Parameter uncertainty analysis of water quality model for small river

Every model is, by definition, a simplification of the reality under investigation. Although it would be desirable to reduce to zero the gap between the simulated and the observed system behavior, this is generally impossible owing to the unavoidable uncertainties inherent in any modeling procedure. In literature, generally, these prediction uncertainties are linked to measurement errors associated with system input and output, to the incapacity of calibration procedures and, finally, to the model structural errors arising from the aggregation of real world process into a modeling simplification. In this context, a good modeling practice requires that the modeler provides an evaluation of the confidence in the model, possibly assessing the uncertainties associated with the modeling process and with the outcome of the model itself. A measure about the significance of the model results in order to understand the level of confidence characterize them is necessary. With this regards, uncertainty analysis can provide useful hints as well as information regarding the best model approach to be used with respect to its significance and reliability degree. Further, the evaluation of parameter uncertainties is necessary to estimate their impact on model performance and for their calibration (Beck, 1987). More specifically, uncertainty and sensitivity analysis can offer valid tools for characterizing the uncertainty associated with a model. In any case, sensitivity analysis may help understanding the contribution of the various sources of uncertainty to the model output uncertainty and system performance in general. Then, uncertainty is a measure of the 'goodness' of a result; without such a measure, it is difficult to judge the fitness of the value as a basis for making decisions relating scientific excellence. In this context the uncertainty of a river water quality model is presented. The main goal is to gain insight in the modeling approaches concerning small rivers. Indeed, previous works generally focused on modeling of large river neglecting the small one. Such aspect is likely due to the fact that small river are often considered unworthy from practical and economic viewpoint (Marsili-Libelli and Giusti, 2008). However, such considerations are not completely fulfilled for Mediterranean region where there is a strong variably among the seasons and therefore the rivers are generally ephemeral (i.e. river characterized by long dry season and intense flow for short periods following precipitations). This aspect is relevant since the role played by the physical/chemical/biological processes is different and the parameter values are different of order of magnitude. In order to demonstrate such fact, a simplified river water quality model was calibrated after an extensive data gathering campaign on an Italian river. Following a model calibration, the model uncertainty has been assessed by means of the GLUE (Generalized Likelyhood Uncertainty Estimation). The results showed that small rivers have different behaviors respect to the large ones in terms of importance of physical chemical processes. Such fact is reflected on the parameter values of the kinetic constant that are order of magnitude different from the large river ones. On the other hand, concerning the model uncertainty assessment, the uncertainty bounds were found to be relatively wide. These results have revealed that the model is unable to reproduce the pollutant discharges consistently and that the resulting predicted pollutant loads must be associated with significant uncertainty. This may be due in part to interaction between model parameters leading to equifinality between parameter sets. However, in terms of model capability to reproduce measured data, the results are in good agreement with the observed water quality data, therefore the model is consistent and can be a useful tool for water resource management.