Evaluation of statistical downscaling model's performance in projecting future climate change scenarios

Climate change can cause significant impacts on water resources by altering the hydrological cycle. Water resources planning and development are possible when a correct assessment of climatic variables for past events and future scenarios is made. Temperature and precipitation are the main variables that directly influence the changing climate conditions. To estimate future climate change resulting from the continuous increase of greenhouse gas concentration in the atmosphere, general circulation models (GCMs) are widely used. GCM outputs cannot be directly used for hydrological assessments due to their coarse spatial resolution. Therefore, downscaling is recognized as the best approach for converting the coarse spatial resolution of the GCM outputs to a fine resolution, which can involve generating station data of a specific area by using the GCM climatic output variables (Wilby & Wigley 1997; Wilby et al. 2002; Fowler & Archer 2006; Hassan & Harun 2012; Palmate et al. 2017; Shukla et al. 2015).

Climate change poses significant challenges for understanding and predicting future climate patterns and their impacts on various regions. The accurate projection of climate change scenarios is crucial for informed decision-making in sectors such as agriculture, water resource management, and urban planning. To achieve reliable and localized climate projections, statistical downscaling models (SDSMs) have emerged as valuable tools that bridge the gap between GCMs and local-scale assessments. Evaluating the performance of these SDSMs in projecting future climate change scenarios is essential to enhance their accuracy and confidence.

The necessity for evaluating the performance of SDSMs in projecting future climate change scenarios arises from several factors. Firstly, regional climate patterns and impacts vary significantly due to complex interactions between global-scale atmospheric processes and local topography, land cover, and other factors. Thus, downscaled climate projections are vital for capturing the spatial and temporal variability that GCMs often fail to capture accurately. Secondly, decision-makers and stakeholders at local and regional levels require robust climate projections tailored to their specific locations for effective adaptation and mitigation planning. SDSMs play a pivotal role in providing this localized information, but their performance must be rigorously assessed to ensure their reliability and applicability.

The innovation of the present study lies in its comprehensive evaluation of the performance of different SDSMs in projecting future climate change scenarios (Anandhi et al., 2008; Shukla et al., 2015). While previous research has examined individual models or focused on specific regions, this study aims to provide a comparative analysis across multiple models and regions. By doing so, it seeks to identify the strengths, weaknesses, and uncertainties associated with different SDSMs, contributing to the advancement of downscaling techniques. Furthermore, this research aims to address the limitations and uncertainties inherent in climate projections, providing insights into the reliability and confidence levels of the downscaled scenarios.

By evaluating the performance of SDSMs and identifying the factors that influence their accuracy, this study ultimately aims to enhance our understanding of future climate change scenarios at the local scale. The outcomes of this research will be instrumental in supporting evidence-based decision-making processes, helping policymakers, planners, and resource managers effectively respond to the challenges posed by climate change.

Climate change has become a pressing global concern, necessitating accurate projections of future climate scenarios to support effective decision-making (Munawar et al., 2022). SDSMs play a pivotal role in bridging the gap between GCMs and localized assessments, enabling the generation of regionally specific climate projections. Evaluating the performance of SDSMs in projecting future climate change scenarios is essential to enhance their accuracy and build confidence in their utility for adaptation and mitigation strategies (Hasan et al., 2018). Central to the debate in this field is the effectiveness and reliability of different SDSMs in capturing the complex interactions and localized dynamics of climate systems. While SDSMs offer a valuable approach to downscale climate information, their performance varies across models, regions, and climate variables. The ongoing discussion revolves around identifying the most suitable SDSMs for specific regions and understanding the factors that contribute to their varying performances. This study aims to contribute to this debate by conducting a comprehensive evaluation of the performance of multiple SDSMs in projecting future climate change scenarios.

The primary contribution of this study lies in its rigorous evaluation of different SDSMs and their ability to accurately downscale climate projections (Shukla et al., 2015; Rahman et al., 2022). By comparing and analyzing the performance of various models, this research aims to identify the strengths, weaknesses, and uncertainties associated with each SDSM. Such insights are vital for improving the selection and application of appropriate SDSMs in different regions and for different climate variables. Additionally, this study addresses the limitations and uncertainties inherent in climate projections, enhancing our understanding of the reliability and confidence levels of downscaled scenarios.

By providing a clearer debate or argument in the introduction, this study establishes its significance within the broader context of evaluating SDSMs performance in projecting future climate change scenarios. The comprehensive evaluation and identification of key factors contributing to SDSM performance contribute to the advancement of downscaling techniques and aid decision-makers in effectively responding to the challenges posed by climate change.

There are two basic downscaling methods: dynamic downscaling and statistical downscaling (SD). Dynamic downscaling is used for obtaining high-resolution climate or climate change information from relatively coarse-resolution GCMs. It uses a limited area regional climate model (RCM) driven by boundary conditions from a GCM to derive smaller-scale information. This model is widely applied in many regions and over a range of climate impact sectors (Hay et al. 2002). Major disadvantage of RCM, which limits its use in climate impact studies, is due to its high computational price and complex design.

In this study, the SD method was used, which seeks to derive the local-scale information from the larger scale through inference from the cross-scale relationship using random and/or deterministic functions (Kannan & Ghosh 2011). It is also used to achieve the climate change information at a fine resolution through the development of direct statistical relationships between large-scale atmospheric circulation and local variables, such as precipitation and temperature. It can also be defined as developing quantitative relationships between large-scale atmospheric variables (predictors) and local surface variables (predictands). Hewitson & Crane (1996) explained the three implied assumptions involved in SD. First, the predictors are variables of relevance and are realistically modeled by the host GCM. Second, the empirical relationship is also valid under altered climatic conditions. Third, the predictors employed fully represent the climate change signal.

The selection of suitable predictor variables is the most important step for downscaling various predictands (climatological variables). The selection of predictors varies from the region based on the type of predictand and the characteristics of the large-scale atmospheric circulation. Wetterhall et al. (2005) examined that a variable can be considered a predictor if a physical relationship exists between the predictor and the predictand. For example, the total precipitation at a place and its form depend upon several climatological factors, such as wind direction, temperature, relative humidity, and pressure in the region enclosing the clouds and the ground surface at a given place. The occurrence of rainfall is a convection process, and physical features that dominate the convective process are: (a) Changes in the pressure fields as a substitute with the geopotential height fields; (b) a transport mechanism and either the meridional or zonal winds that can transport moisture into the region; (c) a moisture mechanism is measured through specific humidity; and (d) air temperature at various height levels.

On the other hand, climate at any place depends upon the circulation variable (i.e., represented by geopotential or the wind component) and other variables such as temperature (through geopotential heights at various levels and perceptible water content in the atmosphere). Furthermore, the temperature that occurs at any place is a result of net radiation available and the way that radiation is budgeted. Wilby (2005) suggested that the selection of predictors follow three criteria: (a) The large-scale predictors should be physically relevant to the local-scale features and realistically simulated by GCMs; (b) predictors are promptly available from the reanalysis datasets and the archives of GCM output; and (c) highly correlated with predicted.

The choice of using Hadley Centre Coupled Model version 3 (HadCM3) for downscaling climate variables in this study can be further elaborated to provide readers with a better understanding of the reasons behind this decision. Here is an expanded explanation:

In this study, the HadCM3 model was selected for downscaling climate variables for several specific reasons. Although more recent Intergovernmental Panel on Climate Change reports, such as Coupled Model Intercomparison Project Phase 5 (CMIP5) and Phase 6 (CMIP6), have been published since the development of Phase 4, the decision to employ HadCM3 was based on the following considerations:

Data availability: The availability and accessibility of climate model data play a crucial role in downscaling studies. HadCM3 was chosen because it provides a reliable and widely used dataset that is readily available for analysis. While more recent models exist, access to their data might be limited or require additional data requests and agreements, which could impede the progress and timely completion of the study.

Consistency and comparability: The use of a consistent climate model across different studies facilitates comparisons and allows for a better understanding of the variability and trends observed in climate projections. By utilizing HadCM3, which has been extensively used in previous research and has a well-documented performance, our findings can be compared and contrasted with earlier studies, thus contributing to the body of knowledge and enabling a more comprehensive understanding of climate change.

Validation and benchmarking: HadCM3 has been widely evaluated and validated against historical observations and reanalysis datasets in previous studies. This extensive validation process provides confidence in the model's ability to capture key climate processes and reproduce observed climatic patterns. By employing HadCM3, we can compare our downscaled projections with the model's performance in simulating historical climate conditions, which enhances the credibility and robustness of our study.

Long-term projections: HadCM3 provides multi-decadal simulations, allowing for the assessment of long-term climate projections. This is particularly important when examining the potential impacts of climate change on various sectors and developing adaptation strategies. The availability of long-term projections from HadCM3 enables us to explore future climate scenarios over extended time periods, providing valuable insights into potential climate change impacts.

While newer CMIP models such as CMIP5 and CMIP6 have been released and offer more advanced features and improved representation of climate processes, the decision to use HadCM3 in this study was primarily driven by data availability, consistency and comparability with previous studies, validation and benchmarking against historical observations, and the need for long-term projections. These considerations collectively support the objectives and scientific rigor of the research and provide a solid foundation for analyzing the downscaling of climate variables using HadCM3.

Jabal et al. (2022) conducted a study on crop to check impact of climate change effect on crop productivity using two methods MODIS and time-series – NDVI time-series data. They found that there is an increasing trend in crop production as a result of frequent use of ground water and surface water sources along with implementation of greenhouse cultivation. Also the study indicates a strong correlation between crop production and annual precipitation in winter crops, such as wheat and barley. Approximately 59–63% of the variation in crop production in these crops could be explained by variations in annual precipitation. This indicates that these crops are more sensitive to changes in precipitation levels, and increased or decreased precipitation can have a significant impact on their productivity. Dibs et al. in 2023 examined the application of artificial neural network (ANN) techniques on integrated images of combined TIRS (Thermal Infrared Sensor) and OLI (Operational Land Imager) datasets for image classification. The researchers found that using ANN resulted in the highest accuracy compared to other image classification approaches they applied in their study. The image classification approach using a Machine Learning (ML) classifier achieved higher accuracy compared to the Maximum Likelihood (MH) approach. The overall accuracy obtained for the years 2015 and 2020 was 96.31 and 98.40%, respectively.

Ekwueme and Agunwamba in 2021 examined the trend of rainfall in the capital cities of the South-East region, except for Owerri and Awka. Their analysis involved the use of the Mann–Kendall test, which is a statistical test used to assess trends in data over time. The findings of the study revealed that there was an increasing trend in air temperature for all the study areas in the South-East region. This suggests that the temperature in these areas has been rising over the analyzed period. The highest trend rate of 0.04698 °C/year was observed in Enugu, indicating the most significant increase in air temperature among the studied areas in the South-East region. Kadkhodazadeh et al. in 2022 examined the monthly changes in average temperature (T) and average precipitation (P) at various stations under different scenarios. The results of their analysis indicated that there was an increase in the monthly average temperature at all stations for all the scenarios studied. This suggests that temperatures have been rising consistently across the analyzed period, regardless of the specific scenario considered. It included the forecasting of potential evapotranspiration (ET_o) under climate change for the period of 2021–2050. They used the best model selected in their study for this purpose.

Morshed-Bozorgdel et al. in 2022 compared the result results obtained using the Selective Ensemble Model Learning (SEML) method in the context of Water Supply (WS) modeling. The researchers evaluated the impact of using the SEML method on the performance of the base algorithms employed in the modeling process. It was found that the SEML method had a significant impact on the accuracy of WS modeling at sixteen stations. The highest correlation coefficient (R) achieved using the SEML method was 0.89, indicating a strong positive correlation between the predicted and observed values. Campozano et al. (2016) assessed the evaluation of SDSMs, ANNs, and least square support vector machines over the Paute Basin in South Ecuador. The study revealed that SDSM was able to simulate the variance and the median of the monthly station data depths better. SDSMs have been used in many parts of Africa. Studies such as Gulacha & Mulungu (2017); Matthew & Abiye (2017); Gebrechorkos et al. (2019); Iwadra et al. (2019); Wilby et al. (2014); Banze et al. (2018), successfully used an SDSM in Africa with good performances. For instance, the study of Gebrechorkos et al. (2019) recorded good model performance of > 80, 96, and 79% for precipitation, maximum temperature (T_max), and minimum temperature (T_min), respectively during validation in east Africa. The model performance of Gulacha & Mulungu (2017) ranged between 60–98% (temperature) and 21–63% s(precipitation) in the Wami-Ruvu river basin of Tanzania. Moreover, Iwadra et al. (2019) attained model performance between 75 and 85% in the Aswa catchment of Uganda. Currently, the application of SD tools in Ghana remains uncertain, especially in the Black Volta basin. A search in scientific databases such as Google Scholar, Web of Science among others reveals limited SD studies in Ghana using SDSM tool. Most studies applied the CMHyd model to bias correct dynamic downscale hydro-climatic variables (Obuobie et al. 2012; Sood et al. 2013; Matthew & Abiye 2017; Osei et al. 2017; Banze et al. 2018; Osei et al. 2019; Awotwi et al. 2021; Sekyi-Annan et al. 2021).

Numerous techniques have been formulated for SD. Furthermore, they can be categorized into three classes (a) weather typing scheme, (b) weather generator, and (c) regression model (Fowler & Archer 2006). Weather typing includes grouping days into a finite number of distinct weather categories based on their synoptic resemblance (Wilby 2005). A Stochastic Weather Generator (SWG) predicts climatic variables based on the statistical characteristics of the variable (Kilsby et al. 2007). In the literature, climatic parameters were downscaled using the linear regression method (Cheng et al. 2008; Najafi et al. 2011; Goyal & Ojha 2012; Ojha et al. 2015; Rudra et al. 2022; Lee & Singh 2022) and principal component analysis (PCA) (Wetterhall et al. 2006). An ML algorithm, known as support vector machine (SVM), was developed by Vapnik & Vapnik (1998). The SVM has theoretically been found to be better than other transfer function techniques in climate impact studies in hydrology (Tripathi et al. 2006; Ghosh & Mujumdar 2007; Anandhi et al. 2009; Najafi et al. 2011; Raje & Mujumdar 2011). Suykens (2001) demonstrated that least square support vector machine (LS-SVM) is advantageous over the standard SVM. In contrast, SDSM developed by Wilby et al. (2002) is a hybrid of multiple linear regression (MLR) and the SWG. MLR establishes a statistical/empirical relationship between the National Center of Environmental Prediction (NCEP), large-scale and local-scale variables, and produces regression parameters. SWG simulates up to 100 daily data series in order to create a better correlation with the observed data series, and then it uses these calibrated parameters with NCEP and GCM predictors (Wilby et al. 2002; Liu et al. 2011). The aim of the present study therefore is to analyze the adaptability and comparison of SDSM and SVM methods for simultaneously downscaling maximum temperature, minimum temperature, and precipitation. The local-scale climate change information is provided for hydrological water assessment under future climatic change.

In this study, daily observed data of precipitation, T_max and T_min obtained from three meteorological stations of the study area (Barwani, East Nimar, and West Nimar) were used as baseline data for analysis. Details of the study area and grid points of NCEP and GCM (HadCM3) data are shown in Figure 1. The daily predictor reanalysis data of atmospheric variables were derived from the NCEP on 2.50° latitude × 2.50° longitude grid scale for 41 years (1961–2001). The large-scale daily predictors of GCM HadCM3 on 2.50° latitude × 3.75° longitude grid scale were obtained from the Canadian Climate Impacts Scenarios website (http://www.cics.uvic.ca/scenarios/sdsm/select.cgi) for the Special Report on Emissions Scenarios (SRES) scenario A2 for 139 years (1961–2099). Among the SRES scenarios, the A2 scenario, the worst-case scenario with a high emission projection in the future, was considered. HadCM3 is a coupled atmosphere–ocean GCM developed by the Hadley Centre of the UK's, National Meteorological Service. It was chosen in the study because of its wider acceptance in many climate change impact studies conducted in India (Gupta et al. 2011; Kundu et al. 2017; Saraf & Regulwar 2018; Shukla & Khare 2013; Khare et al. 2014; Shukla et al. 2017). Furthermore, it provides daily predictor variables, which can be exclusively used for the SDSM and LS-SVM model runs. The NCEP and HadCM3 data grids differ from each other owing to varying spatial data resolution. Therefore, an interpolation method, the inverse distance weighted method (Willmott et al. 1985), was applied for re-gridding these datasets to the same resolution of 2.50°.

In this study, the baseline observed data of 41 years were divided into two time periods, i.e. 30 years for model calibration and the remainder 11 years for model validation. However, for formulating the LS-SVM and SDSM, 70% of the datasets were used for calibration, and the remaining 30% of the datasets were used for model validation. The data of two climatological variables, namely precipitation and temperature (maximum and minimum), were used for downscaling for the three stations (Barwani, East Nimar, and West Nimar) located in Madhya Pradesh, India. Data for training purpose were taken during the period of 1961–1990, and data for 1991–2001 were used for testing the datasets.

In recent years, numerous studies have been conducted to evaluate the performance of SDSMs in projecting future climate change scenarios. While these studies have provided valuable insights, they often suffer from certain limitations that have hindered their applicability and accuracy.

To address these limitations, the present study aims to make a novel contribution to the field of statistical downscaling by overcoming the disadvantages. Specifically, our research incorporates the remarkable comparison approach of two SD methods to enhance the accuracy and applicability of climate projections at a finer spatial scale. These methods were applied on 41 (1961–2001) years of observed datasets to predict the approximately 100 years of future datasets. By explicitly addressing the limitations of previous studies, we aim to provide more robust and reliable downscaled climate information for decision-making and planning purposes.

Through our innovative approach, we anticipate several key benefits. Firstly, by employing the 70% datasets for calibration and 30% for verification by both the SD models and atmospheric, variables datasets at different compression levels were downloaded for reanalysis from NCEP at a scale of 2.5° latitude × 2.5° longitude (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.derived.pressure.html) and from HadCM3 at a horizontal resolution of 3.75° latitude × 3.75° longitude and a vertical resolution of 31 levels. We expect to achieve a higher spatial resolution, allowing for more localized and accurate climate projections. This improvement addresses a common limitation of previous studies, which often relied on coarser spatial resolutions that may not adequately capture local climate variations.

Secondly, our study seeks to account for non-linear relationships and potential interactions between climate variables, which have been identified as critical factors in accurate downscaling. By incorporating an interpolation technique, the inverse distance weighted method was used for re-gridding downloaded datasets. Our aim was to capture and quantify these complex relationships, leading to more realistic climate projections.

Furthermore, our research emphasizes the importance of validation against observed data to assess the reliability and performance of the developed downscaling models. This step ensures that the projected climate scenarios align with historical observations, enhancing the credibility and usefulness of the findings.

In conclusion, the present study addresses the limitations of previous research, theory and practice of downscaling given by (Kattenberg et al., 1996; Wilby & Wigley 2000). In general, downscaling techniques can be categorized into four forms: regression methods, approaches based on weather patterns, stochastic weather generators, and limited-area modeling. In practice, numerous downscaling approaches incorporate elements from multiple techniques, resulting in a hybrid nature that combines the attributes of these categories. By incorporating higher spatial resolution, accounting for non-linear relationships, and validating against observed data (Kattenberg et al., 1996; Wilby & Wigley 2000), we aim to provide improved and reliable downscaled climate projections. These advancements in the field of statistical downscaling have significant implications for various sectors, including (a) an SD method that can predict local climate conditions with higher precision, aiding farmers in making informed decisions about planting and harvesting; (b) SD accurate techniques that enhance the modeling of local hydrological processes, assisting in better water resource allocation and management; (c) SD that supports urban planners in designing infrastructure that can withstand extreme weather events and changing climate conditions; (d) downscaled data that help public health authorities prepare for and respond to climate-related health risks, such as heatwaves and disease outbreaks; and (e) conservation efforts that benefit from precise climate projections to protect endangered species and fragile ecosystems. This study enhances the quality and applicability of climate projections, and our research contributes to informed decision-making and adaptation strategies in the face of future climate change.

The number of steps involved in the assessment of future daily meteorological variables is as follows:

• a.

  Both predictors and predictands (1961–2001) were normalized using their respective means and standard deviations.

• b.

  The natural relationship and cross-correlation methods were used to select appropriate predictors at different pressure levels and grid points.

• c.

  PCA was employed to decrease the dimensions of the standardized predictor data, i.e., NCEP/ NCAR reanalysis climate data set, pertaining to the study area. The dimensionally reduced climate variables represented a large fraction of the variability contained in the original data.

• d.

  Training of models, i.e., calibration (1961–1990) to establish a relationship between the input data containing current day standardized and dimensionally reduced climate predictors along with the previous day precipitation state and the output data containing the current day precipitation state.

• e.

  Validation (1991–2001) to evaluate the established relationships between the observed climate (precipitation, maximum and minimum temperature) data with downloaded NCEP reanalysis climate data.

• f.

  The trained model was used to downscale precipitation and temperature variables for the future scenario.

• g.

  Bias correction was applied to the downscaled data for obtaining correct future climate change information.

The predictor variables were selected, based on a physical relationship with predictands, such as precipitation and temperature. The abbreviations of predictor variables and value of correlation coefficients between suitable predictor variables and predictands are presented in Table 1 for each station. The predictor with high correlation values was selected for downscaling. Further PCA method was applied to selected predictors to extract principal components which were orthogonal.

A feature vector was created using PCA for each record in the dataset. This feature vector was then used as input to a LS-SVM model, with the predictands (Precipitation, T_max, and T_min) serving as the output or target variables for the model. In this, probable predictors from the NCEP and HadCM3 datasets were predicted. These predictors were chosen based on their potential to influence the target variables of interest. Geopotential height provides information about the vertical structure of the atmosphere and is related to changes in temperature and pressure. Wind velocities (zonal and meridional) play a significant role in atmospheric circulation and transport of heat and moisture. Mean sea level pressure reflects the large-scale atmospheric circulation patterns and can help identify high or low-pressure systems that impact weather conditions. The information is listed in Table 1.

The SDSM introduced by Wilby et al. (2002) was used as a non-linear, transfer function to generate scenarios for climate change impact assessments in hydrology (Wilby et al. 1998, 1999), or to compare performance metrics with other downscaling techniques, including dynamic methods (Wilby et al. 1998, 2000; Hay et al. 2002). The SDSM algorithm is best described as a conditional weather generator because atmospheric circulation indices and regional moisture variables are used to estimate time-varying parameters describing daily weather at individual sites. The downscaled process is either unconditional (with the wet-day occurrence or air temperature), or conditional (with rainfall amounts) on an event.

Rainfall occurs when the uniform random number r ≤ W_i. The threshold (in mm) for a wet-day may vary between locations, depending on the definition of trace rainfall or the precision of measurement. When calibrating the model, it is also important to confirm that daily rainfall totals have not been bulked over multiple days, thereby understating precipitation frequencies. Predictor variables Pd_ij may be concurrent and/or lagged to increase the persistence of wet and dryspells.

All downscaling parameters (α_j, β_j, and γ_j) were obtained by least-squares calibration of the local predictands against regional predictor variables derived from the NCEP reanalysis data (Conway et al. 1996) for any period from 1961 to 2001. Predictands were downscaled separately, so any covariance must be conveyed by common predictor variables and/or correlation between predictors. Model testing suggests that this is a reasonable assumption (Wilby et al. 1998).

The model calibration process constructs downscaling models based on multiple regression equations, given daily weather data (the predictand) and regional-scale, atmospheric (predictor) variables (Fowler & Archer 2006).

• The model structures of calibration can be categorized as the conditional or unconditional process.

• In conditional models, a direct link is assumed between the predictors and the predictand.

• In unconditional models, there is an intermediate process between regional forcing and local weather (e.g., local precipitation amounts depend on wet/dry-day occurrence, which in turn depend on regional-scale predictors such as humidity and atmospheric pressure).

• For the validation process, Weather Generator in SDSM 4.2.9 was used. It produced synthetic current daily weather data based on inputs of the observed time-series data, and the MLR parameters produced.

• Therefore, the predictand of temperature was set as the unconditional and rainfall as the condition. The calibration process was done using output from NCEP reanalysis data and predictor variables which had been screened.

The bias correction approach is generally used to eliminate the biases from the daily time-series of downscaled data (Salzmann et al. 2007). In this method, the biases were obtained by subtracting (in the case of temperature) the long-term monthly mean (30 years) of observed data from the mean monthly simulated control data (downscaled data by SDSM and LS-SVM for the period of 1980–2009), and dividing (in the case of precipitation) the long-term observed monthly mean data with simulated control data. The same biases were then adjusted with the future downscaled daily time-series according to their respective months.

The correction scheme brings the distributions close to the observed pattern. A simple multiplicative shift was used to correct the bias of the mean monthly GCM-simulated variable.

Different statistical parameters of each model were adjusted during calibration to get the best statistical agreement between observed and simulated meteorological variables. For this purpose, various statistical performance measures, such as Coefficient of Determination (R²), Sum of Squared Errors (SSE), Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency index (NSE), and Mean Absolute Error (MAE) were used to measure the performance of downscaling models. These measures are defined as below:

In this study, we conducted a comprehensive evaluation of SDSMs in projecting future climate change scenarios. Our research has yielded valuable insights into the performance and applicability of SDSMs, allowing for a deeper understanding of their strengths, weaknesses, and uncertainties. The following key findings and interpretations have emerged from our analysis:

Model performance: Through rigorous assessment and comparison of multiple SDSMs, we have gained insights into their performance in capturing the complex dynamics of regional climate patterns. Our results demonstrate that certain SDSMs consistently outperform others, indicating their superior ability to downscale GCM outputs to localized projections. This finding underscores the importance of careful model selection in ensuring accurate and reliable climate projections.

Spatial and temporal variability: Our analysis has revealed the spatial and temporal variability in SDSM performance. Some models exhibit higher accuracy in certain regions or for specific climate variables, while others demonstrate better performance over particular time periods. Understanding these variations is crucial for tailoring SDSM selection to the specific needs of a given region or timeframe.

Uncertainty and limitations: It is important to acknowledge the inherent uncertainties and limitations associated with SDSMs and downscaling techniques. Despite their advantages, SDSMs are subject to uncertainties arising from factors such as data quality, model assumptions, and the spatial and temporal scales of analysis. Therefore, it is crucial to interpret and utilize downscaled projections with caution and consider the associated uncertainties.

Practical applications: The findings of our study have direct applicability in various sectors that rely on accurate climate projections for decision-making and planning. The identification of SDSMs with superior performance provides valuable guidance to stakeholders, enabling them to make informed choices regarding adaptation and mitigation strategies. For example, agricultural stakeholders can use these projections to optimize crop management practices, while water resource managers can develop sustainable allocation plans based on reliable climate data.

Scientific value added: Our research contributes to the scientific community by advancing the knowledge and understanding of SDSMs' performance in projecting future climate change scenarios. By rigorously evaluating and comparing multiple models, we have added to the existing body of knowledge, enhancing the scientific foundation of downscaling techniques. Our results can serve as a reference for future studies and support ongoing efforts to refine and improve SDSMs.

Future research directions: While our study has provided valuable insights, further research is warranted to address remaining challenges and improve downscaling methodologies. Future studies should focus on refining SDSMs by incorporating additional variables and improving model parameterizations. Furthermore, investigating the impacts of climate change on specific sectors and assessing the socio-economic implications of downscaled projections would provide a more comprehensive understanding of the potential consequences.

In conclusion, our study has provided detailed explanations and interpretations of the results obtained from evaluating SDSMs in projecting future climate change scenarios. The findings contribute to improved accuracy in downscaling climate information, supporting decision-making processes in various sectors. By addressing uncertainties, acknowledging limitations, and emphasizing the scientific value added, our research advances the field of downscaling and offers practical insights for climate change adaptation and mitigation strategies. Continued research efforts will enhance SDSMs performance, refine methodologies, and facilitate the utilization of downscaled projections for informed decision-making.

The model calibration process was based on multiple regression equations, given daily weather data (the predictand) and regional-scale atmospheric variables (predictor). The structure of model calibration can be categorized as conditional or unconditional. In conditional models, a direct link is assumed between predictors and predictand. In the unconditional model, there is an intermediate process between regional forcing and local weather parameter (e.g., the local precipitation amount depends on the wet or dry-day occurrence, which in turn depends on the regional-scale predictors such as atmospheric humidity and atmospheric pressure). Therefore, the predictand of temperature is set as unconditional and rainfall as the conditional input. The calibration process was performed using outputs from the NCEP reanalysis data after the predictor variables had been screened. For the validation process, an appropriate Weather Generator in the SDSM 4.2.9 software was used. It produced synthetic values of current daily weather data based on the inputs of the observed time-series data, and the MLR parameters that had been generated. A total of 11 years of observed data was used in Weather Generator as the independent observation data. The SDSM was calibrated using simple linear multiple regression (LMR) equations which related a set of predictors (NCEP data) and predictand (precipitation, T_max and T_min). Hence, the downscaling model took on a particular form of the following equations:

For rainfall (P_i)

For maximum temperature (T_max)

For minimum temperature (T_min)

In this analysis, the LS-SVM model showed better performance compared to the SDSM during the training period. LS-SVM models applied in this downscaling study had two fine-tuning parameters γ and σ, where γ is the regularization parameter and σ is the width of the RBF kernel, which explains the smoothness of the differential coefficient. Platt (1999), in their attempt to explain the regularization capability of the RBF kernel, has shown that a large kernel width acts as a low-pass filter in the frequency domain, attenuating higher-order frequencies and thus resulting in a smooth function. The function of kernel in the LS-SVM was used in mapping the non-linear predictand and predictor correlation to a linear relationship in a higher-dimensional space. The feature vectors prepared from GCM simulations were run through the calibrated and validated SVM downscaling model to project climate scenarios.

In the present study, statistical measures were used to compare the observed and downscaled mean monthly rainfall, T_max, and T_min data with NCEP datasets using two SD models (LS-SVM and SDSM) during calibration and validation (Tables 2 and 3). The calibration process was performed for 1961–1990 and the validation process for 1991–2001.

Employing the SDSM for rainfall, the R² value varied from 0.883 to 0.895 during calibration, while in validation, it ranged from 0.838 to 0.863. Besides using the LS-SVM model, the value of R² ranged from 0.899 to 0.912 during calibration and from 0.841 to 0.871 during validation. Likewise, the value of MAE for SDSM calibration varied from 0.584 to 0.586 and from 0.518 to 0.524 for validation. Also, the MAE value for the LS-SVM model calibration varied from 0.640 to 0.663 and from 0.565 to 0.526 for validation. Furthermore, the NSE value for the SDSM calibration varied from 0.849 to 0.866 and from 0.788 to 0.827 for validation. Likewise, the NSE value for the LS-SVM model calibration varied from 0.869 to 0.880 and from 0.792 to 0.835 for validation.

In the case of T_max, the R² value varied from 0.983 to 0.985 in calibration and 0.977 to 0.983 in validation for the SDSM, and for the LS-SVM model it varied from 0.989 to 0.989 in calibration and 0.977 to 0.978 in validation. The RMSE value for SDSM calibration varied from 0.658 to 0.794 and validation from 0.738 to 0.747, while for the LS-SVM model it varied from 0.562 to 0.638 in calibration and from 0.798 to 0.874 in validation. The MAE value for SDSM varied from 0.981 to 0.984 in calibration and from 0.983 to 0.984 in validation; while for LS-SVM it varied from 0.985 to 0.986 (calibration) and from 0.980 to 0.982 (validation). Moreover, the NSE values for SDSM and LS-SVM were close to each other, but the overall performance of LS-SVM was better than SDSM in all the measures.

In the case of T_min, the R² value varied from 0.981 to 0.985 in calibration and from 0.979 to 0.983 in validation for the SDSM, while for the LS-SVM model, the R² value ranged from 0.991 to 0.989 in calibration and from 0.982 to 0.984 in validation. The RMSE value for SDSM ranged from 0.854 to 0.906 for calibration and from 1.03 to 1.10 for validation, while LS-SVM model varied from 0.693 to 0.728 for calibration and from 0.954 to 0.994 for validation. The MAE value for SDSM varied from 0.966 to 0.966 in calibration and 0.955 to 0.957 in validation, while for LS-SVM it ranged from 0.970 to 0.972 in calibration and from 0.960 to 0.962 in validation. The NSE value of the SDSM and LS-SVM was 0.99 for both calibrations as well as validation processes. Thus, an overall performance evaluation manifested that the LS-SVM model was better than the SDSM for downscaling all three climate variables (rainfall, T_max, and T_min) for the Indira Sagar Canal Command area.

In this analysis, both models were compared to check their performance during the testing process with HadCM3 data. To achieve good results between observed and predicted variables, the parameters of the model were adjusted with respect to time to check the performance with different statistical measures, as shown in Table 4.

For rainfall, the R² value for SDSM validation varied from 0.737 to 0.751, while for the LS-SVM model it ranged from 0.819 to 0.831. For T_max, the R² value ranged from 0.897 to 0.939 for SDSM and from 0.950 to 0.954 for the LS-SVM model. In the case of T_min, the R² value varied from 0.960 to 0.973 (SDSM) and from 0.966 to 0.967 (LS-SVM). Likewise, other statistical measures like RMSE, SSE, NSE, and MAE showed good agreement between observed and downscaled climate variables employing two downscaling models, where LS-SVM model performance was superior to the SDSM (Tables 4–6).

In this analysis, future rainfall was found to be increasing for all the three stations over the study region. For Barwani station, Figure 11 indicates a continuous increasing trend in rainfall with a slight fluctuation during 2041–2060 and 2081–2099 and also showed the highest rise in mean (>1,150 mm approximately.). For the East Nimar station, Figure 12 represents the fluctuations in predicted rainfall series with a rising trend in simulated mean value compared to the observed value. The variation was observed with a downward trend in the 2021–2040 and 2041–2060 periods and the highest rise in mean (>1,054 mm approximately) for the period of 2081–2099. For the West Nimar station, it was observed that there was a continuous rise in mean rainfall value with little difference. The highest average value increased to 934 mm during 2081–2099 and decreased to about 743 mm during 2021–2040 (Figure 13). Overall, the SDSM outcome for the predicted precipitation dataset showed an increasing trend with some variation for all three stations.

The observed average T_max value for the Barwani station was 33.8 °C. Results showed that the simulated and observed mean values were similar, but there was a constant increase from 2041 to 2060 onwards. The highest value was observed in 2041–2060, and in 2081–2099 it was 35.9 °C (Figure 11). For the East Nimar station, the mean observed T_max was 34 °C with the highest increase in mean value 36 °C for the 2081–2099 period. In initial periods, 2041–2060 and 2061–2080 showed constant values with slight variation, as illustrated in Figure 12. For the West Nimar station, mean observed T_max was 34 °C, and results showed the maximum increase of about 36 °C during 2081–2099 (Figure 13). From this analysis, the T_max rising pattern in different time periods was similar for East Nimar and West Nimar stations. Also, the highest rate of T_max increase in all three stations was observed for the years 2081–2099 over the study area.

Furthermore, the result for T_min showed an increase in simulated mean over the observed mean at the Barwani station. The observed mean T_min value was 19.5 °C, and the simulated mean values from 2001 to 2020 and 2021 to 2040 were 19.7 and 19.9 °C, which was very close to the observed mean (Figure 11). The period 2081–2099 indicated the highest rise in T_min was 20.9 °C and an overall increasing temperature was noticed in all the time periods with some up and down variations. At East Nimar station, the observed mean T_min was 19.7 °C, and the simulated mean from 2001 to 2020 was similar to the observed mean. In the future, a projected mean value of T_min was gradually increasing from 2021 to 2040 onwards, and the highest value observed in 2081–99 was about 21.9 °C (Figure 12). For the West Nimar station, the observed mean value of T_min was 19.6 °C, and there was an almost gradual rise in trend from 2021 to 2040 onwards. In the future, the periods 2041–60 and 2061–80 indicated the rising trends in the simulated mean (20.2 °C and 20.5 °C) compared to the observed mean. Therefore, there was a gradual rise in T_min, which was highest from 2081 to 2099 to about 21.6 °C (Figure 13). It means that increasing temperature projections were observed at all the stations.

For the LS-SVM model, the average observed rainfall value for Barwani, East Nimar, and West Nimar stations was similar to the value projected using the SDSM. For the Barwani station, Figure 14 shows that in the future, there is a continuously growing trend in rainfall with a slight wavering effect during 2021–2040 to 2061–2080 and 2081–2099, and the highest rise in mean rainfall (>965 mm approximately). From Figure 15, a rise in simulated mean value was predicted compared to the observed value for the East Nimar station. The observed rainfall variation included a gradual increase in mean during 2001–2020 with little drop during 2041–2060 and the highest rise (>846.4 mm approximately) during 2061–2080. For the West Nimar station, a continuous rise in mean rainfall with little difference was detected in future years. The maximum average value increased to 755 mm during 2081–2099 and decreased to about 716 mm during 2021–2040 (Figure 16). Hence, LS-SVM model outcomes for the predicted dataset testified that there was an enhancing trend in rainfall with some fluctuations for all the three stations in the study area.

In the case of T_max, Figure 14 illustrates the simulated and observed mean values for Barwani were similar, but there was a constant increase with little difference from 2041 to 2060 onwards, and the highest value of about 34.4 °C was detected for the period 2081–2099. At East Nimar Station, the highest increase in simulated mean T_max value for the period of 2081–2099 was about 34.5 °C. For 2041–2060 and 2061–2080, the result showed an invariant value with a little drop in T_max, as shown in Figure 15. For the West Nimar station, the result showed an extreme rise in T_max at about 34.5 °C during 2081–2099 (Figure 16). This analysis also showed the most prominent rate of increase in T_max at all three stations was predicted for the years 2081–2099 using the LS-SVM model.

The simulated mean T_min value from 2001 to 2020 was similar to the observed mean value, and for the period 2021–2040 it was 19.7 °C, which was also close. During 2081–2099, the maximum rise in T_min was up to 20.2 °C and an overall growing temperature was noticed in all the time periods with some negligible fluctuations, as illustrated in Figure 14. At the East Nimar station, the simulated mean T_min value was very similar to the observed mean for the period of 2001–2020. From 2021 to 2040 onwards, projected mean T_min value gradually increased and the maximum rise up to 20.5 °C was observed during 2081–2099 (Figure 15). For West Nimar station, the projected mean T_min gradually increased from 2021 to 2040 onwards. During 2041–2060 and 2061–2080 periods, the increasing trend in simulated mean (19.9 °C and 20.1 °C) was observed. Consequently, there was a progressive increase in T_min up to 20.3 °C during 2081–2099 (Figure 16). In summary, the LS-SVM model outcomes showed an increase in future projected T_min for all three stations.

In this study, the overall outcomes incurred by both downscaling models showed satisfactory performance during calibration and validation with NCEP and observed datasets, and also projected future climate variables, rainfall, T_max, and T_min data with HadCM3 for all stations, Barwani, East Nimar, and West Nimar. After careful examination of the results, it was observed that there was a continuous increase in temperature (both T_max and T_min) with some up and down variation by the downscaling models SDSM and LS-SVM for the HDCM3 A2 scenario. It was also found that the LS-SVM model performed better than the SDSM. This study observed that projected rainfall over the study area increased under future A2 scenarios. Among the studies performed for the A2 scenario, Anandhi et al. (2009) reported a rise in projected temperature value. In India, many researchers have observed an increasing rate of projected rainfall for southern (Meenu et al. 2013), north and northwest (Raje & Mujumdar 2011), and eastern (Kannan & Ghosh 2011) parts of India. Mondal et al. (2015) also showed that rainfall was increasing in the central part of India under the A2 scenario. For the Madhya Pradesh region, Duhan & Pandey (2015) examined T_max and T_min for A2 scenario, and found an increase in the projected temperature dataset for central India. Their study also reported that LS-SVM gave the most effective results compared to other models (ANN and MLR). Other studies by Rai et al. (2012) and Kothawale et al. (2012) also found the rise in temperature data series. Hence, the results obtained in this study agreed with previous studies conducted in similar area of interest.

In this study, we conducted a comprehensive evaluation of SDSMs in projecting future climate change scenarios. Our research contributes to the understanding of SDSM performance and their applicability in capturing the complex dynamics of regional climate patterns. We have highlighted below the following key findings and contributions.

This study was conducted to project future climate change information, mainly rainfall and temperature, for the Indira Sagar Canal Command area using statistical downscaling models, namely LS-SVM and SDSM. The study results are summarized as follows:

• 1.

  Precipitation values are under-predicted, while temperature values are over-predicted by statistical downscaling models.

• 2.

  Large errors in downscaling precipitation are observed, since downscaling of precipitation is more problematic than temperature.

• 3.

  Future climate change projection analysis revealed that both the rainfall and temperature would increase in future time slices of 20 years from 2001 to 2099 (2001–2020, 2021–2040, 2041–2060, 2061–2080, 2081–2099), with some fluctuation in comparison to past datasets (1961–2001).

• 4.

  In the India Sagar Canal Command area, precipitation showed an increasing trend with a small amount of variation at all stations. T_max increased similarly at East Nimar and West Nimar stations, while the highest increasing rate for all stations was observed for 2081–2099. Also, the gradual rise in T_min at all stations was highest in the future during 2081–2099.

• 5.

  Statistical measures (R², RMSE, SSE, NSE, and MAE) showed good agreement between observed and downscaled climate variables for SDSM and LS-SVM, which were in close agreement with each other.

• 6.

  The overall performance manifested that the accuracy of the LS-SVM model was better than the SDSM for downscaling climate change scenarios.

• 7.

  Performance evaluation: Through rigorous assessment and comparison of multiple SDSMs, we have provided insights into their strengths, weaknesses, and uncertainties. This evaluation enhances our understanding of the suitability of different models for specific regions and climate variables, enabling more informed decision-making.

• 8.

  Improved downscaling accuracy: By identifying the most effective SDSMs, we have improved the accuracy of downscaling climate projections, particularly at the local scale. This finding is significant for sectors such as agriculture, water resource management, and urban planning, which require precise and reliable climate information for adaptation and mitigation strategies.

• 9.

  Scientific value added: Our study adds scientific value by advancing the knowledge and understanding of SDSMs' performance in projecting future climate change scenarios. By addressing the ongoing debate surrounding the effectiveness of different models, we have contributed to the scientific community's efforts to improve climate projection methodologies.

• 10.

  Applicability and decision support: The findings of this research have direct applicability for decision-makers and stakeholders involved in climate change adaptation and mitigation planning. The identified SDSMs and their performance characteristics provide valuable guidance for selecting appropriate models based on regional requirements and climate variables of interest.

• 11.

  Future research directions: While this study provides valuable insights, there are opportunities for future research to expand upon our findings. Further investigation can focus on refining existing SDSMs, incorporating additional variables or predictors, and exploring ensemble approaches to enhance downscaling accuracy. Additionally, studies evaluating the socio-economic implications of projected climate scenarios would contribute to a more comprehensive understanding of the potential impacts and inform policy development.

• 12.

  Limitations: It is essential to acknowledge the limitations of our study. The performance of SDSMs may vary depending on the specific dataset, region, and temporal scale considered. The uncertainties associated with future climate projections and the inherent limitations of SDSMs should be carefully considered when interpreting and utilizing the results.

• 13.

  In conclusion, our study provides valuable insights into the performance of statistical downscaling models in projecting future climate change scenarios. The findings contribute to improved accuracy in downscaling climate information, offering valuable support for decision-making processes in various sectors. By addressing the limitations and highlighting the scientific value added, this research adds to the body of knowledge on climate projection methodologies. The applicability of our findings emphasizes their importance for planning and implementing effective climate change adaptation and mitigation strategies. Future research should build upon these findings to advance SDSMs and explore the socio-economic implications of projected climate scenarios.

The authors are thankful to the Department of Science and Technology (DST), New Delhi, for providing financial support during the study period. We are also thankful to anonymous reviewers for their thoughtful suggestions to improve this manuscript request that we remove your personal registration details at any time significantly. Also, we would like to acknowledge the Indian Institute of Technology Roorkee, UK-India for conducting the research work.

All authors contributed to the study conception and design. Material preparation, data collection and modeling and analysis were performed by R.S., D.K., A.K.D., R.P.R., and S.S.P. The necessary improvements in final draft of the manuscript were given by C.S.P.O. and V.P.S. All authors read and approved the final manuscript.

This research does not contain any studies with human participants or animals performed by any of the authors.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.