The methodology adopted for assessing climate change impacts on water resources in the VRB is summarized in Fig. 2. The main steps consist of the bias correction of the RCMs forced by the GCMs, the modelling of hydrological processes based on the climate projection datasets, and the analysis of the future changes in the modelled hydrological processes.

Uncertainties in the climate projections are addressed by employing a large ensemble of 12 general circulation models (GCMs) downscaled by five regional climate models (RCMs) under three Representative Concentration Pathways (RCPs; Moss et al., 2010; Van Vuuren et al., 2011). The RCMs are obtained from the Coordinated Regional-climate Downscaling Experiment (CORDEX) for Africa (Giorgi et al., 2009). Only considering the highest RCP8.5 scenario as the business-as-usual scenario in climate change studies is increasingly criticized because the assumption of the heavy use of coal in RCP8.5 is unrealistic (Hausfather and Peters, 2020; Ritchie and Dowlatabadi, 2017). However, the current emissions are found to be in line with the RCP8.5 scenario (Peters et al., 2013), and there are suggestions for giving RCP8.5 a high priority (O'Neill et al., 2016).

The RCM–GCM datasets are first evaluated by comparing them to the best-performing satellite and reanalysis datasets of rainfall and temperature for hydrological modelling in the VRB. Subsequently, a multivariate bias correction is applied to the climate projection datasets using the Rank Resampling for Distributions and Dependences (R2D2) method (Vrac and Thao, 2020). Finally, the bias-corrected climate projection datasets are used as input in the fully distributed mesoscale Hydrologic Model (mHM) to assess the impact of climate change on multiple hydrological fluxes and state variables. Although the performance of a model during past and present conditions does not guarantee its reliability for future projections (Stanzel et al., 2018), having a well-performing model that simulates realistic hydrological processes is a prerequisite for any sound impact study (Krysanova et al., 2018).

CORDEX generates high-resolution historical and future climate projections for regional domains, by downscaling GCMs participating in the fifth Coupled Model Intercomparison Project (CMIP5; Taylor et al., 2012). Based on data availability on the Earth System Grid Federation (ESGF) platform (https://esgf-data.dkrz.de, last access: 22 March 2020), 12 GCMs from CMIP5 dynamically downscaled with five RCMs available from the CORDEX-Africa initiative are selected for this study (Table 1). The spatial resolution of the RCMs is 0.44∘ (∼ 50 km) in latitude and longitude. As the RCMs do not downscale all the GCMs, there are 21 RCM–GCM combinations available for the global runs in the historical period (1951–2005), while 43 RCM–GCM combinations are available for the future projections (2006–2100) under various representative concentration pathways (RCP2.6, RCP4.5, and RCP8.5). The RCPs correspond to different scenarios of future concentrations and emissions of greenhouse gases and air pollutants, and land use change until 2100, relative to the preindustrial times (Moss et al., 2010; Van Vuuren et al., 2011). The three RCPs used in this study are (i) RCP2.6, corresponding to a mitigation scenario with a very low radiative forcing level that peaks at ∼ 3 W m-2 (∼ 490 ppm CO2 eq.) and declines to ∼ 2.6 W m-2 by 2100; (ii) RCP4.5, representing a medium stabilization scenario without overshoot pathway to 4.5 W m-2 (∼ 650 ppm CO2 eq.) at stabilization after 2100; and (iii) RCP8.5, corresponding to a very high emission scenario with rising radiative forcing pathway leading to 8.5 W m-2 (∼ 1370 ppm CO2 eq.) by 2100. Approximatively, RCP2.6 corresponds to a +2 ∘C global temperature stabilization by 2100, while RCP4.5 and RCP8.5 correspond to +3.5 and +5 ∘C increase in global temperature by 2100 (Konapala et al., 2020). The climate variables used in this study are daily data of rainfall and minimum, maximum, and average air temperature, which are obtained for the climate model realization r1i1p1.

Assessing the reliability of climate projections data for reproducing observations is a precondition to impact studies (Eyring et al., 2019). However, observations are also subject to uncertainties. To address these uncertainties, the climate projection datasets are evaluated with respect to 10 satellite-based and reanalysis-based rainfall datasets and six temperature datasets (Table 2). The selected satellite-based and reanalysis-based rainfall datasets demonstrated the best performances for large-scale hydrological modelling in the VRB, as shown by Dembélé et al. (2020c). Hereafter, the datasets composed of both satellite and reanalysis products will be referred to as observations.

As discrepancies are observed between the cumulative distribution functions of the observations and the climate projection datasets (Fig. 3), a bias correction is applied before using the climate datasets for hydrological modelling, as usually recommended (Hakala et al., 2018; Teutschbein and Seibert, 2012). The R2D2 method (Vrac and Thao, 2020) is adopted for a multivariate bias correction of the climatic variables. R2D2 is a rank analogue-based method that adjusts not only the univariate distributions of climatic variables but also the inter-variable and inter-site dependence structures (Vrac, 2018). Bias correction with the R2D2 approach is achieved in two steps. First, the marginal distributions of univariate time series are adjusted using any univariate bias correction method. Here, the cumulative distribution function transform (CDF-t) approach (e.g. Vrac et al., 2012) is used to adjust the marginal properties of the univariate time series. Second, R2D2 is used to adjust the dependence structure between several variables, independently of their marginal distribution (i.e. empirical copula function). R2D2 has performed better compared to other bias correction methods, as demonstrated by François et al. (2020).

In the current multivariate bias correction, rainfall and temperature datasets are corrected simultaneously to preserve the temporal and spatial dependences between the climatic variables. The bias correction is done using only one of the observational datasets as reference data, the WFDEI, because it has both rainfall and temperature data over a long period (1979–2016). Furthermore, the WFDEI dataset previously demonstrated good performances in the VRB (Dembélé et al., 2020b). Therefore, it is chosen as reference data to limit uncertainties in the bias correction (Tarek et al., 2021). The period 1981–2005 is taken as the reference period for training the bias correction of the climate projection datasets, whose time series are divided into several 25-year periods over the period 1951–2100 to correspond to the length of the reference period. The multivariate bias correction is applied by grouping the data per calendar month in each sub-period of 25 years, which improves seasonality in the corrected data.

Variability in the model inputs and outputs resulting from different climate models are assessed using the second-order coefficient of variation (V2), which addresses the limitations of the classical coefficient of variation (Kvålseth, 2017), and is defined as follows: 7V2=s2s2+x‾21/2, where s is the standard deviation, and x‾ is the mean of a sample data x= (x1, …, xn)∈Rn. V2 represents the distance between x and x‾ relative to the distance between x and the origin zero, and it varies from 0 to 1 or 0 % to 100 %.

The relative changes in hydroclimatic variables between the various future periods and the historical period are calculated as follows: 8ΔXfuture=X‾future-X‾baselineX‾baseline, where ΔX corresponds to the relative future change in the average variable X over a given future period (2021–2050; 2051–2080; 2071–2100) as compared to the baseline or historical period (1991–2020). Only the numerator of Eq. (8) is considered for the calculation of absolute changes.

Finally, the percentage of the RCM–GCM agreement is calculated as the number of models agreeing on the same direction of change (i.e. increase or decrease) relative to the total number of models, which shows the robustness of the ensemble of climate projections.

The raw RCM–GCM datasets are evaluated by comparing their cumulative distribution functions to those of the observations over the period 1983–2005 corresponding to the concomitant availability period of all the observation datasets (Fig. 3). The distribution of most of the raw RCM–GCM datasets presents discrepancies with the observations, with larger gaps for temperature than rainfall. The multivariate bias correction with the R2D2 method visually performs well by adjusting the distributions of the RCM–GCM datasets to the WFDEI reference dataset for all the climatic variables. Therefore, the corrected RCM–GCM datasets are expected to provide reliable hydrological simulations in the VRB.

The general plausibility, here used to mean water and energy balance consistency within the Budyko framework, of the hydrological simulations using various RCM–GCM datasets as inputs to the mHM model under various RCPs and various periods is illustrated in Fig. 4.

All the RCM–GCM datasets provide plausible hydrological simulations, at least in terms of water and energy balance, as they respect the water and energy limits imposed within the Budyko framework. On average, the evaporative index (Ea/P) is between 0.86 and 0.97, while the aridity index (Ep/P) is between 2.2 and 4.4, which corresponds to expected values for sub-humid and semi-arid environments such as the VRB (Gunkel and Lange, 2017). It is noteworthy that future projections are shifted towards a lower evaporative index, and they have larger model-dependent variability in aridity ranges, particularly under RCP4.5 and RCP8.5.

The annual cycles of climatic and hydrological variables are illustrated in Fig. 5 for RCP8.5 (see Figs. S1–S10 for other RCPs). The hydroclimatic variables analysed are rainfall (P), average air temperature (Tavg), potential evaporation (Ep), actual evaporation (Ea), root zone soil moisture (Su), terrestrial water storage (St), total runoff (Qrun), and groundwater recharge (Rr). It is noteworthy that Tavg and Ep show a clear bimodal annual cycle in the VRB, with the first mode peaking between March and April, corresponding to the hottest period, while the second mode starts in September and peaks around October and November. For the hydroclimatic variables depicting a unimodal annual cycle, the peak of the cycle is observed around August and September, corresponding to the rainiest period.

The hydroclimatic variables depict contrasting seasonal changes across the RCPs over the future projection periods (Figs. 6 and 7). The mean monthly changes are calculated as the differences between the future periods and the historical period. Figures S11–S30 illustrate the distribution of changes in the seasonal cycle of the hydroclimatic variables across RCM–GCM combinations. Overall, monthly P is projected to increase between +2.9 % (RCP2.6) and +136.7 % (RCP8.5), on average, in the dry months (November–March) and decrease between -14 % (RCP8.5) and -0.6 % (RCP2.6) in the wet months (May–September) over the 21st century. However, the reduction in rainfall over the wet months is more accentuated from the beginning to the middle of the rainy season (May–July), whereas there is an increase in rainfall intensity over the late rainy season (August–September). Consequently, monthly rainfall is projected to be more concentrated at the end of the rainy season, i.e. in August and September, as compared to the baseline period. All RCM–GCM models agree for air temperature on the increasing trend across all RCPs over the 21st century. There is a clear increase for Tavg in all months with a similar pattern for each month, depicting an increase with time from 2021 to 2100 and with increasing radiative forcing level from RCP2.6 to RCP8.5. On average, Tavg increases between +2.4 % and 16.3 % (i.e. +0.6 and +4.4 ∘C) across RCPs and over the 21st century. Similar to future projections of Tavg, monthly Ep also shows a consistent increase across RCPs and for different periods in the 21st century. The average changes in Ep are projected from +1.1 % in 2021–2050 for RCP2.6 to +10.2 % in 2071–2100 under RCP8.5 (Fig. 6). The changes in simulated monthly Ea follow a similar pattern to P, with an average increase between +0.2 % under RCP2.6 and +8.1 % under RCP8.5 for Ea in the dry months and a reduction of -0.2 % and -9.9 %, respectively, under RCP2.6 and RCP8.5 in the wet months (Fig. 7).

Projected monthly Su and monthly St (the sum of all water stored below and above land) denote a clear decline in the future for all RCPs, except for some months in the period 2021–2050 and in the period 2071–2100 under RCP8.5 (Fig. 7). The average decrease varies between -4.1 % and -0.1 % for Su and between -3.6 % and -0.2 % for St. The monthly Qrun and Rr mainly increase, with the exception of some scenarios in some months. The projected monthly changes vary between -16.5 % and +173.9 % for Qrun and between -21.8 % and +344.3 % for Rr. The strong increases in Qrun and Rr are identified in April, when all RCM–GCMs project a decrease in Ea (Fig. 7).

Overall, the inter-model (i.e. RCM–GCMs) variability is lower for the historical period than for the future periods and increases with increasing radiative forcing level from RCP2.6 to RCP8.5 (Fig. 8). Among the climatic variables, low inter-model variabilities are simulated for monthly temperatures and potential evaporation, with an average V2 varying from 1 % to 4 % over the 21st century. However, Pshows higher inter-model variabilities with V2 ranging between 30 % and 44 %, which have a direct repercussion on the simulated hydrological variables. The highest inter-model variabilities are observed for groundwater recharge, which exceed V2 of 48 %. The monthly inter-model variability for all the hydroclimatic variables and all the RCPs are illustrated in Fig. S31. It is noteworthy that the inter-model variability for monthly rainfall, actual evaporation, total runoff, and groundwater recharge is lower during the wet months (May–September) than the dry months (November–March), while an almost constant trend across months is simulated for the other variables (Fig. S31).

Considering all RCPs over the historical period in the VRB, the multi-model ensemble mean of long-term annual estimates of climatic variables is as follows: Tavg= 28.4 ∘C, Ep= 2580 mm yr-1, P= 994 mm yr-1. The trends in annual estimates of projected hydroclimatic variables and water availability are illustrated in Fig. S32. Water availability is assessed as the net water flux into the land surface, using a proxy metric that is the difference between rainfall and actual evaporation (P-Ea) (Konapala et al., 2020; Greve and Seneviratne, 2015; Mishra et al., 2017).

The changes in the future projections of annual climatic and hydrological processes over the 21st century (2021–2100), as compared to the historical period (1991–2020) show contrasting trends between RCPs and between projection periods (Fig. 9). All climatic variables (rainfall, temperature, and potential evaporation) are projected to increase over the 21st century for all RCPs and projection periods, with the exception of rainfall that is expected to decrease under RCP2.6 and RCP4.5 and increase under RCP8.5.

The median annual changes in climatic variables over 2021–2100 are amplified with increasing radiative forcing levels and vary between RCP2.6 (Tavg=+1 ∘C; Ep=+2.3 %; P= -1.6 %), RCP4.5 (Tavg=+1.6 ∘C; Ep=+3.5 %; P= -0.5 %), and RCP8.5 (Tavg=+2.7 ∘C; Ep= +5.3 %; P=+2.82 %). More importantly, there is a 100 % agreement among the RCM–GCM models concerning the increase in air temperature across all the RCPs and projection periods. Therefore, there is a high confidence in future climate warming of the VRB region in West Africa during the 21st century. These findings align with previous studies in West Africa (Dosio et al., 2020; Todzo et al., 2020; Jin et al., 2018; Yeboah et al., 2022). Similar to Dosio et al. (2019), a lower RCM–GCM agreement of 63 % is found for future changes in rainfall, thereby highlighting the complexity of modelling climate in West Africa (Fitzpatrick et al., 2020; Panthou et al., 2012).

In contrast to the climatic variables, the hydrological variables (total runoff, actual evaporation, groundwater recharge, soil moisture, and terrestrial water storage) decrease under RCP2.6 and RCP4.5, and only increase under the RCP8.5 scenario during the period 2021–2100 (Fig. 9), thereby following the patterns of the projected changes in rainfall. The multi-model ensemble mean of long-term annual estimates of hydrological variables for all RCPs over the historical period is as follows: Ea= 929 mm yr-1, Qrun= 71 mm yr-1, Rr= 11.4 mm yr-1, Su= 0.58 mm mm-1, and St= 490 mm (Fig. S32). The median annual changes in hydrological variables over 2021–2100 vary between RCP2.6 (Ea=-1.2 %; Qrun=-9.9 %; Rr=-10.9 %; Su=-1.7 %; St=-1.9 %), RCP4.5 (Ea=-0.8 %; Qrun=-2.9 %; Rr=-4.2 %; Su=-1.9 %; St=-1.7 %), and RCP8.5 (Ea=+1.3 %; Qrun=+21.4 %; Rr=+18.3 %; Su=+0.3 %; St= +1.1 %). It can be concluded from these findings that an intensification of the hydrological cycle (i.e. increase in the magnitude of hydrological variables) in the VRB is projected only under the RCP8.5 scenario.

The multi-model ensemble mean of water availability is 65 mm yr-1 over the historical period. The changes in water availability are driven by the variations in rainfall, with a projected median increase of +20.3 % only under RCP8.5 over the 21st century, and a reduction of -11.3 % under RCP2.6 and -0.6 % under RCP4.5.

The spatial patterns of the inter-model median of annual climatic variables show a north–south gradient of increasing rainfall and decreasing air temperature and decreasing potential evaporation (Fig. 10), which is in line with the aridity gradient of the eco-climatic zones in the VRB (Fig. 1). The spatial average of the multi-model ensemble of hydroclimatic variables per climatic zones in the VRB, considering all RCPs over the historical period, is given in Table 3.

The changes in spatial patterns of climatic variables under RCP8.5 illustrate a clear increase in air temperature and potential evaporation over the 21st century, with higher increase rates in the Sahelian zone and the northern regions of the VRB (Fig. 10; see other RCPs in Figs. S33–S37). The future projections show a decrease in rainfall under RCP2.6 and RCP4.5 from the Sahelian to the Sudanian zones, which correspond to the northern and central parts of the VRB (Figs. S33–S37). The increase in rainfall is projected mainly under RCP8.5, with higher increase rates localized from the Guinean to the Sudano-Sahelian zones, which correspond to the south and central regions of the VRB (Fig. 10).

The spatial patterns of the hydrological variables under RCP8.5 are depicted in Fig. 11 (see Figs. S38–S43 for other RCPs). Changes in annual actual evaporation, total runoff, and groundwater recharge depict similar spatial patterns to those of rainfall, with the exception that total runoff and groundwater recharge tend to increase in the Sahelian zone. Soil moisture and terrestrial water storage projections show a persistent decrease over most of the VRB area and particularly over the eastern regions. The analysis of projected future water availability per climatic zones in the VRB reveals an opposite pattern to the “dry gets drier, wet gets wetter” paradigm (Byrne and O'Gorman, 2015; Greve et al., 2014). The dry regions of the VRB (Sahelian and Sudano-Sahelian zones) are projected to become wetter, while the wet (Sudanian and Guinean zones) are projected to become drier under RCP2.6 and RCP4.5. However, all climatic zones in the VRB are projected to become wetter under RCP8.5.

The spatial inter-model variability depicts different patterns across hydroclimatic variables and across RCPs and projection periods (Figs. S44–S54). The highest differences among the simulations from climatic models are found generally in the northern dry regions (Sahelian zone) and in the forested southwestern wet region (Guinean zone) of the VRB under RCP8.5.

The projected future changes in high and low flows are summarized in Fig. 12 (Fig. S55 illustrates historical and future changes). Changes in low flows indicate an overall median increase in Q90 in all the sub-basins under RCP8.5 as follows: Black Volta (+30 %), White Volta (+16 %) and Oti (+14 %), with an RCM–GCM agreement on the direction of change of 69 %, 63 %, and 57 %, respectively. It is noteworthy that median Q90 is projected to decrease by -4 % in the White Volta over the period 2051–2080 under RCP8.5. The trends in the median changes in Q90 are contrasted across the future periods for RCP2.6 and RCP4.5. Tables S1–S2 provide details on the direction of change between the RCM–GCM combinations, which, on average, varies between 50 % and 78 % for Q90 and between 56 % and 75 % for Q10, depending on RCPs and climate projection periods.

For high flows, Q10 is projected to increase in all the sub-basins under RCP8.5, on average, by +20 % in the Black Volta, +2 % in the White Volta, and + 6 % in the Oti over the period 2021–2100, with an RCM–GCM agreement on the direction of change of 65 %, 63 %, and 59 %, respectively. However, it is noteworthy that Q10 for the period 2051–2080 under RCP8.5 is projected to decrease by -14 % in the White Volta and by -10 % in the Oti. Under RCP2.6 and RCP4.5, a decrease in Q10 is projected from 2051 to 2100 in all the sub-basins. The highest median decrease in Q10 over the 21st century in the sub-basins is -6 % in the Black Volta under RCP4.5, -16 % in the White Volta under RCP2.6, and -20 % in the Oti under RCP2.6. Both high and low flows are projected to increase with different magnitudes under all RCPs in the Black Volta and the White Volta over the period 2021–2050, while low flows are projected to increase under all RCPs in the Oti over the period .2051–2080.

Among the sub-basins, the Black Volta presents the highest probability of an increase in the 10-year flood over the 21st century. The White Volta is prone to an increase in flood risk in the period 2021–2050, while river drought risk is projected to increase over the period 2051–2100.

The evolutions of the dates of occurrence and the concentration of the date of occurrence of Q10 and Q90 are illustrated in Figs. 13 and S57. The median date of occurrence of Q10(DQ10) varies between the Julian calendar days 254 and 261 (second dekad of September), on average, across the three sub-basins (Black Volta, White Volta, and Oti) over the historical period, and it is projected to drop by -2 d under RCP2.6 and RCP4.5 and increase by +2 d under RCP8.5 over the 21st century. However, higher changes are projected in the Black Volta (ΔDQ10=-4 d under RCP2.6), White Volta (ΔDQ10=-6 d under RCP2.6), and the Oti (ΔDQ10=+5 d under RCP8.5) over 2051–2080. The concentration of the date of occurrence (R) of DQ10 shows a high seasonality in the occurrence of high flows (RQ10= 0.94) across sub-basins, which does not change considerably over the 21st century (Fig. S57).

In contrast to DQ10, the median DQ90 varies between 126 and 132 (first to second dekad of May) over the historical period and rises on average by +5 d over future periods and across sub-basins. However, notable rises in DQ90 are observed in each sub-basins during 2071–2100 as follows: Black Volta (ΔDQ90=+9 d under RCP8.5), White Volta (ΔDQ90=+11 d under RCP8.5), and Oti (ΔDQ90=+10 d under RCP2.6), which might be explained by the forward shift of the rainy season. The median RQ90 is 0.74 on average across sub-basins and slightly drops in the future, denoting a higher variation in the seasonality of low flows.

The sensitivity of selected hydrological variables to changes in climatic variables over the historical and future periods is illustrated in Fig. 14 (see Fig. S58 for additional variables). The relative changes in hydroclimatic variables are estimated in percentage over the three future periods compared to the historical period. Larger changes in hydroclimatic variables are simulated with increasing radiative forcing levels over the future period.

The VRB illustrates highly nonlinear behaviour. An increase in annual rainfall by 10 % results in an increase in total runoff by ∼ 50 % and an increase in actual evaporation by ∼ 6 %. A 10 % decrease in annual rainfall leads to ∼ 30 % decrease in total runoff and ∼ 7 % decrease in actual evaporation. Annual actual evaporation represents 93 % of annual rainfall, while total runoff represents 7 % of annual rainfall. However, small changes in the rainfall regime might strongly affect the total runoff regime. A 5 % increase in annual average air temperature leads to an increase of ∼ 3 % in potential evaporation. However, heteroscedasticity is observed for changes in air temperature and potential evaporation as the variability increases with higher rates of change (Fig. 14f). This analysis reveals a high sensitivity of major fluxes (Qrun and Ea) to even small changes in P in the VRB, a finding consistent with previous studies in the region (Roudier et al., 2014), and more generally in dryland regions globally (Berghuijs et al., 2017).