Statistical downscaling of the General Circulation Model (GCM) simulations are widely used for accessing climate changes in the future at different spatiotemporal scales. This study proposes a novel Statistical Downscaling (SD) model established on the Convolutional Long Short-Term Memory (ConvLSTM) Network. The methodology is applied to obtain future projection of rainfall at 0.25° spatial resolution over the Indian sub-continental region. The traditional multisite downscaling models typically perform downscaling on a single homogeneous rainfall zone, predicting rainfall at only one grid point in a single model run. The proposed model captures spatiotemporal dependencies in multisite local rainfall and predicts rainfall for the entire zone in a single model run. The study proposes a Shared ConvLSTM model providing a single end-to-end supervised model for predicting the future precipitation for entire India. The model captures the regional variability in rainfall better than a region-wise trained model. The projected future rainfall for different scenarios of climate change reveals an overall increase in the rainfall mean and spatially non-uniform changes in future rainfall extremes over India. The results highlight the importance of conducting in-depth hydrologic studies for different river basins of the country for future water availability assessment and making water resource policies.

  • Statistical downscaling with superior predictive capabilities.

  • Assessment of four different statistical downscaling techniques.

  • Coverage of entire Indian land mass at finer spatial and temporal scales.

  • Capability to capture spatial non-homogeneity around India.

  • Best capturing of the extreme events and distribution of daily precipitation around India.

The changes in Earth's climate and their associated impacts on different components of the ecosystem have been earning increasing human attention in recent years. Unexpected spurts of extremely high temperature and precipitation, and intensification of hydrological cycles, are some of the globally experienced implications of climate change (IPCC 2012). The country of India is no exception to this. The climate change repercussions portray a bleak picture for India, for two main reasons. First, as the agricultural activities forming the backbone of the Indian economy largely depend on the monsoon rainfall, any changes in the features of monsoon rainfall directly lead to changes in crop productions, which affects the livelihoods of the greater part of the country. Secondly, the heavy population density of the country increases its vulnerability to climate extremes such as heat–cold waves, heavy precipitation–floods, and cyclones.

The knowledge of the long-term changes in climate conditions, scientifically termed as climate projections, is highly important in generating strategic knowledge to overcome such disastrous situations. The well-informed planning policies conditioned on realistic and region-specific future projections form a crucial information source in dealing with the impact of climate change. The impacts of global scale climate change on a regional scale are in general evaluated by downscaling of the simulated large-scale climate variables of the General Circulation Models (GCMs) (Intergovernmental Panel on Climate Change – Task Group on Scenarios for Climate Impact Assessment 1999; Prudhomme et al. 2002). Although the GCMs are capable of projecting large-scale circulations and spatially uniform climate variables such as temperature and pressure with some skill, they often fail to capture the spatially non-uniform fields such as precipitation (Hughes & Guttorp 1994; Meehl et al. 2005). At the same time, GCM outputs cannot be directly applied for impact assessment owing to their coarser spatial resolution ranging from 0.5° to 3°. The application of downscaling therefore becomes essential to have a realization of the regional-scale hydrometeorological variables.

The downscaling process aims at obtaining data at fine resolution with the help of the available coarse-scale information. There are a plethora of methodologies categorized under this topic. These methodologies are broadly classified into Dynamical Downscaling (DD) and Statistical Downscaling (SD). DD involves operating a physics-based high-resolution Regional Climate Model (RCM) taking input from the coarse-resolution GCM dataset. DD is computationally expensive. At the same time, SD deals with developing a statistical relationship between the large-scale atmospheric variables (predictors) and a fine resolution surface variable of interest (predictant). SD models are usually computationally inexpensive.

Different SD techniques have been developed, which are overall categorized in the following three classes: (1) Weather Generators, (2) Weather Typing, and (3) Transfer function. The weather generators are also considered as random complex number generating functions on the basis of witnessed structures of climate variables (Katz & Parlange 1996). Their outputs are similar to daily weather data at a specific place (Wilks & Wilby 1999; Soltani & Hoogenboom 2003; Wilby & Dawson 2007). The weather typing methodologies encompass combining atmospheric circulation variables into different categories (Wilby 1998). This is a standard approach to SD. The various downscaling methods differ mainly based on the predictor variables, selection of statistical transfer function, or the mathematical procedure followed. Linear and non-linear regression (Wilby et al. 2004), Support Vector Machine (SVM) (Vapnik et al. 1995), Artificial Neural Network (ANN) (Karamouz et al. 2009), canonical correlation (Conway et al. 1996), and Relavance Vector Machine (RVM) (Ghosh & Mujumdar 2006) have been used to establish the relationship between predictor and preditand. Transfer functions or Regression are popular because of their simplicity, but they cannot model the variability and extreme events very well. Generalized Linear Model (GLM) (Yang et al. 2005), Markov chain models (Hughes et al. 1999), hidden Markov chain models (Bellone et al. 2000), spell length models (Lall et al. 1996), Conditional Random Field (CRF) (Raje & Mujumdar 2009), beta regression (Mandal et al. 2016), fuzzy logic-based methodologies (Ghosh & Mujumdar 2006), Bayesian Joint Probability (BJP) modelling methodology (Robertson & Wang 2009), ANN-based methods (Crane & Hewitson 1998; Mondal & Mujumdar 2012), Machine Learning Models (Kumar et al. 2023), and Stochastic Space Random Cascade (SSRC) methodology for precipitation downscaling with the help of GCM data (Groppelli et al. 2011) are few of the documented SD approaches used for climate variable projections.

The SD models show credibility in capturing certain properties of the evidentiary target datasets. However, some limitations of the data-driven approaches lower the overall skills. The previously developed SD methodologies based on kernel regression (KR) model (Kannan & Ghosh 2011), LSTM model (Misra et al. 2017), SVM (Ghosh 2010), and CRF (Raje & Mujumdar 2009) depict different skills in capturing the statistical properties and spatial structure of the Indian summer monsoon rainfall (ISMR). Most SD models underperform mainly because they flatten out the gridded input data in one dimension before passing it to the mathematical modelling framework. Furthermore, the traditional multisite downscaling models typically perform downscaling on a single homogeneous rainfall zone, predicting rainfall at one grid point in a single model run.

Convolutional Neural Networks (CNNs) (Krizhevsky et al. 2012) were designed to deal with multidimensional input volumes. CNN helps in maintaining the spatial structure of input data. Therefore, the predictor inputs can directly be passed to the CNN model without distorting their spatiotemporal structure. Vandal et al. (2017) used CNNs for downscaling daily precipitation over the continental United States. CNNs seldom fail to capture temporal dependencies in the input data because of the missing element of temporal corrections in their architecture (Vandal et al. 2017). At the same time regression-based SD models, e.g. KR (Kannan & Ghosh 2013), pose limitations to capture extremes values (Salvi et al. 2013). Addressing these complications, Shi et al. (2015) proposed the architecture for Convolutional Long Short-Term Memory (ConvLSTM). The study showed that the ConvLSTM network captures both temporal and spatial correlations in input better than CNNs.

This study proposes a modified approach to ConvLSTM, termed as ‘Shared ConvLSTM framework,’ as an SD model. This model is applied to obtain rainfall projections over the Indian land mass. The genesis of the name ‘Shared’ lies in the previous works by Kannan & Ghosh (2013), where the homogeneous regions lie for which the rainfall and predictor data share spatial relationships and have overlapping boundaries. This study is planned to explore the advantage of using the rainfall and predictor data for the whole of India for training a single model, which we name the Shared ConvLSTM model. The paper is organized as follows: Section 2 describes the study region and data used, Section 3 explains the methodology adopted to obtain the rainfall projections. Results and discussions are provided in Section 4, followed by listing of major contributions from this work in Section 5, and summary and conclusion in Section 6.

The study uses three datasets, namely, gridded precipitation data, climate reanalysis data, and GCM data. The gridded daily rainfall data for the Indian land mass (6.5°N–38.5°N and 66.5°E–100.5°E) at spatial resolution 0.25° latitude × 0.25° longitude is obtained from the India Meteorological Department (IMD) (Rajeevan & Bhate 2008). These gridded precipitation data provide a total of 4,954 grid points at 0.25° spatial resolution constituting the entire Indian landmass. The rainfall projection is obtained for all these (4,954) grid points. The gridded rainfall data at 0.25° spatial resolution is referred to as observed rainfall with the following discussion.

The climate variables that are realistically simulated by GCMs are selected as input to the SD models (termed as predictor variables) to simulate the local-scale climate variable (termed as predictand variable), which is rainfall in this study. Following Salvi et al. (2013) and Shashikanth et al. (2017), this study uses five climate variables as predictors representing the atmospheric circulation patterns of the western coast. These predictor variables are, namely, surface-level air temperature (AIRTEMP), mean sea level pressure (MSLP), specific humidity (SHUM), horizontal component of wind velocity (UWIND), and vertical component of wind velocity (VWIND). The gridded predictor variable dataset having a spatial resolution of 2.5° latitude × 2.5° longitude spanning the region 5°N–40°N and 65°E–100°E is obtained from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis dataset (Kalnay et al. 1996). Akhter et al. (2019) evaluated the performance of SD models based on selected atmospheric predictor variables in providing simulations of monsoon precipitation over India and identified that most of these predictors show better predictive skills over different climate zones of the country. The geographical extent of the predictor variables are selected on the basis of Salvi et al. (2013). Here it is important to mention that some other reanalysis datasets, which may be seen as a superior choice considering the relative coarse resolution of NCEP data, are not selected for the following two major reasons. First, the NCEP data allows a longer period of analysis (1969–2008) and secondly, the methodology is developed to support climate conditions at coarse resolution.

The future state of the selected climate variables is obtained from simulations by the Canadian Centre for Climate Modelling and Analysis (CCCma), using the second generation Earth System Model (CanESM2). CanESM2 provides long-term projection of climate variables from the atmosphere-ocean model coupled to a terrestrial and ocean carbon model. CanESM2 is credibly used to study climate variability, to understand the processes governing the climate system and also to make quantitative projections of future long-term climate change. The model outputs utilized in this analysis are collected from the PCMDI CMIP5 data archive available at (https://pcmdi.llnl.gov/mips/cmip5). We obtain the historical outputs from CCCma-CanESM2 available for the period 1969–2005. The future projections of the selected five climate variables are obtained for the period 2030–2100 for the emission scenarios called Representative Concentration Pathway 4.5 (medium) and RCP 8.5 (high). CCCma-CanESM2 provides required climate data projections for different important climate variables for the emission scenarios (RCPs) prescribed by IPCC for the period of the entire 21st century. These GCM outputs were credibly applied by previous researchers for ISMR studies (Shashikanth et al. 2014; Sarthi et al. 2015; Preethi et al. 2017; Pichuka & Maity 2018; Upadhyay et al. 2021; Chandu et al. 2023).

The use of multiple GCMs and the ensemble approach to incorporate GCM uncertainty have significant effects on projections (Sharma 2000; Christensen & Lettenmaier 2007; Zhu et al. 2008; Sun & Chen 2012; Ahmed et al. 2013; Das & Nanduri 2018). Similarly, the uncertainty associated with the application of different climate reanalysis datasets is also not addressed by this study. This study uses the output from a single GCM and single reanalysis dataset for a complete focus on the methodology development and its comparative evaluation to three established methodologies for downscaling of daily precipitation over the Indian sub-continental region. Here we would like to mention that the study is conceptualized so as to develop a novel downscaling approach that serves as a single end-to-end supervised model for predicting the future precipitation for the entire Indian region and capturing the regional variability of ISMR. The following section elaborates on the methodology development.

SD methodology statistically links coarse-resolution predictor variables with the fine resolution predictand variable. This study aims to propose a computationally efficient and reliable SD methodology to obtain realistic projection of ISMR. We obtain projections of ISMR at 0.25° resolution using a ConvLSTM and Shared ConvLSTM modelling framework. The results of the obtained projections are viewed in light of those from two most recently used approaches, non-parametric KR (Salvi et al. 2013) and LSTM (Misra et al. 2017). A brief description of KR and LSTM methodologies is provided in Supplementary material, Sections S1 and S2, respectively. This section provides an overview of the modelling framework and data pre-processing followed by the steps for developing a standard ConvLSTM model as well as a Shared ConvLSTM model.

SD framework and data pre-processing

The overview of the ConvLSTM-based SD methodology is represented in Figure 1. The basic steps of the ConvLSTM-based SD model are as follows: Preparation of the predictor dataset, and application of the ConvLSTM model. The model is trained with the help of NCEP/NCAR reanalysis dataset of the period 1951–2000, and is validated using data of the period 2001–2013. The training period of 50 years is considered long enough to establish the correctness of an SD model. The model trained and tested using NCEP/NCAR reanalysis dataset is applied to the GCM data. The model is first applied to historical GCM data of the period 1969–2005, to check the correctness of the developed model application for GCM dataset. The model validated for GCM historical data is thereafter applied to GCM near future data of the period 2030–2070 and far future 2070–2100 to obtain rainfall projections under changing climate conditions. The GCM data depicts systematic variation with respect to the climate reanalysis data, known as bias. Bias in GCM data may result in uncertainty in model predictions. Therefore, it is essential to bias correct the GCM before it is taken as input to the model. The bias correction of GCM predictors is carried out prior to SD, to reduce systematic biases in the mean and variance of various GCM predictors. The bias correction is carried out with respect to that of NCEP/NCAR predictors. Supplementary material (Section S3) presents the description of the quantile-based bias correction method for GCM predictors (Li et al. 2010). Validation of the bias correction procedure is included with Supplementary material (Figure S3(a)–(d)) presenting a spatial plot of rainfall mean for the historical period (1979–2005) for GCM raw data along with NCEP data and GCM bias-corrected data.
Figure 1

Overview of the proposed ConvLSTM- and Shared ConvLSTM-based downscaling algorithms. For region-wise ConvLSTM models, the output data for training the model is the actual gridded precipitation data formed by gridding of the region-wise data, whereas that for the Shared ConvLSTM model is the actual gridded and zero-padded precipitation data, other steps remain the same.

Figure 1

Overview of the proposed ConvLSTM- and Shared ConvLSTM-based downscaling algorithms. For region-wise ConvLSTM models, the output data for training the model is the actual gridded precipitation data formed by gridding of the region-wise data, whereas that for the Shared ConvLSTM model is the actual gridded and zero-padded precipitation data, other steps remain the same.

Close modal
To account for highly variable climate patterns of the Indian landmass, the downscaling is performed independently for the seven climatologically homogeneous zones of the country (Parthasarathy et al. 1996). The extents of these regions are illustrated in Figure 2(a). The spatial extents for the NCEP/NCAR predictor variables used for predicting rainfall in these regions are shown with the boxes bounding over the rainfall zones (Figure 2(b), Table 1). The geographical extent of predictor region is selected following Salvi et al. (2013). Apart from the climate data representing the large-scale circulation over a greater region around the selected region (zone), lag-1 (previous day) rainfall of the zone is also included in the predictor dataset. The ConvLSTM model mandates the data input in the form of regular shaped boundaries (square/rectangular box). Therefore, the smallest square bounding box covering all the grid points in a particular zone is selected for training the ConvLSTM model.
Table 1

Extent of rainfall zones in India

ZoneLatitude (°N)Longitude (°W)Zone code
Jammu and Kashmir 27.5–40 70–82.5 
Western 17.5–35 65–80 
Northern 15–32.5 72.5–92.5 
Southern 5–22.5 70–90 
Northeastern hills 25–32.5 90–100 
Northeastern 20–32.5 85–100 
Central 12.5–30 70–87.5 
ZoneLatitude (°N)Longitude (°W)Zone code
Jammu and Kashmir 27.5–40 70–82.5 
Western 17.5–35 65–80 
Northern 15–32.5 72.5–92.5 
Southern 5–22.5 70–90 
Northeastern hills 25–32.5 90–100 
Northeastern 20–32.5 85–100 
Central 12.5–30 70–87.5 
Figure 2

Meteorologically homogeneous regions in India (a) and the spatial extent of predictors selected for each region (b). The latitudinal and longitudinal extents of the region-wise predictors selected for the seven meteorologically homogeneous regions are shown with rectangles of the same colour as the regions. For all India, the entire predictor region from 5° to 40°N, 65°to 100°E is selected. The cross-marks represent the centre of the predictor grids.

Figure 2

Meteorologically homogeneous regions in India (a) and the spatial extent of predictors selected for each region (b). The latitudinal and longitudinal extents of the region-wise predictors selected for the seven meteorologically homogeneous regions are shown with rectangles of the same colour as the regions. For all India, the entire predictor region from 5° to 40°N, 65°to 100°E is selected. The cross-marks represent the centre of the predictor grids.

Close modal
The selected NCEP/NCAR variables, namely, MSLP, SHUM, horizontal component of wind velocity (UWIND), and vertical component of wind velocity (VWIND), have different numerical ranges. Therefore, it is difficult to utilize them together as a combined predictor dataset. The process of standardization of the predictor dataset is applied to normalize the variables to the range [0, 1]. The standard deviation and mean of predictor variables is computed with the help of a daily dataset of respective predictor variables for monsoon period (JJAS) for the defined time period. Large-scale climate predictor variables are standardized by subtracting the mean and dividing by the standard deviation of the respective variables taken over the predefined period. To unify the size (geographical extent) of grids within the complete predictor dataset, the NCEP/NCAR predictor dataset having a geographical resolution of 2.5° is interpolated to grid size 0.25°, to match the size of the rainfall data. The interpolation of NCEP/NCAR predictor dataset is performed using the bilinear interpolation methodology. NCEP/NCAR data and gridded lag1 rainfall data are concatenated to form the input. For example, for the central region, the size of the gridded precipitation data is 48 × 48. The size of the NCEP/NCAR data is 8 × 8 × 5 (for 5 predictor variables), which is interpolated to 48 × 48 × 5. Hence, the size of the final input to the model is 48 × 48 × 6. To ensure that the interpolated variables do not lose any information and maintain their spatial structure, we check the statistical properties of selected variables at each grid point. Figure 3 presents the mean value of NCEP/NCAR predictor variables before and after bias correction.
Figure 3

Mean value of NCEP/NCAR predictor climate variables over Indian landmass for JJAS months from 1951 to 2013. (a) surface air temperature, (b) mean sea level pressure, (c) surface specific humidity, (d) surface uwind, (e) surface vwind. (f) to (j) same as (a) to (e) but interpolated to 0.25° resolution to match with the IMD gridded rainfall data.

Figure 3

Mean value of NCEP/NCAR predictor climate variables over Indian landmass for JJAS months from 1951 to 2013. (a) surface air temperature, (b) mean sea level pressure, (c) surface specific humidity, (d) surface uwind, (e) surface vwind. (f) to (j) same as (a) to (e) but interpolated to 0.25° resolution to match with the IMD gridded rainfall data.

Close modal

The traditional multisite downscaling models typically perform downscaling on a single homogeneous rainfall zone, predicting rainfall at one grid point in a single model run. In contrast to this, the proposed ConvLSTM-based modelling framework projects rainfall for all the grids in a zone with a single model run. Further to this, the study proposes a Shared ConvLSTM model with a novel modelling framework that shares a ConvLSTM model across multiple neighbouring regions. The Shared ConvLSTM model captures the similarity in rainfall patterns of the neighbouring regions and customizes it to individual grid points. This downscaling approach provides a single end-to-end supervised model for predicting the future precipitation series for entire India. It captures the regional variability in rainfall better than a region-wise trained model. The following sub-section provides a description and functioning of the ConvLSTM model applied to the pre-processed predictor dataset. Importantly, this model does not need specific feature engineering and can learn the features by itself. Moreover, ConvLSTMs can take three-dimensional inputs. The dimensionality reduction techniques such as Principal Component Analysis (PCA) reduce the dimensions of predictor data; however, this may cause loss of a few important features. The proposed methodology completely omits the commonly mandated step of dimensionality reduction, and hence preserves the complete information of the predictor dataset.

ConvLSTM model

LSTM is a Deep Learning (DL), Recurrent Neural Network (RNN) model proposed by Hochreiter and Schmidhuber. LSTM is designed to model temporal sequences with their long-range dependencies (Hochreiter & Schmidhuber 1997). A standard Neural Network (NN) contains several simple, connected processors termed as neurons, each of them producing a series of real-valued activations. The input neurons are triggered with the help of sensors that perceive the environment, at the same time the other neurons are triggered with the help of the weighted connections with previously activated neurons. The network may also function in a reverse order, that is, few of the neurons triggering actions that influence the environment. Recurrent Neural Networks (RNNs) are special kinds of neural networks designed to handle sequence dependence. The NN credit assignment or learning is referred to as finding optimal weights that help NN demonstrate the desired behaviour. A simple traditional NN that captures information in input fails to capture long-term information dependency in input data. As the name suggests, LSTMs are specially designed to remember information for long periods and avoid the problem of long-term dependency. DL in the context of NN is referred to assigning credit across long causal computational stages, where each stage governs a non-linear comprehensive activation of the network. LSTM is a widely used RNN that is proven to work well on a large range of problems, such as: language modelling, image captioning, speech recognition, and translation.

LSTMs function with a chain-like structure, the same as a traditional RNN, except that the repeating module has four interactive network layers in place of a single NN layer. LSTM removes or adds information to the cell state through a carefully controlled structure termed as gate. Gates are composed of a point-wise multiplication operation and sigmoid neural net layer. An LSTM has three different sigmoidal gates to determine the state of the cell. The sigmoid layer outputs number between zero and one, describing the weight of the information retention, i.e. value zero means no retention while the value one means a complete retention.

The first sigmoid layer that decides on the information that will be discarded is termed as the ‘forget gate layer’. For any time step (t) a forget gate layer considers hidden output at the previous time step (t − 1) denoted as ht−1 and the current input data denoted as xt to output between 0 and 1 corresponding to each number in the cell state Ct−1 given as
formula
(1)

Here, W denotes the weight matrix, suffixes x, f, t, h denote variable, forget layer, time step, and hidden output, respectively.

The next step decides new information retention in the cell state. This is achieved in two different parts. First, a sigmoid layer termed as the ‘input gate layer’ decides the values to be updated. Second is the tanh layer. This layer creates a vector of new candidate values, Ĉt, that could be added to the state.
formula
(2)
formula
(3)
The following step combines these two inputs to update the old cell state, Ct−1, to the new cell state Ct. This is achieved by multiplying the old state by ft, discarding information, and adding it * Ĉt to determine the new scaled state of the cell at time step t.
formula
(4)
The output of an LSTM cell is determined based on cell state Ct. The filtered output is determined by running a sigmoid layer deciding the parts of the cell state that will be retained in the output. To achieve this, the cell state is set through tanh to confine the values to range from −1 to 1 and multiply it by output of the sigmoid gate.
formula
(5)
formula
(6)
ConvLSTM is a variation of LSTM that comprises a convolution operation inside an LSTM cell. The fully connected RNN layers in a standard LSTM are replaced by convolutional layers in a convolutional LSTM block. The model, therefore, consists of 2 basic units, convolutional layers and LSTM cells. These layers are tailored for spatiotemporal input–output based prediction problems, as here in the case of rainfall projections. A basic unit of a convolutional LSTM cell is depicted in Figure 4.
Figure 4

Basic repeating module in a standard ConvLSTM. The notation it, ft and ot denote the input, forget, and output gates at time step ‘t’, respectively. W, xt, Ct, xt−1, ht−1, xt+1, and xt+1 denote the weight matrix, current input data, cell state at time step t, input and hidden state output at previous time step (t − 1), and input and hidden state output at the next time step (t + 1), respectively. Each rectangular box denotes a single time step for the same ConvLSTM block. All the rectangular boxes are similar. The detailed architecture of each block is presented in the middle box.

Figure 4

Basic repeating module in a standard ConvLSTM. The notation it, ft and ot denote the input, forget, and output gates at time step ‘t’, respectively. W, xt, Ct, xt−1, ht−1, xt+1, and xt+1 denote the weight matrix, current input data, cell state at time step t, input and hidden state output at previous time step (t − 1), and input and hidden state output at the next time step (t + 1), respectively. Each rectangular box denotes a single time step for the same ConvLSTM block. All the rectangular boxes are similar. The detailed architecture of each block is presented in the middle box.

Close modal
Convolutional LSTMs (Krizhevsky et al. 2012) can be used to model dependencies between a three-dimensional input–output volume with temporal dependencies, which is the same as a rainfall projection problem. In this study, large-scale climate circulation and lag-1 rainfall act as predictors or the input volume and the gridded rainfall data is taken as the output volume. The ConvLSTM model is thus applied to all grid locations in the input and output at the same time. The network connections in a ConvLSTM, as shown in Figure 5, are built in such a way that it captures the relationship between the target (rainfall variable) at a grid point and the input (predictor variables) at all the grid locations in the input volume. A high degree of autocorrelation is generally observed in the daily rainfall series of any region. This autocorrelation can improvise the predictive ability of a downscaling model by a significant proportion. Capturing autocorrelation in daily rainfall series is climatologically important in daily rainfall prediction studies. The ConvLSTM model thus essentially captures the relationship between large-scale predictors and local rainfall. It also captures the spatial correlation between both input predictors and target rainfall fields. Due to the backward network connections in the ConvLSTM model, (as illustrated in Figure 4), the model automatically takes care of the autocorrelation in the rainfall series. Shi et al. (2015) used the ConvLSTM model for precipitation nowcasting, showing a high accuracy in precipitation prediction. This study demonstrates that the model possesses a noteworthy skill of capturing all these dependencies and the autocorrelation in the daily rainfall series.
Figure 5

Overview of the ConvLSTM Methodology: Flowchart for statistical downscaling using ConvLSTM methodology.

Figure 5

Overview of the ConvLSTM Methodology: Flowchart for statistical downscaling using ConvLSTM methodology.

Close modal

ConvLSTM model training

A four-layer Convolutional LSTM model is trained with the input dataset and the current day rainfall as output. This model, as depicted in Figure 5, consists of four ConvLSTM layers. The first three layers are with 64 filters, each having size 5 × 5, whereas the last layer has 1 filter of size 1 × 1, which enables us to get the output of the desired volume (48 × 48 × 1 in case of central region). Here, it is essential to note that there are different combinations of hyperparameters for training the ConvLSTM model. The model training is performed using all possible combinations of 1–5 ConvLSTM layers, each layer with filter size 3 × 3, 5 × 5, and 7 × 7. The number of filters is chosen to be 4, 8, 16, 32, 64, and 128, and the learning rate is selected as 0.0001, 0.001, 0.01, 0.1. The number of iterations is chosen from 5 to 500, with a stride of 5. Following this, the best performing model is identified based on the weighted mean squared error estimation.

The selection of optimization methodology plays a key role in the training of the DL models. The advanced optimization method, namely, Adam (Kingma & Ba 2015), is adopted especially for training very deep networks. Here, the Adam optimizer is selected, mainly as it is an optimized version of stochastic gradient. This optimization algorithm is widely used for finding minima for convex optimization problems. It is generally expected to reach the global minima in a certain number of iterations if the learning rate is carefully chosen. The model is trained with an Adam optimizer with an initial learning rate of 10−5.

The model is developed in Tensorflow (Abadi et al. 2016) using Keras library and Python on a NVIDIA Tesla P100-PCIE GPU. The rainfall is highly variable across the grid points in a region, therefore, to appropriately capture both mean and extremes of the rainfall at every grid point in a region, weighted normalized mean squared error (WNMSE) ConvLSTM loss function is used. The WNMSE applies weighting of individual observed rainfall values at every grid in the training set. The rainfall data have a vastly skewed distribution with values greater than 30 mm per day covering approximately 5% of the entire training set over the Indian region. The loss is summation of losses over all grid points within the zone for which prediction of the rainfall distribution is made. The training loss function for the ConvLSTM model is as follows:
formula
(7)
where n is a subset of the gridded output data having size r×c, ti is the true value of the target, and mi is the mean value of the predictive distribution.
The following weighting scheme is used for model evaluation:
formula
(8)

The trained model is validated using the predictor dataset for the validation period. Multiple efforts of model training and testing are carried out to obtain an optimum weight matrix. The LSTM model is trained and validated with the help of historical GCM data. The trained model is applied to the future GCM data to generate future rainfall projections. This modelling framework is applied independently for each rainfall zone. The basic architecture of the ConvLSTM models for each region is depicted in Table 2.

Table 2

Region-wise bounding boxes for gridded rainfall

ZoneLatitude (°N)Longitude (°W)Bounding box
Jammu and Kashmir 27.5–40 70–82.5 36 × 36 
Western 17.5–35 65–80 48 × 48 
Northern 15–32.5 72.5–92.5 54 × 54 
Southern 5–22.5 70–90 48 × 48 
Northeastern hills 25–32.5 90–100 25 × 25 
Northeastern 20–32.5 85–100 42 × 42 
Central 12.5–30 70–87.5 48 × 48 
ZoneLatitude (°N)Longitude (°W)Bounding box
Jammu and Kashmir 27.5–40 70–82.5 36 × 36 
Western 17.5–35 65–80 48 × 48 
Northern 15–32.5 72.5–92.5 54 × 54 
Southern 5–22.5 70–90 48 × 48 
Northeastern hills 25–32.5 90–100 25 × 25 
Northeastern 20–32.5 85–100 42 × 42 
Central 12.5–30 70–87.5 48 × 48 

Gridded rainfall bounding boxes are taken as square shaped so that the NCEP predictor input volumes can be easily interpolated to the shape of the gridded rainfall. The regridded data are concatenated to form the final ConvLSTM-based downscaling model input. For example, for all India rainfall data, NCEP predictors are of size 15 × 15 and gridded rainfall is of size 129 × 135. So, here we need to make the rainfall data of a shape such that the predictors can be easily interpolated to. Hence, we take a larger region-based rainfall data of size 135 × 135. We could have also padded the data with zeros instead of taking a larger region. The experimental investigation revealed that taking lag-1 rainfall from a larger region as input in the loss function worked better than the zero-padding approach.

Shared ConvLSTM modelling framework

The previous works in the literature proposed region-based downscaling methodologies for larger regions of heterogeneous rainfall patterns like India by dividing the region into homogeneous zones. This study also applied the same design with the previous models. NN have been shown to benefit from sharing of related data and multitasking. Therefore, this study considers proposing a model, termed as Shared ConvLSTM. The Shared ConvLSTM model tries to explore whether the rainfall zones and the corresponding predictor data taken as a whole improve or worsen the results. This modelling framework considers a gridded rainfall dataset of size 129 × 135 and a spatial resolution of 0.25° × 0.25°. To ease training, we convert it to size 135 × 135 by padding with zeros. The zeros in the region outside the Indian landmass are ignored during training by the use of the weighted loss function WConvLSTM. The NCEP/NCAR dataset size for the whole of India that we are using is 15 × 15 at a resolution of 2.5 × 2.5°. We interpolate it to size 135 × 135 using bilinear interpolation as discussed previously. The basic architecture of this model is the same as that presented in Figure 5. The basic steps are similar to the ConvLSTM model with the following differences: gridded precipitation data with padding are used as the predictor and the interpolated NCEP/NCAR data are used as predictand for training the model. NCEP/NCAR data and gridded lag-1 rainfall data are concatenated to form the final input to the model. The four-layer ConvLSTM model is trained with this input and current day rainfall as output. This model is trained using Adam optimizer with an initial learning rate of 10−5 and the same WNMSE ConvLSTM loss function as discussed previously. The trained model is then validated using NCEP/NCAR data and rainfall data for the validation period. Bias correction of GCM data is performed followed by validating the model for CanESM2 GCM data for the historical period. The future rainfall predictions are generated using CanESM2 GCM data for the future periods.

This section provides a brief discussion regarding the obtained results and their interpretation. It presents details on the application of four different downscaling models, namely, KR, LSTM, ConvLSTM, and Shared ConvLSTM, to provide rainfall projections at 0.25° spatial resolution over the Indian sub-continental region. All four models are trained and tested using the NCEP/NCAR reanalysis dataset. The best performing model is identified and applied to the historical dataset of CCCma GCM. A fair evaluation of the model results is carried out using the cross-validation period long enough to estimate relevant persistence characteristics of projected rainfall. The statistical performance indices are estimated on the basis of the results of 13 year (2001–2013) realizations of the rainfall occurrences using the NCEP/NCAR reanalysis dataset and 37 years (1969–2005) realizations of the GCM historical dataset. The results are evaluated based on the realization of various statistics representing spatiotemporal characteristics of rainfall, which are essential for planning and management of water resources. The numerical comparisons are made based on an estimation of the three basic statistical parameters, namely, mean, standard deviation, and extremes in rainfall. Here, we consider the 95th percentile of the data (both predicted and observed) as extremes. To evaluate the spatiotemporal properties of future rainfall, we use data for RCP4.5 (medium) and RCP8.5 (high) climate scenarios of CCCma GCM.

Scalability of the models

Scalability of an SD model depicts its ability to scale well with increase in input data size, i.e. time taken to run the model does not increase in parallel with the increase in the size of the region of rainfall prediction. Hence, for efficient real-time prediction and retraining of the model for changing input data or scenarios, it is important that the model scales well with increase in input data size.

For this study model, simulations are carried out on an NVIDIA Tesla K80 GPU computing system. The simulation periods are noted down for all four models. The KR model takes nearly 30 hours for training for all regions of India. The LSTM model takes approximately 5 hours for training for all regions of India; however, it performs poorly because of the simple single-layered network architecture used to predict multisite rainfall having very high variability. The region-wise ConvLSTM model takes about 10 hours for training on all regions of India. The Shared ConvLSTM model takes approximately 8 hours for convergence on the entire Indian region.

Model validation over baseline period: comparison of statistical parameters

The ability of a model to capture the mean of a precipitation series is aptly measured using the mean square as well as mean absolute error metrics. We evaluate the difference between mean, standard deviation, and extremes of observed and predicted rainfall dataset over each grid point for the four selected models. The spatial distribution of mean absolute errors for selected models using NCEP/NCAR data for the testing period (2001–2013) are presented in Figure 6. Here, it is observed that the KR Model performs reasonably well in capturing the mean rainfall (Figure 6(a)) and rainfall extremes (Figure 6(c)) with the difference in mean ± 10 mm, except for the regions of high rainfall like the Western Ghats and NE hills, where an underestimation up to ± 20 mm is observed. The KR model at the same time underestimates the standard deviation in many parts of the country by 20 mm and overestimates in parts of Western Ghats and NE hills (Figure 6(b)). The LSTM model performs inferiorly to the KR model in terms of predicting the mean rainfall condition with positive difference between observed and modelled rainfall all over central India and Western Ghats (Figure 6(j)). The model completely fails in capturing standard deviation (Figure 6(k)) and extremes (Figure 6(l)). The blue colour domination indicates a higher deviation in observed rainfall. The difference delimits from 0 to +20 mm for more than 80% grid points (Figure 6(k)). The difference between extremes of the observed and projected rainfall with this model is as large as 100 mm for most parts of the country. This may be attributed to the simple architecture, i.e., a single hidden layer LSTM network used for predicting rainfall at grid points having highly varied rainfall patterns. The region-wise ConvLSTM model performs well in capturing the mean, except for spurts of underprediction in regions of high rainfall like the Western Ghats (Figure 6(g)). Here, it is important to note that the underestimation of standard deviation as observed with the KR model is partly overcome with the region-wise ConvLSTM model (Figure 6(h)). The model, however, depicts the limitation to predict both extreme rainfall condition with difference of +50 mm and STD over Western Ghats and parts of central India with a difference of 10–20 mm. The Shared ConvLSTM model shows the least deviation in the mean rainfall condition standard deviation and extremes from the observed values for all the regions as compared with the other three models (Figure 6(d)–6(f)). The model performs efficiently with error in mean, standard deviation, and extremes delimited to 0–5 mm (Figure 6(d)–6(f)). Supplementary material (Figure S4) provides quantification of model performances for different climate zones of the country with the help of bar plots. It is observed that the KR model slightly overpredicts the mean rainfall for the central zone and underpredicts the same for all the other zones. The STD and extremes for all the zones except NE hills with KR model differs from that observed for the particular zone. The LSTM model underestimates the mean, standard deviation, and extremes to a larger extent for all the zones. Both KR and LSTM models depict an overprediction for mean, STD, and extremes for NE hills and NE zone. This model consistently underestimates STD and extremes for all the zones except the NE zone. The ConvLSTM model predicts the mean rainfall with a higher precision than both KR and LSTM models for all the zones including the NE zone. However, this methodology underestimates STD and extremes of rainfall. The ConvLSTM model depicts an inferior performance compared with the KR model, but better than the LSTM model in capturing STD and extremes, except for the Jammu and Kashmir region. The Shared ConvLSTM model performs superiorly in capturing all the three statistical properties consistently for different climate zones of the country. Table 3 further quantifies the rainfall projection results with the help of mean squared error and mean absolute error. The LSTM model depicts the largest error in the prediction of rainfall followed by KR. The ConvLSTM and Shared ConvLSTM models confirm lower error in rainfall projection results. Simulation of extreme events is challenging because of the small sample size. It is worthwhile to note here that ConvLSTM and Shared ConvLSTM models perform superiorly to KR and LSTM models in terms of capturing the extremes of rainfall with errors limited to ±20 mm.
Table 3

Mean squared error and mean absolute error in prediction of rainfall

ModelMean squared errorMean absolute error
LSTM 402.17 9.64 
KR 264.42 8.24 
ConvLSTM 232.20 7.42 
Shared ConvLSTM 225.58 7.18 
ModelMean squared errorMean absolute error
LSTM 402.17 9.64 
KR 264.42 8.24 
ConvLSTM 232.20 7.42 
Shared ConvLSTM 225.58 7.18 
Figure 6

Comparison of statistical properties; mean, standard deviation, and extreme precipitation (95th percentile) of observed and rainfall projected using NCEP/NCAR predictor data for testing period (2001–2013) over India at 0.25° resolution. The errors in the gridded rainfall projections from KR model (a) mean, (b) standard deviation, and (c) extreme precipitation. (d)–(f), (g)–(i), and (j)–(l) are the same as (a)–(c) but for rainfall projections from the Shared ConvLSTM model, region-wise ConvLSTM model, and LSTM model, respectively. The error values in mean and standard deviation across different models range from −20 to 20 mm, whereas error values in extreme precipitation across different models range from −100 to 100 mm. The error magnitudes are higher for the grids having high mean rainfall compared with other grids in India. The overestimation of mean (standard deviation) are indicated by the colour blue, while red colour indicates that a model is underestimating rainfall values (variability). The mean projected rainfall values for entire India show good match in magnitude as well as spatial variability for all four models. However, (j) the application of the Shared ConvLSTM model results in lowest error values in projected mean rainfall values. The Shared ConvLSTM also performs best in capturing standard deviation and extremes (k)–(l), which remains poorly captured with KR (b)–(c), LSTM (e)–(f), and region-wise ConvLSTM (h)–(i) models.

Figure 6

Comparison of statistical properties; mean, standard deviation, and extreme precipitation (95th percentile) of observed and rainfall projected using NCEP/NCAR predictor data for testing period (2001–2013) over India at 0.25° resolution. The errors in the gridded rainfall projections from KR model (a) mean, (b) standard deviation, and (c) extreme precipitation. (d)–(f), (g)–(i), and (j)–(l) are the same as (a)–(c) but for rainfall projections from the Shared ConvLSTM model, region-wise ConvLSTM model, and LSTM model, respectively. The error values in mean and standard deviation across different models range from −20 to 20 mm, whereas error values in extreme precipitation across different models range from −100 to 100 mm. The error magnitudes are higher for the grids having high mean rainfall compared with other grids in India. The overestimation of mean (standard deviation) are indicated by the colour blue, while red colour indicates that a model is underestimating rainfall values (variability). The mean projected rainfall values for entire India show good match in magnitude as well as spatial variability for all four models. However, (j) the application of the Shared ConvLSTM model results in lowest error values in projected mean rainfall values. The Shared ConvLSTM also performs best in capturing standard deviation and extremes (k)–(l), which remains poorly captured with KR (b)–(c), LSTM (e)–(f), and region-wise ConvLSTM (h)–(i) models.

Close modal
Cross-correlation between the observed and predicted rainfalls at individual grid points is an essential property indicating the correctness of the spatial nature of projected rainfall. The spatiotemporal variability captured in rainfall patterns is evaluated by observing the spatial cross-correlation between observed and predicted rainfalls. The grid-wise observed and predicted rainfall association is provided in Figure 7 for all the zones. The figures show that the zone-wise cross-correlation between observed rainfall at different grid points is best captured by Shared ConvLSTM model as compared with the KR, LSTM, and ConvLSTM models. The Shared ConvLSTM model is therefore applied for prediction of future rainfall patterns from the CCCma GCM dataset. The rainfall projected using the Shared ConvLSTM model with the help of GCM-simulated predictor variables is equated with observed rainfall to access the capability of the GCM data to obtain the rainfall projections. The following sub-section provides details of model performance using a bias-corrected historical GCM dataset.
Figure 7

Box plots for zone-wise cross-correlations between observed and projected rainfall. (a) Jammu and Kashmir, (b) Western, (c) Northern, (d) Southern, (d) Northeastern hills, (f) Northeastern, (g) Central.

Figure 7

Box plots for zone-wise cross-correlations between observed and projected rainfall. (a) Jammu and Kashmir, (b) Western, (c) Northern, (d) Southern, (d) Northeastern hills, (f) Northeastern, (g) Central.

Close modal

Validation of model using bias-corrected historical GCM dataset

The performance of Shared ConvLSTM model using historical GCM data (1969–2005) in capturing mean, STD, and extremes in rainfall is presented in Figure 8. The model performs well in capturing the statistical properties of rainfall using the bias-corrected historical GCM data. The spatial distribution of observed mean rainfall (Figure 8(a)) is well captured by the projected rainfall (Figure 8(d)) obtained using the Shared ConvLSTM model. The absolute difference between model simulated and observed mean rainfall as depicted by Figure 8(g) indicates that the model captures the mean rainfall with a high degree of accuracy. The rainfall variability in terms of standard deviation (Figure 8(b)) is also well captured by the Shared ConvLSTM model (Figure 8(e)). The difference in standard deviation of the projected rainfall from the observed rainfall is presented in Figure 8(h). The overall positive differences indicate that the model projects standard deviation in lower magnitude as related to observed rainfall. The spatial variability of the extremes in the observed rainfall (Figure 8(b)) is also well captured by the Shared ConvLSTM model (Figures 8(e)). The difference in observed and model predicted rainfall as presented with Figure 8 indicates overall low absolute differences in rainfall extremes. Supplementary material (Figure S3) demonstrates the added value of downscaling by comparing the original GCM mean precipitation (subplot, a) and observations (sublot, b) with downscaled mean historical GCM precipitation with the ConvLSTM model (subplots, e) and the Shared ConvLSTM model (subplots, f). Supplementary material (Figure S5) provides quantification of model performances for different climate zones of the country with the help of a bar plot. It is observed that the shared ConvLSTM model overpredicts mean rainfall and underpredicts the standard deviation and extremes for all the zones except NE hills. The model at the same time performs superiorly to capture all the three statistical properties consistently for different zones of the country.
Figure 8

Statistical properties (mean, standard deviation, extremes) of observed and projected downscaled GCM-simulated rainfall for historical period (1979–2005) for the entire India at 0.25° resolution. The mean of observed rainfall data (a) and of the projected rainfall data (d) obtained using five surface-level predictors for the entire India at 0.25° resolution show good match in terms of magnitude and spatial variability, leading to errors in the range of ±20 mm for most of the Indian landmass (g). Similarly, the standard deviations of rainfall for the observed (b) and projected rainfall (e), and rainfall extremes for the observed (c), and projected rainfall (f) extremes show errors in the range of ±20 mm for most of the Indian landmass. The model estimates the variability of rainfall to a larger extent.

Figure 8

Statistical properties (mean, standard deviation, extremes) of observed and projected downscaled GCM-simulated rainfall for historical period (1979–2005) for the entire India at 0.25° resolution. The mean of observed rainfall data (a) and of the projected rainfall data (d) obtained using five surface-level predictors for the entire India at 0.25° resolution show good match in terms of magnitude and spatial variability, leading to errors in the range of ±20 mm for most of the Indian landmass (g). Similarly, the standard deviations of rainfall for the observed (b) and projected rainfall (e), and rainfall extremes for the observed (c), and projected rainfall (f) extremes show errors in the range of ±20 mm for most of the Indian landmass. The model estimates the variability of rainfall to a larger extent.

Close modal

Future rainfall projections using the Shared ConvLSTM model

The validated Shared ConvLSTM model is applied to the future period 2030–2070 for RCP4.5 (stabilization scenario) and RCP8.5 (business-as-usual or high-emission scenario) using bias-corrected CCCma GCM data to obtain rainfall projections. The statistics of projected rainfall scenarios for RCP 4.5 and RCP 8.5 are presented in Figure 9. It is important to check variation of downscaled future products as compared with the original GCM changes. Supplementary material (Figure S6) presents the difference between the mean and standard deviation of GCM Bias-corrected rainfall for the historical period (1979–2005) and future period (2030–2070) for RCP 4.5 and RCP 8.5. Here it is significant to state that the rainfall change direction is consistent between the original GCM and the downscaled outputs. The difference between the mean of the observed rainfall data from 1951 to 2000 and predicted rainfall for the years 2030–2070 is illustrated in Figure 9 ((g), (i)). The results reveal a remarkable increase of the mean rainfall in the NE region and NE hills. A moderate increase in the mean rainfall is observed in the northern plains and the Jammu and Kashmir region, the Western zone, and a majority of Southern India. The Western Ghats, NE region, NE hills, and parts of central India show increase in STD and extremes. Similar to the mean rainfall, the standard deviation and extremes are notably low in the Jammu and Kashmir region, the Western zone, and a major part of South India.
Figure 9

Statistical properties (mean, standard deviation, extremes) of downscaled rainfall for GCM-future period (2030–2070). The (a) mean, (b) standard deviation, and (c) extremes of the projected rainfall data for RCP 4.5. (d)–(f) same as (a)–(c) but for RCP 8.5. The differences in future projections (2030–2070) from the observed rainfall (1951–2000) reveal spatially non-uniform changes (g)–(h)–(i) (increase at some grid points and decrease at some grid points). This pattern is consistent for the RCP 8.5 scenario (j)–(k)–(l) as it presents the maximum changes with the business-as-usual scenario.

Figure 9

Statistical properties (mean, standard deviation, extremes) of downscaled rainfall for GCM-future period (2030–2070). The (a) mean, (b) standard deviation, and (c) extremes of the projected rainfall data for RCP 4.5. (d)–(f) same as (a)–(c) but for RCP 8.5. The differences in future projections (2030–2070) from the observed rainfall (1951–2000) reveal spatially non-uniform changes (g)–(h)–(i) (increase at some grid points and decrease at some grid points). This pattern is consistent for the RCP 8.5 scenario (j)–(k)–(l) as it presents the maximum changes with the business-as-usual scenario.

Close modal

The summary of results drawn from this analysis is as follows:

The Convolutional LSTM model efficiently captures the mean, STD, and extremes in rainfall pattern and shows a considerable improvement over the existing models like non-parametric KR and LSTM. Here it is essential to note that the region-wise ConvLSTM methodology functions based on evaluating single model parameters to predict rainfall over the entire region, as compared with the KR model, where grid-wise estimation of model parameters are made. The Convolutional LSTM can be used for gridded data of any size. ISMR depicts a huge variability in both space and time. The ConvLSTM model shows an efficient way to predict future rainfall with high precision and greater computational efficiency. The Shared ConvLSTM model shows a higher performance as compared with the region-wise ConvLSTM model, which gives the effectiveness of multitask learning. The results also support the hypothesis that the neighbouring regions in the Indian sub-continent have spatiotemporal similarities in the rainfall patterns.

Precipitation downscaling improvises the depiction of precipitation in global climate models, and benefits end users to evaluate the probable effects of climate change on hydrological parameters. We review and assess skills of four SD model outputs with a focus to obtain realistic representation of the space time variability of precipitation that helps end users. To the best of our knowledge this study presents the first application of Convolutional LSTM for SD of daily precipitation. While different earlier efforts examined the skill of rainfall projections over the Indian land mass using multiple GCMs, this analysis provides a useful guide to determine the skill of statistically downscaled seasonal precipitation using multiple models. The skills of four different SD models in precipitation projections are evaluated for the Indian landmass at spatial scales relevant to local decision-making. We provide an evaluation of the comparative performance of the proposed statistical methods using DL methods. Three SD approaches, namely, K), ConvLSTM, and Shared ConvLSTM model exhibit similar correlative skill measures. However, the Shared ConvLSTM model shows superior skill measures as compared with the other three models. This is because the ConvLSTM model takes advantage of convolution and LSTM. At the same time the model extracts features from the region in place of using one-dimensional time series data. Furthermore, the LSTM model completely fails to capture the precipitation variation (standard deviation) and therefore the extremes. The DL models, namely, LSTM, ConvLSTM, and shared ConvLSTM, are trained to explore the dependence of the occurrence of precipitation on the predictor variables with time lag 1. At all times, the DL methodologies were trained to minimalize mean squared error between estimated and observed mean, STD, and extremes in every epoch for the training time period. Both KR and shared ConvLSTM have similar results, with each producing near to observed mean rainfall. However, the study observes a higher skill of the estimated STD and extreme of precipitation with shared ConvLSTM as compared with the KR model (Table 3).

Geographic variations in downscaled precipitation reveal that these three models are skilled to capture patterns across the diverse topography of the Indian land mass, principally in regions subject to high variability in orographic precipitation. The previously proposed models perform region-wise, whereas here we propose a multitask learning-based stacked ConvLSTM model for predicting rainfall all over India using a single model with a considerable higher accuracy. The underestimation of the mean rainfall condition as observed with the previous models is significantly overcome by application of this method. This model performs well in terms of capturing standard deviation and extremes in rainfall. This model is well suited for predicting gridded precipitation.

Climate change derives a clear response to ecological and socioeconomic drivers. In terms of its global context, it is therefore one of the most concerning subjects today. Although GCMs are considered to be credible tools to predict future climate change, the larger uncertainties between different GCMs and the coarse spatial resolution of the GCM dataset mainly poses a limitation to the application of GCM outputs, especially for regional-scale water management. The introduction of downscaling techniques largely overcomes this limitation of GCM data application. The present study aims to present a comparative performance evaluation of four different STD techniques for Indian landmass at finer spatiotemporal scales to suit advance hydrological impact studies. The validation and calibration of the result demonstrates that the Shared ConvLSTM downscaling procedure shows comparable ability to simulate the precipitation. The evaluation of results revealed that Shared ConvLSTM using CCCMa CMIP5 GCM reproduces accurate long-term STD of daily precipitation resulting in best capture of extreme events and distribution of daily precipitation in the entire data range. Here, the usage of multiple GCM data is purposefully avoided, with the focus on methodological development. The result from the CCCMa GCM shows an increase in mean precipitation. The relative change in precipitation mean ranges from ±20 mm. The result under both RCP 4.5 and RCP 8.5 scenarios agrees with the increasing precipitation mean. The comparative change in downscaled precipitation STD ranges from ±20 mm, while the change for extreme annual precipitation is in the range ±100 mm. Importantly, the changes in STD and extremes in future rainfall are spatially non-uniform.

The present study shows Shared ConvLSTM as a promising SD methodology, although there are some limitations in the experimentation taken up. The study evaluates model performance trained for a sufficiently longer period. The performance of the model trained with a sparse training dataset is a potential work to examine. Further to this, the capability of the proposed modelling framework for downscaling climate variables other than precipitation may be attempted. Follow-up studies may be taken up to address the enduring problems of climate change such as application of multiple reanalysis datasets, multiple GCMs, and the role of different climate variables within the predictor datasets with the proposed modelling framework. The present study provided a comparison between four SD models, namely, KR, LSTM, ConvLSTM, and Shared ConvLSTM, with the help of standard statistical measures. A comparison of the results of the proposed model with other models is important and considered a potential limitation of the present study. In addition to this, sensitivity experiments can be conducted to observe the effect of the selection of different GCMs, selection of predictor variables, the interpolation of reanalysis data from 2.5° to 0.25° as well as the geographical extent of variables. This is considered a potential future scope of study. When the proposed model well captures orographic precipitation all across the country, high bias was observed in the western coastal areas featuring the Western Ghats mountain range running parallel to the sea coast. Varikoden et al. (2019) reveal contrasting rainfall trends and caution about the significant long-term climate change implications in this region. The present analysis highlights the need for specific investigations to address ISMR rainfall projections in this region as an important future scope of study. Most importantly, the proposed model depicts the capability to capture spatial non-homogeneity around the downscaled projections within a zone that is a key factor in obtaining reliable regional level rainfall projections for adapting to climate change. Therefore, despite the above mentioned limitations, the study presents a conformable novel architecture for SD with superior predictive capabilities.

Future climate projections play an important role in providing better understanding of the climate systems and form the basis for addressing a number of science and policy problems. Long-term hydrometeorological monitoring networks as well as future climate projections serve as the backbone to explore strategies and to anticipate the suitability of large-scale water resources projects. The advances in rainfall projections help to improve decision-making across water management objectives and stakeholder groups. Additionally, the increases in spatial resolution of climate projections support planning for individual watersheds to provide detailed information to water resources managers to explore the strategies to anticipate climate change. Hence, the proposed model shall enhance the information background for hydrological studies and water resource policies. With the development and availability of Phase 6 of the Coupled Model Intercomparison Project (CMIP6) that provides multimodel climate projections of future emissions and land-use changes, the state-of-the-art methodological development on the downscaling models as the one presented here will strengthen a wide range of integrated studies across the climate science modelling, such as on impacts, adaptation, and vulnerability. This kind of future prediction will positively help policymakers for effective decision-making about water storage and sustainability in regions of drought (very low rainfall) and dealing with regions of flood (very heavy rainfall).

The authors would like to thank the Indian Meteorological Department for its constant support and encouragement. We extend our thanks to Dr Kaustubh Salvi from the Alabama Transportation Institute, the University of Alabama, Tuscaloosa, Alabama, United States, for support and assistance on the KR modelling framework.

The authors would like to thank the Ministry of Human Resource Development, India, for funding this work as a part of the project ‘Artificial Intelligence for Societal needs’.

All codes for data cleaning and analysis associated with the current submission are available from the corresponding author on request.

S.S. and P.M. conceived the idea and designed the problem. S.M. and H.S. collected and downloaded the data related to the study. S.M. developed codes for the analysis taking inputs and ideas from H.S., S.S., and P.M. S.M. and H.S. discussed the results with S.S. and P.M. and interpreted the findings. H.S. and S.M. prepared the plots. S.M. and H.S. wrote the paper taking inputs from S.S. and P.M.

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

The authors declare there is no conflict.

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