Application of first-order and Monte Carlo analysis in watershed water quality models

Abstract

To achieve effective environmental control, it is important to develop methodologies for dealing with uncertainties in model simulation of pollution behaviour and effects. Several procedures have been proposed to quantify uncertainties in modelling studies. This paper utilizes the two methods that are widely applied, i.e. functional analysis and Monte Carlo Simulation. The first-order part of the functional analysis method provides a measure of uncertainties in dependent variables in terms of uncertainties in independent variables. The procedure is based on first-order terms in the Taylor series expansion of the dependent variable about its mean value with respect to one or more independent variables. The major assumption in this procedure is that all independent and dependent variables are the second moment variables (SMV), which means that the behaviour of any SMV is completely described by its mean and standard deviation. The mathematical simplicity of the procedure allows application by simple input-output models. Consequently, it has been applied to many environmental simulators, e.g. hydrological models, stream water quality models, lake water quality models and ground water pollution models. The Monte Carlo Simulation (MCS) method uses a large number of repeated trials or simulations with the values for stochastic inputs or uncertain variables selected at random from their assumed parent probability distributions to establish an expected range of model uncertainty.