Forecasting monthly peak flows for the flood-prone River Jhelum in the Kashmir Valley, India

Floods make up a significant threat to human lives and property and have detrimental effects on the environment. Therefore, pre-emptive prevention is critical for assuring the sustainable management of river basins besides the safety of human life and property. Measures of flood management may vary from the construction of flood control structures to the development of hydrological forecasting models (Yang & Liu 2020). Flood forecasting measures are more efficient than constructional measures, which require substantial investment and also alter the fluvial environment. In the recent past, accurate flood forecasting and warning have become an integral part of sustainable management of water resources (Parvaze et al. 2021, 2023). Medium- to long-range forecasting at weekly, monthly, seasonal, or annual time scales are also useful for assessment of risks associated with floods. Streamflow forecasting is also vital for demand–supply estimation in river basins, undertaking timely and necessary activities to avoid or minimise flood damages (Parvaze et al. 2022).

Operational hydrology uses time series models for streamflow simulation and forecasting time series models (Strauch et al. 2012). These also serve as efficient tools for modelling change in hydrological variables through time (Modarres & Ouarda 2013). Time series models for flood prediction are presented using graphs or expressed in terms of mathematical equations derived from statistical analysis of historical data. Stream flows obtained by time series modelling are neither historic flows nor estimates of future flows, but these are representatives of probable future flows in a statistical sense (Yurekli et al. 2005).

The present study was conducted for monthly peak forecasting using deseasonalised ARIMA models for various gauging stations of the River Jhelum, India. The river's catchment area is exceptionally prone to flooding as floods occur anytime from spring to autumn (March–September). Flood frequency analysis of the river shows that floods occur in the area almost every alternate year (Bhat et al. 2019). River Jhelum and its tributaries carry substantial volumes of water, and during floods, these water bodies are incapable of carrying the discharge owing to their limited carrying capacities. The river system's inability to contain high flow volumes leads to recurrent floods in the adjoining plains. Floods cause catastrophic consequences on agriculture and other socio-economic activities of the people (Ahmad et al. 2016).

Despite being vulnerable to flooding, no reliable scientific study has been carried out for flood forecasting of the River Jhelum. There is no system for forecasting floods or issuing timely alerts. Flood management measures are confined to rescue and relief efforts after the occurrence of floods. No long-term management practices have been put to practice for flood management and mitigation. The aim of the present study is to perform the long-term flood forecasting analysis at various flood-monitoring stations of River Jhelum using ARIMA modelling technique.

ARIMA models are well suited for time series analysis and forecasting, particularly in hydrology. These models effectively capture temporal dependencies and recognise patterns in streamflow data (Ben Aissia et al. 2017). The deseasonalised ARIMA approach, which accounts for seasonal variations, is especially advantageous in regions such as the Kashmir Valley, where flood occurrences are influenced by seasonal climate factors (Ahmad et al. 2023). The application of ARIMA models enables evidence-based decision-making in flood management. By forecasting monthly peak flows with reasonable precision, these models furnish vital information to support the planning and execution of flood mitigation strategies. This can facilitate the scheduling of dam releases, the design of flood control infrastructure, and the development of emergency response plans, thereby mitigating flood-induced damages.

In contrast to structural flood mitigation approaches that necessitate significant financial outlay and may disrupt the natural fluvial ecosystem, ARIMA-based forecasting proves to be a cost-effective and adaptable solution. These models can be regularly updated with new data, thereby maintaining their relevance and accuracy over time. This adaptability is essential for addressing the evolving nature of flood risks in the Kashmir Valley (Parvaze et al. 2023). ARIMA models for streamflow forecasting align with sustainable water resource management practices. By delivering early warnings and forecasts, these models facilitate long-term planning and management of water resources, ensuring that flood mitigation measures are environmentally responsible and socioeconomically advantageous. This proactive approach enhances the resilience and sustainability of the region.

Given the above reasons, this study was undertaken to address the critical need for an effective flood forecasting system in the Kashmir Valley. The primary objective is to apply the ARIMA modelling technique to perform monthly flood forecasting for the Jhelum River. In doing so, the study aims to assess the ARIMA model's ability to capture the temporal dependencies and seasonal variations inherent in streamflow data. Furthermore, the study evaluates the accuracy and reliability of the ARIMA model's flood event predictions. Through this comprehensive approach, the research demonstrates the feasibility and merits of utilizing ARIMA models for proactive flood management in a region highly vulnerable to recurrent and severe flooding.

Historical records of the River Jhelum reveal that it has witnessed a range of floods for centuries, and several amongst them have caused widespread destruction (Lawrence 1895; Uppal 1955). Floods are a reoccurring phenomenon in Jhelum in recent times as well. Some notable flood events that occurred recently are that of 1963, 1994, 1996, 2004, 2006, and 2014 (Meraj et al. 2015; Bhat et al. 2019). The Kashmir flood of September-2014 inundated the most floodplain and resulted in an immense loss of life and property. With an approximated discharge of ∼3,263 cumecs upstream at Sangam, ∼2,055 cumecs at Ram Munshi Bagh in Srinagar city and ∼1,348 cumecs downstream at Asham, the magnitude of this event was pronounced the greatest ever instrumentally recorded on the River Jhelum.

A comprehensive understanding of the initial research conditions was necessary to guarantee the ARIMA model's relevance and robustness for flood forecasting in the Kashmir Valley. This entailed detailing the specifics of the data collection process and addressing any challenges encountered during the research.

The study collected data from three key hydrological stations situated along the Jhelum River: Sangam, Ram Munshi Bagh, and Asham. 35-year dataset (1978–2018) of monthly peak discharge measurements for these stations along the Jhelum River, obtained from the I&FC Department of Kashmir. The data were crucial for developing a reliable ARIMA model capable of forecasting monthly peak flow patterns. The stations were chosen to provide a comprehensive understanding of the river's behaviour across its different sections. The selection criteria were based on the historical data availability for the stations, their strategic locations along the river, and their ability to capture the variability in streamflow patterns. The stream gauging stations are crucial for flood control and management strategies within the Kashmir Valley. Data collected from these stations are leveraged by local government agencies to monitor and regulate river discharges, rendering them essential components of any holistic flood forecasting framework.

The ARIMA models for each discharge station were trained using 35-year data in calibration set (1978–2012) and tested using 6-year data in validation set (2013–2018).

Here, is the number of observations in the dataset, and are observed and predicted monthly peak flow values, and represents the mean of observed monthly peak flow values.

Streamflow analysis shows that the maximum streamflow occurred in September 2014 for Sangam (3,263 cumecs) and Ram Munshi Bagh (2,055 cumecs) stations while for the Asham station, the highest value of streamflow was recorded in June 1996 (1,494 cumecs). The descriptive statistics of monthly peak flow at the three stations are presented in Table 1. The data are positively skewed, showing that the mean is higher than the median. For a normal distribution, skewness has a value of 0. Kurtosis highlights the heaviness of the distribution tails. Kurtosis has a value of 3 for normal distribution. Table 1 shows that the values of skewness and kurtosis are not even close to that of normal distribution. The descriptive summary of deseasonalised monthly peak flow data is given in Table 2. Table 2 shows all datasets are close to a normal distribution as the values of skewness and kurtosis are approximately 0 and 3, respectively.

The best-fit models were then used for forecasting one-step ahead peak flow data using forecast() function of the forecast package in R software. The models generated rolling forward forecasts, i.e. the model parameters were modified for every month to be forecasted when a new observation was available. To evaluate the performance of the models, one-month-ahead forecasts were compared with the observed values for the period from January 2013 to December 2018 (72 months) for all the three stations. Model residuals at each time step were checked for normality, independence and homoscedasticity. Models which failed at least one of these tests were eliminated and the next best model was selected.

Monthly peak flow forecasting is of crucial importance to decision-making in flood mitigation and long-term flood management. The study represents a deseasonalised ARIMA modelling technique for generating real-time flood forecasts for highly flood-prone River Jhelum in Kashmir valley. Monthly peak flow time series at the Sangam, Ram Munshi Bagh and Asham stations on River Jhelum were used to generate one-month-ahead model forecasts.The RMSE values were 75.19, 85.51, and 92.15 m³/s and MAPE values at these stations were 31.94, 29.81, and 32.96%, while NSE values were 0.89, 0.85, and 0.86 for Sangam, Ram Munshi Bagh and Asham stations, respectively. The performance of prediction estimated by using NSE, RMSE and MAPE showed a suitable ability to model the monthly peak flows of River Jhelum. The results demonstrate that the deseasonalised ARIMA modelling approach is acceptable for modelling monthly peak flow time series and present a good representation of hydrologic forecast. The results can be used for long-term planning and management of floods for the study area. The models can also be used for agricultural and urban water management by forecasting water availability during different months of the year.

The authors are thankful to College of Agricultural Engineering and Technology, SKUAST-Kashmir for providing all facilities to carry out the research. The authors also acknowledge the Planning and Design Division of Irrigation and Flood Control Department, Jammu and Kashmir, for providing discharge data of the river Jhelum.

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

The authors declare there is no conflict.