Statistical downscaling using principal component regression for climate change impact assessment at the Cauvery river basin

Climate change is denoted as a change in the long-term statistics of atmospheric variables over a specific region. Urbanization and increased industrial activities led to changes in the concentration of greenhouse gases in the atmosphere. The Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) (IPCC 2014) stated that the role of greenhouse-gas emissions and the severity of potential risks and impacts remain unmanageable, especially for the developing countries with their limited ability. The climate change induced by CO₂ has affected the globe in enormous ways and is likely to become more furious shortly. Therefore, it is essential to assess the impacts of climate change over the globe to illustrate the evidence to decision-makers and stakeholders.

Climate change impact assessment studies require long-term climate data at various spatio-temporal scales. Finer spatial resolution-observed data for the historical time scale are required for such studies and they are available for certain regions over the past few decades. However, future climate projections are required to predict and analyze future climate changes. General circulation models (GCMs) are mathematical models projecting future climate scenarios. But the spatial resolution of these model outputs is coarser and can not be used directly for regional climate impact studies (Oo et al. 2019, 2020; Burciaga 2020; Javadinejad et al. 2020). Additionally, the GCM model outputs contain significant errors and require correction to ensure an appropriate outcome. Consequently, the downscaling of GCM model output is necessary to make use of it for the regional climate impact assessment (Ahmed et al. 2013; Wilby et al. 2014; Yang et al. 2020).

There are two different methods to downscale the GCMs, which are dynamic downscaling and statistical downscaling. Dynamic downscaling requires high-end computational power and consumes a lot of time (Busuioc et al. 2001; Brown et al. 2017; Li et al. 2020). Thus, it is not feasible to perform dynamic downscaling in the required region, whereas statistical downscaling requires less computational power and can be performed in a short span (Aribarg et al. 2016; Asong et al. 2016; Tiwari et al. 2019). Numerous studies stated that the performance of dynamic and statistical downscaling was comparable in regional-scale climate studies over historical time-scales (Wilby et al. 1998; Feddersen & Andersen 2005). A detailed study comparing the dynamic and statistical downscaling stated that the dynamic downscaling did not perform any better than the statistical downscaling (Chávez-Arroyo et al. 2013, 2015).

Statistical downscaling is developed based on the assumption that the statistical relationship between the historical observed and historical GCM output will remain constant in future climate projections (Wilby & Dawson 2013). There are numerous atmospheric parameters to consider for climate change impact studies. But the primary weather variables, such as precipitation (Pr), mean temperature (Tas), maximum temperature (Tasmax), and minimum temperature (Tasmin), play a major role in representing the hydrological system in a given region. It is also evident from previous studies that the different GCMs' output performance varies significantly in representing the regional climate scenario (Hessami et al. 2008; Meaurio et al. 2017; Shamir et al. 2019). Various downscaling models have been developed to handle the bias and variance in projecting future climate for a regional scale (Sarr et al. 2015; Yue et al. 2016; Preethi et al. 2019).

In this study, an improvised principal component regression (PCR)-based downscaling approach is carried out using a dataset of daily precipitation and temperature (mean, minimum, and maximum) for the climate change impact assessment over the Cauvery river basin. Also, 26 different Coupled Model Intercomparison Project Phase 5 (CMIP5) GCM outputs were used to project the future scenarios and rank their performance for the study area. The designed model performance is evaluated using calibration and validation. Besides, the outcomes are compared with the existing methods to state the pick over other techniques in representing the regional climate scenario.

The primary objectives of the present study are:

• (i)

  To perform statistical downscaling using improvised PCR and compare it with the existing methods for its leads.

• (ii)

  To model climate scenarios using different CMIP5 GCMs and prioritize models based on performance evaluation.

A brief picture of the study area is delivered in the next section. Particulars of the datasets used in this study are presented in the ‘Data description’ section. The model design and performance evaluation are provided in the ‘Methodology’ section, and the penultimate section explains the results and discussions. The last section explains the ‘Summary and conclusion’ of the study.

The Cauvery river basin is a part of peninsular India which lies between 75°27′–79°54′E and 10°9′–13°30′N. It is estimated to be 85,000 km² with many streams, including Kabini, Bhavani, and Noyyal. Cauvery covers three states (Tamil Nadu, Karnataka, and Kerala) and a Union Territory (Puducherry). It is guarded by the Western Ghats on the west and by the Eastern Ghats on the east and south. A map demonstrating the location and the border of the study area is shown in Figure 1. The main regions of the Cauvery basin are covered with agricultural land up to 67% of the total area, and 20% of the basin is covered by the forest area (CWC & NRSC 2014). The Cauvery river basin has four seasons, namely winter (December–February), summer (March–June), South-West monsoon (July–September), and North-East monsoon (October–November). The basin remains dry in the majority of the area except for the monsoon duration. The basin has both tropical and subtropical climate zones where the temperature variation in the upper reaches of the basin is less compared to the lower reaches. April is the hottest and January turns out to be the coldest month in the basin, where the average monthly temperature ranges from 18 to 33 °C. Northern parts of the basin are comparatively colder than the southern parts of the basin.

The CMIP5 GCM was used in this study considering the daily ensemble realization run r1i1p1. Twenty-six models from various institutions were selected, namely ACCESS1-0, ACCESS1-3, bcc-csm1-1-m, BNU-ESM, CanCM4, CanESM2, CCSM4, CMCC-CESM, CNRM-CM5, CSIRO-Mk3-6-0, EC-EARTH, FGOALS-g2, GFDL-CM3, HadGEM2-AO, HadGEM2-C, HadGEM2-ES, inmcm4, IPSL-CM5A-MR, MIROC5, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3, MRI-ESM1, and NorESM1-M. The description of the selected models is presented in Table 1. The weather parameters considered in the present study are precipitation (Pr – mm/day), mean temperature (Tas – °C/day), maximum temperature (Tasmax – °C/day), and minimum temperature (Tasmin – °C/day).

The daily observed station data are obtained from the India Meteorological Department (IMD) for the 35 stations located in the Cauvery river basin from 1951 to 2005. The description of the stations is presented in Supplementary Table S1. The river basin is divided into the upper, middle, and lower Cauvery river basin based on its weather pattern and discharge statistics. Furthermore, the historical GCM datasets are re-gridded to the station scale and trimmed to the observed data specifications. The observation stations and their location are represented as a thematic map in Figure 2.

The observed station-wise climate data (1951–2005) and historical simulation from various CMIP5 GCMs are collected and re-gridded using the Bicubic Spline Interpolation technique to ensure that all datasets are in the same dimension and co-ordinates. Furthermore, the re-gridded data are separated into calibration (1951–1990) and validation (1991–2005) for the betterment of the model. The designed dataset is trained and tested with existing well-established statistical machine learning (ML) models such as multiple linear regression (Joshi et al. 2013), partial least-squares regression (PLSR) (Matulessy et al. 2015), artificial neural network (ANN) (Khan & Coulibaly 2010), support vector machine (SVM) (Tabari et al. 2012), and K-nearest neighbor (KNN) (Caraway et al. 2014). Later, the ML models considered are compared with the proposed improvised PCR (Sahriman et al. 2014) to state the advantages over other techniques. The comparison of considered models was performed with the help of performance evaluation parameters. The ranking of CMIP5 GCM models based on regions and parameters is identified using the suggested PCR model. A brief methodology for downscaling the CMIP5 GCM is represented in Figure 3.

The PCR applies ordinary least-squares regression to a different set of independent variables determined by the principal components.

The performance of each GCM based on the ability to capture the monotonic trend is evaluated using performance indices, such as normalized root-mean-square error (NRMSE) and the coefficient of determination (R²) (Woldemeskel et al. 2012; Roozbeh 2018). The equations for computing selected performance evaluation parameters are as follows.

Various research suggests several ranking techniques that were applied around the globe. However, very few studies were performed over the Indian subcontinent (Das et al. 2018). The present study considers the Cauvery river basin located in southern-peninsular India which is classified into the upper, middle, and lower basins for a better understanding of subbasin-level changes in climatic conditions over the past few decades. Subbasin-wise values of precipitation and temperature are analyzed to assess how various models represent the actual scenarios of the basin. A map illustrating the subbasins of the Cauvery river basin is presented in Figure 4. The subbasin-wise climate data are calculated using the station-wise-observed mean weather data for each subbasin. The reliability of each model is validated through performance evaluation parameters (NRMSE % and R²) of model results. The following section presents the results obtained from this study and the discussion related to it.

The performance of selected models in replicating the actual scenario based on the region and parameters is evaluated using nominated performance evaluation parameters (Ruan et al. 2018). The calibration and validation scores of each model are evaluated, and the performance evaluation scores of the calibration and validation dataset are represented in Table 2. The validation results show that all the CMIP5 GCMs were better at replicating temperature than precipitation in each subbasin considered (MacAdam et al. 2010; Das et al. 2018). Also, the PCR model performed remarkably well compared to other ML models (Noori et al. 2010; Chávez-Arroyo et al. 2013). The proposed technique enables the ranking of GCM concerning a local scale such as a specific river or subbasin. The variance between the observed and simulated climate data for all the regions and parameters considered in the study was below 7% in PCR, and the other models' results ranged between 12 and 30%. Moreover, the time engaged for the PCR model to train and test the data is almost half the time taken for other individual models selected in this study.

The overall length of historical subbasin-wise climate data for 55 years (1951–2005) is split into 75% calibration and 25% validation. The evaluation is carried out with a calibration period of 40 years (1951–1990) and a validation period of 15 years (1991–2005) for a better understanding of the performance of each ML model. The comparative bar plots clearly explain that the performance of every model during the validation phase is slightly lower than the calibration phase. It is also evident that the RMSE % values of the PCR model are far lower than other ML models for each subbasin and parameter. Furthermore, the R² values of the PCR model are above 0.9 for calibration and 0.7 for validation at every combination. This illustrates that the variance of the PCR model is very less, and the model performance is higher compared to other renowned ML models.

The priority of CMIP5 models was assessed by evaluating the performance of the PCR model using individual GCM. The priorities of these models were evaluated by providing equal scores to the performance evaluation parameters. The test statistics obtained from the analysis are presented in Table 3. The results state that CCSM4, inmcm4, EC-Earth, MIROC-ESM-CHEM, and BNU-ESM are good at projecting the historical precipitation events in all three subbasins. Whereas GFDL-CM3, CNRM-CM5, IPSL-CM5A-MR, and inmcm4 are performing exceptionally well in projecting the temperature changes (average, maximum, and minimum) over the Cauvery river basin.

Downscaling of climate data over a certain region requires the selection of suitable GCM and appropriate models to replicate the regional scenario. The model adopted for downscaling is expected to be effective and computationally economical. It is necessary to identify the suitable downscaling model for the selected region and the applicable GCMs for the selected parameters to represent the actual scenario. The performed downscaling technique is well suitable for the Cauvery river basin, and the applicability of the same at other basins depends on the performance metrics since each river basin has unique properties. The following conclusions have been drawn from this study: (i) the PCR downscaling model performs exceptionally well compared to other conventionally used ML models. (ii) The time taken to develop a PCR downscaling model for a given subbasin is reduced by almost half the time taken to build a conventional downscaling model. (iii) The variance in calibration results of the PCR model is ranged between 2 and 5%, whereas the validation results were <7% throughout all subbasins and for each parameter under consideration. (iv) The prioritizing of GCMs based on PCR proposed that for precipitation, CCSM4, inmcm4, and EC-Earth are best in representing the historical scenario. (v) The temperature statistics are captured well in GFDL-CM3, CNRM-CM5, and inmcm4. Also, inmcm4 stays among the top rank for precipitation and temperature for all subbasins.

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