A Bayesian Tool for Validating Process-Based Models

Process-based models provide an effective means of studying and evaluating the response of watersheds to varying hydrological and ecological conditions. The conventional approach to modeling watersheds is first calibrating the model with some observed data, and then validating it with additional observed data. The calibration process typically involves varying some of the independent input parameters within their plausible ranges until the model results match observations in the real world. The model is deemed validated if it is able to match the additional observed data. The problem, however, is that most models are validated at the same locations for which they were calibrated, typically the watershed outlet. This means that any inferences for a sub-area within the watershed, for which a calibration was not performed, may not be justified as there is no guarantee that the correct non-linear processes are being captured. In soil erosion studies, although landscapes are heterogeneous with regards to soil properties and land use, calibration and validation usually involves the use of aggregated soil samples, making it difficult to assess whether or not model predictions for the different land uses are correct. These aggregated samples are the result of non-linear mixing that occurs between soils from different land uses as they travel from their points of origin to the point of sampling. To provide a greater degree of confidence in calibrated models, therefore, this study presents a Bayesian statistical tool that can be used to provide an added level of validation to process-based models. The presented tool is an un-mixing model that is furnished with probability distributions capable of simulating the non-linear mixing of soils as they travel to sampling points. The output from the model is the proportion of eroded soil that originates from each land use in the watershed. This allows for the direct evaluation of process-based models to determine if they are able to predict adequately the proportion of eroded sediment from each land use. In addition, the Bayesian tool provides a direct means of quantifying the uncertainty related to simulated results.