Abstract
The importance of the mean annual runoff (MAR)-hydrological variable is paramount for catchment planning, development and management. MAR depicts the amount of uncertainty or chaos (implicitly information content) of the catchment. The uncertainty associated with MAR of quaternary catchments (QCs) in the Upper Vaal catchment of South Africa has been quantified through Shannon entropy. As a result of chaos over a period of time, the hydrological catchment behavior/response in terms of MAR could be characterized by its resilience. Uncertainty (chaos) in QCs was used as a surrogate measure of catchment resilience. MAR data on surface water resources (WR) of South Africa of 1990 (i.e., WR90), 2005 (WR2005) and 2012 (W2012) were used in this study. A linear zoning for catchment resilience in terms of water resources sustainability was defined. Regression models (with high correlation) between the relative changes/variations in MAR data sets and relative changes in entropy were established, for WR2005 and WR2012. These models were compared with similar relationships for WR90 and WR2005, previously reported. The MAR pseudo-elasticity of the uncertainty associated with MAR was derived from regression models to characterize the resilience state of QCs. The MAR pseudo-elasticity values were relatively small to have an acceptable level of catchment resilience in the Upper Vaal catchment. Within the resilience zone, it was also shown that the effect of mean annual evaporation (MAE) was negatively significant on MAR pseudo-elasticity, compared to the effect of mean annual precipitation (MAP), which was positively insignificant.
Highlights
The second law of thermodynamics related to the most appealing concept of entropy, which expresses the chaos, uncertainty or disorder of a system
It was shown that the effect of mean annual evaporation (MAE) was negatively significant on mean annual runoff (MAR) pseudo-elasticity, compared to the effect of mean annual precipitation (MAP), which was positively insignificant
Data extracted from the WR2012 report [75], were used to compute the entropy values associated with MAR for the different quaternary catchments (QCs)
Summary
The second law of thermodynamics (in physics) related to the most appealing concept of entropy, which expresses the chaos, uncertainty or disorder of a system. The concept of Shannon or theoretic entropy, used for the first time in communication theory, was extended in the last two decades to water related fields, e.g., [1,2]. Shannon used entropy to express the information transmitted through a communication channel [3]. The versatility of the entropy concept is shown across several disciplines: chemistry, engineering metallurgy, environmental sciences, urban planning, hydrology and water resources. In the field of hydrology and water resources, it was shown that entropy could be used to measure the degree of complexity or uncertainty of streamflow in catchments [2,4,5,6]. The connection between entropy and resilience was established, e.g., for urban systems [7], for social systems [8], for coupled human and natural systems [9], and, recently, for catchments as complex dynamic systems [10]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
