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

Abstract

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.

Probabilistic Approach to Precipitation-Runoff Relation in a Mountain Catchment: A Case Study of the Kłodzka Valley in Poland

“…This study is part of the analysis of the synchronous occurrence of hydro-meteorological phenomena using the copula function. In a similar approach, relationships between the amount of rainfall [40] and runoff [21,22,37,41], as well as between the flow and the amount of material transported by water [36,42,43], and also relations between snowmelt flood volume and peak discharge [44], and between the water levels of coastal lakes and sea water levels [45] were analyzed. These papers are evidence of successful application of the copulas in hydro-meteorological studies, but these methods also have their limitations.…”

Uncertainty analysis of water environmental capacity based on the copula model

“…The copula model has strong flexibility and adaptability and can connect any form of marginal distribution function to obtain their joint distribution function (Yu et al 2014;Reddy et al 2012). The construction of the copula model includes three steps: correlation measurement of variables, construction of the marginal distribution function and construction of the joint distribution function (Sobkowiak et al 2020).…”

Contemporary Trends in High and Low River Flows in Upper Indus Basin, Pakistan

“…The impact of a changing climate may alter the operational role of existing water resources in terms of capacity and planning for new installation [41,42]. However, most studies [17][18][19]26,43,44] conducted in UIB were restricted to mean flow, and no study has addressed the variability in maximum and minimum flows. Specifically, [17] presented an analysis of eight stations in the period 1966-2005, and [26] analyzed 19 stations in the period 1961-1998.…”

“…Previously, several significant papers have been published in the same study area using more or less similar gauging stations with different data periods and study objectives [44][45][46][47][48]. Some of them used innovative methods for flow measurements in UIB [44] while others analyzed trends variability in hydroclimatic variables [36]. Several focused-on snow cover variability, flows simulation and restricted to hydrological modelling rather than trend analysis [46][47][48].…”