Influence of soil hydraulic properties on surface fluxes, temperature

and humidity in the one-dimensional SISPAT model.

A. Mangeney1,2, J. Demarty1,2, C. Ottlé1, C. François1,3, and I. Braud4

1Centre d’Etudes Terrestres et Planétaires, 10-12 avenue de l’Europe, 78140 Vélizy, France

2Laboratoire d’Environnement et de Développement, Case 70-71, 2 Place Jussieu, F75251

Paris cedex 05, France

3Laboratoire d’Ecophysiologie végétale, Orsay, France

4Laboratoire d’étude des Transferts en Hydrologie et Environnement, B.P. 53, 38041 Grenoble Cédex

09, France

Received 2000 - Revised - Accepted

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The offset requests should be send to Anne Mangeney

Département de Sismologie, IPGP

Tour 24-25, 4eme et., Case , 4 Place Jussieu,

F75251 Paris cedex 05

Email:anne.mangeney@ccr.jussieu.fr

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Abstract.

Richards’ equation describing water movement in soil requires knowledge of the soil water retention

characteristic, ( )θh , and the hydraulic conductivity function ( )θK . Uncertainties in soil hydraulic

parameters affect the performance of land-surface schemes used in climate and weather prediction. The

SVAT model SISPAT used in this study, solves coupled equations of mass and heat exchanges in the

soil and can deal with several horizons for vertically non-homogeneous soil. We perform here a series of

numerical experiments to assess the sensitivity of the SISPAT model to soil parameters and compare the

results with Alpilles-ReSeDA data set under bare soil conditions. The simulations, using the simplest

version of SISPAT with a single horizon (i. e. homogeneous soil), show that water content and land

surface water and energy fluxes are very sensitive to these parameters when soil humidity is lower than

a certain value of the water content corresponding to approximately 90% of the water content at

saturation. It is found that, in bare soil condition, latent heat flux is the most sensitive factor to soil

hydraulic properties. For wetter soils the energy fluxes are totally independent of the soil water content.

Within the range of studied parameters, SISPAT with a single horizon appears to be unable to reproduce

soil moisture profiles.

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1 Introduction1

One objective of the Alpilles-ReSeDA project was to assess the ability of Soil Vegetation

Atmosphere Transfer (SVAT) models to assimilate remote sensing data, such as radiative surface

temperature or surface moisture content, in order to provide better estimates of surface heat and water

fluxes. In order to achieve such a goal there is a need of SVAT models able to reproduce both surface

fluxes and remote sensing data. Alpilles experiment has provided a comprehensive data set to test

existing schemes describing land surface processes (Braud and Chanzy, 1999). Several SVAT-type

models have been compared in the framework of this experiment (Olioso et al., this issue). Different

scenarios have been defined depending on the set of parameters used in the models. The number of

parameters used in SVAT models obviously depends on the degree of complexity in the description of

heat and mass exchanges at the soil-biosphere-atmosphere interface.

We use here a rather detailed model, SISPAT, solving the complete set of coupled mass and heat

equations, both for vapor and liquid exchanges in the soil-vegetation-atmosphere continuum. This one-

dimensional model, developed by Braud et al. (1995 ) is able to deal with non-homogeneous soil made

of several horizons with different hydraulic and thermal properties. Such a model has the potential to

predict with accuracy soil temperature and humidity profiles close to the soil surface. It has been

developed for field studies and its suitability for larger scales applications has to be assessed. It is more

specifically true if remote sensing data are to be used. Our purpose was to evaluate if a simplified

version, with only one horizon made of an homogeneous soil with mean hydraulic and thermal

properties, is sufficient to simulate soil moisture, temperature and surface fluxes. A major problem is

Correspondance to : A. Mangeney

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then to evaluate the sensitivity of the calculated fluxes, temperature and humidity to soil parameters. In

order to separate the effects linked to vegetation and soil, we apply this model for bare soil conditions

corresponding to the period during two months from November to December 1997 on field 101 of the

Alpilles experiment.

Hydraulic transfer in the soil are generally described by the specification of the relation between soil

matric potential h and hydraulic conductivity K as a function of soil water content θ. The soil matric

potential defines the energy state of water retained in the soil by capillarity and surface adsorption. The

hydraulic conductivity characterizes the ability of the soil to drive water. The retention curve ( )θh and

hydraulic conductivity curve ( )θK can often only be estimated locally from in situ or laboratory data,

using fitting procedures. These two relations introduce two shape parameters linked to soil texture and

three normalization parameters linked to soil structure with a greater spatial variability. We focus here

on these structure parameters. A parametric study has been performed to evaluate the influence of the

parameter’s value on fluxes prediction by comparing the numerical results to the data set obtained

during Alpilles-ReSeDA experiment.

1 Material and methods

1.2 The SISPAT model

SISPAT is a vertical 1D model, forced at a reference level with climatic series of air temperature and

humidity, wind speed, incoming solar and long-wave radiation and rainfall. This model consists of three

components: soil thermal and hydraulic processes, (soil-plant)-atmosphere interface transfer, soil-plant

transfer (root extraction). We will focus here on soil processes. An extensive description of the SISPAT

model can be found in Braud et al. (1995) and Braud (1996). The performance of the model has been

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validated against several data sets (e. g. Braud et al., 1995; 1997; Boulet et al., 1997; Braud, 1998;

Boulet at al., 1999; Gonzalez et al., 1999). The soil module solves the heat and mass equations, both for

vapor and liquid phase following the approach of Philip and De Vries (1957), modified by Milly (1982).

The variables are the temperature T and the soil matric potential of water h. The one-dimensional

equations for vertical motion along z-axis read

( )

−

∂

∂+

∂

∂+

∂

∂=

∂

∂K

z

TmTD

z

hvDK

zt

hhC (1)

∂

∂+

∂

∂

∂

∂=

∂

∂

z

T

z

h

chD

zt

TTC λ (2)

where the storage coefficients are the capillary capacity ThhC

∂

∂=

θ, defined by the retention curve ( )θh

and the volumetric heat capacity T

C calculated with De Vries’s (1975) model by summing the

contribution of organic matter, minerals and water. The apparent thermal conductivity ( )θλ is a function

of the water content given by Laurent (1989). The transport coefficients Di are given in details in

Passerat de Silans et al. (1989) and K is the liquid hydraulic conductivity. These various coefficients are

function of water content and/or temperature. Their specification introduce empirical relations and other

parameters which have not been investigated here. Solution of equations (1) and (2) requires closure

relationships between K, h and θ. These relations will be described in the next section.

The numerical model is based on a classical finite-difference method. We use here N=20 layers of

variable thickness. The numerical domain extend over 1m40 from the surface to deep soil in the vertical

direction. At the upper and lower boundary the resolution is increased. Initial conditions have to be

imposed for temperature and water matric potential profile. Dirichlet condition for h and T at the upper

boundary are provided by the solution of the soil-plant-atmosphere interface. At the lower boundary, a

sinusoidal time-variation of the temperature fitted on soil temperature series measured on the

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meteorological site is prescribed and gravitational flow is imposed, i. e. .0=∂

∂

Nz

h When rainfall

exceeds the infiltration capacity of the soil, saturation of the surface occurs. The matric potential at the

surface is set to zero and the runoff is calculated from the mass budget equation. Note that on the site

(the Alpilles plain) the topographic relief is very small, so that the topographical-horizontal discharge is

assumed to be negligible.

1.3 Soil hydraulic properties

Richards’ equation describing water movement in soil requires knowledge of the soil water retention

characteristic, ( )θh , and the hydraulic conductivity function ( )θK . Uncertainties in the determination of

both relationships is large. Uncertainties in soil hydraulic functions and soil hydraulic parameters affect

the performance of land-surface schemes. A great number of mathematical expressions for both water

retention and hydraulic conductivity functions is currently available (e. g. Brooks and Corey, 1964;

Mualem, 1976; van Genuchten, 1980; Hutson and Cass, 1987; Rossi and Nimmo, 1994), in which

several retention models are related theoretically to the conductivity models to estimate the unsaturated

hydraulic conductivity from measured data. For the sake of simplicity, we will use here a single S-

shaped (i. e. unimodal) function for the retention curve although Othmer et al. (1991) and Mallants et al.

(1997) have shown that soil water pressure was much better estimated with bimodal or superposition of

three unimodal curves compared with unimodal functions. Note that Mallants et al. (1996) demonstrated

that the use of nonoptimal retention and conductivity functions in the simulation of free drainage from a

saturated soil profile resulted in an underprediction of the cumulative drainage by as much as 30% for a

macroporous soil.

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Fuentes et al. (1992) and Zammit (1999) showed that the combination of van Genuchten’s (1980)

expression for ( )θh obtained with the capillary model of Burdine (1953) and of Brooks and Corey’s

(1964) expression for ( )θK was the one which was better fulfilling mathematical criteria linked to static

or dynamical constraints. The van Genuchten model for ( )θh and the Brooks and Corey model for ( )θK

were individually also observed to be capable of reproducing well soil hydraulic properties for HAPEX

data (Shao and Irannejad, 1999). Following Zammit (1999), retention curves ( )θh and ( )θK can be

written as

( ) ( )nmg

hh

1

1−Θ=θ with n

m2

1−= (Burdine, 1953) (3)

( ) ηθ Θ=s

KK (4)

wherers

r

θθθθ

−−

=Θ and where the so-called residual water content θr is taken equal to zero. Here, n, m, η

are shape parameters linked to soil texture corresponding to geometrical and static properties. These

parameters are rather stable in space and time and will not be investigated here even though their

variation may affect significantly fluxes, in particular latent heat flux in dry conditions. On the other

hand, hg, Ks, and θs are normalization parameters, which are related to soil structure linked to poral

network, and are more variable. The hydraulic conductivity at saturation Ks is the more sensitive

parameter related to macroporosity, stones, cracks, fractures and other soil irregularities. It has a major

influence on the determination of fluxes as will be shown in the next section, since it controls flow

dynamic.

1.4 Sensitivity study methodology

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Numerical simulations of the temperature, soil moisture and fluxes have been performed on field 101

of the Alpilles experiment for various values of the soil structure parameters. The period of simulation,

from 17 November to the end of December 1997, corresponds to bare soil condition. During this period

three major precipitation events occurred, allowing to test soil behavior under wetting and drying

conditions (Figure 1). The drawback of this data set is the lack of data on surface temperature and latent

heat fluxes. However, soil temperature measurement in the layer 0-5cm and surface humidity allow to

validate surface temperature and latent heat flux. Initial conditions for temperature and water content as

a function of depth have been derived from measurements. A series of numerical tests have been

performed for different values of the structure parameters hg, Ks and θs. The range of variation of the

parameters has been defined according to the variability observed on the several test fields:

( ) [ ] ( ) [ ] ( ) [ ]45.0,3.033;510,9101;5.0,6 ∈−−−∈−−−∈ mmsmssKmgh θ .

A first estimation of the parameters has been done by the scenario 1 of the SVAT inter-comparison of

Alpilles project based on in-situ measured values (Olioso et al., this issue). Averaged values on field

101 are: 3337.0;19105;5 −=−−×=−= mmsmssKmgh θ . Simulations have been carried out using 48

sets of parameters in the range indicated above. For each simulation, efficiency criterion defined as

( )( ) ] ],1,,1

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2

∞−∈−

−−=

∑∑

Eff

ffE

obsobs

obssim

has been calculated, where simf and obsf are the calculated and measured variable, respectively. Best

results correspond to efficiency values near unity. Negative value of the efficiency shows that the

average of observed variables provides better result than the simulated variables. Efficiency has been

calculated independently for humidity, temperature and fluxes, globally for all the calculated variables

(total efficiency) and for all calculated surface variables (surface efficiency).

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2. Results

From the results, it appears that efficiency related to humidity is always negative varying from –1 to –13

whereas the efficiencies related to temperature (0.88<E<0.93) and fluxes (0.47<E<0.72) are always

positive. It is partly due to the strong daily variation of temperature and fluxes. Referred to the total

efficiency, the best simulation is obtained for 3337.0;1910;5.0 −=−−=−= mmsmssKmgh θ with total

efficiency E=0.12 whereas referred to surface efficiency the best result is obtained for

3337.0;1610;3 −=−−=−= mmsmssKmgh θ with Esurf=0.47. In fact, different set of parameters are

obtained depending on the considered efficiency, suggesting that no set of parameters allows to

reproduce the vertical distribution of mass and heat within the soil.

The relative importance of hg, Ks and θs is investigated by varying these parameters in the range

indicated above. The more sensitive situations are observed for middle values of Ks and low values of hg

and θs. In fact for values of Ks as high as 10-5 almost no variations of soil moisture is observed. Figure 2

compares the calculated net radiation Rn, latent heat flux LE and surface soil heat flux G by varying Ks

the values of hg and θs being fixed to values given by scenario 1 of the SVAT inter-comparison of

Alpilles project. From these results, it appears that the predicted fluxes depends strongly on the value of

Ks for the first 20 days before the first precipitation event, within the range of studied values. In

particular, the calculated latent heat flux is 300-350 W.m-2 for Ks =10-7ms-1, i. e. almost one order of

magnitude larger than for Ks =10-8. Note that a threshold Kth seems to appear in the values of Ks in this

first period. In fact, the calculated fluxes obtained for Ks =10-7ms-1 are very far from those obtained both

with Ks =10-8ms-1 and Ks =10-9ms-1. These results show the necessity to determine accurately this

parameter in this range of water content. Less sensitivity is observed after the first precipitation event

whereas fluxes are almost independent of soil hydraulic conductivity in the last period although the

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water contents are not the same (Figure 3). A kind of threshold θth corresponding to approximately 90%

of the water content at saturation is observed. For wetter soil, fluxes and temperature are insensitive to

soil hydraulic properties. Figure 2 indicates that the net radiation Rn can be reproduced within this range

of parameters whereas the surface soil heat flux G is always overestimated. This latter observation

concerns the whole range of studied parameters. The only way to improve G was to lower the apparent

thermal conductivity λ. However, it leads to wrong calculated temperatures. This feature seems to be a

general problem which has been observed for simulations on other fields of Alpilles experiment but has

not been investigated deeper here.

On the other hand, Figure 4 indicates that the temperature is rather well estimated for Ks =10-7ms-1.

With this value of Ks, the calculated latent heat flux is of the order of 300W/m2 for the first 15 days. The

much lower values of LE calculated with Ks =10-8ms-1 and Ks =10-9ms-1 seems to be unrealistic. In this

case the low values of the hydraulic conductivity do not allow the water to go up from deep layers to the

surface in order to satisfy the evaporative demand (Figure 3). It is then obvious that the evaporation

results in uptake from deep layers instead of drying of surface layers. This process explains the fact that

the model cannot reproduce the drying of surface layers. For low values of Ks the movement of water is

more difficult, the water content in deep layers is almost constant as it is observed on the data

suggesting that these values of Ks are appropriate for the deep part of the soil horizon. At the surface the

drainage after a precipitation is slower for lower values of Ks. Figure 3 indicates that no values of Ks can

reproduce the draining of the soil. Mallans et al. (1997) have shown that the use of unimodal retention

curves leads to an underestimation of observed water contents near saturation, while an overestimation

is found in the drier range. However, this process cannot alone explain the incapacity of the model to

reproduce surface drying. Obviously, distinction of the properties of surface layers and deeper layers has

to be taken into account to reproduce the real rate of flow within the soil.

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Another problem has to be underlined, concerning the penetration of water in soil after precipitation.

In fact, the model always overestimates the depth reached by rainfall, simulating infiltration depth of

approximately 70 cm whereas data show a depth of only 30 cm. It is worth pointing that these features

are observed in the whole range of investigated parameters. The threshold 10-8<Kth<10-7 is well

observed on water content and seems to define two rates of flow: for K< Kth the infiltration of water is

low since for K>Kth water uptake from deeper layers is allowed. Note that Kth is higher for lower values

of hg (10-7ms-1<Kth<10-6ms-1for hg=-1m). It can be explained when looking at equation (1). The

dominance of the term z

hK

∂

∂ requires higher values of Ks when hg is lower (see equations (1) and (3)).

Finally, we have tried to reproduce the drainage of surface layers without any consideration about the

realism of the parameter values. The best simulation was obtained with unrealistic low values of hg =-

0.05m (Figure 5). In fact, even with this value, drainage after rainfall is poorly reproduced. However the

corresponding values of the latent heat flux is by far too low (Figure 6). In fact, for such values of hg, the

water is no more retained in the soil by capillarity or surface adsorption and the flow is essentially

gravitational. Water from precipitation immediately flows towards deep layers and is no more available

for evaporation. It is worth pointing that no values of hg can avoid the problems underlined below. The

same observation can be made for θs. Higher values of θs lead to higher values of the water content

almost everywhere.

5 Conclusion

We studied the impact of soil hydraulic normalization parameters on soil moisture simulation and land-

surface modeling. Numerical results imply that water content and land surface water and energy fluxes

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are very sensitive to soil structure parameters when soil humidity is lower than a certain value,

corresponding to approximately 90% of the water content at saturation. It is found that, in bare soil

condition, latent heat flux is the most sensitive factor. For wetter soil the energy fluxes are completely

independent of the soil water content.

Numerical tests have shown that SISPAT with only one horizon is not able to reproduce soil moisture

profile at the field scale since vertical heterogeneity in soil hydraulic properties cannot be taken into

account. This version of SISPAT cannot be used easily for remote sensing purposes since it is then

necessary to estimate both fluxes and humidity vertical profile. The use of more horizons is problematic

for regional or global studies since the number of parameter to be estimated greatly increases.

Acknowledgments. This work was supported by the PNRH/INSU. The authors would like also to thank

all partners for providing ground-truth data.

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Fig. 1. Cumulative precipitation as a function of Day of Experiment (day 626 corresponds to 17

November 1997).

Fig. 2. Influence of Ks on calculated fluxes for fixed values of hg=-5m and θs=0.37m3m-3. Dashed lines

represent the results with Ks=10-7ms-1, dotted lines with Ks=10-8ms-1, and full lines with Ks=10-9ms-1.

The a) net radiation, Rn, b) latent heat flux, LE, c) surface soil heat flux, G, are given during the period

of bare soil of field 101 of the Alpilles experiment as a function of Day of Experiment (day 626

corresponds to 17 November 1997). Crosses represent the measured fluxes.

Fig. 3. Influence of Ks on calculated volumetric water content within layer a) 0-5 cm, b) 20-30 cm, and

c) 80-120 cm for fixed values of hg=-5m and θs=0.37m3m-3. Dashed lines represent the results with

Ks=10-7ms-1, dotted lines with Ks=10-8ms-1, and full lines with Ks=10-9ms-1. Volumetric water content is

expressed as a function of Day of Experiment (day 626 corresponds to 17 November 1997). Crosses

represent the measured water content.

Fig. 4. Influence of Ks on calculated temperature at a) 0.5 cm, b) 10 cm and c) 50 cm for fixed values of

hg=-5m and θs=0.37m3m-3. Dashed lines represent the results with Ks=10-7ms-1, dotted lines with Ks=10-

8ms-1, and full lines with Ks=10-9ms-1. Temperature is expressed as a function of Day of Experiment

(day 626 corresponds to 17 November 1997). Crosses represent the measured temperature a) at 0.5 cm,

b) at 7.5 cm and c) at 49 cm.

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Fig. 5. Influence of hg on calculated volumetric water content within layer a) 0-5 cm, b) 20-30 cm, and

c) 80-120 cm for fixed values of Ks=10-7ms-1 and θs=0.37m3m-3. Dashed lines represent the results with

hg=-50m, dotted lines with hg=-5m, full lines with hg=-0.5m, and dashed-dotted lines with hg=-0.05m.

Volumetric water content is expressed as a function of Day of Experiment (day 626 corresponds to 17

November 1997). Crosses represent the measured water content.

Fig. 6. Influence of hg on calculated latent heat flux for fixed values of Ks=10-7ms-1 and θs=0.37m3m-3

expressed as a function of Day of Experiment (day 626 corresponds to 17 November 1997). Dashed

lines represent the results with hg=-50m, dotted lines with hg=-5m, full lines with hg=-0.5m, and dashed-

dotted lines with hg=-0.05m.

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