A reliability-based approach to calibration and exploration for water quality modeling

Management of water quality in streams and rivers requires the use of calibrated and reliable water quality models for the prediction of pollutant concentrations. There is uncertainty in the predicted pollutant concentration due to sampling, extrapolation, calibration, and the model itself. Uncertainty due to calibration and the model itself is from the inability of the simulation model to represent precisely the system's true physical and/or chemical behavior. The uncertainties in model input parameters and observations are from data inadequacies and errors, which usually can be reduced when more samples are obtained. However, the more samples that are collected, the higher is the cost of the sampling.; The purpose of this study is to develop a quantitative approach to aid in calibration and sampling for water quality simulation, namely the reliability-based approach for calibration and exploration (RBCE). The RBCE can provide a reliability index to indicate how well the model-predicted result represents the water quality process that it intends to describe, while at the same time describing the probability that water quality standards will be met. The reliability provided by the RBCE includes not only the information about the model-predicted result and observations, but also the uncertainties associated with them. The RBCE applies a first-order Taylor series expansion to estimate the uncertainty in the model results by combining the uncertainty in input parameters with the sensitivities due to changes in each input parameter. Uncertainties in input parameters and observations are determined through data extrapolation techniques, specifically a variogram function and the multivariate conditional probability calculation, while sensitivity is calculated by directly coding sensitivity derivatives into a model using ADIFOR2.0. The reliability in meeting a regulatory limit is also computed by comparing the probability distribution of the model-predicted result with regulatory limit. The RBCE can quantitatively determine new sampling locations and the parameters to sample, which will reduce the uncertainty in model-predicted concentration and the sampling cost while at the same time improving the reliability. The approach is demonstrated on a One-dimensional Transport with Inflow and Storage (OTIS) model to simulate the concentration of iron (Fe) in Mineral Creek, Colorado.