Sensitivity of bias correction step on generating hydrological scenarios Open Access

Sensitivity of bias correction step on generating hydrological scenarios Étienne Guilpart a,*, Vahid Espanmanesha, Amaury Tilmantaand Marc-André Bourgaultb a Department of Civil and Water Engineering, Laval University, Pavillon Adrien-Pouliot, 1065, av. de la Médecine, Québec (Qc) G1V 0A6, Canada b Department of Geography, Laval University, Pavillon Abitibi-Price 2405 rue de la Terrasse, Québec (Qc) G1V 0A6, Canada *Corresponding author. E-mail: [email protected]; etgu[email protected] ÉG, 0000-0001-9762-4159 ABSTRACT Significant shifts in hydro-climatic regimes are expected in many parts of the world during the 21st century, affecting the water cycle. Vulnerability, impact, and adaptation studies often use tailored modeling chains to assess the expected effects of climate change, but the robustness of these chains is rarely investigated. This highlights the need for more rigorous evaluation of modeling chains to ensure that they are reliable for informed decision-making processes. To address this gap, we propose a framework for evaluating the sensitivity of hydrological scenario production to the bias correction step. We apply the framework to the Senegal River Basin, using three bias correction methods (linear scale, empirical quantile mapping, and nested bias correction) and three procedures (climate-correction, hydrological-correction, and climate-hydrological-correction). Our results show that the choice of modeling chain has a significant impact on future hydroclimatic trajectories. In particular, the combination of climate-and-hydrological-correction procedures may be optimal when both climate biases and hydrological model errors are significant. Moreover, using multiple bias correction methods can strengthen the ensemble of future hydro-climatic conditions. These findings have implications for vulnerability–impact–adaptation studies and underscore the importance of rigorous modeling chain design and sensitivity analysis. Key words: bias correction, climate change, hydrological scenario production, Senegal River Basin HIGHLIGHTS •The choice of bias correction method can significantly impact the resulting hydrological scenarios. •Removing the biases with a climate-correction procedure, hydrological-correction procedure, or a combination of both also notably influences the hydrological-scenario outcomes. •Resorting to several bias correction methods can be seen as a factor to strengthen the ensemble of future hydro-climatic conditions. 1. INTRODUCTION For over a century (IPCC 2021), anthropogenic factors such as global warming and land conversion have altered the Earth’s climate to the point where the stationary hypothesis is no longer realistic (Milly et al. 2008). Significant shifts in precipitation and evaporation regimes are expected in many parts of the world (Nikulin et al. 2012;Knutti & Sedlácek 2013), which in turn affect the water cycle and water management (Olmstead 2014). Water resources system performances are highly dependent on water availability. To address the non-stationary issues imposed by climate changes, many modeling frameworks have been proposed since the 2000s. Those frameworks can be broadly classified into two categories (Füssel 2007): (i) deterministic frameworks (the so-called ‘top-down’approach) and (ii) stress-tests (the ‘bottom-up’approach). In top-down approaches, a modeling chain is developed to derive future hydro-climatic conditions and to assess their impacts on water resources systems. In general, the first link of the modeling chain is the climate simulation. For catchment scale studies, the use of a set of downscaled simulations provided by regional circulation models (RCMs) is encouraged as their refined resolution allows for the reflection of hydro-climatic features and basin heterogeneity, which global circulation models (GCMs) cannot provide (Maraun 2016;Giorgi 2019;Lee et al. 2019). As highlighted by Bergström et al. (2001) and mentioned in Teutschbein & Seibert (2012), the hydrological variables from RCMs (such as runoff) might not be directly used This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). © 2024 The Authors Journal of Water and Climate Change Vol 15 No 4, 1712 doi: 10.2166/wcc.2024.555 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 due to their inability to capture certain physical feedbacks (such as infiltration and re-evaporation) at the local scale in RCMs. Instead, it is recommended to feed an independent land surface model (LSM) with RCM climate information. The modeling chain typically includes a climate model, an LSM (such as a hydrological model), and a water management model (WMM). On the other hand, bottom-up approaches aim at improving our understanding of regional and sectoral climate-related vulnerabilities by conducting stress-tests. In this case, future hydro-climatic conditions may be used as stressors to identify the hydro-climatic conditions that lead to system failure. GCM/RCM projections are then used to assess the possibility of system failure due to climate change (Brown & Wilby 2012;Culley et al. 2016). Generally speaking, the use of GCM and RCM simulations has become a common practice in most vulnerability, impact, and adaptation (VIA) studies (Brown et al. 2015;Giorgi & Gutowski 2015;Enayati et al. 2021). However, both GCM and RCM outputs display systematic errors, failing to reproduce the observed climate’s statistics accurately (Boé et al. 2007;Giorgi et al. 2009;Teutschbein & Seibert 2012) due to differences in their conceptualization, discretization, and assumptions (Knutti & Sedlácek 2013). These biases exist in both the historical and projection parts of the simulations, and can propagate across the modeling chain. To address this issue, several methods have been developed since the 2000s (Maraun et al. 2010;Johnson & Sharma 2012;Chen et al. 2021). Univariate bias correction methods such as linear scaling (Boé et al. 2007) adjust a single statistical parameter, such as the mean, while multivariate methods correct statistical parameters while addressing spatial and/or temporal correlations between variables (Vrac & Friederichs 2015; Cannon 2018). Regardless of the method, biases are identified in a reference period and then removed from the historical and projected parts of the simulation, assuming that biases remain constant over time. Properly removing the bias across a modeling chain is a challenging topic, which can be summarized in two questions. First, how does using different types of bias correction methods affect future trajectories? Second, should we correct the climate simulations before driving a LSM (also known as the ‘climate-correction procedure’), or should we feed an LSM with raw climate simulations and then correct the hydrological outputs (also known as the ‘hydrological-correction procedure’)? Ghimire et al. (2019) delved into the consequences of employing multiple bias correction methods on hydrological outputs (with a climate-correction procedure). However, this investigation was restricted to the historical part of the simulations and did not encompass any frequency-based bias correction methods (which could substantially alter year-to-year variability: Nguyen et al. 2016). Chen et al. 2021 studied the impacts of adopting either a climate-correction procedure or a hydrological-correction procedure across 12 small to medium watersheds (with the empirical quantile mapping method). Nevertheless, their focus was solely on the historical part of the simulations. Therefore, the existing literature lacks a comprehensive exploration of the sensitivity associated with the bias correction step in generating hydrological scenarios. This gap includes the integration of (i) diverse bias correction methods and (ii) distinct bias correction procedures such as climate and hydrological adjustments, all with a specific focus on the projection part of the simulations. In this study, we propose to investigate this gap. We designed a framework to evaluate the sensitivity of hydrological scenario production to the bias correction step for a future horizon. In addition to the climate-correction procedure and hydrological-correction procedure, the framework incorporates the climate-and-hydrology correction procedure, which embeds both procedures. The framework is illustrated using the Senegal River Basin (SRB) as a case study. This basin has experienced significant shift in its precipitation regime since 1940s, and undergoes actually flourishing development. Applying our framework to such a basin will help basin authorities in documenting plausible future hydro-climatic trajectories, an area where the future hydro-climatic trajectories display no clear trend (IPCC 2022). It will also provide to the scientific community a concrete example of how sensitive a modeling chain can be to the bias correction step. 2. FRAMEWORK PRESENTATION The proposed framework aims at showing how sensitive is the production of hydrological scenarios to the bias correction step using either a climate-correction or a hydrological-correction procedure, or a combination of both. Figure 1(a) provides an overview of the generic framework. Each panel in the Figure 1(a) represents a specific bias correction method (denoted as X). Within each panel, three cases are defined as follows. Afirst case that corresponds to the climate-correction procedure (denoted X C , and depicted by the green boxes in Figure 1(a)). The bias correction method is applied to climate simulations to provide climate scenarios. The LSM is then fed with these climate scenarios to produce hydrological scenarios. Journal of Water and Climate Change Vol 15 No 4, 1713 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 A second case that refers to the hydrological-correction procedure (denoted X H , and depicted by the blue boxes in Figure 1(a)). The LSM is fed with raw (uncorrected) climate simulations to produce hydrological simulations. The correction method is then applied to these hydrological simulations. A third case that refers to the climate-and-hydrological-correction procedure (denoted X CH , and depicted by the orange boxes in Figure 1(a)). First, we correct the climate simulations and then feed the LSM with these climate scenarios. Finally, we apply the correction method to the LSM outputs. The procedures described above are based on certain expectations and assumptions. The climate-correction procedure (X C ) aims to eliminate climate biases, but the errors of the LSM may still persist. The hydrological-correction procedure (X H ) Figure 1 |(a) Framework proposed to evaluate the sensitivity of the hydrological scenario production to the bias correction step. The framework consists of establishing npanels, each referring to a specific bias correction method X. Inside each panel, three cases are defined. Green, blue, and orange boxes refer to the climate-correction procedure, hydrological-correction procedure and the climate-and-hydrological-correction procedure, respectively. (b) Application of the generic framework to the Senegal River Basin. Journal of Water and Climate Change Vol 15 No 4, 1714 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 addresses both climate biases and LSM errors simultaneously, but using uncorrected climate data in the LSM can potentially impact the model’s operation (see Section 5.3 for further details). By combining both the climate-correction and hydrologicalcorrection procedures (X CH ), we can ensure the removal of climate biases and LSM errors without any potential distortion of the LSM. Finally, the evaluation phase assesses the sensitivity of hydrological scenario generation to the bias correction step. 3. STUDY CASE: THE SRB 3.1. Background The Senegal River drains a basin shared by four countries: Guinea, Mali, Mauritania and Senegal (Figure 2(a)). The headwaters are located in the Fouta Jalon (Guinea), where the Bafing River runs northward until merging with the Bakoye in Mali, forming the Senegal River. Running north-west, it collects water from the Faleme river before reaching Bakel, a keypoint for the water allocation decision in the basin. Downstream of Bakel, incremental inflows are insignificant (Bader et al. 2015). So, only the active part of the basin has been modeled, whose corresponding outlet is Bakel (draining an area of 393,754 km 2 ). The observed annual flow at Bakel is 21.5 +8.7 km 3 per year (calculated on 1904–2011 using monthly inflow time-series (Bader et al. 2015)). The monsoon onset brings the wet season (typically from July to October), which represents 88% of the annual discharge (Figure 2(b)). The dry season follows (from November to June) during which ∼12% of the annual flow is discharged. During the 21st century, the SRB experienced shifts between well-distinct dry, wet, and neutral periods (Figure 2(c))(Bodian 2014;Bader et al. 2015;Faye et al. 2015;Guilpart et al. 2021). In the 1970s, l’Organisation pour la mise en valeur du fleuve Sénégal (OMSV, the basin authorities) initiated the construction of two major hydraulic infrastructures: the Manantali dam on the Bafing and the Diama dam close to the river mouth. Today, water-related activities in the basin are flourishing. New major infrastructures will support the development of irrigation, navigation and hydropower generation (CSE et al. 2011). Also, the storage capacity will increase from 6.5 km 3 (today) to Figure 2 |(a) The Senegal River Basin, boundaries, infrastructures and river network. The basin has been delimited with the help of the ArcGis model (version 10.4), and the digital elevation model of the SRTM (resolution: 1 arc-second) Werner (2001). (b) Boxplot of monthly inflows at Bakel (the blue line represents the annual cycle). (c) Annual volume of flow at Bakel (the red line represents the ten year moving average). Data come from the actualization of the SRB monograph (Bader et al. 2015). Journal of Water and Climate Change Vol 15 No 4, 1715 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 13 and to 27 km 3 with the construction of the so-called second generation of dams by 2050 (to reach a total of six dams) and the construction of the third-generation dams by the end of the century (to reach a total of 12 dams). Due to notable changes in precipitation patterns, ongoing basin development, and the substantial discrepancies in climate models projecting the future hydro-climatic conditions (IPCC 2022), the SRB stands as an ideal case study for implementing the proposed framework. 3.2. Implementation of the framework in the SRB This study aims to evaluate the sensitivity of hydrological scenario production to the bias correction step. The first step toward achieving this goal is to carefully select the bias correction methods for testing. The choice of a bias correction method is dependent on the objectives of the study. In earlier studies focused on vulnerability–impact–adaptation, mean-based adjustments and distribution-based adjustments were the most commonly used methods. However, in recent years, frequency-based correction methods have emerged as a viable alternative (Nguyen et al. 2016). For the purposes of water management, the long-term persistence of hydrological variables is of particular importance in high storage-capacity systems, which is the case for the SRB. Also, we propose an application of the general method by involving the three following bias correction methods (Figure 1(b)). Consequently, this provides us with nine distinct cases, comprising the following methods: 1. The Linear Scaling method (LS) (Boé et al. 2007): This method focuses on correcting the mean of the simulation. Further details on the algorithm can be found in the Supplementary Material (Section C.1.). 2. Empirical Quantile Mapping method with a scale transformation (EQM-ST) (Piani et al. 2010): EQM-ST seeks to adjust the mean and distribution of the simulation at the monthly time-step by defining a sequence of quantiles. Refer to the Supplementary Material (Section C.2.) for more information on the algorithm. 3. Nested Bias Correction method (NBC) (Johnson & Sharma 2012): NBC adjusts the mean, standard deviation, and Lag-1 autocorrelation at both monthly and yearly time steps. Further details on the method and its application can be found in the Supplementary Material (Section C.3.). Before applying bias correction methods, it is important to discuss how the trend in hydro-climatic variables is handled. In this study, we follow the guidelines provided by Maraun (2016). Precipitation is a major driver of the inflows in the basin, meaning it plays a critical role in determining the amount of water that flows into the river system. The physical processes inherent to West African monsoon are poorly represented by the GCMs (Philippon et al. 2010) and by the RCMs (Sylla et al. 2016). Indeed, processes involved in precipitation dynamics range from global scale (as sea surface temperature patterns) to cumulus-scale, and significant biases are reported in RCM outputs over the past periods (Akinsanola et al. 2015). Because the precipitation processes are still poorly represented, so precipitation trends in simulations might be implausible, and the associated biases are time-dependent. As a result, there are significant biases in the outputs of these models. In particular, the biases in the simulation of precipitation are time-dependent, which means that they change with time. Given the limitations in simulating precipitation, we do not consider the trends in precipitation to be reliable enough for use in bias correction methods. As precipitation is the main driver of the inflows in the basin, we do so when we apply a bias correction method to inflows. However, as the trend in potential evapotranspiration (PET) is mainly driven by the increase of the temperature due to global warming (Ndiaye et al. 2021), we consider that trends in PET simulations are more reliable. Therefore, in this studywe explicitly conserve the trend in PET by removing it prior to applying a bias correction method, and then adding it back afterward. This helps to ensure that any errors in the simulated PET data are corrected while still preserving the underlying trend in the data. Please note that the selected Land Surface Model (LSM) requires spatially averaged time-series to run, as explained in Section 3.2.1. When applying a climate-correction procedure, each grid cell of climate simulations is independently corrected, followed by spatial averaging over the basin. On the other hand, when applying a hydrological-correction procedure, the climate simulations are first spatially averaged to feed the LSM. Finally, bias correction methods are applied to LSM outputs. Figure 1(b) illustrates the necessary elements for deriving future hydrological conditions in the SRB, which include a set of climate simulations, selecting an appropriate LSM, and climate and hydrological observations to correct and calibrate the LSM. It is also important to define a reference period and a horizon for the evaluation. As depicted in Figure 1(b), the following elements are required to derive the future hydrological conditions in the SRB: 1. A set of climate simulations. 2. Selecting an LSM. Journal of Water and Climate Change Vol 15 No 4, 1716 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 3. A set of climate and hydrological observations in order to correct the climate simulations as well as calibrate and validation the LSM. 4. Defining a reference period and a horizon on which the evaluation will be carried out. 3.2.1. The GR2M as the LSM Since the data are too sparse and incomplete in the SRB to use a distributed hydrological model based on physics, our choice inclines toward a conceptual LSM. Operating at a monthly time-step and already having proven good performances in the SRB (Ardoin-Bardin 2004;Bodian et al. 2012;Guilpart et al. 2021), we adopted the conceptual hydrological model GR2M (Figure 3)(Mouelhi 2003). Due to its conceptualization, the GR2M is not able to account for dam operations. Thus, the GR2M requires a naturalized time-series of inflows for the calibration/validation step, wherein the effects of dam operations have been removed. The model calibration and validation process are carried out using the differential split-sample test described by Klemeš(1986), along with the three-states Hidden Markov Model classification method developed by Guilpart et al. (2021). The Kling–Gupta efficiency (KGE) is used as the objective function for the model. We set the warming-up period for the GR2M model to two years. More information on the calibration and validation procedures can be found in the Supplementary Material (Section A). 3.2.2. Observation data sets The GR2M requires PET and precipitation (P) data for running. Observed inflows (Q) are also needed for the calibration/validation step. Thus, we constituted our hydro-climatic database with observations (PET, P, and Q) and with climate simulations (PET and P). We selected (i) the precipitation distributed dataset from the HSM-SIREM database (Boyer et al. 2006;Dieulin et al. 2019) (covering the 1940–1998 period); and (ii) the PET from the Climate Research Unit database (Harris et al. 2020) (covering the period from 1901 to 2018). Naturalized inflows are retrieved from Bader et al. (2015) (1903–2012). 3.2.3. The climate simulation dataset GCMs used to simulate the SRB’s climate have a coarse spatial resolution of approximately 200 km, insufficient for capturing the region’s strong climatic variability (Faye et al. 2015). To obtain a more detailed representation, we used high-resolution RCMs from the CORDEX-Africa project (Giorgi & Gutowski 2015). From the ensemble of CORDEX-Africa climate Figure 3 |The GR2M hydrological model. Journal of Water and Climate Change Vol 15 No 4, 1717 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 simulations, we extracted 55 precipitation simulations and 22 evapotranspiration simulations (listed in Table 1). These simulations cover the period from 1951 to 2099 and provide a more accurate representation of the propagation of the monsoon front toward the north in the SRB. As the GR2M requires two spatially averaged time-series to run, climate simulations and climate scenarios were averaged over the basin. Having at our disposal 55 simulations of Pand 22 simulations of PET, we combined them to get 1,210 hydrological scenarios for each case (LS C ,LS H ,LS CH , EQM C , EQM H , EQM CH , NBC C , NBC H , and NBC CH ). 3.2.4. Identification of the reference period and the horizon In the SRB, the climate has exhibited dry, normal, and wet periods in the past, which are not fully captured in the historical part of the GCM and RCM simulations (Figure C in the Supplementary Material). Also, particular attention must be paid to avoid any non-stationary issues when defining the transfer functions. To avoid that kind of instability during the correction factor computation, we set the reference period to be as long as possible. Thus, the reference period stretches from 1951 to 1998 when correcting climate variables, and from 1953 to 1998 when correcting hydrological variables (the 1951 and 1952 years are considered as a warming period by the GR2M, as mentioned before). To avoid computation and transfer issues of the yearly Lag-1 autocorrelation when using the NBC method, the length of the future horizon is set equal to that of the reference period. Thus, the future horizon for this study stretches from 2050 to 2095. This allows us to generate reliable hydrological scenarios for the future period while avoiding any instability during the computation of correction factors. 4. RESULTS The results of the study are structured as follows. First, we present the hydro-climatic trajectories in the SRB for precipitation (P), PET, and streamflow (Q) based on different bias correction methods (Section 4.1). Next, we assess the performance of bias correction procedures in reproducing the hydrological conditions of the reference period (Section 4.2) and the future horizon (Section 4.3). As the three bias corrections aim to correct the mean, distribution, and/or long-term persistence of time-series, the performance of the corrections is therefore evaluated using the mean, the standard deviation and the Acf-Lag1 value at the yearly Table 1 |Simulations extracted from CORDEX-Africa; GCMs–RCMs coupling and RCP used in this study RCMs CCLM4-8-17 CSC HIRHAM5 RACMO22T RCA4 REMO2009 CRCM5 GCMs CCCma-CAn ESM2 þþ /þþþ **/*** þþ CNRM-CERFACS-CM5 þþ/þþþ þþ/þþþ **/*** CSIRO-Mk3-6-0 þþ/þþþ **/*** NOAA-GFDL-GFDL-ESM2G þþ/þþþ **/*** MOHC-HadGEM2-ES þþ/þþþ þ/þþ/þþþ þ/þþ/þþþ */**/*** ICHEC-EC-EARTH þþ/þþþ þþ/þþþ þþ/þþþ þ/þþ/þþþ þ/þþ/þþþ */**/*** IPSL-CMSA-LR þþ/þþþ **/*** MPI-M-MPI-ESM-LR þþ/þþþ þ/þþ/þþþ þ/þþ/þþþ */**/*** þþ MIROC-MIROC5 þ/þþ/þþþ */**/*** NCC-NorESM1-M þ/þþ/þþþ */**/*** Symbols þ,þþ, and þþþ refer to RCP2.6, RCP4.5, and RCP8.5 precipitation simulations, respectively. Similarly, symbols *, **, and *** refer to RCP2.6, RCP4.5, and RCP8.5 PET simulations. Journal of Water and Climate Change Vol 15 No 4, 1718 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 time-step (please refer to Section D (Supplementary Material) for details about its computation). These metrics are also relevant for an advised water allocation policy in the SRB (Espanmanesh & Tilmant 2022). 4.1. P, PET, and Qtrajectories in the SRB Figure 4 presents the hydro-climatic trajectories in the SRB depending on the bias correction method. The trend of the precipitation simulations ensemble (i.e. the mean of all the simulations) exhibits low values for the whole period (0.13 mm/y, 1951–2095), leading to a drop of 2.0% of the precipitation rates between the reference period (652 mm/y, 1951–1998) and the future horizon (639 mm/y, 2050–2095). Similar results with LS, EQM-ST and NBC climate scenarios are found with low modification rates (1.3%, þ1.0%, and 2.2%, respectively). This illustrates that climate models display no consensus in the trend of precipitation in the SRB. Figure 4 |Precipitation, PET, and inflow trajectories in the SRB. The dashed black line refers to the mean of the simulations (55 for P, 22 for PET, and 1,210 for Q), the continuous black line to the mean of the LS-scenarios, the blue line to the mean of the EQM-ST scenarios, and the red line to the mean of the NBC scenarios. Green lines refer to the observations. The historical part, the projection part and the studied horizon are displayed. Journal of Water and Climate Change Vol 15 No 4, 1719 Downloaded from http://iwaponline.com/jwcc/article-pdf/15/4/1712/1413562/jwc0151712.pdf by guest on 06 October 2025 The PET simulation ensemble trend displays higher values for the whole period (þ1.8 mm/y), leading to a significant increase (þ175 mm/y, or þ7.3%) of the PET between the reference period (2,223 mm/y) and the future (2,399 mm/y). This increase is mainly attributed to the increase of temperature, as highlighted by Ndiaye et al. (2021). Although the PET is supposed to be explicitly conserved during the bias correction step (see Section 3.2), we note that LS, EQM-ST and NBC climate scenarios display different trend values (þ7.6%, þ4.9%, and þ8.3%, respectively), and the spread is significant with the EQM-ST method. During the correction, we assume a linear trend. This is generally true for simulations forced by the RCP 8.5 scenario, but not for simulations forced by RCP 2.6 and RCP 4.5. Indeed, as stated in these two RCP scenarios, a decrease of the greenhouse gas emissions is assumed during the 21st century, leading to a compression of the temperature increase that impacts the PET trend. Also, in most simulations of RCP 2.6 and RCP 4.5, when the trend is removed in the projection part of the simulations, the residual PET values are triggered, and the association with quantile is discrupted with the EQM-ST method. Consequently, the correction applied to the future horizon becomes excessive, leading to values lower than expected, which impact the trend at the final stage. Here, we highlight the limits of the willingness to explicitly conserve a trend in a bias correction procedure. Table 2 gives trend values and mean annual volumes of inflow depending on the procedure and the bias correction method. First, we note that the future horizon remains generally dryer than the reference period. The reduction in the river’s annual volume is attributed not solely to the slight decline in precipitation rates, but also to the PET increase. Here, we observe that the effects of climate change become evident first in the rise of PET rather than in an alteration of the rainfall pattern. Second, we note that the mean annual volumes of the reference period are aligned with the observations (19.3 km 3 /y) with a hydrological-correction procedure, while an underestimation with the climate-correction procedure (around 16.4 km 3 /y) can be noticed. The underestimation remains on the future horizon, and the climate-correction procedure leads to minimizing the annual volume by 15.4% or 9.8% compared with the hydrological-correction procedure and climate-and-hydrological-correction procedure. This can be attributed the GR2M errors (which are not removed in the climate-correction procedure). A thorough examination of this issue is undertaken in the following sections. 4.2. Statistical evaluation of bias correction procedures for the reference period In this section, we first focus on the bias in climate simulations and the effectiveness of bias correction methods in eliminating bias over the reference period. Then, we focus on the hydrological scenarios produced through three correction procedures: the climate-, hydrological-, and climate-and-hydrological-correction procedures. This approach allows us to elucidate the potential propagation of bias throughout the modeling chain. The left panel of Figure 5 illustrates the statistical parameters (the annual mean, standard deviation, and Acf-Lag1) of both the climate simulations and scenarios for the reference period. The precipitation simulations exhibit a pseudo-Gaussian distribution centered around the mean annual precipitation rate observed. Nevertheless, the standard deviation and Acf-Lag1 of precipitation simulations are underestimated. All PET simulations display a dry bias (i.e. an overestimation of the PET), high standard deviation, and a weak long-term persistence. These characteristics illustrate that climate models generate simulations with a too-strong year-to-year variability compared with the observations. Generally speaking, the three bias correction methods successfully adjust the statistic of climate simulations they aim at correcting. However, NBC seems to well adjust the standard deviation and the Acf-lag1 of the precipitation simulations. Table 2 |Trend values over 1951–2095 (first row), mean annual volumes of inflow depending on the procedure, and the bias correction methods for the historical horizon (second row) and the future horizon (third row) Climate-correction Hydrological-correction Climate-and-hydrologicalcorrection Simulation LS EQM-ST NBC LS EQM-ST NBC LS EQM-ST NBC Trend [km 3 /y] 0.016 0.009 0.01 0.016 0.024 0.53 0.014 0.011 0.008 0.015 Historical An. 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