Boltzmann–Shannon entropy and river flow stability within Upper Indus Basin in a changing climate

Abstract

Water resource in Upper Indus Basin is highly vulnerable to climate change because seasonal snows and glacial melts are the principal components (70%) of river flows in this basin. Here, we apply the concept of Boltzmann-Shannon entropy to long-term discharge records along the main stem of the Upper Indus and its most important tributary Shyok River to determine the relative stability of flows in the four main seasons of the basin. Spring flows are most unstable possibly due to variations in onset of snow melting time in a changing climate. Summer flows, which account for bulk of the annual flows, have remained relatively stable, indicating general stability of the cryosphere of the basin during the past six decades. We draw support of this conclusion from observation of the trend of long-term time series (1962 -2013) of summer inflows at the Tarbela reservoir located at the outlet of Upper Indus Basin. Within the summer flow regime, August flows show greatest instability possibly due to changing rate of production of glacial melts under a changing climate. Upper Indus flows are stabilized by flows from the Karakoram where glaciers have either mostly remained stable or gained mass slightly in the recent decades in spite of widespread glacier wastage or ice losses in the western Himalayas. The approach presented here can be used to determine predictabilities of monthly and seasonal flows in water resources management and planning challenged by changes in climate and by land and water usage in concert with economic and social changes.

Climate Change Impacts on the Upper Indus Hydrology: Sources, Shifts and Extremes

“…Analysis of a 1961 to 2009 record of reservoir inflow at Tarbela, which is the largest reservoir on the main stem of the Indus river (Fig 1), indicates a declining trend, although statistically insignificant [6]. Further upstream trend analysis on streamflow records at different locations identified stable or declining trends in runoff too [32,39,40]. These studies indicate that large parts of the UIB are (not yet) experiencing accelerated melt, which could indeed be partly attributed to the Karakoram anomaly.…”

A joint analysis of river runoff and meteorological forcing in the Karakoram, upper Indus Basin

“…By examining the 50‐year trend of the Indus flows at Tarbela Reservoir, it is apparent that the spring/summer high flows exhibit an essentially stable trend from 1961 to date (Mukhopadhyay & Khan, ). The annual reservoir inflow volumes for the 1999–2009 decade are 4% below the 1961–2009 50‐year average (Reggiani & Rientjes, ).…”

Decadal‐Scale Climate Forcing of Alpine Glacial Hydrological Systems

“…Work has identified the importance of objective quantification of hydrograph shape in proglacial streams (e.g., Cauvy‐Fraunié et al, ; Hannah et al, ; Jobard & Dzikowski, ; Lafreneire & Sharp, ; Swift et al, ). Here we apply the Shannon entropy as a means of describing hydrograph shape following its application in hydrograph quantification in nonglaciated basins (e.g., Amorocho & Espildora, ; Krasovskaia, ; Maruyama et al, ; Pan et al, ; Fleming & Weber, ; Mukhopadhyay & Khan, ). We use these entropy measures to test the hypothesis that climate warming is leading to a systematic and measurable change in the discharge hydrographs found in glaciated basins.…”