'% Journal of

I Hydrology k ELSEVIER Journal of Hydrology 188- I89 í 1997) 9 12-94.5

1 1

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. Vandervaerea, M. J Vauclina J

1 Fonds [ascumentalre s 11 (Section 4). Then the validation (Section 5) was done by running the model for 54 days ( OY 239-292), with the observed atmospheric forcing and the evolution of the leaf area 1

010021 628

"LTHE (CNRS UMR 5564 INPG, UJF). BP 53. 38041 Grenoble Cédex 9. France 'Méteo-Fro,ice/CNRM/4M, 42 Avenire Coriolis. 31057 Toirloine Cérlex, Fronce

'ORSTOM, Laboratoire d'Hydrologie. BP 5045, 34032 Montpellier Cédex. Fronce

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 was used, at the field scale, to calibrate and validate the SiSPAT (simple soil plant atmosphere transfer) model, a ID 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 1 D 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 Huxes. soil temperature and soil moisture for the intense rainfall events and for an elongated dry period. Never- theless, 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 intil- tration). When a c y s t 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 donsequentlv on the bare soil

913

scale, no runoff was generally observed. Lateral redistribution of water between crusted a n d non- crusted zones was observed in the plot. However, this cannot be taken into account with the pre- sented ID deterministic modelling. Hence further model development is needed to yield a better representation of soil water Huxes at the field scale.

,$- .E-

Fr f

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 para- meterization 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 ID 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 (Braud et al., 1995b), which is a 1D mechanistic and deterministic model describing coupled heat and mass transfer in the soil-plant- atmosphere 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 foi- lowed 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 ID 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 valida- tion 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 con-

.

9 I4 I. B r a d et al./Joirmal 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 min 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. Schädler 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 rain- fall. 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. I(a)). The upper boundary conditions are provided by the solution of the soil-plant- atmosphere interface (schematized in Fig. l(b)), which provides the surface soil heat and mass fluxes and the surface mauic potential h I and temperature TI. 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 (1 978), bare soil and vegetation are considered separately in a two-source model (Shuttleworth and Wallace, 1985; Taconet et al., 1986) (Fig. I(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.l). Leaf temperature T,, canopy temperature Ta,, canopy specific humidity qav, soil surface temperature TI and surface matric potential hl 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 hf (Section A.l) 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 uf (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.

i '

1. Bniird et nl./Jounial of Hydrology 188-189 (19971 912-945 915

Table I List of symbols

11 , H. H, . H ,

RA. RA,. RA,

RG. RG,. R G , Ri] . Riz ?, RIZ,

si

Capillary capacity (m-l) Specifc heat at constant pressure (J kg-' K-l) Volumetric heat capacity (J mV3 K-') Displacement height (m) Isothermal vapour conductivity (W m-') Apparent thermal conductivity (W m-' K-') Isothermal moisture conductivity (m s-') Thermal vapour diffusivity (m' s-' K-I) Isothermal vapour diffusivity (kg m-' s-I) Vapour diffusivity associated with temperature gradients (kg m-' s-' K-') Vapour pressure at level (Pa) Saturated vapour pressure at temperature 7' (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-') Surface soil heat flux (W m-') 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-') Soil hydraulic conductivity (m s-') 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-' soil) Precipitation above the canopy (m s-') Precipitation reaching the ground or throughfall (m s-I) Exponent in the Van Genuchten formula for the suction curve Specific humidity of air at level ra and z.,., respectively (kg kg-') Darcian non-isothermal flow crossing the soil surface (kg m-'s-') Aerodynamic resistance between level ;a and rar for momentum. heat and vapour. respectively (s m-9 Aerodynamic resistance between the soil surface and level ::,, for momentum. heat and vapour, respectiveiy (s r ñ ' ) T O ~ ~ I plant resistance (s m-' root) Root resistance of layer j (s) Soil resistance of layer j (s) Maximum stomatal resistance (s m-') Minimal stomatal resistance (s m-0 Stomatal resistance (s m? Aerodynamic resistance between the canopy and level :>, for momentum. heat and vapour. respectively (s in-') Incoming long-wave radiation, long-wave radiation for the bare soil and canopy, respec- tively (W m-') Incoming solar radiation. solar radiation for the bare soil and canopy, respectively (W m-') Total net radiation. net radiation for the hare soil and canopy. respectively I W m-') Plant root uptake of layer j (kg m-"s'')

o I h

Table I Continued

1. Bruird el d./J~iitriid ($Hyt/roh,~y 188-189 ( 1997) 912-945

Time (s) Soil temperature (K) Soil temperature of layerj ( K ) Air temperature at level :,, and zd,. respectively (K) Radiative surface temperature (K) Leaf temperature f K) Wind speed at level :,, and ;i,,, respectively (m s-0 c,,,,(TJ) - m = vapour pressure deficit (Pa) Vertical coordinate (m) Height of the atmosphere reference level and canopy artificial leve Roughness length for momentum and heat Mean canopy height (m) Scale parameter in the Gardner hydraulic conductivity model (m-') Bare soil and vegetation albedo, respectively Exponent in the Brooks and Corey model for hydraulic conductivity Wet Fraction of the canopy Bare soil and vegetation emissivity, respectively Thermal conductivity ( W m-' K-') Volumetric water content (m' m-'1 Residual volumetric water content (m' m") Saturated volumetric water content (m' m") Air density (kg m-.') Liquid water density (kg m-.') Stephan-Boltzmann constant (5.67 X IO-' W m-' KA) Shielding factor

3. Description of field data

3. I . Atmospheric forcing niid 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 Banizoum- bou (13"3 1'97"N, 2O39'62"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 from the Southern site. Rainfall was measured locally. Two teams collected micro- meteorological data on this site using the Bowen ratio and eddy correlation method (ORSTOM and CNRM, respectively). For the Bowen ratio method, net radiation was measured at 11.5 m above the soil surface and the soil heat flux was measured with Thornthwaite plates situated at 2 cm into the soil (mean of three plates). For the eddy correlation method, net radiation was taken at 8 m, sensible and latent heat fluxes were estimated using eddy correlation and soil heat flux was obtained from energy budget considerations. All data were averaged over 20-min time intervals. The forcing was linearly interpolated between the observations to fit the time step of the model which varies between 50 and 100 s if it is not raining. In the case of rainfall, the time step value is around 1 s. Such a small value is needed to correctly reproduce the infiltration front and

. I

5

f--

m e?. er 1 PI

M cn

W M W - k

c F

N- e w Q

91s 1. Brarrd et al./Joiirnal of Hydrology 188-189 (1997) 912-945

ensure conservation of the water balance as shown by Haverkamp et al. (1977). A com- parison 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 influ- ences 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 Iatent 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 experi- mental 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 min. 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 O 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 con- ductivity 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, 19951, 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. I . Schematic description of the SiSPAT model. (a) The soil module: the total soil depth is divided into horizons, each horizon being discretized into layers. The temperature and matric potential are calculated at the nodes and the fluxes at the interfaces between layers. The resistance scheme shows the root extraction module. (b) The soil-plant-atmosphere interface sub-model.

~~

I. Brniid et al./Jorrrtial of Hydrology 188-189 (1997) 912-945 919

w -

m - I - :

- I I 4 - œ - l - - Z I w - u - + " a - < - w :

- _

z : z - < - > I 4 . w - 3 : o . _ I -

-I: 4 . I L -

-

-

h

W Q

€

W c3 4 f- z w U o: W a c- O O e:

o: 4 w > u

6. O >. d a

XBCINI V 3 t l V dV3'7

Y20 1. Braird et crl./Jouriial q" Hydrolqp?. 188-189 (1997) 912-945

. in the model by introducing a shielding factor (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).

af=l-exp(-O.S(LAI+O.l)) 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 ma3 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.

2 -. G I

39 e!

I I - I 4. Choice of the parameters and calibration I I 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).

r - - p' - 3

I c - - p'

I ' c .1

-. 3 4.1. Soil parameters

I V T < 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 in Table 1):

I I (Van Genuchten, 1980) with m = I - 2/q (Burdine, 1953).

K(@ = %it les,,)^ (2b)

K(0) = Ky,, exp(ah) (2c)

(Brooks and Corey, 1964)

(Gardner, 1958) Parameters of the retention and hydraulic conductivity curves, fitted on surface (0-

1 O cm) data, were extended for the complete first horizon (0-20 cm) because no data was available between 10 and 20 cm. They are given in Table 2. Note that for the hydraulic

I 2

923- I. Braud et al./Joiirnal of Hydro1og.v 188-189 (1997) 912-945

- conductivity, two different Gardner models were fitted for h > - O. 1 15 m of water. This is related to the rapid increase of infiltration near saturation, when macropore Row becomes important. Measurements were only representative of near saturation conditions (h > - O. 1 15 m). In a first attempt, Gardner's model was extrapolated to dry condition, but this led to a very rapid decrease in conductivity and unrealistically low values. In a second attempt, for h < - 0.1 15 m, a Brooks and Corey model was used. The shape parameter 0 was deduced from particle size distribution at the surface using the fractal approach of Fuentes et al. (1996a, b) and the saturated hydraulic conductivity was calculated to get a continuous function over the whole matric potential range. For deeper horizons, only dry bulk density and particle size distribution profiles were available. The saturated water content O,,, was calculated as 90% of porosity. The fractal approach mentioned above was used to derive the shape parameters of the suction curves q and hydraulic conductivity curves p. This method does not produce reliable values of the scale parameters h, and K,,,. The h, values were chosen to ensure continuity of the matric potential profile at the interface between horizons. The saturated hydraulic conductivities were fitted on the rainfall event of the calibration period in order to reproduce the observed moisture profiles (Braud et al., 1994a) (Table 2).

The model also needs the specification of the thermal conductivity. The De Vries (1963) model is implemented into the model but the prediction of the soil temperature series was poor. Furthermore, from an attempt to derive the thermal diffusivity from these series using the method of Horton and Wierenga (1983), it was found that the 0-2-cm layer had a lower thermal conductivity than deeper levels. By fitting two values for the 0-2-cm and 2-cm-4-m depths, soil temperature series were better predicted than with the De Vries

.

I. Braid et nl./Journal of Hydrology 158-159 (1997) 912-945 93-3

(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.

Table 3 Surface and plant parameters used in the model

Parameters Values Sources

Bare soil albedo

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

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

CY: = 0.4( 1 - O h ) + 0.08Oln corrected for the sun zenithal position

d = 0.38 m zu,,, = 0.07 m :enJ:o~ =. 100" eg = 0.97 CY \. = 0.2

E, = 0.96 /ifc = - 140 m'l R,,,,,, = 80 s m" R, = 6.5 x IOIL s m-' root" Mrd= 17900 m root m-' soilJ

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)

(GSTS Strasbourg in Monteny, 1993) (J.L. Roujean. personal communication. 1994) (GSTS Strasbourg in Monteny, 1993)

(Hanan and Prince. 1997)

Values were calibrated. This value corresponds to the maximum value of the profile shown in Fig. ?(b). When the root density profile is

integrated over depth. the mean root density associated is 6950 m root m-' soil.

4.2. Su$ace 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 measure- ments 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,, which controls water transfer between the roots and the leaf, appears to be a very sensitive parameter. It greatly influ- ences 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

1;:

(Vari(mod)-Vari(obs))' 1 (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 without 'Observations' crust at the surface

Rainfall 14.4'' I U.4

Transpiration 128.0 Bare soil evaporation 40.8

Runoff 0.0 0.0 Change in water storage - 42.4 - 25.0

Total evapotranspiration 168.8 - (138.0) ( 1 3 1 .O)

- Deep drainage 18.0 Not estimated

a Input for the model.

924 I. Broird et uL/Joirriral oj' Hydrology 185-189 (1997) 912-945

140

40 i .._.._..-..-..-..-.. -..- ..-..-.. -..-..-..-..-..-..-.._ 20

HOURS SINCE AUGUST 26 1992 AT O GMT

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 pre- dicted 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 daily 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 tran- spiration 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

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

DOY Observed daily Calculated daily Calculated Calculated bare ETR ETR transpiration bo11 evaporation

Case I 244 5 .o 4.4 1.3 3.1 245 4. I 3.8 1.0 I .8 246 2.4 2.2 I .? 0.9

249 3. I 2.7 2.5 0.2

247 3.6 3.7- 2.6 0.6 248 2.7 2.2 I .9 0.3

Total 20.9 18.5 11.6 6.9

Cose 2

252 3.6 4.1 '5 I .6

254 3.6 3.2 2.5 0.4

255 Total 19.4 19.2 12.5 6.4

Cose 3

25 I 5.1 4.7 I .5 3.2

253 3.7 3.6 3.5 0.8

3.4 3.6 - :l .- 0.4

261 (3) 3.8 4. I 2.9 I .2 266 (5) 3.1 5 3 ~ :7 .- o. 1 273 ( 15) 2.8 2.9 2.9 0.0 7-76 (IS) 2.3 2.7 1.7 0.0 280 (22) 2.1 2.5 1.5 0.0

1.8 . 2.7- -1- 3' 0.0 286 (28)

Case I , rainfall of 34 mm in the night between DOY 242 and 213: Case 2. rainfall of 26.5 mm in the night between DOY 250 and 25 I; 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 gen- erally 20 W m-' 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 I. Braud et al./Joumal of Hydrology 188-189 (1997) 912-945

5.5b t

5 . 0 L - 4 4.5: v

E 4.0:

3.5:

2 3.0:

e W

a w 2.5: i. 4

u $ 1.5: u

2 2.0:

1 .O;

. 5 i , I , , , , !

I I; :0 , : 0 l 15 'i :0l '3 : 5l '4 :5! '5 . o 5.58&

OBSERVED DAILY ETR (MM) Fig. 4. Scatterogram of modelled versus observed daily evapotranspiration (ETR).

locally, but a few kilometres away, whereas net radiation was measured in the field. This implies that the occurrence of clouds is not always synchronized between the measured solar and net radiation. The model prediction of net radiation follows the course of the measured solar radiation, leading to discrepancies with the observed net radiation (Fig. 6) . This problem of synchronization also affects the comparison of calculated and observed soil heat fluxes because the 'measured' values were deduced from the surface energy budget. We can compare the performances of SiSPAT on this data set to what was found in a recent study by Linder et al. (1996) who compared seven surface schemes of various complexity. The comparison was performed under semi-arid conditions, on four data sets gathered on four vegetation types in the framework of the EFEDA (Echieval Field Experiment in a Desertification Threatened Area) 1991 experiment (Bolle et al., 1993). Linder et al. (1996) found that, independently of the complexity of the surface scheme, the minimum achievable error on weekly surface fluxes was 20 W m-l. The RMSE, on a simulation period ranging from 6 days to 1 month, was of the order of 25-35 W m-' for sensible and latent heat fluxes, 10-20 W m-* for net radiation and 25-40 W m-' for soil heat flux. The results obtained in this study are comparable, but were obtained under more severe conditions. The problem of synchronization between input solar and measured net radiation leads to higher RMSE for net radiation and soil heat flux.

921 I. Braud et nl./Jorimal of Hydrology 188-189 (1997) 912-94s

i l EDDY w i u x L A ' r 1 o N (w/eiz)

Fig. 5. Scatterograms of modelled versus observed 7-O-min time interval (a) net radiation, íbl sensible heat tiux. (c) latent heat flux and (d) soil heat flux-turbulent flux.

I - 928 I. Braud et nlJJoumn1 of Hydrology 188-189 (1997) 912-945

- ?I B

U

L L L / I I - I Q 0 0 ' I @ @ 2W0 40O 5630 600

L E E D D Y CORRELATION (CY/M2)

. /I r:

G IIESIDUdL O F T H E ENERGY B U D G E T (W/M2)

Fig. 5. Continued.

i I

! 0 2 4 6 8 10 I 2 1 4 16 18 20 22 26

7001 '

OBSERVATION 680 F

700 i

930 I. Brniid et nl./Joumal of Hydrology 188-189 (1997) 912-945 93 1 I. Brnud et ol./Joirmal of Hydrology 158-159 (19971 912-945

(4

0 2 4 6 8 10 12 1 4 16 18 20 22 24

!

_ _ _ I - -- -1UUC I

0 2 4 6 8 10 12 1 4 76 18 20 22 2 4 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 condi- tions (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 mm 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-? instead of 450 W m-I - difference of 0.8 mm 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

Table 6 (a) Coefticient of determination R'. slope and intercept of the regressions Var(mod) = Slope x Var(obs) + Intercept and RMSE. Except for daily ETR. regressions were performed with 3-O-min time interval data. (b) Comparison of observed (eddy correlation station) and calculated mean values of surface Huxes ( W m-') (a)

~~

~

RiMSE Intercept Model variable Observed variable R' Slope used in regression

Daily ETR

Rn H LE G Bare soil surface temperature

T,,,i 9 cm

T,,,¡ 28 cm T,,,I 5 1 cm

T ~ , I 7- cm

T ~ I 14 cm

Daily ETR from eddy correlation Rn 8 m H eddy correlation LE eddy correlation G residual T,,,¡ 0.5 cm

~

0.80

0.98 0.8 I 0.90 0.83 0.92

0.82 0.9 I 0.90 0.77 0.79

0.84

I .o0 0.70 I .O4 0.96 0.93

I .O7 0.9 I 0.9 I 0.93 0.88

0.62 mm

-1.1 w mW2 10.5 w m-' 5.1 w m-'

- 10.4 W m-' 1.4-2

- 3.5"C I .6"C I .9"C I .3"C 3.0"C

0.43 mm

3 I .7 W m-' 19.3 w m-' 34.5 w m-' 39.3 w m-' 2.5"C

1.9"C I .9"C 1.6"C I .7"C 12°C

~

~

I26 36 81 9 Calculated I12 36 89 3 Observed

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 diumal cycle ampli- tude 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-cm 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 diumal 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. Further- more, 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 t l 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

4

I - 937 I. Braird r i cilJJoirninl r,fHydrology 188-189 (19971 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 O 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. Discussion

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 runoff-

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., 199% 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

I infiltration process. Gaze et al. (1997) reported little runoff at the field scale, for a sparse

20' ' ' a 50 laQ 150 200 250 300 350 400 a50 500 550 600

HOURS SINCE AUGUST 26 1992 AT O GMT FALLOV SAVANNAH E IST CENTRAL SITE

24 26 E 22 t- 2 0 t ' " ' . ' " "

J 650 700 750 800 850 900 950 l00B 1050 -1100 1150 1200 1250

Fig. 7. Examples of time evolution ofsoil temperature for the model (dotted line) and the observation (full line1 at (a) 9 cm and (b) 5 I cm. Noisy observed values are associated with LI rainfall event.

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 com- pared. This work was beyond the scope of this paper. One of the objectives was to define to what extent 1D modelling of .such a complex environment could provide reasonable results.

Another point worth discussing is how the model handles the progresdve increase of plant water stress and the corresponding prediction of transpiration. Fig. 9 compares the observed and predicted latent heat flux for DOY 254 (3 days after a rainfall) and DOY 280 (21 days after the last rainfall). The calculated stomatal resistance (not scaled by LAI) is also plotted together with the measurements taken the same days at the West Central site for guiera and herb in order to compare the orders of magnitude. When soil moisture becomes a limiting factor, a plateau appears around midday for the latent heat flux (DOY 280). This is not the case if the vegetation is well supplied with water (DOY 254). This

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

50

100:

150; I

200!

&50 300;

FlLLOY SAVat4NAH EAST CENTRAL SlTE

40[' " ' " " " i

I T S 5 l / X

i

i

3 8 t

3501 , , , , , , I , , , , , , , , ,

4000 . O 2 .04 06 .O8 . IQ . 12 . 14 .

- HOURS S I ~ C E AUGUST 26 1992 AT o GMT

16

FlLLOU SRVANNAH EAST CENTRAL SITE

38

28 30 i 26

L

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).

(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 U- shape 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). Never- theless, the values do not exceed 600 s m-' and the value of 1200 s m-' predicted by the

~~~~~~ 1

I. Braicd et al./Joiimal of Hvdrology 188-189 (1997) 912-945 935

4000 350L .02 04 06 08 10 12 . I 4 16

02 04 86 08 10 12 1 4 1 6 , .

+ + .

+ +

+

4.

+ + + + L 1

4000 02 04 0b O8 10 I 2 .14 16

00 . O 2 .04 06 .O8 .10 .12 . l 4 16 C ' " " ' ' ~ ' ~ ' i ' I ~ I

+ 100

150 x + . + 2 0 0 +

t +

+ 1.11, , , ': ,I', , ;+:, , ,

300

350

4000 02 .04 .06 .08 .10 .12 .14 . l 6

100

16

00 . 0 2 04 .06 .08 10 . 1 2 ,14 16 [ " , . . . , , . , , , ,

VOLUMETRIC WATER CONTENT (CMJ/CMJ) VOLUMETRIC WATER CONTENT (CMJ/CM3]

Fig. S. Comparison of observed mean ("1 1 standard deviation (+) soil water content profiles with predicted profiles without crust (full line) and with a crust of? cm at the surface with K,,(crust) = 2.67 x 10" m s-' (dotted line). Raintill occurred between DOY 7-11 and 246 (63.6 mm). 246 and 758 (55.0 mm), 7-58 and 260 (77.1 mm).

I 1

7 J U - ~ IZBrmid et al./Jonnml of Hydrology 185-189 (1997) 912-945

-600 r: \500 "'400. + 300 !x 200

C L

O

rA

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 258- 271), 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 conduc- tivities 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,) s e sensitive parameters (which are closely related). If Mrd is divided (resp. multiplied) by 2, total evapotranspiration is equal to 143 (resp. 188) mm, leading to a change of -14 (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. over- estimated) in the dry period for both the calibration and validation simulations. If R , is divided (resp. multiplied) by 10, total ETR is equal to 199 (resp. 88) mm, leading to a change of +I8 (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, RP) 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 sto- matal resistance was available for the studied field, during large water stress conditions. Thus, definite conclusions cannot be drawn on that point.

- -

-

-

1. Brcirid r t d. /Joi i rnd of'Hydrolo,qy ISS- IS9 (1997) 912-945 937

L 1

FALLOY 5AYlNNAH EAST CENTRAL S I T E

300 250 200

Cd 150 z \ 100 ?= 50

a +I -50

n

W

LI

OBSERVATION

-100 -150

0 2 4 6 8 10 12 14 16 18 20 22 24 ' ' ' '

% - - i ' 4 ' 6 ' 8 1 0 ' 1 2 1Q -16 18 2 0 . 2 2 214

FALLOW SIVAHHIH E ~ S T cEnrRiL SITE

DOY 254 -bO -80 -100

.x- - 120 U - , & @ - _ - ---- - - - - - - - --- I& -160 _I/j, -200 , , , , , , , , , , , , , , , , , , 1

-220 -240

0 2 4 6 8 10 12 14 16 18 20 22 24

I '

- 1000 2 \ 800.- m - 6 0 0 - O E; 400-

200:

953 I. B r ä Z Z al./Jorrmal of Hydrology Ï&-ÏS9 (1997) 912-945

-

r

U -59) J

-100 i '

-1 1 0 2 4 6 8 10 12 14 16 18 20 22 24

50 '

1200 400r-- I t ' I

DOY 280

0 ' ' " '

0 2 4 6 8 I 0 12 14 16 18 20 22 24

0 -20

' " 1 '

-40

-100 2 -120

k -160 -180 -200 -220 -2401 , , , , , , , , , , . ,

0 2 4 6 8 10 12 14 16 18 20 22 24

I. Braud et al./Joumal of Hydrology 188-189 (1997) 912-94s 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 esti- mation 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 (4 .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 over- estimated 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 t,o 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 (Y of the Gardner model (eqn (2)) was found to be equal to 20 and the saturated hydraulic conductivity estimated at 1.95 x 10" m s-' with a confidence interval 4 x IO-' < K5e,(crust) < 4.9 x 10" m s-' (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 Ky,, 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 Ksa,(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 valuë 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 measurements of stomatal resistances for guiem and herb, respectively. performed on the West Central site those particular days (N.P. Hanan, HAPEX data base). (Bottom) Calculated leaf water potential. (a) DOY 254 and (b) DOY 250.

t

i 940

Table 7 . Mass balance for the non-crusted soil and for soils includin,o a crust of 2 cm with different values of the saturated hydraulic conductivity OF the crust. All quantities are in mm

l. Brci i~ l et cil./Jo~iirt~cil of Hxclrologx 158-159 (1997) 912-9415

Non-crusted soil K,,,(crust) = K,,,(crust) = K,,,(crust) = . 5 x IO-' m s-' 1.95 x IO" m s-' 2.67 x m s-'

144.4 144.4 144.4 Rainfall 144.4 Evapotranspiration . 168.8 Soil evaporation 40.8 Transpiration 128.0 Deep drainage 18.0 Runoff 0.0 Change in water - 42.4 - 126.2 storage (0-4 m)

128.6 153.0 156.7 11.1 23.6 26.0

1 17.2. 129.4 130.7

130.6 56. I 45.8 11.4 12.1 12.2.

- 76.8 - 70.3

94 I

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 Ksa,(crust) = 2.67 x 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 sensit.ivity 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 run- off-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 ID mechanistic model, describing coupled heat and mass transfer in the soil-plant- atmosphere continuum was applied to a fallow savannah site of the HAPEX-Sahel experi- ment. 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 model- ling, greatly influences the runoff-infiltration-evaporation process. Given the shortness of

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 matchin, 0 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 :tomatal resistances would also be needed both under wet and dry conditions in order to validate the stomatal resistance model of SiSPAT. The sensjtivity 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, evapotranspira- tion 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 I 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.

1 - 942

Appendix A. Short description of the SiSPAT model

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

L

Appendix A.I. Main equations solved by SiSPAT 7

Model compartment Equations Outputs of the compartment

Atmosphere Forcing Ta, qar U,, RG, RA, P

Rn, =H, + L,Es +G H = H, + H,

Soil-plant-atmosphere interface Rn, = H, + / E , Taw 41. T,, qav, U,,, TI

E=E,+E, E, + Qms -P,pw =O

Soil Upper boundary condition: h I, TI hi, Tj, j = 1. . ..., N C,, ?$= $ ( D ~ ~ g + D,,,~,%- K ) - S

PU CT = $( ~~h $ + D ~ T g) Lower boundary condition: T pre- scribed, h prescribed or flux pre- scribed or gravitational flux

/,.-I,,-, h f , Sj, j = I. .... N Tr -

Soil-plant interface Z- &.V>lf R,CR,,. All symbols are defined in Table I.

Appendix A.2. Expression of the Juxes at the soil-plant-atmosphere inter$ace

Rn,=RG,+RA, ur = I - exp(4.4 LAI) T"d = [(RA - RA" - RA ,)/u] Turbulent transferb Hg = - PSp(T.w - TI)/RgH Hv = - PaCp(Tnv - Tv)/RIH H = - P&&Ta - TwYRaH

E = - p ( a q d - qov)/R,v R v o = (R,m,IsRdRG,fhl(~~~)

E, =Ew t Tr= --q, , , (TV))@/Rv~+( 1 -6 ) l (Rvv + R , d I

l fvpdVPD))/LAI fRG (Noilhan and Planton. 1989); fhf (Choudhury and Idso, 1985)

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

i

!

1. Braud et aL/Journal of H.vdrology 188-189 (1997) 912-945

Appendix A.3. Coeficients of the soil module

943

Storage coeflcients

CT

c -($E) h - T h(8): Van Genuchten (1980)

(De Vries, 1975)

Transport coejîcients Dmì, = K + D d P , D n l ~ = D d p ,v

Dch = L,.D,h D c ~ = X + L,D,.T

K(8): Brooks and Corey (1964) D,,, D V ~ : De Vries (1975)

h: De Vries ( 1963)

All symbols are defined in Table I .

As compared with the original paper by Braud et al. (1995b), the root extraction module has been modified and replaced by the Federer (1979) model. For each soil layer, a soil- root and a root-leaf resistance are put in series (Fig. I(a)). The moisture extraction in layer j is proportional to the water potential difference between the leaf (h f ) and the soil hk 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 condi- tions. 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 (Bégué et al., 1994):

fVPD(VPD)= l.+gVPD with g=2.4x Pa-'

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