Model Calibration and Uncertainty Estimation

All rainfall-runoff models are, by definition, simplifications of the real-world system under investigation. The model components are aggregated descriptions of real-world hydrologic processes. One consequence of this is that the model parameters often do not represent directly measurable entities, but must be estimated using measurements of the system response through a process known as model calibration. The objective of this calibration process is to obtain a model with the following characteristics: (i) the input-state-output behavior of the model is consistent with the measurements of catchment behavior, (ii) the model predictions are accurate (i.e. they have negligible bias) and precise (i.e. the prediction uncertainty is relatively small), and (iii) the model structure and behavior are consistent with current hydrologic understanding of reality. This article describes the historic development leading to current views on model calibration, and the algorithms and techniques that have been developed for estimating parameters, thereby enabling the model to mimic the behavior of the hydrologic system. Manual techniques as well as automatic algorithms are addressed. The automatic approaches range from purely random techniques, to local and global search algorithms. An overview of multiobjective and recursive algorithms is also presented. Although it would be desirable to reduce the total output prediction error to zero (i.e. the difference between observed and simulated system behavior) this is generally impossible owing to the unavoidable uncertainties inherent in any rainfall-runoff modeling procedure. These uncertainties stem mainly from the inability of calibration procedures to uniquely identify a single optimal parameter set, from measurement errors associated with the system input and output, and from model structural errors arising from the aggregation of real-world processes into a mathematical model. Some commonly used approaches to estimate these uncertainties and their impacts on the model predictions are discussed. The article ends with a brief discussion about the current status of calibration and how well we are able to represent the effects of uncertainty in the modeling process, and some potential directions.