Next Article in Journal
A Symmetric Plaintext-Related Color Image Encryption System Based on Bit Permutation
Previous Article in Journal
Towards Experiments to Test Violation of the Original Bell Inequality
Previous Article in Special Issue
Application of Entropy Ensemble Filter in Neural Network Forecasts of Tropical Pacific Sea Surface Temperatures
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(4), 281; https://doi.org/10.3390/e20040281

Cross Mean Annual Runoff Pseudo-Elasticity of Entropy for Quaternary Catchments of the Upper Vaal Catchment in South Africa

Department of Civil and Chemical Engineering, College of Science, Engineering and Technology, Florida Campus, University of South Africa, Florida 1710, South Africa
Received: 2 November 2017 / Revised: 21 December 2017 / Accepted: 21 December 2017 / Published: 13 April 2018
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
View Full-Text   |   Download PDF [4549 KB, uploaded 13 April 2018]   |  

Abstract

This study focuses preliminarily on the intra-tertiary catchment (TC) assessment of cross MAR pseudo-elasticity of entropy, which determines the impact of changes in MAR for a quaternary catchment (QC) on the entropy of another (other) QC(s). The TCs of the Upper Vaal catchment were used preliminarily for this assessment and surface water resources (WR) of South Africa of 1990 (WR90), of 2005 (WR2005) and of 2012 (WR2012) data sets were used. The TCs are grouped into three secondary catchments, i.e., downstream of Vaal Dam, upstrream of Vaal dam and Wilge. It is revealed that, there are linkages in terms of mean annual runoff (MAR) between QCs; which could be complements (negative cross elasticity) or substitutes (positive cross elasticity). It is shown that cross MAR pseudo-elasticity can be translated into correlation strength between QC pairs; i.e., high cross elasticity (low catchment resilience) and low cross elasticity (high catchment resilience). Implicitly, catchment resilience is shown to be associated with the risk of vulnerability (or sustainability level) of water resources, in terms of MAR, which is generally low (or high). Besides, for each TC, the dominance (of complements or substitutes) and the global highest cross MAR elasticity are determined. The overall average cross MAR elasticity of QCs for each TC was shown to be in the zone of tolerable entropy, hence the zone of functioning resilience. This could assure that water resources remained fairly sustainable in TCs that form the secondary catchments of the Upper Vaal. Cross MAR pseudo-elasticity concept could be further extended to an intra-secondary catchment assessment. View Full-Text
Keywords: entropy; cross elasticity; mean annual runoff; water resources; resilience; quaternary catchment; complement; substitute entropy; cross elasticity; mean annual runoff; water resources; resilience; quaternary catchment; complement; substitute
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Ilunga, M. Cross Mean Annual Runoff Pseudo-Elasticity of Entropy for Quaternary Catchments of the Upper Vaal Catchment in South Africa. Entropy 2018, 20, 281.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top