Journal

ELSEVIER

Journal of Hydrology I88- 189 (1997) 912-945

Unidimensional modelling of a fallow Savannah during the HAPEX-Sahel experiment using the SiSPAT model I. Brauda’*, P. Bessemoulinb, B. Montenyc, M. Sicot’, J.P. Vandervaere”, M. Vauclin a “LTHE (CNRS UMR 5564, INPG, WF), BP 53, 38041 Grenoble Cidex 9, France hM6teo-France/CNRM/4M, 42 Avenue Coriolis, 31057 Toulouse Ckdex. France ‘ORSTOM, Laboratoire d’Hydrologie, BP 5045, 34032 Montpellier Ckdex, France

Abstract In the framework of the HAPEX-Sahel experiment, a data set was gathered on a fallow Savannah site of the Central East Supersite. This includes 54 days of atmospheric forcing (air temperature and humidity, wind speed, solar and long-wave radiation and rainfall), net radiation, sensible, latent and soil heat fluxes and soil temperature series at a time step of 20 min. Furthermore, 17 soil moisture profiles, the evolution of the leaf area indices and some soil characteristics were available. The data set W~.S used, at the field scale, to calibrate and validate the SiSPAT (simple soil plant atmosphere transfer) model, a 1D model of coupled heat and mass transfer in the soil-plant-atmosphere continuum. The objectives of the study were (i) to assess the performances of the model in the prediction of the diurnal cycle of net radiation, turbulent fluxes, soil temperatures and the evolution of soil water content over a period of 54 days (day of the year 239-292, 1992), characterized by early stage intense rainfall events and fast drying afterwards, (ii) to analyse the influence of soil surface crust on the water balance and (iii) to identify the 1D modelling limits when the surface area consists of two strates: a ground sparse herb layer, characterized by a large spatial variability of surface properties and water content with scattered bushes. The model was calibrated over a 2-week period and then run over the whole 54-day period. We were able to reproduce the main characteristics of the observed net radiation, turbulent fluxes, soil temperature and soil moisture for the intense rainfall events and for an elongated dry period. Nevertheless, when the crust was not taken into account, the rainfall-runoff-infiltration process and the evapotranspiration after rain were poorly predicted (overestimation of evapotranspiration and infiltration). When a crust was considered to model the water balance at the field scale, its influence was found to be substantial on the runoff generation and the infiltration, and consequently on the bare soil evaporation. However, runoff predictions were much larger than the observations. Indeed, at the field

* Corresponding author. 0022-1694/97/$17.00 0 1997- Elsevier PII SOO22-

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177-O

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L Braud et al./Journal of Hydrology 188-189 (1997) 912-945

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scale, no runoff was generally observed. Lateral redistribution of water between crusted and noncrusted zones was observed in the plot. However, this cannot be taken into account with the presented 1D deterministic modelling. Hence further model development is needed to yield a better representation of soil water fluxes at the field scale.

1. Introduction One of the aims of the HAPEX-Sahel experiment (Goutorbe et al., 1994) is to address the problem of aggregation of surface heat and mass fluxes from a sparse canopy. The experimental part of the project was conducted in a climatic zone, which proves to influence greatly the global atmospheric circulation. Another goal is to improve the parameterization of surface processes used in atmospheric and climatic models. The strengths and weaknesses of these parameterizations can be assessed by comparing their outputs directly with observed data and/or by comparing their outputs with more sophisticated models which can be considered as a 'reference', provided they are properly validated. This strategy, applied to 1D modelling with imposed forcing, is discussed in the first part of Goutorbe et al. (1997). The ISBA scheme (interface soil-biosphere atmosphere) (Noilhan and Planton, 1989) is compared with observed data from a fallow savannah of the East Central Supersite and with results from the SiSPAT (simple soil-plant-atmosphere transfer) model (Brand et al., 1995b), which is a ID mechanistic and deterministic model describing coupled heat and mass transfer in the soil-plantatmosphere continuum. The present paper is dedicated to the preliminary and necessary stage of this strategy: assessing the performances of the more complex model SiSPAT on the same fallow savannah in order to see if the validation status of the model allows to draw conclusions for improving simple parameterizations (for instance the ISBA scheme). For this study, a data set of 54 days taken from the intensive observing period of 1992 (day of the year, DOY, 239 to 292) was gathered for fallow savannah, a composite vegetation consisting of two layers: a ground layer of sparse grass and scattered bushes, mainly Guiera Senegalensis. The observation period includes intense rainfall events followed by an elongated dry period. Furthermore, the soil is very heterogeneous, both vertically (several horizons with different soil properties) and horizontally (existence of crusted and non-crusted areas). In this paper, which describes a 1D modelling of the site, only vertical heterogeneity is taken into account explicitly. The influence of the crust is nevertheless assessed by comparing model outputs with and without crust. For the validation of the model, performed on non-crusted soil, the most complete data set was assembled (Section 3). All measured parameters were introduced into the model. Those for which no measurements were available (mainly plant parameters and hydraulic conductivities of deeper horizons) were calibrated over a sub-period of 2 weeks (DOY 258271), characterized by a rainfall event of 23 mm the first day followed by a drying of the soil (Section 4). Then the validation (Section 5) was done by running the model for 54 days (DOY 239-292), with the observed atmospheric forcing and the evolution of the leaf area

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L Braud et al./Journal of Hydrology 188-189 (1997) 912-945

index (LAI) as inputs and after an initialization of soil moisture and temperature profiles from observations on DOY 239. The validation is performed on several types of variables: net radiation, sensible and latent heat fluxes, soil temperatures series at several depths at a time step of 20 rain and soil moisture profiles are compared with observations during the 54-day period. It must be pointed out that the data set allows for the validation of the diurnal cycle of these quantities over a long period, with contrasting weather conditions. This quality label of the experimental data set is often not available when testing models similar to SiSPAT. Most often the diurnal cycle is validated over a few days (e.g. Sch~idler et al., 1990; Braud et al., 1995b). If longer series are available, data are often treated on a daily basis (Lascano et al., 1987; Flerchinger and Pierson, 1991 for sparse canopies studies). In Section 6, the sensitivity of the water balance to the existence of a crust will be assessed and conclusions and perspectives will follow in the last section.

2. Model description An extensive description of the SiSPAT model can be found in Braud et al. (1995b). The various equations solved by the model are summarized in and notations are defined in Table 1. Basically, SiSPAT is a vertical 1D model, forced with climatic series of air temperature and humidity, wind speed, incoming solar and long-wave radiation and rainfall. In the soil, coupled heat and mass transfer equations are solved for temperature T and matric potential h. They include both liquid and vapour transfers as formulated by Philip and De vries (1957) or Milly (1982). The model deals with vertically heterogeneous soils (Fig. 1(a)), The upper boundary conditions are provided by the solution of the soil-plantatmosphere interface (schematized in Fig. l(b)), which provides the surface soil heat and mass fluxes and the surface matric potential h l and temperature T~. The soil module can thus be run by setting the fluxes (Neumann condition) or the values of temperature and matric potential (Dirichlet condition). In the case study, the Dirichlet condition proved to be numerically more stable and was thus used for all of the simulations. If saturation of the surface occurs, the matric potential is set to zero and the runoff is calculated from the mass budget equation. At the soil-plant-atmosphere interface, following Deardorff (1978), bare soil and vegetation are considered separately in a two-source model (Shuttleworth and Wallace, 1985; Taconet et al., 1986) (Fig. l(b)). Five equations can be written: energy budget over bare soil and vegetation; continuity of the sensible and latent heat fluxes through the canopy and continuity of the surface flux at the soil surface (Section A.1). Leaf temperature Tv, canopy temperature Tar, canopy specific humidity qav, soil surface temperature Tl and surface matric potential h l can thus be calculated and the fluxes are deduced from the formulae given in Section A.2. In the soil, a root extraction term is included and the assumption that the total root-extraction is equal to the plant transpiration allows for the computation of the leaf water potential ht (Section A. 1) used to compute the stomatal resistance water stress function (Section A.2). The incoming energy is partitioned between bare soil and vegetation through a shielding factor ot (Deardorff, 1978; Taconet et al., 1986). As compared with the original paper by Braud et al. (1995b), the root extraction module has been modified and in the stomatal resistance model, a function of the vapour pressure deficit was added. All details are provided in Appendix A.

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

915

Table 1 List of symbols Ch cp

CT d Dch DoT Dmh DmT Dvh D ,'T ea

e~,(73 E, E~, E,., E .

G h hj hf hf¢ h~ H, Hg, H,, K K,;a~ L~ LAI m /,/

Mrd P P8 q q~, q~v Qm~ RaM, Rail, Ray

RgM, Rgn, Rgv Rp R~, R~:, R stmax R stmin R ~,o RvM, RvH, R,v RA, RAg, RAv RG, RG g, RG v Rn, Rn g, Rn, Sj

Capillary capacity (m -~) Specific heat at constant pressure (J kg -~ K -~) Volumetric heat capacity (J m -3 K -I) Displacement height (m) Isothermal vapour conductivity ( W m -2) Apparent thermal conductivity (W m -I K -t) Isothermal moisture conductivity (m s -~) Thermal vapour diffusivity (m 2 s -~ K -~) Isothermal vapour diffusivity (kg m -2 s -t) Vapour diffusivity associated with temperature gradients (kg m -~ s -* K -I) Vapour pressure at level z~ (Pa) Saturated vapour pressure at temperature T (Pa) Evapotranspiration above the canopy, evaporation from the ground, total evapotranspiration from the vegetation and evaporation from the wet fraction of the canopy, respectively (W m -2) Surface soil heat flux (W m -2) Soil water matrix potential (m) Soil water matrix potential of layer j (m) Leaf water potential (m) Critical leaf water potential (m) Scale factor in the Van Genuchten formula for the suction curve (m) Sensible heat flux above the canopy, from the ground and the canopy, respectively (W m-2) Soil hydraulic conductivity (m s -1) Saturated liquid hydraulic conductivity (m s -I) Latent heat of vaporization (J kg -~) Leaf area index Exponent in the Van Genuchten formula for the suction curve Soil porosity Maximum root length density (m root m -3 soil) Precipitation above the canopy (m s -~) Precipitation reaching the ground or throughfall (m s -t) Exponent in the Van Genuchten formula for the suction curve Specific humidity of air at level za and z,v, respectively (kg kg -~) Darcian non-isothermal flow crossing the soil surface (kg m -2 s -I) Aerodynamic resistance between level Za and zav for momentum, heat and vapour, respectively (s m -~) Aerodynamic resistance between the soil surface and level zav for momentum, heat and vapour, respectively (s m -~) Total plant resistance ( s m -I root) Root resistance of layer j (s) Soil resistance of layer j (s) Maximum stomatal resistance (s m -t) Minimal stomatal resistance (s m -~) Stomatal resistance (s m -~) Aerodynamic resistance between the canopy and level zav for momentum, heat and vapour, respectively (s m -I) Incoming long-wave radiation, long-wave radiation for the bare soil and canopy, respectively (W m -2) Incoming solar radiation, solar radiation for the bare soil and canopy, respectively (W m-2) Total net radiation, net radiation for the bare soil and canopy, respectively (W m -2) Plant root uptake of layer j (kg m -3 s -I)

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1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

Table I Continued t

T Ta, Ta~ Trod T~

U., U~, VPD

7.ore, Z,oh t~ O~g, O/v

c5 ~g, Ev

0 O, 0 sat Pa PW cr Of

Time (s) Soil temperature (K) Soil temperature of layerj (K) Air temperature at level z~ and zo,, respectively(K) Radiative surface temperature (K) Leaf temperature (K) Wind speed at level za and z,,, respectively (m s -I) e~at(Ta)- ea = vapour pressure deficit (Pa) Vertical coordinate (m) Height of the atmosphere reference level and canopy artificial level (m) Roughness length for momentumand heat Mean canopy height (m) Scale parameter in the Gardner hydraulicconductivitymodel (m-~) Bare soil and vegetation albedo, respectively Exponent in the Brooks and Coneymodel for hydraulic conductivity Wet fraction of the canopy Bare soil and vegetationemissivity,respectively Thermal conductivity(W m-~ K-I) Volumetric water content (m3 m-3) Residual volumetricwater content (m 3 m-3) Saturated volumetricwater content (m3 m-3) Air density (kg m-3) Liquid water density (kg m-3) Stephan-Boltzmannconstant (5.67 x 10-8 W m-z K-~) Shielding factor

3. Description of field data 3.1. Atmospheric forcing and turbulent fluxes The fallow savannah considered here is situated in the East Central site (13°33'48"N, 2°40'94"E) (see Goutorbe et al., 1997, this issue, for the description of the sites). For the forcing of the model, air temperature and humidity measured at 2 m and wind speed at 10 m were used. Incoming solar radiation was taken from the climatic station of Banizoumbou (13°31'97"N, 2°39'62"E) after recalibration using data from the West Central site (decrease of 5%). The incoming long-wave radiation, not measured on the site, was taken

I. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

917

+

,d

I

[-

+

+

II

> 11

[-

,

(

Z ~0 0 rr

0 -~r; I-

r~ o

I-

(

II

'~1'~ ~1~

+

)

f

i

% f t'q

..~

I

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L Braud et aL/Journal of Hydrology 188-189 (1997) 912-945

ensure conservation of the water balance as shown by Haverkamp et al. (1977). A comparison of the measurements of the two net radiometers performed afterwards showed that the net radiometer at 11.5 m was providing values 8% higher than radiation measured at 8 m around midday (P. Bessemoulin, personal communication, 1994). This error influences directly sensible and latent heat fluxes calculated by the Bowen ratio method. As corrected values were not available at the time of the study, the comparison between model and observation will only be done with net radiation measured at 8 m, with the sensible and latent heat flux measured by eddy correlation and with the soil heat flux estimated from the corresponding residual of the energy budget. Separate measures of radiative temperature over the bushes and the grass layer were also available, but were not relevant for validation of the model. Note that no separate measure of bare soil evaporation was available. Thus the partition of evapotranspiration between bare soil evaporation and vegetation transpiration as calculated by the model will not be compared with experimental values. 3.2. Soil data

For the initialization and validation of the model, seven soil temperature series were available at 0.5, 2, 9, 14, 28, 51,101 cm depth at a time interval of 20 rain. Furthermore, the site was instrumented with 11 neutron probe access tubes. The mean moisture profile, arithmetically averaged over all tubes, was used for initialization of the model on DOY 239 at 0 GMT. For each of the 11 tubes, 16 moisture profiles were measured during the simulation period. The validation being performed at the field scale, their arithmetic mean and standard deviation were used for validation of the calculated soil moisture profiles. For the soil characterization, dry bulk density and particle size distribution profiles were available down to 3 m depth. The surface (0-10 cm) suction curve was derived from tensiometer and gravimetric water content measurements. The surface hydraulic conductivity curve was estimated by multi-disc infiltrometers (Vandervaere, 1995). The surface crust was also characterized (Vandervaere et al., 1997). It would have been interesting to compare moisture profiles of crusted and non-crusted soils, but it could not be achieved because the crusts evolve in time and are modified by rainfall events (Peugeot, 1995), leading to difficulties in classifying tubes in crusted and tubes in non-crusted zones. 3.3. Plant data

The evolution of the leaf area indices (LAIs) (Fig. 2(a)) was deduced from biomass measurements (Monteny, 1993) and from relationships between LAI and biomass as calibrated on the West Central site for similar vegetation (N.P. Hanan, HAPEX data base). Incoming radiation is intercepted partly by vegetation. This is taken into account Fig. 1. Schematic description of the SiSPAT model. (a) The soil module: the total soil depth is divided into horizons, each horizonbeing discretized into layers. The temperature and matric potential are calculated at the nodes and the fluxesat the interfacesbetweenlayers.The resistance schemeshowsthe rootextraction module.(b) The soil-plant-atmosphere interface sub-model.

919

I. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

t~D fN ,D

oa 0 0 co O

.o.~

E o

r~ t~

~D)HId~G 1

cq

V1

r~

c~

I

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eu

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1

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7~

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V~HV

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O

L Braud et al./Journal of Hydrology 188-189 (1997) 912-945

920

in the model by introducing a shielding factor at. (Deardorff, 1978). Multiple reflections between bare soil and vegetation are taken into account as proposed by Taconet et al. (1986) (see Section A.2). The following relationship was used for the shielding factor (J.L. Roujean, personal communication, 1994). tIf =

1 - e x p ( - 0 . 5 ( L A I +0.1))

(1)

For guiera and herb, root density data and stomatal resistances were available from observations at the West Central Site (N.P. Hanan, HAPEX data base; Hanan and Prince, 1997). A root density profile (in % of total root mass) was composed from the herb and guiera data and this result (Fig. 2(b)) was fitted by two linear functions for different depth intervals. Note that measurements were restricted to 2 m depth but roots of guiera were suspected to go deeper. This is taken into account in the model fitted. To get the root density profile in m root m -3 soil, as needed by the model, the maximum root length density must be prescribed but was not available from these measures and was thus calibrated.

4. Choice of the parameters and calibration As mentioned before, measured parameters were directly introduced into the model. The missing ones were calibrated over a 2-week period (DOY 258-271) with a rainfall event of 23 mm on the first day (Braud et al., 1994a). 4.1. Soil p a r a m e t e r s

The soil texture is sandy following USDA classification. The soil depth was fixed at 4 m in order to contain all of the roots. The lower boundary for the mass flux is represented by gravitational flow and for heat, the temperature of the last node was fixed at 34°C. According to dry bulk density profiles (Monteny, 1993), the soil was divided into three horizons (0-20 cm; 20 cm-2.5 m; 2.5 m - 4 m). For each one, parameters of the suction curve and hydraulic conductivity curves must be defined. The three parametric models below were used (parameters are defined

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

921

% X

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=

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% X

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I

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ol

~V'~ E E I

,~

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lib

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.~. ,~

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,~

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922

L Braud et aL/Journal of Hydrology 188-189 (1997) 912-945

conductivity, two different G a r d n e r m o d e l s were fitted for h > - 0.115 m of water. This is related to the rapid increase o f infiltration near saturation, w h e n m a c r o p o r e flow becomes important. M e a s u r e m e n t s were o n l y representative o f near saturation conditions (h > - 0.115 m). In a first attempt, G a r d n e r ' s m o d e l was extrapolated to dry condition, but this led to a very rapid decrease in c o n d u c t i v i t y and unrealistically low values. In a second attempt, for h < - 0.115 m, a Brooks a n d Corey m o d e l was used. The shape parameter/3 was deduced from particle size distribution at the surface u s i n g the fractal approach of Fuentes et al. (1996a, b) and the saturated hydraulic c o n d u c t i v i t y was calculated to get a continuous function over the whole matric potential range. For deeper horizons, o n l y dry bulk density and particle size distribution profiles were available. T h e saturated water content 0sat was calculated as 9 0 % o f porosity. The fractal approach m e n t i o n e d above was used to derive the shape parameters o f the suction curves q and hydraulic conductivity curves/3. This method does not p r o d u c e reliable values of the scale parameters hg and KsatThe hg values were chosen to e n s u r e c o n t i n u i t y of the matric potential profile at the interface b e t w e e n horizons. T h e saturated hydraulic conductivities were fitted on the rainfall event of the calibration period in order to reproduce the observed moisture profiles (Brand et al., 1994a) (Table 2). The model also needs the specification o f the thermal conductivity. T h e De Vries (1963) model is i m p l e m e n t e d into the m o d e l b u t the prediction of the soil temperature series was poor. Furthermore, from an attempt to derive the thermal diffusivity from these series using the method o f Horton and W i e r e n g a (1983), it was f o u n d that the 0 - 2 - c m layer had a lower thermal conductivity than deeper levels. By fitting two values for the 0 - 2 - c m and 2 - c m - 4 - m depths, soil temperature series were better predicted than with the De Vries Table 3 Surface and plant parameters used in the model Parameters

Values

Sources

Bare soil albedo

t~g = 0.4(I - O/n) + O.0801n corrected for the sun zenithal position

Displacement height Roughness length for momentum Roughness length for heat Bare soil emissivity Vegetation albedo

d = 0.38 m Zorn= 0.07 m Zom/Zoh = 100a eg = 0.97 cry = 0.2

Passerat de Silans (1986) consistent with measurements on a soil of the West Central site with the same colour as the studied field (J.L. Roujean, personal communication, 1994) (Tuzet et al., 1994) (Tuzet et al., 1994)

Vegetation emissivity Critical leaf water potential Minimal stomatal resistance Total plant resistance Maximum root density b

e v = 0.96 hfc = - 140 m ~ Rstmin = 8 0 S m -I

(GSTS Strasbourg in Monteny, 1993) (J.L. Roujean, personal communication, 1994) (GSTS Strasbourg in Monteny, 1993) (Hanan and Prince, 1997)

Rp = 6.5 x 1012 s m -I root a Mrd = 17900 m root m -3 soil ~

a Values were calibrated. b This value corresponds to the maximum value of the profile shown in Fig. 2(b). When the root density profile is integrated over depth, the mean root density associated is 6950 m root m -2 soil.

L Braud et al./Journal of Hydrology 188-189 (1997) 912-945

923

(1963) model and the results for surface fluxes were very similar. This latter choice was thus retained for all the simulations. For vapour diffusivities, De Vries (1975) formulae were used. 4.2. Surface and plant parameters

Values are summarized in Table 3. For the bare soil albedo, the relationship proposed by Passerat de Silans (1986), calibrated for a loamy soil, proved consistent with measurements performed in Niger (J.L. Roujean, personal communication, 1994) and was thus used. The roughness length for heat was chosen to reproduce correctly the sensible heat flux for the calibration period. Plant parameters (total plant resistance, critical leaf water potential and maximum root length density) were calibrated to match modelled and observed latent heat fluxes. The total plant resistance R p, which controls water transfer between the roots and the leaf, appears to be a very sensitive parameter. It greatly influences the diurnal course of the stomatal resistance. It was thus varied until consistency was obtained between measured and modelled diurnal courses of stomatal resistance from the West Central site and between modelled and observed latent heat fluxes (calibration). However, the three fitted plant parameters are not independent and the set of 'optimum' values is probably not unique.

5. Results and discussion for the simulation without surface crust For the comparison between an observed Var(obs) and calculated variable Var(mod), regressions of the form Var(mod) = Slope x Var(obs) + Intercept were performed. The root mean square error (RMSE) was calculated by RMSE=

Ni

( V a r i ( m ° d ) - Vari(°bs))2

(3)

where N is the number of pairs available. Table 4 Mass budget as calculated by the model and some estimates of the corresponding values from observations. In brackets are given estimates of cumulated ETR on the days without missing values Model simulation w i t h o u t crust at the surface Rainfall Total evapotranspiration Transpiration Bare soil evaporation Deep drainage Runoff Change in water storage Input for the model.

144.4~ 168.8 (138.0) 128.0 40.8 18.0 0.0 - 42.4

'Observations' 144.4 (131.0) Not estimated 0.0 - 25.0

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

924

160 140 ~120

__F I

~100 ,~

F

80

4 0

., - - - -' - "- "'

HOURS

SINCE

AUGUST FAtt~

160 140 120

_.--,-'-'l"

s~v*~

~

26 t,ST

~ - a - , ~qz,

1992

....

~.;--~. . . . . . . . . .

AT 0 GMT

CtNr~L S i l t _.-,

.--, . _ - - , _

_.,

-

100 80 60 40 20

Fig. 3. Time evolution of observed cumulative rainfall ( ) and cumulative modelled fluxes: total evapotranspiration (- - -), transpiration ( - - - - - - ) and bare soil evaporation ( - - * * - - * * - - ) .

5.1. Model results

Table 4 provides the water balance as predicted by the model for the considered soil column for the reference period (DOY 239-292). Evapotranspiration (ETR) is well predicted by the model with a relative error of less than 6%. The partitioning of ETR between bare soil evaporation and transpiration is also given (evaporation of intercepted rainfall is negligible in this case given the low values of LAIs). The time course of the corresponding cumulative amounts and that of rainfall is given in Fig. 3. Both the observed and model predicted latent heat fluxes at the 20-min time interval were aggregated to get daily values of ETR. Values for selected days are given in Table 5. Fig. 4 shows the scatterogram of modelled versus observed dally ETR while the parameters of the linear regression are given in Table 6. Modelled and observed values agree reasonably well, given the error bars associated with the measurement of latent heat flux. Bare soil evaporation represents 24% of the total ETR. However, as shown in Fig. 3 and Table 5 this is only significant during the rainy period. The day following a rainfall event, bare soil evaporation exceeds transpiration and decreases progressively over 5 days (Table 5). For the same time interval, the transpiration tends to increase slightly (especially Case 2). This behaviour was also observed and modelled by L.P. Simmonds (unpublished results, 1995) on a sparse millet site in Niger. During the dry period, the ETR is due to plant transpiration. The model captures reasonably well the decrease in ETR associated with the progressive drying of the soil (Table 5). Note that the assumption of a composite vegetation made of grass and bushes produces reasonable results for ETR. Unfortunately, no separate measures of bare soil evaporation and transpiration were available. Thus, the partition of the latent heat flux

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

925

Table 5 Observed and calculated values for the daily ETR (mm), bare soil evaporation and transpiration, for two rainfall events and selected days in the dry period Observed daily ETR

Calculated daily ETR

Calculated transpiration

Calculated bare soil evaporation

Case 1 244 245 246 247 248 249 Total

5.0 4.1 2.4 3.6 2.7 3.1 20.9

4.4 3.8 2.2 3.2 2.2 2.7 18.5

1.3 2.0 1.3 2.6 1.9 2.5 I 1.6

3. I 1.8 0.9 0.6 0.3 0.2 6.9

Case 2 251 252 253 254 255 Total

5.1 3.6 3.7 3.6 3.4 19.4

4.7 4.1 3.6 3.2 3.6 19.2

1.5 2.5 2.8 2~8 3.2 12.8

3.2 1.6 0.8 0.4 0.4 6.4

3.8 3.1 2.8 2.3 2. I 1.8

4.1 3.3 2.9 2.7 2.5 2.2

2.9 3.2 2.9 2.7 2.5 2.2

1.2 0.1 0.0 0.0 0.0 0.0

DOY

Case 3 261 (3) 266 (8) 273 (15) 276 (18) 280 (22) 286 (28)

Case I, rainfall of 34 mm in the night between DOY 242 and 243; Case 2, rainfall of 26.5 mm in the night between DOY 250 and 251; Case 3, selected days in the dry period. Figures between brackets are the number of days since the last rainfall.

between bare soil and vegetation, as calculated by the model, cannot be validated and more complex modelling of the two layers of vegetation could not be validated or invalidated. Table 6(a) and (b) summarizes the comparison between the observed and the modelled values of net radiation, sensible, latent and soil heat fluxes and soil temperature. For their comparison, the 20-min time step data were considered for the complete simulation period leading to more than 3500 pairs of values. Scatterograms for the fluxes are shown in Fig. 5. Table 6(b) shows that the surface energy budget is well reproduced by the model for mean values. For the net radiation, the latent heat and the soil heat flux, the slopes of the regression are close to one with a small intercept. The regression is significantly worse for the sensible heat flux, although the energy balance is always closed. In this case, the regression is strongly influenced by nightly values where the model predicts values generally 20 W m -2 higher than the observed ones. From the information available, it is not possible to conclude if measurement errors of sensible heat flux can be responsible or if the problem is linked to a bad prediction of vegetation and soil surface temperature at night. For the net radiation, the agreement is good. However, the RMSE is higher than generally expected for this variable. This can be explained easily. Solar radiation was not measured

926

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945 FALLOW 6

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Fig. 6. Examples of corresponding diurnal cycles of energy budget between the model and observations for (a) DOY 254 (3 days after a rainfall of 27.6 mm), (b) DOY 256 (the day following an intense rainfall of 28.7 mm), (c) DOY 280 (21 days after the last rainfall). In the study by Linder et al. (1996), no rainfall was encountered (except for an irrigated maize field) but the present work was performed under very contrasting weather conditions (intense rainfall events followed by an elongated dry period). Comparison of the time course of the fluxes is not shown because figures are almost illegible given the length of the time series. Instead, Fig. 6 yields the comparison of observed and modelled terms of the energy balance for 3 selected days. DOY 254 follows an intense rainfall of 27.6 mm, with a time lag of 3 days (Fig. 6(a)). DOY 256 follows a rainfall of 28.4 m m the night before (Fig. 6(b)) while DOY 280 is selected during the dry period (21 days after the last rainfall) (Fig. 6(c)). Fig. 6 shows that the energy budget is generally well predicted, both a few days after a rainfall event and during the dry period. This is not the case the day just following a major rainfall event (DOY 256), where the latent heat flux is overestimated (peak value of 600 W m -2 instead of 450 W m -2 - difference of 0.8 m m of water on the daily value). This is probably linked to a bad prediction of the infiltration process at the field scale with the 1D model as will be discussed later. As mentioned before, radiative surface temperatures were only measured above grass and cannot be used for the comparison with model outputs. Nevertheless, the radiative surface temperature calculated in the model (Section A.2) can be assumed to be correct, because the net radiation is well predicted. This radiative temperature depends

L Braud et al./Journal of Hydrology 188-189 (1997) 912-945

931

Table 6 (a) Coefficient of determination R 2, slope and intercept of the regressions V a r ( m o d ) = Slope x Var(obs) + Intercept and RMSE. Except for daily ETR, regressions were performed with 20-min time interval data. (b) Comparison of observed (eddy correlation station) and calculated mean values of surface fluxes (W m-2) (a) Model variable

Observed variable used in regression

R2

Slope

Intercept

Daily ETR

Daily ETR from eddy 0.80 correlation

0.84

0.62 m m

Rn

Rn8m

H

H eddy correlation

LE

LE eddy correlation

G

G residual

0.98 0.81 0.90 0.83

1.00 0.70 1.04 0.96

-4.1Wm -2 10.5 W m -2 5.1 W m-2 - 10.4 W m -2

Bare soil surface temperature

T~oil 0.5 cm

0.92

0.93

1.4°C

2.5°C

Tsoil 2 cm Tsoil 9 cm Tr, oi I 14 cm T~oil 28 cm TsoiI 51 cm

T~oil 2 cm T~oil 9 cm T~oil 14 cm Tsoil 28 cm T~oiI 51 cm

0.82 0.91 0.90 0.77 0.79

1.07 0.91 0.91 0.93 0.88

- 3.5°C 1.6°C 1.9°C 1.3°C 3.0°C

2.9°C 1.9°C 1.6°C 1.7°C 1.2°C

Rn

H

LE

G

126 122

36 36

81 89

9 3

RMSE

0.43 m m 31.7 29.3 34.5 39.3

Wm 2 W m 2 W m-2 W m -2

(b)

Observed Calculated

non-linearly on the bare soil surface temperature and the leaf temperature. The first one was compared with soil temperatures at 0.5 cm depth. Normally, the diurnal cycle amplitude of surface temperature should be larger than that at 0.5 cm. This is the case for the wet period, but not for the dry one (not shown). On the other hand, at 2 cm, the model predicts larger amplitudes than observed. This is perhaps linked with the assumption of a constant thermal conductivity for the 0 - 2 - c m layer. Nevertheless, soil temperature is relatively well predicted at deeper levels (Table 6 and Fig. 7) with a RMSE < 1.9°C, for both low frequencies (progressive increase of the deep temperature during the dry period for instance) and high frequencies represented by the diurnal cycle of temperatures. Given the uncertainty of the depth of the sensors (which not always corresponds to the depth of the nearest node chosen for comparison), results can be judged as satisfactory. Furthermore, modelling is supposed to be representative for the whole field, which is not the case for a single measurement point. Fig. 8 provides examples of modelled and observed soil moisture profiles. As for soil temperature, a single tube does not represent the whole field. Hence, the comparison was performed with the mean and standard deviation of the 11 tubes at each depth. Model prediction is situated within the _+1 standard deviation interval. After a rainfall event, water infiltrates quickly towards deeper layers and the surface dries out quickly. In the latter case, vapour flow is important and temperature gradients also influence moisture transfer (Boulet et al., 1997). The vertical structure of the moisture profile, especially the

932

L Braud et aL/Journal of Hydrology 188-189 (1997) 912-945

lower values of the deepest horizon are well described with the model because the model is able to take into account the vertical stratification of the soil associated with different soil characteristics. A simulation conducted with an assumed uniform soil, characterized with the soil surface properties, showed that the stratification had little effect on ETR. On the other hand, deep drainage was multiplied by a factor of 10, leading to a very dry moisture profile at the end of the simulation (completely out of the 1 standard deviation interval). This shows the importance of representing correctly the vertical structure of the soil in the model. Nevertheless, it is obvious that, when a rainfall event occurs, too much water is infiltrated (DOY 246, 258) and the drying period begins with a water storage exceeding the observed one (DOY 260). At the end of the dry season, the calculated profile is close to observation (DOY 286). Note that in the calibration phase, with an initialization of soil moisture on DOY 258 at 0 GMT, the moisture profiles were fitting mean observed ones quite well (Braud et al., 1994a). This shows that, in the validation phase, too much water has been infiltrated during the previous rainfall events. For the deepest layer (2.5-4 m), only one measurement depth was available. Thus, calibration of its saturated hydraulic conductivity was difficult and deep drainage calculated with the model has a large uncertainty. 5.2. D i s c u s s i o n

One of the aims of the study was to assess the capability of SiSPAT to reproduce, for variables of a different nature, and for a long period but at a small time step (20 min), the main features of observed data. Given the complexity of the land surface, the intensity of rainfall events and the length of the drying period, the test was very severe for the model. The model was able to reproduce quite well the evapotranspiration for the whole period. Generally, the diurnal cycle of the energy budget was also well predicted. However, after a major rainfall event, the latent heat flux was overestimated. This problem shows the limits of a 1D modelling strategy when horizontal heterogeneity greatly influences the runoffinfiltration process. Gaze et al. (1997) reported little runoff at the field scale, for a sparse millet crop on a similar soil. Under their observation, lateral redistribution of rainfall occurred. It was found that the ratio of infiltrated versus precipitated rainfall could range from 0.3 to 2.5, leading to a large variability of observed humidity profiles for the individual tubes. This large horizontal variability of soil moisture (which was also obvious from the large spatial standard deviation of neutron probe measurements used in this study) was not taken into account in the 1D modelling but greatly influences runoff and bare soil evaporation. It must be mentioned, however, that, despite this bias, the total ETR was well predicted over the whole simulation period. Several studies have shown that the spatial variability of surface properties has an influence on predicted surface fluxes (Sherma and Luxmore, 1979; Freeze, 1980; Loague, 1988; Mihailovic et al., 1992; Bonan et al., 1993; Braud et al., 1995a among others). Famiglietti and Wood (1992) have shown that at scales smaller than what they called a representative elementary area (REA) ( 1 - 2 km for evapotranspiration), the spatial variability of soil properties must be taken into account explicitly, if non-biased computation of surface fluxes as compared with the use of a mean parameter is wanted. To go further in the present study and try to address the problem of variability of surface properties at the field

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

(a)

933

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scale, several strategies could be used: distributed modelling using distributed parameters (Famiglietti and Wood, 1992) or a stochastic approach using statistical distributions of the parameters (Avissar, 1992; Famiglietti and Wood, 1994; Braud et al., 1995a) and compared. This work was beyond the scope of this paper. One of the objectives was to define to what extent I D modelling of such a complex environment could provide reasonable results. Another point worth discussing is how the model handles the progressive increase of plant water stress and

I. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

934

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38 36 34 32 30 28 26 Fig. 7. Continued. behaviour, reported by Lynn and Carlson (1990) is well captured by SiSPAT. In the case of water stress, the calculated stomatal resistance increases around midday and decreases at the end of the afternoon. This shape is related to the diurnal cycle of the calculated leaf water potential (Fig. 9), which reaches values lower than the critical value (for instance -180 m at midday for DOY 280). In this case, the water stress function, given by Eq. (4) increases very rapidly (5 for DOY 280). fhe(hf) = 1 +

(4)

When the plant is not stressed (DOY 254), the leaf water potential remains higher than the critical value (-80 m for DOY 254) and the stress function is close to 1. In this case, a Ushape is obtained for the stomatal resistance. Measured values of stomatal resistance show the same trends: U-shape when no water stress occurs, increase around midday and decrease in the afternoon at least for herb when the soil has dried out (DOY 280). Nevertheless, the values do not exceed 600 s m -I and the value of 1200 s m -I predicted by the

1. Braud et al./Journal @Hydrology 188-189 (1997) 912-945

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Fig. 8. Comparison of observed mean (*) I standard deviation (+) soil water content profiles with predicted profiles without crust (full line) and with a crust o f 2 cm at the surface with K~,(crust) = 2.67 x 10 -6 m s -I (dotted line)• Rainfall occurred between D O Y 241 and 246 (63.6 mm), 246 and 258 (55.0 mm), 258 and 260 (22.1 mm).

936

L Braud et al./Journal of Hydrology 188-189 (1997) 912-945

model has not been observed. During the calibration phase of the model, these large values were not obtained, probably because it was only the beginning of the elongated dry period. The calibrated set of three plant parameters was perhaps not 'optimum' for the whole simulation period. Note also that with a more simple scheme using a stress function depending on the mean water content of the soil column (ISBA, Noilhan and Planton, 1989), the right latent heat flux was obtained on DOY 280 with a U-shape for the stomatal resistance (Braud et al., 1994b). This shows that some parameters are really linked to the model structure and can hardly be compared with observation. As a whole, model results are satisfactory. Of course, a calibration phase was needed, but this is in general the case, even for more simple schemes (see Goutorbe et al., 1997, for instance), because not all of the parameters are measured, or they cannot be directly related to observations. In the present study, independence between calibration and validation was respected. Indeed, the calibration was performed on a sub-period of 2 weeks (DOY 258271), including the last rainfall event. Then the validation was performed on the whole period, by initializing the moisture and temperature profiles on DOY 239. Then, the model was let to predict surface fluxes, soil moisture and temperature profiles, by using the atmospheric forcing and the same parameters as those of the calibration phase. The outputs were compared with observations afterwards. It was therefore a good result to see that (i) the model was working quite well in the rainy period (the rainfall event used for the calibration was less strong that the others) and (ii) during the elongated dry period, the model well captured the progressive decrease in evapotranspiration, associated with increased water stress of the vegetation (during the calibration, water supply was still sufficient). Of course, if values of some calibrated parameters are modified, predicted values are different. For instance, by changing the calibrated saturated hydraulic conductivities of deeper horizons, deep drainage is modified, but surface fluxes, and especially evapotranspiration, are not modified, because they are mainly controlled by the surface horizon. No reliable estimate of deep drainage was available to evaluate model prediction. For plant transpiration, maximum root length density (Mrd) and total plant resistance (R p) are sensitive parameters (which are closely related). I f M r d is divided (resp. multiplied) by 2, total evapotranspiration is equal to 143 (resp. 188) mm, leading to a change o f - 1 4 (resp. +12) % as compared with the reference value of 168 mm. The bare soil component is not affected, and only plant transpiration is modified, but only in the dry period. Indeed, in the wet period, water supply is sufficient and plant transpiration is controlled by atmospheric conditions. However, with these values, latent heat flux is underestimated (resp. overestimated) in the dry period for both the calibration and validation simulations. If R p is divided (resp. multiplied) by 10, total ETR is equal to 199 (resp. 88) mm, leading to a change of +18 (resp. --48) % in total ETR. In the first case, no water stress is observed, which is obviously not in agreement with observation, and in the second case, water stress occurs even in the wet period, which is also not consistent with the observations of stomatal resistance available. Thus, the set of calibrated (Mrd, R p) values is the one which better reproduces the fluxes. For the predicted stomatal resistance at the end of the dry period, uncertainty remains on a possible deficiency of the model, which could predict too high values. Unfortunately, no detailed measure of the diurnal cycle of stomatal resistance was available for the studied field, during large water stress conditions. Thus, definite conclusions cannot be drawn on that point.

(a)

938

1. Braud et al./Journal of Hydrology 188-189 (1997) 912-945

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L Brand et al./Journal of Hydrology 188-189 (1997) 912-945

939

Models which, like SiSPAT, use equations derived from the Richards equation into the soil, are mainly sensitive to the specification of the soil retention curves. For instance, Haverkamp et al. (1996) have shown that cumulative infiltration was modified by fitting either the Brooks and Corey (1964) or the Van Genuchten (1980) model on the same experimental data. This result would also hold for evapotranspiration. Experimental estimation of retention curves is difficult, especially in dry conditions because (i) in the field, tensiometers are rapidly out of range when the soil dries out, (ii) calibration of neutron probes is not easy when the soil is heterogeneous, (iii) if measurements are done on soil samples in the laboratory to explore the dry part of the retention curve, they are not always consistent with field data under wetter conditions (appearance of discontinuities). Thus, a large degree of uncertainty is expected for model outputs. For instance when the parameter hg and q of the Van Genuchten model for the first horizon are equal to -0.21 m and 2.8 (-0.308 and 3.54 for the reference value), total evapotranspiration is equal to 198 mm (with 90 mm of bare soil evaporation and 108 mm of plant transpiration). Thus as compared with figures in Table 4, bare soil evaporation is substantially increased. Latent heat flux is fairly well predicted in the dry period, but largely overestimated in the wet period. The links between retention curve, surface humidity and transpiration and bare soil evaporation is now under study, in connection with microwave measurements.

6. Sensitivity of the mass balance to the existence of a surface crust

In this section, it was not attempted to model the horizontal heterogeneity of the surface with crusted and non-crusted zones but to assess the sensitivity of the runoff-infiltration process to the presence of a crust in the vertical structure of the soil. Thus, simulations were performed by adding an horizon 2 cm thick at the surface, with soil properties for the crust estimated using the method described in Vandervaere et al. (1997). The suction curve of the crust is the same as the underlying soil. Only the hydraulic conductivity curve is modified. For the fallow savannah crust, parameter t~ of the Gardner model (eqn (2)) was found to be equal to 20 and the saturated hydraulic conductivity estimated at 1.95 x 10 -6 m s -I with a confidence interval 4 x 10 -7 < K~at(CruSt) < 4.9 x 10-6 m s -j (J.P. Vandervaere, personal communication, 1995). The saturated conductivity of the underlying soil is thus 11 to 140 times higher than that of the crust. Three values of K.,at were chosen in the confidence interval. The corresponding water balances are given in Table 7. When the crust is added, runoff is generated at the field scale whatever the value of K~t(crust). A ratio of 10 between the conductivities of the underlying soil and the crust is enough to generate runoff. When the saturated hydraulic conductivity of the crust decreases, runoff increases as does the change in water storage. For the lowest value of the confidence

Fig. 9. (Top) Observed (full line) and calculated (dotted line) latent heat flux. (Middle) Calculated stomatal resistance. Black dots and stars represent measurementsof stomatal resistancesfor guiera and herb, respectively, performed on the West Central site those particular days (N.P. Hanan, HAPEXdata base). (Bottom)Calculated leaf water potential. (a) DOY 254 and (b) DOY 280.

940

I. Braud et aL/Journal of Hydrology 188-189 (1997) 912-945

Table 7 Mass balance for the non-crusted soil a n d for soils including a crust o f 2 c m with different values o f the saturated hydraulic conductivity of the crust. All quantities are in m m

Rainfall Evapotranspiration Soil evaporation Transpiration Deep d r a i n a g e Runoff C h a n g e in water storage ( 0 - 4 m)

Non-crusted soil

K~t(crust) = 5 × 10 -7 m s i

K,~(crust) = 1.95 x 10 -6 m s -I

K~t(crust) = 2.67 × 10 -6 m s

144.4 168.8 40.8 128.0 18.0 0.0 - 42.4

144.4 128.6 11.1 117.2 11.4 130.6 - 126.2

14 4 . 4 153.0 23.6 129.4 12.1 56.1 - 76.8

144.4 156.7 26.0 130.7 12.2 45.8 - 70.3

interval, almost all rainfall is lost through runoff. Transpiration and deep drainage are little affected by the crust, and total evapotranspiration is mainly affected through its bare soil component, leading to too low values of the latent heat flux after rainfall contrary to the non-crusted case (not shown). If we look at the soil moisture profile when the crust is included (dotted line on Fig. 8 for K~at(CruSt) = 2.67 x 10 -6 m s-I), they are closer to the observations than without crust in the wet period. The drying phase begins with the 'right' soil moisture content (DOY 260) but at the end of the drying period soil moisture content is too low. With the inclusion of the crust, water content of the deepest layer seems to be better predicted. This sensitivity study shows that, locally, the presence of a crust enables the generation of runoff. Nevertheless, at the field scale, no runoff was observed. However, moisture profiles are better predicted than with the non-crusted simulation. In the latter case, the predicted field scale runoff was consistent with observation, but the infiltration process was poorly simulated (Section 5.2). Thus, neither the simulation without crust, nor the inclusion of a crust (horizontally homogeneous) was able to reproduce properly the runoff-infiltration process at the field scale. As the real surface is made of a composite of crusted and non-crusted areas, a stochastic or distributed modelling strategy rather than the ID modelling strategy would be needed. But this was beyond the scope of this paper. 7. Conclusions A 1D mechanistic model, describing coupled heat and mass transfer in the soil-plantatmosphere continuum was applied to a fallow savannah site of the HAPEX-Sahel experiment. The most complete data set was gathered from different sources. After a calibration of missing parameters, performed independently on a sub-period of 2 weeks, the outputs of the model were compared with observations at a time step of 20 min over 54 days. The modelling exercise showed the internal consistency of the observed data. Indeed, once calibrated, the model captures the main features of the diurnal cycles of surface fluxes, net radiation and soil temperature, except the day just following a rainfall event. In the latter case, the horizontal heterogeneity of the surface, not taken into account in the 1D modelling, greatly influences the runoff-infiltration-evaporation process. Given the shortness of

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the rainfall events (a few hours) and the quick vertical redistribution of moisture within the sandy soil profile, the model recovers rapidly. The model describes the soil moisture during the drying phase quite well. In addition, because it takes into account the vertical structure of the soil, the discontinuities in the observed profiles are well reproduced. During a rainfall event, the model has more problems in matching the observed mean water content profiles. Indeed, the horizontal heterogeneity of the surface associated with crusted and non-crusted areas leads to a large spatial variability of infiltration and soil moisture. The sensitivity study conducted with the inclusion of a crust in the vertical structure of the soil showed that the amount of runoff and infiltration was very sensitive to the value of the saturated hydraulic conductivity of the surface crust. This horizontal heterogeneity was not taken into account in the 1D modelling strategy, showing the limits of the deterministic approach in modelling water transport in such a complex environment. A further research direction could be to try and see if either a distributed or a stochastic approach, using for instance the surface saturated hydraulic conductivity as a random parameter, could help improve this problem. Nevertheless, except for just after a rainfall event, model results are quite satisfactory. This provides some degree of confidence in the capability of the model to predict heat and mass transfer in the soil-plant-atmosphere continuum. However, complete validation of the model could not be achieved. The data set missed observations on the partition of fluxes between vegetation and bare soil and this essential part of the model could not be tested. Observations of diurnal cycles of stomatal resistances would also be needed both under wet and dry conditions in order to validate the stomatal resistance model of SiSPAT. The sensitivity of model results to the specification of retention curves should also be investigated further, given the experimental uncertainty of those curves, and the large response of the model to changes in their values. Then, the model could be used as a 'reference' in order to test the pertinence of simplified parameterization because it includes the main physical processes involved and enables the definition of the most important ones in a given environment and climate. Such a study can help to understand the interactions between vegetation, evapotranspiration and surface humidity and can thus provide useful information for microwave retrieval. Indirectly, the model can also be used to parameterize soil surface resistance as function of moisture content or soil suction. Indeed, the model explicitly calculates vapour transport between the 'evaporation front' and the surface, without any assumption about any soil resistance. The use of this type of deterministic modelling at larger scale in a distributed way is questionable, given the quantity of information needed. However, if a stochastic procedure is adopted, it can provide useful information on the variables and the spatial variability of the parameter which must be implemented into simplified surface schemes.

Acknowledgements N. Hanan and J.L. Roujean are greatly acknowledged for providing some of the data used in this study and for useful discussions. This work was funded by the French Institut des Sciences de l'Univers (PATOM contract). Anonymous reviewers helped to improve the quality of this paper. M. Vanclooster carefully read the manuscript.

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Appendix A. Short description of the SiSPAT model

Appendix A.1. Main equations solved by SiSPAT Model compartment

Equations

Atmosphere S o i l - p l a n t - a t m o s p h e r e interface

Forcing T=, q~, U,, RG, RA, P

Rnv = Hv +LvEv Rns = Hs + I-.,,Eg + G

Outputs of the compartment

T=~, ql, T,, q**, Ua~, T~

H=Hg+H~ E=Eg+Ev Eg +Qmg-Pgpw =O Upper boundary condition: h t, Ti

Soil

hj, T j . j = l . . . . . N

C a h _ i, I n ;~h~r~ aT v ~ _ S h ~ - - ~ L I m h ~= TLImT ~. --~x)

L o w e r boundary condition: T prescribed, h prescribed or flux prescribed or gravitational flux T r _ Z j , hj>hf h/-.h.f-:, -~. -R.~+ Rrj

S o i l - p l a n t interface

hf, Sj, j = 1..... N

All symbols are defined in Table 1.

Appendix A.2. Expression of the fluxes at the soil-plant-atmosphere interface Radiative transfer a i,

ea~ =eGO - ~v)of~1 + %0 -of)~ 1 -- ° f OtsO~vJ

RA [ ,n, ,,4, ~ v ~ o t ~ - ~ ) + ( I - * f X l - ~ ) ~ , ( ~ - a ~ ) ~ - °f [ e~ fft,,'! - oL~) + t -o,(t -~,Xl - ~ ) )

Rnv = R G , + R A y RGg = RG(I-alXI-of) I -°racav

RA s = O -oO~(RA -~C)-~I~,*~*(C - C) I -af[i -=~XI -el)

Rns = RGs + RA ~ °e = 1 - e x p ( - 0 . 4 LAI) T ~ = [(RA - RAv - RA s)/o] °'~5 Turbulent transfer b H 8 = - O,cp(T=v - TI)IRsH H~ = - p=cp(Ta~ - T~)IR~H H = - p =cp(Ta - T~)/R =n Ev =E.,,, + Tr= -Pa(qa., -q~at(T.,))OS/R w + ( l - ~ ) / ( R v v + Rsto)) E = - Pa(qa - qav)lRav R sto = (R stmiJP.o(RG)fhf(hf) fvm(VPD))/LAI

f a c ( N o i l h a n a n d P l a n t o n , 1 9 8 9 ) ; f h f ( C h o u d h u r y a n d l d s o , 1985)

a cog is a function of surface soil moisture and position of solar angle (Dantas-Antonino, 1992). b Aerodynamic resistances are taken from Taconet et al. (1986) and Brand et al. (1995b). All the symbols are defined in Table I.

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Appendix A.3. Coefficients of the soil module Storage coefficients Ch = (~h) T

CT Transport coefficients Dmh = K + Dvh/p~ D mT= D ~T/P,~ Dch = L,.Dvh Dcv = X + LvD~T

h(0): Van Genuchten (1980) (De Vries, 1975) K(0): Brooks and Corey (1964) Dvh, DvT: De Vries (1975) X: De Vries (1963)

All symbols are defined in Table 1.

As compared with the original paper by Brand et al. (1995b), the root extraction module has been modified and replaced by the Federer (1979) model. For each soil layer, a soilroot and a root-leaf resistance are put in series (Fig. 1(a)). The moisture extraction in layer j is proportional to the water potential difference between the leaf (hf) and the soil h i. The leaf water potential is calculated by assuming steady state at each time step and that total moisture extraction is equal to the transpiration calculated from the atmospheric conditions. The leaf water potential controls the water stress function of the stomatal resistance. A stress function of the VPD has been added in this study as deduced from measurements on a fallow savannah of the West Central site (B6gu6 et al., 1994): fVPD(VPD)= 1 +gVPD with g = 2.4 x 10 - 4 P a - t

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