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.

Keywords:

• Boltzmann–Shannon entropy
• flow regime
• stability of river flows
• Upper Indus Basin
• Karakoram glaciers

Acknowledgements

The authors are immensely grateful to the Water and Power Development Authority (WAPDA) of Pakistan for making the river flow data available for research. We express a great indebtedness, with deep sincerity, to Mr Daniyal Hashmey of WAPDA for providing us the Tarbela inflow data in a very timely fashion to help us establish a supporting evidence of our previous analysis. Reviews by two anonymous reviewers have considerably helped to bring the paper to its present form. We owe to them too.