Optimal complexity analysis of total phosphorus models.

Abstract

The study of water pollution problems in lakes is often concerned with the dynamic behavior of total phosphorus. Several total phosphorus models are available that may be suitable for the study of these problems. Depending on the management objectives and data availability, some models may be more appropriate than others. In this thesis, criteria are defined to help modelers select the most appropriate total phosphorus model for different lakes. These criteria consider processes such as sediment feedback, stratification, and algal uptake and recycle. It is possible to fit a phosphorus model to system response data with parameters outside the normal range. It is also possible that models with improper mechanisms look reasonable for short-term predictions. However, it may be misleading if those models were used for long-term predictions. Therefore, extended validation approaches including the independent measurements of fluxes and coefficients are recommended to verify models. In reality, there exist uncertainties in model parameters and errors in field measurements. Therefore, the model performance should be evaluated considering such uncertainties. To obtain maximum reliability, it is necessary to select the optimal model complexity for a given system. Many techniques have been developed in the context of specific applications but no single method is suitable for all models. In addition, there have been no attempts to date to include uncertainties caused by errors in field observations in model reliability analyses. A new method is presented to quantify the reliability of a model considering uncertainties in model parameters and field observations. This method considers average squared differences between model predictions and observed data with penalty function which is larger for a more complex model. The proposed method prefers a less complex model if this model can provide reasonable simulation capability. However, this probabilistic approach may not be applied for extended prediction purposes. Therefore, expanded validation approaches are also recommended for stochastic analysis. The error of model is not only a function of model parameter uncertainty but also a function of model structure. Therefore, it is of great importance that model structure be considered in error and reliability analyses.