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

A Method for the Optimized Design of a Rain Gauge Network Combined with Satellite Remote Sensing Data

“…A higher entropy value corresponds to greater uncertainty in the change in the representative variable and more information represented by the variable. In recent years, it has been widely used in hydrological sequence analyses [62,63], station network layouts [64], water resources assessment [65], and other aspects.…”

Tsallis Entropy for Assessing Spatial Uncertainty Associated with Mean Annual Runoff of Quaternary Catchments of the Middle Vaal Basin in South Africa

“…Entropy has been related to complexity [ 3 ], unstructured behaviour and the unpredictability of hydrological systems [ 4 ]. Since the complexity reduction of a system is translated into information gain [ 5 ], the two concepts could be used interchangeably, depending on the context. There is no doubt about the popularity of the Shannon entropy in diverse fields [ 6 ], in particular, hydrology and water resources [ 7 , 8 , 9 ].…”

“…The Lower Vaal together with the Upper Vaal and Middle Vaal basins form the current Vaal Management Area (VMA). Like [ 5 ], surface water resources (WR90) of the South Africa 1990 (WR90), 2005 (WR2005) and 2012 (WR2012) data sets were used for the MAR, specifically for the Middle Vaal. In the history of South African hydrology, these data sets have been comprehensively published in 1994, 2011 and 2016, respectively.…”

“…Moreover, no data has been published referring to the new configuration. Hence, the new configuration does not impact the hydrological records in the Middle Vaal basin at all levels, i.e., primary, secondary, tertiary and quaternary catchments [ 5 ]. In this study, the word “basin” is used more than “WMA”, for the Middle Vaal.…”

“…The rest of the study is structured in the following way: Section 2 presents very briefly the Middle Vaal catchment and data sets used, nonetheless, further details can be found in [ 5 ]. Section 3 firstly gives the methodological approach to determine the q-information deviation curves that depict the dynamical behavior of QCs for each data set.…”