Bayesian analysis of input uncertainty in hydrological modeling: 2. Application

TLDR

The Bayesian total error analysis (BATEA) methodology directly addresses both input and output errors in hydrological modeling, requiring the modeler to make explicit, rather than implicit, assumptions about the likely extent of data uncertainty. This study applies BATEA to two North American catchments, evaluating the Variable Infiltration Capacity model with and without precipitation uncertainty and examining BATEA’s performance under severe model errors. The authors use BATEA to analyze the VIC model’s performance, compare scenarios with and without precipitation uncertainty, and explore computational cost reductions via Newton-type methods for robust VIC implementations. The analysis shows precipitation errors significantly affect hydrograph predictions and calibrated parameters, and while BATEA directly handles input uncertainty, it offers limited insight into model errors, depends on poorly understood error models, and creates computationally challenging high-dimensional problems.

Abstract

The Bayesian total error analysis (BATEA) methodology directly addresses both input and output errors in hydrological modeling, requiring the modeler to make explicit, rather than implicit, assumptions about the likely extent of data uncertainty. This study considers a BATEA assessment of two North American catchments: (1) French Broad River and (2) Potomac basins. It assesses the performance of the conceptual Variable Infiltration Capacity (VIC) model with and without accounting for input (precipitation) uncertainty. The results show the considerable effects of precipitation errors on the predicted hydrographs (especially the prediction limits) and on the calibrated parameters. In addition, the performance of BATEA in the presence of severe model errors is analyzed. While BATEA allows a very direct treatment of input uncertainty and yields some limited insight into model errors, it requires the specification of valid error models, which are currently poorly understood and require further work. Moreover, it leads to computationally challenging highly dimensional problems. For some types of models, including the VIC implemented using robust numerical methods, the computational cost of BATEA can be reduced using Newton‐type methods.