Assessing Catchment Resilience Using Entropy Associated with Mean Annual Runoff for the Upper Vaal Catchment in South Africa

Abstract

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.

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

“…Nonetheless other parameters have been shown to influence positively or negatively rainfall elasticity of streamflow, e.g., temperature/evapotranspiration [ 7 , 8 , 9 ], land use, water use [ 10 ]. The notion of elasticity has been linked recently to entropy concept to assess catchment resilience, i.e., mean annual runoff (MAR) pseudo elasticity [ 11 ]. The notion of pseudo-elasticity of entropy was derived for linear regression models and measured the relative change in entropy with respect to the relative change in MAR for tertiary catchments (TC), which are comprised of quaternary catchments (QCs).…”

“…Cross elasticity concept was later applied to other fields; e.g., transportation [ 6 , 18 ], marketing [ 13 ], electricity [ 19 ], etc. The following could also support the introduction of cross elasticity concept in hydrology and water resources: In the same hydrological zone (TC) and beyond, different QCs are not considered in isolation (hence are interdependent) and are usually subject to activities such as domestic, industrial, social and economic [ 20 ], which are likely to impact on MAR [ 11 ]. For instance exaggerated inefficient water use from one part of the catchment may impact over time on other parts of the catchment, e.g., uneven distribution of water availability coupled with unbalanced water demand/supply; change in MAR, etc.…”

“…In the same hydrological zone (TC) and beyond, different QCs are not considered in isolation (hence are interdependent) and are usually subject to activities such as domestic, industrial, social and economic [ 20 ], which are likely to impact on MAR [ 11 ]. For instance exaggerated inefficient water use from one part of the catchment may impact over time on other parts of the catchment, e.g., uneven distribution of water availability coupled with unbalanced water demand/supply; change in MAR, etc.…”

“…Climatic conditions and human activities may cause changes in hydrological variables such as streamflow (runoff) [ 20 , 22 , 23 , 24 , 25 , 26 ], which has been associated with a degree of uncertainty expressed as Shannon entropy, e.g., [ 23 , 25 , 27 , 28 ]. As mentioned earlier, natural climatic conditions [ 7 , 8 , 9 , 11 , 29 , 30 , 31 ] and/or human activities [ 10 ] may influence positively or negatively streamflow elasticity. Nonetheless, naturalized streamflows, thus naturalized MAR plays an important role in South Africa for water resources planning, development and management; hydraulic structure control, natural variability associated with climatic conditions; and ecological water requirements [ 32 ].…”

“…The use of maps for the spatial distribution analysis of the catchment under investigation, is common. This study is built on MAR pseudo-elasticity concept that was introduced recently [ 11 ]. It is a preliminary study that investigates cross MAR pseudo-elasticity concept within TCs.…”