Shannon Entropy for Measuring Spatial Complexity Associated with Mean Annual Runoff of Tertiary Catchments of the Middle Vaal Basin in South Africa

Masengo Ilunga

doi:10.3390/e21040366

Shannon Entropy for Measuring Spatial Complexity Associated with Mean Annual Runoff of Tertiary Catchments of the Middle Vaal Basin in South Africa

Entropy (Basel). 2019 Apr 4;21(4):366. doi: 10.3390/e21040366.

Author

Masengo Ilunga¹

Affiliation

¹ Department of Civil and Chemical Engineering, College of Science, Engineering and Technology, Private Bag X6, Florida Campus, University of South Africa, Florida, 1710 Johannesburg, South Africa.

Abstract

This study evaluates essentially mean annual runoff (MAR) information gain/loss for tertiary catchments (TCs) in the Middle Vaal basin. Data sets from surface water resources (WR) of South Africa 1990 (WR90), 2005 (WR2005) and 2012 (WR2012) referred in this study as hydrological phases, are used in this evaluation. The spatial complexity level or information redundancy associated with MAR of TCs is derived as well as the relative change in entropy of TCs between hydrological phases. Redundancy and relative change in entropy are shown to coincide under specific conditions. Finally, the spatial distributions of MAR iso-information transmission (i.e., gain or loss) and MAR iso-information redundancy are established for the Middle Vaal basin.

Keywords: Shannon entropy; complexity; iso-information redundancy; iso-information transmission; mean annual runoff; tertiary catchment; water resource.