Incorporation of Bootstrapping Needful for Sensitivity Analysis: An Eudiometric Theoretic-Approach to Modelling the Assimilative Capacity of a River

Abstract

The mathematical physics underlying the adsorption and subsequent desorption of dissolved oxygen (DO) in an effluent-loaded water body had previously rarely been studied. Although the current state of play in this field reflects the use of various analyses, the use of hat matrix and bootstrapping techniques to study the phenomenon of chemical adsorption and desorption of DO at the molecular level in a polluted waterbody has not been investigated thoroughly. This research seeks to use a matrix projector, H-hat (H), to cast virtual spectrum rays on pollutant loadings in a water body, unravelling the dynamics of chemical and biological gravitation of dissolved oxygen towards constituents of effluent pollutants in the process. This methodology is based on multivariate linear regression's ordinary least squares methodology. The proposed method is supported by a mathematical physics analysis of the phenomenon. Bootstrapping was used to calculate the means and variances of regression parameters, as well as the confidence intervals of parameter point estimates. Tricking technique adopted facilitated the development of extreme values of the dissolved oxygen and hence the supremum and infimum of assimilative capacity of the river which fluctuates with intensity of effluent loadings and season of the year (rainy, dry, and harmattan seasons). The results of bootstrapping revealed that assimilative capacity fluctuated widely from the values detected by point estimates of regression parameters, implying that tricking of regression parameters tunes up the regression model and thus fine tunes the value of assimilative capacity through necessary model parameter adjustments. The findings of this study obviate the need to use a eudiometer for the laborious direct measurement of dissolved oxygen in a body of polluted water. In this study, an elegant technique for crossing the stream where it is shallowest was developed. The method is considered as a great improvement on previous approaches that seem to dawdle.