Modeling the response of soil moisture to climate variability in the Mediterranean region

Future climate scenarios for the Mediterranean region indicate a possible decrease in annual precipitation associated with an intensification of extreme rainfall events in the coming years. A major challenge in this region is to evaluate the impacts of changing precipitation patterns on extreme hydrological events such as droughts and floods. For this, it is important to understand the impact of climate change on soil moisture since it is a proxy for agricultural droughts and the antecedent soil moisture condition plays a key role on runoff generation. This study focuses on 10 sites, located in Southern France, with avail5 able soil moisture, temperature, and precipitation observations on a 10 year time period. Soil moisture is simulated at each site at the hourly time step using a model of soil water content. The sensitivity of the simulated soil moisture to different changes in precipitation and temperature is evaluated by simulating the soil moisture response to temperature and precipitation scenarios generated using a delta change method for temperature and a stochastic model (Neyman-Scott rectangular pulse model) for precipitation. Results show that soil moisture is more impacted by changes in precipitation intermittence than precipitation 10 intensity and temperature. Overall, increased temperature and precipitation intensity associated with more intermittent precipitation leads to decreased soil moisture and an increase in the annual number of days with dry soil moisture conditions. In particular, a temperature increase of +4 ◦C combined with a decrease of annual rainfall between 10 and 20 %, corresponding to the current available climate scenarios for the Mediterranean, lead to a lengthening of the drought period from June to October with in average +22 days of soil moisture drought per year. 15


Introduction
The Mediterranean region is a transitional zone between dry and wet climates and in these semi-arid areas the direct evaporation from the soil plays an important role on the surface energy balance, with evapotranspiration strongly dependent on available soil moisture (Koster et al., 2004;Seneviratne et al., 2010;Taylor, 2015). Consequently, the Mediterranean has been identified as a region with a strong coupling between the atmosphere and the land surface, with feedback effects of soil moisture on 20 temperature and also precipitation (Seneviratne et al., 2010;Knist et al., 2017;Hertig et al., 2019). Indeed, soil moisture is a key variable in the hydrological cycle for the partitioning of rainfall into infiltration and runoff and also for the mass and a function of soil layer depth. The integration of the measurements at various depths enables to have a representation of the average soil moisture in the root zone layer.   The soil moisture model developed by Brocca et al. (2008) is used to simulate present soil moisture and soil moisture response under different climate scenarios. The soil moisture model (SMmodel) incorporates a Green-Ampt approach for infiltration, a gravity-driven approximation for drainage, and a linear relationship between actual and potential evapotranspiration as a 5 function of soil moisture. The SMmodel simulates the hourly temporal evolution of soil moisture and actual evapotranspiration.
Hourly precipitation and air temperature are used as input into the SMmodel, potential evapotranspiration is computed from air temperature through the Blaney and Criddle approach. Details on the model equations can be found in Brocca et al. (2008) and Brocca et al. (2014). The model has been applied at multiple sites in Italy and Europe (e.g., Brocca et al. (2014)) with satisfactory results.

Soil moisture model calibration
The SMmodel uses fixed and calibrated parameters. The fixed parameters values (Table 2) were estimated based on the observed soil moisture and geographic location of the stations. Three parameters were calibrated: hydraulic conductivity K s , root zone depth Z, exponent of drainage m, and coefficient for evapotranspiration K c (calibration ranges in Table 2). These parameters are calibrated for each station using the total period of observed data, but two additional calibrations were performed on sub-15 periods (first half and second half of the total period) in order to analyze the stability of the calibration. For the calibration process, missing precipitation and temperature data are reconstructed by replacing missing precipitation with an intensity of 0 mm/hr, and by linearly interpolating temperature data for gaps of less than 3 hours or using the climate mean otherwise. Time steps with reconstructed precipitation and temperature are not taken into account in the calculation of the NSE coefficient used as optimization criterion for the calibration (Nash and Sutcliffe, 1970). Details on missing data at each stations are presented 20 in Annexe 4.

Generation of temperature and rainfall scenarios
For each station, a 20 years temperature data serie is generated by repeating the hourly climatic mean. Temperature scenarios are generated by applying a delta of ranging between +0 • C and +4 • C.
The stochastic weather generator, Neyman-Scott rectangular pulse model, NSRP (Cowpertwait et al., 1996) is used to generate 20 series of hourly rainfall data time series. The peculiarity of the model lies in its capability to preserve the statistical 5 properties of benchmark rainfall time series over a range of time scales. As the model has been extensively described in previous papers (e.g. Cowpertwait et al., 1996;Camici et al., 2011) here only a brief discussion is given.
The NSRP model has 5 parameters: λ: mean waiting time between adjacent storm origins [hr].
β: mean waiting time between raincell origins after storm origins [hr],

10
n: mean number of raincell per storm, A Poissonian process with parameter λ controls the generation storm origins. For each storm origin, a random n number of raincell origins are generated displaced from the storm origin according to a β parameter exponentially distributed process. 15 Duration and intensity of each raincell are expressed by two other independent random variables assumed exponentially distributed with parameter η and ξ respectively. These parameters are estimated, for each month of the year, by minimizing an objective function evaluated as the weighted sum of the normalized residuals between the statistical properties of the observed time series and their theoretical expression derived from the model.
As studies on future precipitation patterns in the Mediterranean region predict an increase of dry days frequency associated with an intensification of extreme precipitation events (Paxian et al., 2015;Polade et al., 2017;Tramblay and Somot, 2018), we generate precipitation scenarios with increasing precipitation intermittence and increasing mean intensity by applying deltas 5 from +0 to +50 % on λ and ξ parameters (see details in Sect.3.4). For each precipitation scenarios, 20 precipitation data series are generated with the NSRP model over a 20 years period and used as input of the soil moisture model.
3.4 Sensitivity analysis of the simulated soil moisture to precipitation and temperature changes

Direct analysis
We first analyze the sensitivity of the simulated soil moisture for specific changes in temperature and precipitation. We consider 10 three temperature scenarios with ∆T = +0, +2, and +4C, and 121 precipitation scenarios with ∆ξ and ∆λ regularly spaced between +0 and +50 % with a 5 % step. The soil moisture model is then run for each precipitation and temperature scenarios (i.e. 363 scenarios per stations) to analyze the sensitivity of the simulated soil moisture to temperature and precipitation changes. year under soil water excess, and drought. We consider episodes of soil water excess as consecutive days with a daily soil moisture above the reference scenario 95 th percentile, and drought episodes as days with soil moisture below the 5 th percentile.
Considering the modeling chain as (i) the NSRP model (depending on the calibrated values of β, ν, η, λ and ξ and the applied perturbations ∆λ and ∆ξ); (ii) the temperature scenario generation perturbed of ∆T and (iii) the SM model, for a given set 20 of parameters, the modeling chain is processed 20 times. Quantiles and annual numbers of days under drought or soil water excess are computed for each of the 20 corresponding soil moisture results and then averaged to produce a unique scenario.

Global Sensitivity Analysis
A Global Sensitivity Analysis (GSA) (Saltelli et al., 2008;Pianosi et al., 2016) assess the model behavior (model output sensitivity to the input parameters) in the whole parameter space using a variance decomposition method. Considering Y = f (X) with Y the output of the model f to a set of parameters X = (X 1 , X 2 , ..., X N ). A functional ANOVA decomposition is applied to Y (e.g. (Sobol, 1993;Saltelli et al., 2010)) : where N represents the number of sampled parameters. V (Y ) is the total variance of the model output, V i the first order variance of Y due to parameter X i , V ij the second order variance (covariance) of Y due to X i and X j and the ) and higher order variance due to more than 2 parameters. A first-order Sobol index S i corresponds to the ratio of the corresponding variance V i to the total variance V (Y ) : and is thus always between 0 and 1. The sum of all the (first and higher 10 order) Sobol indices is equal to unity.
Assuming that the changes in temperature and precipitation are stochastic variables, the first-order Sobol indices are computed using the state dependent parameter modelling proposed by (Ratto et al., 2007). For the Global Sensitivity Analysis, a different set of 1000 sets of temperature and precipitation changes, generated randomly in the range of values presented in section 3.3, is used in order to cast continuously the range of values (∆T = [+0; +4 • C], ∆λ = [0; 50%] λ and ∆ξ = [0; 50%] ξ).
The objective of this sensitivity analysis is to estimate the relative influences of changes in temperature and precipitation 5 characteristics on soil moisture.

NSRP model calibration and generated rainfall scenarios
Rainfall series generated with NSRP model for the reference scenario show good agreement with the observed rainfall characteristics. Figure 4a shows that the mean annual amount of rainfall is well reproduced by the model (r2=0.99) and that the range 10 of values of annual amount of rainfall is also comparable to the range of observed values. The mean annual number of dry days (i.e. days with precipitation below 1 mm) is similar to observations reproduced (r2=0.63) (Fig. 4b). NSRP model tends to slightly overestimate lower values of the daily intensities distribution (Fig. 4c), but overall, the simulated distributions are in good agreement with observed distributions.
The perturbation of the NSRP parameters for the mean intensity ξ, and for the rainfall intermittence λ, from +0 to +50 %, 15 enables to produce rainfall scenarios with different patterns. An increase of +50 % of the rainfall mean intensity with an unchanged intermittence leads to a mean increase of the annual rainfall of 432 mm associated with an increase of mean rainfall intensity of wet days of +4.8 mm/day. On the opposite, an increase of +50 % of the rainfall intermittence with an unchanged mean intensity leads to a mean decrease of of the annual rainfall of -350 mm (35 % of original annual rainfall) and an increase of +23 days/yr of dry days. An increase of +50 % of both parameters leads to an unchanged mean annual rainfall but with an 20 increase of mean rainfall intensity of +4.0 mm/day and an increase of +20 days/yr of dry days.  The calibrated parameters are then used to simulate soil moisture under different scenarios of temperature and precipitation. The bias between the mean soil moisture from the reference scenario and the mean observed soil moisture is low and ranging from -0.003 to 0.01 m 3 .m -3 for the different stations. 4.3 Sensitivity of soil moisture to precipitation and temperature changes Figure 6 shows the sensitivity of the median of simulated soil moisture to changes in precipitation patterns. Results show that the median soil moisture is more sensitive to changes in precipitation intermittence (∆λ) than to changes in precipitation mean intensity (∆ξ). For the +0 • C scenario, an increase of the precipitation intermittence of +50 % leads to a decrease between -8 and -21 % on the median soil moisture, whereas an increase of 50 % in the precipitation mean intensity only leads to an 5 increase of the median soil moisture ranging between +2 and +17 %. Results also show that stations have different sensitivity to precipitation and temperature changes. Stations such as Villevielle, Narbonne seems to be more sensitive to climate variability, whereas Barnas, La Grand-Combe, Mouthoumet and Prades-le-Lez stations show a lower impact of changing precipitation patterns and temperature on the median soil moisture. Figure 7 shows the correlation between the median soil moisture change to different scenarios with the stations climatic characteristics (observed annual mean temperature and precipitation). Results

10
show that the soil moisture response is correlated to the station local temperature and also to local precipitation to a lesser extent (Fig. 7). Southern stations presenting a warmer and dryer climate seem to be more impacted by changes in precipitation and temperature than northern stations located in the Cevennes mountain range with a colder and wetter climate. No correlation was 13 https://doi.org/10.5194/hess-2020-302 Preprint. Discussion started: 25 June 2020 c Author(s) 2020. CC BY 4.0 License.
found between the soil moisture response and the NSRP model and SM model parameters values, meaning that the observed variability between station is independant from the models calibrations.  For instance, the Sobol index of the soil moisture to a parameter is the percentage of the soil moisture variance explained by the considered parameter. Over all the stations, the sum of the 1st-order Sobol indices are between 0.94 and 1.005 for median soil moisture, between 0.92 and 0.99 for the number of days below the 5th percentile and between 0.93 and 0.99 for 5 the days above the 95th percentile, which indicates that the GSA is based on a sufficient number of simulations. The Sobol sensitivity analysis shows that soil moisture variance is more impacted by changes in precipitation intermittence than changes in precipitation intensity and temperature, especially for the median soil moisture and the number of days with drought (i.e. low soil moisture values). Changes in precipitation intensities have a larger impact on higher soil moisture values and can became almost equivalent to the changes in precipitation intermittency, as for example in the Pezenas station. There is a link with the 10 mean precipitation and Sobol indices related to changes in precipitation intermittence and intensity. Indeed, the smaller the annual precipitation, the higher the Sobol index to the precipitation intermittence is for the median and 95th percentile of soil moisture (with correlations equal to respectively r=-0.71, r=-0.56). It is the opposite relationship between annual precipitation and precipitation intensity (with correlations equal to r=0.77 for median soil moisture, r=0.33 for the 5th percentile and r=0.74 for the 95th percentile). This indicates that changes in precipitation intermittence are more strongly impacting soil moisture in 15 locations with low annual precipitation.

Impact of changing precipitation and temperature on extreme soil moisture
In this section we analyse the response of extreme soil moisture to the precipitation and temperature scenarios. Figure  There is a large variability in the evolution of the mean annual number of days with wet conditions with results ranging from -14 to +12 days per year for the +2 • C scenario and from -15 to +8 days per year for the +4 • C scenario (Fig. 9a). For the +2 between -10 and -20 % and a +4 • C temperature increase) lead to an average of 10 days per year with wet conditions, i.e. a decrease of 8 days per year relatively to the reference scenario (Fig 10).
Concerning the impact of changing precipitation and temperature on dry soil moisture conditions, Figure 9b shows that almost all scenarios lead to an increase of the mean annual number of dry days. For the +4 • C scenario, the increase of the frequency of days with dry soil moisture can reach up to +40 days/yr for the Mazan and Narbonne stations. Only a few scenarios 10 with a high increase of precipitation intensity and a low increase of precipitation intermittence result in decrease dry conditions (10 % for the +2 • C scenario, and 2.4 % for the +4 • C scenario). RCP8.5 scenarios show a mean number of dry days per year ranging between 34 and 52 days/yr, corresponding to a mean increase of +22 days per year comparing to the reference scenario ( Fig 10). This increase of dry days mainly impacts the summer and autumn seasons from June to October (Fig. 11). None of the stations show an increase of extreme dry days during winter. These results show that agricultural drought events in the 15 Mediterranean region are likely to be more intense with longer episodes extending until the months of October and November.
Overall, results show that changes in precipitation patterns and temperature have a larger impact on lowest range of the soil moisture distribution than on the highest. This means that climate change is very likely to have a major impact on agricultural droughts with dryer soil moisture and longer drought events. Regarding the impact on flood events, it is difficult to make conclusions based on the results of this study as we do not simulate runoff generation. Our results show a decrease of the 20 median soil moisture for most of the considered scenarios as well as a decrease of days under saturated conditions suggesting a higher infiltration capacity of the surface soil layer with a potential lower runoff generation. Figure 9. Sensitivity of the annual number of days (a) with saturated soil (i.e. with soil moisture above the observed 95th percentile) and (b) under extreme drought (i.e. with soil moisture below the observed 5th percentile), according to changes in precipitation intensity (y axis), precipitation intermittence (x axis) and temperature, for the Barnas and Pezenas stations.

Discussion
One of the main limitations to this study lies in the constant soil moisture model parameters under different climate scenarios.
The use of constant parameters implies that processes such as the adaptation of vegetation to soil water stress or the impact of rising CO 2 on the vegetation physiology, which may have a sensitive impact on evapotranspiration and thus soil moisture (Berg and Sheffield, 2018), are not taken into account in this study. To avoid this issue, it would be required to consider 5 land surface modelling schemes that are able to take into account the feedback effects between vegetation and land surface processes (Albergel et al., 2017). In addition, offline computation of potential evapotranspiration with standard formulas such as the Blaney and Criddle or Penman-Monteith equations can be problematic since it neglects several factors, in particular the surface conditions (Barella-Ortiz et al., 2013). The impact of different formulations of potential evapotranspiration on soil moisture changes needs also to be investigated, since simple temperature-based formulas may overestimate the temperature effects on evapotranspiration (Sheffield et al., 2012;Vicente-Serrano et al., 2019).
Another source of uncertainties is related the selection of temperature and precipitation scenarios, while currently the majority of available climate simulations are at the daily time step. The projected changes on hourly climate characteristics remains largely unknown, and this is why we adopted a stochastic simulation approach to encompass the plausible range of future 5 scenarios. However, convection-permitting regional climate models (CPRCM) are increasingly being implemented over Europe during the last years to reproduce hourly changes in precipitation (Coppola et al., 2018) and these simulations should be considered in future experiments. Similarly, the approach considered in the present paper is based on distributional changes, while the impact of possible changes in the seasonal to inter-annual variability of precipitations on soil moisture cannot be taken into account. This issue could be also resolved by using CPRCM simulations instead of a stochastic rainfall generator to 10 simulate the soil moisture response to various changes in precipitation including seasonal and inter-annual variability.
Finally, this study relies on a set of soil moisture observations from different sites located in Southern France and, despite different annual precipitation and temperature patterns, the vegetation at the different locations belongs to the same biome. It would be interesting to perform this type of analysis on a larger set of sites located in various Mediterranean environments, including North Africa and the Middle East with more arid climate conditions, to investigate the possible relationships between 15 soil moisture dynamics and soil types, vegetation cover and climate characteristics for different degrees of aridity. Indeed, the Mediterranean region includes a great variety of types of vegetation, forming mosaic patterns created by variations in soil, topography, climate, fire history and human activity (Geri et al., 2010). Therefore, it would be very useful to produce a typology of the sensitivity of soil moisture changes for a variety of Mediterranean landscapes.

20
Soil moisture is an important variable to consider in a climate change context since its strongly influences agricultural droughts and flood generation processes. Future climate scenarios for the Mediterranean indicate an increase in temperature, associated with an increased frequency of dry days but also an intensification of extreme rainfall events. This study considered soil moisture monitored at 10 plots located in southern France, in a modelling framework aiming at estimating its sensitivity to changes in precipitation and temperature. For that purpose, a range of precipitation and temperature variations coherent with 25 current climate scenarios available for the Mediterranean region have been generated with a stochastic model to investigate the response of soil moisture to these climatic changes. The main result of this study shows that the sensitivity of soil moisture to changes in precipitation and temperature is similar at the different sites, with a higher sensitivity of soil moisture to intermittent precipitation and the number of dry days rather than their intensity or the temperature increase. However, these changes are modulated by the climate characteristics of the different stations, with a higher sensitivity of soil moisture to precipitation 30 intermittence in locations with dryer and warmer climate characteristics. Overall, it is observed that changes in precipitation and temperature have a greater impact on low soil moisture values than on conditions close to soil saturation. This implies that the current climate change scenarios may induce longer periods of depleted soil moisture content, corresponding to agricultural drought conditions. About the potential impacts of soil moisture changes on flood generation, more research is needed to better understand the joint influence of lower antecedent soil moisture conditions associated with higher rainfall intensity on flood magnitude and occurrence.