Bayesian Total Error Analysis For Hydrological Models: Preliminary Evaluation Using Multi-Site Catchment Rainfall Data

The Bayesian Total Error Analysis methodology (BATEA) provides the opportunity to directly address all sources of uncertainty (input, model and response error) in the calibration of conceptual rainfall-runoff (CRR) models. BATEA has the potential to overcome the parameter biases introduced by poor conceptualisations of these sources of errors and enhance regionalisation capabilities of hydrological models. This study is a preliminary evaluation of the robustness of the parameter estimates and the robustness in validation of the BATEA framework using multi-site catchment rainfall data. The aim was to compare how BATEA performed when provided with "degraded" rainfall from a single site compared to average rainfall from the entire catchment. The methodology used was to calibrate the same model to streamflow from the same catchment using six different rainfall time series; catchment average from the SILO gridded rainfall product, four individual gauges and the average of these four gauges. The catchment chosen was the Horton catchment, located west of the Great Dividing Range in Northern New South Wales, Australia. Markov chain Monte Carlo methods were used to compare the parameter estimates and their uncertainty using the BATEA and standard least squares (SLS) approaches for treating the sources of errors. It was found that the BATEA parameter estimates for the different rainfall time series were more consistent with each other, with average deviations from the overall average parameter value of the order of 0.5 to 1.2 times the parameter standard deviation. In comparison the SLS parameters estimates were more sensitive to the differences in the input rainfall data with average deviations from the overall average parameter value varying from 1 to 11 times the parameter standard deviation. For validation, it was found that using the catchment average rainfall the BATEA and SLS parameters provided similar Nash-Sutcliffe (NS) statistics. However, it was found that catchment average rainfall does not necessarily provide the best streamflow predictions. Figure 1 compares the NS statistic for the 2 year validation period for the twelve parameter sets, which arise from using both BATEA and SLS approaches to calibrate to each of the six rainfall time series. Figure 1(a) shows NS using gauge 054021 as input, while Figure 1(b) shows the NS using the SILO rainfall as input. Gauge 054021 was chosen as it had the lowest BATEA rainfall error and was located in the high rainfall region of the catchment. In general, the BATEA parameter estimates with the 054021 rainfall provide higher NS statistics then SLS. This indicates that BATEA has the potential to utilise rainfall data from more productive areas of the catchment to enhance streamflow predictions. These results have several caveats, as they are based on a single catchment, and the validation period was relatively short, with the potential for biases. Nonetheless, these initial results are promising for the potential of BATEA to improve regionalisation. Future research will investigate the generality of these results with further case studies. [GRAPHICS] .