Model error propagation and data collection design. An application in water quality modelling

The scope of this paper is to analyse the error propagation structure of a simple two compartment water quality model, and to describe the effect on model predictions from uncertainties in initial conditions and forcing inflow. Following a brief review of linear dynamic systems, a variance estimation model for the water quality model is described. The methodology employed in relating model prediction uncertainty and data collection design, is based on systems or ordinary differential equations combined with first-order second moment analysis (FOSMA). In the paper some important characteristics of uncertain water quality systems are discussed, namely the steady-state concentration and system time scale. Applying FOSMA, the variance expressions of the system characteristics lead to some specific suggestions in the practical design of water quality models and the relation to data collection accuracy. Further it was found that the variance estimator for the steady-state concentration, provided that the system matrix is deterministic, is expressed as a weighted sum of the variances of the initial concentrations and the inflow transport. The weights are functions of the system time scales and thus related to the model parameters.