Underestimation of uncertainty in statistical regression of environmental models: influence of model structure uncertainty.

As the quality of sensors increases, systematic discrepancies between measurements and model outputs become more apparent Applying regression type analysis in these cases leads to autocorrelated residuals, biased parameter estimates, and underestimation of uncertainty. This paper examines how parameter estimates are affected by model structure uncertainty for an application from wastewater treatment. A Monod model is fitted to synthetic data generated by a reference system exhibiting predefined Tessier kinetics and a known error process. A range of methods are suggested to test if the resulting residuals fulfill the IID (independent and identically distributed)-requirement visual examination of time series, autocorrelation, and partial autocorrelation functions, the Jarque-Bera normality test, the Runs test for independence, and the BDS test for IID. The tests are shown to perform well at low measurement noise but not at higher levels of noise where transferring the parameter estimates gained from a batch system leads to erroneous estimation of steady state concentrations in a completely stirred tank reactor. Additional diagnostics are suggested which include second order autocorrelation functions of the residuals in the case of a single experiment and examination of moving averages of residuals in the case of multiple experiments.