Investigation of model and parameter uncertainty in water quality models using a random walk method

A mathematical model to predict the effect of chemical spills in the Forth estuary in Scotland has been in use for many years. The model, based on the random walk method, predicts chemical concentrations in the estuary waters and estimates the elapsed time before the dilution is sufficient to render the spill harmless (making use of a toxicity measure such as the LC50 or a water quality standard). The model gives a deterministic result without any estimate of the uncertainty. Field studies using tracer dyes to measure the horizontal and vertical mixing rates in the estuary show that these rates vary over time. The literature on turbulent diffusion includes modelling applications using different parameterisations of the mixing process. This paper investigates the uncertainties in predicted concentrations due to model parameterisation of horizontal mixing and due to the variability in the measured mixing rates determined from surveys in the estuary. Estimates of the range of concentrations for a specific spill scenario are presented. The study shows that model formulation and parameter uncertainty are both important factors in estimating the uncertainty in model predictions. The uncertainty caused by the variations with time found in the measured mixing rates is found to be of similar magnitude to the differences in concentration resulting from using three different methods for modelling the horizontal mixing in the estuary. Uncertainties associated with model formulation could be reduced if a small number of longer timescale (e.g. 24 h) dispersion experiments were available. In addition, further data from short-term ( 3 h) dispersion experiments would give a better understanding of the distribution of mixing coefficients and how the mixing relates to other parameters such as tidal range and wind speed and direction.