On constraining the predictions of a distributed model: The incorporation of fuzzy estimates of saturated areas into the calibration process

Distributed hydrological models are generally overparameterized, resulting in the possibility of multiple parameterizations from many areas of the parameter space, providing acceptable fits to observed data. In this study, TOPMODEL parameterizations are conditioned on discharges, and then further conditioned on estimates of saturated areas derived from ERS-1 synthetic aperture radar (SAR) images combined with the In (a/tan beta) topographic index, and compared to ground truth saturation measurements made in one small subcatchment. The uncertainty associated with the catchment-wide predictions of saturated area is explicitly incorporated into the conditioning through the weighting of estimates within a fuzzy set framework. The predictive uncertainty associated with the parameterizations is then assessed using the generalized likelihood uncertainty estimation (GLUE) methodology. It is shown that despite the uncertainty in the predictions of saturated area the methodology can reject many previously acceptable parameterizations with the consequence of a marked reduction in the acceptable range of a catchment average transmissivity parameter and of improved predictions of some discharge events.