Prediction of the peak discharges is of great significance for water resource management and flood mitigation strategies. In this study, the performance of the deseasonalised ARIMA modelling technique was tested to evaluate its suitability for streamflow prediction in flood-prone Kashmir Valley. Monthly peak flow modelling and forecast was performed for the following three key discharge stations of the River Jhelum: Sangam, Ram Munshi Bagh, and Asham. Based on the results, the models were found to perform reasonably well for simulation and forecasting of the monthly peak flows. The values of root mean square error (RMSE) were 75.19, 85.51, and 92.15 cumecs, and MAPE values were 31.94, 29.81, and 32.96% for Sangam, Ram Munshi Bagh, and Asham stations. Nash–Sutcliffe efficiency (NSE) values for these stations were 0.89, 0.85, and 0.86. The results showed that the models could recognise the patterns in the observed time series and recognise the basic relations. The models will contribute towards designing an efficient decision support tool for flood planning and management in the flood-prone valley.

  • Great significance for water resource management and flood mitigation strategies.

  • Performance of the deseasonalised ARIMA modelling technique was tested.

  • Evaluate its suitability for streamflow prediction in flood-prone Kashmir Valley.

  • By monthly peak flow modelling and forecasts, the models will contribute towards designing an efficient decision support tool for flood planning and management in the flood-prone valley.

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.

River Jhelum is a major tributary of the Indus River and its corresponding river basin is mostly confined within Kashmir Valley in India. The basin lies between the latitudes 33° 22′ N and 34° 43′ N and the longitudes 73°20′ E and 75°36′ E. The area of the basin in Kashmir Valley is about 17,622 km2 and is stretched between the altitudes ranging from 1,575 m amsl in the plains to about 6,000 m amsl in the upper reaches (Manzoor & Ahanger 2023). The basin is encompassed by Pir Panjal and Greater Himalayan mountain ranges from northeast and southwest, respectively. River Jhelum is the principal river flowing through entire Kashmir valley. The river receives water from all the water bodies in the valley. The length of the river in Kashmir valley in India is 165 km (Ganjoo 2014). For monitoring the flood in the river, three gauging stations have been designated by Irrigation and Flood Control (I&FC) Department as the principal flood-monitoring sites for the River Jhelum. These stations, namely Sangam, Ram Munshi Bagh, and Asham are in the upstream, mid- and downstream reaches of River Jhelum. Discharge data at these stations were used for developing ARIMA models at each site. Figure 1 shows the location of the study area and the flood-monitoring sites.
Figure 1

Location of the Jhelum Basin and flood-monitoring sites of river Jhelum (arrows show the direction of river flow).

Figure 1

Location of the Jhelum Basin and flood-monitoring sites of river Jhelum (arrows show the direction of river flow).

Close modal

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.

Statistical analysis and ARIMA modelling

The descriptive analysis of the streamflow data during the study period provides an insight into the hydrological behaviour of the River Jhelum. Monthly peak flow data at three gauging stations was analysed for the period 1978–2018. The gauging stations selected for the study are described in Table 1. ARIMA stochastic models were developed by Box & Jenkins (1976) to identify complex patterns in univariate data. These are used in different forms to model stationary or simple non-stationary univariate time series (Machiwal & Jha 2012). The ARIMA model comprises three components, the Autoregressive (AR) component; Integrated (I) component, and Moving Average (MA) component. AR term represents the lags of the differenced time series in the forecasting equations; MA component represents the lags of forecasting errors. A time series which needs differentiation to become stationary should be ‘Integrated (I)’. The model is presented as ARIMA (p,d,q)X, where p represents the number of AR terms, d the number of non-seasonal differences, q the number of lagged forecast errors in the prediction equation and X the independent external variables. There are three steps to ARIMA modelling. First, the estimated autocorrelation function (ACF) and partial autocorrelation function (PACF) were used to determine the order of differencing (d) and the degrees of AR (q) and MA (p) polynomials. The second step was to ensure that the residuals were white noise by estimating suitable parameters. Third, the residual analysis was used to get the best-fit model. Akaike information criterion (AIC) (Akaike 1998). AIC and mean absolute percentage error (MAPE) were used to compare the models. ARIMA model with the least value of AIC and MAPE were selected as the best-fit model and applied to generate the forecast. An ARIMA (p, d, q) model is expressed by Equation (1) (Mohammadi et al. 2005).
(1)
Table 1

Location of gauge stations and the descriptive summary of monthly peak streamflow (cumecs) for 1978–2018

StatisticSangamRam Munshi BaghAsham
Latitude 33 ° 49′ 37.2″ 34 ° 4′ 15.6″ 34 ° 14′ 52.8″ 
Longitude 75 ° 3' 46.8″ 74 ° 48' 10.8″ 74 ° 36' 43.2″ 
Typea Q, M Q, M Q, M 
No. of observations 480 480 480 
Minimum 20 30 42 
Maximum 3,263 2,055 1,494 
Mean 246 253 315 
Variance 96,532.10 51,919.09 68,250.91 
Standard deviation 310.70 227.86 261.25 
Skewness 4.61 2.42 1.74 
Kurtosis 9.96 5.10 3.58 
StatisticSangamRam Munshi BaghAsham
Latitude 33 ° 49′ 37.2″ 34 ° 4′ 15.6″ 34 ° 14′ 52.8″ 
Longitude 75 ° 3' 46.8″ 74 ° 48' 10.8″ 74 ° 36' 43.2″ 
Typea Q, M Q, M Q, M 
No. of observations 480 480 480 
Minimum 20 30 42 
Maximum 3,263 2,055 1,494 
Mean 246 253 315 
Variance 96,532.10 51,919.09 68,250.91 
Standard deviation 310.70 227.86 261.25 
Skewness 4.61 2.42 1.74 
Kurtosis 9.96 5.10 3.58 

aQ indicates discharge, M indicates manually.

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).

Monthly streamflow data are non-stationary because of presence of seasonality and need to be transformed before applying ARIMA model. The series was thus deseasonalised and then a suitable non-seasonal stochastic ARIMA (p, d, q) model was fitted (Mohanasundaram et al. 2019). Equation (2) gives the standard deseasonalization procedure used for the study:
(2)
Here, is the deseasonalised monthly flow for the month τ; is the original monthly flow for the month τ; is the sample mean of original monthly flow for the month τ and is the sample standard deviation of original monthly flow for the month τ.

Evaluation of model performance

The forecasting capability of deseasonalised ARIMA models was estimated by computing three different forecast consistencies. The NSE (Nash & Sutcliffe 1970), RMSE, and MAPE are the most common statistics applied for evaluating the performance of time series models (Fung et al. 2019). RMSE and MAPE are used for determining the errors between observed and predicted values (Farooque et al. 2016). A model exhibiting the least values of these indices is preferred. The NSE value of 1 determines a perfect fit between the observed and predicted values (Bennett et al. 2013). These indices are defined in Equations (6)–(8).
(3)
(4)
(5)

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.

Statistical analysis

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.

Table 2

Descriptive summary of deseasonalised monthly peak streamflow (cumecs) at different gauge stations for 1978–2018

StatisticsSangamRam Munshi BaghAsham
No. of observations 480 480 480 
Minimum −2.03 −2.36 −2.68 
Maximum 7.34 7.95 9.93 
Mean −0.25 −0.34 0.18 
Variance 1.30 1.90 1.35 
Standard deviation 1.14 1.38 1.16 
Skewness 0.29 0.18 0.07 
Kurtosis 3.06 2.99 2.87 
StatisticsSangamRam Munshi BaghAsham
No. of observations 480 480 480 
Minimum −2.03 −2.36 −2.68 
Maximum 7.34 7.95 9.93 
Mean −0.25 −0.34 0.18 
Variance 1.30 1.90 1.35 
Standard deviation 1.14 1.38 1.16 
Skewness 0.29 0.18 0.07 
Kurtosis 3.06 2.99 2.87 

Figure 2 shows the distribution of observed monthly peak discharge at the three gauging stations. Box-whisker plots use statistical summaries of the minimum values, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values to describe groups of quantitative data. The box plots in Figure 2 show that monthly peak flows at Sangam, which is in the upstream reach of the river Jhelum, are consistent with the peak flows at Ram Munshi Bagh and Asham stations, which are in the mid- and downstream reach. Figure 2 also shows the outliers for each gauging station, which exceed the normal range of peak flows at their respective stations. These values of streamflow correspond to the catastrophic floods that frequently occur in the basin.
Figure 2

Box–Whisker plots of monthly peak discharge data for Sangam, Ram Munshi Bagh, and Asham Stations (1978–2018).

Figure 2

Box–Whisker plots of monthly peak discharge data for Sangam, Ram Munshi Bagh, and Asham Stations (1978–2018).

Close modal

ARIMA modelling

Appropriate ARIMA models were established for the three gauging stations following the modelling procedure given by Box and Jenkins. Models were built in the R software environment by utilising suitable packages available in the Comprehensive R Archive Network (CRAN) repository (Dalgaard 2010). ARIMA models were constructed by applying the auto.arima() function from the ‘forecast’ package of R. The function returns the best-fit model of a time series based on the minimum value of AIC. The order of the models at each time step was cross-validated through AutoCorrelation function (ACF) and Partial Auto Correlation Function (PACF) plots. Autocorrelation (AC) values up to 20 lags were used to identify the usefulness of the selected model. ACF and PACF plots of the gauging stations for the first-time step are illustrated in Figure 3. It is clear from Figure 3 that the components of the time series are neither pure AR nor MA models, but ARMA models. The order of differencing was also identified by the auto.arima() function for each time step.
Figure 3

AC and PAC plots for monthly peak flow time series at different gauging sites of the River Jhelum.

Figure 3

AC and PAC plots for monthly peak flow time series at different gauging sites of the River Jhelum.

Close modal

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.

The hydrographs of the observed and predicted monthly peak flow values at each station are shown in Figure 4. It is observed from Figure 4 the predicted data follows the observed data very closely. However, the peak flood value at Sangam and Ram Munshi Bagh stations for September 2014 was highly underestimated. This is because these stations did not witness a flood of this magnitude during the calibration period. The underestimation of peak values is also due to a sudden rise in historical data just before the peak value, which cannot be foreseen by the ARIMA model (Wang et al. 2018). ARIMA models were suitable for simulating long-term hydrological behaviour of River Jhelum and predicting future flows.
Figure 4

Comparison of observed and predicted peak flow data for the River Jhelum from the year 2013 to 2018 with a time step of 1 month.

Figure 4

Comparison of observed and predicted peak flow data for the River Jhelum from the year 2013 to 2018 with a time step of 1 month.

Close modal

Evaluation of model performance

This study was aimed at investigating the forecasting capability of ARIMA modelling procedure for forecasting the monthly peak flows of River Jhelum. Observed and predicted values of monthly peak flow for the testing period (2013–2018) were used for evaluating the efficiency of the models at each gauge station. The performance of the models was evaluated in terms of RMSE, MAPE and NSE. These values show the strength of fit between the observed and generated values of data. For Sangam station, the NSE, RMSE and MAPE were 0.89, 75.19 cumecs and 31.94%, respectively. For Ram Munshi Bagh station the values of these indices were 0.85, 85.51 cumecs and 29.81% and that of Asham station were 0.86, 92.51 cumecs and 32.96%. The NSE values indicate a fairly good performance of the models for forecasting streamflow values. Lower values of RMSE and MAPE at each station specify that the performance of the deseasonalised ARIMA models is satisfactory for prediction of monthly peak flows of river Jhelum. The scatter plots of observed and predicted values of data during the testing period for all gauging stations are presented in Figure 5. These plots act as a convenient visual aid for assessing the accuracy of a model. The predictive accuracy of a model is higher when the scatter points representing the data are closer to the line of best fit. Most of the scatter points are close to the line of best fit for all the gauging stations (Figure 5). The models at various gauge stations represent a close relationship between observed and predicted values of monthly peak flow. The results indicate that ARIMA models are very efficient in recognizing the pattern of monthly peak flows and show good performance for forecasting streamflow in River Jhelum.
Figure 5

Scatter plots of observed versus predicted monthly peak flow data during the testing period.

Figure 5

Scatter plots of observed versus predicted monthly peak flow data during the testing period.

Close modal

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.

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