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Pakistan’s agricultural economy is reliant on the Indus River’s irrigation system, which is fed by the water coming from the great Himalayas-Karakoram Glacier Mountains. Because of hilly terrain areas, the climatic variations have an intense effect on the river flow, especially during the winter and monsoon months. Consequently, significant variations, which are observed annually, result in flooding situations in the monsoon months and reduced flows in the winter season. Thousands of people have lost their lives and massive property destruction has taken place due to disastrous floods that occurred during 2010 and 2016. Past studies have focused on proper water resources and the management of extreme events such as floods and droughts; however, modelling and forecasting based on the various climatic factors and stochastic variations are rare. This paper attempts to forecast Indus River flows using multiple linear regression (MLR), the stochastic time series, the seasonal autoregressive integrated moving average (SARIMA), and its reduced heteroscedasticity model, i.e., SARIMA-GARCH (generalized autoregressive conditional heteroscedasticity) methods at the Kalabagh station. The results show that MLR is best over the short-term; SARIMA is better over the long-term, and SARIMA-GARCH may be superior for a very long-term forecast.

The assessment for long-term and extreme river flow events is necessary for water resource management and early preparation for any expected hazardous event in the country. This paper considers the probabilistic estimation of the annual maximum flow (AMF) series (1967 to 2015) of the Indus River, Pakistan at Kotri station. Four extreme value distributions Gumbel, Frechet, Weibull and Generalized Extreme Value (GEV) models were tested. Based on the goodness of fit tests of Kolmogorov Smirnov (KS) and Anderson Darling (AD), it was found that GEV is the most suitable distribution for modelling AMF series. The Bayesian and Maximum Likelihood Estimation (MLE) techniques have been used to estimate the parameters of GEV distribution and also compute their return levels. The relative absolute squared error (RASE), relative root mean squared error (RRMSE), maximum absolute error (MAE) and probability plot correlation coefficient (PPCC) were employed to evaluate the forecasting efficiency. Moreover, the forecast efficiency indicators show that the Bayesian technique is relatively better than MLE for observing the AMF in Indus River Pakistan. The improved results of this paper demonstrate that can be helpful for government in establishment of water resources management policies of the country. This is in order to utilise their efforts to reduce or control the risk of significant losses in future upcoming events. [ABSTRACT FROM AUTHOR]