Research papersIntercomparison of downscaling methods for daily precipitation with emphasis on wavelet-based hybrid models
Graphical abstract
Introduction
Studying the impact of global warming-induced climate change on water resources has become a key area of research in recent decades. To project future climate change scenarios, General Circulation Models (GCMs), which are computer models working at the global scale, are commonly used. These models generally produce climate outputs (e.g. precipitation, temperature) at coarser spatial scales, typically having horizontal grid size ranging from 100 km to 600 km. Such coarse-scale climate outputs, however, are not appropriate for most hydrologic studies, since hydrologic studies generally require data at much finer spatial scales corresponding to catchments. Therefore, to properly study the impact of climate change on hydrology and water resources, it is required to downscale the coarse-scale climate outputs to catchment-scale hydrologic variables (Sehgal et al., 2018, Wilby et al., 1998).
Downscaling of GCM outputs assumes that the local climate is a function of both the global atmospheric features (large-scale climatic conditions) and the local conditions (topography, land surface characteristics). Generally, deriving local climatic characteristics from GCM outputs through downscaling is a multistep process involving a multitude of assumptions and approximations. The methods for downscaling can be broadly classified into (1) Dynamic downscaling, and (2) Statistical downscaling.
Dynamical downscaling uses an appropriate GCM to generate regional climate models (RCMs) to be used at regional scales (Srinivas et al., 2014). The RCMs consider the coarse-scale GCM outputs as boundary conditions and detailed physical processes (complex terrain and land surface characteristics) at regional scale to model the regional-scale climate. The RCMs have better ability in capturing the basic regional patterns in time and space. Contrary to this, statistical downscaling models use empirical relationships (Wilby et al., 1998, Wilby et al., 1999) between predictors (atmospheric processes) and predictands (local climatic variables, such as rainfall) to generate the data at finer spatiotemporal resolutions. Even though dynamical downscaling has shown robust performances, it requires large amount of data, high level of expertise to analyze the results, and is also computationally intensive, which make it beyond the reach of institutions in most countries (Fowler et al., 2007, Hay and Clark, 2003, Sachindra et al., 2014, Mahmood et al., 2016). The number of experiments for climate scenarios is limited by the intensive computational requirements, which is a function of resolution, domain size, and accuracy. Further, the RCMs are limited by systematic errors branching from the GCMs, as the RCMs are strongly dependent on the outputs from the GCMs.
Compared to the RCM, statistical downscaling methods have gained much wider acceptance, due to their simplicity and low computational burden (Okkan and Inan, 2015, Rashid et al., 2015, Sachindra et al., 2018, Sachindra et al., 2016, Sehgal et al., 2018). However, establishing robust linkage between local climatic variables and large-scale atmospheric processes requires long historical data (Hay and Clark, 2003). Depending on the assumed relationship, statistical downscaling consists of a heterogeneous group of methods that vary in sophistication and applicability. These methods are classified into three categories: stochastic weather generators, weather classification-based approaches, and regression-based methods. Stochastic weather generators involve fitting probability distribution function to the variable. The weather classification-based methods involve classification of the state variables into weather types using the k-means algorithm in addition to the stochastic weather generation. The weather generator methods are based on the statistical properties of the climatic variables. They are sensitive to outliers in the training set and involve the generation of an ensemble of time series and statistical analysis of the results. Furthermore, the weather generator and weather classification methods are data-intensive, need large computational resources, and do not have prediction capability outside the historical data range. These issues led the regression-based methods to gain popularity, especially due to their ease in application (Sachindra et al., 2018).
The regression-based downscaling methods primarily depend on developing a predictor-predictand relationship. Some of these methods include Multiple Linear Regression (MLR) (Sachindra et al., 2014, Joshi et al., 2015, Duhan and Pandey, 2015, Ravansalar et al., 2017), Generalized Linear Model (GLM) (Asong et al., 2016, Beecham et al., 2014), Artificial Neural Networks (ANNs) (Yeditha et al., 2020, Chithra et al., 2016, Hassan-Esfahani et al., 2015), Genetic Programming (GP) (Coulibaly and Burn, 2004, Sachindra et al., 2018), Random Forests Regression (RFR) (Hutengs and Vohland, 2016, Pang et al., 2017, Mishra et al., 2017), Support Vector Machines (SVMs) (Kannan and Ghosh, 2011, Srinivas et al., 2014), and Extreme Learning Machines (ELMs) (Sachindra et al., 2018, Zhu et al., 2019). These studies have shown that the regression-based downscaling methods are robust and accurate in capturing the local climatic patterns. Further, the results from the past studies indicate that techniques based on artificial intelligence (AI), which take into account the complexity and nonlinearity in the relationship between predictors and predictands, perform better in comparison with the other (linear) methods.
Many past studies (Kurths et al., 2019, Guntu et al., 2020, Maheswaran and Khosa, 2015, Rashid et al., 2016) have reported that the relationship between rainfall and atmospheric variables is a function of time-scale. For instance, Maheswaran and Khosa (2015), studying the Cauvery River Basin in India, showed that the relationship between climatic indices and rainfall varied within the time–frequency domain. Therefore, the popular traditional approach to downscaling based on single-scale models might not be able to capture the variability at different time scales (Rashid et al., 2016). In light of this limitation with single-scale models, there has been a special emphasis on the multi-scale dynamics of the climate system involving interactions and feedbacks among different processes at different temporal and spatial scales (Agarwal et al., 2017, Agarwal et al., 2018, Agarwal et al., 2019, Carey et al., 2013, Maheswaran and Khosa, 2012a, Maheswaran and Khosa, 2012b, Addison, 2005, Torrence and Compo, 1998). In this regard, wavelets have become a highly popular tool. With their inherent advantages, including time–frequency localization and multiscale resolution, wavelets decompose the given time series into scale-specific components as proxies of the physical processes at those scales. Several studies (Kaheil et al., 2008, Adamowski and Sun, 2010, Maheswaran and Khosa, 2012a, Maheswaran and Khosa, 2012b, Nourani et al., 2014, Nourani et al., 2018, Rathinasamy et al., 2013, Niu and Sivakumar, 2013, Beecham et al., 2014, Shafaei and Kisi, 2017, Nourani et al., 2009, Nourani and Farboudfam., N, , 2019, Baghanam et al., 2019, Rashid et al., 2018) have shown that wavelet transform-based modelling has aided in unravelling the multiscale dynamics in different processes. A recent study by Sun et al. (2019) investigated the efficiency of the wavelet-based models over the single (stochastic, ANN, regression) models for daily streamflow forecasting and reported better performance of the wavelet-based models. On similar lines, Ravansalar et al. (2017) used wavelet transform-based linear genetic programming (WLGP) models for predicting monthly streamflow in Iran. They found that the wavelet-based models significantly improved the flow prediction in comparison with GP, ANN, and MLR models. Djerbouai and Souag-Gamane (2016) showed that the accuracy of drought prediction in the Karkheh basin in Iran improved with wavelet pre-processing of inputs when compared to single models without wavelets.
Most of the above studies have combined the wavelets with other models in developing hybrid models for hydrologic forecasting applications. Even though there has been extensive research on the application of wavelets for hydrologic forecasting, there have only been very few studies on the application of wavelets for statistical downscaling. Among such studies, Kaheil et al. (2008) combined wavelets and SVM for downscaling and forecasting evapotranspiration. Rashid et al. (2015) used the wavelet GAMLSS model for downscaling of precipitation in the Onkaparinga River catchment in South Australia. The results showed that the WT-GAMLSS models were accurate in reproducing the time series properties when compared to the orthodox GAMLSS models. More recently, Lakhanpal et al. (2017) used a wavelet-based second-order Volterra model for downscaling monthly temperature in the Krishna River Basin in India and found that the wavelet-Volterra model performed better when compared to other models, including ANNs and MLR. Sehgal et al. (2018) used a similar model for downscaling monthly precipitation using the NCEP data and showed that the model results were closer to the local precipitation.
It is important to note that most of the above-mentioned studies have focussed on downscaling of precipitation (and other variables) at the monthly scale and there have hardly been any studies on evaluating the hybrid models for precipitation downscaling at the daily scale, despite the fact that downscaling of precipitation at the daily scale (and even sub-daily scales) is very important, especially in the context of extreme events. Furthermore, thus far, there has not been any serious attempt to conduct a detailed investigation to compare different methods for downscaling of daily precipitation.
In view of these, the present study proposes the application of wavelet-based hybrid methods for statistical downscaling of daily precipitation. The proposed wavelet-based hybrid models are applied for downscaling daily precipitation in five selected grid points (in different locations) in the Krishna River Basin in India, with varying climatic characteristics. The performances of these models are also compared with some popular models, including MLR, SDSM, GP, and single-scale ANN models.
Section snippets
Study area and data
The Krishna River Basin, being the fourth-largest basin in the Indian peninsula, originates at Mahabaleshwar in the state of Maharashtra, India and joins the Bay of Bengal at Hamasaladeevi (near Koduru) in Andhra Pradesh (Fig. 1). The catchment of the basin spreads between 73° to 82° E and 13° to 19° N, covering a total area of 260,401 km2. Fig. 2(a–d) shows the topography, mean annual rainfall distribution, Land Use Land Cover (LULC), and climate classification, respectively, of the Krishna
Methodology
In this study, several traditional and modern methods are applied for downscaling daily precipitation in the Krishna River Basin and for comparing their performances. These methods include Multiple Linear Regression (MLR), Statistical Downscaling Model (SDSM), Genetic Programming (GP), Artificial Neural Networks (ANNs), and Wavelet–Neural Network (WNN) hybrid model. The first four models are single-scale models, while the last one is a multiscale model. A brief description of these methods is
Model application
In any downscaling strategy, the selection of the predictors and its spatial domain plays a major role. Based on the climatic characteristics of the Krishna River Basin and reports by some previous studies (Lakhanpal et al., 2017, Sehgal et al., 2018), a total of 16 probable predictors is considered, as listed in Table 1. The list of probable predictors considered here is similar to that used by Sehgal et al. (2018) for the Krishna River Basin, Sachindra et al. (2018) for Australia, and Yang et
Discussion
In this study, wavelet-based hybrid models were proposed for downscaling daily precipitation and their performances were compared with those of some key traditional and other modern methods, including MLR, SDSM, GP, and ANN models. Among the nine downscaling methods applied in this study, machine-learning methods were found to generally outperform the basic MLR and SDSM. Among the single-scale machine-learning models, the NARX-NN model outperformed the FF-NN model and the GP model. The better
Conclusions
In this study, nine downscaling models, including MLR, SDSM, GP, ANN, and wavelet-based hybrid models, were developed and applied for downscaling daily precipitation at five selected grid points in different locations in the Krishna River Basin in India. Using the NCEP data and the IMD data over the period 1948–2017, calibration and validation of the models were carried out. Based on the results obtained for the five selected grids, in terms of several performance measures (NRMSE, NSE, R2, and
CRediT authorship contribution statement
Yeditha Pavan Kumar: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft. Rathinasamy Maheswaran: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing. Ankit Agarwal: Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft, Writing - review
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
RM gratefully acknowledges the funding received through the Inspire Faculty Award (IFA-12/ENG 28) from the Department of Science and Technology, India. AA acknowledges the funding support provided by the Indian Institute of Technology Roorkee through Faculty Initiation Grant number IITR/SRIC/1808/F.I.G and COPREPARE project funded by UGC and DAAD under the IGP 2020-2024. BS acknowledges the support from the IIT Bombay seed grant (RD/0519-IRCCSH0-027). The authors would like to thank the three
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