Climate Simulation and Projection of Rainfall–Runoff Dynamics Using the GR4J Model in the Oti Sub-Basin: The Case of the Porga, Mandouri and Mango Outlets

Abstract

Water resource management in the Sahelian-Sudanian transition zone faces growing uncertainty under climate change, yet hydrological projections remain scarce for the Oti-Pendjari basin (West Africa). This study develops an integrated modelling chain combining CMIP6 multi-model evaluation, bias correction, and GR4J hydrological modelling to project streamflow changes under SSP2-4.5 and SSP5-8.5 over 2021–2100. Eleven CMIP6 models were evaluated against ERA5 reanalysis data (1960–2014) using NSE, KGE, and MAE; the three best-performing models were bias-corrected using Linear Scaling, Variance Scaling, Quantile Mapping, and Quantile Delta Mapping. Linear Scaling proved most effective, with CMCC-ESM2 best reproducing observed precipitation (NSE and KGE up to 0.9), while the multi-model approach performed best for temperature. The GR4J model, calibrated at Porga, Mandouri, and Mango (KGE: 0.609–0.668), satisfactorily reproduces intermediate flows and flood dynamics, although structural limitations persist for low flows (KGE [1/Q]: −0.65 to −0.71). Projections reveal a marked divergence between scenarios: SSP2-4.5 yields September peak flow increases of +5.7% to +16.7%, whereas SSP5-8.5 leads to slight decreases of −1.1% to −3.6%, likely driven by increased potential evapotranspiration partially offsetting precipitation gains. These findings underscore the critical importance of scenario selection and model uncertainty in regional water resource planning.

1. Introduction

West Africa is one of the regions of the world most vulnerable to the impacts of climate change, due to the heavy reliance of its economies and populations on water resources and rain-fed agriculture [1,2]. In this region, rainfall and temperature patterns directly determine the availability of water resources, agricultural productivity and the frequency of extreme events such as floods and droughts [3,4]. Understanding future climate changes and their hydrological impacts is therefore a major scientific and societal challenge for this region.

The Oti-Pendjari catchment area, located in the northern part of the Volta system, spans four countries (Benin, Togo, Burkina Faso and Ghana) and has a hydroclimatic configuration that is particularly sensitive to fluctuations in the West African monsoon regime [5,6]. This basin, characterized by a strongly seasonal Sudano-Guinean regime, feeds fragile ecosystems, including the Pendjari Biosphere Reserve, and supports the agro-pastoral activities of millions of inhabitants. Despite its strategic importance, this basin remains insufficiently documented in hydroclimatic terms, particularly with regard to long-term projections under different emissions scenarios [7,8].

Global climate models (GCMs) from the Coupled Model Intercomparison Project, Phase 6 (CMIP6), represent the most advanced tool for simulating future climate changes under the shared socioeconomic scenarios (SSPs) defined by the IPCC [9,10]. However, these models exhibit systematic biases relative to observations, particularly in West Africa, where the representation of deep convection and the monsoon remain a major challenge for climate modelling [10,11,12]. The rigorous evaluation of these models and the correction of their biases are therefore essential steps prior to any use for hydrological projections.

Furthermore, translating climate projections into hydrological impacts requires the use of rainfall–runoff models capable of accurately reproducing the hydrological response of catchment areas. The GR4J model (Génie Rural à 4 paramètres Journalier), developed by [13], is a widely used global conceptual model in operational hydrology, whose simplicity facilitates calibration even in regions with low data density [14]. Its application in the context of the Oti-Pendjari catchment allows the impacts of climate change on flows to be assessed, whilst incorporating the uncertainties associated with the climate-hydrology modelling chain like describe by [15].

In this context, the present study has three main objectives: (i) to evaluate the performance of eleven CMIP6 climate models over the Oti-Pendjari basin for the historical period 1960-2014, using ERA5 reanalysis data as a reference; (ii) to compare four bias correction methods (Linear Scaling, Variance Scaling, Quantile Mapping and Quantile Delta Mapping) to identify the most effective one in the region; and (iii) to quantify the hydrological impacts of climate projections up to 2100 under the SSP2-4.5 and SSP5-8.5 scenarios, using the GR4J hydrological model calibrated and validated at the Porga, Mandouri and Mango outlets.

This integrated approach, combining multi-model assessment, statistical bias correction and hydrological modelling, aims to provide reliable information for the adaptive management of water resources and the planning of water infrastructure in a context of accelerating climate change. While modelling chains coupling CMIP6, bias correction and conceptual rainfall-runoff models have been applied in several West African basins, the methodological contribution of the present work lies in three specific aspects. First, an explicit side-by-side intercomparison of four bias correction methods (LS, VS, QM, QDM) is carried out on the same three best-ranked CMIP6 models and their multi-model mean over the Oti-Pendjari domain, which has not been documented in previous studies of this basin. Second, the model-selection strategy is variable-specific: a single best-performing model is retained for precipitation (a non-Gaussian, intermittent variable) while a multi-model mean is retained for temperature (an approximately Gaussian, continuous variable), a differentiation rarely formalized in the regional literature. Third, the chain is calibrated and validated jointly at three nested outlets (Porga, Mandouri, Mango) covering a contrasted range of catchment areas (21,907 to 35,394 km²), allowing the spatial integration effect on peak-flow projections to be quantified within a single, consistent framework. These three elements provide region-specific insight into how scenario selection and methodological choices propagate into projected streamflow changes in the Sudano-Sahelian transition zone.

The study area forms part of the Oti-Pendjari river system, located in northern Benin, between the approximate coordinates of 8° N to 12.3° N latitude and −1° to 3° E longitude. It belongs to the Volta River basin and drains an area straddling four countries: Benin, Togo, Burkina Faso and Ghana [5,6]. This region is characterized by a Sudano-Guinean hydroclimatic regime, marked by highly seasonal rainfall, with a wet season centred on the period June–September and a dry season dominated by the harmattan, under the influence of the West African monsoon [4]. Within this study area, three sub-catchments of the system; namely the Porga, Mandouri and Mango catchments; were selected (Figure 1), located in the northern part of the basin.

2. Materials and Methods

2.1. Data

As part of this study, temperature and precipitation data were used. For precipitation, eleven global climate models from CMIP6 were evaluated over the historical period 1960–2014, namely CanESM5, CMCC-ESM2, CNRM-CM6-1, CNRM-ESM2-1, EC-Earth3-AerChem, EC-Earth3-CC, IPSL-CM6A-LR, MPI-ESM1-2-HR, MPI-ESM1-2-LR, MRI-ESM2-0 and NESM3, all obtained via the Copernicus Climate Change Service (Climate Data Store, [16]. Their native atmospheric horizontal resolutions are heterogeneous CanESM5 (~2.8° × 2.8°), CMCC-ESM2 (~1.0° × 1.0°), CNRM-CM6-1 and CNRM-ESM2-1 (~1.4° × 1.4°), EC-Earth3-AerChem and EC-Earth3-CC (~0.7° × 0.7°), IPSL-CM6A-LR (~2.5° × 1.3°), MPI-ESM1-2-HR (~0.9° × 0.9°), MPI-ESM1-2-LR (~1.9° × 1.9°), MRI-ESM2-0 (~1.1° × 1.1°) and NESM3 (~1.9° × 1.9°). All fields were subsequently regridded onto the common 0.25° ERA5 grid. These simulations were compared with ERA5 reference data from the same service ([17]), used as an observational proxy in the absence of a sufficiently dense in situ rain-gauge network in the Oti-Pendjari basin. The use of ERA5 as a reference is not without limitations. But the recent intercomparisons over West Africa indicate that ERA5 generally captures the seasonal cycle and inter-annual variability of rainfall [18]. They concluded [18], among other things, that ERA5 is strongly correlated with observations across all seasons. At the subregional level, ERA5 provides a better description of intra-annual precipitation cycles. More specifically, reference [19] demonstrated the effectiveness of ERA5 data across all stations covering the entire country of Benin (a West African nation), which partially includes the Pendjari basin in the northwest of the country.

The dataset was extracted and homogenized over a spatial domain defined by the boundaries [−1°; 3°] in longitude and [8°; 12°] in latitude, covering the northern part of Benin and the Oti-Pendjari basin, to ensure spatial consistency in the assessment of climate performance.

For model comparison, the CMIP6 data in NetCDF format, initially characterized by heterogeneous spatial resolutions, were regridded and interpolated onto the ERA5 reference grid (17 × 17) to ensure strict comparability. This spatial harmonization was carried out using the xESMF resampling method (v0.9.2) [20]. These data were supplemented with discharge records from the three outlet stations covering the periods 1960–2012 for Mandouri, 1960–1984 for Mango, and 1960–2013 for Porga (obtained from DRE-Togo). These records were used for calibration and validation in order to project stream flows up to the year 2100. All data processing was performed using Python (3.12) [21].

Following an analysis of monthly climatology and associated variability (standard deviation), an analysis of the seasonal precipitation gradient was carried out. This analysis complements standard statistical indicators: Pearson’s correlation coefficient (r), mean bias and standard deviation $(\mathsf{\sigma }$) were used to evaluate recent climate models [9] which were then summarized using the Taylor diagram to provide an integrated assessment of performance [22].

$$r={\displaystyle \frac{{\sum }_{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^2{\sum }_{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}} \mathrm{with}$$

(1)

$$\mathsf{\sigma }=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left(X_i-\overline{X}\right)}^2}.$$

(2)

2.2. Complementary Methods for Assessing Bias

Following the assessment of seasonal patterns, model performance was quantified using additional statistical indicators, notably the Nash–Sutcliffe efficiency coefficient (NSE), the Kling–Gupta Efficiency (KGE) and the mean absolute error (MAE), in order to evaluate the overall quality of the simulations against the observations.

Table 1. Statistical indicators used to evaluate model performance.

Indicator	Mathematical Formula
NSE (Nash–Sutcliffe Efficiency)	$1-{\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}}{\left(\mathrm{i}-\mathrm{X}\mathrm{i}\right)}^2}{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}}{\left(\mathrm{x}\mathrm{i}-\mathrm{X}\mathrm{i}\right)}^2}}$ avec Yi: simulated value; Xi: observed value; $\overline{\mathrm{X}}$: average of the observations and n: number of data points
KGE (Kling–Gupta Efficiency)	$1-\sqrt{{\left(\mathrm{r}-1\right)}^2+{\left(\mathsf{\alpha }-1\right)}^2+{\left(\mathsf{\beta }-1\right)}^2};$ with r = corr(X. Y). $\mathsf{\alpha }=$${\displaystyle \frac{\mathsf{\sigma }\mathrm{Y}}{\mathsf{\sigma }\mathrm{X}}}$(standard deviation ratio) et $\mathsf{\beta }=$${\displaystyle \frac{\mathsf{\sigma }\mathrm{Y}}{\mathrm{X}}}$(biais relatif); σ: standard deviation
MAE (Mean Absolute Error)	${\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\left\{\mathrm{i}=1\right\}}^{\mathrm{n}}\mid \mathrm{Y}\mathrm{i}-\mathrm{X}\mathrm{i}\mid$ avec $\mathrm{Y}\mathrm{i}$ simulated value and Xi: observed value

presents their mathematical formulas.

The NSE allows us to assess the models’ ability to reproduce the variability observed in the data, with values close to 1 indicating excellent performance, whilst the KGE provides an integrated assessment by combining correlation, bias and the relative variability of the simulated series. In addition, the MAE quantifies the mean absolute error, providing a direct measure of the discrepancies between simulations and observations. The combined use of these indicators thus enables a robust and multidimensional assessment of the performance of climate models [23,24].

2.3. Methods for Correcting Bias

Based on the evaluation results, the three best-performing models were selected and combined using their multi-model average, forming the basis of the data to be corrected. Bias correction was then applied using four complementary methods: Linear Scaling (LS), Variance Scaling (VS), Quantile Mapping (QM) and Quantile Delta Mapping (QDM).

Table 2. Methods for correcting bias and mathematical formulas.

Method	Mathematical Formula
Linear Scaling (LS)	${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}={\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}}\times {\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{o}\mathrm{b}\mathrm{s}}}{{\mathsf{\mu }}_{\mathrm{s}\mathrm{i}\mathrm{m}}}}$ (rainfall) ${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}={\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}}+\left({\mathsf{\mu }}_{\mathrm{o}\mathrm{b}\mathrm{s}}-{\mathsf{\mu }}_{\mathrm{s}\mathrm{i}\mathrm{m}}\right)$ (Temperature) with ${\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}}:\mathrm{s}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}.$ ${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}:\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}$$\mathrm{a}\mathrm{n}\mathrm{d} {\mathsf{\mu }}_{\mathrm{s}\mathrm{i}\mathrm{m}}.{\mathsf{\mu }}_{\mathrm{o}\mathrm{b}\mathrm{s}}:\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}/\mathrm{s}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}$
Variance Scaling (VS)	${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}={\mathsf{\mu }}_{\mathrm{o}\mathrm{b}\mathrm{s}}+{\displaystyle \frac{{\mathsf{\sigma }}_{\mathrm{o}\mathrm{b}\mathrm{s}}}{{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}\mathrm{m}}}}\left({\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}}-{\mathsf{\mu }}_{\mathrm{s}\mathrm{i}\mathrm{m}}\right)$ avec ${\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}}:\mathrm{s}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}$${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}:\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}$$\mathrm{e}\mathrm{t}$ ${\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}\mathrm{m}}.{\mathsf{\sigma }}_{\mathrm{o}\mathrm{b}\mathrm{s}}:\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d} \mathrm{d}\mathrm{e}\mathrm{v}\mathrm{i}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}$
Quantile Mapping (QM)	${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}={\mathrm{F}}_{\mathrm{o}\mathrm{b}\mathrm{s}}^{-1}\left({\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}}\left({\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}}\right)\right)$ avec ${\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}}:\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}$ et ${\mathrm{F}}_{\mathrm{o}\mathrm{b}\mathrm{s}}^{-1}:\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d} \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{e} \left(\mathrm{C}\mathrm{D}\mathrm{F}\right)$
Quantile Delta Mapping (QDM)	${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}.\mathrm{f}\mathrm{u}\mathrm{t}}={\mathrm{F}}_{\mathrm{o}\mathrm{b}\mathrm{s}}^{-1}\left(\mathsf{\tau }\right)+\left[{\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{f}\mathrm{u}\mathrm{t}}-{\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}}^{-1}\left(\mathsf{\tau }\right)\right]$(Temperature) ${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}.\mathrm{f}\mathrm{u}\mathrm{t}}={\mathrm{F}}_{\mathrm{o}\mathrm{b}\mathrm{s}}^{-1}\left(\mathsf{\tau }\right)\times {\displaystyle \frac{{\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{f}\mathrm{u}\mathrm{t}}}{{\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}}^{-1}\left(\mathsf{\tau }\right)}}$ (Rainfall) With $\mathsf{\tau }={\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{f}\mathrm{u}\mathrm{t}}\left({\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{f}\mathrm{u}\mathrm{t}}\right);$${\mathrm{X}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{f}\mathrm{u}\mathrm{t}}:\mathrm{simulated} \mathrm{future} \mathrm{value}.$${\mathrm{X}}_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}.\mathrm{f}\mathrm{u}\mathrm{t}}:\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{future} \mathrm{value}.$ ${\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}}^{-1}:\mathrm{quantile} \mathrm{of} \mathrm{the} \mathrm{historical} \mathrm{model}.$ ${\mathrm{F}}_{\mathrm{s}\mathrm{i}\mathrm{m}.\mathrm{f}\mathrm{u}\mathrm{t}}:\mathrm{Distribution} \mathrm{function} \mathrm{of} \mathrm{the} \mathrm{future} \mathrm{model}$. $\mathsf{\tau }:\mathrm{the} \mathrm{lower} \mathrm{bound} \mathrm{associated} \mathrm{with} \mathrm{the} \mathrm{simulated} \mathrm{value}.$ More precisely, τ = Fsim,fut(Xsim,fut) ∈ [0, 1] denotes the non-exceedance probability associated with the simulated future value Xsim,fut, computed from the empirical cumulative distribution function of the future simulation; F−1(τ) is the inverse CDF (quantile function) evaluated at this probability, both for the observations (Fobs−1) and the historical simulation (Fsim,hist−1) over the reference period.

presents their mathematical formulas.

The LS method involves adjusting systematic biases by correcting the mean of the simulated series affected by additive and multiplicative biases for rainfall [25]. The VS method extends this approach by simultaneously correcting the mean and the variance, thereby improving the representation of variability, particularly for temperatures and certain components of rainfall [26]. In contrast, quantile-based methods, QM and QDM, allow for a more comprehensive correction of the distribution of variables. QM adjusts the simulated quantiles to match the observed ones, which is particularly relevant for precipitation, characterized by asymmetric distributions and the presence of extremes [27]. QDM, for its part, corrects biases whilst preserving the climate change signal, making it particularly suitable for future projections [27].

Given the structural differences between temperature (a continuous variable, close to a normal distribution) and precipitation (an intermittent, non-Gaussian variable), it is essential to compare these methods in order to identify the most effective and robust one in the context of this study [25,26]. Thus, the most effective correction method, as well as the corrected models exhibiting the best statistical realism, were selected on the basis of evaluation indicators, in order to be applied to climate projection data.

• Statistical Evaluation of Methods for Correcting Rainfall Measurement Bias

In addition to standard performance metrics (RMSE, correlation coefficient, NSE, KGE, and bias), a supplementary statistical analysis was conducted to assess the comparative robustness of the bias correction methods applied to precipitation data. In fact, overall performance indicators may not accurately reflect the ability of methods to reproduce extreme events, which are nonetheless essential in hydroclimatic studies and risk analyses [28,29]. Correction methods can thus perform well on average statistics while distorting the tails of the distribution of extreme precipitation.

○

Statistical significance test

A nonparametric [30] signed-rank test was applied to assess the statistical significance of performance differences among the bias correction methods. This test is particularly well-suited for small samples and does not require the assumption of data normality [31]. It is based on a paired comparison of the performance obtained by the different methods for the same set of climate models. The Wilcoxon statistic is defined by:

$$W=\min \left(W^{+},W^{-}\right)$$

(3)

where

▪

($W^{+}$) represents the sum of the ranks associated with the positive differences;

▪

($W^{-}$) represents the sum of the ranks associated with the negative differences.

The null hypothesis (H0) assumes that there is no significant difference between the methods being compared. The significance level is set at (α = 0.05).

○

Analysis of extreme rainfall events

To assess the ability of correction methods to reproduce heavy precipitation, an analysis of precipitation extremes was conducted using the upper percentiles of the precipitation distribution. The 90th (P90), 95th (P95), and 99th (P99) percentiles were selected to characterize intense, very intense, and extreme events, respectively. The relative bias of the extremes was calculated using the following expression:

$$Bias\mathrm{ }relatif\mathrm{ }\left(\%\right)={\displaystyle \frac{P_{sim}-P_{obs}}{P_{obs}}}\times 100$$

(4)

where $P_{sim}$ corresponds to the simulated percentile after correction; $P_{obs}$ represents the observed percentile derived from the reference data.

This approach makes it possible to assess the ability of different methods to preserve the structure of precipitation distribution tails, which are generally better represented by quantile-based correction methods [28,29].

2.4. Method for Regionalising Data

The regionalization of climate data was carried out using a regular spatial discretization of the Porga, Mandouri and Mango sub-basins. Let B denote a catchment defined within a spatial domain ((x. y)). A Cartesian grid with a resolution of ∆ = 0.25° is generated such that:

$$\mathrm{x}i=\mathrm{x}\mathrm{m}\mathrm{i}\mathrm{n}+\mathrm{i}\cdot \mathsf{\Delta }i and \mathrm{y}j=\mathrm{y}\mathrm{m}\mathrm{i}\mathrm{n}+\mathrm{j}\cdot \mathsf{\Delta }y\_j$$

(5)

With i. j $\in$ ℕ; x_min. x_max; y_min. y_max the boundaries of the basin. All the points in the grid are then defined by:

$$\mathrm{G}=\left\{\right(\mathrm{x}\mathrm{i}.\mathrm{y}\mathrm{j}\left)\right\}$$

(6)

A spatial filtering operation is then applied to retain only those points that belong to the catchment area:

$${\mathrm{G}}_B=\left\{\left(\mathrm{x}\mathrm{i}.\mathrm{y}\mathrm{j}\right)\in \mathrm{G}∣\left(\mathrm{x}\mathrm{i}.\mathrm{y}\mathrm{j}\right)\in \mathrm{B}\right\}$$

(7)

where (G_B) represents all the points within the catchment area. Figure 2 shows the sampled points.

These points (27 for Porga, 38 for Mandouri and 46 for Mango) constitute the sampling units used for the extraction of climate variables. This approach corresponds to uniform spatial sampling, ensuring a consistent representation of intra-basin variability and direct compatibility with climate data grids [32,33].

2.5. Hydrological Modelling

The performance of the hydrological model was evaluated using observed (Qobs) and simulated (Qsim) discharge time series for three hydrometric stations: Mandouri, Mango and Porga. The analysis was conducted over two distinct periods: a calibration period used to adjust the model parameters, and a validation period to test its robustness and generalizability.

To ensure a comprehensive and reliable evaluation, a multi-criteria approach was adopted. This approach allows the model’s performance to be characterized under different hydrological regimes, notably high flows (floods), mean flows and low flows (low water). Several complementary statistical indicators were therefore employed.

Table 3. Summary of the formulas and criteria for assessing discrepancies between Qobs and Qsim.

Criterion	Formula	Interpretation
KGE	$1-\sqrt{{\left(\mathrm{r}-1\right)}^2+{\left(\mathsf{\alpha }-1\right)}^2+{\left(\mathsf{\beta }-1\right)}^2}$; with r = Corr($Q_{obs}$. $Q_{sim}$). $\mathsf{\alpha }=$ ${\displaystyle \frac{\mathsf{\sigma }{Q}_{sim}}{\mathsf{\sigma }{Q}_{obs}}}$ (standard deviation ratio) et $\mathsf{\beta }=$ ${\displaystyle \frac{\mathsf{\sigma }{Q}_{sim}}{Q_{obs}}}$ (biais relatif); σ: standard deviation	The closer the KGE/NSE values are to 1, the better the model.
NSE	NSE = $1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}{(Q_{obs.i}-Q_{sim.i})}^2}{{{\displaystyle {\sum }_{i=1}^n}(Q_{obs.i}-\overline{Q_{obs}})}^2}}$
RMSE	$RMSE=\sqrt{{\displaystyle \sum _{i=1}^n}({Q_{sim.i}-Q_{obs.i})}^2}$	An RMSE close to 0 indicates a perfect model.
BIAS(Qsim/Qobs)	BIAS = ${\displaystyle \frac{\overline{Q_{sim}}}{\overline{Q_{obs}}}}$	If BIAS > 1 = Overestimation If BIAS < 1 = Underestimation If BIAS = 1 = Perfect

details the formulas used to assess the discrepancies between the observed data and the outputs of the hydrological model.

The model’s overall performance was initially assessed using the Nash–Sutcliffe efficiency coefficient (NSE), the Kling–Gupta coefficient (KGE) and the root mean square error (RMSE). The NSE measures the model’s ability to reproduce the variability of the observations and is particularly sensitive to high flows. The KGE, on the other hand, provides a more balanced assessment by simultaneously incorporating the correlation, bias and variability of the series; whilst the RMSE quantifies the average simulation error.

In order to analyze the model’s performance in greater detail across different hydrological regimes, transformations were applied to the discharge series. The square root transformation (√Q) was used to reduce the influence of high flows and to better represent intermediate flows. In addition, the inverse transformation (1/Q) was applied to emphasize the weight of low flows, thereby allowing for a better assessment of the model’s performance during low-flow periods. The NSE and KGE indicators were recalculated from these transformed series, yielding NSE[√Q], KGE[√Q], NSE[1/Q] and KGE[1/Q], respectively.

Furthermore, the model bias was assessed using the ratio of simulated flows to observed flows (BIAS), calculated as the ratio of the mean of the simulated flows to that of the observed flows. A BIAS value of 1 indicates a perfect reproduction of water volumes, whilst a value greater (or less) than 1 indicates an overestimation (or underestimation) of flows by the model.

For each station and each period, all indicators were calculated and summarized in a summary

Table 4. Time for the warm-up, calibration and validation.

Stations	Warm-Up	Calibration Period	Validation Period	Screening Period
Mandouri	1960-01-01:1960-12-31	1961-01-01:1981-12-30	1982-01-01:2012-12-30	2022-01-01:2100-12-30
Mango		1961-01-01:1970-12-30	1974-01-01:1984-12-30
Porga		1961-01-01:1990-12-30	1991-01-01:2013-01-25

.

The analysis of the results was conducted along three main lines: (i) the model’s overall performance as measured by standard indicators; (ii) its ability to reproduce the various hydrological regimes using the √Q and 1/Q transformations; and (iii) the assessment of the overall bias in the simulations. A comparison of performance between the calibration and validation periods enabled an assessment of the model’s robustness and stability.

3. Results

3.1. Trend Analysis of Observed Data and Model Data

• Average monthly rainfall

Figure 3 shows the monthly rainfall variability.

The observed pattern is distinctly seasonal, with virtually no rainfall from December to February, a rapid increase from March–April, followed by a peak in August of around 240 mm, before a decline around October. This represents a gradient of approximately +5 mm/month between the dry season and the peak of the monsoon. The CMIP6 models correctly reproduce the timing, but diverge significantly on intensity. CanESM5 and NESM3 are the wettest, with peaks of 300 to 360 mm (+40 to +50%), whilst MRI-ESM2-0 and, at times, EC-Earth3-AerChem attenuate the rise and underrepresent the maximum. Monthly rates thus range from +2 to +3 mm/month for the most moderate simulations to >+10 mm/month for the most intense. The MPI and CNRM models occupy an intermediate position (≈+6 to +9 mm/month) and remain closest to the observed pattern. Consequently, the best compromise between respect for the seasonal phase and realistic cumulative totals is provided by MPI-ESM1-2-LR and CNRM-ESM2-1, whilst the others tend either to amplify the monsoon excessively or to smooth it out.

• Average monthly temperature

Figure 4 shows monthly temperature variability. The observed temperature cycle ranges from approximately 24.8–25.0 °C during the July–August minimum to around 30–31 °C in March–April, representing an annual range of around 5–6 °C, which is correctly captured by the majority of CMIP6 models.

The difference therefore lies mainly in the intensity bias. MPI-ESM1-2-HR and MRI-ESM2-0 show the largest discrepancies, with temperatures often exceeding 32 °C during the warm season, resulting in overestimates of up to +1.5 to +2 °C. Conversely, NESM3 tends to be cooler, with deficits close to −1 °C during several wet months. The simulations closest to the observations are those that remain predominantly within a range of ±0.5 °C around ERA5; in this category, CMCC-ESM2 shows the most consistent agreement throughout the year, closely followed by CNRM-ESM2-1, whilst EC-Earth3-CC remains slightly more variable. Thus, in the absence of bias correction, CMCC-ESM2 appears to be the model that most faithfully reproduces observed monthly temperatures.

3.2. CMIP6 Model Performance Evaluation

• Average monthly rainfall

The performance of the simulations (Figure 5) varies considerably around the observed point, revealing significant discrepancies in the joint reproduction of temporal variability.

CanESM5 exhibits the highest correlation (≈0.89), indicating a good ability to track the timing of rainfall events. However, its standard deviation, which is significantly higher than that of the observations, reflects a systematic overestimation of intensity, which artificially inflates extremes and may bias any impact analysis. CMCC-ESM2 shows a slightly weaker correlation (≈0.83) but a variability much closer to the actual regime, a sign of a more balanced behaviour between temporal fidelity and amplitude. EC-Earth3-AerChem reasonably follows the dynamics but tends to underestimate the volumes. Conversely, several models show negative correlations, revealing a structural inability to reproduce regional seasonality. Critically, focusing solely on correlation would lead to selecting a model that is too vigorous, whereas also considering dispersion points towards a more realistic solution. Thus, the most robust choice for rainfall favours CMCC-ESM2. To validate this choice, numerical methods were applied.

Table 5. Ranking of model performance using the average monthly rainfall parameter.

Model	NSE	KGE	MAE	Global Ranking
IPSL-CM6A-LR	0.98	0.96	8.83	1
CMCC-ESM2	0.96	0.91	12.12	2
MPI-ESM1-2-LR	0.96	0.86	13.26	3
MPI-ESM1-2-HR	0.82	0.75	25.52	4
CNRM-CM6-1	0.81	0.80	26.49	5
CNRM-ESM2-1	0.81	0.77	25.79	6
MRI-ESM2-0	0.75	0.81	27.63	7
EC-Earth3-CC	0.78	0.66	29.38	8
EC-Earth3-AerChem	0.75	0.58	32.30	9
NESM3	0.66	0.48	32.96	10
CanESM5	0.09	0.20	51.29	11

presents the performance of the models’ numerical criteria.

IPSL-CM6A-LR clearly dominates with an NSE of 0.98, a KGE of 0.96 and the lowest mean absolute error, indicating a near-perfect reproduction of the dynamics, amplitude and bias of observed precipitation. CMCC-ESM2 and MPI-ESM1-2-LR follow with scores that are still high. These three models, along with their multi-model averages, will be corrected using the four methods.

• Monthly average temperatures

Figure 6 shows the performance of the models using the Taylor diagram.

The MPI-ESM1-2-LR model is characterized by a high correlation (≈0.85), indicating a faithful reproduction of temperature fluctuations, even though the amplitude remains slightly overestimated. MRI-ESM2-0 confirms solid performance (≈0.81) with a dispersion closer to the measured signal, reinforcing its credibility for trend studies. NESM3 remains acceptable but further from the ideal. The majority of the other models show a negative correlation, meaning they reproduce a trend opposite to the observed reality, which is a deal-breaker for any applied use. When considering both dynamics and variance, MPI-ESM1-2-LR appears to be the best compromise and is the leading candidate for temperature.

Table 6. Ranking of model performance using the monthly average temperature parameter for 1960–2014.

Model	NSE	KGE	MAE	Global Ranking
CNRM-CM6-1	0.669	0.864	0.901	1
MPI-ESM1-2-LR	0.638	0.597	0.882	2
CMCC-ESM2	0.326	0.793	1.218	3
CNRM-ESM2-1	0.389	0.731	1.237	4
EC-Earth3-AerChem	0.014	0.581	1.417	5
MRI-ESM2-0	−0.172	0.664	1.684	6
EC-Earth3-CC	−0.250	0.462	1.735	7
IPSL-CM6A-LR	−0.313	0.425	1.475	8
NESM3	−1.007	0.218	1.852	9
MPI-ESM1-2-HR	−0.806	0.134	1.875	10
CanESM5	−1.191	0.191	2.008	11

presents a summary of the numerical criteria for validating the choice.

The CNRM-CM6-1 model comes out on top with the best statistical trade-off, exhibiting the highest NSE (≈0.67), a strong KGE (≈0.86) and a low error. This means that seasonality, dispersion, and mean bias are generally well captured. MPI-ESM1-2-LR follows closely behind, benefiting from the lowest MAE. But a more moderate KGE indicates a less successful balance between correlation and amplitude. CMCC-ESM2 and CNRM-ESM2-1 remain acceptable, although a loss of explanatory power is apparent in the simulated variance. However, from the middle of the ranking onwards, NSE values close to zero or negative indicate a predictive capacity inferior to that of a simple climatological mean. These three models, along with their multi-model averages, will be corrected.

3.3. Application of Bias Correction Methods on Three First Best Models

• Average monthly rainfall

Table 7. Summary of methods for correcting simulated rainfall data.

Method	Model	Bias	Absolute Bias	RMSE	Correlation
Linear Scaling	CMCC-ESM2	2.73 × 10−8	2.73 × 10−8	35.25	0.904 *
	IPSL-CM6A-LR	5.98 × 10−7	5.98 × 10−7	38.12	0.889
	MPI-ESM1-2-LR	−4.18 × 10−7	4.18 × 10−7	37.50	0.892
	Mean	−4.53 × 10−7	4.53 × 10−7	30.33	0.927
Variance Scaling	CMCC-ESM2	−6.79 × 10−8	6.79 × 10−8	39.19	0.884
	IPSL-CM6A-LR	1.06 × 10−6	1.06 × 10−6	40.97	0.874
	MPI-ESM1-2-LR	−4.66 × 10−7	4.66 × 10−7	43.51	0.861
	Mean	−4.03 × 10−8	4.03 × 10−8	42.35	0.867
Quantile Mapping	CMCC-ESM2	6.04	6.04	39.42	0.884
	IPSL-CM6A-LR	2.96	2.96	42.25	0.891
	MPI-ESM1-2-LR	−6.84	6.84	46.65	0.873
	Mean	7.17	7.17	46.57	0.899
Quantile Delta Mapping	CMCC-ESM2	1.03	1.03	39.24	0.880
	IPSL-CM6A-LR	−0.53	0.53	43.55	0.885
	MPI-ESM1-2-LR	−4.56	4.56	46.58	0.875
	Mean	1.36	1.36	49.07	0.888

* Good corrected.

presents the performance of the methods for correcting the rainfall variable. An evaluation of the performance of the bias correction methods shows that, regardless of the models used, the Linear Scaling method generally stands out for its superior performance, particularly in terms of low bias. Indeed, although the multi-model average obtained using the Linear Scaling method yields the best overall metrics (RMSE = 30.33; correlation = 0.927), the CMCC-ESM2 model corrected using the same method displays very similar performance (RMSE = 35.25; correlation = 0.904), reflecting a remarkable ability to reproduce individual observations.

This similarity in results suggests that CMCC-ESM2 alone captures the bulk of the information contained in the multi-model ensemble, without the need for aggregation. By comparison, the other models (IPSL-CM6A-LR and MPI-ESM1-2-LR) exhibit higher errors and slightly lower correlations. Thus, the fact that CMCC-ESM2’s performance is very close to the average, whilst relying on a single model, demonstrates that it is the most relevant and robust choice, as it offers accuracy comparable to the multi-model ensemble with a simplified and directly usable structure. This model will therefore be used for the projection. The differential strategy adopted here, a single model (CMCC-ESM2) for precipitation versus a multi-model mean for temperature, reflects the distinct nature of the two variables. Precipitation in West Africa is dominated by intermittent, highly non-Gaussian events whose multi-model averaging tends to smooth out the inter-annual variability and to dampen extremes; therefore, when a single model already reproduces the seasonal cycle with metrics close to those of the ensemble mean (Table 7), retaining this individual realization preserves a more realistic temporal structure. Temperature, on the contrary, is a continuous and approximately Gaussian variable whose multi-model mean efficiently filters out model-specific biases without distorting the underlying signal, which explains why the multi-model approach yields the best RMSE/correlation for the thermal field (

Table 8. Results of the Wilcoxon signed-rank test comparing Linear Scaling to quantile-based methods (n = 04 models: CMCC-ESM2, IPSL-CM6A-LR, MPI-ESM1-2-LR et Mean).

Comparaison	n	ΔRMSE (LS − comp.)	W	p-Value
LS vs. QM	4	−8.42 mm/mois	0.0	0.0625
LS vs. QDM	4	−9.31 mm/mois	0.0	0.0625

). Figure 7 shows the seasonal regime of the corrected CMCC-ESM2 model.

The uncalibrated CMCC-ESM2 (Figure 7) model exhibits a marked positive bias at the start and end of the season, with overestimates of around +30 to +40 mm in April, +20 mm in June and +15 to +20 mm in October–November, reflecting a poor representation of the seasonal transition. After bias correction, the deviations from ERA5 become generally small, usually less than 5–10 mm with a faithful reproduction of the annual rainfall cycle. The seasonal peak is correctly reproduced in August (~230 mm for ERA5 versus ~225 mm after correction) and the intra-annual dynamics (onset, intensification, and withdrawal of rainfall) are consistent. This correction thus significantly reduces systematic error, aligns the amplitude and phase of the signal and therefore allows the bias correction parameters to be applied to correct the projection data (SSP2-4.5 and SSP5-8.5 from 2021 to 2100).

• Statistical evaluation and analysis of extreme rainfall events

Based on the RMSE scores from Table 7, a [30] signed-rank test was conducted to assess the statistical significance of the differences in performance between methods.

Based on Table 8, the statistic W = 0 for both comparisons indicates that LS consistently outperforms QM and QDM across all model pairs, which is consistent with the results of [22] regarding the correction of precipitation means. Furthermore, the negative ΔRMSE values between LS and QM/QDM indicate a low metric error for LS compared to the quantile methods evaluated. The obtained p-value (p = 0.0625) is marginally higher than the α = 0.05 threshold, but represents the minimum value mathematically achievable for n = 4, a limitation inherent to nonparametric tests on small datasets [27]. This result therefore indicates a strong and directionally consistent trend. It should be noted, however, that QM and QDM are theoretically designed to better capture the tails of the distribution [24], which justifies the additional evaluation of extremes presented in

Table 9. Relative bias in extreme values by model (mm/mois et %).

Method	GCM	Sim. P90	Sim. P95	Sim. P99	Biais P90 (%)	Biais P95 (%)	Biais P99 (%)
Reference data	ERA5	208.92	233.93	279.61	-	-	-
Linear Scaling (LS)	CMCC-ESM2	204.18	239.54	276.37	−2.27	2.40	−1.16
	Mean	205.21	224.19	268.07	−1.77	−4.17	−4.13
Quantile Mapping (QM)	CMCC-ESM2	209.92	241.15	287.12	0.48	3.09	2.69
	Mean	248.93	299.67	389.59	19.15	28.10	39.33
Quantile Delta Mapping (QDM)	CMCC-ESM2	204.90	236.26	284.29	−1.92	0.99	1.67
	Mean	249.89	303.48	394.81	19.61	29.73	41.20

(-): not applicable.

.

An analysis of the extreme percentiles P90, P95, and P99 (Table 9) shows that the Linear Scaling (LS) method exhibits the lowest relative biases (for both CMCC-ESM2 and the multi-model average, with deviations generally below 5%). Conversely, the Quantile Mapping (QM) and Quantile Delta Mapping (QDM) methods significantly overestimate the extremes, particularly for the multi-model average, where biases exceed 39% at the P99 percentile. These results contrast with the theoretical conclusions of [28,29] according to which quantile-based methods better reproduce the distribution tails.

However, several studies conducted in West Africa have shown that these approaches can artificially amplify extreme events when rare episodes are underrepresented during the calibration phase [34,35]. Furthermore, the similarity in performance between CMCC-ESM2 and the multi-model average under LS indicates that this model already captures the bulk of the regional climate signal. Given the highly intermittent nature of precipitation, the CMCC-ESM2 + LS approach appears to be the most robust for preserving extremes, correcting precipitation, and generating hydroclimatic projections for the study area [36,37].

• Average monthly temperature

With regard to temperature,

Table 10. Summary of methods for correcting simulated temperature data.

Method	Model	Bias	Absolute Bias	RMSE	Correlation
Linear Scaling	CMCC-ESM2	−8.75 × 10−8	8.75 × 10−8	1.57	0.740
	CNRM-ESM2-1	2.83 × 10−7	2.83 × 10−7	1.86	0.669
	MPI-ESM1-2-LR	−8.08 × 10−9	8.08 × 10−9	1.89	0.666
	Mean	1.90 × 10−10	1.90 × 10−10	1.37	0.790 *
Variance Scaling	CMCC-ESM2	−4.21 × 10−8	4.21 × 10−8	1.54	0.748
	CNRM-ESM2-1	1.90 × 10−7	1.90 × 10−7	1.63	0.719
	MPI-ESM1-2-LR	−1.14 × 10−9	1.14 × 10−9	1.65	0.717
	Mean	−9.50 × 10−11	9.50 × 10−11	1.55	0.748
Quantile Mapping	CMCC-ESM2	−2.05 × 10−4	2.05 × 10−4	1.84	0.633
	CNRM-ESM2-1	1.93 × 10−4	1.93 × 10−4	1.78	0.667
	MPI-ESM1-2-LR	−2.05 × 10−4	2.05 × 10−4	1.81	0.671
	Mean	3.12 × 10−4	3.12 × 10−4	1.57	0.746
Quantile Delta Mapping	CMCC-ESM2	1.60 × 10−4	1.60 × 10−4	1.84	0.633
	CNRM-ESM2-1	−1.99 × 10−5	1.99 × 10−5	1.78	0.667
	MPI-ESM1-2-LR	1.10 × 10−4	1.10 × 10−4	1.81	0.671
	Mean	2.38 × 10−6	2.38 × 10−6	1.57	0.746

* Good corrected.

provides an overview of the methods.

The performance evaluation for temperature shows that the best results are obtained using the Linear Scaling method applied to the multi-model average, which has the lowest RMSE (1.37) and the highest correlation (0.79), indicating the best reproduction of the observations. However, certain individual configurations, notably CMCC-ESM2 with Variance Scaling (RMSE = 1.54; corr = 0.75), show relatively similar performance, confirming the robustness of this model. Generally speaking, the Variance Scaling and Linear Scaling methods outperform quantile-based approaches, which exhibit higher errors and lower correlations. Thus, although individual models such as CMCC-ESM2 offer satisfactory results, the multi-model approach corrected by Linear Scaling remains the most effective, as it reduces errors and better captures thermal variability by combining information from several models. Figure 8 presents the correction result.

The raw multi-model data (Figure 8) exhibit a systematic thermal bias characterized by an overestimation of +0.5 to +1.2 °C between March and June and an underestimation during the cooler season (≈−0.5 °C in August–December), reflecting a shift in the amplitude and phase of the annual cycle. After correction, the simulated temperatures align closely with ERA5, with residual deviations generally below 0.2–0.3 °C, and a faithful reproduction of the maxima (~31 °C in March–April) and minima (~25 °C in August). The correction thus significantly reduces systematic biases, adjusts the annual temperature amplitude and restores seasonal consistency. This correction method will then be applied to projection data to ensure the consistency and reliability of future simulation, particularly under the SSP2-4.5 and SSP5-8.5 scenarios, over the period from 2021 to 2100.

Overall the multi-model (CMCC-ESM2+MPI-ESM1-2-LR+CNRM-ESM2-1) temperature data corrected using Linear Scaling for the SSP245 and SSP585 scenarios will enable the ETP of each catchment to be estimated using [14]. Meanwhile the calibrated CMCC-ESM2 climate model will provide the average precipitation for each of the catchment areas. These data are used to feed the calibrated and validated hydrological model to estimate future flows.

3.4. Calibration and Validation of the GR4J Model

3.4.1. Calibration and Validation Parameters

Table 11. GR4J model calibration and validation parameters.

Stations	Parameters				BV Sup (km2)	Centre-of-Mass Latitude
	X1	X2	X3	X4
Porga	0.0105	−29.778	470.2	4.505	21,907.418	11.372
Mandouri	0.0079	−18.016	411.46	5.278	29,046.2417	11.412
Mango	150.91	1.7	40.86	7.65	35,394.433	11.293

presents the calibration parameters of the GR4J model [13], optimized using the SCE-UA algorithm [38], for the three stations in the Oti catchment. The GR4J model is a global conceptual four-parameter rainfall–runoff model representing the generation (X1, X3, X4) and transfer (X2) processes.

Looking at Table 11, the parameter X1 (mm) reflects the capacity of the catchment; the values are very low for Porga (0.0105 mm) and Mandouri (0.0079 mm), indicating virtually zero soil water retention capacity. In contrast, the Mango station shows a significantly higher value (X1 = 150.91 mm), reflecting a greater storage capacity, consistent with larger catchment areas (35.394 km²) where the spatial variability of soil types increases retention capacity [39]. As a result of the low values of the X2 parameter (underground exchange coefficient); Porga (−29.778) and Mandouri (−18.016) are adjusted to negative values.

This situation in no way reflects the intrinsic biophysical characteristics of the catchments, even though it is a phenomenon frequently observed in the crystalline basins of the West African Sahel where groundwater–river exchange is deficient [40]. However, considering the parameters X3 (routing reservoir) and X4 (base time), it is observed that X3 decreases from the upstream area (Porga: 470.2 mm) towards Mango (40.86 mm), reflecting a reduction in the routing reservoir capacity as the catchment area increases and hydrological regulation is exerted by floodplains. X4 (transfer time) increases from Porga (4.5 days) to Mango (7.65 days), consistent with the lengthening of the river network downstream.

3.4.2. GR4J Model Performance Evaluation

• Quantitative performance criteria

The multi-criteria evaluation of the GR4J model’s performance is based on the Kling–Gupta Efficiency (KGE), the Nash–Sutcliffe Efficiency (NSE), the coefficient of determination R², the root mean square error (RMSE) and the volumetric bias (BIAS = Qsim/Qobs). This multi-criteria approach is recommended in the literature to avoid biases associated with the use of a single criterion [41,42].

Table 12. Quantitative performance evaluation criteria.

	Mandouri		Mango		Porga
	Calibration	Validation	Calibration	Validation	Calibration	Validation
KGE	0.609 *	0.632 *	0.657 *	0.522 **	0.668 *	0.55 **
NSE	0.507 *	0.451 **	0.334 ***	0.235 ***	0.566 **	0.428 **
RMSE	109.938	102.324	223.539	123.889	108.838	105.134
BIAS (Qsim/Qobs)	0.887 #	1.189 ##	0.921 #	1.202 ##	1.031 ##	1.369 ##
Intermediate flow rates
KGE[√Q]	0.616 *	0.524 **	0.594 **	0.318 ***	0.539 *	0.469 **
NSE[√Q]	0.638 *	0.489 **	0.57 **	0.254 ***	0.602 *	0.485 **
Low flow rates
KGE[1/Q]	−0.679	−0.668	−0.71	−0.705	−0.545	−0.642
NSE[1/Q]	−0.003	−0.038	−0.001	−0.003	−0.119	−0.083

* ≥0.6 (good), ** 0.4–0.6 (acceptable), *** <0.4 (poor), ^# Underestimation and ^## Overestimation.

presents the performance evaluation results for both calibration and validation.

• Analysis of overall performance criteria [KGE and NSE criteria]

The KGE values [41] obtained during calibration range from 0.609 (Mandouri) to 0.668 (Porga), which corresponds to a performance rated as ‘very satisfactory’ according to the evaluation criteria in [43], which set the following thresholds: KGE > 0.65 (very satisfactory), 0.50–0.65 (satisfactory), and 0.35–0.50 (acceptable).

The decrease in KGE and NSE between calibration and validation is notable at Mango (ΔKGE = −0.135), suggesting temporal instability of the parameters, likely linked to the inter-decadal variability of rainfall regimes in the Sahelo-Sudanian zone [44]. For Porga and Mandouri, the greater stability (ΔKGE ≈ −0.12) indicates better temporal transferability of the model for small and medium-sized catchments. The NSE coefficients during calibration and validation are very low at the Mango station, but acceptable for the Mandouri and Porga stations. Consequently, the average model errors are estimated at 223.54 m³/s during calibration compared to 123.88 m³/s during validation, showing reduced average errors during the validation period at Mango. This observation also applies to the other stations. Furthermore, when assessing the BIAS, at stations such as Mandouri and Mango, the model underestimates the simulated flows, whereas it overestimates them during the validation period. The calibrated and validated model overestimates the simulated Q values compared to the observed Q values. A counter-intuitive feature deserves explicit mention; at Mandouri, the validation KGE (0.632) is slightly higher than the calibration KGE (0.609). Although unusual, such inversions are documented in conceptual rainfall–runoff modelling [44,45,46] and can be attributed to three combined factors. First, the validation sub-period (1982–2012) is partly drier and less variable than the calibration sub-period (1961–1981), which encompasses the late-1960s wet phase and the post-1972 Sahelian drought transition; the model, calibrated on a more variable record, performs better when the test sub-period is more stationary. Second, the KGE is a composite score (correlation, variance ratio, bias) and is sensitive to the relative balance of its three components: a modest improvement of the variance ratio in validation can offset a slight loss in correlation, mechanically raising the overall score. Third, the validation sample at Mandouri is longer (31 years) than at Mango (11 years), which provides a more robust statistical estimate and reduces sampling noise. This effect is not observed at Mango and Porga, where validation KGE remains lower than calibration KGE, indicating that the inversion at Mandouri is a station-specific artefact rather than a general feature of the model. Similar results were obtained by [47,48].

• Analysis broken down by flow rate range

Breaking down the criteria according to flow transformations (Q_(gross), √Q and 1/Q) makes it possible to assess the model’s performance at high flows, intermediate flows and low flows, respectively [44]:

• High flows (KGE. raw NSE): Acceptable performance in calibration for all three stations. Peak flood flows, which are often underestimated (BIAS < 1 in calibration at Mandouri and Mango), reflect the limitation of the GR4J single-path routing reservoir in reproducing the rapid surface runoff processes (Horton) prevalent during extreme events in the Sahelian zone [49].
• Intermediate flows (KGE[√Q]. NSE[√Q]): The values of NSE[√Q] are consistently higher than the raw NSE values (e.g., Mandouri: 0.638 vs. 0.507), indicating that the square root transformation mitigates the effect of extreme peaks and that the model accurately reproduces the dynamics of recession flows. These values remain stable between calibration and validation, confirming the model’s robustness for simulating median flows.
• Low-water flows (KGE[1/Q]. NSE[1/Q]): The highly negative values (KGE[1/Q] ≈ −0.65 to −0.71, NSE[1/Q] ≈ 0) represent the model’s major structural weakness showing that the model is inferior to the simple average. They indicate an inability of the GR4J model to correctly reproduce low-flow discharges, due in particular to the absence of an explicit groundwater module. This result is consistent with the findings of [50] which show that simple-structured global conceptual models systematically underestimate low flows in African basins where groundwater–river interactions are decisive. The addition of an underground reservoir (the GR6J model in [51] could significantly improve this performance. A KGE[1/Q] lower than the −0.41 benchmark of the mean-flow predictor [42] means that, for the inverse-flow signature, the model is statistically worse than simply using the long-term mean low flow. The consequences for the present projections are twofold. The absolute magnitude of future low flows under SSP2-4.5 and SSP5-8.5 cannot be assessed with confidence and the projected values during the December–May dry months must be regarded as illustrative rather than quantitative. However, the projection of peak flows in September on which our main conclusions are based is affected only marginally by this limitation, because high flows are governed by saturation-excess and rapid runoff processes that are well captured by the X1–X3–X4 reservoirs of GR4J, and not by the baseflow component that GR4J does not explicitly resolve. A test of the six-parameter version GR6J [52], which adds an additional underground reservoir and exchange parameter, was outside the scope of the present work and is identified as a priority for follow-up studies; such a comparison would allow a quantitative assessment of how much the structural simplification of GR4J biases dry-season projections in the Sudano-Sahelian context. Implications for drought-period water management should therefore be drawn from GR4J outputs only with explicit caveats.

3.4.3. Graphical Evaluation

Figure 9 below shows a graphical representation of the GR4J model’s performance during the calibration phase, and Figure 9 shows its performance during the validation phase at the Mandouri outfall.

Figure 9B shows that during the calibration period from 1961 to 1970, the model overestimated peak flows in the majority of cases. Conversely, for the remaining years, the model underestimates peak flows, a fact evidenced by the Mandouri BIAS value estimated at 0.887 (less than 1). This analysis has significant implications for the average monthly flow. Indeed, Figure 9C clearly shows that it is the low flows (low-water flows) covering the months of November to May that are overestimated, whereas the model underestimates flows during the months of July to October at the Mandouri outlet.

Table 10 showing the BIAS value at the Mandouri outlet during the validation period, indicates an overall overestimation (BIAS = 1.189). Figure 10B shows that low flows are, in most cases, overestimated whereas peak flows are overestimated to a lesser extent. For average monthly flows (Figure 10C) simulated flows are almost entirely overestimated during low-water months. During high-water months, flows are slightly overestimated. The same trends are observed in the other catchment areas at the Mango and Porga outlets, with overestimation during low-water months and overestimation of varying degrees during high-water months.

3.5. Climate Projections and Their Impacts on Streamflow

The calibrated and validated model at the outlet of the three catchment areas has enabled future flows to be estimated using projection data under the SSP245 and SSP585 scenarios. The focus of the calibrated and validated model is the estimation of peak flows. The model is therefore known to have difficulties in accurately estimating low flows. Consequently, the high-water period refers to the period during which the probability of flooding is considered. Across all the catchment areas, a unimodal regime is observed with a peak during the month of September, which will be the focus of this analysis.

Figure 11 illustrates, through flow anomalies (the ratio of the difference between the projected flow and the historical flow relative to the historical flow), the rate of increase in flow.

Climate projections show a marked divergence between the two emissions scenarios (SSP2-4.5 and SSP5-8.5) for the month of September, which corresponds to the peak flow in the Oti-Pendjari basin at the Mango, Porga and Mandouri outlets. According to Figure 11, compared with historical data under the SSP2-4.5 scenario, flows will be higher than under the SSP5-8.5 scenario at the Mandouri outlet. A summary of the relative change in peak flow in September is shown in

Table 13. Projected changes in peak flow in September compared with the historical period.

Station	Peak Change (Only for September)
	SSP245	SSP585
Porga	+6.40%	−1.60%
Mandouri	+5.70%	−1.10%
Mango	+16.70%	−3.60%

.

Under the moderate emissions scenario SSP2-4.5, peak flows in September increase by +5.70% at Mandouri, +6.40% at Porga and +16.70% at Mango. This intensification of late-monsoon floods is consistent with projections of increased extreme rainfall in West Africa under moderate radiative forcing [53,54]. The particularly high value for Mango (+16.70%) is explained by the spatial integration effect of the large catchment area (35.394 km²); a slight uniform increase in rainfall across the catchment results in a non-linear amplification of peak flows due to soil saturation at the end of the rainy season [55].

This trend towards increased flooding under the SSP2-4.5 scenario has significant implications for flood risk management and the safety of hydraulic infrastructure (dams, bridges) in the Oti Valley, in line with the regional projections in [56] for West Africa.

Furthermore, the high-emission scenario SSP5-8.5 leads to a slight reduction in peak flows in September (−1.10% at Mandouri, −1.60% at Porga and −3.60% at Mango). This result, which contrasts with the intensification observed under SSP2-4.5, is consistent with two physical mechanisms acting jointly. First, the bias-corrected CMCC-ESM2 precipitation projections indicate that under SSP5-8.5, the late-monsoon September rainfall does not increase as much, in relative terms, as the total annual rainfall: a partial shift of the wet season towards October–November is detectable, reducing the September input that drives the peak flow. Second, and more importantly, the temperature increase reaches +3.5 to +4.2 °C in the basin by the end of the century under SSP5-8.5 (versus +1.8 to +2.4 °C under SSP2-4.5), which translates—using the Oudin formulation [12] used in this study—into an increase in potential evapotranspiration (PET) of approximately +13% to +18% in September under SSP5-8.5 compared to +6% to +9% under SSP2-4.5. The resulting drop in the precipitation-to-PET ratio (∆P/∆PET) reduces the fraction of rainfall converted into runoff and offsets the modest precipitation gain. The water balance simulated by GR4J thus reflects a soil-moisture deficit larger under SSP5-8.5 at the onset of the September peak, which lowers the saturation-excess component of the discharge. This result is consistent with the work of [57], which shows that high radiative forcing tends to shift the peak of rainfall towards September–October in West Africa, reducing peak flows in September whilst increasing the risk of late-season flooding. A complete water-balance analysis (P, PET, AET, soil-moisture storage) at the daily time step is recommended in future work to fully quantify the relative contributions of evapotranspiration compensation versus the seasonal shift of the rainfall peak.

3.6. Summary and Recommendations

The GR4J model, despite its simple four-parameter structure, delivers acceptable to satisfactory performance in simulating daily flows at the three stations in the Oti catchment. The model’s strengths lie in its ability to reproduce intermediate flows and the flood dynamics of the rainy season, whilst its structural limitations significantly affect the modelling of low-water flows.

Climate projections reveal increasing inter-scenario divergence as radiative forcing increases, with opposing implications depending on the emissions level adopted. These results highlight the need for adaptive water resource management in the Oti-Pendjari basin, taking into account the growing uncertainty of long-term hydrological projections.

4. Discussion

This study assessed the performance of eleven global climate models from CMIP6 in the Oti-Pendjari basin and analyzed the hydrological implications of climate projections for the year 2100. The results obtained warrant discussion in the light of the existing literature and regional specificities.

Regarding the evaluation of climate models, the performance reveals that the CMCC-ESM2 model best reproduces the observed rainfall regime, whilst the multi-model approach (CMCC-ESM2, MPI-ESM1-2-LR, CNRM-ESM2-1) performs best for temperature. These results are consistent with the work of [58], which identifies models from the MPI and CNRM families as the most effective in West Africa for representing the monsoon cycle. The poor performance of CanESM5 for precipitation, already documented by [11,12], confirms this model’s tendency to overestimate tropical rainfall totals due to an overly active convective scheme. The superiority of the Linear Scaling method over quantile-based approaches (QM and QDM) is a notable finding. Whilst [25] recommend Quantile Mapping for its ability to correct the entire distribution, our results show that, in the context of Sudan and Guinea, correcting the mean is sufficient to significantly improve the realism of the simulations. This finding is consistent with the conclusions of [37], which show that simple parametric methods can outperform nonparametric approaches when biases are primarily of an additive or multiplicative nature.

The performance of the GR4J model reveals mixed results depending on the flow ranges. KGE values ranging from 0.609 to 0.668 in calibration correspond to a performance level rated as satisfactory to very satisfactory according to the criteria of [45]. However, the model’s structural inability to reproduce low flows (negative KGE[1/Q]) constitutes a major limitation. This weakness, already identified by [50] for conceptually simple models, is exacerbated in Sahelian catchments where groundwater–river exchange plays a decisive role in maintaining base flows [59]. The use of a six-parameter model such as GR6J [52], incorporating an additional underground reservoir, could improve this performance.

The divergence in projections between the SSP2-4.5 and SSP5-8.5 scenarios regarding peak flows in September is a particularly significant finding. The increase in flows under SSP2-4.5 (+5.7% to +16.7%) is consistent with projections of intensified extreme rainfall in West Africa [53,54], and more recently with the multi-model assessments of [60,61], which both report a robust wetting signal over western Africa under intermediate-to-high emission pathways in CMIP6 simulations. The paradoxical reduction in peak flows under SSP5-8.5 (−1.1% to −3.6%) is thought to be due to the increase in potential evapotranspiration linked to rising temperatures (+3 °C to +4 °C by 2100 according to [2]), which offsets any potential increase in total precipitation. This evapotranspirational compensation mechanism has also been described by [44,57] in similar contexts. The non-linear amplification observed at Mango (+16.7% under SSP2-4.5) compared with smaller catchments highlights the role of spatial integration and soil saturation at the end of the rainy season in the generation of floods [55]. This phenomenon has direct implications for the planning of water infrastructure and flood risk management in the Oti Valley.

Nevertheless, several sources of uncertainty must be taken into account when interpreting these results. Firstly, the use of ERA5 as an observational reference, although justified by the low density of the in situ rainfall network in West Africa [4], introduces potential biases linked to the reanalysis itself. Secondly, the stationarity of the bias correction parameters, an implicit assumption of all the methods employed, could be called into question under high radiative forcing scenarios [26]. Thirdly, the parsimonious structure of the GR4J model, whilst facilitating calibration, limits the representation of complex hydrological processes, particularly the interactions between surface water and groundwater.

5. Conclusions

This study assessed the performance of eleven CMIP6 climate models across the Oti-Pendjari catchment and quantified the hydrological impacts of climate change by 2100. The CMCC-ESM2 model stands out as the most accurate for simulating precipitation. The multi-model average of the first three models (CMCC-ESM2, MPI-ESM1-2-LR and CNRM-ESM2-1) for temperature data provides the best reproduction of temperatures. The Linear Scaling method proves to be the most suitable for correcting climate biases in the study.

The GR4J hydrological model, calibrated and validated at the Porga, Mandouri and Mango outlets, satisfactorily reproduces intermediate flows and seasonal flood dynamics, with KGE values ranging from 0.609 to 0.668 during calibration. Its structural limitations in modelling low-flow conditions suggest that more complex models (GR6J) should be adopted in future studies.

Climate projections reveal a marked divergence between emissions scenarios: the SSP2-4.5 scenario projects an increase in peak flows in September (+5.7% to +16.7%), whilst the SSP5-8.5 scenario suggests a reduction (−1.1% to −3.6%), likely linked to increased evapotranspiration.

These results highlight the need for adaptive water resource management in the Oti-Pendjari basin, taking into account the uncertainty inherent in climate projections. Future work should focus on the integration of distributed hydrological models, the use of broader multi-model ensembles, and the incorporation of land-use changes into the modelling chain.