Modelling of water and energy exchanges over a 1 sparse olive orchard in semi-arid areas . 2

In the Mediterranean basin, olive orchards occupy a large fraction of agricultural lands 10 due to its sustainability to harsh conditions, drought in particular. Since most modeling tools to 11 simulate vegetation functioning are not meant to represent very sparse crops (i.e., rainfed olive trees 12 have a vegetation fraction cover ranging from 2 to 15 %), computing the water needs and the 13 vulnerability to drought of an olive orchard is a challenge. There is indeed a very high contribution 14 of the bare soil signal to the total fluxes, and it is difficult to decipher the contribution of the tree 15 from that of the entire surface. In this context, in an attempt to study the olive tree hydrological 16 functioning at field scale (38 ha), an experimental site was setup and a Soil-Vegetation-Atmosphere 17 (SVAT) model has been applied. To represent the orchard soil-plant-atmosphere interactions, a 18 simulation with default settings was assessed using parameters derived from both the literature and 19 ground measurements. In this default configuration, neither the predicted actual nor the potential 20 transpiration could reach the observed transpiration acquired during the wet season (R2=0.67, the 21 Root Mean Square Error (RMSE)=5.63 mm week-1). We show that the model fails to reproduce the 22 relevant leaf surface that transpires. To address this issue and to improve the estimate of the year23 to-year variability of the olive tree transpiration, we propose guidance on how a SVAT model can 24 be modified to more appropriately represent the hydrological functioning of a sparse orchard. Once 25 the tree transpiration is accurately simulated (R2=0.93, RMSE=1.62 mm week-1), we evaluated 26 whether the fully coupled (single patch) or a fully uncoupled (two patch) system better reproduced 27 the total fluxes and their components. Owing to the independent characteristics of the soil columns 28 inherent in the assumption of the 2-patch version, the bare soil column shows a deficiency if the 29 topsoil root extraction is not accounted for. We deduced that we cannot accurately reproduce the 30 soil evaporation in this configuration. This study open perspectives for a better representation of 31 water fluxes over sparse tree crops into both hydrological and SVAT models. 32

to-year variability of the olive tree transpiration, we propose guidance on how a SVAT model can 24 be modified to more appropriately represent the hydrological functioning of a sparse orchard. Once 25 the tree transpiration is accurately simulated (R²=0.93, RMSE=1.62 mm week -1 ), we evaluated 26 whether the fully coupled (single patch) or a fully uncoupled (two patch) system better reproduced 27 the total fluxes and their components. Owing to the independent characteristics of the soil columns 28 inherent in the assumption of the 2-patch version, the bare soil column shows a deficiency if the 29 topsoil root extraction is not accounted for. We deduced that we cannot accurately reproduce the 30 soil evaporation in this configuration. This study open perspectives for a better representation of 31 water fluxes over sparse tree crops into both hydrological and SVAT models.

35
For sparse agrosystems, it is difficult to describe the exchanges at the soil-plant-atmosphere 36 interfaces with classical one dimensional (vertical) water and energy transfer models when large area in the case of fraction cover partitioning. Clumping index would even decrease this fraction.

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The overall objective of this study is to better understand, through SVAT modeling and a

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Therefore, its patch parameterization is classically the same one used to represent the sub-grid 188 variability in land surface models coupled with atmospheric models (such as the SURFEX platform) 189 (Masson et al., 2013). The model is used by a large number of communities (global and regional 190 climate, hydrology …) and over a large range of covers. Consequently, our work contributes to the 191 improvement of the ISBA parameterization within the particular context of isolated trees in semi-arid 192 areas. The choice of this model for the present study can be justified by its ability to test future 193 scenarios based on future climate forcing and to predict the cover response to more recurrent drought 194 periods. It is also a complete physical model, that enables the comparison of the two configurations 195 (coupled/series and uncoupled/patch) and includes different soil water transfer schemes (i.e., force-196 restore and multilayer diffusion).

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The model was applied using parameters determined from observations or from the literature.

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First, the different ISBA outputs were compared with observed data, including an analysis of an 199 inconsistency when dealing with the observed vegetation fraction cover of 7 % as the weighting of 200 the evaporation E and transpiration T components. Then, the model was slightly revised to address 5 of 27 effective area that transpires can be increased to match that observed T. Finally, the second issue deals 203 with the choice between the patch (or uncoupled) approach and the layer (or coupled) approach and 204 which is the configuration that better reproduce the water and energy exchanges, with respect to the 205 vegetation sparseness and structure of this discontinuous canopy.

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The study was conducted during three successive hydrological years from 2013 to 2016 (starting 215 from September to August) at a half-hourly time step. The setup consisted of instrumented towers 216 with adjacent pits, a tall one close to the tree and a shorter one over the bare soil at the center of a 217 square delimited by four trees (including the one that is instrumented). Therefore, one tower/pit 218 couple is dedicated to the tree functioning and another is related to the bare soil at the inter-row. For 219 the meteorological data, the air temperature and the relative humidity were sampled above the tree     In order to mimic the surface heterogeneity, the ISBA model is based on the tiling method that 240 consists in dividing the surface area into as many homogenous entities as vegetation types juxtaposed 241 side-by-side in one grid. The term "patch" is used to designate this sub-grid variability, and each

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This tile version of ISBA allows implementing easily the uncoupled (patch) configuration. One 246 bare soil patch represents the unshaded soil and the other one the vegetated area with the underlying 247 shaded soil (Fig. 1b). This configuration is based on the assumption that the turbulent mixing at the 248 plant-atmosphere interface occurs without disturbing the physical processes of the exposed bare soil.

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The two components are thermally uncoupled and do not exchange water (Kustas and Norman, vegetation patch, and each one receives the whole amount of incoming radiation and precipitation

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Insert Table 1 here   292 For the soil discretization, the number of layers and depth were defined in agreement with 293 the heat and water measurement depths. The vertical soil texture was prescribed for all layers 294 according to observations (Table 2).

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Insert Table 2 here 296 While all the other parameters remain equal, the LAI (Leaf Area Index) is the parameter that varies 297 between both simulations. For the 2P simulation, we consider the LAI on the vegetated patch (veg=1) 298 which is computed as the ratio between the leaf area and the area of the soil below the tree (also 299 named "clump LAI"). However, for the 1P configuration, the LAI includes the area of soil which is 300 not covered by vegetation and is expressed as:

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To overcome this issue, in our case with only 7 % of vegetation fraction cover (almost a bare 370 soil) that represents the limit of the applicability domain of the model, we will try to adjust artificially 371 the appropriate parameters as an attempt to fit the observed transpiration without changing the 372 model formulation. For this purpose, to increase the potential and the actual transpiration, the first 373 assumption was to increase the effective area of leaves that transpires by testing various vegetation 374 fraction covers. A sensitivity study was provided in Table 3.

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(1-fc). So, it is not surprising that the difference between the over-simulated evaporation and this 464 estimated amount of water extracted by the tree is consistent with the reconstructed soil evaporation 465 of the bare soil patch (Fig. 6). In conclusion, it appears that splitting the cover into two different soil 466 water budgets is not representative of the water transfer occurring in reality.
Where Rg and Ratm are the global and the atmospheric radiation respectively, α is the combined 726 soil/vegetation albedo, ɛ is the total surface emissivity weighted by the vegetation cover (veg), σ is the 727 Stefan-Boltzmann constant, Ts is the total surface temperature, ρa is the air density, Cp is the air specific 728 heat, Va is the wind speed, Ta is the air temperature, CH is the drag coefficient, Lv is the latent heat of

734
The surface resistance that monitors the transpiration is defined by (Jarvis, 1976) and controlled by 735 the minimal stomatal resistance parameter Rsmin.

736
The surface heat flux (G) corresponds to the residual term of the energy budget equation and is 737 expressed as follows: The surface temperature, which is associated with the soil temperature at the top soil layer, depends Where ,1 is the uppermost surface soil temperature, is the latent heat of fusion (J.kg −1 ). g Where ,1 is the uppermost soil water content layer, − is the remaining rainfall after 764 interception, F is the soil water vertical flux, is the ground evaporation, R0 is the surface runoff and

765
Drv is the canopy drip of liquid water.

766
The different fluxes are expressed as a function of resistances ( = 1 ) in s.m -1 instead of the 767 dimensionless heat and mass exchange coefficient (CH). The resistances represent the water extraction 768 efficiency at the soil-plant-atmosphere interfaces.

769
The sensible heat fluxes are defined as follows: