Estimation of the River Flow Synchronicity in the Upper Indus River Basin Using Copula Functions

In this study, on the basis of the maximum and mean annual values of flows, dependencies between flows recorded in seven water gauges located in the upper part of the Indus River Basin (IRB) in Pakistan were analyzed. First, the non-parametric Mann–Kendall (M–K) test was used to detect trends in the flows. Next, the Pearson’s correlation coefficient was applied. Then, the selected copulas were used to find joint distributions of the studied time series. In the next stage, the degrees of synchronous and asynchronous occurrence of, respectively, the annual maximum (AMAXF) and mean annual flows (MAF) were calculated. The study revealed that correlations between the flows in selected gauge stations were very strong and statistically significant. These results were confirmed by the synchronicity analysis carried out with the help of the copula functions. The highest relationship was detected in the case of gauges Besham Qila and Kachura on the Indus mainstream, while the lowest was detected in gauges Besham Qila and Naltar on the Naltar River. These findings can be of high practical value in the field of sustainable water resource management, including for flood protection, agricultural water supply, reservoir water storage, and hydropower generation in the IRB.