Consideration of measurement uncertainty in the evaluation of goodness-of-fit in hydrologic and water quality modeling

As hydrologic and water quality (H/WQ) models are increasingly used to guide water resource policy, management, and regulation, it is no longer appropriate to disregard uncertainty in model calibration, validation, and evaluation. In the present research, the method of calculating the error term in pairwise comparisons of measured and predicted values was modified to consider measurement uncertainty with the goat of facilitating enhanced evaluation of H/WQ models. The basis of this method was the theory that H/WQ models should not be evaluated against the values of measured data, which are uncertain, but against the inherent measurement uncertainty. Specifically, the deviation calculations of several goodness-of-fit indicators were modified based on the uncertainty boundaries (Modification 1) or the probability distribution of measured data (Modification 2). The choice between these two modifications is based on absence or presence of distributional information on measurement uncertainty. Modification 1, which is appropriate in the absence of distributional information, minimizes the calculated deviations and thus produced substantial improvements in goodness-of-fit indicators for each example data set. Modification 2, which provides a more realistic uncertainty estimate but requires distributional information on uncertainty, resulted in smaller improvements. Modification 2 produced small goodness-of-fit improvement for measured data with little uncertainty but produced modest improvement when data with substantial uncertainty were compared with both poor and good model predictions. This limited improvement is important because poor model good ness-of-fit, especially due to model structure deficiencies, should not appear satisfactory simply by including measurement uncertainty. (C) 2007 Elsevier B.V. All rights reserved.