Development and evaluation of an efficient soil-atmosphere model ( FHAVeT ) based on the Ross fast solution of the Richards equation for bare soil conditions

In agricultural management, a good timing in operations, such as irrigation or sowing, is essential to enhance both economical and environmental performance. To improve such timing, predictive software are of particular interest. Optimal decision-software would require process modules which provide robust, efficient and accurate predictions while being based on a minimal amount of parameters easily available. The objective of this study is to assess the accuracy of a physically based model with high efficiency. To this aim, this paper develops a coupled model with climatic forcing based on the Ross fast solution for Richards’ equation, heat transfer and detailed surface energy balance. The present study is limited to bare soil, but the impact of vegetation can be easily included. The developed model, FHAVeT (Fast Hydro Atmosphere Vegetation Temperature), is evaluated against the coupled model based on the Philip and De Vries (1957) description, TEC. The two models were compared for different climatic and soil conditions. Moreover, the model allows using various pedotransfer functions. The FHAVeT model showed better performance in regards to mass balance, mostly below 0.002 m, and generally improved computation time. In order to allow for a more precise comparison, six time windows were selected. The study demonstrated that the FHAVeT behaviour is quite similar to the TEC behaviour except under some dry conditions. The ability of the models to detect the occurrence of soil intermediate water content thresholds with a 1 day tolerance was also evaluated. Both models agreed in more than 90 % of the cases.


Introduction 30
In agriculture a good timing of management operation such as tillage, sowing, irrigation or harvesting is an important issue for both economical and environment points of view.Inappropriate irrigation scheduling may lead to water and/or crop losses, whereas using heavy engines on wet soil condition may 35 compact soils that reduces oxygen and water flows.The decision making is multifactorial, involving work organization, meteorological forecast or soil water content.Even if progresses have been made in soil water content probe development (Evett and Parkin, 2005), their implementation remains 40 difficult in operational context as for capturing the spatial soil variability (Evett et al., 2009) or handling in situ probes together with management operation.Modelling the soil water content dynamic is therefore an alternative to support decisions and fast computing is an important issue to obtain real 45 time information and address the spatial variability through 3D or distributed 1D model.
As explained in the review on decision making by Ascough et al. (2008), an optimal decision making software would require process modules which provide robust, efficient and ac-50 curate predictions while being based on a minimal amount of easily available parameters.Moreover, a decision making software should allow the representation of the major processes occurring in the studied object.In regards to decision based on soil water content for agricultural management, some im-latter being important to determine top boundaries conditions from standard climatic data.To represent such processes, soil hydraulic properties characterisation is a critical point since they are rarely measured at the location of interest and have a strong impact on the simulations.The alternative is then to use pedotransfer functions that link those characteristics to commonly measured quantities such as the soil textural fractions.
For agricultural management purposes, capacity-based models are generally used (Bergez et al., 2001;Chopart et al., 2007;Lozano and Mateos, 2008).Such conceptual models represent soil through its water storage capacity and vertical fluxes that are governed by an overflow of a compartment towards the one just below.In general, additional processes are required to better represent infiltration and upwards flux involving empirical parameters that are site specific and need to be calibrated since they are not measurable and thus difficult to address through pedotransfer functions.Moreover, in her work, Blyth (2002) compared a conceptual model to a physically based model.The physically based model showed better performances and more versatility than the conceptual model.It should be noted, however, that the accuracy of a physicallybased model is dependent on modeller's choice, for instance in regards to parametrisation or chosen processes (Hollander et al., 2014).Therefore the development of a versatile, physically-based model is of importance to allow a non-sitespecific decision tool.
In the unsaturated zone, a well-known physically based description of the mass balance, in regards to water flow, is the Richards equation.The Richards equation allows a detailed description of soil water content distribution evolution as well as water fluxes inside the soil domain.It's solving is based on measurable physical parameters which may be obtained through experimentation such as the water retention and the hydraulic conductivity.Moreover, pedotransfer functions are widely developed (Cosby et al., 1984;Rawls and Brakensiek, 1989;Wosten et al., 2001;Schaap et al., 2001) and allow description of the parameters necessary for the resolution of Richards equation using soil characteristics such as the soil texture and bulk density.Chanzy et al. (2008) demonstrated that pedotransfer functions may allow a good approximation for agricultural soil water representation even though the adequacy of pedotransfer functions close to the surface is still under discussion (Jarvis et al., 2013) especially for wet conditions when preferential flow occurs.
The Richards equation is highly non-linear leading to time-consuming numerical resolution and stability issues under some conditions such as the wetting of an initially dry medium.Numerous studies focused on the improvement of the numerical schemes (Short et al., 1995;Zhang et al., 2002;Caviedes-Voullieme et al., 2013) but it should be noted that computing codes based on Richards equation are rarely used for decision making software.Ross (2003) proposed in his paper a fast solution of the 110 Richards equation.This method demonstrated an accurate, robust and efficient behaviour on a variety of case studies.The solution developed by Ross (2003) has been used in different situations in the latest years, proving its efficiency against models based on the classic numerical resolu-115 tion of the Richards equation and analytical solutions.Varado et al. (2006a) tested the solution to evaluate its efficiency and demonstrated that the model shows improved robustness and accuracy compared to analytical solutions and the model SiSPAT (Braud et al., 1995).In their work, Crevoisier et al.

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(2009) proposed a comparison of the solution with the Hydrus software (Simunek et al., 2008) in unfavourable conditions, demonstrating an improvement in computing time efficiency and robustness.
Thanks to its efficiency and robustness a model based on Ross solution is an interesting choice to develop a decision tool based on soil water content estimation.However, it is important to drive the model with a climate forcing and to be able to have a wide range of soil hydraulic functions (retention curve and soil hydraulic conductivity) in order to take 130 profit of the existing pedotransfer functions.
In most of the models based on Ross solution, the introduction of climatic forcing is made through an empirical approach where the top water flux is the minimum of the potential evaporation and the maximum water flux through the 135 top layer.Introduction of climate forcing through the surface energy balance is more straightforward and physically sound.This requires, however, to represent soil heat transfer, which may be done with a soil energy balance.Tightly coupled equations developed by Philip and De Vries (1957) may be used.In 140 such a tightly coupled model water flow in liquid and vapour phases is strongly related to heat transfers.Haverd and Cuntz (2010) actually coupled the Ross solution with an energy and vapour transport equation based on those coupled equations.Such a development increases the number of parameters,such 145 as those related to soil vapour diffusion, and a more complex problem resolution is required.Another possibility is to consider a loosely coupled model.In such a model, the different balances (surface energy, heat transport and water transfers) are evaluated sequentially and vapour transport is neglected.

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To keep a limited amount of input parameters, we prefer to develop a model based on the original Ross approach, which was widely tested in a large range of soil and water flow conditions.
The aim of this paper is to present and evaluate the evo-155 lution made on the model developed in Crevoisier et al. (2009) with the introduction of new soil hydraulic function formalisms as well as new processes (soil heat transfer and surface energy balance).At longer term, the interest would be to enlarge the scope of the soil water and heat transfer 160 model to other processes such as root uptake, solute transport, biogeochemical reaction or soil properties dynamic.It was found that the main challenge in implementing physically based model to estimate soil water content is the evaluation of soil hydraulic properties, requiring the development of estimation strategies such as using PTF or assimilation techniques (Witono and Bruckler, 1989;Zhu and Mohanty, 2004;Medina et al., 2014).Our work focused on the innovation made in the FHAVeT model and will not consider those strategies that are already addressed in other studies (Chanzy et al., 2008).
To evaluate the FHAVeT model, we therefore used a data set simulated by the TEC model (Chanzy et al., 2008) as our reference.It is based on the DeVries approach, which is physically sound to represent water transfers in the soil and at the soil/atmosphere interface.Moreover, Chanzy et al. (2008) have shown the potential of such a model for operational applications by developing an implementation strategy with limited soil characterisation.The question is then to evaluate to which extent the gain in computing efficiency and robustness brought by the Ross method, together with the physical simplification on heat and water coupling, affect the results in comparison to the TEC model that presents a stronger physical background.
In this paper, the work is limited to bare soils in order to focus on the impacts of the innovations brought in FHaveT, which are limited to the soil compartment including the interface with the atmosphere.Moreover, the very dry conditions encountered near the surface on bare soil, are the worst situations to test the lack of soil water vapour assumption.Bare soil is also an important phase in the crop cycle during which important decisions have to be taken by farmers such as crop installation (soil tillage, sowing).

Model description
The model FHAVeT (Fast Hydro Atmosphere Vegetation Temperature) consists in the coupling of a surface energy balance, a soil energy balance and a soil mass balance module.Models development and simulations were performed using the INRA Virtual Soil 1 platform.This platform provides an easy way to use and couple numerical modules representing processes occurring in soils.A scheme of the model is presented Figure 1.The model consists of three main modules computed sequentially in the following order: Surface Energy Balance -Soil Water Transfer -Soil Heat Transfer.As shown in Figure 1 the surface energy balance is driven by climatic forcing, soil surface temperature and soil surface water potential and it computes evaporation and soil surface heat flux.The soil water transfer module is driven by evaporation / rainfall and computes soil water potential, water flux and water content.Finally, the soil heat transfer module depends on water 1 All informations about the platform and how to use it and contribute can be found in the dedicated web site : http://www.inra.fr/sol virtuel

Surface energy balance
An equation of energy budget (Eq. 1) at the soil surface is used to obtain the soil surface heat flux G (W m −2 ) and the soil evaporation flux E g (kg m −2 s −1 ). 215 In this equation, Rn g (W m −2 ) is the net radiation, L v (J kg −1 ) is the latent heat of vaporization and H g (W m −2 ) 220 is the sensible heat flux.The aerodynamic resistances for heat and vapour R aH (s m −1 ) and R av (s m −1 ) are calculated using the formulation by Taconet et al. (1986).T corresponds to the temperature and h to the specific humidity (mass of water in air over mass of humid air), subscripts 'a' relates to the air 225 and 's' to the soil surface level.Moreover, ρ a (kg m −3 ) is the air density and c p the specific heat at constant pressure.Solving equation (1) requires climatic observation parameters, as well as the soil surface temperature and soil surface water potential calculated from the soil heat and water transfers at the 230 previous time step and input parameters as described Table 2.

Soil mass balance
Ross' fast solution for Richards equation is described in Ross (2003) and Fast Hydro, the upgraded implementation of Ross method used in this study is described in Crevoisier et al.  3) by a non-iterative approach.
Where θ (m 3 m −3 ) is the soil water content, h (m) is the soil potential, K (m s −1 ) is the soil hydraulic conductivity and z (m) is the soil depth.Detailed description of the Ross solution may be found in Crevoisier et al. (2009).Similarly to the code developed in Crevoisier et al. (2009) under saturated conditions to allow an exact calculation of the Darcian fluxes (Crevoisier et al., 2009).However, the integration of the hydraulic conductivity is not always straightforward.Ross (2003) used exclusively Brooks and Corey formulation which is integrable analytically.Crevoisier et al. (2009) developed a numerical integration method for the use of Van Genuchten -Mualem hydraulic characteristics with η = 0.5.However, some PTF, including commonly used PTF, require the use of other formulation.For instance, the PTF of Wosten et al. (2001) or Schaap et al. (2001) implies the use of Van Genuchten -Mualem with η potentially different from 0.5.To this end, a method using beta functions was developed for integration of hydraulic conductivity as described by Van Genuchten -Mualem.This method, however, is convergent only for η > −1.Therefore, a numerical iterative method was developed for the utilisability of Van Genuchten -Mualem description with η ≤ −1.A summary of the hydraulic properties that may be used in FHAVeT is shown in Table 1.

Soil energy balance
The soil energy balance is modelled using a simple convection diffusion model (4-5) with convection being limited to the liquid phase.
Where ρ s (ρ w ) (kg m −3 ) is density of solid (water), ρ h (kg m −3 ) is the soil bulk density, θ s (m 3 m −3 ) is the saturated water content (assumed equal to the porosity), C s (C w ) (J kg −1 K −1 ) is the specific heat of solid (water) and λ (W m −1 K −1 ) is the soil heat conductivity.The soil heat conductivity is assumed to have a linear dependence on soil water content following equation ( 6) (Van de Griend and O'Neill, 1986) where Λ s (J m −2 K −1 s −1/2 ) is the thermal inertia at saturation.
Moreover, impact of the rain on fluid transport is considered as a working hypothesis with rain having a constant tempera-285 ture of 283 K.

The reference model: TEC
The TEC model (Chanzy and Bruckler, 1993) is based on the heat and mass flow theory in unsaturated media (Philip and De Vries, 1957).The resulting nonlinear partial differen-290 tial equation system is solved using a Galerkin finite element method.The model is driven by a climatic forcing in case of bare soil.The model was evaluated against various experimental conditions (Chanzy and Bruckler, 1993;Aboudare, 2000;Findeling et al., 2003;Sillon et al., 2003).The major differ-295 ences between the models TEC and FHAVeT are as follows: -TEC is based on Finite Element Method for resolution of the equations, while FHAVeT uses the Ross solution for solving mass balance, energy balance being solved through Finite Difference Method.

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-The coupling of soil mass and energy balances is based on a tightly coupled Philip and De Vries (1957) approach in the TEC while the FHAVeT model uses a loosely coupling, neglecting the vapour transport.
There are however others differences between the two mod-305 els.The evolution of soil heat conductivity with soil water content and the aerodynamic resistances are calculated through different means.Moreover, the numerical spatial discretisations are different with a coarser mesh with FHAVeT near the surface.

3 Model intercomparison
The knowledge of soil water content profile is critical when it comes to agricultural management.Therefore, the prediction capacity in regards to soil water content of the FHAVeT model is going to be the major focus of the intercomparison.
315 Chanzy et al. (2008) developed an implementation strategy under operational conditions when only limited information is available to describe the soil system.Their study was based on a large database covering contrasted climate regime, a large range of soil textures and four PTF.This data set was appro-320 priate to analyse FHAVeT results under various pedo-climatic conditions and test different soil hydraulic functions.

Climatic forcing
The cases studied were chosen so as to offer a variety of climatic and soil conditions that may occur in France and in  (Ross, 2003) Linear Linear S(h) = exp (αG (h − he)) K = KsatS Analytical (Crevoisier et al., 2009) van Genuchten (1980) Mualem ( 1976) modified van Genuchten (1980) Mualem ( 1976) Beta functions † † † Integration method upgraded † † New feature in the FHAVeT model agronomic context.Two climatic sequences are used.The first one was measured at Avignon (southern France, 43.78 • N, 4.73 • E) and represents a Mediterranean climate with occasional heavy rains and long periods of dryness (Figure 2a).Wind velocity also varies strongly.The second climatic sequence was measured at Estree-Mons (northern France, 48.99 • N, 2.99 • E).It represents an oceanic climate with frequent light rainfalls and short dryness periods (Figure 2b).
In order to study specific features of the two climatic sequences, six time windows (TW) were selected (Table 3).TW 1 and 2 are chosen within the first drying period of the Avignon sequence with TW 1 showing strong wind conditions and TW 2 little wind conditions.Indeed, Chanzy and Bruckler (1993) demonstrated that wind has an influence on vapour transport with lower vapour flow when the convective part of the climatic demand is stronger.TW 3 is selected during the heavy rain period of the Avignon sequence.TW 5 covers the drying conditions of the Estree-Mons climate.Finally, TW 4 and 6 were chosen during wet periods of the Estree-Mons sequence, respectively before and after the dry period.A summary of the averaged climatic conditions during those 6 time periods is shown Table 3.

Soil types
Four soils from the sites of Estree-Mons and Avignon with various textures, ranging from silty loam to silt clay loam (Ta-350 ble 4) were chosen for the study.

Soil hydraulic characteristics
To validate the versatility of the model, the three integration methods (Table 1) were solicited through the use of three different PTF.The pedotransfer function developed by Cosby 355 et al. (1984) offers parameters corresponding to a Brooks and Corey set of hydraulic properties and therefore requires the use of analytical integration in the software.The pedotransfer function developed in Rawls and Brakensiek (1989) allows deriving of Van Genuchten -Mualem hydraulic properties pa-360 rameters with the hypothesis of shape parameter, otherwise known as tortuosity, η equals 0.5.Therefore integration with beta functions may be used.Finally, the pedotransfer function of Wosten et al. ( 2001) also derives Van Genuchten -Mualem parameters, but shape parameter η obtained are usually be-

Soil thermal characteristics
Thermal characteristics of the different soils were considered 370 dependent on volumetric soil water content.The heat capacity is calculated as the mean of soil and water capacities weighed by relative volumes.In the FHAVeT model, the heat conductivity dependence on the soil water content is obtained through equation ( 6).The thermal inertia at saturation Λ s has been  The one-dimensional mesh used in FHAVeT is homogeneous with a cell thickness of 2 cm and a total soil thickness of 80 cm while the mesh used in TEC is refined close to the surface with element thicknesses ranging from 0.6 cm to 5 cm.The number of cells is identical for both models.

Models performances
A study on the efficiency of the Ross solution against classic resolution of Richard's equation under various boundary conditions was done in Crevoisier et al. (2009).In their work, they demonstrated that Ross solution allowed a computation time five time per grid cell lower (in average) compared to a regular solution of Richards equation.Similar outcomes, (computation time of around a couple minutes in FHAVeT case and a few tens of minutes if TEC case) were observed in this study.It should be noted noted that in one case (AL-SiCL with the Wosten pedotransfer functions and under the Avignon climate), the computation time using FHAVeT remained in the same order of magnitude than the one of TEC.
To compare the numerical accuracy of both models, a calculation of mass balance was performed .The mass balance absolute error was computed as the absolute difference between cumulated in and outflow of the soil domain and the soil water storage evolution from initial state at each time step.The maximal value along time for the mass balance error is represented Figure 3.As shown in Figure 3 the TEC mass balances are not always respected (error lower than 0.01 m 3 m −2 ) due to strong water potential near the surface in dry conditions.FHAVeT offers improved results in regards to mass balance compared to the TEC model.In most cases the absolute mass balance error was below 0.002 m 3 m 2 with only one case being higher.In this particular point, corresponding to the soil AL-SiCL with the Wosten pedotransfer functions and under the Avignon cli-mate, both the computing time and the mass balance (0.008 m 3 m −2 ) error were too large.As explained in the model de-420 scription, the variables calculated are different when a cell is saturated (Kirchhoff potential) or unsaturated (effective saturation).Therefore, when a cell is going from unsaturated to saturated state (or reversely), the calculation undergoes an error.For the hydraulic conductivity curves from Wosten et al.

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(2001), there is a very steep non linear variation of permeability close to the saturation.This leads to a slow numerical calculation of the permeability close to saturation state as well as a strong discrepancy between the soil saturated and slightly unsaturated state flow characteristics.All these considerations 430 leads to a heightened probability of an "oscillation" to occur between saturated and unsaturated states and the consequent error accumulation.An improvement of the numerical integration method should, however, improve the computation time and allow the use of a more constraining numerical tolerance.

Water content evaluation
Figure 4 shows the comparison of all cases studied between soil water content of both models for the 0-5 cm and 0-30 cm soil layers.A tolerance of 0.04 m 3 m −3 is shown.The 440 models show generally good agreement.For the 0-5 cm layer, only 1.55% (6.76%) of the results are out of the tolerance zone for the Avignon (Mons) climate.The results go down to 0% (1.17%) for the 0-30 cm under the Avignon (Mons) climate.
To study the conditions of the divergences between the two 445 models, the evolution of soil water content with time for the surface layer and in one particular simulation is shown Figure 5.This figure shows that the most significant discrepancy between the two models seems to occur during TW 5, that is during the drying period of the Mons climate.

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In order to extend this analysis to all cases studied, Figure 6 shows the histogram of the absolute difference distribution between the water content averaged over a defined soil depth However, under dry conditions (TW 1,2 and 5) the difference between the two models is more consequent.This is especially true in TW 5, where there is little rain for a long time (1.5 mm in 12 days), which leads to absolute water content difference going over 0.1 m 3 m −3 .Since the discrepancies between the models mostly occur during drying, the lack of vapour transport is likely to be a source of error.In order to investigate the role of vapour transport, the evaporated flux was plotted in Figure 7 for one case.This case shows representative behaviour of all soils and climates studied where there is discrepancy between the two models (with the exception of the case showing numerical issues).
As shown in Figure 7, the model FHAVeT tends to underestimate the evaporation of soil under Mons climate drying conditions and consequently leads to a higher soil water content in the observed soil layer.The errors are larger in the 0-5 cm layer than in the 0-30 cm layer which tends to demonstrate that the impact of vapour transport is most important close to the surface.Such considerations are further observed in Figure 8.This figure compares three water content profiles for each model.Under dry conditions and Mons climate (during TW5) the profiles are comparable below 30 cm and their discrepancy increases when depth decreases.Moreover, the water content simulated by the TEC model during the drying phase is significantly smaller than the one computed with The FHAVeT model.Therefore, the driest conditions at the soil surface must be balanced by vapour flow to produce greater evaporation rate.Under Avignon climate, both models led to similar evaporation rate even in very dry condition and therefore the water content profile (Figure 8) are comparable even close to the surface.In such dry conditions, Chanzy (1991) showed that water vapour flows are much smaller than that at the beginning of the drying phase.Therefore, intermediate water content conditions, such as the ones encountered under Mons Climate, lead to the the strongest discrepancies.After a rainy period, the profile almost seems to be recovered in TW6.While the maximal error between the two models in water content is of 0.087 m 3 m −3 in the dry state (TW5), it is of 0.015 m 3 m −3 eight days later.This result shows that the 500 local error generated during the drying is diluted along the soil profile.Moreover, the error in water amount of the whole domain is reduced by 27 % (from 0.0071 m 3 m −2 in the dry state to 0.0052 m 3 m −2 ), showing a partial recovery of soil water content.

Model ability for water content thresholds estimation
In decision-support software, soil water content thresholds can be applied as criteria for decision on agronomic management such as irrigation or tillage and harvesting to prevent soil compaction (Saffih-Hdadi et al., 2009).Therefore, the ability of a 510 model to accurately detect the day when the soil water content status reaches such thresholds is essential.Figure 9 shows the amount of accurate dates (considering TEC as a reference) at which a given saturation value (for the top 30 cm layer) was detected either from dry to wet conditions (wetting) or from 515 wet to dry conditions (drying) as well as day detection with a one day tolerance.
Due to the little amount of saturation conditions below 50% the lowest threshold showed in Figure 9 is 60%.It can be observed that thresholds are detected at the same date for two 520 thirds of the cases at higher saturation (thresholds 90% and 80%) and a little over half of the cases for thresholds 70% and 60% during drying.The success rate is much higher during wetting.Moreover, the success in day detection with a one day tolerance is quite high in wet conditions (thresholds of 525 90%).
Important day detection delay (or advance) of over three days have occurred in only 0.8 % of the cases and signifi-Fig.9: Day detection success rates.Drying 0day and Wetting 0day show the amount of identical day detection for both models during drying and wetting respectively.Drying+-1day and Wetting+-1day show the success rate for day detection when there is less than 1 day difference between the two models.cant day detection misses (when the threshold is reached for more than three days) in 1.4 % of the cases.The day detection inaccuracy may have different causes.The case where mass balance error is high has lead to an early detection in the FHAVeT model.This is likely due to the numerical error as the discrepancy between soil water volume between the two models and the mass balance error in the FHAVeT model are quite similar.The other cause of day detection miss or delay could be the lack of vapour transport.Indeed, all other day detection misses or delay appear during the drying period and especially TW 5.As mentioned previously, this period corresponds to intermediate water condition that led to the largest discrepancy in evaporation and thus soil moisture.Therefore, in a tightly coupled model such as TEC, the soil is allowed to dry at a higher pace leading to earlier day detection than in a loosely coupled model such as FHAVeT.

Conclusions
FHAVeT extends the model developed by Ross (2003) and improved by Crevoisier et al. (2009) by introducing a coupling with the atmospheric conditions and by considering a wider range of soil hydraulic functions in order to take profit of commonly used pedotransfer functions.The coupled model is based on existing process modules and uses the coupling technology offered by the soil virtual modelling platform to make the software development easier.As a consequence, a loose coupling between soil heat and mass flow is introduced leading to ignore water vapour flows.Moreover, water and heat flow are computed sequentially.The model developed was compared to a reference model, TEC, under two climates typical of France and using four soils textures from different area in France.
The model demonstrated good efficiency and improved 560 mass balance conservation in comparison to the model TEC with the exception of one particular condition.In that case, the soil characteristic curves (soil water retention and relative permeability) are highly non-linear and lead to an "oscillatory" behaviour between saturated and unsaturated state, ac-565 cumulating numerical errors.
The loose coupling lead to little error in rainy conditions.Under dry conditions with the Avignon climate the error is larger, which was to be expected due the more important role of vapour transport.However, the simulated discrepancy is 570 limited to the firsts centimetres and therefore concerns a rather limited volume of water.
Since the developed model is aimed at being a support for decision making software, it is important that it accurately simulates threshold criteria.The FHAVeT and TEC models 575 are in good agreement for around 90% of the day detections with a one day tolerance.Considering the modelling parameters and initial conditions uncertainties in field application, such a tolerance seems to be acceptable.Moreover, due to the lesser computing time (Crevoisier et al., 2009) required by the 580 Ross solution, the FHAVeT model is a much better candidate than TEC for improvement techniques of parameter and initial conditions description such as data assimilation.
However, under drying conditions, the FHAVeT model may fail to correctly simulate the soil drying, especially close to 585 the surface.In such conditions, wrong decisions may be taken even though the model allowed good recovery of the soil water content after a rainy period.It is consequently important to fully identify the specific climatic and soil history conditions that lead to inaccurate description of the soil behaviour 590 in regards to water content.To do so, a wider evaluation of the model, as well as a comparison with experimental field values require further work.Future improvement of the model include a better numerical integration method in order to deal with highly non-linear soil characteristic functions as well as 595 coupling with water transfers due to vegetation.
4 A-J.Tinet et al.: Development and evaluation in bare soil conditions of an efficient soil-atmosphere model (FHAVeT) (2009).It solves the Richards equation ( , a water surface layer and time step optimization are used.The Ross solution is based on a linearisation of the mixed form of Richards equation.The solution evaluates the effective saturation (S = (θ − θ r ) / (θ s − θ r )) under unsaturated conditions and Kirchhoff potential (φ Fig. 2: Climate forcing -Precipitation, air temperature, dew point and wind velocity at 2 m height 435

Fig. 3 :
Fig. 3: Maximum absolute error in mass balance (in water cubic meter per unit soil surface) -Comparison between models.The dotted line corresponds to the 1:1 line.

Table 1 :
Hydraulic properties curves available in FHAVeT and Kirchhoff potential calculation methods

Table 2 :
Input climate forcing and parameters for the FHAVeT model

Table 3 :
Climatic forcing summary for the selected time windows (TW)