Rainwater Harvesting Techniques to Face Water Scarcity in African Drylands: Hydrological E ﬃ ciency Assessment

: The sub-Saharan climate is experiencing a marked increase in temperature and intensiﬁcation of precipitation intensity and variability. Besides, longer dry spells are compromising the reliability of local agricultural practices. The present study provides a comprehensive investigation about the beneﬁts induced by using indigenous rainwater harvesting techniques (RWHT) against hydrometeorological threats a ﬀ ecting the Sahelian areas. Di ﬀ erent RWHT have been tested in term of runo ﬀ retention, inﬁltration increase into the root zone, and soil water stress mitigation. To achieve these purposes, hydrological processes at the ﬁeld scale have been investigated using a two-dimensional distributed hydrological model. To make the study representative of the whole Sahelian areas, several simulations were carried out adopting a wide range of input parameters based on conventional values of those areas. The results reveal that RWHT may lead to a runo ﬀ retention up to 87% and to double the inﬁltration. Intercepting and storing runo ﬀ , RWHT increase the water content in the root zone and the right design can diminish the crop water stress. Furthermore, the results show that adopting RWHT makes it possible to extend the growing season up to 20 days, enhancing the yield. These beneﬁts contribute to the reduction of the climate-related water stress and the prevention of crop failure.


Introduction
Sub-Saharan countries are the poorest regions in the world. Notwithstanding, sub-Saharan Africa has one of the highest fertility rates with 5.4 children per woman, which results in extremely fast population growth [1,2]. The Food and Agriculture Organization of the United Nations (FAO) reports that roughly 30% of the population is undernourished and 40% of infants risk their life due to malnutrition. To face the constant hazard of famine, farmers strive to boost the local agricultural production in their scarcely fertile lands, naturally poor in organic matter. During the last 50 years, the increase in food production was achieved mainly by expanding the extent of cropland but with a scarce cereal yield compared with the rest of the world, since the artificial fertilizers were too expensive for the majority [3,4]. Moreover, the ongoing climate changes are forcing Sahelian farmers to find innovative strategies to deal with droughts, unpredictable rainfall, and depletion of soil nutrients. Climate scientists are studying how global warming is intensifying the hydrological cycle [5]. The warmer atmosphere can store a higher degree of moisture and generate catastrophic rainstorms.

Geographical and Climatological Context
The Sahel, a semiarid area set in a fragile context, has been undergoing dramatic climate and land-use changes since the middle of the 20th century. The Sahelian belt stretches from the parallel 17 • N to 10 • N, from north to south, and spans from the Atlantic Ocean coasts to the coasts of Red Sea, from west to east ( Figure 1). Its climate is predominantly arid at the border with the Sahara Desert, with rainfall almost absent, and semiarid towards the south with an annual pluviometry that ranges from 600 to 800 mm [36,37]. In the next years, this area will be one of the most affected by climate changes [5]. The study conducted by the University of Notre Dame showed that the Sahelian countries are among countries with the highest level of vulnerability to climate changes [38]. Indeed, countries such as Niger, Chad, Sudan, and Mali occupy the last positions in the global rankings.
The study of Todzo et al. [39] reveals that, over the Sahel, a faster increase of temperature and precipitation than the global average is expected. Moreover, accordingly also with the findings of Seidou [12], the rainfall pattern is expected to become more intense and less frequent, leading to lengthening of dry spells and increase the likelihood of droughts. Different studies showed that roughly 50% of annual precipitation falls in the occurrence of a small number of extremely intense and short rainstorms [7,40]. This type of climate and future perspective are not in favor of a farming system based on rainfed agriculture. In the paper "Climate change and variability in the Sahel region: impacts and adaptation strategies in the agricultural sector" it is reported that two Sahelian countries, Chad and Niger, could likely lose nearly all their agriculture that depends on rain by 2100 [41]. For these reasons, farmers living in arid or semiarid areas and Non Governmental Organizations (NGOs) operating in these areas are striving to develop suitable and efficient water management practices.
Along with the harsh climate, the ongoing land degradation due to desertification and anthropic deforestation is reducing the land fertility and increasing the exposure of soil to crustification.
Water 2020, 12, x FOR PEER REVIEW 3 of 23 management, this means an increase in green water availability for the benefit of a reduction in blue water consumption (groundwater extracted for irrigation) [34,35]. Additionally, the increment of the soil water content prevents crops from reaching the condition of soil water stress, maximizing the yield. Upscaling the diffusion of these simple and affordable techniques would represent the first step towards the enactment of adaptation strategies to cope with climate changes and food scarcity. The paper is structured into four parts. The first part reports the contextualization of this study. The second describes the core of the numerical model and delineates the methodology. The third part sets out outcomes. Section four argues the discussions came out from the results. In the last section, conclusions and future perspectives are drawn.

Geographical and Climatological Context
The Sahel, a semiarid area set in a fragile context, has been undergoing dramatic climate and land-use changes since the middle of the 20th century. The Sahelian belt stretches from the parallel 17° N to 10° N, from north to south, and spans from the Atlantic Ocean coasts to the coasts of Red Sea, from west to east ( Figure 1). Its climate is predominantly arid at the border with the Sahara Desert, with rainfall almost absent, and semiarid towards the south with an annual pluviometry that ranges from 600 to 800 mm [36,37]. In the next years, this area will be one of the most affected by climate changes [5]. The study conducted by the University of Notre Dame showed that the Sahelian countries are among countries with the highest level of vulnerability to climate changes [38]. Indeed, countries such as Niger, Chad, Sudan, and Mali occupy the last positions in the global rankings.
The study of Todzo et al. [39] reveals that, over the Sahel, a faster increase of temperature and precipitation than the global average is expected. Moreover, accordingly also with the findings of Seidou [12], the rainfall pattern is expected to become more intense and less frequent, leading to lengthening of dry spells and increase the likelihood of droughts. Different studies showed that roughly 50% of annual precipitation falls in the occurrence of a small number of extremely intense and short rainstorms [7,40]. This type of climate and future perspective are not in favor of a farming system based on rainfed agriculture. In the paper "Climate change and variability in the Sahel region: impacts and adaptation strategies in the agricultural sector" it is reported that two Sahelian countries, Chad and Niger, could likely lose nearly all their agriculture that depends on rain by 2100 [41]. For these reasons, farmers living in arid or semiarid areas and Non Governmental Organizations (NGOs) operating in these areas are striving to develop suitable and efficient water management practices.
Along with the harsh climate, the ongoing land degradation due to desertification and anthropic deforestation is reducing the land fertility and increasing the exposure of soil to crustification.   and isohyets  of the sub-Saharan area [37,42].   and isohyets  of the sub-Saharan area [37,42].

The Numerical Model
Iber is a two-dimensional distributed model originally developed for hydraulic computations of overland and river flow [33,43], and later on expanded to the simulation of hydrological processes of rainfall-runoff transformation [44,45] and subsurface flow [46,47]. The surface runoff depth and velocity fields are obtained from the resolution of the 2D shallow water equations (SWEs), computing the bed friction with the Manning formulation, and including rainfall and infiltration as source terms. The equation system can be written as follows: where h is the water depth, q x,y are the unit discharge components along x and y, respectively, R is the rainfall intensity, I is the infiltration rate, g is the gravity acceleration, z s is the free surface elevation, and n is the roughness coefficient of Manning. The model equations are solved with an unstructured finite volume solver. The spatial domain is represented by an unstructured mesh with cells sizes proportional to the analyzed geometry. The Courant-Friedrichs-Lewy (CFL) stability criterion controls the computational time step based on the flow velocity, the water depth, and the computational cell size. In order to guarantee a high level of stability, the Courant number was set to 0.5 for all analyses. For further details on the model equations and numerical schemes see the studies of Cea and Bladé [33,43,44]. The infiltration is evaluated through the Green-Ampt method [48]. The formulation allows calculating the infiltration rate from the water depth over the surface, computed through the resolution of SWEs, and the physical properties of the soil. The soil characteristics are described by several parameters: the saturated hydraulic conductivity (k s ), the suction head in the nonsaturated layer (Ψ ), the soil porosity (∅), and the initial soil moisture content (θ i ).
The Green-Ampt model allows linking the spatio-temporal distribution of surface water with the subsurface flow through the soil water content variation. The mass conservation between the surface and subsurface is based on the 2D Boussinesq equation-based model for homogeneous unconfined aquifer and can be written as where ∅ is the soil porosity, b is the saturated soil thickness, T is the horizontal transmissivity, H is the hydraulic head, DP is the deep percolation rate, and ET is the evapotranspiration rate. The first term represents the variation of the soil moisture over time, considering the following relation guaranteed by the infiltration model: where θ is the soil moisture and d s is the soil depth. Note that the saturated thickness (b) is always smaller or equal to the soil depth (d s ) and thus, the soil moisture is always smaller or equal to the soil porosity. Considering the small scale of the spatial domain in our study case (see Section 3.2.1), the horizontal transmissivity was neglected.
The water that percolates out of the considered soil layer towards deeper layers is estimated by using the relation proposed by Famiglietti and Wood [49] where k s,p is the saturated hydraulic conductivity of the deep soil, and λ is a model parameter, meaning the pore size distribution index based on the soil layer texture. The soil structure might change along with the vertical profile, varying its permeability. Seeing as how the infiltration and percolation processes occur at a different depth, distinct values of hydraulic conductivities were adopted. The infiltration model's k s represents the topsoil-saturated hydraulic conductivity that controls the partition of rain between runoff and infiltration. On the other hand, the percolation model's k s,p is the saturated hydraulic conductivity that characterizes deep percolation. The evapotranspiration rate was calculated combining the potential evapotranspiration computed through the empirical relation reported in the work of Doorenbos and Pruitt [50] adjusted following the FAO 56 single-crop coefficient method [51], in order to consider the phenological properties of crops.
The present approach follows three steps: 1.
The potential evapotranspiration equation is based on a single climatic data widely available, the temperature: where T is the air temperature in • C, ξ is the percentage of total daytime hours in which the evapotranspiration occurs (approximately 12 h) out of total daytime hours of the year (365 × 12 h), and b is a parameter for calibration.

2.
The ET P is adjusted for a specific crop using a crop coefficient K c , resulting in: where ET c represents the crop evapotranspiration under standard conditions and K c,ij is the crop coefficient that accounts for the evapotranspiration capability during each growth stage i of an individual crop j. Values of K c are listed in the FAO Irrigation and drainage paper 56 [51].

3.
When the soil becomes dry, a limited amount of water is available for plant root extraction. If the depletion of the soil water storage overcomes a threshold, the crop is said to be water stressed and its crop transpiration capability is reduced by a water stress coefficient K s ET = ET c K s 4. The water stress coefficient K s [0,1] can be determined by the equation where θ WP and θ FC are the water content at wilting point and field capacity, respectively, and p is the soil water depletion fraction, which is characteristic for each crop and represents the fraction of the total available water that the plant can uptake without suffering stress.

Model Set-Up
The present study applies the numerical model described in the previous section in two different analyses. The first analysis aims to assess the entire range of possible hydrological performances of RWHT, evaluating multiple scenarios typical of Sahelian agricultural fields, at the time scale of the single rainfall event. In the second, the hydrological balances over the entire wet season were performed for each RWHT, and the potential crop water stress mitigation was evaluated. The first and second analyses will be called "short-term analysis" and "long-term analysis", respectively, throughout the manuscript.

Geometry
Many RWHT have been developed by Sahelian farmers over the centuries. Common practices are small planting pits (zai, tassa), small basins (negarims, meskats, half-moons), semicircular bunds, hand-dug trenches, mechanized Vallerani trenches, or eyebrow terraces. Precisely, we focused on the two most used microcatchment RWHT (half-moons and planting pits) as described in the guidelines of Mekdaschi Studer and Liniger [52].
The geometrical inputs that were used to represent each RWHT follow the conceptualization of the agricultural field delineated in Tamagnone et al. [32]. RWHT were shaped following the technical specification reported into the Global Database on Sustainable Land Management [53]. Frequently, semicircles with a radius of 4 m, spaced 2 m, are dug for half-moons, while circles with a diameter of 0.4 m, spaced about 1 m, are dug for small planting pits. The geometrical schemes and features of the spatial domains are reported in Figure A1 (see Appendix A). Moreover, supplementary simulations were carried out varying the entity of the excavation in order to observe how the storage volume affects their hydrological performances.
The hydrological efficiency of these RWHT was compared to a plain configuration that represents the case in which no agricultural technique is implemented.
For the long-term analysis, the plain configuration was manipulated to simulate the traditional sowing method used by Sahelian farmers. This method consists of breaking the surface crust along rows with rudimentary hand hoes or pickaxes (locally called "iler" or "daba"). The rows are commonly tilled 1 m apart transversely to the slope.
Identification codes were used to label each configuration, as shown in Table 1.

Meteorological Data
Iber is a fully distributed hydrological model which needs meteorological inputs to compute the intensity of incoming and outgoing hydrological fluxes from the study domain [44]. The spatial and temporal resolution of these inputs depends on the timescale of the simulations. Regarding rainfall, the typical evolution of Sahelian storms can be associated to an Organized Convective System (OCS) [54]. It generates hyetographs characterized by very fast and high-intensity peaks (frequently shorter than 1 h) followed by a low-intensity tail [7]. Thus, a high-resolution of rainfall records is necessary to detect every cloudburst. Consequently, hyetographs with a time resolution of 5 min were generated for both analyses.
In the short-term analysis, the extreme rainfall hyetograph calculated in the previous work of Tamagnone et al. [32] was adopted. This hyetograph is characterized by a rain depth of 40 mm with a peak intensity of 80 mm/h ( Figure 2a).
Instead, for the long-term analysis, a hyetograph representative of a rainy season was used. The representative wet season was identified from the analysis of rainfall time series recorded at a gauging station placed in central Sahel (Koyria station, 1997-2016), extracted from the AMMA-CATCH (Analyse Multidisciplinaire de la Mousson Africaine-Couplage de l'Atmosphère Tropicale et du Cycle Hydrologique) database [55]. From this time series, a representative year was selected as the Water 2020, 12, 2646 7 of 23 one with the highest correlation with the following three statistical parameters of the complete time series: the average of annual rainfall depth, the average of maximum hourly rainfall intensity, and the average number of rainy days.
The second meteorological input needed to evaluate the water balance is the air temperature. The variability of temperature over one characteristic year was calculated as the mean temperature registered in the decade 2004-2014 at the Wankama gauging station [55], with a time resolution of 30 min. The rainfall and temperature data used in the long-term simulations are displayed in Figure 2b.
Water 2020, 12, x FOR PEER REVIEW 7 of 23 time series: the average of annual rainfall depth, the average of maximum hourly rainfall intensity, and the average number of rainy days. The second meteorological input needed to evaluate the water balance is the air temperature. The variability of temperature over one characteristic year was calculated as the mean temperature registered in the decade 2004-2014 at the Wankama gauging station [55], with a time resolution of 30 min. The rainfall and temperature data used in the long-term simulations are displayed in Figure 2b.

Input Parameters
In order to investigate a vast range of cases characterizing the Sahelian farm fields, multiple Monte Carlo simulations were run using different sets of model parameters. The parameter sets were sampled using the Latin Hypercube Sampling (LHS) method [56,57]. Many authors have revealed that LHS can significantly cut down on processing time versus a standard Monte Carlo random sampling [58].
For the short-term analysis, 300 parameter sets were generated within defined ranges. Each set is composed of six parameters that we identified as the most influential on model performance. The first one is the roughness expressed by the Manning's coefficient and the others are parameters of the infiltration model. The parameter ranges are listed in Table 2. The set of parameters adopted for the long-term analysis is composed of: the previous six parameters, corresponding to the simulation closest to the mean model behavior, and the four soil parameters (Table 3); -the phenological parameters for each analyzed crop (Table 4). During the growing period, the evapotranspiration potential of the given crop will vary accordingly to the development of its height and leafage. The growing season can be divided into four different growth stages labeled

Input Parameters
In order to investigate a vast range of cases characterizing the Sahelian farm fields, multiple Monte Carlo simulations were run using different sets of model parameters. The parameter sets were sampled using the Latin Hypercube Sampling (LHS) method [56,57]. Many authors have revealed that LHS can significantly cut down on processing time versus a standard Monte Carlo random sampling [58].
For the short-term analysis, 300 parameter sets were generated within defined ranges. Each set is composed of six parameters that we identified as the most influential on model performance. The first one is the roughness expressed by the Manning's coefficient and the others are parameters of the infiltration model. The parameter ranges are listed in Table 2. The set of parameters adopted for the long-term analysis is composed of: the previous six parameters, corresponding to the simulation closest to the mean model behavior, and the four soil parameters (Table 3); -the phenological parameters for each analyzed crop (Table 4). During the growing period, the evapotranspiration potential of the given crop will vary accordingly to the development of its height and leafage. The growing season can be divided into four different growth stages labeled as follows: L 1 (initial), L 2 (development), L 3 (mid-season), L 4 (late-season). To each stage is associated a distinct value of crop coefficient K c . Table 3. Parameters used in the long-term analysis [51,64].

Parameter Values Unit
Manning coefficient (n) 0

Evaluation of the Hydrological Efficiency
The impact of the analyzed configurations in the hydrological processes related to rainfall-runoff transformation was evaluated in terms of three different efficiency measures: outflow reduction: calculated as the reduction on the cumulated volume of water that flows out of the domain with and without the implementation of RHWT (Vol.out RWHT and Vol.out PL , respectively) infiltration increase: calculated as the increase on the cumulated volume of water infiltrated in the subsurface with and without the implementation of RHWT (I RWHT and I PL , respectively) stress mitigation: calculated as the increase on soil moisture needed to reach the availability threshold with and without the implementation of RHWT (θ RWHT and θ TM , respectively)

Hydrological Behaviour
The hydrological behavior of each RWHT configuration was analyzed in terms of surface runoff generated, water retention, and infiltration, using for that purpose the output of the Monte Carlo Water 2020, 12, 2646 9 of 23 simulations performed with the fully distributed hydrological model. The computed hydrographs at the outlet of the considered Sahelian farming plot, as well as the cumulative infiltration in the field are displayed in Figure 3, showing the different responses of each RWHT configuration to the extreme rainfall event. In addition to all the Monte Carlo results, the average and the 25-75% percentiles were added to each graph.
Water 2020, 12, x FOR PEER REVIEW 9 of 23 are displayed in Figure 3, showing the different responses of each RWHT configuration to the extreme rainfall event. In addition to all the Monte Carlo results, the average and the 25-75% percentiles were added to each graph. The hydrographs computed for the PL and HM30 configurations show a wide difference in magnitude but a similar shape, since the half-moons do not get filled and just the rainfall that is not intercepted by them contributes to the outlet hydrograph. On the other hand, the hydrographs computed for the PP20 configuration show two distinct branches. At the beginning of the event, the discharge increases very slowly because the planting pits are still being filled with water. Once they get filled, there is a sharp increase in the hydrographs, reaching peak discharges in between the PL and the HM30 configurations. This behavior showing two branches and a delayed peak has already been described in Tamagnone et al. [32], and it also occurs for certain parameter sets in the HM10 configuration (see Figure A2). The outcomes computed for all the RWHT configurations defined in Table 1 are included in Appendix A.
The amplitude of the results range is directly correlated to the sensitivity of model output to the input parameters. For the PP configuration, the Monte Carlo simulations produce hydrographs significantly different from each other, meaning that the hydraulic behavior of this type of configuration is strongly affected by the input parameters (and thus, by the terrain and soil characteristics). Conversely, the HM30 configuration is less affected by the input parameters, being the shape and magnitude of the hydrograph mostly determined by the configuration geometry. The hydrographs computed for the PL and HM 30 configurations show a wide difference in magnitude but a similar shape, since the half-moons do not get filled and just the rainfall that is not intercepted by them contributes to the outlet hydrograph. On the other hand, the hydrographs computed for the PP 20 configuration show two distinct branches. At the beginning of the event, the discharge increases very slowly because the planting pits are still being filled with water. Once they get filled, there is a sharp increase in the hydrographs, reaching peak discharges in between the PL and the HM 30 configurations. This behavior showing two branches and a delayed peak has already been described in Tamagnone et al. [32], and it also occurs for certain parameter sets in the HM 10 configuration (see Figure A2). The outcomes computed for all the RWHT configurations defined in Table 1 are included in Appendix A.
The amplitude of the results range is directly correlated to the sensitivity of model output to the input parameters. For the PP configuration, the Monte Carlo simulations produce hydrographs significantly different from each other, meaning that the hydraulic behavior of this type of configuration is strongly affected by the input parameters (and thus, by the terrain and soil characteristics). Conversely, the HM 30 configuration is less affected by the input parameters, being the shape and magnitude of the hydrograph mostly determined by the configuration geometry.
Observing the infiltration trends in Figure 3, each configuration presents a different behavior. For the plain PL configuration, given the absence of retention, the infiltration trend follows the rainfall trend. Thus, the infiltration finishes with the end of the rainfall. For the half-moons, there is, on average, a return to the dry condition at 300 min (when the curve becomes horizontal), whereas the planting pits present a positive infiltration trend up to 400 min. The delay between the end of rainfall and infiltration contributes to the increase of the evaporation of the water retained inside the ponds after the downburst.
The influence of each input parameter on model output was also investigated. The correlation between the runoff coefficient, evaluated as the ratio between the volume of water flowing out of the domain and the cumulated rainfall, and the input parameters show that the hydraulic conductivity outside of the holes (k s,sur f ace ) plays the main role in the formation of the outflow discharge (Table 5). The differences between the HM and PP configurations show that the influence of k s,sur f ace is stronger for HM configuration, while the n more heavily affects PP (Figure 4). The explanation lies in the behavior of PP which get overfilled during the event. When the PP retention fails, more water flows on the surface between the ponds and this makes the correlation with k s,sur f ace weaker and the correlation with the roughness coefficient stronger. This is also confirmed by the increase of ρ s value related to n in the HM 10 configuration. The specular behavior might be seen in the correlation with the total volume of water infiltrated during the event. Thus, with all positive correlations. The weak correlation with k s,hole might be linked with the fact that the entire runoff harvested by the RWHT is however infiltrated independently by the entity of the hydraulic conductivity.
Water 2020, 12, x FOR PEER REVIEW 10 of 23 Observing the infiltration trends in Figure 3, each configuration presents a different behavior. For the plain PL configuration, given the absence of retention, the infiltration trend follows the rainfall trend. Thus, the infiltration finishes with the end of the rainfall. For the half-moons, there is, on average, a return to the dry condition at 300 min (when the curve becomes horizontal), whereas the planting pits present a positive infiltration trend up to 400 min. The delay between the end of rainfall and infiltration contributes to the increase of the evaporation of the water retained inside the ponds after the downburst.
The influence of each input parameter on model output was also investigated. The correlation between the runoff coefficient, evaluated as the ratio between the volume of water flowing out of the domain and the cumulated rainfall, and the input parameters show that the hydraulic conductivity outside of the holes ( , ) plays the main role in the formation of the outflow discharge (Table  5).  The differences between the HM and PP configurations show that the influence of , is stronger for HM configuration, while the more heavily affects PP (Figure 4). The explanation lies in the behavior of PP which get overfilled during the event. When the PP retention fails, more water flows on the surface between the ponds and this makes the correlation with , weaker and the correlation with the roughness coefficient stronger. This is also confirmed by the increase of value related to in the HM10 configuration. The specular behavior might be seen in the correlation with the total volume of water infiltrated during the event. Thus, with all positive correlations. The weak correlation with , might be linked with the fact that the entire runoff harvested by the RWHT is however infiltrated independently by the entity of the hydraulic conductivity. is the Spearman's correlation coefficient between the couple of datasets.

Hydrological Efficiency Assessment
As reported in Section 3.3, the hydrological efficiency of each RWHT analyzed represents the degree of improvement in water retention, when compared to the plain configuration. The comparison was made simulation by simulation in order to compare couples of configurations with the same input parameters.
Considering outflow reduction φ V (Figure 5), the HM configurations show an efficiency of more than 30% higher than the PP configurations. For both RWHT, the configurations with the bigger excavation have a higher performance than the smaller ones. For half-moons, the efficiency shows a very slight variation between the three configurations, from 0.87 to 0.85 for the deeper hole and the shallower hole, respectively. Instead, in the PP configurations, the depth of the holes has a higher impact on the water volume retained in the plot. Indeed, halving the depth of the excavation leads to a 15% drop in φ V . Moreover, from the results shown in Figure 5, it is clear how the input parameters strongly influence the PP results, while they slightly impact the efficiency of the HM configurations.
Water 2020, 12, x FOR PEER REVIEW 11 of 23

Hydrological Efficiency Assessment
As reported in Section 3.3, the hydrological efficiency of each RWHT analyzed represents the degree of improvement in water retention, when compared to the plain configuration. The comparison was made simulation by simulation in order to compare couples of configurations with the same input parameters.
Considering outflow reduction (Figure 5), the HM configurations show an efficiency of more than 30% higher than the PP configurations. For both RWHT, the configurations with the bigger excavation have a higher performance than the smaller ones. For half-moons, the efficiency shows a very slight variation between the three configurations, from 0.87 to 0.85 for the deeper hole and the shallower hole, respectively. Instead, in the PP configurations, the depth of the holes has a higher impact on the water volume retained in the plot. Indeed, halving the depth of the excavation leads to a 15% drop in . Moreover, from the results shown in Figure 5, it is clear how the input parameters strongly influence the PP results, while they slightly impact the efficiency of the HM configurations. Commonly, the Sahelian storms drop down a consistent amount of rainfall in a few minutes. Thus, the process of water retention starts with catching the runoff and rainfall inside the microbasins and continues with the infiltration of this amount of water into the subsurface. Thus, the infiltration efficiency is dependent on the geometry and changes over time. For this reason, it was evaluated for different times lags after the extreme event occurs, labeling the results in Figure 6 with the subscript of the related time lag. Commonly, the Sahelian storms drop down a consistent amount of rainfall in a few minutes. Thus, the process of water retention starts with catching the runoff and rainfall inside the micro-basins and continues with the infiltration of this amount of water into the subsurface. Thus, the infiltration efficiency φ I is dependent on the geometry and changes over time. For this reason, it was evaluated for different times lags after the extreme event occurs, labeling the results in Figure 6 with the subscript of the related time lag.
HM configurations have a storage volume large enough to harvest all the water that falls during the simulated extreme event in almost all simulations, i.e., independently of the input parameters. This means that each half-moon has the same volume of water that will infiltrate into the soil, although the infiltration rate will vary depending on the soil parameters. Observing the differences between the deepest and shallowest HM configurations (HM 30 and HM 10 , respectively), the variation of φ I over time is noticeable (Figure 6). At the end of the event (φ I1h ), the HM 10 shows an efficiency 10% higher than HM 30, meaning that more water has been infiltrated during the rainfall. At such early stages, the infiltration in the shallower HM is higher due to the conformation of the excavation, that presents a slightly wider hole bottom than in the HM 30 . After 6 h (φ I6h ) the two efficiencies are equal, while later on the efficiency of HM 30 becomes higher than that of HM 10 . This highlights that, for this RWHT, the infiltration process is more affected by the geometry rather than by differences in water depth inside the hole.
For the PP technique, the difference between the two configurations increases over time. Since both configurations are overfilled during the event, the PP 20 has a higher volume of water retained, and it will produce more infiltration. Thus, the efficiency of PP 20 is only 4% higher than PP 10 at a time lag of 1 h (φ I1h ), while it reaches a difference of 28% at 10 h (φ I10h ).
Water 2020, 12, x FOR PEER REVIEW 12 of 23 Figure 6. Boxplot of infiltration increase efficiency. In each box, the upper and lower edges indicate the first and third quartile, respectively, the red central line is the median, and the green x symbol is the mean. The whiskers length was set equal to the interquartile distance. Outliers have been hidden.
HM configurations have a storage volume large enough to harvest all the water that falls during the simulated extreme event in almost all simulations, i.e., independently of the input parameters. This means that each half-moon has the same volume of water that will infiltrate into the soil, although the infiltration rate will vary depending on the soil parameters. Observing the differences between the deepest and shallowest HM configurations (HM30 and HM10, respectively), the variation of over time is noticeable (Figure 6). At the end of the event ( ), the HM10 shows an efficiency 10% higher than HM30, meaning that more water has been infiltrated during the rainfall. At such early stages, the infiltration in the shallower HM is higher due to the conformation of the excavation, that presents a slightly wider hole bottom than in the HM30. After 6 h ( ) the two efficiencies are equal, while later on the efficiency of HM30 becomes higher than that of HM10. This highlights that, for this RWHT, the infiltration process is more affected by the geometry rather than by differences in water depth inside the hole.
For the PP technique, the difference between the two configurations increases over time. Since both configurations are overfilled during the event, the PP20 has a higher volume of water retained, and it will produce more infiltration. Thus, the efficiency of PP20 is only 4% higher than PP10 at a time lag of 1 h ( ), while it reaches a difference of 28% at 10 h ( ).

Water Stress Assessment
Besides simulating infiltration and runoff for the different configurations, the hydrological model was used to evaluate the impact of RWHT on soil water dynamics and their influence on the crop conditions over the growing season.
The rainfall season in the Sahel is always preceded by a long dry period in which no precipitations occur. Thus, the initial conditions were considered strongly arid, meaning a dry surface and subsurface with a minimum soil water content equal to the permanent wilting point [23]. With the onset of the wet season, the soil storage recharge, uptake, and the resulting variation in soil moisture were calculated over the entire season with the hydrological model.
The analyses aim to investigate the improvement in the reduction of water stress on traditional Sahelian crops that can be achieved with the use of RWHT compared with traditional sowing Figure 6. Boxplot of infiltration increase efficiency. In each box, the upper and lower edges indicate the first and third quartile, respectively, the red central line is the median, and the green x symbol is the mean. The whiskers length was set equal to the interquartile distance. Outliers have been hidden.

Water Stress Assessment
Besides simulating infiltration and runoff for the different configurations, the hydrological model was used to evaluate the impact of RWHT on soil water dynamics and their influence on the crop conditions over the growing season.
The rainfall season in the Sahel is always preceded by a long dry period in which no precipitations occur. Thus, the initial conditions were considered strongly arid, meaning a dry surface and subsurface with a minimum soil water content equal to the permanent wilting point [23]. With the onset of the wet season, the soil storage recharge, uptake, and the resulting variation in soil moisture were calculated over the entire season with the hydrological model.
The analyses aim to investigate the improvement in the reduction of water stress on traditional Sahelian crops that can be achieved with the use of RWHT compared with traditional sowing methods. The analyses are focused at two scales: (1) the field scale, in which all simulation results are aggregated over the whole domain, (2) the small scale, in which hydrological conditions are locally examined where crop seeds are actually sown.
For the field scale analysis, all simulations were carried out based on millet phenological parameters. The presence of RWHT markedly increases the fraction of precipitation that infiltrates and fills the soil water storage. The best improvement is tied to the HM 30 with a cumulative infiltration two times greater than TM. However, the difference between the deepest and shallowest HM is lower than 10%. Figure 7 shows the soil moisture dynamics over the wet season. The aggregation of zones influenced by cultivation and not produces a trend that even if it is always below the threshold, constant permanence of stress condition (red zone), it is closer to the green zone when RWHT are adopted. The improvement is more marked in correspondence with the highest precipitation when the effect of retention plays a crucial role. moisture lower than the threshold. The threshold is defined as the soil moisture at the field capacity multiplied by the depletion factor of the crop [51]. The higher level of soil water content induced by the RWHT indicates that there is an improvement of the hydrological efficiency of the whole system, meaning the farm field. In terms of water stress mitigation ( ), HM configurations show an efficiency comprised between 20.7% and 23% while PP lead to significantly lower values of 3.75% and 2.85% (Table 6).  The presence of zones characterized by different soil physical characteristics indicates a slightly large spatial variability of hydrological conditions. Downscaling the observation from the field scale to the single row/pond it is possible to deeply investigate the impact of farming practices on soil moisture dynamics. Focusing on the growing period of the analyzed crop, the water stress is stated by a level of soil moisture lower than the threshold. The threshold is defined as the soil moisture at the field capacity multiplied by the depletion factor of the crop [51]. The higher level of soil water content induced by the RWHT indicates that there is an improvement of the hydrological efficiency of the whole system, meaning the farm field. In terms of water stress mitigation (φ S ), HM configurations show an efficiency comprised between 20.7% and 23% while PP lead to significantly lower values of 3.75% and 2.85% (Table 6). Table 6. Water stress mitigation efficiency.

RWHT φ S (%)
HM 30 23.02 HM 20 22.92 HM 10 20.72 PP 20 3.75 PP 10 2.85 The presence of zones characterized by different soil physical characteristics indicates a slightly large spatial variability of hydrological conditions. Downscaling the observation from the field scale to the single row/pond it is possible to deeply investigate the impact of farming practices on soil moisture dynamics.
For HM, the soil moisture inside of the pond is higher than the threshold most of the time, avoiding that the crop sowed inside of the pond is affected by water shortage (Figure 8). Comparing the three HM configurations it can be noticed that soil moisture in HM 30 is close to the saturation most of the time and never reaches the threshold. Conversely, shallower HM overcome the threshold leading to 2 and 7 days of plant water stress for HM 20 and HM 10 , respectively. In those days, the limitation in soil water availability induces a condition of stress to the crop which limits its evapotranspiration, implying a K s lower than 1. The number of stressed days rises to 60 days in case of traditional sowing method.
Hence, considering a growing season of 105 days for a millet crop, the crop will suffer water stress more than half the time whether cultivated with the traditional method. The percentage considerably decreases to 0%, 2%, and 7% if half-moons are adopted. Instead, both PP configurations show a soil water content higher than the threshold over the entire growing season. evapotranspiration, implying a lower than 1. The number of stressed days rises to 60 days in case of traditional sowing method. Hence, considering a growing season of 105 days for a millet crop, the crop will suffer water stress more than half the time whether cultivated with the traditional method. The percentage considerably decreases to 0%, 2%, and 7% if half-moons are adopted. Instead, both PP configurations show a soil water content higher than the threshold over the entire growing season.
What also stands out in Figure 8 is that the soil water content rapidly decreases with the end of the wet season and the increase of the temperature (see Figure 2). This is due to the high intensity of outcoming fluxes and absence of inflows. In TM configuration, the soil moisture reaches the threshold on 8th of October, just 2 days after the last simulated rainfall, and then starts to decrease from the onset of the dry season. The higher storage induced by the RWHT allows extending the growing season up to 20 days, avoiding the stress condition almost until the end of the month. To observe the influence of RWHT on crops, the growing seasons of millet, sesame, and sweet potato with the conventional sowing method was compared against HM10 practice. The different phenological parameters of these crops lead to different evapotranspiration trends. The benefit induced by the presence of RWHT was measured as the reduction of cumulative plant water deficit (PWD), see Figure 9. PWD was calculated as the difference between the crop evapotranspiration (evapotranspiration under unstressed condition, see Equation (6)) and the actual evapotranspiration. What also stands out in Figure 8 is that the soil water content rapidly decreases with the end of the wet season and the increase of the temperature (see Figure 2). This is due to the high intensity of outcoming fluxes and absence of inflows. In TM configuration, the soil moisture reaches the threshold on 8th of October, just 2 days after the last simulated rainfall, and then starts to decrease from the onset of the dry season. The higher storage induced by the RWHT allows extending the growing season up to 20 days, avoiding the stress condition almost until the end of the month.
To observe the influence of RWHT on crops, the growing seasons of millet, sesame, and sweet potato with the conventional sowing method was compared against HM 10 practice. The different phenological parameters of these crops lead to different evapotranspiration trends. The benefit induced by the presence of RWHT was measured as the reduction of cumulative plant water deficit (PWD), see Figure 9. PWD was calculated as the difference between the crop evapotranspiration (evapotranspiration under unstressed condition, see Equation (6)) and the actual evapotranspiration.
The maximum reduction is obtained for the sesame since no deficit is produced when using HM 10 . This occurs since the sesame harvesting takes place around mid-September, hence before the end of rainfalls and increase of temperature. Instead, the longer growing season of sweet potato undermines the traditional system leading to a higher PWD. On the contrary, HM 10 highlights a great efficiency producing a deficit even lower than for the millet. The maximum reduction is obtained for the sesame since no deficit is produced when using HM10. This occurs since the sesame harvesting takes place around mid-September, hence before the end of rainfalls and increase of temperature. Instead, the longer growing season of sweet potato undermines the traditional system leading to a higher PWD. On the contrary, HM10 highlights a great efficiency producing a deficit even lower than for the millet.

Discussion
The principal aim of using RWHT is to intercept the rainfall and surface runoff in order to maximize the availability of water for crop and to minimize the water deficit during the entire growing season [22]. In drylands, where food security is the first challenge, reducing water stress means decreasing the probability of crop failure [65]. The results presented here using numerical modeling and Monte Carlo simulations provide a deep analysis on the functioning of indigenous RWHT under a wide range of possible scenarios that might be faced in Sahelian rural areas.
In the case of choosing PP, the wide range of variation of the numerical results highlights the importance of field surveys and sampling to evaluate the correct physical parameters characterizing the site. On the contrary, for HM, the small sensitivity of model output to the soil parameters means that the hydrological efficiency is mostly controlled by the geometry. Thus, during the planning phase, the design is more important than the characterization of the site. In fact, from results, we can assert that (under the same hydrological conditions as the simulated ones) it is preferable to shape RWHT with shallower and wider holes instead of deeper and smaller holes. During the planning phase, once the project rain has been detected, the critical volume that avoids the overfilling of RWHT should be calculated and used to define the shape of the optimal agricultural practice.
Since Sahelian countries are among the poorest in the world, farmers have no access to tillage machines and all phases of the cultivation are handmade. Thus, the entity of the manual labor is strongly correlated to the RWHT design. The results showed in the previous section show that it is worth excavating deeper RWHT only if there is a relevant efficiency improvement. Especially for HM, it would be preferable to choose HM10 instead of deeper ponds, saving in that way many hours of manual labor, since the volume to dig is almost one-third of HM30. On the contrary, making the effort of digging deeper planting pits leads to consistent improvements, harvesting more water into the farming field and promoting soil water storage recharge.
Comparing the common results obtained in this study with the ones of the previous work of Tamagnone et al. [32], it is possible to appreciate the benefits induced by a hydrological modeling instead of pure hydraulic modeling. Considering the evaluation of the outlet discharge reduction,

Discussion
The principal aim of using RWHT is to intercept the rainfall and surface runoff in order to maximize the availability of water for crop and to minimize the water deficit during the entire growing season [22]. In drylands, where food security is the first challenge, reducing water stress means decreasing the probability of crop failure [65]. The results presented here using numerical modeling and Monte Carlo simulations provide a deep analysis on the functioning of indigenous RWHT under a wide range of possible scenarios that might be faced in Sahelian rural areas.
In the case of choosing PP, the wide range of variation of the numerical results highlights the importance of field surveys and sampling to evaluate the correct physical parameters characterizing the site. On the contrary, for HM, the small sensitivity of model output to the soil parameters means that the hydrological efficiency is mostly controlled by the geometry. Thus, during the planning phase, the design is more important than the characterization of the site. In fact, from φ I results, we can assert that (under the same hydrological conditions as the simulated ones) it is preferable to shape RWHT with shallower and wider holes instead of deeper and smaller holes. During the planning phase, once the project rain has been detected, the critical volume that avoids the overfilling of RWHT should be calculated and used to define the shape of the optimal agricultural practice.
Since Sahelian countries are among the poorest in the world, farmers have no access to tillage machines and all phases of the cultivation are handmade. Thus, the entity of the manual labor is strongly correlated to the RWHT design. The results showed in the previous section show that it is worth excavating deeper RWHT only if there is a relevant efficiency improvement. Especially for HM, it would be preferable to choose HM 10 instead of deeper ponds, saving in that way many hours of manual labor, since the volume to dig is almost one-third of HM 30 . On the contrary, making the effort of digging deeper planting pits leads to consistent improvements, harvesting more water into the farming field and promoting soil water storage recharge.
Comparing the common results obtained in this study with the ones of the previous work of Tamagnone et al. [32], it is possible to appreciate the benefits induced by a hydrological modeling instead of pure hydraulic modeling. Considering the evaluation of the outlet discharge reduction, accounting for the infiltration leads to an increase of 17% and 27% for the HM and PP configurations, respectively. This means that even though the main role is played by the geometrical features of the RWHT, neglecting the hydrological components of the water balance leads to a consistent underestimation. Therefore, future studies cannot disregard the use of a hydrological model for the study of all processes involved in the runoff formation and propagation.
Observing the relation between parameters and the runoff coefficient, the strong correlation between the runoff coefficient and k s,sur f ace means that is also important to treat the surface between ponds in order to reduce the overland flow and to keep the water inside the farm field. As reported in previous works [23,66], the improvement of soil moisture is a phenomenon spatially limited under the pond, since the lateral transport is negligible. For this reason, the soil between the ponds is much drier than below them. Hence, combining RWHT with other surface treatments, such as soil scarifying, will improve the hydrological efficiency of the whole system. It will also help the recovery of grass between the basins, for the sustenance of cattle, or the implementation of intercropping. A recent study showed how the application of intercropping strategies lead to a greater yield as compared with the monoculture [67].
The great usefulness of RWHT can be observed at the beginning of the rainfall season. With the first rainfall, there is a fast increase in soil moisture making the soil more suitable to accommodate new seeds. The higher level of soil moisture enhances the biological activity which contributes to improving the soil structure avoiding the reduction of hydraulic conductivity [68]. The water balance also confirms that with the use of RWHT it is not possible to extend the growing season much after the end of the rains since the high magnitude of outflowing fluxes rapidly empty the soil water storage. Commonly the rainy season ends at the beginning of October, however, the use of HM or PP may guarantee a sufficient availability of water up to the end of the month. Furthermore, in such hydrometeorological conditions, it is preferable to cultivate from the beginning of June to the mid of September and harvest no later than the end of September.
The analysis at the two spatial scales allowed to appreciate the real effectiveness of RWHT for agricultural purposes. For PP, the observation at the field scale produced a scarce attenuation of the soil water stress. On the contrary, at the small scale, the results revealed that both PP configurations lead to a soil moisture trend even higher than HM.
RWHT have their limitations in the fight against food insecurity. Their advantages mainly concern the increase in available water for crop and overland flow management. However, they are not able to improve the nutrient in soils that are naturally poor in organic matter. Thus, in order to increase the crop yield, the realization of RWHT should be always followed by the addition of manure or fertilizer [4,17]. However, altering the surface roughness and slowing overland fluxes (runoff and wind), RWHT help to capture organic debris which provides nutrients for the natural regeneration of shrubs and agropastoral bush-woodland [24].

Conclusions
Water and food scarcity are among the main problems that condition the livelihood of Sahelian inhabitants. To cope with these threats, a growing number of farmers living in sub-Saharan drylands are already taking advantages from the use of improved water and soil management practices. This study exploits advanced numerical models to investigate the hydrological functioning of those RWHT locally used in the Sahel, solving some limitations recognized in previous investigations [32]. The benefits induced by the adoption of RWHT, such as the increment of infiltration and the reduction of crop water stress along the growing season, were analyzed.
Our findings suggest that RWHT always enhance the hydrological efficiency of agricultural fields, but the level of efficiency is strongly related to their design. Thus, once the location is identified, the best design should be evaluated based on the meteorological features of that area. Furthermore, considering the ongoing climate trend, the intensification of rainstorm should be evaluated in the planning phase. In terms of water stress mitigation, the right design can bring the soil water deficit to zero, maximizing the crop yield and avoiding the necessity of supplementary irrigation.
The methodology presented here could be very useful to scrupulously plan the irrigation to avoid crop water stress, in areas where water scarcity makes the value of water even higher. The irrigation can be quantified in terms of the amount of water needed to meet the crop demand and scheduled, introducing the right amount of water when soil water content goes below the threshold. Indeed, maximizing the water use efficiency and avoiding the crop water stress, the crop yield increases, approaching the food security in the Sahel. Likewise, the approach used for the evaluation of Sahelian agricultural practices may be applied to other agricultural studies elsewhere in the world. The high costs of in-situ studies and the increasing availability of data makes the use of numerical modeling an effective choice that can be easily replicated for different sites.
To deeply analyze the crop life cycle, the simple formulation chosen to evaluate the potential evapotranspiration could represent a weakness point since it does not take into account all physical and physiological factors governing the evapotranspiration process. Notwithstanding these limitations, it addresses a preliminary ET P calculation coping with the scarcity of data that often characterize developing countries. Further implementations could involve more complex formulations including more parameters such as solar radiation, humidity, and wind speed (e.g., the FAO-56 Penman-Monteith or the Hargreaves-Samani equation).
The present study makes a step forward in the comprehensive investigation of RWHT in the numerical modeling framework. The methodology proposed would enlarge the field of application of hydraulic and hydrological models to ecological/agronomic context. Agro-hydrological physically based models could be effective tools to investigate impacts of climate on the crop life cycle, its health, and yield, without neglecting the hydrodynamics that controls the transformation from rainfall to runoff.
In the Sahel, despite the considerable effort in embracing improved land and water management practices, the adoption of these strategies remains too limited to lead a considerable change in Africa's food and environmental security. Thus, this research should encourage to scale up these practices to make widespread the fight against food/water scarcity and environmental degradation. The present study demonstrates that, in these contexts, it is not necessary to resort to "high-tech" solutions and unaffordable strategies to deal with such problems. National policies should invest in the education of farmers so that they can gain awareness of the benefits derived from appropriate practices.
Author Contributions: P.T.: methodology, analyses, elaboration of data, and writing-original draft; E.C., L.C. and M.R.: methodology, supervision, validation, writing-review and editing. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.