The objective of this study was to evaluate the best performed bias correction methods to simulate the regional climate models for future climate change projections in Muger Subbasin. Delta change methods perform very well with a coefficient of correlation of 0.99 and a percent of bias –3. When we compare its corrected simulation result with observed data, the delta change method seems to have with no biases for maximum temperature, but increases by 1.67 °C from the mean for minimum temperature of 0.39 and 38.41 mm for monthly and annual precipitation, respectively. Delta change methods underestimate the model result for both temperature and precipitation. Linear scaling and variance scaling methods overestimate the maximum temperature of the simulation by 0.002 and 0.004 °C from the mean of the observed data, but it underestimates 1.59 and 1.56 °C the minimum temperature, respectively. The long-term temperature projection values (2060–2090) are higher than the near-term projections (2030–2060) for both RCP2.6 and RCP8.5 scenarios. Similarly, the change in annual precipitation for the long-term is higher than the near-term projections. As a conclusion, the results draw attention to the fact that bias-adjusted regional climate models data are crucial for the provision of local climate change impact studies in the Muger Subbasin.

  • It evaluates the method of bias correction methods.

  • Assess changes in precipitation and temperature in the future.

  • Select the best bias correction methods.

Due to the greenhouse gas emissions, which are released from human activities, the world's climate is being affected by global warming, which is mostly caused by the global surface temperature rising by 1.1 °C (IPCC 2023). Numerous weather and climatic extremes are already being impacted by anthropogenic change in every corner of the world (Yeboah et al. 2022; IPCC 2023). This has many negative impacts on human health, the security of food and water, as well as economies and society, resulting in losses and harm to both nature and humans (IPCC 2023).

The main data source for climate impact assessment has been global climate models (GCMs), which also serve as the foundation for analyses of the effects of climate change at all spatial scales, from the local to the global (IPCC 2015). Due to the significant inaccuracies in GCM models compared to historical observations, impact studies rarely directly use GCM outputs (IPCC 2015; Rathjens et al. 2016; Worku et al. 2020). Climate models may be affected by significant errors (Villani et al. 2015; Derdour et al. 2022) than observed data. Also, GCM data are given on a coarser grid (around 2° × 2°) than the observational data. However, such a variability change is not captured by a simple interpolation of the GCM data. This is too coarse for a realistic representation of most hydrological processes that act over a large area, and therefore, downscaling this coarse data into the regional climate model (RCM) is plausible. As a result, their output often cannot be used directly as input for impact assessment (Gudmundsson et al. 2012; Teutschbein & Seibert 2012). Inaccurate model representations of atmospheric physics, improper model initialization, or mistakes in the parameterization chain are the most frequent causes of inaccuracy or bias in the output of GCM models (Ehret et al. 2012).

Different scholars recommend the use of bias correction of RCM outputs since it is a practical and affordable approach for error reduction (Mami et al. 2021). Correction of bias is essential to obtain realistic model data for future climate projection and to assess its impact (Teutschbein & Seibert 2012; Yeboah et al. 2022). Sometimes, the bias can be potentially reduced by statistical analysis after some processing techniques. These biases or errors can be reduced by correcting the variance of the model data, and it may help to obtain a more realistic understanding of the influences that depend on the variation of both the average and variability of the data (Teutschbein & Seibert 2012; Rathjens et al. 2016). The motivation behind comparing these methods likely involves addressing the methodological gaps and uncertainties in climate projections by evaluating the performance of different bias correction techniques.

Linear scaling (LS) adjusts only the mean of climate model simulation, whereas other methods like distribution mapping (DM) and power transformation (PT) correct the mean and frequency of model values with the statistical values of the observations (Teutschbein & Seibert 2012; Rathjens et al. 2016; Worku et al. 2020). Compared to other bias correction methods, DM is a better bias correction technique for adjusting the frequency of rainfall and temperature events (Worku et al. 2020). A recent study by Daniel (2023) compares the performance of RCMs and bias correction methods in Gelana and Deme watersheds in Ethiopia. The result reveals that empirical quantile mapping (EQM) and DM perform better than LS and PT to correct precipitation and maximum temperature, and minimum temperature, respectively, in the watershed. However, the study assesses only the bias correction performance and does not estimate the precipitation and temperature of the watershed in the future. Also, another study by Nigussie et al. (2023) uses three bias correction (delta, EQM, and quantile mapping) methods to evaluate different satellite rainfall products in the main Beles watershed, Upper Blue Nile (Abbay) Basin, and they conclude that the performance of bias correction methods are different from one station to another and also its performance varies for different satellite rainfall products. But it does not evaluate the performance of GCM data that are used for future climate study. Unlike these two studies, this study aims to evaluate the performance of different bias correction methods for climate change simulations. Moreover, a recent study by Yersaw & Chane (2024) in the Katar watershed of Lake Ziway Subbasin in Ethiopia on RCMs and bias correction methods for rainfall–runoff modeling shows that the empirical cumulative distribution function method performed best in removing bias from the frequency-based statistics of rainfall and streamflow. Even though the study evaluates different bias correction methods for rainfall–runoff modeling, it does not show the spatial distribution of precipitation and temperature in the study area. Because developing the spatial distribution map is crucial to identify the deviation between observed and simulated data.

Also, the aforementioned three studies were conducted in a specific area. But, when it comes to a regionalized study area, not all bias correction methods are performed equally (Gudmundsson et al. 2012; Thomas et al. 2013; Derdour et al. 2022). Bias correction methods that have good performance in one area may not be good in other areas. Hence, to select the best performance bias correction methods for a specific study area, evaluating the performance of multiple bias correction methods is mandatory (Villani et al. 2015; Das et al. 2022; Gado et al. 2022).

This study aimed to compare different bias correction methods to simulate the CORDEX Africa RCMs of the rainfall and air temperature over the Muger Subbasin. The main intention was not to check all the available bias correction methods, but to evaluate selected bias correction methods that have been frequently used in climate impact studies at the local-scale level (Mendez et al. 2020; Worku et al. 2020; Derdour et al. 2022; Gado et al. 2022; Daniel 2023; Nigussie et al. 2023). The selected bias correction methods were evaluated based on annual and seasonal temperatures and precipitation. In addition, we developed a spatial rainfall distribution for the study area and considered the average observed and raw simulated data to know the areal extent of the temperature and precipitation in the study area. The analysis and intercomparison of the individual bias correction methods will help us to better understand how the bias correction performs in areas with complex topography to project and assess future climate impacts, as in the case of Muger Subbasin, Upper Blue Nile Basin, Ethiopia. Ethiopia, like many other regions globally, is vulnerable to the impacts of climate change. These impacts include changes in precipitation patterns, temperature variations, and shifts in hydrological cycles. Understanding these changes at a regional level is crucial for effective adaptation and mitigation strategies.

These objectives are designed to provide actionable insights that can inform adaptation strategies and contribute to scientific knowledge in the field of climate change research. The outcomes of this research have direct implications for policy formulation and decision-making processes related to climate change adaptation and water resource management in the Upper Blue Nile Basin to reduce the vulnerability of the community under climate change.

The study offers a unique contribution to climate change research through its regional focus, methodological rigor, and practical relevance. By narrowing its scope to the Muger Subbasin within the Upper Blue Nile Basin, it provides a detailed examination of climate change impacts tailored to the specific geographic context of Ethiopia. Its emphasis on comparing bias correction methods adds a methodological dimension, contributing to advancements in climate modeling and enhancing the reliability of future projections. Moreover, it offers actionable insights for addressing the socioeconomic and environmental challenges exacerbated by climate variability. This interdisciplinary approach, which likely integrates climate science and hydrology, underscores the study's holistic perspective on climate resilience and its potential to inform decision-making processes in developing countries like Ethiopia.

Study area

The Muger Subbasin is located to the southeast of the Upper Blue Nile Basin. Muger Subbasin is one of the tributaries of the Upper Blue Nile Basin in the Blue Nile River that covers a total drainage area of 7,240 km2. Geographically, it is located between 9°09′03″ and 9°50′10″N latitude and 37°40′05″ and 39°00′04″E longitude (Figure 1).
Figure 1

Location map of the study area.

Figure 1

Location map of the study area.

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The topography of the Muger Subbasin is characterized by varied topographic conditions, with elevation ranging from 3,534 m above mean sea level (a.m.s.l) in the mountainous area to 975 m a.m.s.l in near the outlet (Figure 1).

Most areas of Ethiopia are characterized by the tropical climate, which is affected by elevation. The eastern lowland is much drier with a hot semi-arid to a desert climate. However, the southwestern and highlands of the country obtain high rainfall distribution greater than 1,000 mm annually. As one part of the country, the climate of Muger Subbasin is characterized by high rainfall with low temperature in the highland and low rainfall with high temperature in the low-land area. Most precipitation occurs in the summer (wet) season from June through September, and a little precipitation occurs in the mild season from February to May. It is characterized by a unimodal type of precipitation. Annual precipitation has been found to range from 1,200 to 1,600 mm. The mean annual minimum and maximum temperature varied from 4–11 °C and 23–25 °C, respectively.

When we see the aquifer system, it is connected to the upper Awash Basin, which flows in the southeast direction. The mean contribution of the Muger Subbasin to the Blue Nile Basin is 0.97% (Roth et al. 2018).

Data collection and database preparation

Observed climate data

The meteorological (temperature and precipitation) data were collected from the Ethiopia Meteorological Institute (EMI). Daily rainfall and temperature data for 20 years were collected from nine gauging stations in the Muger Subbasin (Figure 2). The raw data were processed for filling in missed data and quality checks. The missing data were filled using arithmetic mean and regression methods, and the two methods were selected based on the percentage error of the missing value.
Figure 2

Observed climate data location with the background of elevation of the study area.

Figure 2

Observed climate data location with the background of elevation of the study area.

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CORDEX Africa simulated data and climate scenarios

To better understand and estimate plausible future climate, there are diverse global and climate models (GCMs) and RCMs now available to simulate both precipitation and temperature to a basin or local levels (Gado et al. 2022; Yeboah et al. 2022). Future climate projection data for precipitation and minimum and maximum temperatures from the CORDEX project were considered. Historical and future meteorological data have been collected from the climate model output of the Coordinated Regional Climate Downscaling Experiment Project (CORDEX) data source center https://esgf-data.dkrz.de/search/cordex-dkrz/. The CORDEX Africa dataset is a CORDEX domain, developed specifically for climate impact study in the Africa zone. It was designed using multiple RCMs to provide rationalized, predictable variations in local climates and to evaluate any basis for uncertainty in the projection (Yeboah et al. 2022). Also, it is a reliable source for RCMs (Rathjens et al. 2016). Among the different data nodes in GCMs like Max Planck Institute for Meteorology Earth System Model version 1.2 (MPI-ESM1.2) (Mauritsen et al. 2019), the Centre National de Recherches Météorologiques (CNRM-CM5) (Voldoire et al. 2013), the Hadley Centre Global Environmental Model Earth System (HadGEM2-ES) (Collins et al. 2011), and the GFDL NOAA's Earth System Models (ESMs) (Dunne et al. 2020), this study has used only the Hadley Centre Global Environmental Model Earth System (HadGEM2-ES) model to develop climate scenarios under RCP2.6 and RCP8.5 concentration scenario. RCP2.6 and RCP8.5 were selected because these concentration scenarios represent possible radiative forcing levels in the year 2100 relative to pre-industrialization. RCP8.5 represents high concentration scenarios with increasing radiative forcing pathway, resulting in 8.5 W/m2 by 2100, while RCP2.6 represents low concentration levels of 2.6 W/m2 that could be reached at stabilization after 2100.

Bias correction procedures

Climate data are obtained from GCMs or RCMs. Simulated historical (1980–2004) and future (2030–2090) climate data were obtained from CORDEX datasets under low concentration scenario RCP2.6 and high concentration scenario RCP8.5. Climate variables such as rainfall and temperature obtained from such coarse-resolution climate models are highly affected by different factors such as mountains and clouds, which may not be taken into consideration in the GCM development process because of their coarse resolution (Rathjens et al. 2016). Thus, to reduce the deviation of climate models output from the real observed data of meteorological stations, the bias correction process was needed.

In this study, we used the CMhyd (Climate Model data for hydrologic modeling) tool, designed to provide bias correction of simulated climate data obtained from GCMs and RCMs (Rathjens et al. 2016). Bias correction procedures performed a transformation algorithm for adjusting climate model output with the assumption that the correction algorithm and its parametrization for current climate conditions are to be valid for future conditions as well. The tool has been widely used for bias correction of precipitation and temperature for various applications (Worku et al. 2020; Mami et al. 2021; Yeboah et al. 2022). The overall procedure in the bias correction as adopted in this article is described in Figure 3.
Figure 3

General framework of bias correction of climate data (Rathjens et al. 2016).

Figure 3

General framework of bias correction of climate data (Rathjens et al. 2016).

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Bias correction methods

Bias correction methods are often applied within climate impact assessment to correct the climate input data provided by GCMs or RCMs for systematic statistical deviations from observational data. Bias correction methods aim to adjust the mean, variance, and/or quintile of the model time series variable using a certain correction factor so that the corrected model time series matches closely with the observed variable. They generally adjust the long-term mean by adding the average difference between the simulated and observed data over the historical period to the simulated data or by applying an associated multiplicative correction factor (Rathjens et al. 2016; Worku et al. 2020). In addition, differences between the variance of the simulated and observed data are often corrected. Bias correction for maximum temperature, minimum temperature, and rainfall data obtained from RCM climate models has been done using CMhyd software (Rathjens et al. 2016). CMhyd software uses various bias correction methods. The following are the basic methods used to adjust the control data in the present study: (1) LS, (2) local intensity scaling, (3) PT (precipitation), (4) DM, (5) variance scaling (temperature), and (6) delta change approach (Rathjens et al. 2016). The tool has been widely used for bias correction of precipitation and temperature for various applications (Worku et al. 2020; Mami et al. 2021; Yeboah et al. 2022).

Linear scaling: The LS, or simply the scaling method, is based on monthly correction values calculated as the differences between observed and simulated data. It is the simplest approach. In the case of precipitation, it consists of scaling the model rainfall data using a corrective factor calculated as the ratio of observed and simulated monthly mean precipitation data (Villani et al. 2015). Each of the daily values from the uncorrected precipitation, , for the particular month, m, and day, d, is typically corrected using Equation (1).
formula
(1)
where is the corrected model precipitation, is the mean value of the observed precipitation (), and uncorrected model precipitation. However, model temperature data are corrected using an additive term based on the difference between observed and simulated mean (Equation (2)):
formula
(2)
where for the day d, is the corrected value, is the original daily temperature value from the RCM, is the observed average for the month m, and is the simulated average (Villani et al. 2015).
Local intensity scaling: The local intensity (LI) method widely reported that GCMs/RCMs precipitation works on the daily precipitation. This simulated precipitation from the GCM/RCM is corrected based on frequencies and the intensity of the wet and drizzle days. Although this method reported that the daily precipitation of RCMs simulation is larger than the observation, the threshold values of the wet days are adjusted for future wet-day frequencies (Das et al. 2022).
formula
(3)
formula
(4)
where (Equation (3)) and (Equation (4)) are the daily precipitation of the historical and future climate, respectively, is the observed daily precipitation, is the future daily precipitation for the control period, and is the threshold value (Das et al. 2022). Then, the scaling factor is calculated based on the long-term mean wet-day frequencies. The intensity scaling is estimated from the S ratio (Equation (5)):
formula
(5)
Finally, the bias-corrected daily precipitation was estimated using the scaling factor and daily precipitation (Equations (6) and (7)):
formula
(6)
formula
(7)
where (Equation (6)) (Equation (7)) are represented for the bias-corrected historical and future daily precipitation, respectively, and is the same as shown in the equations.
Power transformation of precipitation: The precipitation is usually varied spatially, temporal, and highly nonlinear. PT is a nonlinear method that corrects both the mean and variance of precipitation (Teutschbein & Seibert 2012). In this nonlinear correction in an exponential form, a×Pb can be used to adjust the variance statistics of a precipitation time series. The parameters a and b are determined for each month. The correction method is applied by comparing the daily observed precipitation at each station with the nearest grid point of the RCM considering the grid points as a single station on the watershed. The PT method is explained in Equation (8):
formula
(8)
where is corrected precipitation and P is simulated precipitation. Parameters a and b are estimated by equalizing the coefficient of variation (CV) of the corrected simulations and the CV of the observed values. The remaining parameter and procedures for estimating the corrected precipitation are expressed by Teutschbein & Seibert (2012).
Variance scaling of temperature: The PT method is an effective method to correct both the mean and variance of precipitation, but it cannot be used to correct temperature time series, as the temperature is known to be approximately normally distributed (Bhatti et al. 2016). This method was developed to correct both the mean and variance of normally distributed variables like temperature (Teutschbein & Seibert 2012) using Equation (9).
formula
(9)
where is the corrected daily temperature, is the uncorrected daily temperature obtained from the RCM model, is observed daily temperature, are the mean of the observed and simulated daily temperature, respectively, and and are the standard deviation of the observed and simulated daily temperature, respectively.
Delta change method: The delta change (DC) method creates a scenario based on adding anomalies for the future climate obtained from the RCMs simulation. It assumes that the regional-level bias is constant over time (Das et al. 2022). Although the evaluation of the DC method is expressed by many researchers (Teutschbein & Seibert 2012; Li et al. 2019; Mendez et al. 2020; Enayati et al. 2021; Derdour et al. 2022; Gado et al. 2022; Sundaram & Radhakrishnan 2022), this method is evaluated using the following equations.
formula
(10)
formula
(11)
formula
(12)
where p is the daily precipitation, ‘Contr’ is the simulated RCMs during the period, ‘obs’ represents the observational time series, ‘Pfrc’ is the future RCMs scenario during the period (Equation (11)), ‘t’ shows the time step, and is the long-term yearly average. ‘ are the simulated anomalies of temperature based on the present temperature (Equation (12)), is the daily observed temperature, and ‘’ is the simulated daily temperature during the year and ‘t’ is the time after bias term simulated temperature.

Distribution mapping: The DM technique compares the distribution function of the simulated data with that of the observed data. There are two types of DM techniques. The first is EQM and the second is theoretical quantile mapping (TQM). EQM is a nonparametric approach and compares the cumulative density function of the historical result of RCM and the observed data (Teutschbein & Seibert 2012; Gado et al. 2022). But TQM is based on the cumulative density function of the historical RCM match with the theoretical cumulative density function of the observed data. However, due to the assumptions that the observed data follow the proposed distribution, TQM lacks correctness and may result in new biases (Gado et al. 2022). Therefore, in this study, EQM has been compared with other bias correction methods.

Performance evaluation of bias correction methods

Like any other modeling process, the bias correction method outputs also need to be validated by using the observed data (Schoetter et al. 2012). However, selecting the best method for bias correction is challenging. But, mostly it is evaluated by two types of evaluation indices such as frequency-based indices (mean, median, standard deviation, and 10th and 90th percentiles) and time series-based indices using different performance evaluation criteria, including correlation coefficient (R), percent of bias , mean absolute error (MAE), and root-mean-square error (RMSE) (Li et al. 2019; Mendez et al. 2020; Sundaram & Radhakrishnan 2022). This evaluation is used to obtain the best bias correction method to obtain the future climate change scenario. The best bias correction method was applied for developing the near-term (2030–2050) and long-term (2075–2095) climate scenarios at the Muger Subbasin.

The correlation coefficient (R) indicates the correlation between the simulated and observed data, and its optimal value is 1 (Equation (15)).

MAE describes the average error between the observed and simulated precipitation data (Mendez et al. 2020). It is a good indicator of the average model performance, which shows the average model prediction error as it gives the same weight for all errors (Equation (13)).

Percent of bias ( is the measure of the percentage change in the model simulation with the observed data as shown in Equation (14). It ranges between −25 and 25, and negative values of PBias indicate that the simulated data overestimate the observed data and vice versa, with the optimal value being 0. This constraint often stems from practical considerations and the characteristics of the data being analyzed. The range simplifies interpretation and normalization, making bias values more comparable across different datasets and variables, particularly where extreme biases are less common or of lesser concern. In many applications, biases exceeding ±25% may be considered significant and potentially problematic, especially in water resource management or flood forecasting, where large biases could lead to substantial errors in decision-making and risk assessment. By limiting PBias to a narrower range, analysts can establish quality control criteria for model evaluations, ensuring that modeling results meet the required standards for decision-making and scientific validity. Overall, constraining PBias to a range like −25 to 25% balances the need for meaningful interpretation, normalization, practical relevance, and quality control in assessing model performance relative to observed data in hydrological and environmental modeling contexts.

The RMSE is usually used in evaluating model performance studies, as it provides the standard deviation of the simulated error, as shown in Equation (16):
formula
(13)
formula
(14)
formula
(15)
formula
(16)
where and are the observed and simulated values at the ith time step, respectively, and N is the number of datasets.

Spatial variation of observed and uncorrected RCM simulation

There was a substantial difference in the capability of RCM models to produce bias-free precipitation and temperature under the current climate conditions (Teutschbein & Seibert 2012). There was a significantly high greenhouse gas emission and also spatial variation of precipitation and temperature (Figure 4).
Figure 4

Average spatial distribution: (a) raw RCM minimum temperature, (b) observed maximum temperature, (c) raw RCM maximum temperature, (d) observed precipitation, (e) raw RCM precipitation, and (f) observed minimum temperature.

Figure 4

Average spatial distribution: (a) raw RCM minimum temperature, (b) observed maximum temperature, (c) raw RCM maximum temperature, (d) observed precipitation, (e) raw RCM precipitation, and (f) observed minimum temperature.

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Performance assessment of different bias correction methods

In this study, the five bias correction methods including LS and PT for precipitation, Variance Scaling (VS) for temperature, DC, LI, and DM are effective for adjusting the mean annual RCM simulation of rainfall (Rathjens et al. 2016). However, a significant variation was obtained between RCM and raw RCM for the rainfall in the Muger Subbasin (Figure 4). Four evaluation indices (R, RMSE, MAE, and ) was selected to evaluate the performance of bias-corrected individual RCM (Tables 1 and 2). Statistical description comparison for station-averaged observed precipitation and RCM output of Muger watershed for the base period (1983–2004) is shown in Tables 1 and 2, and most of the statistical criteria of the observed precipitation are not good in agreement with the base period except DC and PT for precipitation. In line with this study by Mendez et al. (2020), performance evaluation of bias correction methods for climate change monthly precipitation projections over Costa Rica reveals that DC and EQM outperform the other bias correction methods.

Table 1

Statistical indices of precipitation for different bias correction methods

Bias correction methodsPrecipitation
RMAEPBiasRMSE
Linear scaling 0.25 5.1 0.1 12.33 
Local intensity scaling 0.24 5.2 0.2 12.63 
Power transformation 0.39 4.38 0.2 7.48 
Delta change 0.99 0.37 −3 0.69 
Distribution mapping (empirical quantile mapping) 0.2 3.65 −45.6 6.19 
Bias correction methodsPrecipitation
RMAEPBiasRMSE
Linear scaling 0.25 5.1 0.1 12.33 
Local intensity scaling 0.24 5.2 0.2 12.63 
Power transformation 0.39 4.38 0.2 7.48 
Delta change 0.99 0.37 −3 0.69 
Distribution mapping (empirical quantile mapping) 0.2 3.65 −45.6 6.19 
Table 2

Statistical indices of temperature for different bias correction methods

Bias correction methodsMaximum temperature
Minimum temperature
RMAEPBiasRMSERMAEPBiasRMSE
Linear scaling 0.4 1.65 0.1 2.17 0.21 2.46 −16.8 3.36 
Variance scaling 0.41 1.66 2.2 0.26 2.021 −16.5 2.6 
Delta change 0.98 0.27 −10 0.31 0.89 1.68 −17.7 1.79 
Distribution mapping (empirical quantile mapping) 0.39 1.7 0.1 2.21 0.29 1.99 −16.8 2.63 
Bias correction methodsMaximum temperature
Minimum temperature
RMAEPBiasRMSERMAEPBiasRMSE
Linear scaling 0.4 1.65 0.1 2.17 0.21 2.46 −16.8 3.36 
Variance scaling 0.41 1.66 2.2 0.26 2.021 −16.5 2.6 
Delta change 0.98 0.27 −10 0.31 0.89 1.68 −17.7 1.79 
Distribution mapping (empirical quantile mapping) 0.39 1.7 0.1 2.21 0.29 1.99 −16.8 2.63 

RMSE evaluates the standard deviation of the error distribution between the observed and corrected RCM data. DC methods reveal that it gives fewer error results to estimate climate projection in the future. However, the LS and local intensity scaling (LIS) methods show a significantly high deviation of 12.33 and 12.63, respectively, relative to the other methods. Conversely, the PT and EQM methods have revealed a slight deviation of 7.48 and 6.19, respectively (Table 1). From this result, it can be summarized that the DC bias correction method shows good performance compared to others. When we see the correlation of the simulated and observed data, in DC bias correction methods, the correlation is very good, which is approximately 0.99 (Table 1). For maximum temperature, except DC methods, all bias correction methods show approximately equal deviations with 2.2 (Table 2), but in the case of minimum temperature, the LS method shows the highest deviation of 3.36 relative to the other bias correction methods. Tumsa (2022) study a performance assessment of six bias correction methods using observed and RCM data at upper Awash Basin in Ethiopia. The result reveals that the LS method performed best in terms of the time series-based indices (Nash Sutcliffe Efficiency (NSE) = 0.87, R2 = 0.78, MAE = 3.14 mm/°C, PBias = 0.24).

When we compare its corrected simulation result with observed data, the DC method seems to have no biases for maximum temperature, but it increases by 1.67 °C from the mean for minimum temperature, and 0.39 and 38.41 mm for monthly and annual precipitation, respectively. Generally, DC methods underestimate the model result for both temperature and precipitation. LS and VS methods overestimate the maximum temperature of the simulation by 0.002 °C (Figure 5(a) and 5(b)) and 0.004 °C from the mean of the observed data, but it underestimates 1.59 and 1.56 °C the minimum temperature (Figure 5(c) and 5(d)), respectively. Figure 5 shows the basin average with an average historical period.
Figure 5

Observed and corrected: (a) annual maximum temperature, (b) monthly maximum temperature, (c) annual minimum temperature, (d) monthly minimum temperature, (e) annual precipitation, and (f) monthly precipitation.

Figure 5

Observed and corrected: (a) annual maximum temperature, (b) monthly maximum temperature, (c) annual minimum temperature, (d) monthly minimum temperature, (e) annual precipitation, and (f) monthly precipitation.

Close modal

Similarly, PT shows that it underestimates the monthly precipitation amount by 0.22 mm and overestimates the annual mean precipitation by 2.04 mm from the mean of the observed data (Figure 5(e) and 5(f)). Also, the LI method reduces the mean of the monthly simulated precipitation by 0.23 mm and increases by 1.96 mm from the observed data (Figure 5(e) and 5(f)). However, the DM method gives very different results for precipitation both annually and monthly, which underestimates the model result by 580.44 and 48.76 mm from the mean of the observed data, respectively (Figure 5(e) and 5(f)).

Based on the aforementioned results either in the statistical or the mean of the simulation and observed bias calculation result, it is presumed that the DC method is better for bias correction in the case of the Muger Subbasin, followed by the PT method, and it is adapted for future climate change analysis and impact assessment. Such robust RCM outputs can be useful to develop climate change adaptation and mitigation strategies, such as devising sustainable watershed management practices that help to cope with the challenges of climate variability for building environmental resilience (Worku et al. 2020). The deviation between minimum and maximum temperature estimates in bias correction methods can be influenced by several factors. One possible explanation for the substantial deviation in minimum temperature estimates is that these methods may not adequately account for local microclimatic effects, such as variations in elevation, land use, or surface characteristics. These factors can have a greater impact on minimum temperatures, leading to larger deviations in their estimates compared to maximum temperatures.

In addition, the bias correction methods may not fully capture the complex interactions between different atmospheric variables that affect minimum temperatures, leading to larger discrepancies in their estimates. It is important to carefully consider these factors when applying bias correction methods to temperature data in climate modeling.

Future climate projection

The DC method was used to correct the biases in both RCP2.6 and RCP8.5 scenarios. Then, the corrected future climate data are grouped into two as near-term projection (2030–2060) and long-term projections (2060–2090). To assess future climate change, the raw and corrected historical periods (1983–2004) were compared to the corresponding raw and bias-corrected future precipitations based on the two scenarios RCP2.6 and RCP8.5, for near term (2030–2060) and long term (2060–2090).

The near-term projection (2030–2060) under RCP2.6 and RCP8.5 scenarios

The historical value of rainfall, and the average minimum and maximum temperature of the basin are 1,273.66 mm, 9.45 °C, and 22.37 °C, respectively. The average annual precipitations for RCP2.6 and RCP8.5 were 1931.07 and 1971.49 mm, respectively, which shows an increase of 34.04% in the case of RCP2.6 and 35% from the base period (Figure 6). Annually, the maximum precipitation was 3131.4 mm in RCP2.6 and 3048.46 mm in RCP8.5, which occur in 2030. The maximum precipitation occurs in the month of July with 347.21 and 357.46 mm for RCP2.6 and RCP8.5 scenarios, respectively. Observed and bias-corrected data project a remarkable annual minimum temperature increase on average under the RCP2.6 and RCP8.5 scenarios at 0.15 and 1.45 °C, respectively (Figure 7). The mean maximum temperature for RCP2.6 and RCP8.5 scenarios reveals an increase of 1.22 and 2.73 °C from the observed data, respectively. The highest temperature increase is likely to occur in May with 26 and 28 °C for RCP2.6 and RCP8.5 scenarios, respectively. A study by Fenta Mekonnen & Disse (2018) in the Upper Blue Nile Basin to evaluate the future climate change using statistical downscaling techniques showed that the future precipitation and temperature will be increased with a relative change in precipitation ranged from 1.0 to 14.4%, while the change for mean annual maximum temperature may increase from 0.4 to 4.3 °C and the change for mean annual temperature may increase from 0.3 to 4.1 °C.
Figure 6

Near-term annual precipitation for both scenarios.

Figure 6

Near-term annual precipitation for both scenarios.

Close modal
Figure 7

Near-term annual minimum and maximum temperature for both scenarios.

Figure 7

Near-term annual minimum and maximum temperature for both scenarios.

Close modal

The long-term projection (2060–2090) under RCP2.6 and RCP8.5 scenarios

The long-term temperature (ΔT) projection values (2060–2090) are higher than the near-term projections (2030–2060) for both RCP2.6 and RCP8.5 scenarios. Similarly, the change in annual precipitation (ΔP) for the long term is higher than the near-term projections (Figure 8). The mean annual minimum temperature varies from 0.03 to 1.92 °C for RCP2.6 and RCP8.5 scenarios, respectively. Similarly, the annual maximum temperature varies from 1.63 to 3.5 °C for RCP2.6 and RCP8.5 scenarios, respectively. The results draw attention to the fact that bias-adjusted RCM data are crucial for the provision of regional climate change impact and adaptation studies for the Muger Subbasin. A similar study in Jemma Subbasin of Upper Blue Nile Basin on statistical bias correction of RCM simulations for climate change projection by Worku et al. (2020) indicates that the precipitation will decrease for all ensembles, but in line with this study, the temperature for both ensembles and scenario will be increased.
Figure 8

(a) Long-term annual precipitation for both scenarios and (b) future mean monthly precipitation for both near-term and long-term projection under RCP2.6 and RCP8.5 scenarios.

Figure 8

(a) Long-term annual precipitation for both scenarios and (b) future mean monthly precipitation for both near-term and long-term projection under RCP2.6 and RCP8.5 scenarios.

Close modal

Selecting the best bias correction algorithm is important in assessing the impacts of climate change. The main goal of this analysis is to document, evaluate, and finally recommend the most appropriate bias correction method and to project future climate data under two emission scenarios (RCP2.6 and RCP8.5) for both precipitation and temperature at the district scale. The improvement was achieved for the observed data with all bias correction methods with significant differences. Among different bias correction methods, the study considers four methods for temperature and five bias correction methods for precipitation were compared. The performance of these bias correction methods was evaluated using four statistical parameters including correlation coefficient (R), percent of bias , MAE, and RMSE. Even though all the methods are efficient based on the performance evaluation indices of the bias correction methods, the DC method performs better to correct the bias that is available in the simulated historical and future RCM data. The future climate projections of the bias-corrected ensemble show considerable changes throughout the century. The long-term temperature (ΔT) projection values (2060–2090) are higher than the near-term projections (2030–2060) for both RCP2.6 and RCP8.5 scenarios. Similarly, the change in annual precipitation (ΔP) for the long term is higher than the near-term projections. The results draw attention to the fact that bias-adjusted RCM data are crucial for the provision of regional climate change impact and adaptation studies for the Muger Subbasin. The limitation of the study is that it only considers one ensemble dataset (HadGEM2-ES), and as a recommendation for the future, it is better to use different ensemble datasets such as CanESM2, CNRM-CM5, MIROC5, GFDL-ESM2M, NorESM1-M, and so on. Also, we recommend using the recent shared socioeconomic pathway projection to evaluate the future climate change in the study area. Moreover, as a recommendation, using some skill scores such as Brier Skill Score and ranked probability Skill Score may be appropriate to evaluate the suitability of the chosen bias correction methods.

We acknowledge Wolaita Sodo University.

This work was not supported financially from any institute or organization.

Manamno Beza developed the study's conception and design, did the analytic calculations, and performed the model simulations. Material preparation, data collection, and analysis were performed by Alene Moshe. Both Manamno Beza and Alene Moshe contributed to the final version of the manuscript and then approved the last edited manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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