Stochastic modelling of DO and BOD components in a stream with random inputs

A stochastic model for the evolution of DO and BOD components along a river with independent BOD point inputs has been developed. The model examines the case in which the initial conditions and the concentrations of the inputs are affected by uncertainty. The uncertain quantities are modelled as random variables, for which any kind of probability distribution can be adopted. The possibility of separately analysing the different components of BOD (e.g., CBOD and NBOD) is included. A semi-analytical expression for the joint probability density function (pdf) of the concentrations is derived. The application of this relationship greatly reduces the computation efforts compared to Monte-Carlo methods. A procedure for the analytical determination of the concentration moments is also described.