Multivariate multi-step LSTM model for flood runoff prediction: a case study on the Godavari River Basin in India

Environmental disasters have gradually risen to the forefront of every country's economic and development forum due to their enormous impact on a nation. The frequently changing climate and urbanisation propel these. Within the context of natural disasters, the most frequent and common type of disaster is flooding. Floods are regarded as the most costly disaster globally. Floods result in significant human casualties and the destruction of agriculture, infrastructure, property, and public services. Between 1998 and 2017, more than 2 billion people were impacted by floods globally (Floods 2022). India is highly susceptible to flooding. Over 40 million hectares (mha) of the 329 mha total geographical region is prone to flooding. (Floods NDMA 2007). This vulnerability to floods is further exacerbated by rapid urbanisation, population growth, expanding economic and development activity in flood plains, and climate change. The damage caused by floods in a developing country is devastating. Hence, developing a foolproof data-driven model for predicting floods is essential to mitigate the potential damage. Data-driven models primarily analyse historically observed data to create an input–output mapping for the next timestep for which the prediction will be made (Solomatine et al. 2009; Ha et al. 2021).

Flood runoff is an attribute of utmost importance in flood risk management. It is defined as the excess water that flows in the river during any flood-like event. The amount of flood runoff is affected by several factors, like the duration and intensity of precipitation, soil type, size, and river basin drainage. Thus, accurate flood runoff forecasting can help to plan efficiently for flood management and mitigation. Flood event runoff prediction can help to identify vulnerable areas and effectively utilise the resources. It is also a critical component of flood warning systems. It can be used for flood risk assessment, disaster management, and evacuation planning. It enables authorities to take proactive measures that can help to save lives, reduce property damage, and improve emergency response planning. Deep learning-based predictive models can be used to forecast flood runoff values. The accuracy of these models can be enhanced with time through continuous learning. The performance of these models improves with the addition of new data into the model over time, leading to more reliable forecasts in the future.

In the past decade, many machine learning (ML) and statistical models (Bagherzadeh et al. 2021; Sampurno et al. 2022) like Long Short-Term Memory (LSTM), Artificial Neural Network (ANN), Support Vector Machine (SVM), and Convolutional Neural Network (CNN) were proposed for hydrological prediction. It has been demonstrated that ML models perform better in predicting floods than traditional hydrological models (Mosaffa et al. 2022). Ding et al. (2020) considered the LSTM network along with two dynamic attention modules to build the model. Using these modules, spatial–temporal weights can be dynamically adjusted to improve the performance of existing LSTM cells. Ighile et al. (2022) used ML techniques to map Nigeria's flood-prone regions. They used ANN and logistic regression models on the historical flood data along with flood-affecting features to show the flood susceptibility of areas. Yoosefdoost et al. (2022) compared data-mining algorithms like ANN, SVM, and Genetic Expression Programming (GEP) to simulate dam reservoir input runoff in an arid region. Another work (Miau & Hung 2020) used a Conv-GRU model to forecast the level of a river in Taiwan. Kim & Kim (2020) developed an LSTM model for predicting urban runoff according to rainfall input, and the flood hazard was mapped spatially. SWMM was used to simulate rainfall events. Zhu et al. (2020) compared standard models such as SVM, AutoRegressive Integrated Moving Average (ARIMA), and LSTM and found that RMSE is the minimum for LSTM. (Li et al. 2021) attempted to compare LSTM models having different architectures and assess their usability in hydrological applications. They concluded that synced sequence input and output (SSIO) architecture are more accurate than SISO and consume fewer computational resources. Rahimzad et al. (2021) aimed to compare the results of four data-driven techniques for daily streamflow forecasting. The methods used are LSTM, SVM, MultiLayer Perceptron (MLP), and Linear Regression. The results indicated that the LSTM is the best technique to efficiently capture the behaviour of time series data in hydrological modelling/ flood forecasting-related applications. Liu et al. (2020) used the Yangtze River streamflow data from 1952 to 2018 to create a stream flow prediction model using a combination of Encoder-Decoder LSTM and the Empirical Mode Decomposition (EMD) algorithm. A major drawback of this work was that it only considered the streamflow data and no other vital data like precipitation, evapotranspiration, and temperature. Another study of the Yangtze Basin (Jiang et al. 2022) uses a combination of four ML algorithms and weather forecasts to predict the water level, rainfall, and estimation of disaster losses in the Yangtze River basin. The four ML algorithms used were Random Forest (RF), MLPR, CNN, and LSTM. Atashi et al. (2022) have presented a case study of the Red River, where they predicted the water levels. They have compared three models – the classical statistical model ARIMA, the traditional ML model RF and the deep learning model LSTM and have used hourly water level data for the same.

Wu et al. (2020) presented a data-driven forecasting model for water accumulation in urban scenarios. They found peak rainfall, concentration skewness, and rainfall as key determinants of urban floods. Damle & Yalcin (2007) used a time-delayed embedding method for predicting the occurrences of events in the future. A multi-objective formulation is used to model the optimisation formulation and is solved using a genetic algorithm. A hybrid SOM–RNARX model for flood forecasting in the Kemaman River basin was proposed by Chang et al. (2018). Ramos Filho et al. (2021) aimed to develop a method for estimating the rainfall threshold needed to forecast floods and flash floods in Sao Paulo, Brazil. An existing technique to identify the threshold for peak rainfall intensity was improved in this paper. (Elsafi 2014) built an ANN model to predict the flow of the Nile River at Sudan's Dongola station. Based on the flow at upstream sites, the model was constructed to simulate the flow at a particular location in the reach of the river. Panigrahi et al. (2018) used a Cascaded Functional Link Artificial Neural Network (C-FLANN) model for predicting water flow prediction 14 days in advance. Differential Evolution (DE) and Harmony Search (HS) were utilised to model parameters, and important features were chosen using the map-reduce-based ANOVA technique. Keum et al. (2020) developed an urban flood prediction system wherein the runoff values of each representative timestep were initially predicted, followed by flood map creation using SWMM and Lidar. Zhu & Zhang (2022) developed a Flood Disaster Index model to analyse the threat of flooding in the Guanzhong area. The authors used ArcGIS 10.1 software to analyse the flood hazard. The dataset used in this study included land use data, remote sensing data, geographical data, and land use records. Puttinaovarat & Horkaew (2020) presented a flood forecasting approach based on integrating data of various types. The geospatial, hydrological, and meteorological data was fetched from GLOFAS, hourly rainfall predictions were obtained from the TMD big data platform, and crowdsource data from government websites (where people can report for help in comment-like structures) and social media. (Le et al. 2019) suggested the development of an LSTM neural network for predicting floods, taking rainfall and daily discharge data as input features. Time series data of the past 24 years, i.e., from 1961 to 1984, was considered for the dataset. (Furquim et al. 2016) deployed a Wireless Sensor Network (WSN) in São Carlos River, São Paulo State, Brazil. Data like rainfall volume, river pressure, river water level, etc., were collected from these sensors, followed by applying Efficient Recurrent Neural Network (E-RNN) and MLP models.

It is found that existing studies on runoff prediction using deep learning do not incorporate the impact of climate, land, vegetation, and hydrological parameters on floods collectively. Incorporating satellite-based data (Basheer Ahammed & Pandey 2022) with the gauge station data can help better understand the region in which floods are predicted. Moreover, studies exploring flood forecasting for Indian rivers (Barbetta et al. 2016; Paul et al. 2017; Nanditha & Mishra 2021; Vogeti et al. 2022) are less. It has been demonstrated in various studies that the climatological, land, and hydrological parameters have a key role (Stein et al. 2021) in determining the flood profile of a river. Hence, this research proposes a deep learning model trained on a dataset consisting of climatological, hydrological, land components, and vegetation-related historical real-world data parameters like water level, precipitation, evaporation, temperature, pressure, river discharge, etc. for the Godavari River at the Perur water monitoring station.

In this study, a comprehensive dataset has been created from various sources consisting of historical real-world data parameters like water level, precipitation, evaporation, temperature, pressure, river discharge, etc. The relevant features are selected from the complete dataset. The study shows that the LSTM model performs best among ARIMA, Prophet, NeuralProphet and LSTM. The RMSE values and R² of the models are compared. A multivariate multi-step LSTM model is used to predict the flood runoff for each day over the next week. Root mean squared error (RMSE), Mean Absolute Error (MAE), Willmott's Index (WI) of Agreement (WI), Legates-McCabe's Index (LMI) and R² metrics are used to evaluate the performance of the proposed LSTM architecture.

The study area selected for this research is the region around the Perur water monitoring station at the Godavari River in Telangana. This area was chosen because the Godavari basin has:

• 1.

  Large area – The Godavari River stretches for 1,465 km and is the largest in the Indian peninsular region. The basin covers a territory of 3,12,812 km² (Water Resources Karnataka 2022), and the Perur station monitors the gauge, discharge, sediment, and water quality of the river in the Godavari lower sub-basin.

• 2.

  Prone to flooding – The Godavari basin receives maximum rainfall during the southwest monsoon. The annual rainfall during this period can reach a maximum of 1,000 mm. The high rainfall in the Godavari basin is the primary cause of flooding. Over the past two decades, the annual runoff of the Godavari River has changed by nearly 113%, and the frequency of floods has risen sharply in recent years (Brakenridge et al. 2010).

• 3.

  Data availability – Data for the Godavari basin are available on various websites (Government of India – WRIS, DFO, etc.)

In this research, a comprehensive dataset consisting of various climatological, hydrological, land, and vegetation-related data parameters collected from different sources at a daily frequency have been combined for a duration of 18 years, i.e., from 2002 to 2019 for the Godavari River. Initially, data were collected for the Godavari River from the DFO Flood Observatory, University of Colorado (Brakenridge et al. 2010). The DFO is a comprehensive source for historical river discharge and major flood event runoff data for various rivers across the globe. This data ranged from 1998 to 2023. Flood runoff is inextricably linked with various land and climatological data (Stein et al. 2021). To include these, climate data were extracted for the Perur region from the Indian Meteorological Department (IMD)-gridded climate dataset, which is a collection of gauge stations' data in India. The data were collected using the IMD API (IMDLIB 2020) accessed through Python scripts. Other climatological and land attributes data were sourced from the Copernicus Climate Change Service (C3S) and extracted via Google Earth Engine (Muñoz-Sabater et al. 2021). The data are a collection of satellite images of Earth, which are processed to fetch the relevant land, vegetation, and climate attributes. The ERA5-Land Daily Aggregated Dataset was used to get the historical climate records for the area of interest. The data are available from July 1963 onwards and provides a comprehensive overview of the change in land and climate attributes on a daily cadence. It includes 32 different climate and land attributes, including surface runoff, precipitation, temperature, soil moisture, and land evaporation. Finally, the historical river water dataset from India WRIS (India Water Resources Information System) (India-WRIS 2016) was used to make the dataset more comprehensive. Data on daily river water level, historical flow, and discharge were sourced from the Perur River Point Observatory in Telangana. Thus, a comprehensive historical flood dataset for the Godavari River region around the Perur monitoring station has been created.

Different models have been used to forecast the next-day flood runoff. RMSE and R² were used to compare the models. The first model used was ARIMA (Box et al. 2015). It is a statistical model that predicts future values based on historical trend analysis. It uses lagged moving averages to make predictions. It is used for non-seasonal data series. This did not perform well on this dataset due to seasonality in data. Then, the Prophet model developed by Facebook was used (Taylor & Letham 2017). It is an additive time series forecasting model that can fit non-linear trends of the data. It is robust to missing values and can handle them quite well. The main idea of the Prophet is signal decomposition. This model performed better than ARIMA but did not give satisfactory results. Next, the NeuralProphet model by Facebook (Triebe et al. 2021) was used. The NeuralProphet model was designed to overcome the shortcomings of the Prophet model. In NeuralProphet, an autoregressive model is fit using neural networks to enhance accuracy. This model performed better than the previous two. Finally, the deep learning model LSTM (Gers et al. 2000) was used, and it outperformed other models for one-day prediction on the combined dataset. Therefore, a multivariate multi-step LSTM model is proposed to predict the flood runoff for a week ahead.

For sequential data, LSTM (Gers et al. 2000) is frequently employed because it can detect complex patterns in input data. It can learn the significance of order while predicting the data. LSTM can figure out the long-term dependency in data through the three gates interacting with each other. Gates are made of a sigmoidal neural layer and multiplication operator. The forget gate is the initial gate, and it is required to do away with data that is not useful. Next is an input gate layer that selects what attributes should be updated, and then a tanh layer builds a new candidate vector to be added to the state. The output of the forget gate and fresh candidate vector are used to update the cell state. Finally, the output gate calculates the output based on cell state and tanh function. Stacked LSTM is a model with multiple LSTM layers in which each layer functions independently with its own set of parameters. This structure allows the model to learn abstract and complex patterns in the input sequence. Multivariate LSTM takes in multiple features as input and provides output for the target variable. It can analyse the interactions among input features, leading to better predictions. The multi-step multivariate LSTM model takes in multiple features as input and predicts multiple future steps.

The multi-step LSTM model was trained on varying look-back window sizes. The look-back window changed between 30 days (1 month) to 548 days (1.5 years). The RMSE decreases on increasing the look-back window. However, WI, LMI and R² are best for a look-back window of 183 days, as discussed in Section 3.2.

The dataset contained data spanning 6,222 days and was divided into train and test in the ratio of 70:30. Thus, the train dataset contained 4,355 days' data, and test data had 1,867 days' data. The model is trained on the train data and then validated using the test data. Experiments were conducted to select the most optimal parameters for the proposed models. The epochs while training the model varied from 50 to 100. It was observed that the model gave optimal results when trained on 100 epochs with a batch size of 64 and Adam optimiser. ReLU and linear functions were used as LSTM and dense layer activations, respectively.

Several models were used to predict the runoff values – ARIMA, Prophet, NeuralProphet, and LSTM. The performance of these models was compared using root mean square error (RMSE) and R² metrics. The values of RMSE and R² are depicted in Table 1. The values show that deep learning models, i.e., NeuralProphet and LSTM, perform better than the traditional statistical model ARIMA and the forecasting model Prophet. This highlights that deep learning-based approaches can predict time series better than statistical methods. Specifically, a lower RMSE indicates that predictions made by deep-learning models were closer to the actual values than statistical models. Among these, LSTM performs the best, showing promising results for forecasting. This is likely because LSTM, a deep learning model, can detect complex patterns in data. Hence, further experiments were conducted on variants of the LSTM model.

The performance of the LSTM models is evaluated using RMSE and mean average error (MAE), WI of Agreement (WI), LMI, and R². RMSE measures the mean difference between actual values and values predicted by a model. It is used to evaluate the accuracy of the results obtained through regression. R² is the statistical value in regression that explains what proportion of the dependent variable can be explained by the independent variable, and it explains the goodness of fit. WI of Agreement (Willmott et al. 2011), and LMI (Legates & McCabe 1999) are indices ranging between 0 and 1 used for hydrological model evaluation. According to the results shown in Table 2, it is concluded that the model with a look-back window of 183 days performs the best with RMSE of 0.05, MAE of 0.007, R² of 0.67, WI of 0.83, and LMI of 0.584 for one-day predictions. It is also found that the optimal look-back window is within the range of 3–6 months. However, the model with a 548-day look-back window has a lower RMSE, but the R² value indicates that it fits poorly on data – probably overfitting the data.

For multi-day prediction, the experiments were conducted on the identified look-back window sizes of 3 months and 6 months, and the results are shown in Table 3.

The data used in all the above models only had the 20 attributes selected through feature selection and previous runoff values. This LSTM model showed significant improvement in performance as compared to statistical models. The model with a look-back window of 183 days (approximately 6 months) gave the best 7-day predictions.

To further evaluate the predictions of the proposed model, the actual flood event that occurred during the period of test data is compared with the predictions of the model during the same period. As visible in Figure 6, there is a peak in the flood runoff prediction during the timesteps 1,308–1,313. These timesteps correspond to 2 August to 7 August 2019 in our dataset. According to the news articles during this period (Smart City to Flood City: Residents Suffer as Heavy Rains Inundate Telangana's Warangal 2019), there was a flooding event in the Godavari River Basin at Perur. This shows that the predictions of the proposed model are valid.

The paper presents a promising way to predict floods by predicting the flood runoff. Different models were employed to accomplish this task: ARIMA, Prophet, NeuralProphet, and LSTM. The selected study area is the Godavari River region at the Perur water gauge station. The step-by-step construction of a comprehensive and interpretable dataset of climatological, hydrological, land, and vegetation-related parameters is also presented. The data were collected for 18 years (2002–2019) from four different sources. To identify the important features affecting flood runoff in a region, feature selection has been performed. The selected features include river water level, precipitation, temperature, surface pressure, evaporation, soil water content, daily runoff, and average river flow. Various experiments show that deep learning models give better results than statistical approaches. Among the LSTM, ARIMA, Prophet, and NeuralProphet models, the LSTM model performs the best. The best one-day prediction achieved on the proposed LSTM model has a RMSE value of 0.05, MAE of 0.007, WI of 0.83, LMI of 0.58, and R² of 0.67. The identified optimal look-back window is 3–6 months. The deep learning model proposed in this research to predict flood runoff can be a vital component of the flood warning system to help in generating timely warnings, planning evacuation drives, formulating emergency responses, and, hence, mitigating the damage from floods. However, this study does not consider the frequently changing demographics of the flood-prone area, the factor of concretisation around the areas near the river, and the effect of global warming. Though difficult to quantify, these parameters might sometimes have a role in inducing floods. This kind of study will be useful in flood mapping and hot spot analysis with improved spatial resolution of the target area. For future work, the factors related to urbanisation and global warming can be incorporated into the model.

N.G., S.N., R.N., and S.R. performed the methodology, did software analysis, did validation, did formal analysis, investigated the study, and wrote the original draft. K.R.S. conceptualised and performed the methodology, supervised the study, wrote, reviewed, and edited the article.

All relevant data are available from an online repository or repositories. https://floodobservatory.colorado.edu/SiteDisplays/20.htm; https://imdlib.readthedocs.io/en/latest/index.html; https://indiawris.gov.in/wris/#/; https://essd.copernicus.org/articles/13/4349/2021/.

The authors declare there is no conflict.