The effect of complexity on parameter sensitivity and model uncertainty in river water quality modelling

Snowling and Kramer [2001. Evaluating modelling uncertainty for model selection. Ecol. Modell. 138(1), 17–30] proposed a hypothesis stating that as a model becomes more complex in terms of increased number of parameters and variable, the error between simulations and measurements decreases and the overall model sensitivity increases. In this paper, the hypothesis is tested using a river water quality model of the lower course of the Saale river, Germany. The eutrophication module of WASP5 (5th version of Water quality Analysis Simulation Program), which was developed by the U.S. EPA, was implemented. The model allows the complexity of the dissolved oxygen balance and dynamics in a water body to be easily varied from a simple Streeter–Phelps approach of dissolved oxygen–biological oxygen demand (DO–BOD) interaction to more complex phytoplankton–nutrient dynamics. Five complexities were modelled and plotted against a normalized root-mean-squared error and a normalized global sensitivity. The results verify the hypothesis. A utility function, which minimizes both error and sensitivity, shows that the most complex model is not necessarily the most “useful”. In the case of the lower Saale river, modelling only the phytoplankton–nutrient cycle has almost as much descriptive power as when the complexity is increased by adding the DO–BOD cycle. The low sensitivity of the parameters linking the two cycles also indicates their weak coupling in the Saale river system. This verifies the observations that the source of the organic loading in the Saale has shifted from primary (point load) to secondary (phytoplankton) origin.