Investigation of satellite precipitation product driven rainfall-runoff model using deep learning approaches in two different catchments of India Open Access

Rainfall–runoff modelling is vital in reservoir management, hydropower, environmental flow, water management, flood assessment, and so on. Owing to its immense importance, this topic has gathered attention worldwide, and numerous approaches were developed for rainfall–runoff modelling. Broadly, rainfall–runoff models can be classified into the following: (i) data-driven-based methods (Khac-Tien Nguyen & Hock-Chye Chua 2012; Elsafi 2014; Nguyen et al. 2014; Yaghoubi et al. 2019; Hadid et al. 2020; Xiang et al. 2020), (ii) conceptual model-based approaches (Nash & Sutcliffe 1970; Brath & Rosso 1993; Kan et al. 2017; Unduche et al. 2018), and (iii) physical model-based methods (Vieux et al. 2003; Chen et al. 2016; Setti et al. 2020). Of these methods, data-driven-based models were found to be of a great value due to their accuracy and simplicity (Teegavarapu & Chandramouli 2005; Wu et al. 2009; Wu & Chau 2010; Orouji et al. 2013; Nguyen et al. 2014; Steyn et al. 2017; Ahani et al. 2018; Mazrooei & Sankarasubramanian 2019). Precipitation is a significant input variable of the different input parameters required for rainfall–runoff models (Mazrooei & Sankarasubramanian 2019; Guntu et al. 2020). For reliable modelling, precipitation plays a crucial role; hence, the quality of the precipitation used must be reliable. For many decades, ground-based data sets were used to develop forecasting models, but it is also well-known that ground-based gauged data are scarce and are limited to few locations.

In recent decades, there is a rise in remote sensing data to analyze various meteorological parameters like temperature, precipitation, humidity, and several others. Some of the recent successful applications of remote sensing data included the works of Yeditha et al. (2020) and Valipour & Bateni (2021). In the case of precipitation, due to an increase in various satellite-derived precipitation products and having advantages of easy availability in real-time and high temporal and spatial coverages, they are being used as alternatives for ground-based gauged data sets. Some of the commonly used satellite precipitation products (SPPs) include Tropical Rainfall Measuring Mission (TRMM); Precipitation Estimation from Remote Sensed Information using Artificial Neural Networks (PERSIANN) (Hiep et al. 2018); Global Precipitation Measurements (GPM); Global Precipitation Measurement-Integrated Multi-Satellite Retrievals (GPM-IMERG) (Huffman et al. 2020; Tang et al. 2020); and Climate Hazards Group Infrared Precipitation with Station data (CHIRPS) (Funk et al. 2015).

A multitude of studies have been reported on the utility of these SPPs for applications such as hydrological modelling, water balance (Su et al. 2008; Zhang et al. 2015; Xu et al. 2017; Vu et al. 2018; Gadhawe et al. 2021), drought monitoring (Lai et al. 2019), streamflow modelling (Munzimi et al. 2019; Sulugodu & Deka 2019; Yeditha et al. 2020), and water quality modelling (Ali & Shahbaz 2020). Indeed, a large number of studies have been carried out to understand the application of satellite precipitation and their evaluation (Janowiak et al. 2004; Nair et al. 2009; Rahman et al. 2009; Bitew & Gebremichael 2011; Meng et al. 2014; Prakash & Gairola 2014; Prakash et al. 2015; Tang et al. 2016; Li et al. 2018; Wei et al. 2018). A very few studies showed the evaluation of different SPPs to apply data-driven rainfall–runoff models.

There are a significant number of studies (Adamowski et al. 2012; Kişi 2008; Islam 2010; Yaseen et al. 2015; Couta et al. 2019; Ding et al. 2019; Ali & Shahbaz 2020; Kasi et al. 2020; Wagena et al. 2020; Yadav et al. 2020; Yeditha et al. 2020) reporting the efficiency of machine learning methods such as artificial neural networks (ANN), extreme learning machines (ELM) (Huang et al. 2006), and long short-term memory (LSTM) (Kratzert et al. 2019) models based on the rain gauge data for rainfall–runoff applications. Several studies (Huang et al. 2006; Atiquzzaman & Kandasamy 2016; Yaseen et al. 2018; Sulugodu & Deka 2019) showed that ELM models outperformed ANN, Support Vector Regression (SVR), and General Regression Neural Network (GRNN) in terms of modelling accuracy and computation time. This increase in performance is because ELM does not use gradient-based techniques, which makes it run faster and also it is not subjected to an issue like local minima, improper learning as observed in the ANN models. Furthermore, all the parameters are tuned once, and ELM does not need iterative training and also produces the same result at all times, unlike ANN (Alizamir et al. 2018).

Similarly, in recent years, the LSTM variant of recurrent neural networks has higher capabilities than the traditional neural network in producing robust results when dealing with long-time series information (Sit & Demir 2019; Xiang et al. 2020). On comparing the performance of LSTM with other traditional models like convolutional neural networks and multilayer perceptron for different hydrological applications, LSTM showed better understanding (Kratzert et al. 2018; Tiwari & Vaibhaw 2020). Along similar lines, Couta et al. (2019), Ding et al. (2020), and Hu et al. (2020) used LSTM models for streamflow forecasting. Li et al. (2020) and Ni et al. (2020) employed LSTM for rainfall–runoff modelling and streamflow and rainfall forecasting. Similarly, Zhou & Ushiama (2019) have developed LSTM models for forecasting streamflow in the Tunxi catchment in Southeast China and compared the performance of the LSTM model with SVM. The results showed superior performance of LSTM compared to SVM. Similarly, Li et al. (2020) developed a high-resolution rainfall–runoff model using the LSTM approach and found that the models efficiently predicted discharge and achieved robust modelling performance.

The critical analysis of the recent literature revealed that despite significant progress in new machine learning algorithms and their applications for hydrological problems, there has been little work reported on the application of SPPs for rainfall–runoff modelling and their forecasting capabilities. With increasing reliance on SPPs in the modern age due to either poor ground-based data or unavailability, it is of utmost importance to understand their accuracy and capabilities in the domain of rainfall–runoff modelling and forecasting. Therefore, this study aims to build machine learning-based rainfall–runoff models driven by different SPPs. For this purpose, deep learning models were developed for two river basins using state-of-the-art methods such as ELM and LSTM models. We have selected these models since many studies have shown them superior to other contemporary models (Yaseen et al. 2015; Le et al. 2019; Sahoo et al. 2019; Sulugodu & Deka 2019; Li et al. 2020; Ni et al. 2020). As a part of the study, we also develop models based on the traditional methods such as feedforward neural networks (FFNN) and multiple linear regression (MLR) for benchmarking the results.

We considered two major river basins, namely Vamsadhara river basin (VRB) and Mahanadi river basin (MRB), in India. Figure 1 shows the geographical location of the VRB and the MRB in India. Both the river basins are prone to frequent floods leading to loss of lives and property. During monsoon seasons, >150 villages and thousands of acres face flood threats. Flash floods were observed in 1980 and 2013, leading to a severe loss of lives and property in the VRB. The MRB is considered to have recorded one of the most notorious floods in India. Some of the recent flood events recorded are the floods during the monsoon months in 2008, where 16 people lost lives during the river bank breach. Flash floods during the year 2011 in the monsoon season led to the flooding of 25 villages upstream of the river. The Central Water Commission has developed a rainfall–runoff model using MIKE tools for flood forecasting applications; however, the model is data-intensive and requires higher computational effort. Hence, there is an urgent need for a straightforward and dependable model for these river basins with high reliability.

Vamsadhara river is an east-flowing river originating from Lanjigarh in the Kalahandi district of Orissa at 18°15′ to 19°55′ North latitudes and 83°20′ to 84°20′ East longitudes that joins the Bay of Bengal at Kalingapatnam in Andhra Pradesh. The total catchment area is 10,830 km², out of which 8,015 km² is in Odisha and the remaining 2,815 km² is in Andhra Pradesh that runs for about 254 km between the Mahanadi and Godavari rivers. The basin receives 1,400 mm of annual average rainfall, and its average discharge is 125 m³/s. Climate is characterized by hot summers and mild winters. The maximum temperature in plains during May rises to 43 °C and goes down to 12 °C in December–January. The river basin is influenced by the southwest monsoon and occasional cyclones due to depressions in the Bay of Bengal.

Mahanadi river is an east-flowing river originating from Sihawa in the Dhamtari district of Chhattisgarh at 85°40′ to 86° 45′ East longitudes and 19°40′ to 20°35′ North latitudes. It flows through a distance of 900 km from Chhattisgarh to Odisha. Mahanadi river has a total catchment area of about 139,681 km² and is the eighth largest basin in India. The average discharge is 2,119 m³/s with a maximum discharge of 57,000 m³/s, almost as the Ganges during monsoon, and has an annual average rainfall of 1,291 mm. Of the tributaries, the upstream catchment of the Basantpur gauging station (having a catchment of 59,000 m²) is considered in this study as it is flood-prone and contributes to maximum flow. The climate in the region of Mahanadi is sub-tropical. The temperature in summer and winter is around 29 and 21 °C, respectively. The southwest monsoon starts in the middle of June and continues until the end of September.

This study has assessed the utility of two SPPs, namely GPM-IMERG V6 and CHIRPS. For comparison, we have used the gauge-based India Meteorological Department (IMD)-gridded data set. A brief description of the data set is provided here.

The GPM project is developed by the combined effort of the Japan Aerospace Exploration Agency and the National Aeronautics and Space Administration of the United States. GPM is a widely used precipitation product over the globe, and it is also an updated precipitation product of the TRMM. GPM has two primary sensors: GPM Microwave Imager, which means precipitation size, type, and intensity; and Dual-frequency Precipitation Radar, which gauges the storm's internal structure of clouds (Kim et al. 2017). GPM Microwave Imager has more frequency channels than TRMM, and the precipitation radar is more advanced (Tan & Santo 2018). More importantly, the spatial coverage (60°S–60°N) and the spatiotemporal resolution (30min and (0.1°×0.1°)) have been improved compared to the previous SPPs.

The GPM team has developed GPM-IMERG precipitation products using the IMERG algorithm, which combines three SPP features, including PERSIANN-CDR, CMORPH, and TRMM (Prakash 2019). Three types of IMERG products are made available: early run, late run, and final run with a latency period of 4 h, 14 h, and 3.5 months. The first two products are useful in a real-time application, whereas the latter can be used for water balance studies. All these products are available at 0.1°×0.1° spatial resolution over the fully global domain.

Presently, IMERG is at its Ver 06 stage (https://gpm.nasa.gov/missions/two-decades-imerg-resources). The latest update is Ver 06 IMERG that allows for fusing the data collected during the TRMM era (2000–2014) with the precipitation estimates compiled during the GPM era. Owing to this, IMERG is now available from June 2000 (https://pmm.nasa.gov/data access/downloads/gpm). The ‘Final run’ of IMERG combines the GPCC monitoring product, the V8 Full Data Analysis, for most of the time (currently 1998–2019). Here, we have used the GPM-IMERG V6 final run precipitation product.

CHRPS is a satellite-based precipitation product that provides a quasi-global rainfall data set at about three decades. The data set is available at 0.05° with the integration of station data from 1981 to near the current date. For extracting CHIRPS data, IMD-gridded point coordinates over the catchment areas of Vamsadhara and Mahanadi were considered. They were downloaded from the website of the Climate hazards Center, UC Santa Barbara (https://data.chc.ucsb.edu/products/CHIRPS-2.0/global_daily/netcdf/p25/).

The downloaded data sets are obtained as NetCDF files and are extracted using a script in MATLAB 2019a.

We used IMD-gridded daily data (IMD 4), having a spatial resolution of 0.25°×0.25° and covering the entire Indian landmass, as ground validation. The data sets were developed based on the rainfall records from 6,955 rain gauges spread across the country (Pai et al. 2014). These rain gauges were partly maintained by the IMD, Agromet Department and mainly by the state government. Using the Shepard Interpolation method, the rain gauge collected rainfall has been converted into the gridded data set. For detailed information, see Pai et al. (2014). The data set is available from 1901 to date; however, the data set for 2000–2018 is considered for this study. The data sets can be obtained from the IMD, Pune (http://www.imdpune.gov.in/).

The daily streamflow data sets used to develop forecasting models were obtained from the Central Water Commission and were downloaded from https://indiawris.gov.in/wris/. The gauging stations chosen for the VRB and the MRB are Kashinagar and Basantpur stations, respectively (Figure 1). This study used the data from 2000 to 2018 to calibrate and validate the models.

We have shown a schematic of the proposed methodology in Figure 2. We used two different SPPs (GPM-IMERG and CHIRPS) for VRB and MRB catchments to understand the relationship between rainfall–runoff and predict 1 day ahead of streamflow. A sensitive analysis was carried out to understand the accuracy by comparing SPP with IMD data sets based on detection and error components in the SPP. Furthermore, correlation analysis was carried out for the three data sets (GPM-IMERG, CHIRPS, and IMD) with runoff to understand their relationship and determine the lagged variables used as input models. Linear regression (MLR) and machine learning models (FFNN, ELM, and LSTM) were developed for 1-day ahead runoff prediction using the selected variables. After successful calibration and validation of the models, the accuracy of the resulted runoff from the models was checked using evaluation measures like root-mean-squared error (RMSE), Nash–Sutcliffe Efficiency (NSE), and correlation. Based on the values of the evaluation measures, the best models were chosen, and their accuracy for the prediction of peak flow was tested. A few case studies of the peak flow analysis are carried out using the best models, and its accuracy is analyzed using evaluation measures. The best-performing model and the best-performing SPP are determined for each considered catchment.

To assess the SPP's ability to capture the occurrence of rainfall, we have used specific statistical measures known as detection metrics. In this study, GPM-IMERG and CHIRPS data sets are compared with the IMD data sets to evaluate the chosen satellite data sets for 16 years from 2000 to 2015. The following metrics were used in this study.

Hit represents the number of days when rainfall events are recorded at the rain gauge and the satellite. Miss represents the number of days where rainfall event is not recorded in the satellite. Still, its presence is shown in the IMD data set. The POD value ranges from 0 to 1. If the obtained value of POD tends towards 0, the data sets have less accuracy, whereas it represents high accuracy if it tends towards 1.

False Alarm shows that the rainfall event is recorded at the satellite when no event is represented in IMD data. If the obtained FAR value tends towards 0, it denotes that the data are accurate, whereas if the value tends towards 1, it represents that the value is inaccurate regarding IMD data.

Recurrent neural networks are the models which use input data over long sequences to obtain outputs based on the previous computations. These models help deal with non-linear time series but have drawbacks when dealing with predetermining time lags to learn temporal sequence processing (Gers et al. 1999; Gers & Schmidhuber 2001). To overcome the disadvantage of long-distance dependence tasks and diminish gradient in RNNs, LSTMs were introduced by Hochreiter (1997). Typically, an LSTM is made up of memory cells, and memory is transferred based on cell state and hidden state. The cell state's primary role is to pass the unchanged data forward, and the data in this cell state can be changed using sigmoid gates. Gates are similar to layers that are assigned individual weights. To avoid dependency problems for long intervals, LSTMs use gates for control of the memory process.

• 1.

  Input gate: The input gate of the model generates input coefficients (⁠⁠) generated based on the current input (⁠⁠) and the previously hidden layer (⁠⁠), and based on the input coefficient (⁠⁠), the cell state (⁠⁠) is calculated based on the amount of information used out of the current input (⁠⁠).

• 2.

  Forget gate: The amount of information of the previous cell state (⁠⁠) to be stored in the current cell state (⁠⁠) is determined based on the coefficient of forget gate (⁠⁠).

• 3.

  Output gate: The final output of the network (⁠⁠) is governed by the output coefficient (⁠⁠) based on the relation = tanh (⁠⁠)

The structure and equations of each gate used for the development of LSTM are presented in Figure 3.

LSTMs capture short-term and long-term relationships in time series using these three gate mechanisms and avoid vanishing the gradient. The main feature of the LSTM is to store the components of input for each time step in input features for developing long-term memory. In addition, all the information features up to the current moment are stored in the hidden layers. Generally, these hidden layers are expressed using vectors of defined length and hence as time passes, the network compresses all the information from input components.

The output weights from the N data sets used in the modelling procedure are represented as ⁠.

Readers are encouraged to refer to the works of Huang et al. (2006, 2015a, 2015b) for a detailed explanation of ELM. Figure 4 represents a distinct network of ELM. The descriptions of FFNN and MLR are presented in the Appendix.

Choosing the potential input variables based on their relationship with output variables is more important than the algorithm's choice. This work's primary purpose is to understand the capability of SPPs in capturing the rainfall–runoff relationship, which can be an alternative ground-based rainfall data sets in real-time applications.

In this study, a rainfall–runoff modelling framework is considered where the dependent variable is runoff (output variable) and precipitation and historical runoff are the independent variables (input variables).

The total data length is divided into 70:30 for calibration and validation of the developed models. All the models were developed in MATLAB 2019a.

For MLR models, the regression model was fitted using the least-squares approach, and the error statistics were estimated for both calibration and validation periods. In FFNN, the number of hidden neurons used varied between 10 and 15. The transfer function used is TANSIG, and the Levenberg Marquardt (LM) algorithm is used as a training function. Several studies (Adamowski & Sun 2010; Maheswaran & Khosa 2013) have shown that the LM algorithm is the most robust training algorithm for feedforward networks.

For the ELM model, the number of neurons is determined using a trial and error approach to obtain the best calibration result. Validation data sets are then used as inputs at the same neurons for obtaining the forecasted results. For LSTM models, in order to determine the hyperparameters such as gradient threshold, initial learn rate, learn rate drop period, and learn rate factor, an optimization algorithm, namely Adam optimization (Kingma & Ba 2015), is used as it has been proven to be fruitful in determining the hyperparameters in LSTM models. Following the approach of Le et al. (2019), the maximum number of epochs was taken as 100,000 and early stopping techniques were used for the prevention of overfitting of the model.

Performance measures have been used as an index to determine the performance and understand the confidence limits of the model. The performance measures used in this study are RMSE, correlation (R²), and NSE.

If the value of R² and NSE is inclined towards 0, it represents that the model's output is not a good representation of the original values. Whereas, if the value is inclined towards 1, the model is a good representation of the original system and its values. RMSE represents the amount of error in the output value of the model when compared to the original value. The lower the value of RMSE, the better the fitness of the model to the original system.

The performance measures are mathematically represented as

• 1.
  RMSE

  

  (13)
• 2.
  Correlation (R²)

  

  (14)
• 3.
  NSE

  

  (15)

  where denote the observed and model-simulated streamflow values at any time instant ‘i’; represent the mean values of ‘n’ observed and simulated values, respectively.

We presented results in three sections. The first section shows the statistical analysis of SPP compared with the IMD data using metrics such as POD, FAR, and CSI. The selection of dominant timestep for input variables, namely CHIRPS, GPM-IMERG, and IMD, using Auto Correlation Function (ACF), Partial Auto Correlation Function (PACF), and cross-correlation to develop rainfall–runoff models is shown in section 4.2. Furthermore, the performance analysis of all the developed rainfall–runoff models is discussed. Finally, the accuracy of the best-performing models is shown to predict flood peaks in section 4.3.

This section presents the results from comparing precipitation products with ground-based (IMD) data sets using the metrics mentioned in section 3.1. In this study, the satellite-derived products are GPM-IMERG and CHIRPS, which are compared with IMD data sets (actual values) for accessing the capabilities of SPPs for the prediction of runoff. The cumulative distribution function (CDF) plots of IMD, GPM-IMERG, and CHIRPS data during the entire period for the VRB and the MRB are shown in Figure 5(a) and (b) with x-axis representing rainfall (x) and y-axis representing the probability. Based on the CDF plots, both the SPPs have similar CDF patterns compared to IMD data sets for the VRB and the MRB (Figure 5(a) and (b)). However, for Figure 5(a) in the rainfall range of 10–30 mm, underestimation is evident from the inset figure (zoomed plot) for both the data sets. In Figure 5(b), an underestimation of the rainfall event is observed in GPM-IMERG data for the range of 10–30 mm, whereas an underestimation in the 10–40 mm range is observed in the CHIRPS data.

In Table 1, POD values are in the range of 0.67–0.75, highlighting that both SPPs perform satisfactorily in capturing light rainfall (1–10 mm). However, for moderate (10–50 mm) and heavy (>50 mm) rainfalls, the POD values range between 0.29 and 0.45 for both the SPPs in both catchments. The same is in congruence with the FAR, highlighting false alarm for moderate and heavy rainfall in both the catchments for both SPPs. The CSI values show that SPPs have more than a 50% success rate for capturing light rainfall. However, the success rate ranges from 27 to 38% in capturing medium and heavy rainfall. All the observations from statistical parameters were further supported by RMSE, both the SPPs exhibited low RMSE values (<1.5) for the rainfall range of 1–10 mm, confirming that the accuracy of SPPs in capturing lower rainfall is robust. Whereas for medium and high rainfall (10–50 and >50 mm), higher RMSE values are observed, indicating a significant deviation of the rainfall values from the original values (IMD).

Based on the above analysis, both the SPPs are close to IMD data sets, but CHIRPS data are better than GPM-IMERG for medium and high rainfall. Based on this understanding, models for 1-day ahead discharge prediction and peak flow prediction are developed. Also, this analysis helps understand the probable reason for abnormalities in the predictive capacity of the model inflows, along with the proposal of the best replacement of IMD data.

The cross-correlation function between the input variables such as CHIRPS, GPM-IMERG, and IMD data and runoff is plotted in Figure 6(a)–(c), (e) and (f) for the VRB and the MRB, respectively. To select the number of lags in rainfall time series having significant correlation with runoff, a threshold value of 0.25 is considered. The cross-correlation (Figure 6) reveals that rainfall–runoff dependency is up to 4 days, 1 day, and 7 days for the VRB and 3 days, 3 days, and 4 days for the MRB, respectively. The ACF and PACF corresponding to the river basins’ runoff variable are plotted in Figure 7(a)–(d), respectively.

The ACF and PACF show that the runoff has significant lag memory up to 7 days and 8 days. Selected lagged variables are used to develop the rainfall–runoff models, including linear regression (MLR) and machine learning models like FFNN, ELM, and LSTM. All the models are calibrated and validated for rainfall–runoff using the approaches mentioned in section 3.4. Each model is trained until the calibration error decreases and reaches a minimum. For the least error model, validation data set is used for obtaining the predicted runoff. In MLR, a simple linear relation is used for training, whereas in FFNN, ELM, and LSTM models, the least error is obtained by trial and error by changing the number of neurons and learning rates. The obtained predicted runoff data sets are compared to the observed data sets and are evaluated using the performance measures in section 3.5.

Table 2 represents the results of all the rainfall–runoff models generated with different rainfall products resulting from the different models considered in the study. The values of the performance measures for accessing the quality of the predicted discharge are mentioned in section 3.5, i.e., RMSE, R², and NSE for both the VRB and the MRB in calibration and validation stages. Values of these measures are used to understand the best-performing model and the best SPP as a replacement of IMD data sets. Results are discussed for each considered basin separately.

Comparing the models developed using IMD data sets (Table 2) shows that the LSTM model performs better than other MLR, FFNN, and ELM models. For example, during the calibration and validation stages, the LSTM model has an NSC value of 0.69 and 0.71, whereas MLR, FFNN, and ELM models have values of 0.23, 0.41, 0.67 and 0.36, 0.49, 0.69, respectively. Similarly, lower values of RMSE and higher correlation were observed for LSTM in validation with values equal to 93.6 and 0.85, respectively.

Investigating the performance of the models with the GPM-IMERG data, models such as MLR, FFNN, and ELM were unable to produce good modelling results during both calibration and validation stages. In this case, LSTM models produced comparatively better results than the rest of the models with NSC values equal to 0.68 and 0.67 in calibration and validation stages. In contrast to this, the values of 0.25, 0.51, 0.3 and 0.37, 0.51, 0.63 were observed for MLR, FFNN, and ELM models, respectively. Similarly, better values are observed for RMSE and correlation in LSTM models.

Using CHIRPS as input data, Table 2 shows that the LSTM model produces better results than the other developed models. Higher values of RMSE and correlation were observed for LSTM models along with high NSC values. For example, MLR, FFNN, and ELM models produced results with NSC values of 0.39, 0.57, 0.60 and 0.40, 0.59, 0.61 in calibration and validation stages. Whereas, LSTM models produced values of 0.68 and 0.65, respectively, in calibration and validation stages.

Investigating the performance of several linear regression (MLR) as well as machine learning models (FFNN, ELM, and LSTM) with IMD data sets, results (Table 2) show that MLR, FFNN, and LSTM have obtained NSC values of 0.39, 0.74, 0.87 and 0.69, 0.77, 0.92 in calibration and validation stages. The best model output was observed in ELM models with NSC values of 0.89, 0.92 in calibration and validation stages. Similarly, the least RMSE and high correlation values are observed in ELM models.

Several models were developed using GPM-IMERG data as input for the rainfall–runoff modelling. ELM models produced the best results with high correlation, NSC with least RMSE in both calibration and validation stages. For example, ELM obtained NSC values of 0.86 and 0.87 in calibration and validation stages, respectively. Whereas the MLR, FFNN, and LSTM produced values of 0.70, 0.79, 0.82 and 0.71, 0.76, 0.85 in calibration and validation stages, respectively.

Comparing the results obtained using CHIRPS data sets as input, ELM models showed better modelling results with the least RMSE and high NSE and correlation. For example, MLR, FFNN, and LSTM models have NSE values of 0.69, 0.78, 0.82 and 0.70, 0.75, 0.88 in calibration and validation stages, respectively, when compared to the ELM models having NSE values of 0.89 and 0.88.

Overall, LSTM models in the VRB and the MRB outperform other models with all precipitation sets. Comparing LSTM models with GPM-IMERG and CHIRPS data sets for the VRB, both the models were found to produce similar results, but comparatively, CHIRPS model results were closer to the results of models with IMD data. For example, the correlation of IMD-based models is 0.85, whereas GPM-IMERG- and CHIRPS-based models have a significance of 0.81 and 0.84, respectively, in the validation stage. Similarly, comparing the results of ELM models with GPM-IMERG and CHIRPS data sets for the MRB, both the models were found to produce similar results. Still, the CHIRPS model results were closer to the results of models with the IMD data. For example, the correlation of IMD-based models is 0.92, whereas GPM-IMERG- and CHIRPS-based models correlate at 0.89 and 0.92, respectively.

Although promising results were observed in models for 1-day ahead runoff prediction, there is yet a concern regarding the capabilities of the models for peak flow prediction during extreme events. Models have been applied to estimate 1-day ahead flood prediction during the monsoon season to assess their ability to capture the peak events. For this purpose, we analyzed four flood events, each in the VRB and the MRB, and the corresponding results obtained from the models. In this section, only the best models for each river basin are reported, as their superiority over other models has been proven in the earlier section. Accordingly, for Vamsadhara, the LSTM model is considered, and the ELM model is considered for the Mahanadi basin. Figure 8(a) and (b) represents the spatial variation of 1-day GPM-IMERG precipitation in the VRB and the MRB for one of the extreme events that occurred on 8 August 2009. Figure 9(a) and (b) shows the results of LSTM and ELM models with different precipitation products along with the observed runoff for the VRB, and Figure 9(c) and (d) shows the runoff forecasts from LSTM and ELM models for the MRB. The result statistics only for the best models are presented in Table 3.

In the VRB, for the year 2009, based on the value of peak error percentage, the IMD-LSTM model produced a reasonable forecast of the flood peak with 17.65%, followed by CHIRPS-LSTM with 27.23%. Similarly, in 2010, the percentage error in estimating the flood peak was least for IMD-LSTM with 9.60%, followed by CHIRPS-LSTM with 16.20%. In the flood event in 2011, the least peak error was observed in IMD-LSTM, followed by the model with CHIRPS as input. In 2012, CHIRPS-LSTM was the best model with a peak error percentage of 25.61%, which outperformed the model with IMD data, an error percentage of 35.85%. In all the years, the performance of GPM-IMERG-based models in terms of flood peak is not satisfactory.

In the MRB, for the year 2009, the CHIRPS-ELM model produced good flood peak forecasts based on the peak error percentage with a value of 7.75%, followed by IMD-ELM models with −7.32%. Similarly, in 2010, the percentage error in the estimation of flood peak was least for IMD-ELM with −8.30%, followed by CHIRPS-ELM with 19.23%. In the flood event in 2011, the least error was found for the ELM model with CHIRPS input. For the flood event in 2012, the CHIRPS-ELM model obtained an error percentage of 3.05%, which outperformed IMD-ELM. The results show that CHIRPS models have produced good results in predicting flood peaks with the least errors in most flood events and were closely followed by models with IMD data sets, which over-predicted the flood events.

Overall, for both river basins, the models were able to capture the peak floods and the time to peak to greater accuracy. Comparing the performance of the models between two rivers basins, the models perform less accurately in the VRB than the MRB. This difference in the model performance across the two river basins could be attributed to higher variations in the hydrograph and more complexity in rainfall–runoff relationships in Vamsadhara. Owing to the large catchment size, in the MRB, the storage-induced inertia dampens the non-linear features and makes the catchment more amenable for modelling (Maheswaran & Khosa 2012). Whereas, the non-linear features are more prominent in the VRB, which is 10 times smaller.

This study aims to develop a machine learning-based rainfall–runoff model using SPPs. The statistical analysis of the precipitation products showed that the performance of the SPPs was dependent on the rainfall ranges. GPM-IMERG is sensitive to light and medium rainfall; however, it underestimates heavy rainfall. On the contrary, the performance of the CHIRPS data set can capture the heavy rainfall more accurately than GPM-IMERG.

Further comparison of the model performance observed that the LSTM and ELM models performed better than the FFNN and linear regression models. Of the two best models, LSTM was more accurate for the VRB and ELM to be the best model for the MRB. Comparing the results for 1-day ahead forecasts in the MRB obtained by Nanda et al. (2016) from TRMM-driven wavelet-based non-linear autoregressive with exogenous inputs (WNARX) models found that that the results from the present are superior. In their study, Nanda et al. (2016) reported NSE values of 0.85 during the testing period using the TRMM-RT rainfall dataset-driven WNARX model. However, the present study showed that the GPM-IMERG-ELM models and CHIRPS-ELM model yielded NSE values of 0.87 and 0.88, respectively.

Furthermore, models using GPM-IMERG and CHIRPS data in combination with ELM and LSTM have been shown to outperform the TRMM-based WNARX models as reported by Nanda et al. (2016). Similarly, in another study, Yeditha et al. (2020) developed WNARX models using TRMM for the VRB and obtained NSE results of 0.629 during the validation period. Comparing that with the present study using GPM-IMERG-LSTM (NSE = 0.67) and CHIRPS-LSTM (NSE = 0.65) shows that the present study results are superior.

From the above comparison of the results, the GPM-IMERG and CHIRPS data sets are performing better in capturing the rainfall than the TRMM data set for the two river basins. Similar observations were obtained by Liu & Zipser (2015) and Prakash et al. (2018). The authors show that the GPM-IMERG data set shows significant improvement in reduced false alarms and improved extreme rainfall detection over the TRMM data. Furthermore, the deep learning models, ELM and LSTM, showed a better rainfall–runoff relationship than the other contemporary models. Overall, these SPPs can be used as an alternative for ground-based data for rainfall–runoff modelling with prediction capability. Since GPM-IMERG data are available in real time, they can be explored for real-time forecasting purposes. Additionally, these models can be applied reliably for multistep ahead forecasting when precipitation forecasts from weather models such as European Center for Medium Weather Forecast are used.

One possible alternate method to improve the model performance is developing a framework for correcting the SPPs and the same can be considered as a future direction. Similarly, considering the ensemble model approach and wavelet-based hybrid approach would reduce the uncertainty in the model results.

A novel data-driven rainfall–runoff model is proposed using two different satellite-based precipitation products. Satellite-based precipitation products GPM-IMERG and CHIRPS were evaluated with ground-based IMD data sets. Results showed that the CHIRPS data sets are a better proxy of the IMD data sets compared to the GPM-IMERG data. Following this, the model is tested on two flood-prone river basins. These SPPs were used to drive ELM, LSTM, FFNN, and MLR rainfall–runoff models. SPP-driven LSTM and ELM models produced reliable forecasts in both the river basins and are comparable to the IMD data-driven models. The CHIRPS-LSTM and CHIRPS-ELM models produced robust VRB and MRB results, respectively. For simulating the peak floods, the models driven by the CHIRPS data set were accurate than the GPM-IMERG data. Nevertheless, the results based on the latter were promising.

Nonetheless, the present outcomes regarding the applicability of the SPPs, their accuracy, and the capabilities of the proposed models need to be confirmed and supported further through their application to various river basins with different climate and catchment characteristics.

M.R. gratefully acknowledges the funding received through the Inspire Faculty Award (IFA-12/ENG 28) from the Department of Science and Technology, India and SERB through ECRA/16/1721. A.A. acknowledges the funding support provided by the Indian Institute of Technology, Roorkee through Faculty Initiation Grant number IITR/SRIC/1808/F.I.G COPREPARE project funded by UGC and DAAD under the IGP 2020–2024.

The authors declare that they have no conflict of interest.

P.K.Y., S.S.N., and M.R. conceptualized the work, performed primary data collection and analysis, and wrote the initial version of the paper. P.K.Y., M.R., and A.A. had an extensive discussion and structured the initial draft of the manuscript. B.B. participated in revising the work, providing important intellectual content as well as interpretations and conclusions. All the authors contributed to the revision.

All relevant data are available from an online repository or repositories. https://data.chc.ucsb.edu/products/CHIRPS-2.0/global_daily/netcdf/p25/http://www.imdpune.gov.in/. https://pmm.nasa.gov/data access/downloads/gpm.