Hypothesis Testing and Parameter Uncertainty Analysis in Simple Phytoplankton-P Models

Abstract

System identification and parameter estimation are necessary steps preceding the application of any mathematical model designed for management and control. As outlined in Chapter 2 (Figure 2.2) in a typical modeling procedure first a model is postulated, usually based on some a priori knowledge of the system under study; then an attempt is made to estimate a unique set of parameters by matching model results with available data; and finally the error sequence is examined in order to detect structural deficiencies in the model. Although one should attempt to follow this procedure as closely as possible, its application is often hampered in a number of practical cases, particularly in the early stages of a lake eutrophication study, for three major reasons:

• (1) Large uncertainty in observation data, mostly because of sampling errors, and partly because of chemical identification uncertainty.

• (2) Uncertainty in forcing functions and input data due to stochastic variability combined with deficient recording.

• (3) Incomplete knowledge of biological, chemical, and hydrophysical processes.

Several of these problems have been addressed in previous chapters are well as in the literature. The effect of observation errors on parameter reliability and prediction uncertainly is discussed in Di Toro and va Straten (1979) and Beck et al. (1979).