A comparison between the uncertainties in model parameters and in forcing functions: its application to a 3D water-quality model

This paper illustrates the application of both local and global sensitivity analysis techniques to an estimation of the uncertainty in the output of a 3D reaction–diffusion ecological model; the model describes the seasonal dynamics of dissolved Nitrogen and Phosphorous, and those of the phytoplanktonic and zooplanktonic communities in the lagoon of Venice. Two sources of uncertainty were taken into account and compared: (1) uncertainty concerning the parameters of the governing equation; (2) uncertainty concerning the forcing functions. The mean annual concentrations of Dissolved Inorganic Nitrogen (DIN) was regarded as the model output, as it represents the largest fraction of the Total Dissolved Nitrogen, TDN, for which the current Italian legislation sets a quality target in the lagoon of Venice. A local sensitivity analysis was initially used, so as to rank the parameters and provide an initial estimation of the uncertainty, which is a result of an imperfect knowledge of the dynamic of the system. This uncertainty was compared with that induced by an imperfect knowledge of the loads of Nitrogen, which represent the main forcing functions. On the basis of the results of the local analysis, the most important parameters and loads were then taken as the sources of uncertainty, in an attempt to assess their relative contributions. The global uncertainty and sensitivity analyses were carried out by means of a sampling-based Monte Carlo method. The results of the subsequent input–output regression analysis suggest that the variance in the model output could be partitioned among the sources of uncertainty, in accordance with a linear model. Based on this model, 79% of the variance in the mean annual concentration of DIN was accounted for by the uncertainty in the parameters which specify the dynamics of the phytoplankton and zooplankton, and only 5% by the uncertainties in the three main Nitrogen sources.