Identification of a Mechanistic Model for the Diurnal Dissolved Oxygen Pattern in Lakes with Discrete Time Series Analysis

Discrete time data analysis indicates that a first-order autoregressive model with exogenous variables (ARX) is sufficient to describe observed diurnal dissolved oxygen patterns in a lake. It is shown that this model is equivalent to a simple three parameter mechanistic model, augmented with a first-order noise filter. The noise dynamics can be interpreted in terms of natural stochastic parameter variations. Tests with data simulated with the identified stochastic model structure reveal that the usual least squares (LSQ) fitting of the mechanistic model without the noise term leads to biased parameter estimates. Therefore, with the actually measured data, ARX parameter estimates are probably preferable to LSQ estimates, even though the output error is larger. In the true system slow parameter variations probably also occur which are not covered by the simple model.