Hydrological models provide extrapolations or predictions, which are not lacking of uncertainty, which reduces the confidence in their results. One phase of the hydrological implementation process, which significantly contributes to that uncertainty, is the calibration phase in which values of the unknown model parameters are tuned by optimizing an objective function. Traditionally, the most commonly used fitting criterion,has been the simple least squares (SLS), regardless of the SLS criterion involves assumptions about the probability distribution of the errors. Failure of these assumptions introduces noise into the estimation of the parameters, which leads to the phenomenon called model divergence, where the errors variance of the (spatially and temporally) forecasted flows, far exceeds the errors variance in the fitting period. In the present paper it has been carried out an estimation of the parameters of TETIS, a distributed hydrological model with a particular split structure of the effective model parameters (Francés et al., 2007). Such an estimate has been performed with the aid of a Markov Chain Monte Carlo (MCMC) algorithm called Dream-ZS (Laloy & Vrugt, 2012). MCMC algorithm quantifies the uncertainty of the parameters by getting the posterior probability distribution, conditioned on the observed flows. The calibration process is performed with three error model assumptions. The greater or lesser suitability of the three parameter sets is evaluated through the temporal, spatial and spatiotemporal validation of each one. It is concluded that hydrological models calibrated with a correct hypothesis of the error model, significantly reduces the model divergence phenomenon. Similarly a global sensitivity analysis (GSA) reveals that the relative influence of each parameter in the hydrological model is not independent of the assumed error model. In conclusion, model divergence phenomenon appears meaningful when it have been achieved a very good hydrological model results during calibration, but for the wrong reasons.
Francés, Félix and Hernández, Mario R., "On The Influence Of Error Model In The Good Performance Of The Hydrological Model For The Right Reasons." (2014). CUNY Academic Works.