Estimating water fluxes in the critical zone using water stable isotope approaches in the Groundnut and Ferlo basins of Senegal

Sustainable water management in semi‐arid agriculture practices requires quantitative knowledge of water fluxes within the soil‐vegetation‐atmosphere system. Therefore, we used stable‐isotope approaches to evaluate evaporation (Ea), transpiration (Ta), and groundwater recharge (R) at sites in Senegal's Groundnut basin and Ferlo Valley pasture region during the pre‐monsoon, monsoon, and post‐monsoon seasons of 2021. The approaches were based upon (i) the isothermal evaporation model (for quantifying Ea); (ii) water and isotope mass balances (to partition Ea and Ta for groundnut and pasture); and (iii) the piston displacement method (for estimating R). Ea losses derived from the isothermal evaporation model corresponded primarily to Stage II evaporation, and ranged from 0.02 to 0.09 mm d−1 in the Groundnut basin, versus 0.02–0.11 mm d−1 in Ferlo. At the groundnut site, Ea rates ranged from 0.01 to 0.69 mm d−1; Ta was in the range 0.55–2.29 mm d−1; and the Ta/ETa ratio was 74%–90%. At the pasture site, the ranges were 0.02–0.39 mm d−1 for Ea; 0.9–1.69 mm d−1 for Ta; and 62–90% for Ta/ETa. The ETa value derived for the groundnut site via the isotope approach was similar to those from eddy covariance measurements, and also to the results from the previous validated HYDRUS‐1D model. However, the HYDRUS‐1D model gave a lower Ta/ETa ratio (23.2%). The computed groundwater recharge for the groundnut site amounted to less than 2% of the local annual precipitation. Recommendations are made regarding protocols for preventing changes to isotopic compositions of water in samples that are collected in remote arid regions, but must be analysed days later. The article ends with suggestions for studies to follow up on evidence that local aquifers are being recharged via preferential pathways.

most reliable, and most resilient source of water for drinking, industry, and irrigation. Identification of groundwater-recharge (R) mechanisms in semi-arid regions is especially difficult due to the mechanisms' high spatial and temporal variability Scanlon et al., 2006).
Quantification of atmospheric losses (ET a ) in these regions-particularly the relative contributions of soil evaporation (E a ) and plant transpiration (T a )-is additional challenge (Sprenger et al., 2017). As a result, important gaps exist in the research community's understanding of arid regions' hydrological processes, and of the associated water-flux partitionings within the soil-vegetation-atmosphere (SVA). Filling those gaps is crucial because semi-arid regions are highly sensitive to the projected changes in climate (Pörtner et al., 2022).
These experimental approaches require sophisticated, expensive, high-maintenance instruments. Another experimental, data-driven method is based upon analyses of stable isotopes of hydrogen (δ 2 H) and oxygen (δ 18 O) in the various water fluxes. This method can provide time-integrative information on these fluxes even in remote areas (Adomako et al., 2010;Mueller et al., 2014).
The evaporation fronts within the unsaturated zone have been a particular target of previous works that used water stable isotopes Dawson & Ehleringer, 1998). One such study (Zimmermann et al., 1967) showed that at the surface of a saturated soil column, evaporation enriches the soil water in heavy isotopes.
The enrichment then decreases exponentially with depth. Formation of the similar enrichment profiles was confirmed by follow-up studies, which developed theories (e.g., isothermal evaporation) to explain them , 1985Barnes & Allison, 1988;Christmann & Sonntag, 1987). For example,  have shown that in a soil that has been subject to evaporation, the observed isotope profiles result from a balance between the upward evaporative flux and the downward diffusive flux. According to , the assumption that the evaporative loss occurs isothermally and at thermodynamic equilibrium is reasonable as long as sufficient time has elapsed since the preceding rainfall event, so that the soil's hydrological parameters are not changing rapidly. This condition is generally satisfied in arid regions, except during the period immediately after a rainfall event (Barnes & Allison, 1988).
Quantitative calculations of groundwater recharge (R) have been another target of studies that employed water stable isotopes as tracers (e.g., Beyer et al., 2015). These studies have been addressed actively in older and recent reviews (Allison et al., 1994;Koeniger et al., 2016;Scanlon et al., 2002). In one study,  developed the piston displacement method, which has proven to be a simple and suitable technique for making quantitative estimates of groundwater recharge in semi-arid climates (e.g., Boumaiza et al., 2021;Gaj et al., 2016). However, we note that the relationship on which this technique is based is empirical (Barnes & Allison, 1988), and may be site-specific. The few subsequent investigations of this relationship (e.g., Herczeg & Leaney, 2011;Selaolo et al., 2003) did not confirm it. Therefore, its applicability may be limited.
The use of stable isotopes to study ET a partitioning (into T a and E a ) has benefitted recently from the advent of new laser spectrometers that can analyse even small amounts of water-such as samples extracted from soils. In addition, stable isotopes in soil pore water can be analysed using the water-vapour-equilibrium method (Wassenaar et al., 2008).
For example, Wenninger et al. (2010) and Sutanto et al. (2012) used a combination of lysimeter measurements and stable-isotope analyses to calculate the partitioning of ET a for grass vegetation in laboratory setups. The necessary calculations were based upon mass balances of water and isotopes in the soils of those setups. Subsequently, Liebhard et al. (2022) successfully adapted these laboratory experiments to soybean crops under field conditions, based upon the assumption that the isotopic composition of the transpired (δ Ta ) water fraction is related to a crop-specific root-water uptake profile. The authors combined hourly weather data with measured ET a rates to calculate the fractionation factors for each evaluation period. In addition, the authors based their determinations of δ Ea upon isotope ratios in the evaporation zone near the soil surface, rather than in the mean soil column. However, the methods that Liebhard et al. (2022) used in soybean fields may be less suitable for arid regions, where lysimeters are difficult to instal and maintain. Other concerns include the possibility of a flow-edge effect (due to the drying of the soil) and sensitivity to different vegetation conditions inside and outside of the lysimeter (Nouri et al., 2013).
Information on ET a partitioning and quantitative R estimation in the two regions is very limited, despite the region's importance to Senegal's water and food security. As one example of that importance, statistics from Senegal's National Agency for Statistics and Demography (ANSD) show that in 2020, 63.15% of the nation's total planting area was devoted to raising groundnut (also known as peanut, Arachis hypogaea L). The Ferlo region's importance is similar. There, extensive livestock-raising is the most important source of food and income for many households, including the region's semi-transhumant and seminomadic pastoralists (Niemi et al., 2015).
The specific objectives of our study are to use different isotope approaches to (1) quantify E a ; (2) partition E a and T a for groundnut crops and natural pasture vegetation; (3) estimate R; and (4) compare these results to those from numerical-modelling approaches that have been carried out in the Groundnut basin experimental site (Diongue et al., 2022). We formulate three hypotheses: (i) that E a can be estimated accurately from soil-water isotope profiles (because the necessary isothermal equilibrium is maintained); (ii) that the isotopic composition of the transpired water (δ Ta ) fraction is related to a specific root-water uptake profile (and therefore that both E a and T a can be partitioned by calculating mass balances for water and isotopes); and (iii) that the assumption of piston flow is valid for the studied environment, and can therefore be used to estimate groundwater-recharge rates (R).

| MATERIALS AND METHODS
The research described in this section was performed during 2019-2021.

| Study sites
The two sites selected for this study are located in mid-western and northern Senegal, along a rainfall gradient decreasing from south to north ( Figure 1). Site 1 is located in the agro-ecological zone of Groundnut basin (mid-western part of Senegal) in the region of Fatick F I G U R E 1 Locations of the two study areas. Site 1 is in the groundnut basin, within an agroforestry park dominated by Faidherbia albida trees that are associated with rainfed groundnut crops. Site 2 is located in the Ferlo Valley within the Great Green Wall, near a temporary pond used by Peul herders to water their cattle during the rainy season. Vegetation at site 2 is dominated by thorny species such as Balanites aegyptiaca, and is influenced by seasonal grazing. The annual-precipitation basemap is from Agence national de l'Aviation Civile et de la Météorologie (ANACIM). Photos show the sites' landscapes during the dry and rainy seasons.
(135 km from Dakar), where rainfed agriculture is the dominant activity. Site 2 is located in the silvo-pastoral zone of the Ferlo Valley (northern part of Senegal) in the region of Louga (400 km from Dakar), where livestock farming is the main activity.

| Site 1: Groundnut basin
Site 1 is part of the "Faidherbia-Flux" (FLUXNET/SN-Nkr) collaborative platform (https://lped.info/wikiObsSN/?Faidherbia-Flux) in the agroforestry parkland of Sob village. The landscape is flat with a gentle northward slope, characterized by a tree-based cropping system dominated by Faidherbia albida (Del.) A. Chev. The density of the stand is 6.8 trees ha À1 , and the canopy cover is 9.6% . Faidherbia is a nitrogen-fixing species with a reverse phenology (i.e., it has no leaves during rainy season). It is known to boost the yields of associated crops Sileshi, 2016). During the rainy season, farmers in the agroforestry zone raise rainfed pearl millet and groundnut crops, in annual rotation. Groundnut farming accounts for over 35% of the local household revenue, and constitutes an important component of Senegal's local staple foods (Diagne, 2014).
Rainfall occurs only during the five-month rainy season (June-October). From July to September, mean monthly rainfall exceeds the ET 0 , thus allowing percolation and groundwater recharge to occur. In contrast, the dry season's high ET 0 drives evaporation from surface and soil water, and consequently may induce upward water fluxes from groundwater into the soil. During the year 2021, measured values of rainfall, ET 0 , and actual evapotranspiration (ET a , from eddy covariance) were 478 mm, 1512 mm, and 453 mm, respectively (Diongue et al., 2022).
The soil at Site 1 is of a type known locally as "Dior soil," and contains less than 20% clay. According to the FAO classification, it is an Arenosol (loamy sand or coarser texture). The Continental Terminal (CT) formations constitute the upper, unconfined aquifer. A shallow, brackish groundwater table is at a depth of around 6 m. The CT consists of detrital sea-origin formations that were deposited during the Cenozoic period (Oligo-Miocene to Pliocene). Later, the deposits underwent an intense ferralitic alteration that caused crusting, significant silica movement, formation of ferruginous concretions, and neoformation of kaolinite (Conrad & Lappartient, 1987).

| Site 2: Ferlo
Site 2 is located in Widou Thiengoly village near a small temporary pond . The area is part of the Great Green Wall zone, which was reforested with Acacia senegalensis (L.) and Balanites aegyptiaca (L.) Del. This region is characterized by intense livestock breeding of zebus, sheep, goats, and camels. Human and livestock populations increased by a factor of about 2.3 between 1950 and 1983 (Vincke et al., 2010).
The climate is of Sahelian type (arid), with a 9-month dry season (from June to October) and a short rainy season (July to September).
The annual mean temperature is 28 C, and the mean long-term (50 years) rainfall is 371 mm (Ndiaye et al., 2015). During June to December of 2021, rainfall and ET 0 values were, respectively, 280 and 1080 mm.
The topography is mainly flat, with low, gently undulating dunes of aeolian sand that remain from erg deposits during the Middle to Recent Quaternary period (Tappan et al., 2004). The soils have loamysand to sandy clay-loam textures (Faye, Diallo, et al., 2020). According to the French classification, they are degraded red-brown sub-arid soils. (Or "Cambic-Luvic Arenosols" according to the FAO (Maignien, 1965)). Clay contents are less than 25%. Edaphic conditions prevailing near temporary ponds and on the slopes of dunes play a significant role in microclimate aridity, which in turn influences the soil water balance, and therefore vegetation development (Vincke et al., 2010). Vegetation consists of thorny trees, shrubs, and a seasonal herbaceous-species cover. The shrub stratum is composed mainly of Calotropis procera (Ait.) and Boscia senegalensis (L.) (Ndiaye et al., 2015;Niang, 2009). The dominant herbaceous (pasture) species during rainy seasons are Heteropogon contortus (L.) P.Beauv (which is investigated in the present study) and Indigofera senegalensis (L.) (Grouzis et al., 1998).
The temporary ponds that form during the rainy season are used for livestock needs. In addition, two aquifers provide groundwater resources: the CT aquifer (water table depth

| Soil and water sampling
The sampling scheme used in this study was designed to provide the data that are needed for calculating values of E a and T a per the mass balances that the previous authors had applied to grass vegetation and soybean fields (Wenninger et al. (2010); Sutanto et al. (2012); and Liebhard et al. (2022)).
At both sites, daily precipitation events were sampled with a rainfall collector (Rain Sampler RX1, Palmed ltd, Croatia) during the 2019-2021 rainy seasons. The collector was located in an open area, at a height of 2 m. Precipitation samples were preserved in airtight vials, with an additional covering of parafilm, then stored in a refrigerator at 4 C until they were subjected to isotope analysis. Eighty-three (83) samples were collected from Site 1, and 44 from Site 2.
Soil profiles were sampled in 2021, along gentle slope transects.
Specifically, the samples were taken during February and June (bare soil, during the dry season); in December (after harvest, during the dry season); and during the August wet season, which corresponds to the growing stage of groundnut crops and pasture. At Site 1, samples were collected from the upper, middle, and lower slopes. Only the middle and lower slopes were sampled at Site 2. Continuous soil cores were collected with a hand auger (Eijkelkamp, Netherlands). At Site 1, two core soil profiles were carried out at each slope location, from a depth of 5 cm down to the capillary fringe (500 cm below ground level at the upper and middle slopes, and 400 cm below ground level at the lower slope). One of the profiles was sampled underneath the Groundwater was sampled at Site 1 in three piezometers during the 2020 wet season, and during each soil sampling campaign during 2021. Piezometers were purged for 10-15 minutes before taking samples, which were then stored in airtight vials covered with parafilm and stored at 4 C in a refrigerator.

| Soil physical properties
To determine their textures and dry bulk densities (ρ b ), soil profiles from Site 1 were sampled with a calibrated cylinder (100 cm 3 ). The ρ b values were then determined in Dakar by the "Laboratoire d'Ecologie Microbienne des Sols et Agrosystèmes Tropicaux", LMI IESOL, by weighing the soil samples after oven-drying for 48 h at 105 C. Porosities (p) of soil samples were calculated following Black et al. (1965), assuming a particle density of 2.65 g cm À3 .
The particle size distributions (PSDs) of samples were determined via the laser diffraction method at the laboratory of "LEHNA-ENTPE," in Lyon, France. With these PSD results as inputs, the GRADISAT V9.1 package (Blott, 2001) was used to compute the fractions of sand, silt, and clay, and thus to classify the soil textures according to the USDA. For Site 2, we used soil-texture data from Faye, Diallo, et al. (2020), Faye, Fall, et al. (2020), which covered the 0-100 cm depth on the mid-slope locations as well as on the lower-slope locations, near the pond.
The gravimetric water content (GWC) of each soil sample (all had been stored in double Ziplock bags; Section 2.2) was determined by weighing and drying before and after isotope analyses. The volumetric water content (VWC) was calculated according to Gardner (1965), using the measured ρ b and assuming a water density (ρ w ) of 1 g cm À3 .
ET a values for the groundnut crop at Site 1 were derived from latent heat (λE) flux analysis via the eddy-covariance technique. For that purpose, an antenna equipped for eddy-covariance measurements (Li-7500A (LiCor) + Windmaster Pro (Gill)) had been installed in Site 1, at a height of 4.5 m. Raw data were acquired at 20 Hz, using Tourbillon (INRAE) software. Post-processing of binary files was done with EdiRe (University of Edinburgh, Scotland). Additional details are provided in Diongue et al. 2022).

| Stable isotopes analyses
Oxygen and hydrogen isotope ratios of bulk soil waters were determined from soil samples, using the water-vapour equilibration method described by Wassenaar et al. (2008). To detect any water loss that might have occurred during sample preparation, the samples in their respective Ziploc bags were weighed upon arrival at the laboratory, and again before and after analysis. No water loss was observed. Bags were inflated with dry air and left for 3 days to reach equilibrium. The isotope ratios of the vapour were determined using a laser-based isotope analyser (Picarro L2130-i). Isotope ratios of the bulk soil water samples were calculated from calibrations that were based upon iso- 2.4 | Quantification of water fluxes

| Evaporation
Evaporation losses (E a ) from the unsaturated soil profiles were quantified using the steady-state isothermal evaporation model developed by : where ha (À) is the relative humidity; N sat is the saturated water vapour density (kg m À3 ); τ is the tortuosity (estimated by Penman (1940)

| Evapotranspiration partitioning
We used the two mass-balance equations that follow (developed by Sutanto et al. (2012) and Liebhard et al. (2022)) to compute the partitioning of ET a between soil evaporation (E a ) and transpiration (Ta, by groundnut crops or pasture). The E a and T a rates obtained via these mass balances are averages for a given time interval. The subscript i denotes values at the beginning of the interval, and the subscript f denotes values at the end.
In Equation (4), each m represents the mass of water (normalized per unit volume of soil in the sampled profile) that corresponds to a particular component of the mass balance. Specifically, m i and m f are, respectively, the initial and final amounts of water stored within the soil; p is the amount of precipitation during the time interval; e is the loss due to evaporation; t is the loss due to transpiration; and l is the loss due to percolation. In Equation (5), each x k is the fraction of total water that corresponds to component k. For example, x p = m p /m total .
When used to calculate mass balances on 18 O, each δ k in Equation (5) represents component k's value of δ 18 O. The same δ k 's represent the components' respective values of δ 2 H when calculating mass balances on Deuterium.
In the present research, the factors δ i , x i , δ p , x p , δ f , x f , δ l , and x l were obtained from measurements. As detailed below, the δ i and δ f for the isotopes in a given soil-profile are weighted means for the soil water in those samples. δ p is the weighted mean of precipitation; and δ l is the ratio of the sample at the bottom of the soil-profile. The data used to calculate the δ e were (i) the fractionation factor ε total (see below), and (ii) the value of δ that was present at the soil surface (5 cm depth). δ t was calculated from a combination of the weighted mean of δ, the soil volumetric water content (VWC), and the rootlength density (RD) of soil layer j (see Liebhard et al., 2022): Following Dongmann et al. (1974), each isotope's overall fractionation by evaporation (ε total ) was calculated as the sum of the isotope's equilibrium fractionation between liquid water and water vapour (ε eq ), and its kinetic fractionation (ε k ). The values of ε eq were computed per Horita and Wesolowski (1994): 10 3 ln α þ 18 O h i ¼ À7:685 þ 6:7123 10 3 T ! À 1:6664 10 6 T ! þ 0:3504 10 9 where α + is the difference between the isotopic compositions of liquid and vapour phases at isotopic equilibrium, and T (K) is the air temperature.
The kinetic fractionation ε k quantifies isotopic effects during net evaporation, and results from the higher diffusivities of isotopically lighter molecules. It was estimated following Gat (1996) andHorita et al. (2008): where θ is close to unity for soil water and small water bodies (Gat, 1996). The factor n accounts for the aerodynamic regime above the evaporating liquid-vapour interface, and is assumed to equal one for fully diffusive transport, as is appropriate for dry soil conditions (Benettin et al., 2018). h (À) is the relative humidity of the air overlying the evaporating surface. The term D i /D is the ratio between the diffusivities of the heavy and light isotopes. Per Merlivat (1978), the com- Under the assumptions that they described in their respective works, Sutanto et al. (2012) and Liebhard et al. (2022) determined x t and x e as residuals of the mass balances that are given in Equations (4) and (5): As noted earlier, the present study computed mass balances based on both δ 2 H and δ 18 O. The results are reported as the mean and standard deviation. Data from isotope profiles down to a depth of 100 cm were used to cover the entire root zone of groundnut (at Site 1) and pasture (at Site 2). It is essential to consider the whole root zone because δ t was weighted with the root-length density (see Equation 7) For groundnut crops, 72.4% of the root system was within the 0-20 cm soil layer depth, while 27.6% was found at 20-50 cm depth (Siegwart et al., 2022). Root-length density in the pasture at Site 2 was assumed to decrease linearly from its maximum value at the soil surface down to its minimum at the maximum root length (around 40 cm, according to Glendening (1941)). Rainfall amounts were measured at both sites with a weather station (Campbell TE25MM at Site 1, and Campbell Climavue 50TM at Site 2). Values for the soil-water storage (m i and m f in Equation 4) were derived from the VWC of each soil profile, and ET a was estimated from eddy covariance fluxes at Site 1 (Diongue et al., 2022). For that site, the only unknown variable in the mass balance was the percolation, which was calculated as the residual from the water balance equation (Equation 4). Percolation at Site 2 could not be estimated because the ET a was unknown. Therefore, percolation at that site was assumed to negligible due to the low level of water storage in the soil (Moriana et al., 2003;Nielsen & Vigil, 2010).

| Groundwater recharge
The groundwater recharge rates (R in mm y À1 ) were estimated by applying the piston displacement method  to data from deep soil samples (>150 cm; see Figure 3). The method is based upon a simple empirical relationship. As given in Clark and Fritz (1997), the relationships for δ 2 H and δ 18 O are where δ 2 H shift is the difference between (i) the deuterium excess of the local meteoric water line (LMWL), and (ii) the intercept of the linear regression for isotope data from deep soil samples.
We used soil data from Site 1 to assess the relevance of the piston displacement method and to quantify the annual groundwater recharge of the CT aquifer. We could not estimate the groundwater recharge for Site 2, because the groundwater table is at 50-70 m depth, and our soil profiles extended down to only 300 cm. Nor were any wells or boreholes available for sampling the CT at that location.

| Further data analysis
To assess the influence depth of isotope fractionation, the lineconditioned excess (lc-excess; Landwehr & Coplen, 2006) was calculated for each soil sample: where a and b are, respectively, the slope and intercept of the LMWL.
The lc-excess expresses the degree to which the δ 2 H of the sample deviates from the LMWL. The physical significance of that deviation is that non-equilibrium, dynamic fractionation has been caused by
Soil moisture during the dry season is significantly higher (p < 0.05) at the low-slope location (0.8%-10.9%) than at the midslope (0.5%-3.5%). The vertical distribution of the VWC for the wet season is difficult to interpret because only the upper part of the profile was sampled. However, the means for the lower slope and midslope are similar (p = 0.51), at around 8.3%.

Calculation of evaporation using the isothermal evaporation model
The isothermal evaporation model developed by  is used to calculate evaporation rates (E a ) from the isotope profiles of soil water. Evaporation fronts could not be identified from wet-season profiles. Rates that were calculated from dry-season data ranged from 0.02 to 0.09 mm d À1 at Site 1, and from 0.02 to 0.11 mm d À1 at Site 2. The lowest E a values are for June, when the VWC are the lowest (Table 1). At Site 1, mean values are similar between locations, at around 0.05 mm d À1 . At the upper-and mid-slope locations in Site 1, the mean E a underneath the canopy is higher than in open areas ( Figure 5), but the difference is not significant (p = 0.34). Estimated E a values for Site 2 indicate that more evaporation takes place at the lower slope (0.08 ± 0.03 mm d À1 ) than at the mid-slope (0.04 ± 0.01 mm d À1 ). Again, the difference is not significant (p = 0.121).
However, lc-excess values confirm that evaporation is higher at the lower slope.
Evaporation and transpiration partitioning for the groundnut crop (Site 1) and pasture (Site 2) The isotope mass balance approach (Section 2.4.2) was used to calculate this partitioning. The times (and corresponding field conditions) during which we ran this calculation were: (i) February-June (bare soil, no crop and pasture); (ii) June-August (initial growing stage); and (iii) August-December (vegetative growing stage and harvesting).  supplementary material, Table S2). Figure 6 displays the mean values of E a and T a rates obtained by using δ 18 O and δ 2 H isotope data separately. The standard deviation of these rates is less than 0.25 and 0.27 mm d À1 for E a and T a rates, respectively, during all evaluation periods at both sites.
Because crops at Site 1 are rainfed, the soil is bare during the dry season (February to June). Therefore, soil evaporation is the main component of water loss. During this period, evaporation varies underneath and outside the canopy cover from 0.03 to 0.01 mm d À1 on the mid-slope, and from 0.05 to 0.06 mm d À1 on the upper slope.
T A B L E 1 Parameters used for estimating evaporation rates (E a ) via equation 5 for sites 1 and 2 at different slope locations during the three evaluation periods. z ef is the depth of the evaporation front (i.e., where δ 18 O is highest, and lc-excess values are lowest); VWC is the weighted mean of the soil volumetric water content in the shallow soil; and ha and T are, respectively, the relative humidity and air temperature. D v (the diffusivity of water vapour in the air) is a function of T.
Site T A B L E 2 Summary of the mass balances for water and isotopes in the top 100 cm of soil profiles at Sites 1 and 2 during the three evaluation periods. N is the number of days between two consecutive sampling periods. VWC is the soil water storage; δ is δ 18 O, rain is the rainfall amount; ET a is the actual evapotranspiration (from eddy-covariance fluxes); and Q is the percolation. The subscripts i and f indicate, respectively, values at the beginning and end of the time interval between samplings. p is precipitation, e is evaporation, t is transpiration, and q is percolation. ET a and Q were not available at Site 2. Due to low soil water storage at that site, percolation there was assumed to be insignificant for the purposes of the isotope mass balance.
Standard deviations of the recharge estimates ranged from 0.1 to 1.4 mm y À1 .
The estimated recharge rates are less than 2% of annual rainfall. The difference between recharge rates under canopy and in open ground is not significant (p = 0.8). In contrast, the estimated recharge is significantly lower (p = 0.032) at the upper slope than at the mid-slope and lower slope. Specifically, the δ 2 H shift -based mean at the upper slope is 3.37 mm y À1 , versus 3.57 mm y À1 according to the δ 18 O shift -based calculation. The same means for the mid-slope are, respectively, 6.47 and 6.83 mm y À1 . At the lower slope, the means are 6.16 and 7.02 mm y À1 .

| Isotopic composition of rainfall at the two sites
The differences between the sites' LMWLs appear to reflect differences between the sites' local climates, and possibly between their F I G U R E 6 Daily evaporation and transpiration rates during the three evaluation periods for (a) groundnut crops at site 1 and (b) pasture at site 2. The error bars show the standard deviation using δ 18 O and δ 2 H separately for the mass balance calculations.
distances from the coastline. The sites' LMWLs differ, too, from the LMWL that Travi et al. (1987) calculated for Senegal as a whole. We explore the differences below.
The LMWLs for Sites 1 and 2 are, respectively, δ 2 Η = 7.61 ± 0.20 Â δ 18 O + 7.50 ± 1.23 (R 2 = 0.98), and δ 2 Η = 7.48 As monsoon vapour moves inland, it becomes enriched in heavy isotopes due to evaporation. For that reason, the slopes and intercepts of the study sites' LMWLs are lower than those calculated by Travi et al. Moreover, the slope and intercept for Site 2 are lower than those of Site 1-as would be expected, because Site 2 is both farther from the coast and more arid: the annual rainfall is about 500 at Site 1, but only 300 mm at Site 2 ( Figure 1). We note, too, that Travi et al. found that in the north of Senegal (at Richard Toll, close to Site 2), the heavy-isotope contents of rainfall increased with temperature, especially as the amount of rainfall decreased. However, no such "amount F I G U R E 7 Relationship between δ 2 H and δ 18 O ratios in site 1 soil samples collected from the upper slope, under and outside tree canopies, during the months of February (a1, a2), June (b1, b2), and December (c1, c2). The blue dashed line is the LMWL. Red circles (with a red regression line) correspond to soil samples from the near-surface zone below the evaporation front. Grey circles and the dashed grey regression line correspond to soil samples from the zone below the evaporation front. Note that the grey regression line is parallel to the LMWL, but has an offset. (I.e., a different δ 2 H intercept.) F I G U R E 8 Mean annual groundwater recharge of the CT aquifer underneath and outside tree canopies at site 1, based upon analyses of the δ 2 H shift and δ 18 O shift . Error bars show the standard deviation associated with each sampling period (February, June, and December).
effect" (i.e., relationship between rainfall amount and depletion in the heavy isotope) was evident in the present study.

| Stage II evaporation and the applicability of the isothermal-evaporation model
Evaporation from a bare soil surface proceeds in two fairly distinct stages (Fisher, 1923;Pearse et al., 1949). During Stage I (the "constant-rate" stage), evaporation occurs isothermally at a constant rate from a wet soil that meets the evaporative demand. As the soil surface begins to dry, the evaporation rate falls quickly at first, then enters Stage II (the "falling-rate" stage), during which the rate decreases gradually over time (Gardner, 1959). At both of our experimental sites, the evaporation process is probably in Stage II during the long dry season.
As applied to those sites, the bias in the isothermal model may be significant, primarily because of the uncertainty in the position of the evaporation front, which is the most critical input to the evaporation estimates (see Table 2). A relative standard deviation of about 25% was estimated by  in their study. Although the uncertainty associated with the position of the evaporation front may be smaller in our study (because of the high vertical resolution of our sampling near the soil surface), other significant errors may have resulted from ignoring the vertical temperature gradient in the topsoil (Barnes et al., 1989). For example, the average soil temperature at 14:00 h at Site 1 during February fell from 39.8 C at the 2 cm depth to 30.4 C at 30 cm.
These caveats notwithstanding, we note that even allowing for the significant uncertainty in the E a estimates, the estimated E a at Site 1 amounts to only 4.7% of the total ET a (which was based upon eddy covariance). The explanation for this low, unexpected E a /ET a ratio may be that most of the evaporation occurred during Stage I, when both the E a and the T a are high. This phenomenon was reported in the previous research on semi-arid sites, and which used the same approaches (e.g., Liu et al., 1995;Busari et al., 2013). Overall, the assumption of isothermal equilibrium evaporation seems to be valid. However, the model itself was developed for long-term evaporative losses, and therefore does not account for the first stage of evaporation, which is the most important one in semi-arid climatic conditions.

| Partitioning of E a and T a in groundnut fields and pasture
The calculated E a and T a rates for groundnut and pasture covers are reasonable, and within the range found in the literature for semi-arid regions under rainfed conditions (Chibarabada et al., 2020;Halilou et al., 2015;Kizito et al., 2012;Ratnakumar et al., 2009;Yepez et al., 2005). During the first evaluation period (the dry February-June months), the E a fraction derived from the isotopic mass balance is low (0.02-0.06 mm d À1 ) at both experimental sites, and on the same order of magnitude as values obtained from the steady-state isothermal model. These low rates may be attributable to the low water contents and hydraulic conductivities of the sites' sandy soils during the dry season. However, we found that during the same period, E a rates are much higher at the lower-slope locations in Site 2: 0.16 mm d À1 according to the isothermal model, versus 0.12 mm d À1 according to the isotope mass balance. These higher rates are probably due to the higher clay contents (and therefore greater water retention) in the topsoil at those locations.
During the second evaluation period (the dry-wet months June-August) and the last one (the wet-dry months August-December), the evaporation rates at both sites, as derived from the isotopic mass balance, are higher than during the first period. The difference is due to the increase in soil wetness in the wet season. These mass-balance evaporation rates are also higher than those obtained from the isothermal model (second-stage evaporation) for the same period. Therefore, the isotope mass balance captures both first-and second-stage evaporation from June to December. However, this method gave a negative E a fraction (reported here as 0 mm d À1 ) for the lower-slope location under the canopy cover (Site 1) during June-August. At the end of this period, the soil water at this location was more depleted in heavy isotopes (δ f = À5.6 ‰) than at the beginning (δ i = À1.4 ‰). It was also more depleted in heavy isotopes than the rainfall (δ p = À4.9 ‰). This discrepancy cannot be the result of evaporation or nonfractionating processes (transpiration or percolation). However, a possible explanation is that the rainfall that had recently infiltrated the shallow soil may have been more depleted in heavy isotopes than the bulk samples from the rain collector, which took time-integrative samples for the whole evaluation period. This idea is supported by data in the present study, from both sites, that show a high variability in the isotopic compositions of rainfall samples that had been collected during short time intervals. Similar variability is reported by other authors (e.g., Robertson & Gazis, 2006;Smith et al., 1979). In the present study, satisfactory ET a partitioning values were obtained from timeintegrative data (e.g., over the space of a season). However, more detailed information on the time dependence of partitioning could be obtained by sampling the soil more frequently (e.g., monthly, or weekly during the growing season) or via in-situ isotopic measurements of soil water (e.g., Gaj et al., 2016).
Regarding the reliability of the water-vapour equilibration method, it should be emphasized that to avoid fractionation effects, our samples were analysed as soon as possible after collection-a protocol that is challenging to implement when samples are taken in remote arid areas, and laboratories are far away. Still, it has been shown that even after being stored for several days in Ziploc bags of the specific type used in the present study, water samples do not fractionate to a degree that biases isotope analyses significantly (Hendry et al., 2015;Wassenaar et al., 2008). For longer storage, metallized bags might be used. However, gas build-up could bias the isotope analyses (Gralher et al., 2016(Gralher et al., , 2018 probably due to differences among the models' respective assumptions and partitioning approaches. Specifically, the HYDRUS-1D model's procedure calculates the partitioning by reducing ET 0 to rates of T a and E a . The calculation of T a is accomplished by applying (i) a surface-cover fraction that is based upon Beer's law (Ritchie, 1972), and (ii) a water-stress-reduction function (Feddes et al., 1978;Van Genuchten, 1987). To compute E a , HYDRUS-1D uses a surface-pressure threshold (hcrit A ) and boundary conditions (Šimů nek et al., 2008). In contrast, the isotope approach is based upon measurements of isotope ratios (of precipitation and bulk soil water) at the beginning and end of a time interval. Those measurements are used as inputs to a simple mass balance, which assumes that deep percolation and transpired water are not affected by fractionation.
Overall, the isotope mass balance method gives higher values of T a , while HYDRUS-1D gives higher values of E a . Results from the isotope approach are more consistent with previous studies (e.g., Ferretti et al., 2003;Liebhard et al., 2022;Robertson & Gazis, 2006;Sutanto et al., 2012;Wang et al., 2010;Wenninger et al., 2010;Zhang et al., 2011). Those studies estimated the T a /ET a ratio at around 70%.
In addition, the transpiration ratio obtained by the isotope approach is on the same order of magnitude as those reported by global studies (e.g., Jasechko et al., 2013). In contrast the E a /ET a ratios that were calculated via HYDRUS-1D were around 76.8%. These differences suggest that to predict the partitionings of E a and T a accurately for sites such as ours, the HYDRUS-1D model may require further improvements (Kool et al., 2014). The improvements might include (i) optimizing the water-stress function (e.g., Feddes threshold) for groundnut crops (not yet performed, to our knowledge); and (ii) improving the above-mentioned ET 0 partitioning to potential evaporation and transpiration, which are currently based upon rough assumptions such as the surface-cover fraction and the Leaf Area Index (Beer's law).

| Soil water movement and groundwater recharge
Mechanisms of soil water movement can be identified by comparing the isotopic compositions of rainfall, soil water, and groundwater.
During the dry season, the heavy-isotope enrichment of shallow soil water at both sites was higher than in the local rainfall. At the same time, a distinct evaporation front-the location of the most-negative  Figure S5b). One mechanism that would not have been detected via TDR sensors is groundwater recharge through preferential pathways-or perhaps by lateral flow. Those mechanisms might explain why the water table had risen about 50 cm by the end of the wet season ( Figure S5c), and also why there was a nearly two-month delay between rainfall events and groundwater fluctuations.
The plausibility of preferential pathways and lateral flow at Site 1 is increased by reports that groundwater recharge of the CT aquifer in Sahel regions occurs mainly through "focused" mechanisms (e.g., Desconnets et al. 1997;Massuel et al. 2011, Favreau et al. T A B L E 3 Cumulative evapotranspiration (ET a ) and the partitioning between evaporation (E a ) and transpiration (T a ) at the mid-slope location outside the canopy at site 1 during the three evaluation periods, as determined via the isotope mass balance (imb), isothermal evaporation model (iem), and HYDRUS-1D numerical model (Hyd 2009). Preferential flow allows water to bypass the soil matrix (Beven & Germann, 1982). As a result, young water can infiltrate deeply into the ground (Thomas et al., 2013), thereby contributing rapidly to groundwater replenishment rather than refilling the soil matrix. In this way, replenishment occurs with little exchange or mixing between young, mobile water and bulk soil water Evaristo et al., 2019;Sprenger et al., 2019;).
An example of this phenomenon is reported by Favreau et al. (2009), who showed that in Niger, at a site similar to our Site 1, recharge occurred via preferential flow through the edges of ponds or gullies-including at the outlets of gullies. Because these terrain features were the main recharge sites, aquifer-recharge rates rose tenfold over the space of 50 years as surface runoff increased in response to the clearing of natural savannah lands for rainfed crops.
Specifically, the increase in lengths of gullies and surface areas of ponds (Leblanc et al. 2008) contributed to raising recharge rates from a few mm year À1 in the 1950 s-1960 s to as much as 25 mm year À1 in the 1990s-2000s (Favreau et al. 2009;Boucher et al. 2012).
The possibility of preferential pathways notwithstanding, our estimate that groundwater recharge amounts to <2% of annual rainfall (as calculated per the piston displacement method) is consistent with reported values from other semi-arid regions (e.g., Gaj et al., 2016;Koeniger et al., 2016;Skrzypek et al., 2019;Boumaiza et al., 2021;Edmunds and Gaye, 1994;Scanlon et al., 2006). In addition, our estimate of deep drainage below 2 m depth during the dry season, as calculated by the validated HYDRUS-1D, is similar to the groundwater recharges obtained via the piston-displacement method. The former values ranged from 1.7 mm during February-June to 5.0 mm during June-August. In contrast, the estimated deep drainage for the wet season was 68.3 mm. However, it should be recalled that although the piston-displacement method uses δ 2 H shift and δ 18 O shift values from a deeper soil layer (400-500 cm depth), and therefore takes into account the entire root zone (e.g., potential impact of shrubs and trees), this method fails to capture potential preferential pathways that may have caused the observed substantial fluctuation in groundwater levels.

| SUMMARY AND CONCLUSION
We characterized the stable isotopic compositions of rainfall, soil water, and groundwater at two sites along a climate gradient in Senegal (Site 1 in the Groundnut basin, and Site 2 in the Ferlo Valley).
The slopes and intercepts of both sites' computed LMWLs were lower than those of the GMWL, reflecting isotopic fractionation. Isotopic analyses of bulk soil water revealed two distinct depth zones. The first was a zone of shallow soil water extending from the ground surface down to 150 cm at Site 1, and 100 cm at Site2. Within this zone, isotope ratios of the soil water varied with depth and time due to evaporation and rainfall infiltration. In the second, deeper zone (150-500 cm at Site 1, and 100-300 cm at Site 2), the isotopic composition of the soil water was nearly constant.
During the dry season at both sites, a definite evaporation front was present in the shallow soil zone. This front, whose depth could be identified because it corresponded to the highest isotope ratios in the soil profile, allowed us to use the isothermal evaporation model to estimate second-stage evaporation rates. These ranged from 0.02-0.09 mm d À1 at Site 1, and 0.02-0.11 mm d À1 at Site 2.
In addition, we used mass balances of water and stable isotopes to partition E a and T a from the groundnut crop (Site 1) and pasture (Site 2) over three evaluation periods. During the first period (the dry months February-June), the soil was bare, with limited upward water fluxes due to low soil water contents and reduced soil hydraulic conductivity. E a rates during this period were 0.03-0.06 and 0.02-0.16 mm d À1 for Site 1 and Site 2, respectively. The second period (the dry-wet months June-August) marked the first stage of vegetation growth, when T a is the main component of water loss. Rates for that component during the second period were 0.55-1.25 mm d À1 for groundnut (Site 1), and 0.57-0.9 mm d À1 for pasture (Site 2). During the third period-the wet (August) and dry (December) months, when crops mature and are harvested-T a increased to 1.96-2.24 mm d À1 for groundnut and 1.30-1.63 mm d À1 for pasture.
In general, the isotope approach gave reasonable E a and T a rates for groundnut and pasture, and the partitioning ratios were within the range found in the literature. ET a values from the isotope approach were similar to EC measurements, and also to values computed previously for Site 1 via a validated HYDRUS-1D model. However, the isotope mass balance gave a higher T a /ET a ratio (72%) than the HYDRUS-1D model (23.2%). Therefore, future research should include field measurements of E a (e.g., using lysimeters or flux chamber methods) to further investigate the reliability of the isotope approach versus numerical modelling.
The average groundwater recharge of the CT aquifer, as estimated from the piston displacement method, was 5.44 ± 2.2 mm y À1 -less than 2% of Site 1's yearly rainfall. However, the magnitudes and timings of groundwater-level fluctuations suggest that to some degree, the CT aquifer was being recharged via preferential pathways.
To infer and confirm the local regimes of soil-water movement, a comprehensive investigation should be performed, including the isotopic compositions of both the mobile water and the bulk soil water. In addition, piezometers should be installed along ponds and gullies to monitor groundwater levels. We also thank Dr. James Smith (https://mx.linkedin.com/in/james-smith-1b195047) who revised the English, and the two reviewers, whose observations greatly improved the paper.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available for scientific purposes from the corresponding author upon request.