Probability and stochastic modelling of water quality parameters in the Thames River

Abstract

Baseline information on water quality parameters is essential to the development of policies to manage and control con taminants in streams. Investigations on the probability behaviour of monthly statistical estimates reveal that the governing probability distributions are not fixed but change on a monthly basis; and they are non-Gaussian. Probability density functions are developed using a five-parameter polynomial density function, which allows successful preservation of the key moments of the baseline water quality sequence. Stochastic models for transformed series of concentration of total phosphorus and suspended solids are determined using the ARIMA process. Since the ARIMA family of processes requires that the underlying distributions for monthly events be Gaussian and time-invariant, appropriate transformations are made for mapping the monthly water quality data from its parent distribution to a N(0,1) distribution. The model constructed for the transformed monthly phosphorus variable is an ARIMA [1, 1, 0], while the transformed suspended solids series of monthly time step is adequately described using a white noise ARIMA model. The methodology developed provides a framework for modelling baseline water quality data at various tributaries. The transformations guarantee that the probability distribution of the observed series is incorporated into the model structure. Therefore, synthetic water quality series generated using these models reproduce the non-Gaussian time-varying probability distributions and maintain the serial relationship between consecutive monthly events. Key words: ARIMA process, non-Gaussian probability distribution, water quality time series, suspended solids data, phosphorus concentration series.