations arc performed over each tile at every time step, and each 

tile maintains its own prognost,ic variables. Le.. its own moisture reservoir contents and 

t,emperatmes. The tiles in a grid square respond to the mean conditions in the overlying 

GCM grid box: this grid box. in t,iirn, responds to t,he areally-weighted fluxes of heat and 

moistsure from t,he tiles. The tiles in a grid square do not interact with each other directly, 

though they can affect each other t,hrough the overlying atmosphere. 

As the model is currently used in the GCM, a land surface tile can contain one of eight basic 

surface types: (1) broadleaf evergreen trees; (2) broadleaf deciduous trees; (3) needle-leaf 

trees: (4) grassland (groundcover): (5) broadleaf shrubs: (6) dwarf trees (tundra); (7) bare 

soil: and (8) desert soil. The model parameter values associated with each t,ype are provided 

in Tables 1 through 10 of Appendix 2. Mixtures of vegetation types are not allowed within 

a tile: thus, a grid cell containing savanna would be split. into two tiles, one containing 

trees and the other containing grass. As demonstrated by Koster and Suarez (1992b), 

the treatment of a homogeneous vegetation mixture as two isolated patches of vegetation 

generally has little effect on the average surface energy balance of the region. This method of 

treating homogeneous mixtures produces significant error only if the evaporation resistances 

imposed by thc t,wo types are extrcmcly different. 

The energy balance calculations performed by the Mosaic LSM within each tile are ilhistrated in Figure 1. A fraction of the incoming solar radiation is immediately reflected. The 

sum of absorbed solar radiation and downward longwave radiation is balanced by upwelling 

longwave radiation, outgoing latent heat, outgoing sensible heat, ground heat storage: and 

snowmelt. Canopy resistance: which controls transpiration rates, is allowed to vary with 

environmental stress. Heat transfer int,o the deep soil updates a deep soil temperature. A 

strict energy balance is maintained for the surface/canopy system and for the deep soil at 

cvery time step; energy is never created or destroyed. except possibly through numerical 

round-off. 

The water balance calculations performed within each tile are illustrated in Figure 2. Of 

the precipitation water falling on the land surface: some is added to a canopy interception 

reservoir, which accounts for the ability of leaves and ground litter to hold small amounts of 

“frec-standing” water from which evaporation occurs unhindered. The rest of the precipitation falls through to the soil siirface: and this throughfall is in turn partitioned into surface 

runoff (overland flow) and infiltration into the shallow surface soil layer. Wat8er diffuses 

between the surface soil layer and a second soil layer, which encompasses the remainder of 

the root zone. Water also diffuses between the root layer and a third, larger soil layer that 

allows long-term storage of soil moistsure, and water can percolate out of this third layer and 

thus out of t,he modeled soil column. Evaporation extra,ct,s moisture from the interception 

reservoir, from the top t,wo soil layers: and from any snowpack present. (Though not shown 

in Figure 2, a snow budget, is included.) The Mosaic LSM ensures a strict, water balance 

for every surface reservoir. Only numerical round-off can create or destroy water mass. 

Each land surface tile has eight, prognostic variables. Three are associated with the energy 

2 
incoming outgoing 

longwave longwave latent heat sensible heat 

diation radiation 

////////////////I /// / // / / / /// /// /// I/// // // 

Figure 1: The energy balance at the land surface. The shaded fluxes are computed wit,hin 

t,he Mosaic LSM; the others are provided by the GCM. 

balance equations : 

T, , the t,emperat,urc of the siirface/canopy system, 

Td. the temperat,iire dccp in the, soil, and 

e,: thc vapor prcssure in the canopy air. 

Five arc associated with t,he water balance equations: 

C. the Inoist,iirc content of the canopy interception reservoir; 

W1, the moistme content. of the top soil layer, 

W.L: the moisture content, of t,he middle soil layer: 

Ws. the moistmiire cont,cnt, of t,he bottom soil layer, and 

S. t,hc moisture held within t,he snowpack, if any. 

These prognostic variables arc iipdated at, every time st,cp. 

3 
EVAPORATION 

+ TRANSPIRA 

IMERCEPTON 

RESERVOIR 

THROUGHFALL FACE RUNOFF 

SURFACE LAYER 

1,1, ROOT LAYER 

VI 

SOIL MOISTURE 

DIFFUSION 

DRAINAGE 

Figure 2: Schematic of the water balance calculations performed by the Mosaic LSM. 

3 Energy Balance: Solution Procedure 

The surface energy fluxes are computed at each time step by solving two equations simultaneously at each land surface tile: one for thc surface energy balance itself, and one that 

equates vapor transport into the canopy air with vapor transport away from the canopy 

air. The present section describes how these two equations are set up and solved. Section 

4 will describe how the individual components of the equations are computed. 

3.1 Surface Energy Balance Equation 

The surface energy balance equation, in the absence of snowmelt, is 

+ Rli\y = - cH6Tc + R:bv + H + XE +Go; At 

where 

Rsw-net = net shortwave radiation absorbed at the surface, 

R;, = longwave radiation absorbed at the surface, 

CH = heat capacity associated with surface/canopy system: 

bT, = change in surface-canopy temperature, T,, over t,ime step, 

4 
At = time step duration, 

R!,,, = upward longwave radiation at surface, 

H = sensible heat flux, 

X = latent heat, of vaporization, 

E = evaporation rate. and 

GD = heat flux to deep soil. 

Energy associated with snowmelt is treated separately, as outlined in Section 3.4. 

Each of the energy fluxes in (1) is assumed consistent with the updated surface temperature. 

T,? and canopy air vapor pressure, e,, for the time step. Because these updated values are 

not known a priori when the energy balance is calculated (i.e., because an implicit solution 

is desired). the Mosaic LSM uses the following linearizations: 

and 

where the subscript “old denotes quantities calculated using the previous time step‘s values 

of T, and e,, and where bT, and be, are the changes in the surface temperature and canopy 

vapor pressure, respectively, that occur over the time step. With these linearizations, the 

energy balance can be rewritten as 

aw-net + R:, - [R:, + H + M.3 + GDIold = 

(6) 

CH dR/W dH dE dGD dH dE +-+A-+- bT,+ -+A- be,. [at+= aTc aTc d,],, [a% aealold 

Mosaic LSM Versions 1 and 2 differ from Version 3 in the value of X used when snow is 

present. In Versions 1 and 2, the presence of snow implies that the only evaporation possible 

is snow sublimation, and X is set to the latent heat of sublimation. In Version 3, evaporation 

can occur in parallel from the snowpack and from the snow-free fraction of the land surface 

tile. In Version 3, X is set to 

= fE--snow& + (1 - fE-snow)Ae: (7) 

where A, is the latent heat of sublimation. A, is the latent heat of vaporization of liquid 

water. and f~-~~~~ is the ratio of snow sublimation to total evaporation, which can be 

determined before the evaporation itself is calculated: using (114). (See Section 6.3.2.) 

5 
3.2 Vapor Flux Equation 

Equation (6) has two unknowns. 6TC and be,. and thus another cqiiat.ion is needed. For 

the second equation. t,he Mosaic LSM itSsii1nes t,hat the canopy air has negligible storage 

capacity for water vapor. so t,liat, t,he flux of moisture from the trees and soil into t,he canopy 

air, ESClrf, is exactly balanced by the flux out of the canopy into t-lie overlying atmosphere. 

E, as calculated witfli (4). E,,,,f is conipiitd with: 

where p is air density. c is the ratio of the inolcciilar weight, of water vapor to that of dry 

air, p, is the siirfacc pressure. e,(T,) is the satmxtcd vapor pressure at, the teniperatiirc T,.. 

and reff is t,hc effectivc siirfacc rcsist,ancc to vapor transport. which varies with T, arid e,. 

By linearizing (8) aroiind [T,],~,I and [e,],l,l arid combining with (4). the cqiiation E = E,,,,f 

is transformed into: - [ (E - E,ll,f 1 reff I old - 

where EH is t,hc harmonic mean of [Elold and [Es,lrf]old. In fact. EH in (9) could be replaced 

by either [E],1,1 or [E,,,,f],ld. depending on the order in which the t,errns are linearized. The 

harmonic nican is used t,o increasc the calculation's st(abi1ity. 

Stdility is fiirthr increased by requiring t,hat 

and 

If either slim is ncgativc. it, is reset. to zero before (9) is used. The idea is t,o ensiire that t,he 

indirect changes in e~aporat~ion associated with changes in canopy resist,ance do not, exceed 

the niore direct. changes associat,cd wit,h changes in e, and T,. 

Eqiiathi (9) is niodificd when the surface resistance is zero. e.g.. due t,o the presence of 

snow (in Versions 1 and 2) or a satmat,ed canopy (see Sectmion 4.4). Under these condit,ions. 

the canopy air vapor prcssiire. e,. is assiimed equal to e,(T,). so that. (9) is replaced with: 

[es(Tc) - 

In fact,. siibst,it,iit,ing (8) into (9) and setting r,ff and its derivatives t,o zero produces (12) 

exactly. 

6 
3.3 Solution of Simultaneous Equations 

The Mosaic LSM solves (6) and (9) (or solves (6) and (12), in the case of zero surface 

resistance) to produce values of ST, and he, for the time step. This allows the calculation 

of the sensible heat fliix and evaporation rate for the time step, using (3) and (4). It also 

allows the updating of the prognostic variables T, and e,: 

Before the prognostic variables are updated, though, several checks are made on the calculated fluxes. First. the Mosaic LSM ensures that sufficient water is available for the 

calculated evaporation rate. The available water. Wavail, is calculated in Versions 1 and 2 

a,! 

(15) 

C + W1 + W2, 

S, when snow is present 

when snow is not present 

If the calculated evaporation for the time step, EAt, is greater than Wavail, then all available 

water evaporates during the time step, and the canopy air vapor pressure, e, ~ is reset to the 

GCM-provided vapor pressure in thc overlying air, e,,, . The value of ST, is then recomputed 

using (6) alone, after setting both [~]olcl and [~]O1cl to zero, replacing Sea by e, - e,, 

and replacing XE by XWavail/At. The sensible heat flux is computed using (3) with the 

modified ST,. 

Second: the Mosaic LSM checks that the calculated evaporation rate is consistent with the 

vapor pressure gradients. A positive flux in the presence of a newly-established negative 

gradient (or vice-versa) is possible under certain condit*ions as a result of the linearizations 

used in the solution procedure. Also. the terms and [E],,, are untrustworthy 

when the calculated evaporation and [Elold have opposite sign. Such cases are rare. but 

when they occur. the Mosaic LSM sets the evaporation rate to zero and sets Sea to e, - e,, 

i.e., it, sets the canopy vapor pressure to the vapor prcssixre in the overlying air. It then uses 

(6) alone to recompute ST,: after resetking XE. [g] and [2]01cl to zero. The sensible 

heat flux is recomputed using the modified ST,. 

olcl 

Finally. the Mosaic LSM puts a limit on the computed Se, if Se, is too large. the assumed 

linearizat,ions are invalid. and an instability may develop. (Such problenis are less likely 

with ST,. since temperature change is mitigakd by t,hc surface's heat capacity.) When (6) 

and (9) are used to compute ST, and be,. with no modification. be, is constrained to have 

a magnitude no greater than e0/2. If Sea is indeed reset t,hrough this constraint, ST, is 

recomputed using (6) alone. using the newly prescribed value of be,. Surface fluxes are 

adjusted accordingly. using (3) and (4). 

7 
3.4 Correction for Snowmelt 

If snow is present on t,ho siirfacc at, the beginning of a t,ime step, and if the computed T, 

at the end of the t,iriic stcp is above the freezing point. Tf (=273.16K), then snowmelt is 

asslimed to occiir. and the energy balance riiiist be rcconiput,ed. The approach used in 

Versions 1 arid 2 differs slightly from that uscd in Version 3. 

a. Versions 1 and 2. The assiimed new values of 6T, and Sea are 

and 

Eqitat,ion (17) rcscts T, to Tf. The outgoing longwave radiation. sensible heat fliix. evaporat,ion rate. and ground heating are recomputed wit,h (2) through (5). The rate of snowmelt. 

Srrlelt. is computed by dividing the residual cnergy available for melting (calculated with 

thc new values of ST,. and be,) by the latcnt heat of fusion, Xf: 

At times. the entire snowpack will melt during the time step, with enough energy left over 

to heat the surface abovc Tf. This is not allowed by the snowmelt formulation in Versions 1 

and 2. which for convenience always resets T, to Tf when snowmelt occurs. To maintain a 

strict cncrgy balance in this situation. the residual energy that remains after melting all of 

the snow is arbitrarily added to the sensible heat flux. Thus, for this particular time step, 

the sensible heat flux is artificially high. 

b. Version 3. The energy balance is first recalculated under the extreme assumption that 

all the snow ha.. melted. Equation (6) is rewritten as: 

(20) 

CH dRI!\ BH -+- +-++-+- BE ~GD],,, ST,+ [dH -+A- BE] Se,. 

At dT, BT, BT, dT, de, Be, old 

where S is the snow mas and Esno,\. is the cvaporation rate from snow. calculated with 

(115). Eqiiations (20) and (9) are t,hcn solved simiiltancoiisly for ST, and be,. 

If. in fact. only a fraction of the snow should melt (the most common condition): [T,],I,I 

phis this new valiie of ST, will lie below Tf. and the cncrgy balaricc must, be computcd stsill 

another t,ime. The value of [T,]r,e,~ is set to Tf. iising (17). and be, is computed with (9) 

and (17). The amount, of snowmelt, is then coniputed with (19). 
Version 3 thus differs from Versions 1 and 2 in that it allows the ground to heat above T’ 

and updates e, in a more sensible way. 

3.5 Energy Balance in the Deep Soil 

The deep soil temperature, Td, is not updated implicitly. Once [Elnew is known, [Td],,, is 

computed as 

[Td],ew = [TdIold + GDAt/CH-deep, (21) 

where CH-dep is the heat capacity associated with the deep soil, and where Go is calculated 

with (5). The values used in the Td calculation are consistent with the force-restore equations 

of Deardorf (1978); see Section 4.7 below. 

4 Energy Balance: Components 

Several of the terms in the two equations for 6Tc and he,, (6) and (9), are provided by 

the GCM. For example, the GCM provides the downwelling longwave radiation, RllW. Also, 

because the GCM is assumed to perform all of the boundary layer transport calculations, it 

is expected to provide values for [Elold, [%]old: [%]old, [Hlold, [%]old, and [Zlold, dH using 

the values of T, and e, provided by the LSM at the end of the previous time step. The LSM 

are forced to lie at or above certain critical values, as necessary for the stability of 

modifies the derivatives only when they appear unrealistic - [%]old, [zIold, dH (=]old, aE and 

the energy balance calculations. 

The GCM also supplies values for e,([T,],ld) and [$+]old a in order to ensure consistency 

between the GCM and LSM phase change calculations. The Aries GCM currently provides 

these values only for the liquid/vapor transition, even for sub-freezing temperatures. As a 

result, snow sublimation rates in the coupled system may be slightly overestimated. The 

AEies GCM is now being modified to provide es([TcIold) and for the solid/vapor 

transition when T, lies below the freezing point. 

The formulations used at each land surface tile for the remaining terms in the energy balance 

equations are discussed in the present section. The calculation of Rsw-net in (6) requires 

the assignment of surface reflectances (Section 4.1). The determination of -re~, g, 2, 

and Esurf (and thus EH) in (9) is a rather lengthy process that is described in Sections 

4.2 through 4.5. The linearization of the upward longwave radiation (terms [@w]old and 

[$$]old) is discussed in Section 4.6, and the deep soil heat flux calculation (terms [GIold 

and [$$]old) is discussed in Section 4.7. 

9 
4.1 Surface Reflectance 

Solar radiation must be separated by the GCM into four components: visible direct radiation 

(Rv-dir); visible diffuse radiation (Rv-dif); near-infrared direct radiation (Rni-dir); and nearinfrared diffuse radiation (Rni-dif). The land surface model computes an albedo (av-dir, 

av-dif, ani-dir, and an;-dif) for each component. This allows the calculation of the net 

shortwave radiation at the surface: 

In addition to varying with vegetation type, the reflectances vary seasonally with leaf area 

index and greenness fraction, and they vary diurnally with the solar zenith angle. The 

algorithm used is an approximation to the full two-stream calculations of SiB, though with 

a slight improvement in the calculation of the diffuse reflectances. Full details are provided 

by Koster and Suarez (1991). 

The presence of snow increases surface reflectance and thus decreases Rsw-net. In Versions 1 

and 2, a simple ramping function is used to convert the reflectance associated with vegetation 

to a reflectance associated with a vegetation-snow mixture. If aveg,v-dir is the surface 

reflectance for visible direct radiation in the absence of snow, and if a,no,,v-dir is the 

corresponding reflectance over complete snow cover, then the net reflectance for visible 

direct radiation is computed as: 

aveg,v-dir: S < Scritl 

s-s ’ 

aveg,v-dir + (asnow,v-dir - aveg,v-dir)&, Scritl < s < Scrit2 (23) 

asnow,v-dirt Scrit2 < S, 

where S is the snow mass and Sc-itl and Scrit2 are vegetation-dependent critical snow 

amounts. Corresponding equations are used for the reflectances of the other three shortwave 

radiation components. 

Due to an error in the implementation of this ramping function, Scritl and Scrit2 were set to 

excessively low values, implying an essentially discontinuous jump in reflectance when going 

from snow-free to snow conditions. This discontinuity is present in the coupled GCM/LSM 

simulations using Versions 1 and 2. The error was corrected, however, before Version 1 was 

used in the PILPS intercomparison project (Henderson-Sellers et al. 1993). 

Version 3 of the Mosaic LSM uses a different ramping function: 

where is a vegetation-dependent parameter. (Again, corresponding equations are used 

for the other shortwave radiation components.) This formulation is similar to that used in 

BATS (Dickinson et al. 1986). 

10 
4.2 Canopy Resistance 

I 

The canopy resistance, r,, is the resistance provided by vegetation stomata to transpiration, 

ET : 

(25) 

P' (en,) - ea) ET = - 

Ps TC 

The canopy resistance calculation requires two steps: (1) the determination of an unstressed 

canopy resistance, a function only of vegetation type and incoming photosynthetically active 

radiation (PAR), and (2) the incorporation of stress terms that increase the resistance when 

the vegetation experiences non-optimal environmental conditions. As discussed in Section 

4.4, (25) is not used directly in the energy balance calculations. Instead, T, is combined 

with the resistances for bare soil evaporation and interception loss to produce a net effective 

resistance, Teff, for the surface. 

4.2.1 Unstressed Canopy Resistance 

The formulation of unstressed resistance, Tc-.n,tressed, is taken directly from the SiB LSM 

formulation (Sellers et al. 1986). The unstressed canopy resistance function at the bottom 

of Table 4 in Sellers (1985) is: 

- - 1 

rc-unstressed,green 

where 

a + bc 

CFO 

d= -, 

and where a, b, and c are constants describing the resistance to transpiration provided by a 

single stomate (see equation (17) in Sellers (1985)), Fo is the sum of the visible direct and 

visible diffuse components of the incoming solar radiation (i.e., the PAR flux, provided by 

the GCM), k is an extinction coefficient, Lt is the leaf area index, p is the cosine of the 

solar zenith angle (provided by the GCM): and G(p) is the relative projected area of leaf 

elements in the direction of this angle. This equation represents the integral of the resistance 

function for a single stomate across a vegetation canopy that is assumed to consist only of 

live (green) leaves. Note that (26) can be rewritten as 

Because the solar radiation has both direct and diffuse components, and because (28) applies 

only to direct radiation, the term G(p)/p is replaced by a different function, 9: 

11 
1 

Tc-unstressed,green k 

where Q is a weighted average of two functions, one for direct radiation (G(p)/p) and one 

for diffuse radiation (Qdif): 

where fdir is the ratio of direct solar radiation to total sokar radiation. Following Sellers 

(1985) , 

G(P) = 41 + 421-L: (31) 

42 = 0.877(1 - 241); (33) 

and xr, describes the departure of leaf angles from a spherical distribution. The equation 

used for 4dif was not provided by Sellers (1985) or Sellers et al. (1986) and was thus 

extracted from the SiB computer code itself: 

The extinction coefficient: k, is calculated <as a weighted average of the corresponding values 

for direct and diffuse radiation: 

From Sellers (1985): 

where w is the scattering coefficient. For the diffuse component, 

1 

ZP 

Adiffuse = - (1 - w) f , (37) 

where zfi is a pre-calculated parameter derived from an equation within the SiB computer 

code: 

1 41 41 +42 "=-('-&'"[ 42 I). 

Both kdirect and kdiffuse are forced to lie below 50/Lt. 

For computational efficiency, (1 - w)f is precomputed by the GCM and sent, t,o the LSM 

as an input parameter. It varies seasonally due to the dependence of w on the greenness 

fraction, fq: 

w = fglrt-live + (1 - fg)lrt-dead: (39) 

12 
where Zrt-live is the sum of the leaf-element reflectance and leaf-element transmittance for 

green leaves and irt-dead is the corresponding sum for dead (brown) leaves. 

Finally, to account for the fact that not all of the leaves are transpiring, the resistance 

computed with (29) is divided by the greenness fraction, fg: 

fc - unstressed ,green rc-unstressed = fg 

Thus, a smaller fraction of green leaves leads to a higher canopy resistance. 

4.2.2 Environmental Stresses 

The unstressed canopy resistance calculated with (29) and (40) is the transpiration resistance used when all environmental conditions are optimal. If conditions are sub-optimal, 

the resistance increases: 

where F(VPD), F(T), and F(.JI/) are the stress terms (each greater than or equal to 1) 

associated with vapor pressure deficit, temperature, and leaf water potential, respectively. 

The stress functions used are largely consistent with those outlined by Jarvis (1976). 

a. Vapor Pressure Deficit Stress. Early versions of the Mosaic LSM - as well as the version 

used in the PILPS intercomparison study (Henderson-Sellers et al. 1993) - calculated 

F(VPD) with 

= Max [O., 1. - (es(Tc) - e,)&pn], 

1 

F(VPD) 

where d~p~ is a vegetation-specific parameter. A higher vapor pressure deficit, e,(T,) - e,, 

thus leads to a higher value of F(VPD). (The values of T, and e, used in (42) are the values 

from the previous time step, [Tc]o,d and [e,],ld.) This formulation differs slightly from that 

in SiB, which uses a canopy air temperature, T,, rather than the canopy temperature itself 

to compute the saturated vapor pressure. In SiB, T, and T, can differ due to the imposition 

of a subcanopy aerodynamic resistance. This resistance is absent in the Mosaic model. 

When the Mosaic LSM is coupled to the Aries GCM, however, F(VPD) is set to 1, and thus 

no vapor pressure deficit stress is allowed. Sensitivity studies (Koster and Suarez 1994) show 

that when the vapor pressure deficit stress is activated in this coupled system, tohe nearsurface dry bias in the Aries GCM leads to a stress that excessively reduces transpiration. 

This reduction in the near-surface moisture supply reduces the near-surface vapor pressure 

even further, and this leads to an even further increase in the vapor pressure deficit stress. 

This is a positive feedback that can lead to the unrealistic shutdown of transpiration. It 

must therefore be avoided. 

13 
b. Temperature Stress. Stomates are <assumed to limit transpirat,ion when temperatures are 

either too high or too low. The equation used by SiB (Sellers et, al. 1986) to compute F(T), 

which is based on the work of Jarvis (1976). has t,he form: 

where Tl is the lower temperatiire limit, (below which transpiration ceases), Th is the upper 

transpiration limit, and h3 and h3 are themselves complicated functions of To (the optimum temperat,iire). Tc, and Th. The Mosaic LSM uses a polynomial approximation to this 

equation: 

where c1: cg. and cg are vegetation-specific coefficients that produce an approximation to 

the more complicated, and more computationally intensive, SiB equations. [TcIold is used 

in (44). Figure 3 shows how well the approximation works for the six vegetat,ion types 

considered by the Mosaic LSM. 

c. 

potential stress. Following SiB, this stress is modeled as 

Leaf Water Potential Stress. Drier soils limit transpiration through the leaf water 

where $1 is the leaf water potential at which wilting begins and $2 is the leaf water potential 

at which transpiration is shut down completely. 

Equation (45) is difficult to apply directly. however, because $1 is itself a function of the 

transpiration rate. ET: 

$1 = $r - - ET 7 (46) rplant + rsoi~ 

PW 

where Gr is the root-zone moisture potential, 2 is the height of the canopy. rplant is the 

average resistance to moisture transport imposed by the plant, rs0i1 is the average resistance 

imposed by the soil and root system. and pa is the density of water. The calculation of 

F($,I) is therefore based on an estimated transpiration rate. E+. Combining (45) and (46) 

gives: 

0 $1 < $2 

$1 < $1 

(47) 

1 

UI -Y2 $9 $1 < $1 

14 
BROAMEbf SHRUBS DWARF TREES (TUNWA) 

Figure 3: Tenipcrat8urc stmss fiinctions (l/F(T)) from SIB (solid lines) and the Mosaic LSM 

(dashed lines) for six vegetation t,ypcs. 

with E+ dctcrmincd by incorporating (41) and (47) int,o (25) and then rearranging and 

solving the resilltirig equat,ion. 

To derive &. the Mosaic LSM first computes the average degree of saturation in the root 

zone. ,%!*‘r . as: r--rat 

where Wl and Wz are the moisture contents in the top and middle soil layers, respectively, 

and Wl --sat and W2-sat are the maximum possible moisture contents in these soil layers. This 

degree of satmuration is then employed in (120), an equation that relates moisture potential 

to soil moistsure content,: to be discussed later in the context of groundwater diffusion. 

The values of $1. $2. 2. and Tplant are vegetation-specific and constant. Only rsOi1 varies 

with t8he root,-zone moisture state. As in SiB. the Mosaic LSM computes 

where K is t,he average hydraulic conductivity in the root zone: calculated with (48) and 

(121). The coefficient,s ~,1 and r,2 are precomputed with: 

15 
and 

where R is the resistance per unit root length, Dd is the root length density, Zd is the rooting 

depth, and 

fff = - 1 [ V, - 3 - 21n (-)I Vr , 8rDd 1 - v, 

where V, is the volume of root per unit volume of soil. Seasonal variations in V, result from 

seasonal variations in Dd: 

vr = DdAr, (53) 

where A,. is the average cross-sectional area of a root. 

4.3 Resistance for Bare Soil Evaporation 

Bare soil evaporation, Ebs, is assumed to occur in parallel with transpiration and is effectively calculated with: 

where Tbs is the total resistance 

(54) 

to bare soil evaporation, calculated with 

rbs = (rsurf + Tsca).fhurn. (55) 

Here r,,,,f is the resistance provided by the soil, T,,, is the resistance provided by the 

subcanopy air (Le., by the air between the soil surface and the canopy air space), and fhum 

is a humidity factor. 

To calculate r,,,f: the Mosaic LSM iises: 

which is an approximation to an equation used in SiB. Thus, r,,,f increases strongly as the 

top layer’s soil moisture decreases. The calculation of TSca is also an approximation to a 

more complicated SIB function. The Mosaic LSM uses: 

where cSca is a vegetation-specific constant and U2 is the wind speed at the top of the canopy, 

estimated with 

urn z-d U? = -1n (7) , C, ri, 

where Urn is the wind speed provided by the GCM, ti, is 

canopy height. d is the zero plane displacement height, 

the PILPS intercomparison study, c, is calculated with 

In ($) 

c, = 8.4 + 

ri, 

the von Karman constant, 2 is the 

and zo is the roughness length. In 

(59) 

16 
in accordance with calculations in SiB. When the LSM is coiipled to the Aries GCM. a 

slightly different calciilatiori is used: 

111 (e) 

C“ = (60) h: 

The humidity factor. f~,l,l,l. accounts for the subsatiirated relative humidity, h. within the 

soil pores. Rahr t,han following SiB’s approach for calculating this humidity. the Mosaic 

LSM iiscs a conipiitat,ionally simpler formulation: 

2 I*‘ N‘ 1 

w,-:at \vl-:at P 

> 3. 

h={ 1 (61) 

\VI 

M’1 -sat 1 

The Mosaic LSM then computes 

The formulation used for h in the Mosaic LSM is highly arbitrary and is in fact an approximatlion to the SIB formulation for a soil with a high “b’’ parameter (see (120) and 

(121)). For the parameter values currently used to describe soils: h is underestimated, and 

thus rbs is probably overestimated. Given the small importance of bare soil evaporation 

relative to transpiration. and given the untertainties associated with all of the terms in 

(55) through (62) : particularly the meaning of “average soil moisture content” over a large 

area. the overestimation of rbs is not considered an important problem. In fact: given the 

aforementioned uncertaint,ies, an overestimated Tbs allows the Mosaic LSM to “err” on the 

safe side. Le.. to avoid producing too much bare soil evaporation. 

4.4 Canopy Interception and Snow; Effective Surface Resistance 

Like most other SVAT schemes: the Mosaic LSM includes a representation of the canopy 

interception reservoir. During a precipitation event in nature: canopy leaves and ground 

litter c(an “intercept‘: a fraction of the rainwater so that it never reaches the soil surface: 

and t+his intercepted. free-standing water evaporates at the potential rate. Evaporation of 

intercepted water in the model. ,Tint: thus effectively proceeds according to the equation 

where errC is the vapor pressure in the overlying GCM grid box and T, is the aerodynamic 

resistance. Some models. such as SIB (Sellers et al. 1986). also include a special withincanopy aerodynamic resistance in the ,Tint eqixation bo describe the difficulty of transporting 

water vapor from leaf surfaces to the canopy air space. This resist,ance is ignorcd in the 

Mosaic LSM. 

17 
In the Mosaic LSM, (63) applies only to that areal fraction of the canopy interception 

reservoir assumed to be "filled", i.e., at capacity. A corresponding equation is thus needed 

in the remaining area, from which transpiration, ET, and bare soil evaporation, Ebs, are 

assumed to occur in parallel. An effective resistance to their sum, TTbs is computed with 

where rC and Tbs are calculated with (41) and (55), respectively; the Slim ET +Ebs, or ETbs, 

can then be computed with 

The fraction of the land surface tile from which interception loss occurs is assumed to be E, where C is the amount of moisture in the interception reservoir and C, is the maximum 

amount possible. (Thus: at a given point on the surface, the interception reservoir is either 

completely enipt,y or completely full.) Transpiration and bare soil evaporation occur over the 

remaining fraction, 1 - E. For computational convenience, (63) and (65) can be combined 

into a single equation for interception loss, bare soil evaporation, and transpiration: 

where Esllrf is the total evaporation from the land surface (= Eint + ET + Ebs) and ref is an 

effective resistance that, can be used t80 compute this total evaporation. The Mosaic LSM 

comput,es r,fi with: 

C 

1-.z 

'+E r. 

Teff =rTbs c T31bs. 

This is precisely the value of re% that satisfies the equation 

when E,,,,f. Eirlt: and ETbs are determined with (66): (63), and (65). In other words, T,R in 

(66) is the single resistance that produces the correct net evaporation from the tile, given 

that potential evaporation occurs in the wetted part of the canopy and that transpiration 

and bare soil evaporation occur in the dry part of the canopy. The simple form of (66), 

which is consist,ent wit,h the Penman-Monteith evaporation formulation (Monteith 1965) , 

is made possible by t,he use of a single temperature to describe the soil surface, the wetted 

canopy and the dry canopy. 

As indicated in Section 3.2. T,% from (67) is incorporated into (9), the vapor flux equation. 

Equation (9) also makes use of (8): which is an equivalent form of (66). 

When snow is present. t,he different, model versions adjust re% in different ways. In Versions 

1 and 2. the presence of snow automatically leads to a zeroing of T,R: and sublimation of 

snow is the only evaporation considered in the energy balance calculations (see Sect,ion 3.1). 

In Version 3. potential evaporation from snow surfaces is assumed to occur in parallel with 

18 
interception loss, bare soil evaporation, and transpiration. Version 3 actually uses a slightly 

different form of (67): 

1 - fpot 

Teff = TTbs 1 + fpot y 

where fpot is the fraction of the tile experiencing either interception loss or snow sublimation. 

This fraction is estimated with 

C 

c, fpot = 1 - (1 - fsnow)(l- -1, 

where fsnOw is the fraction of the tile assumed to be covered by snow, calculated with 

S 

fsnow = s -k %id 

in accordance with (24). Note that (69) reduces to (67) in the absence of snow. 

In the case of condensation onto the land surface, Le., when [Elold is negative, 

(71) 

Versions 1 

and 2 reset reff to zero. Version 3 does the same, except that a small ramping function 

is used to ensure continuity in ref as [Elold goes from negative to positive. In Version 3, 

for [Elold smaller (more negative) than a critical value Ecrit, reff is set to zero. For [Elold 

negative but higher than Ecrit, Teff is multiplied by the factor 1 - [E]o]d/Ecrit. 

4.5 Derivatives of Effective Surface Resistance 

The terms 

LSM, however, they are calculated with: 

and in (9) could, in principle, be computed analytically. In the Mosaic 

and 

(73) 

areff - 1 

aea €e -_- [Teff ([Tclold, [ealold + €e) - Teff ([Tclold, [ealold)] 7 

where ET and E, are very small increments of [TcIold and [eaIold, respectively. In other 

words, the Mosaic LSM artificially increases [Tc]old and [eaIold, in turn, and recalculates re^ 

in order to determine the tendency terms. It then resets [TcIold and [eaIold back to their 

original values. 

4.6 Linearization of Longwave Radiation 

The terms [R/w]Old and [ g] in (2) are computed with 

old 

19 
and 

[!EL] 

old 

whcre AI, and B1, mc provided by the GCM 

atmosphere and land calculations. (The Aries 

the linearization in (74).) 

= BIW, (75) 

in order to ensure consistency between the 

atmospheric radiation calculations also use 

For the PILPS intercomparison project, AI, and BI, are computed with 

BIw = 4u[Tc]?ld 

and 

Alw = u[~]& - Blw[Tc]old, 

where u is the Stefan-Boltzmann constant. Note that this implies 

4.7 Linearization of Heat Flux to Deep Soil 

The formulation for heat flux to the deep soil is taken from SiB (Sellers et al. 1986) and is 

consistent with the standard force-restore formulation of Deardorff (1978). The force-restore 

equation can be written as 

dc dT, wdc - -- = G + -(T - TS), 

Jz dt Jz (79) 

where d is the depth over which a diurnal temperature wave is felt, c is the volumetric 

heat capacity, T, is the surface temperature, G is the imposed surface heating, w is the 

frequency of the diurnal temperature cycle, and T is the temperature below the surface that 

is unaffected by the diurnal temperature cycle. The term $(T - T,) can be considered 

the heat flux to or from the deep soil. 

Following this model, the Mosaic LSM computes [Go],ld and in (6) as 

and 

These values are used in (5) to calculate Go, for use in (21). 

For CH-~~~: the deep soil heat capacity, we infer from the equations in Deardorff (1978) 

that 

= 2m, C"-deep 

CH 

a ratio that is related to the ratio of the depths of the diurnal and annual temperature waves. 

This is in one sense a loose interpretation of the Deardorff formulation, since Deardorff forced 

the deep soil temperature with surface heating (G in (79)) rather than with Go. 

20 
5 Water Balance: Solution Procedure 

Each of the five moisture reservoirs within a land surface tile in the Mosaic LSM requires a 

water balance equation: 

a. Canopy interception reservoir. 

[c]new = [Clold + (P + Smelt - Eint - &')At: 

where 

C = moisture in the canopy interception reservoir, 

P = rainfall rate: 

Smelt = snowmelt rate, 

Eint = evaporation from interception reservoir: 

PT = throughfall rate. 

At = time step duration, 

b. Top soil layer. 

[W~Inew = [WI]OI~ + (PT - Rs - Ebs - Etranspl - Q12)At: 

where 

W1 = moisture in the top soil layer: 

R, = surface runoff rate, 

Ebs = evaporation from bare soil: 

Etranspl = water removal via transpiration from top soil layer, 

Q12 = moisture flux from top soil layer to middle soil layer. 

c. Middle soil layer. 

[w2Inew = [w2]01d + (-Etransp2 + Q12 - Q23)At: 

where 

Wp = moisture in the middle soil layer, 

Etransp2 = water removal via transpiration from middle soil layer, 

Q23 = moisture flux from middle soil layer to bottom soil layer. 

d. Bottom soil layer. 

[W3]new = [W3]old + (Q23 - Q303)At 

where 

W3 = moisture in the bottom soil layer, 

Q3= = rate of moisture drainage out of the bottom soil layer. 

(84) 

21 
where 

S = water equivalent in the snowpack, 

Ps = snowfall rate, 

Srrlelt = rate of snowmelt, and 

E,,,, = snow sublimation rate. 

Unlike t+he energy balance equations, the water balance equations are not solved implicitly. 

The individual terms in these equations are discussed in the next section. 

6 Water Balance: Components 

The water balance equations, (83) through (87), contain only two terms that are provided 

by the GCM, namely the precipitation rate, P, and the snowfall rate, Ps. The remaining 

terms are either prognostic variables or moisture fluxes internal to the land surface tile. 

The present section describes how these moisture fluxes are computed. The calculation 

of the throughfall rate, PT, is presented in Section 6.1, along with some discussion on 

the difficulties of modeling canopy interception in a GCM. Surface runoff, R,, is discussed 

in Section 6.2, and the division of the total evaporation into its component parts (Eint, 

Etrarlspl, Etransp2, Eb,, and E,,,,) is discussed in Section 6.3. Sections 6.4 and 6.5 describe 

groundwater diffusion between the soil layers (Q12 and Q23) and drainage out of the soil 

column (Q3m), respectively. The snowmelt term, Smelt, isdiscussed in Section 6.6. 

6.1 Canopy Interception Reservoir 

Two different parameterizations of canopy interception have been used in the Mosaic LSM. 

That in Version 1 was replaced by an improved parameterization (in Versions 2 and 3) that 

produces more accurate estimates of interception loss on the global scale. This improvement 

was deemed necessary given the strong contribution of interception loss to total evaporation 

in the real world (Shuttleworth 1988, Gash et al. 1980) and the importance of interception loss in defining GCM climatology (Koster and Suarez 1994, Scott et al. 1995). The 

two parameterizations of interception differ only in the way the reservoir is loaded during 

precipitation events. 

6.1.1 Interception Reservoir Capacity 

The interception reservoir capacity, in units of 3, is set equal to 0.1L1, where Lt is the 

leaf area index of the vegetation type being modeled. The capacity thus varies with vegetation type and season. Bare soil and desert soil are assumed to have no interception 

reservoir. Also, the interception associated with ground litter below a vegetation canopy is 

not modeled explicitly. 

22 
The factor 0.1 is arbitrary but consistent with that used in other LSMs, such as the SiB 

model of Sellers et al. (1986). In fact, the PILPS intercomparison project (Henderson-Sellers 

et al. 1993) required land surface modelers to set their interception reservoir capacities to 

0.1Li. 

6.1.2 Precipitation Loading 

a. Parameterization Issues. Given a rainwater mass generated by the GCM, an LSM’s first 

job is to determine how much of the rainwater should be added to the interception reservoir. 

Parameterizing this precipitation loading is difficult because rainfall is rarely uniform over 

a modeled land surface area. The calculated loading reflects assumptions made about the 

fractional area coverage, f, of the precipitation, as illustrated in Figure 4. The figure shows 

a simple model in which precipitation is uniform over the prescribed fraction f and is zero 

elsewhere. The part of the local precipitation depth that exceeds the local available capacity 

is assumed to be throughfall, the rainwater that falls through the canopy leaves to the soil 

surface. Smaller values off lead to smaller amounts of intercepted water. 

The assumed fractional coverage, f, for a precipitation volume ... 

f4.5 

f-l 0 

... helps determine the interception reservoir loading and the 

canopy throughfall. 

Figure 4: Demonstration of how differences in assumed fractional area coverage of storms 

can affect the loading of the interception reservoir. 

The interception formulations in SiB (Sato et al. 1989; see Appendix C) and some other 

models use an exponential function rather than an assigned fraction f to describe the 

subgrid distribution of precipitation. Even so, the same general concepts apply; assuming 

a steeper exponential function will produce a smaller amount of intercepted water. 

While most operational LSMs attempt to characterize the fraction of storm area in a re23 
alistic way, very few address the compounding problem of temporal correlation, which is 

potentially as important but more subtle and difficult. The problem stems from the fact 

that a simulated storm can span several GCM time steps. Figure 5, for example, shows a 

storm filling a fraction f of the interception reservoir during time step i. In the next time 

step, the GCM produces more rainfall, again over the fraction f. The figure shows that 

the amount of intercepted water calculated during this later time step relies heavily on how 

(and if) the model redistributes the intercepted moisture from the previous time step. The 

right side of Figure 5 shows some accounting for memory (temporal correlation) in storm 

position, whereas the left side does not. The right side clearly produces less interception. 

U 

+rsI 

Figure 5: Demonstration that the neglect of temporal correlation in storm position can lead 

to higher interception storage. 

Because typical GCM time steps range from minutes to an hour, and because storms in 

nature can last much much longer than this, accounting for temporal correlation in storm 

position is arguably more realistic. If these temporal correlations are ignored, an LSM's 

behavior can vary with time step length. This is a property to avoid. 

In Version 1 of the Mosaic LSM, temporal correlation in storm position is ignored, though 

not precisely in the way illustrated in Figure 5. Version 2 attempts to account for this 

correlation with a very simple approximation. 

b. Version 1: Uncorrelated Placement of Storms. The Mosaic LSM assumes that precipitation water falls uniformly over a fraction f of the tile, as in Figure 6. The fraction 1 - f is 

not wetted at all, and the precipitation intensity over the fraction f is increased by a factor 

24 
l/f. In Version 1. f is set to 0.3 for both moist convective precipitation and large scale 

condensat,ion. 

As discussed in Section 4.4: the Mosaic LSM assumes that the interception reservoir is filled 

in an areal fraction of the tile and dry in the areal fraction 1 - E. Precipitation, P, is 

assumed to fall on t,he independent areal fraction f. As shown in Figure 6: this leads to four 

sub-tile regions. In Region 1, the rain falls on wet leaves and thus immediately falls through 

the canopy to the soil surface. In Region 3, the rain falls on a dry part of the canopy; the 

rainwater is added to this part of the interception reservoir until it fills, and the excess water 

is considered throughfall. Interception calculations are not necessary over Regions 2 and 4. 

The algorithm supplies a net throughfall and a net increase in canopy interception storage 

only; the specific moisture state of Region 3: for example: is not remembered between time 

steps. 

Ew Rain 

Wet canopy 

Figurc 6: Areal fractions of thc tile considered when computing interception of rainwater 

with Version 1. 

In equation form: Pat: the precipitation mass (for a tile of unit area): is separated into: 

and 

C 

cs 

Pwet = P-At, 

where I'dry and P,vet are the precipitation masses that fall on the dry and wet leaves: 

respectively. The maximum amount of rainwater, Cadd : that can be added to the dry leaves 

25 
in Region 3 is 

Caaa = f(C3 - C). 

The total intercepted moisture is therefore iipdated wit,li: 

The throughfall ~nass~ PTA~. is then calciilated with 

c. Versions 2 and 3: Temporal Correlation in Sto,rm, Positaon. The sirniilatcd cvaporation from the intmwption reservoir in Version 1. particiilarly in the tropics. was foiind to 

be excessive rclat,ivc to both the carcfiil point nic~~iirc~nc~it~ of Shiittlcwort~h ( 1988) and 

the global-scale cst,irnat,es generated by Yale Mint,x and Greg Walker (G. Walker. personal 

commiinication: see Listmi et, al. (1993) for a disciission of the cst,imat,iori proccdiirc). Interception loss is overestimated partly bccaiisc Version 1 neglects time correlation in storm 

position. To address this problem. Mosaic LSM Versions 2 aid 3 iisc a simple approximation to time correlation in which part, of each time step's rainfall is assiimed to fall ont,o 

leaves previoiisly wctt,cd by the storm. 

In the algorithm: a valiic is assigned to rsl,,,,,, an arbitrary time scale for storm position 

that must. eqiial or exceed At. the time stq lengt,li. Also: tohe precipitation falling during a 

time step is asslimed to cover an areal fraction f of the land surface. The precipitation mass 

the rain Inass falls onto leaves prcvioiisly wcttcd by the storm, as denoted by Region 2 in 

Figiirc 7. This rainwater drips throiigh the canopy to the soil siirface; it docs not add t,o 

the interception reservoir's moistiirc. Thc rcrnairidcr of t8hc rainwater falls randomly onto 

the canopy. part of which is wet (Region 1) and part, of which is dry (Region 4). Notice 

that Regions 1. 2. and 4 t,ogethcr cover t,lic fract#ion .f of the land surface. Also notice that 

if At = rslorlrl. the area of Region 2 is zero? and all of the rainfall is assigned randomly to 

the canopy -~ 

is then partit,ioned into t8hrce part,s, as indicated in Figiire 7. A large fraction, 1 - -, . of 

no t,crnporal memory is imposed. 

The precipitation mass. PAt. is thus partit8ioned irit,o three components: the portion falling 

on the wet Region 2. 

?' = yPAt, (93) 

the portion falling 011 the wet Region 1: 

C 

cs 

PI = (1 - y)P-At. 

and the port,ion falling oil t-ho dry region 4. 

where y is calciilated wit,h: 

(94) 

26 
5 I-UC, 

Kq Rain 

Wet canopy 

Figure 7: Areal fractions of the tile considered whcn computing interception of rainwater 

with Version 2. 

Because At does not exceed T~~~,.~~. y cannot be negative. Moisture is added to the interception reservoir only in Region 4. which has an available water capacity of 

Cadcl = (1 - r)f(Cs - c>. (97) 

The interception storage is updated using (91); with Pclry replaced with P4 ~ and throughfall 

is computed with (92). 

These equations are adjusted when necessary to ensure that. iinrcalistic amounts of water do 

not fall through the canopy at the onset of storms, whcn the canopy is dry. If the fraction of 

wetted canopy, 8; is less than the assumed storm fraction: f. then y is recalculated with: 

This parameterization differentiates between convective storms: for which f is set to 0.2, 

and large scale condensation events. for which f is set to 1. The value of Tstornl is arbitrarily 

set to 1 hour. 

6.2 Surface Runoff and Infiltration 

Infiltration of throughfall into the soil is computed in Iniich the same way as throughfall 

itself is computed in Version 1. 

27 
a. Versio.ns 1 and 2. The soil in the areal fraction Ivl-t,,t ’*’ of the tile is assumed to be 

sat,iiratcd. where Wl is t8hc nioist,iire cont,ent. of the top soil layer and W1-sat is the storage 

capacit,y of t,hat layer. is thus assumed to be dry. 

Throiighfall falling ont80 the saturat,ed area is immediately converted int,o surface riinoff 

(overland flow). and throughfall falling on the dry fract,ion must fill the local portion of the 

‘I 

Ivl--sat The remaining fraction. 1 - 

t,op soil layer before it can 

throiighfall mass falling on 

Given that the throughfall 

generate surface riinoff. Thus. in analogy with (88) - (92). the 

the dry fraction. PT-~I~~. is 

covers an areal fraction f of the square: the maximum amount. 

of water that can be added to the soil layer. W1-atltl. is 

The tot,al soil moistiirc in the top layer is therefore updated with: 

and the total surface runoff niass. RsAt: is 

The areal fraction of storm coverage, f’ is assumed to be the same as that used in the 

canopy interception loading algorithm. Again: Versions 1 and 2 assume different fractions 

(see Section 6.1). 

b. Version 3. The formulation of surface runoff in Version 3 is very similar to that in 

Versions 1 and 2. the only difference being in the assumed saturated fraction of the tile. 

The tile is divided into two sub-areas. one that is fully saturated and the other containing a 

degree of saturation, W1 -Ey/W1-sat: that is in equilibrium with that in the middle soil layer, 

so that neither upward nor downward moisture diffusion occurs. This formulation is more 

consistent with that, iised for groundwater diffusion; the definition of Wl-ey is discussed in 

more detail in Section 6.4. and the areal partitioning of the tile is identical to that shown 

in Figure 8. 

Given the degrees of ~at~iiration in the two sub-areas and the fact that the total amount of 

water is W1. the saturated fraction. fsat. can be computed with 

Thiis. if the soil is dry cnoiigh. t,hc “satnrat,cd fraction” is zero. The t,hroughfall niass falling 

on the dry fraction is then 

PT-~~,.~ = p~ (1 - fsat) At. (104) 

28 
and the maximum amount of water that can be added to the soil layer is 

Equations (101) and (102) are then used to update the soil moisture and compute the 

surface runoff. As in Version 2, different values of f are used for moist convection and 

large-scale condensation. 

6.3 Evaporation Sink 

Evaporation water is drawn from four possible reservoirs: the snowpack, the canopy interception reservoir: and the upper two soil layers. In Versions 1 and 2, the presence of snow 

implies that all evaporation is snow sublimation. In Version 3, all reservoirs can be tapped 

simultaneously. 

a. Versions 1 and 2. When snow is absent, evaporation extracts water from the intercetion 

reservoir and soil layers using 

where ETbs is equal to ET + the sum of transpiration and bare soil evaporation. This 

breakdown is consistent with the assumptions behind (68). The Mosaic LSM subsequently 

separates ETbs with: 

and 

(109) 

Tbs 

rbs -k Tc 

ET = ETbs 

The moisture associated with Ebs is taken from the top soil layer, whereas that associated 

with ET is taken from the upper two layers: 

and 

When evaporation is negative, i.e. when dewfall occurs, it is added uniformly to the interception reservoir. (Snowmelt water is added at the same time.) Any excess water above the 

interception reservoir’s capacity falls uniformly onto the ground surface. Subsequently, the 

top soil layer is checked for saturation. and any excess water is converted to surface runoff. 
When snow is present, only the snow variable is updated: 

Negative evaporation adds to the snowpack. 

An error in the computer code used for Versions 1 and 2 led to the substitution of r,ff for 

rTbs in (106). Offline integrations with the land surface code (using the PILPS forcing data 

sets) indicate that this error has a negligible effect (less than 0.5%) on the annual energy 

and water balances. 

b. Version 3. Under the assumption that snow sublimation and interception loss both 

proceed at the potential rate and occur in parallel, the sum Esnow + Eint, or Epot, can be 

calculated, in analogy with (106), as: 

ra + rTbs 

ra + fpotrTbs , Efpot 

where fpot is the areal fraction of the tile undergoing potential evaporation, calculated with 

(70). The ratio of snow sublimation to total evaporation, f~-~~~~, in Version 3 is then 

computed with 

Epot fsnow 

fE-snow = - 

E fsnow + 8 

where fsnow is the areal fraction of snow cover (from (71)) and 

wetted interception reservoir. Snow sublimation is then calculated with 

is the areal fraction of 

allowing the calculation of interception loss as 

The sum of bare soil evaporation and transpiration is computed with 

and (108) through (111) are used to update the soil moisture prognostic variables. 

6.4 Groundwater Diffusion 

Groundwater diffusion between soil layers is computed using a bulk form of the Richards 

equation. The downward flow between the middle and bottom soil layers, Q23, is assumed 

to be proportional to a difference in potential, h: 
where pW is the density of water. K is the hydraulic conductivity in the upstream layer (i.e.. 

in the middle laycr if h2 > h3), and A223 is the distance between the centers of the soil 

layers. The hydraulic head. hi, is the sum of a pressure term and an elevation term: 

hi = $i + z2, (119) 

where zi is the elevation of the center of layer i relative to some arbitrary baseline and $i 

is the pressure head (soil moisture potential) in layer i. 

Both $j and Ki in layer i are assumed to vary strongly with the degree of saturation in the 

soil layer. Following Clapp and Hornberger (1978); the Mosaic LSM computes 

and 

w, -b 

$i = 4s (-) Wi-sat 

Wi 2b+3 

Ki = K, (-) 

Wi-sat , 

where $, and K, are the pressure head and hydraulic conductivity, respectively, of a saturated soil, and h is a soil parameter related to the pore size distribution index. The values 

for these parameters (see Table 3) are taken from Rawls et al. (1982). 

Some subgrid variability is accounted for in the calculation of moisture diffusion between 

the top and middle soil layers. For this calculation, the Mosaic LSM first computes WI-~~, 

the water content that the top layer would need in order to have the same hydraulic head 

as the middle layer: 

If W1 > W1-eq, downward flow between the top and middle layers is indicated, and the 

moisture in the top layer is redistributed into two subregions: one for which hydraulic head 

is identical to that in the second layer, so that no flow occurs, and a fully saturated region 

with significant downward flow. This is illustrated in Figure 8. The fractional area over 

which the downward flux occurs, fQ-down, is 

which is equivalent to fsat in (103). The downward flux itself is computed with 

where hl-,at is the hydraulic head of the saturated portion of the top layer. 

If. however, W1 < Wl-eq, upward flow is indicated, and the Mosaic LSM computes 

31 
downward flow 

- Redistribute 

top layer’s 

soil moisture 1 so that downward 

diffusion occurs 

over subgrid 

fraction 

Figure 8: Siibgrid distribiition of soil moistiire assumed for diffiisiori between top two soil 

layers. 

in analogy with ( 118). 

Limitations on Q12 and Q23 go beyond simple checks on wahr availability in the iipst,ream 

layer and storage availabilit,y in the downstre(am layer. To avoid stability problems: the 

absoliite valiie of the flow voliime. IQlrAtl. is forced to remain at or below AW: where 

1 

2 AW = -1W1 - W1-eq(. (126) 

This prevents a large flow volume that would lead to a reversed flow direction in the following 

time step. A similm limitation is placed on IQ23Atl: W2--ec, is computed in analogy to WI-~~,: 

and IQ23Atl is forced to lie at or below kIW2 - - W2-eql. Both Ql? and Q23 me set t,o zero 

if the surface temperatiire. T,. lies at or below the freezing point. 

6.5 Percolation to the Water Table 

Percolation of water oiit t8he bottom of the lowest soil layer. Qsm: is also computed with 

a biilk form of the Richards equation. The vertical gradient of pressure head, however, 

is assumed to be zero: only gravitational drainage operates. Furthermore. the presence of 

bedrock is allowed to reduce t8he flow. The Mosaic LSM computes: 

32 
where cos(0) is the cosine of the bedrock angle. If the bedrock is assumed to be far below 

the lowest soil layer. cos(0) is set to 1. 

6.6 Snow Budget 

The melting of snow as part of the surface energy balance is treated above in Section 3.4. If, 

howcvcr: the surface temperature already exceeds OC when the snow fulls, the snow melts 

immediately and the ground cools accordingly: 

and 

Snowmelt thus proceeds until all snow is depleted or until the ground temperature is reduced 

to OC, whichever comes first. The melted snow is added to any rain falling during the time 

step before the calculation of canopy interception. 

If snow is present when rain falls on the surface: tho rain water does not “freeze” onto 

the snow. The snowpack is simply ignored while the rain water is partitioned into canopy 

interception, infiltration, and surface runoff. 

7 Connection to the GCM 

Sections 2 through 6 of this report describe the Mosaic LSM’s calculations within a single 

land surface tile. The present section describes how the Mosaic LSM, as currently coded, 

can be connected to a GCM or an offline driver. 

The “TILE“ subroutine performs the Mosaic LSM calculations simultaneously for any chosen number: NCH, of land surface tiles. (The calculations performed for one tile, of course, 

do not affect those performed for another.) The subroutine requires several arrays of dimension NCH as input and produces several arrays of dimension NCH i~s output, with the 

nth element in each array corresponding to the nth tile considered. The input arrays hold 

the forcing variables, certain vegetation par[ameters: and the states of the prognostic variables (which will be updated within t,he subroutinc). The output [arrays hold the diagnostic 

quantities. Sections 7.1 through 7.3 describe the inputs and outputs of the subroutine in 

detail. 

The geographical locations of the tiles examined in a single call to TILE are not constrained. 

The tiles need not: for example: reside within the same grid square; all that is required is a 

means of mapping tile quantities and GCM forcing variables into consistent, one-dimensional 

arrays. An example of such a mapping is illustrated in Figure 9. In the example. a different 

33 
leaf area index (LAI) is assigned to each tile. but precipitation is computed in the GCM on a 

grid square basis. Thus. some rcpitition of precipitation data is required in t8he constructmion 

of thc onc-dimcnsional array of precipitation forcing. 

OVERLYING 

GRID BOX A 

Precipitation = P 

tile I tile 2 tile 3 1 w=L] 1 L2 IL3 1 

GRID SQUARE A 

OVERLYING OVERLYING 

GRID BOX B GRIDBOXC 

Precipitation = P B Precipitation = P C 

I 

GRID SQUARE B GRID SQUARE C 

PRECIPITATIONARRAY: PA, PA, PA, PB, PB, Pc , Pc, Pc , ... 

LA1 ARRAY: L,’ L2, Lj, L4, L5) L6, L,. Lg, ... 

Figure 9: Example of the construction of input arrays for the TILE subroutice. 

The subroutine contains no common blocks. It satisfies the conditions for plug-compatibility 

described by Kalnay et al. (1980). 

7.1 Version 1 

Version 1 of the Mosaic LSM requires the following inputs (listed by their FORTRAN 

names) from the GCM at every time step. All quantities are in MKS units. Some of the 

equations requiring these quantities are indicated in brackets. 

All quantities (except for NCH: the number of tiles: and DTSTEP: the time step length) 

are arrays of dimension NCH. 

NCH : The number of t8iles processed during the current call 

(dimensionless) 

DTSTEP : The length of the time step, in seconds. (s) [At in 

ITYP : The surface “type“: where 

1 = Broadleaf evergreen trees. 

2 = Broadleaf deciduous taws. 

to the TILE subroutine. 

34 
3 = Needle-leaf trees. 

4 = Grassland (ground-cover) . 

5 = Broadleafshrubs. 

6 = Dwarf trees (tundra). 

7 = Bare soil. 

8 = Desert soil. 

TRAIN : The rainfall rate (&). [P in (88), (89)l 

TSNOW : The snowfall rate (&). [Ps in (87)] 

UM : The wind speed in the overlying GCM grid box (y). [U, in (58)] 

ETURB : Evaporation rate computed by the GCM using previous time step’s T, and e, (5). [This is immediately divided by X to produce [,!?]old in (4).] 

DEDQA : Derivative of evaporation rate with respect to specific humidity, computed 

by the GCM using the previous time step’s T, and e,. (5) [This is immediately 

multiplied by e/(psX) to convert it to [E],,, in (41, (9~ 

DEDTC : Derivative of evaporation rate with respect to surface temperature, computed 

by the GCM using the previous time step’s T, and e,. (-&) [This is immediately 

divided by A to convert it to in (4), (9).] [ Tc]old 

HSTURB : Sensible heat flux computed by the GCM using the previous time step’s T, 

and ea* ($1- [[H],ld in (3)] 

DHSDQA : Derivative of sensible heat flux with respect to specific humidity, computed 

by the GCM using the previous time step’s T, and e,. (5) [This is immediately 

multiplied by e/ps to convert it to [E],,, in (3).] 

by the GCM using the previous time step’s T, and e,. (&) [[E] old in (3)] 

Mosaic LSM.] 

DHSDTC : Derivative of sensible heat flux with respect to surface temperature, computed 

TM : The temperature in the overlying GCM grid box. (K) [Not currently used in the 

QM : The specific humidity in the overlying GCM grid box. This is immediately multiplied 

by pale to produce e,, the vapor pressure in the overlying grid box. (dimensionless) 

[Used for certain modifications to energy balance calculations] 

CD : Drag coefficient. Its inverse is immediately divided by U, to produce the aerodynamic resistance: T,. (dimensionless) [ (67)] 

SUNANG : The cosine of the solar zenith angle. (dimensionless) [p in (26)] 

PARDIR : The direct component of the photosynthetically active radiation. (5) [Used 

to compute fdir in (30)] 

35 
PARDIF : The diffuse component of the photosynthetically active radiation. (5) [Used 

to compute fdjr in (30)] 

SWNET : The net solar radiation absorbed by the surface. This is in fact computed 

with (22). It appears in TILE’S argument list because up to now, calls to the albedo 

subroutine have taken place outside the calls to the main TILE subroutine. (5) 

[&w--net in @)I 

HLWDWN : The downwelling longwave radiation flux. (5) [RiW in (6)] 

PSUR : Surface pressure, p,. (mb) [Used to compute air density via perfect gas law and 

to convert specific humidities into vapor pressures.] 

ZLAI : Leaf area index. (dimensionless) [Lt in (26)] 

GREEN : Greenness fraction. (dimensionless) [fg in (40)] 

22 : Height of canopy leaves. (m) [Z in (46)] 

SQSCAT : JG, where w is the scattering coefficient. (dimensionless) [(36), (37)] 

RSOIL1 : The ratio &-, where R is the resistance per unit root length, Dd is the root 

RSOIL2 : The ratio 2, where zd is the rooting depth and a~f is defined by (52). (dimendensity, and zd is the rooting depth. (2) [T,I in [(49)] 

sionless) [T,* in (49)] 

RDC : Term used to compute subcanopy aerodynamic resistance. (dimensionless) in 

(5711 

U2FAC : The combination &ln (y), where K. is the von Karman constant, 2 is the 

canopy height, d is the zero plane displacement height, z, is the roughness length, and 

c, is calculated with (59) or (60). (dimensionless) [(58)] 

QSATTC : The saturated specific humidity at the previous time step’s value of T,. This 

is immediately multiplied by pS/e to produce the corresponding saturated vapor pressure, e, (T,) . (dimensionless) [ (8)] 

DQSDTC : The derivative of the saturated specific humidity with respect to temperature, 

evaluated at the previous time step’s value of T,. This is immediately multiplied by 

p,/e to produce the corresponding derivative of saturated vapor pressure with respect 

to temperature, %. (K-l) [(9)] 

ALWRAD : First term in the longwave radiation linearization. (5) [Ai, in (74)] 

BLWRAD : Second term in the longwave radiation linearization. (5) [B,, in (74)] 

The Mosaic LSM uses these inputs to update eight prognostic variables: 

36 
TC : T,, the surface and canopy temperature. (K) 

TD : Td, the deep soil temperature. (K) 

&A : The specific humidity in the canopy air, computed by multiplying the vapor pressure 

in the canopy air. e,: by e/ps. (dimensionless) 

SWETl : The degree of saturation in the top soil layer, equal to Wl/Wl-sat. (dimensionless) 

SWETZ : The degree of saturation in the middle soil layer, equal to W2/W2-sat0 (d' imensionless) 

SWET3 : The degree of saturation in the bottom soil layer, equal to WS/W~-~~~. (dimensionless) 

CAPAC : C: the amount of water contained in the canopy interception reservoir. (3) 

SNOW : S, the amount of snow water equivalent present. (3) 

Version 1 of the Mosaic LSM also produces several model diagnostics: 

EVAP : The evaporation rate in 5, calculated by multiplying E by A, or A,, depending 

on the absence or presence of snow. 

SHFLUX : H: the sensible heat flux. (3) 

RUNOFF : The total runoff generated (sum of R, and Q300). (&) 

BOMB : Debugging diagnostic. (Not currently used.) 

EINT : The interception loss in 5, calculated by multiplying Eint by A,. 

ESOI : The evaporation :ste from bare soil in 5, calculated by multiplying Ebs by A,. 

EVEG : The transpiration rate in 5, calculated by multiplying ET by A,. 

ESNO : The evaporation rate from snowpack in 3, calculated by multiplying Esnow by 

As. 

STRDGl : Special diagnostic. (Not currently used.) 

STRDGZ : Special diagnostic. (Not currently used.) 

STRDG3 : Special diagnostic. (Not currently used.) 

STRDG4 : Special diagnostic. (Not currently used.) 

37 
7.2 Version 2 

Version 2 of the Mosaic LSM has the same inputs and outputs as Version 1 except for the 

TRAIN input variable: which is separated for Version 2 into two input variables: 

TRAINC : The convective rainfall rate (&). [P in (93). (94), (95); interception and 

surface runoff algorithms are pcrfor~iied separately for moist convective and large-scale 

precipitation] 

TRAINL : ~11e large-sca~e rainfall rate (&). [P in (93). (94). (95): interceptmion and 

surface runoff algoritlinis are performed separately for moist convective and largescale precipitation] 

7.3 Version 3 

Version 3 has the same inputs and outputs as Version 2 except for the modificat,ion of 

the definitions of certain inputs and the addit.ion of several diagnostic oiitputs. The newly 

defined inputs are: 

ETURB : Evaporat,ion rate computed by the GCM iising previous time step's T, and e,, 

now provided in &. 

DEDQA : Derivative of evaporation rate wit,li respect, to specific humidity, computed by 

the GCM iising the previous t,inie step's T,. and e, and now provided in -&. This is 

inmediately miltiplied by c/ps to produce DE 

[KI,,a. 

DEDTC : Derivative of evaporat,ion ratme with respect to surface temperature, computed 

by t,he GCM iising the previous time step's T, and e, and now provided in A. 

The new diagnostic outputs are: 

SMELT : Smelt. t,he rate of snowmelt. (-&I 

HLATN : X,E,,,, + X,(Ei,t + ET + Ebs). the latent, heat flux. (5) 

HLWUP : R/\\. t8he oiit,going longwave radiation flux. (5) 

GDRAIN : Q23. the diffusion of moisture across the bottom of the root zone (middle soil 

layer). (&) 

RUNSRF : R,. the overland flow. (&) 

FWSOIL : Pr - R,. t,he infiltration of rainwat,er into the top soil layer. (&) 

38 
Appendix 1: List of Symbols 

Alw 

A, 

a 

BIW 

b 

b 

c 

Cadd 

CH 

CS 

CH-deep 

C 

C 

Csca 

CU 

C1 

c2 

c3 

Dd 

d 

d 

d 

dVPD 

E 

Ebs 

EH 

Eint 

Epot 

Esurf 

Esnow 

ET 

ETbs 

Etranspl 

Etransp2 

ea 

Coefficient used in the linearization of outgoing longwave radiation. (kg s-~) 

Average cross-sectional area of a root. (m2) 

Stomatal resistance parameter. (kg n~-ls-~) 

Coefficient used in the linearization of outgoing longwave radiation. (kg s-~K-') 

Stomatal resistance parameter. (Icg s-~) 

Soil parameter related to pore size distribution index. (dimensionless) 

Amount of moisture in the canopy interception reservoir. (kg 

Amount of precipitation water that can be added to the interception 

Heat capacity associated with the surface/canopy system. (kg s-~K-') 

Maximum amount of water that can be stored in the canopy interception 

Heat capacity associated with deep soil. (kg s-~K-') 

Stomatal resistance parameter. (m-ls) 

Volumetric heat capacity of soil, for use in force-restore formulation. (kg n~-'s-~K-') 

Vegetation specific constant used to determine subcanopy aerodynamic 

Wind profile parameter. (dimensionless) 

Coefficient in temperature stress equation. (K-~) 

Coefficient in temperature stress equation. (K-~) 

Coefficient in temperature stress equation. (K-~) 

Root length density. (rn-2) 

Stomatal resistance term. (dimensionless) 

Zero plane displacement height. (m) 

Depth over which diurnal wave is felt in force-restore formulation. (m) 

Parameter controlling vapor pressure deficit stress. (mb-l) 

Evaporation rate. (kg WZ-~S-') 

Evaporation rate from bare soil. (Icg m-*s-') 

Harmonic mean of Esurf and the evaporation flux between the canopy air 

Evaporation rate from the interception reservoir. (kg ~I-~s-') 

Sum of the evaporation rates from the interception reservoir and 

Evaporation rate from the ground and canopy surfaces into the canopy 

Evaporation rate from the snowpack. (kg rn-*s-l> 

Transpiration rate. (kg m-*~-~) 

Sum of transpiration and bare soil evaporation. (kg m-'s-') 

Water removal via transpiration from top soil layer. (kg WL-~S-') 

Water removal via transpiration from middle soil layer. (kg ~z-~s-') 

Vapor pressure in the canopy air. (mb) 

reservoir during a time step. (kg m-2) 

reservoir. (~cg m-2) 

resistance. (dimensionless) 

and the atmosphere, calculated using old values of T, and ea. (kg m-2s-1 ) 

the snowpack. (kg m-2s-1) 

air. (kg rn-2s-1) 

39 
F(VPD) 

Fo 

f 

fdir 

f E-snow 

fhum 

fs 

fpot 

fQ-down 

fsat 

H 

h 

hi 

hl-sat 

K 

Ki 

Ks 

k 

kdiffuse 

kdirect 

Lt 

lrt -dead 

lrt-live 

Vapor pressure in the air overlying the canopy (e.g., in the lowest GCM 

Saturated vapor pressure. (mb) 

Factor by which canopy resistance increases due to temperature 

stress. (dimensionless) 

Factor by which canopy resistance increases due to vapor 

pressure deficit stress. (dimensionless) 

Factor by which canopy resistance increases due to leaf water 

potential stress. (dimensionless) 

Flux of photosynthetically active radiation, or PAR. (kg s-~) 

Fractional coverage of precipitation. (dimensionless) 

Ratio of direct solar radiation to total solar radiation. (dimensionless) 

Ratio of the snow sublimation mass flux to the total evaporation mas 

Relative humidity factor that increases resistance to bare soil evaporation. 

Fraction of leaves that are green. (dimensionless) 

Areal fraction of the tile experiencing interception loss or snow sublimation. 

Areal fraction of the tile over which downward moisture diffusion occurs 

Areal fraction of the tile in which the top soil layer is saturated. 

Areal fraction of the tile covered by snow. (dimensionless) 

Heat flux to the deep soil. (kg s-~) 

Relative projected area of leaf elements in the direction of the solar zenith 

Sensible heat flux into the atmosphere. (kg s-~) 

Relative humidity in the soil pores. (dimensionless) 

Hydraulic head in layer i. (m) 

Hydraulic head of the saturated portion of the top soil layer. (m) 

Hydraulic conductivity of the soil. (ms-l) 

Hydraulic conductivity of soil layer i. (ms-l) 

Hydraulic conductivity of the soil at saturation. (ms-' ) 

Extinction coefficient. (dimensionless) 

Extinction coefficient for diffuse radiation. (dimensionless) 

Extinction coefficient for direct radiation. (dimensionless) 

Leaf area index. (dimensionless) 

Sum of leaf-element reflectance and leaf-element transmittance for dead 

Sum of leaf-element reflectance and leaf-element transmittance for green 

layer). (mb) 

flux. (dimensionless) 

(dimensionless) 

(dimensionless) 

between top and middle soil layers. (dimensionless) 

(dimensionless) 

angle. (dimensionless) 

leaves. (dimensionless) 

leaves. (dimensionless) 

40 
P 

PS 

pr 

&-dry 

Pwet 

9 

Q12 

Pdry 

PS 

Q23 

Q3oc 

R 

R, 

&w-net 

Rni-dif 

Rni-dir 

Rv-dif 

Rv-dir 

ra 

fbs 

TC 

rc-unstressed 

fc-unstressed,green 

Teff 

TpIant 

rsca 

rsoiI 

S 

Rainfall rate. (kg m-2s-1) 

Rainfall mass falling onto the dry fraction of the canopy. (kg m-2) 

Snowfall rate. (kg m-2s-1) 

Rate of rain throughfall from the canopy leaves to the soil surface. (kg m-2s-') 

Throughfall mass falling onto dry soil. (kg m-2) 

Rainfall mass falling onto the wet fraction of the canopy. (kg m-2) 

Rainfall rate onto region i. (kg m-2s-1) 

Surface pressure. (mb) 

Moisture diffusion flux from top soil layer to middle soil 

layer. (kg m-2s-1) 

Moisture diffusion flux from middle soil layer to lowest soil 

layer. (kg m-2s-1) 

Moisture diffusion flux out the bottom of the lowest 

soil layer. (Icg m-2s-1) 

Resistance to moisture transport per unit root length. (m-ls) 

Surface runoff rate. (kg m-2s-1) 

Net shortwave radiation absorbed at the surface. (kg s-~) 

Longwave radiation absorbed at the land surface. (kg s-~) 

Upward longwave radiation from the land surface. (Icg s-~) 

Near-infrared diffuse radiation flux. (kg s-~) 

Near-infrared direct radiation flux. (kg s-~) 

Visible diffuse radiation flux. (kg s-~) 

Visible direct radiation flux. (kg s-~) 

Aerodynamic resistance. (m-ls) 

Resistance to bare soil evaporation. (m-'~) 

Canopy resistance to transpiration. (m-'s) 

Unstressed canopy resistance to transpiration. (m-'s) 

Unstressed resistance in green leaf fraction of canopy 

Effective resistance to the sum of transpiration, bare soil 

Average resistance to moisture transport within the vegetation 

Resistance provided by subcanopy air to bare soil evaporation. (m-'s) 

Resistance imposed by the soil and root system to 

Resistance provided by the soil itself to bare soil evaporation. (m-ls) 

Coefficient used in the calculation of TSoil. (s) 

Coefficient used in the calculation of Tsoil. (m) 

Effective resistance to the sum of transpiration and bare 

Water equivalent in the snowpack. (kg m-2) 

to transpiration. (m-ls) 

evaporation, interception loss, and snow sublimation. (m-l s) 

itself. (s) 

moisture transport. (s) 

soil evaporation. (m-ls) 

41 
Snow water equivalent below which snow does not modify 

albedo. (Icg m-2) 

Snow water equivalent above which only snow albedo is 

considered. (Icg m-2) 

Snowmelt rate. (Icg m-2s-1) 

Snow water equivalent for which snow and snow-free areas 

contribute equally to albedo. (Icg m-2) 

Temperature of the surface/canopy system. (K) 

Temperature deep in the soil. (K) 

Freezing point of water. (K) 

Temperature above which temperature stress prevents transpiration. (K) 

Temperature below which temperature stress prevents transpiration. (K) 

Wind speed in the overlying air (e.g., in the lowest GCM grid box). (ms-l) 

Canopy air wind speed used in subcanopy aerodynamic resistance 

Volume of root per unit volume of soil. (dimensionless) 

Moisture available during a time step for evaporation. (Icg m-2) 

Moisture in soil layer i. (Icg m-2) 

Moisture holding capacity of soil layer i. (kg m-*) 

Moisture in the root zone (top layer plus middle layer). (Icg m-2) 

Moisture holding capacity of the root zone. (Icg m-2) 

Moisture in the top soil layer. (Icg m-2) 

Maximum amount of precipitation water that can be added 

Water content in the top soil layer that would be in equilibrium 

cdculation. (ms-l) 

to the top soil layer during a time step. (Icg m-2) 

(according to Richards equation) with the water content in 

the middle soil layer. (Icg m-2) 

Moisture in the middle soil layer. (Icg m-2) 

Moisture in the bottom soil layer. (kg m-2) 

Height of the canopy. (m) 

Rooting depth. (m) 

Elevation (relative to some baseline) of the center of layer i. (m) 

Roughness length. (m) 

Parameter used in computing extinction coefficient for diffuse 

Parameter used in computing resistance to moisture transport in 

Albedo for near-infrared diffuse radiation. (dimensionless) 

Albedo for near-infrared direct radiation. (dimensionless) 

Snow albedo for visible direct radiation. (dimensionless) 

Albedo for visible diffuse radiation. (dimensionless) 

Albedo for visible direct radiation. (dimensionless) 

Snow-free albedo for visible direct radiation. (dimensionless) 

radiation. (dimensionless) 

the soil. (m2) 

42 
Y 

At 

AW 

A212 

$3 

$1 

$2 

W 

W 

The fraction of a precipitation mass assigned to the storm's previous 

Time step length. (s) 

Maximum amount of water that can diffuse between soil layers. (kg m-2) 

Distance between the cent,ers of the top and middle 

Distance between the centers of the middle and bottom 

Change in the canopy air vapor pressure, e,, over the time step. (kg m-l s 

Change in the surface-canopy temperature, T,: over the time step. (K) 

Ratio of the molecular weight of water vapor to that of dry 

Increment in e, used to compute p. (Icg m-'~-~) 

Bedrock slope. (dimensionless) 

The von Karman constant. (dimensionless) 

Latent heat of vaporization. 

Latent heat of vaporization of liquid water. 

Latent heat of fusion. 

Latent heat of vaporization of ice (sublimation). 

Cosine of the solar zenith angle. (dimensionless) 

Density of air. (kg m-3) 

Density of liquid water. (kg m-3) . 

Stefan-Boltzmann constant. (kg s-~K-~) 

Time scale of storm position. (s) 

Parameter used in computing G(p). (dimensionless) 

Parameter used in computing G(p). (dimensionless) 

Parameter describing the departure of leaf angles from a spherical 

Weighted average of G(p)/p and Qdif. (dimensionless) 

A function for diffuse radiation corresponding to the function 

Soil moisture potential in layer i. (m) 

Leaf water potential. (m) 

Soil moisture potential in the root zone (the top and middle soil 

Soil moisture potential of a saturated soil. (m) 

Soil moisture potential above which the vegetation is not moistureSoil moisture potential below which transpiration ceases due to 

Scattering coefficient. (dimensionless) 

Frequency of the diurnal temperature cycle. (s-' ) 

position. (dimensionless) 

soil layers. (m) 

soil layers. (m) 

air. (dimensionless) 

Increment in T, used to compute s. a ea (K) 

distribution. (dimensionless) 

G(p)/p for direct radiation. (dimensionless) 

layers). (m) 

stressed. (m) 

wilting. (m) 
Appendix 2: Tables of Parameter Values 

The following tables list the parameter values used for the different land surface types in the 

Mosaic LSM. Many of these values are stored in data statements in the TILE subroutine; 

others are either passed down directly to the subroutine in the CALL statement or are used 

to construct composite variables that are then passed down to the subroutine. Most of 

the parameter values were derived from values used within SIB biomes (e.g., Dorman and 

Sellers 1989). 

The tables also indicate representative equations in t,he text that use the parameters. 

I 

45 
Parameter 

CH 

&& 

fi 

A, 

A, 

Af 

rf 

YL 

lrt -live 

Irt-dead 

U 

CH-deep 

b 

C 

Units 

m2 

7- 

m2 

S2 

m2 

- 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

70000. 70000. 

4.7436 

5.09 

2.454836 

2.836836 

3.820035 

273.16 

0.1 

0.15 

0.161 

2335.9 

0.0 

153.5 

4.7436 

5.09 

2.454836 

2.836836 

3.820035 

273.16 

0.25 

0.15 

0.161 

9802.2 

10.6 

180.0 

70000. 

4.7436 

5.09 

2.454836 

2.836836 

3.820035 

273.16 

0.01 

0.12 

0.161 

2869.7 

3.7 

233.0 

70000. 

4.7436 

5.09 

2.454836 

2.836836 

3.820035 

273.16 

0.175 

0.58 

2582.0 

1.1 

110.0 

-0.3 

5. Broadleaf 6. Dwarf 

shrubs trees 

7. Bare 8. Desert 

soil soil 

70000. 70000. 70000. 70000. 

4.7436 4.7436 4.7436 4.7436 

5.09 5.09 5.09 5.09 

2.454836 

2.836836 

3.820035 

273.16 

0.01 

0.15 

0.161 

93989.4 

0.01 

855.0 

2.454836 

2.836836 

3.820035 

273.16 

0.20 

0.15 

0.161 

9802.2 

10.6 

180.0 

2.454836 

2.836836 

3.820035 

273.16 

0.0 

0.002 

0.002 

0.0 

0.0 

1.0 

2.454836 

2.836836 

3.820035 

273.16 

0.0 

0.002 

0.002 

0.0 

0.0 

1.0 

Table 1: Heat storage and unstressed canopy resistance parameter values assigned to the 

eight fundamental surface types. A relevant equation is provided in parentheses. 

46 
Parameter Units 

K 

K 

54 

?$ 

- 1 

iq 

mm 

m 

m 

m 

- s 

m 

- s 

m 

Units 

K 

K 

?$ 

- 1 '1' 

qJ 

F 

m2 

m 

- s 

m 

m 

m 

m 

m 

- S 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

0.0273 0.0357 0.0310 0.0238 

273. 273. 268. 283. 

318. 318. 313. 328. 

-1.435493-06 -6.835843-07 1.676993-07 -1.434653-06 

7.958593-04 3.720643-04 -7.659443-05 8.240603-04 

-1.115753-01 -5.215333-02 6.149603-03 -1.196023-01 

3.843-07 3.843-07 3.843-07 3.843-07 

1 .oo 1.00 0.50 0.50 

7.5312 7.5312 7.5312 4.0312 

-100. -190. -200. -120. 

-500. -250. -250. -230. 

35. 20. 17. 0.6 

2.45308 2.45308 2.45308 2.50308 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

0.0275 

283. 

323. 

-2.760973-06 

1.576173-03 

-2.26109E-01 

3.843-07 

0.50 

7.5312 

-200. 

-400. 

5. 

2.50308 

0.0275 

273. 

323. 

- 1.580943-07 

8.448473-05 

-1.272723-02 

3.843-07 

0.20 

7.5312 

-200. 

-400. 

0.6 

2.50308 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

1.OE-07 

0.10 

1.312 

-200. 

-250. 

0.1 

2.45308 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

1.OE-07 

0.10 

1.312 

-10. 

-100. 

0.1 

1308 

Table 2: Parameter values related to environmental stress factors: for each of the eight 

fundamental surface types. A relevant equation is provided in parentheses. 

I 

47 
Parameter 

Wl-sat (120) 

WkaI (120) 

W3-saI (120) 

Top layer A2 (124) 

Middle layer A2 (118) 

Bottom layer A2 (118) 

Ks (121) 

$s (120) 

b (120) 

cos8 (127) 

Parameter 

w1 -sat 

W?--sat 

W3-sat 

Top layer A2 

Middle layer A2 

Bottom layer A2 

Ks 

$5 

Soil paramet8er b 

COS8 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees tsrees trees land 

8.4 8.4 8.4 8.4 

621.6 621.6 621.6 197.4 

840.0 840.0 840.0 420.0 

0.02 0.02 0.02 0.02 

1.48 1.48 1.48 0.47 

2.00 2.00 2.00 1.00 

1.2E-06 1.2E-06 1.2E-06 1.2E-06 

-.281 -.281 -.281 -.281 

4. 4. 4. 4. 

0.1736 0.1736 0.1736 0.1736 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

8.704 

204.5 

435.2 

0.02 

0.47 

1.00 

5.833-05 

-.073 

1.69 

1.00 

8.4 

71.4 

420.0 

0.02 

0.17 

1.00 

1.2E-06 

-.281 

4. 

0.1736 

4. 

4. 

130.56 

0.0092 

0.0092 

0.30 

1.2E-06 

-.281 

4. 

0.1736 

4. 

4. 

130.56 

0.0092 

0.0092 

0.30 

5.833-05 

-.073 

1.69 

1.00 

Table 3: Wat8er balance parameter values assigned to the eight fundamental surface types. 

A relevant, equation is provided in parentheses. A2 refers to the thickness of a soil layer. 

48 
1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

See KS91 See KS91 See KS91 See KS91 

See KS91 See KS91 See KS91 See KS91 

See KS91 See KS91 See KS91 See KS91 

See KS91 See KS91 See KS91 See KS91 

5. 5. 5. 5. 

25. 25. 25. 25. 

0.50 0.50 0.50 0.70 

0.50 0.50 0.50 0.70 

0.50 0.50 0.50 0.70 

0.50 0.50 0.50 0.70 

50. 50. 50. 2. 

0.85 0.85 0.85 0.85 

0.85 0.85 0.85 0.85 

0.50 0.50 0.50 0.50 

0.50 0.50 0.50 0.50 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

See KS91 See KS91 0.1 0.3 

See KS91 See KS91 0.1 0.3 

See KS91 See KS91 0.2 0.35 

See KS91 See KS91 0.2 0.35 

5. 5. 5. 5. 

25. 25. 25. 25. 

0.60 0.60 0.70 0.70 

0.60 0.60 0.70 0.70 

0.60 0.60 0.70 0.70 

0.60 0.60 0.70 0.70 

50. 2. 2. 2. 

0.85 0.85 0.85 0.85 

0.85 0.85 0.85 0.85 

0.50 0.50 0.50 0.50 

0.50 0.50 0.50 0.50 

Table 4: Reflect,ance parameters. A relevant equation is provided in parentheses. KS91 

refers to Koster and Suarez [1991]. 

49 
Mont,h 

J aniiary 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

Month 

January 

February 

March 

April 

May 

June 

.July 

August 

September 

Oc t,ober 

November 

December 

1. Broadleaf 2. Broadleaf 3. Needleevergreen decidiioiis leaf 4. Grasstmrees trees trees land 

5.117 0.520 8.760 0.782 

5.117 0.520 9.160 0.893 

5.117 0.867 9.827 1.004 

5.117 2.107 10.093 1.116 

5.117 4.507 10.360 1.782 

5.117 6.773 10.760 3.671 

5.117 7.173 10.493 4.782 

5.117 6.507 10.227 4.227 

5.117 5.040 10.093 2.004 

5.117 2.173 9.827 1.227 

5.117 0.867 9.160 1.004 

5.117 0.520 8.760 0.893 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

3.760 0.739 0.001 0.001 

3.760 0.739 0.001 0.001 

2.760 0.739 0.001 0.001 

1.760 0.739 0.001 0.001 

1.760 0.739 0.001 0.001 

1.760 1.072 0.001 0.001 

1.760 5.072 0.001 0.001 

5.760 5.739 0.001 0.001 

10.760 4.405 0.001 0.001 

7.760 0.739 0.001 0.001 

4.760 0.739 0.001 0.001 

3.760 0.739 0.001 0.001 

Table 5: Seasonal variation of leaf area index. Lt (dimensionless) 
Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

0.905 0.026 0.913 0.568 

0.905 0.026 0.917 0.622 

0.905 0.415 0.923 0.664 

0.905 0.759 0.925 0.697 

0.905 0.888 0.927 0.810 

0.905 0.925 0.905 0.908 

0.905 0.836 0.902 0.813 

0.905 0.697 0.913 0.394 

0.905 0.331 0.898 0.443 

0.905 0.166 0.855 0.543 

0.905 0.015 0.873 0.553 

0.905 0.026 0.913 0.498 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

0.798 0.451 0.001 0.001 

0.532 0.451 0.001 0.001 

0.362 0.451 0.001 0.001 

0.568 0.451 0.001 0.001 

0.568 0.451 0.001 0.001 

0.568 0.622 0.001 0.001 

0.568 0.920 0.001 0.001 

0.868 0.697 0.001 0.001 

0.651 0.076 0.001 0.001 

0.515 0.451 0.001 0.001 

0.630 0.451 0.001 0.001 

0.798 0.451 0.001 0.001 

Table 6: Seasonal variation of greenness fraction, fg (dimensionless). 

51 
Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

2.653 0.52 1.112 0.0777 

2.653 

2.653 

2.653 

2.653 

2.653 

2.653 

2.653 

2.653 

2.653 

2.653 

2.653 

0.52 

0.666 

0.910 

1.031 

1.044 

1.042 

1.037 

1.036 

0.917 

0.666 

0.52 

1.103 

1.088 

1.082 

1.076 

1.068 

1.073 

1.079 

1.082 

1.088 

1.103 

1.112 

0.0778 

0.0778 

0.0779 

0.0778 

0.0771 

0.0759 

0.0766 

0.0778 

0.0779 

0.0778 

0.0778 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

0.245 0.0752 0.0112 0.0112 

0.245 0.0752 0.0112 0.0112 

0.227 0.0752 0.0112 0.0112 

0.200 0.0752 0.0112 0.0112 

0.200 0.0752 0.0112 0.0112 

0.200 0.0757 0.0112 0.0112 

0.200 0.0777 0.0112 0.0112 

0.267 0.0778 0.0112 0.0112 

0.292 0.0774 0.0112 0.0112 

0.280 0.0752 0.0112 0.0112 

0.258 0.0752 0.0112 0.0112 

0.245 0.0752 0.0112 0.0112 

Table 7: Seasonal variation of roughness length, z, (m). 

52 
I 

I 

I 

Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

285.87 211.32 565.41 24.43 

285.87 211.32 587.05 24.63 

285.87 218.78 623.46 24.80 

285.87 243.40 638.13 24.96 

285.87 294.87 652.86 25.72 

285.87 345.90 675.04 27.74 

285.87 355.18 660.24 30.06 

285.87 341.84 645.49 28.86 

285.87 307.22 638.13 25.90 

285.87 244.84 623.46 25.11 

285.87 218.78 587.05 24.80 

285.87 211.32 565.41 24.63 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

103.60 22.86 23.76 23.76 

103.60 22.86 23.76 23.76 

102.35 22.86 23.76 23.76 

100.72 22.86 23.76 23.76 

100.72 22.86 23.76 23.76 

100.72 23.01 23.76 23.76 

100.72 24.36 23.76 23.76 

105.30 24.69 23.76 23.76 

107.94 24.04 23.76 23.76 

106.59 22.86 23.76 23.76 

104.49 22.86 23.76 23.76 

103.60 22.86 23.76 23.76 

Table 8: Seasonal variation of c,,,. (dimensionless). 

53 
Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

19737.8 5010. 9000.0 5500. 

19737.8 5010. 9200.0 5625. 

19737.8 5270. 9533.3 5750. 

19737.8 6200. 9666.7 5875. 

19737.8 8000. 9800.0 6625. 

19737.8 9700. 9866.7 8750. 

19737.8 9500. 9733.3 9375. 

19737.8 8400. 9666.7 6875. 

19737.8 6250. 9533.3 6000. 

19737.8 5270. 9200.0 5750. 

19737.8 5010. 9000.0 5625. 

19737.8 5010. 9000.0 5500. 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

6500. 10625. 1. 1. 

6000. 10625. 1. 1. 

5500. 10625. 1. 1. 

5500. 10625. 1. 1. 

5500. 10625. 1. 1. 

5500. 11250. 1. 1. 

5500. 18750. 1. 1. 

7500. 17500. 1. 1. 

8500. 10625. 1. 1. 

7000. 10625. 1. 1. 

6500. 10625. 1. 1. 

6500. 10625. 1. 1. 

Table 9: Seasonal variation of root length density, Dd (m-?). 

54 
Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

Month 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 

1. Broadleaf 2. Broadleaf 3. Needleevergreen deciduous leaf 4. Grasstrees trees trees land 

27.37 13.66 13.76 0.218 

27.37 13.66 13.80 0.227 

27.37 14.62 13.86 0.233 

27.37 15.70 13.88 0.239 

27.37 16.33 13.90 0.260 

27.37 16.62 13.93 0.299 

27.37 16.66 13.91 0.325 

27.37 16.60 13.89 0.313 

27.37 16.41 13.88 0.265 

27.37 15.73 13.86 0.244 

27.37 14.62 13.80 0.233 

27.37 13.66 13.76 0.227 

5. Broadleaf 6. Dwarf 7. Bare 8. Desert 

shrubs trees soil soil 

2.813 0.10629 0.0001 0.0001 

2.813 0.10629 0.0001 0.0001 

2.662 0.10629 0.0001 0.0001 

2.391 0.10629 0.0001 0.0001 

2.391 0.10629 0.0001 0.0001 

2.391 0.12299 0.0001 0.0001 

2.391 0.21521 0.0001 0.0001 

2.975 0.22897 0.0001 0.0001 

3.138 0.19961 0.0001 0.0001 

3.062 0.10629 0.0001 0.0001 

2.907 0.10629 0.0001 0.0001 

2.813 0.10629 0.0001 0.0001 

Table 10: Seasonal variation of zero plane displacement height, d (m). 

55 
References 

Clapp, R.B., and G.M. Hornberger, 1978: Empirical equations for some soil hydraulic 

properties. Water Resour. Res., 14, 601-604. 

Deardorff, J. W., 1978: Efficient prediction of ground surface temperature and moisture, 

with inclusion of a layer of vegetation. J. Geophys. Res., 83, 1889-1903. 

Dickinson, R. E., A. Henderson-Sellers, P. J. Kennedy, and M. F. Wilson, 1986: Biosphereatmosphere transfer scheme (BATS) for the NCAR Community Climate Model. 

Tech. Note TN-275+STR, 69 pp., Nat. Cent. for Atmos. Res., Boulder, Colorado. 

Dorman, J. L., and P. J. Sellers, 1989: A global climatology of albedo, roughness length 

and stomatal resistance for atmospheric general circulation models as represented by 

the Simple Biosphere model (SiB). J. App. Met., 28, 833-855. 

Gash, J. H. C., I. R. Wright, and C. R. Lloyd, 1980: Comparative estimates of interception 

loss from three coniferous forests in Great Britain. J. Hydrology, 48, 89-105. 

Henderson-Sellers, A., Z.-L. Yang, and R. E. Dickinson, 1993: The project for the intercomparison of land surface parameterization schemes (PILPS). Bull. Amer. Meteor. 

SOC., 74, 1335-1349. 

Jarvis, P., 1976: The interpretation of the variations in leaf water potential and stomatal 

conductance found in canopies in the field. Phil. Trans. R. SOC. Lond., 273,593-610. 

Kalnay, E., M. Kanamitsu, J. Pfaendtner, J. Sela, M. Suarez, J. Stackpole, J. Tuccillo, L. 

Umscheid, and D. Williamson, 1989: Rules for the interchange of physical parameterizations, Bull. Am Met. SOC., 70, 620-622. 

Koster, R., and M. Suarez, 1991: A simplified treatment of SiB's land surface albedo 

parameterization. NASA Tech. Memo. 104538, National Aeronautics and Space 

Administration, Washington, D.C., 11 pp. 

Koster, R., and M. Suarez, 1992a: Modeling the land surface boundary in climate models 

as a composite of independent vegetation stands. J. Geophys. Res., 97, 2697-2715. 

Koster, R., and M. Suarez, 1992b: A comparative analysis of two land surface heterogeneity 

representations. J. Climate, 5, 1379-1390. 

Koster, R., and M. Suarez, 1993: Climate variability studies with a coupled land/atmosphere 

model. Macroscale Modelling of the Hydrosphere (W. B. Wilkinson, ed.), International Association of Hydrological Sciences Publication 214, 173-181. 

Koster, R., and M. Suarez, 1994: The components of a SVAT scheme and their effects on 

a GCM's hydrological cycle. Advances in Water Resources, 17, 61-78. 

57 
Koster, R., and M. Suarez, 1995: Relative contributions of land and ocean processes to 

precipitation variability. Journal of Geophysical Research, 100, 13775-13790. 

Liston, G.E., Y.C. Sud, and G.K. Walker, 1993: Design of a global soil moisture initialization 

procedure for the simple biosphere model. NASA Tech. Memo. 104590, National 

Aeronautics and Space Administration, Washington, D.C., 130 pp. 

Monteith, J. L., 1965: Evaporation and environment. Symposium of the Society for Experimental Biology, 19, 205-234. 

Rawls, W.J., D.L. Brakensiek, and K.E. Saxton, 1982: Est,imation of soil water properties. 

Transactions of the ASAE, 25, 1316-1320 & 1328. 

Sato, N., P. Sellers, D. Randall, E. Schneider, J. Shukla, J. Kinter, Y.-T. Hoii, and E. 

Albertazzi, 1989: Implementing the simple biosphere model (SIB) in a general circulation model, Methodologies and results. NASA Contractor Report 185509, National 

Aeronautics and Space Administration, Washington, D.C., 76 pp. 

Scott, R., R. Koster, D. Entekhabi, and M. Siiarez, 1995: Effect of a canopy interception reservoir on hydrological persistence in a general circulation model. Journal of 

Climate, 8, 1917-1922. 

Scott, R., D. Entekhabi, R. Koster and M. Suarez, submitted: Time scales of land surface 

evapotranspiration response. Journal of Climate. 

Sellers, P. J., 1985: Canopy reflectance, photosynthesis and transpiration. Int. J. Remote 

Sens., 6? 1335-1372. 

Sellers, P. J., Y. Mintz, Y. C. Sud, and A. Dalcher, 1986: A simple biosphere model (SIB) 

for use within general circulation models. J. Atmos. Sci., 43, 505-531. 

Shuttleworth, W.J., 1988: Evaporation from Amazonian rainforest. Proc. R. SOC. Lond. 

B, 233, 321-346. 

58 
Previous Volumes in This Series 

Volume 1 

September 1994 

Documentation of the Goddard Earth Observing System 

(GEOS) general circulation model - Version 1 

L.L. Takacs, A. Molod, and T. Wang 

Volume 2 

October 1994 

Direct solution of the implicit formulation of fourth order 

horizontal diffusion for gridpoint models on the sphere 

Y. Li, S. Moorthi, and J.R. Bates 

Volume 3 

December 1994 

Volume 4 

January 1995 

Volume 5 

April 1995 

Volume 6 

April 1995 

Volume 7 

September 1995 

An efficient thermal infrared radiation parameterization for 

use in general circulation models 

M.-D. Chou and M.J. Suarez 

Documentation of the Goddard Earth Observing System 

(GEOS) Data Assimilation System - Version 1 

James Pfaendtner, Stephen Bloom, David Lamich, 

Michael Seablom, Meta Sienkiewicz, James Stobie, 

and Arlindo da Silva 

Documentation of the Aries-GEOS dynamical core: Version 2 

Max J. Suarez and Lawrence L. Takacs 

A Multiyear Assimilation with the GEOS-1 System: 

Overview and Results 

Siegfried Schubert, Chung-Kyu Park, Chung-Yu Wu, 

Wayne Higgins, Yelena Kondratyeva, Andrea Molod, 

Lawrence Takacs, Michael Seablom, and Richard 

Rood 

Proceedings of the Workshop on the GEOS-1 Five-Year 

Assimilation 

Siegfried D. Schubert and Richard B. Rood 

59 
Volume 8 

March 1996 

Documentation of the Tangent Linear Model and Its Adjoint 

of the Adiabatic Version of the NASA GEOS-1 C-Grid GCM: 

Version 5.2 

Weiyu Yang and I. Michael Navon 

60 
REPORT DOCUMENTATION PAGE 

14. SUBJECT TERMS 

Land surface models, LSM, atmospheric general circulation model, GCM, 

surface energy, water balance, environmental stresses, snow budget, SIB 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 

OF REPORT OF THIS PAGE OF ABSTRACT 

Unclassified Unclassified Unclassified 

Form Approved 

OM8 NO. 0704-0188 

15. NUMBER OF PAGES 

76 

16. PRICE CODE 

20. LIMITATION OF ABSTRACl 

UL 

~ 

Public reporting burden lor this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions. searching existing data sources gathering and maintaining the data needed, and completing and reviewing the collection of information Send comments regarding this burden estlmate or any other aspect of this 

1. AGENCY USE ONLY (Leave blank) 3. REPORT TYPE AND DATES COVERED 

Technical 

4. TITLE AND SUBTITLE 

Technical Re ort Series on Global Modeling and Data Assimilation 

LSM 

Randal D. Koster and Max J. Suarez 

Max J. Suarez, Editor 

Volume 9 - Ep nergy and Water Balance Calculations in the Mosaic 

6. AUTHOR(S) 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS (ES) 

H drological Sciences Branch 

Czmate and Radiation Branch 

Goddard S ace Flight Center 

Greenbelt, bary land 

9. SPONSORING I MONITORING ADGENCY NAME(S) AND ADDRESS (ES) 

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

11. SUPPLEMENTARY NOTES 

Koster and Suarez: Goddard Space Flight Center, Greenbelt, MD 

128. DISTRIBUTION I AVAILABILITY STATMENT 

Unclassified - Unlimited 

Subject Category 46 

This publication is available from the NASA Center for AeroS ace 

Information, 800 Elkridge Landing Road, Linthicum Heights, &D 

21090-2934, (301)62 1-0390. 

13. ABSTRACT (Maximum 200 words) 

emorandum 

5. FUNDING NUMBERS 

C - NAS5-32332 

Code 974 

8. PEFORMING ORGANIZATION 

REPORT NUMBER 

96B0005 1 

10. SPONSORING I MONITORING 

ADGENCY REPORT NUMBER 

TM- 104606, Vol. 9 

12b. DISTRIBUTION CODE 

The Mosaic land surface model (LSM), which is designed for use with an atmospheric general 

circulation model (GCM), computes areally-averaged energy and water fluxes from the land surface 

in response to meteorological forcing. The model allows explicit vegetation control over the computed surface energy and water balances, with environmental stresses acting to increase canopy 

resistance and thus decrease transpiration. The scheme includes a canopy interception reservoir and 

three soil reservoirs: a thin layer near the surface, a middle layer that encompasses the remainder of 

the root zone, and a lower "recharge" layer for long-term storage. Bare soil evaporation, transpiration, and interception loss occur in parallel, and runoff occurs both as overland flow during precipitation events and as groundwater drainage out of the recharge layer. A complete snow budget is 

included. The model was originally derived from the SiB model of Sellers et al. (1986) and still 

maintains certain SiB formulations, particularly those for canopy resistance.