Stochastic simulation of space-time series: Application to a river water quality modelling

This study aims to develop a methodology to simulate the joint behaviour, in space and time, of some water quality indicators of a river, resulting from a mine effluent discharge, in order to enable the prediction of extreme scenarios for the entire system. Considering one pollutant characteristic measured in N monitoring stations along the time T, a random function X(e,t), e=1,...,N, t=1,...,T, can be defined. The proposed methodology, a data driven approach, intends to simulate the realisation of a variable located in station e in time t, based on values located before e and f, and using a sequential algorithm. To simulate one value from the cumulative distribution F{X(e,f)\X(e-l,t),...,X(l,t),X(e,t-1),...,X(e,1)}, the basic idea of the proposed methodology is to replace the e.t conditioning values by a linear combination of those: [X(e,t)]*=Sigma(alpha-1)(e-1)a(alpha)X(alpha,t)+Sigma(beta=1)(t-1)b(beta)X(e,beta) which allows the values to be drawn sequentially from bidistributions. The final simulated time series of pH and dissolved oxygen reproduce the basic statistics and the experimental time and spatial covariances calculated from historical data recorded over 15 months at a selected number of monitoring stations on a river with an effluent discharge of a copper mine located in the south of Portugal.