A bulk similarity approach in the atmospheric boundary layer to determine
regional sensible heat fluxes
Hidekazu Kato(1), Motomu Toda(2), Michiaki Sugita(1)(1) Graduate School of Life and Environmental Sciences, University of Tsukuba(2) Institute of Low Temperature Science, Hokkaido University, Sapporo City, Hokkaido

ABSTRACT
Profiles of potential temperature measured by radiosoundings in the atmospheric boundary layer (ABL)
were used with surface temperature measurements to determine regional sensible heat flux H by means oftransfer parameterizations on the basis of bulk similarity. In the present study, the similarity function C wascalibrated with the FIFE (First ISLSCP (International Satellite Land Surface Climatology Project) FieldExperiment), NOPEX (Northern Hemisphere Climate Processes Land Surface Experiment, TABLE (Tsukuba
Atmospheric Boundary Layer Experiment) and GAME-T data sets. Then the calibrated function was applied
to the data set with the ABL bulk equation to derive H values which were compared well with reference
fluxes of Hs with the rms error of the order of 20 Wm-2.
similarity formation was calibrated with the FIFE (First1.IntroductionThe knowledge of the amount of regional evapotrans-ISLSCP(InternationalSatelliteLand

Surfacepiration is important for forecasting meteorological

Climatology Project) Field Experiment) (Sugita andphenomena and estimating the water resources. One ofBrutseaert,

the ways to determine the amount of evapotranspiration

Climate Processes Land Surface Experiment), TABLE

is through heat balance approach. In this approach the(Tsukuba Atmospheric Boundary Layer Experiment)

latent heat flux is calculated from the observation orand GAME-T (GEWEX Asian Monsoon Experiment-estimation of the sensible heat flux (H), the net radiationTropics).

1992),NOPEX (Northern Hemisphere(Rn) and the soil heat flux (G). In the present analysis, itis assumed that Rn and G are measured, and regional H

2. Method

values should be estimated from the ABL bulk similarity

2-1. Experimentations and Data sets

approach.

2-1-1. TABLE

The surface sensible heat flux H can be written in thebulk similarity formulation as
H = (θ s ,r − θ a )ku* ρc p  hi − d h − d  − C iln L   z oh, r One data set was obtained during the TABLE project,which took place in the summer of 1992 in and around(1)Tsukuba city in Japan. The area of 16 by 16 km can becharacterized by its flat topography and its complex land

where θs,r is the surface potential temperature, θa theusages. Surfaces are covered with forests, agriculturalmean potential temperature of the mixed layer, k( = 0.4)

sites, grass fields, rice paddies and urban structures.

von Karman’s constant, u* the momentum flux, ρ theDetails of the area and experimentations can be found indensity of the air, cp the specific heat at constant pressure,by Sugita et al. (1993).

d the displacement height, zoh, r the scalar roughness for

2-1-2. NOPEX

sensible heat, hi the top of the ABL and L the Obukhov

Another set of data was obtained during NOPEX

length. The symbol C( ) denotes function of the stability

Concentrated Field Effort 2, which took place in theparameter (hi - d)/L.

spring and summer of 1995. The area of 40 by 70 km isIn the present study, the function C of the bulkflat and its surfaces were covered with dense boreal

forest with clearings used for agriculture. Details of thethe flux at the time of the radiosonde launch. Thearea and experimentations can be found in Halldin et al.

fraction ai by which the particular surface type that(1995).

occupies the footprint area was used as weighting factors

2-1-3. FIFE

to produce the area-averaged flux Hs as

The data set was obtained during FIFE Intensive Field
Campaigns (IFC) 1-4 in 1987 and IFC 5 in 1989 innortheastern Kansas. The area of 15 by 15 km is coveredwith tall grass prairie, with the height around 40 cm overa strongly dissected terrain. Details of the area andexperimentations can be found in Sellers et al. (1988)
and Murphy et al. (1991).
The other data set was obtained during a field
campaign within the framework of the GAME-T project,which took place in February and March of 1999 in thecentral part of Thailand. The topography is generally flat
except for a 100-m high hill some 1.5 km away from thesite. Surface are covered with evergreen and deciduous
forests whose height is variable in the range of 5 to 20 m,
paddy fields, grasslands and farmlands, bare soil, water
reservoirs and small villages (Toda and Sugita, 2003).
2-2. data sets
2-2-1. Radiosondinds
For the measurements of the ABL temperature,humidity and wind speed in daytime, radiosonde wasinallexperiments.

(2)

i =1

where Hi represents the flux of the ith surface types of nmajor surface types in footprint area. For the size of thefootprint area, a fan-shaped area with a 30˚central angle
extending 8 km for TABLE (Sugita et al., 1997) and 10
km for NOPEX (Hiyama et al., 1999) in the general

2-1-4. GAME-TusednH s = ∑ ai H iThedetailsofthemeasurementations can be found in by Sugita andBrutsaert (1990a) for FIFE, Sugita et al. (1999) for
TABLE and Hiyama et al. (1999) for NOPEX.
2-2-2. Surface fluxes
In all experiments, surface flux stations were deployed,
where sensible heat flux were obtained and used as
reference values Hs in the following analysis.
In the FIFE data sets, Hs is the averages of 6 stationsin 1987 and is calculated by surface-layer analysis oftemperature profile in 1989 because of difficulties of flux
aggregation due to non-uniform nature of surface soil
moisture. In both experiments of NOPEX and TABLE,
Hs was evaluated by the following way; the stations in
two experiments were deployed on all major surface
types (5 stations in TABLE [Hiyama et al., 1995] and 2in NOPEX [Mölder et al., 1998]. First, the time-averaged
flux of each station was interpolated in time to produce

upwind direction was employed.
In GAME-T, the turbulence measurements of windvelocity and temperature were carried out with a sonicanemometers mounted at 60 m on the tower. The
measured values are treated as Hs.
2-3. The function C for sensible heat
The function form studied with the FIFE data set inBrutsaert and Sugita (1990) and Sugita and Brutsaert(1992) can be given as hi − d 
C = a ln −+bL (3) hi − d 
C = a ln 1 −+bL (4) hi − d 
C = a −L b(5)  hi − d  a 
C = ln 1 + −bL  (6)h −d  az 
 − bC = Ψh  0  + ln i L 
 z0 (7)where a and b are the constants to be determined for andΨh is the stability correction function for sensible heat forthe surface layer profile equation.
The value of a and b are determined in the local
calibration mode by a trial-and-error method.

First, theH values are determined from (1) and (3)-(7) with
arbitrarily selected a and b constants. The resulting
fluxes are compared with independently determinedreference Hs values, and such statistics as the correlation
coefficient r, the ratio of means [Hs]/[H], the regression
coefficient c and e in a linear equation Hs = cH + e, and400

the root mean square (rms) error are evaluated. This
process is repeated by changing a and b constants in acalibrated constants.

3.Results
For all data sets, the result of r, c, e, [Hs]/[H] and theHs (Wm-2 )agreement between Hs and H were finally selected as theHs = H
FIFE87TABLENOPEXGAME-T
FIFE89300

small step, and a and b values that produced the best

200100rms error between Hs and H calculated with thecalibrated C function is listed in Table 1, and the resultfor (1) with (7) is shown graphically in Figure 1.
They indicate that all of the combined data set
calibrated work well with all data sets.

However, the

00

100

200

300

400

H (Wm-2)
Figure 1. Comparison between H values calculated for combined data
set with (1) and (7) with a = 5.13 and reference value Hs.

result for the NOPEX data is slightly worse than theothers. ∆θ (θs,r - θa) value of NOPEX data sets isfor the same –(hi - d)/L change near –(hi - d)/L = 0. This

generally very small, and as such the maximumδH (thealso contributes large error of this data set.

probable error of H) value, contributed by the error of u*,zoh, r and ∆θ (Sugita et al., 1996), is as large as around
14Wm-2. The - (hi - d)/L values of the NOPEX data set
also is closer to zero, and the value of C changes more
Table 1. Statistics in the comparision of Hs and HFIFETABLENOPEXGAMETcombined
data set

equationrce[Hs]/[H]

(4)
(5)
(6)
(7)
(8)
(4)
(5)
(6)
(7)
(8)
(4)
(5)
(6)
(7)
(8)
(4)
(5)
(6)
(7)
(8)
(4)
(5)
(6)
(7)
(8)

0.973
0.971
0.968
0.972
0.981
0.989
0.990
0.988
0.990
0.984
0.839
0.812
0.737
0.818
0.678
0.994
0.996
0.993
0.995
0.995
0.963
0.961
0.947
0.961
0.964

1.01
1.01
1.02
1.01
0.991
0.992
1.00
1.01
0.994
1.02
0.701
0.681
0.567
0.679
0.565
1.16
1.16
1.17
1.16
1.08
1.02
0.989
0.998
1.02
0.989

14.2
14.3
12.9
14.1
12.4
0.535
0.376
-0.563
0.408
-1.15
34.2
36.5
49.0
35.9
54.4
-0.521
-1.55
-2.56
-1.16
1.82
8.10
8.14
9.50
8.25
8.30

1.23
1.24
1.22
1.23
1.18
1.00
1.00
1.00
1.00
0.998
0.922
0.916
0.864
0.907
0.913
1.16
1.14
1.15
1.15
1.10
1.10
1.09
1.08
1.09
1.06

rms
error
24.8
25.1
24.2
24.6
20.6
3.55
3.43
3.84
3.47
4.37
30.1
32.343.4
32.7
40.5
23.0
21.3
22.6
21.8
15.7
21.8
22.2
24.4
22.1
19.9

4.Conclusion
The stability functions C are determined for four datasets (FIFE, TABLE NOPEX and GAME-T) in which thesurface usages are different, and it appears that the bulk
similarity with those functions is capable of producing
regional surface fluxes. However, the result also showsthat depending the data set, the resulting H values tend tooverestimate or underestimate the reference values. Thismight be due to the C-function which includes only thestability effect and which might need additionalparameters to reflect other ABL physics.

Reference
Brutsaert, W. and Sugita, M. 1992. Regional surface
fluxes under nonuniform soil moisture conditions
during drying. Wat. Resour. Res., 28, 1669-1674.
Halldin, S., Gottschalk, L., van de Griend, A. A.,
Gryning, S. -E., Heikinheimo, M., Högström, U.,
Jochum, A. and Lundin, L. -C. 1995. Science plan for
NOPEX. Technical Report No. 12., Nepex Central
Office Uppsala University, Sweden. 38 pp.
Hiyama, T., Sugita, M. and Kotoda, K. 1996. Regionalroughness parameters and momentum fluxes over acomplex area. J. Appl. Meteorol., 35, 2179-2190.

Hiyama, T. Sugita, M. Bergstörm, H. and Mölder, M.

measurements to determine roughness parameters of1999. Wind speed measurements in upper and lower

complex terrain. J. Geophys. Res., 108, D12, 4363,

boundary layer to determine regional momentum

doi: 10. 1029/2002JD002573.

fluxes. Agric. For. Meteorol., 98-99, 145-158.
Kustas, W. P., and Brutsaert, W. 1986. Wind profile
constants in a neutral atmospheric boundary layer overcomplex terrain, Bound.-Layer Meteorol., 34, 35-54.
Mölder, M., Sugita, M., Hiyama T. and Bergstörm, H.
1998. Regional sensible heat flux and thermalroughness length of an inhomogeneous landscape.
Hydrol. Process., 12, 2115-2131.
Parlange, M. B. and Brutsaert, W. 1993. Regional shear
stress of broken forest from radiosonde wind profiles
in the unstable surface layer, Bound.-Layer Meteorol.,64, 355-368.
Sellers, P. J., Hall, F. G., Asrar, G., Strebel, D. E. andMurphy, R. E. 1988. The First ISLSCP FieldExperiment (FIFE) . Bull. Am. Meteorol., Soc., 69,22-27.
Sugita, M. and Brutsaert, W. 1990a. Wind velocity
measurements in the neutral boundary layer above
hilly prairie. J. Geophys. Res., 95, 7617-7624.
Sugita, M. and Brutsaert, W. 1990b. Regional surface
fluxes from remotely sensed skin temperature andlower boundary layer measurements. Wat. Resour. Res.,26, 2937-2944.
Sugita, M. and Brutsaert, W. 1992. The stability
functions in the bulk similarity formulation for theunstable boundary layer. Bound.-Layer Meteorol., 61,65-80.
Sugita,M.,

Kayane,I.

andHiyama,T.

1993.

IGBP/BAHC Field experiment to address scale
problems in land-surface parametarization. IAHS Publ.,
212, 389-396.
Sugita, M., Hiyama, T. and Kayane, I. 1997. How
regional are the regional fluxes obtained from lower
atmospheric boundary layer data? Wat. Resour. Res.,33, 1437-1445.
Sugita, M., Endo, N. and Hiyama, T. 1999. Regionalsurface momentum flux derived from atmosphericboundary layer bulk similarity approach. J. Geophys.
Res., 104, 16965-16972.
Toda, M. and Sugita, M. 2003. Single level turbulence