Modelling groundwater recharge, actual evaporation and 1 transpiration in semi-arid sites of the Lake Chad Basin: The role of 2 soil and vegetation on groundwater recharge

14 The Lake Chad Basin, located in the center of North Africa, is characterized by strong climate seasonality with a pronounced 15 short annual precipitation period and high potential evapotranspiration. Groundwater is an essential source for drinking water 16 supply as well as for agriculture and groundwater related ecosystems. Thus, assessment of groundwater recharge is very 17 important although difficult, because of the strong effects of evaporation and transpiration as well as limited available data. 18 A simple, generalized approach, which requires only limited field data, freely available remote sensing data as well as well-19 established concepts and models, is tested for assessing groundwater recharge in the southern part of the basin. This work uses 20 the FAO-dual K c concept to estimate E and T coefficients at six locations that differ in soil texture, climate, and vegetation 21 conditions. Measured values of soil water content and chloride concentrations along vertical soil profiles together with different 22 scenarios for E and T partitioning and a Bayesian calibration approach are used to numerically simulate water flow and chloride 23 transport using Hydrus-1D. Average groundwater recharge rates and the associated model uncertainty at the six locations are 24 assessed for the 2003-2016 time-period. 25 Annual groundwater recharge varies between

security reasons in 2019. Each of the soil profiles was sampled in 10 cm intervals and filled into headspace glass vials and 161 plastic bags. 162 Each soil fraction was tested for grain size distribution using standard sieving and sedimentation procedures (Tewolde, 2017). 163 Classification follows the soil texture triangle by the US Department of Agriculture (Šimůnek et al., 2011). 164 Chloride concentration was analyzed after aqueous extraction from oven dried (105°C for 24 hours) soil samples following 165 the standard guideline DIN EN 12457-1 (Tewolde, 2017). Data are presented in Tables S2 and S3. 166 Gravimetric water content is the mass of water contained in a sample as a percentage of the dried soil mass. It was obtained 167 by weighing the moist sample, oven drying it at 105°C for 24 to 48 hours, and weighing it again (Tables S2 and S3). Since 168 bulk densities were not measured in the field, volumetric water contents were obtained by multiplying the gravimetric water 169 contents for each soil type and location by typical bulk densities obtained from the Global Gridded Surfaces of Selected Soil 170 Characteristics database (Global Soil Data Task Group, 2000). 171 The type of vegetation and the annual cycle of crops, length of the flooding period, and vegetation throughout the dry period 172 were mapped during field work and documented by surveying resident populations. In addition, MODIS vegetation indices 173 data (Didan, 2015) were used to justify the documented annual cycle of phenology ( Figure 3). 174 can be neglected due to the flat topography). Soil moisture and chloride concentration along the soil profile at a certain time 177 are indicators for evaporation and transpiration processes within the root zone of soils. Chloride concentration in soil depends 178 on its input via precipitation and washing out of dry deposition as well as on the amount of evaporation and transpiration on 179 the soil surface and in the root zone. 180 The first estimation of evapotranspiration was carried out using the FAO-dual crop coefficient approach that assesses E and T 181 individually. The uncertainty of E and T partitioning on soil water and chloride concentration in the six soil profiles was 182 assessed by considering scenarios of mean, maximum, and minimum E and T coefficients (see 3.1). Calculated time series of 183 E and T for the site-specific vegetation were used to estimate soil water and chloride concentration profiles at the sampling 184 time in each of the six locations using Hydrus-1D. A Bayesian approach was applied to consider uncertainties in chloride 185 concentrations of precipitation and dry deposition, in partitioning E and T as well as in the parametrisation of the soil hydraulic 186 model ( Figure 4). 187

Partitioning of evaporation and transpiration
defined crop coefficient (Kc) combined with a reference evapotranspiration (ET0). Two approaches are possible, single crop 192 coefficient and dual crop coefficient. The latter was applied in this work. 193 The dual Kc method (Allen et al., 1998) is the sum of two coefficients, the basal crop coefficient (Kcb) that describes plant 194 transpiration and the soil water evaporation coefficient (Ke) that depicts evaporation from the soil surface. Kcb is defined as 195 the ratio of crop evapotranspiration over reference evapotranspiration (ETc/ET0), when the soil surface is dry and transpiration 196 occurs at a potential rate (i.e. unlimited water availability for transpiration). Ke is highest when the topsoil is wet, but 197 diminishes with drying out of topsoil to become zero, if no water remains near the soil surface for evaporation. 198 The parameters required for the estimation of monthly ETc are the monthly reference evapotranspiration (ET0), the monthly 199 basal crop coefficient (Kcb) and the monthly soil water evaporation coefficient (Ke): 200  Table S4. 209

Model concept, setup, and initial conditions 211
The chloride profiles measured in soil at a certain time represent water and solute budget input from past precipitation events 212 and can be estimated by transient water flow and solute transport modelling. The model concept assumes that atmospheric 213 chloride input is restricted to solute in precipitation and that the chloride concentration profile results from solute enrichment 214 in the soil, due to evaporation and transpiration. An accurate parametrization of the unsaturated flow and transport model as 215 well as a robust quantification of groundwater recharge are not possible with the available data and hence cannot be included 216 within the scope of this study. However, the model results estimate groundwater recharge magnitude and variability based on 217 information regarding soil texture and vegetation as well as associated uncertainty in results. This proposed approach is 218 appropriate for locations with limited availability of long-term soil water measurements. 219 The free software package Hydrus-1D version 4.17.0140 was used to simulate transient water flow and solute transport in the 220 six variably saturated soil profiles. Hydrus-1D numerically solves the Richards (1931) equation for variably saturated water 221 flow, advection-dispersion equations for heat, and solute transport (Šimůnek et. al, 2009): 222 The processes simulated at the six study sites were water flow, solute transport, and root water uptake. Hydrus-1D requires 233 input data at daily time steps, but available precipitation and evaporation data were monthly. Daily values were calculated 234 dividing monthly data by month-specific days. Thus, all days in a month had the same precipitation rate and the same 235

Water flow 245
For calculation of water retention (θ) and unsaturated hydraulic conductivity functions (K(h)), the Mualem-van Genuchten 246 (MVG) model (van Genuchten, 1980) was applied: 247 In the calibration, scaling factors ranging from 0.75 to 1.25 for the MVG parameters (saturated volumetric water content, 317 alpha, and n) were adopted individually. However, ranges for the MVG model parameter n were constrained to n > 1.01. Log-318 transformed saturated hydraulic conductivity for each layer was considered with ranges from -0.5 to 0.5. The scaling factor 319 for transpiration was simultaneously used as a divisor for evaporation to remain within the calculated rate of ET0. Agriculture soil texture triangle. Most profiles are fine-grained soils (clay, sandy clay) and fine-grained soils with intercalation 326 of thin sand and loam layers. Only soil profile ST3 is dominated by sand and sandy clay loam. 327

Model parametrization 328
The calibrated parametrization of the MVG model for each layer of the six sampling locations is plausible (Table 3). The 329 posterior distributions of the Bayesian calibration show the sensitive parameters of the model fit. For ST1, these are n, θs, 330 chloride concentration, and the transpiration fraction in evapotranspiration (T), but the ks is less sensitive (Fig. S1). For ST2, 331 the sensitivities of the model parameters are similar with ks of the upper layer being the most sensitive and chloride 332 concentration the least sensitive (Fig. S2). The model fits of the data from site ST3 are generally insensitive. Only α, n, and ks 333 of the upper layer as well as chloride concentration show tighter posteriori distributions (Fig. S3). For site WL1, the model 334 parameters n of layers 1, 2, and 3 as well as the saturated water content of layers 3 and 5, and subordinately of layer 4, are 335 sensitive (Fig. S4). For WL2, the model parameters n of all layers, ks of layer 3, and θs of layers 2 and 3 are sensitive (Fig.  336   S5). For WL3, θs of layer 2, ks of layers 1 and 2, and the fraction of transpiration in evapotranspiration are sensitive (Fig. S6). 337

Soil water content, chloride concentration and groundwater recharge 338
Measured and simulated water content and chloride concentration profiles for individual scenarios are shown in Figure 6. The 339 average root mean squared error (RMSE) of simulated water content for all individual scenarios ranges from 0.02 to 0.06 cm 3 340 cm -3 (Table 4). In general, the models reproduce well the water content and chloride concentrations. However, the dynamics 341 of measured and simulated water contents differ considerably for ST1 and partly for ST2, although maximum values do match. 342 The models do not match the high chloride concentrations in the uppermost part of soil profiles for ST3, WL1, and WL2. The 343 standard deviations in chloride concentration of the randomly selected model runs are exceptionally high in the lower part of ST2 that corresponds to the poor sensitivity of the chloride concentration at the upper boundary and the comparably wide range 345 of measured chloride concentration in ponding water in the Salamat region (2.5 mg l -1 -25 mg l -1 ). 346 The interannual variability of modelled groundwater recharge differs considerably among locations (Figure 7, Table 5 The highest average annual recharge (93 mm) was calculated for ST3 in Salamat (Table 6)

Evaporation and transpiration 381
The amount of transpiration depends on the availability of water in the root zone and the type of vegetation cover. At ST1, 382 annual transpiration presents two peaks: one related to sorghum and the other to grass (Figure 9). At each location and in every 383 simulation year, soil water content in the root zone reaches the wilting point defined by the specific parametrization of the root 384 water uptake model. 385 The actual evaporation rate depends mainly on the availability of water in the upper soil zone (Table 6)