EUDIOMETRIC THEORETIC-APPROACH TO MODELLING THE ASSIMILATIVE CAPACITY OF A RIVER: INCORPORATION OF BOOTSTRAPPING NEEDFUL FOR SENSITIVITY ANALYSIS

Abstract

The mathematical physics underlying the adsorption and subsequent desorption of dissolved oxygen (DO) in a water body subject to effluent loading had been rarely investigated. The current state of play in this field although reflects use of different analysis, the combine use of hat matrix and bootstrapping techniques to study the phenomenon of chemical adsorption and desorption of DO at molecular level in a polluted waterbody has not been thoroughly investigated. This study seeks to use a matrix projector, H-hat (?), to cast virtual spectral rays on pollutant loadings in a water body and in the process unravel the dynamics of chemical and biological gravitation of dissolved oxygen towards constituents of effluent pollutants in water body. This approach is anchored on the ordinary least squares methodology of multivariate linear regression. The method hypothecated is studded by a mathematical physics analysis of the phenomenon. Bootstrapping was used to establish means and variances of regression parameters, and subsequently, the confidence intervals of point estimates of parameters. 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 result of bootstrapping revealed that assimilative capacity fluctuated widely from the values detected by point estimates of regression parameters thus suggesting that tricking of regression parameters, in turn, tunes up the regression model, and hence, fine tunes the value of assimilative capacity through necessary adjustments of model parameters. The results of this study obviates the need to deploy eudiometer for laborious direct measurement of dissolved oxygen in a body of polluted water. Thus an elegant technique for crossing the stream where it is shallowest has been developed in this study. The method is considered as a great improvement on previous approaches that seem to dawdle.

http://dx.doi.org/10.4314/njt.v35i1.28