Exploring the utility of multi-response calibration in river system modelling

Abstract

Water allocation models can be used to compare water sharing scenarios in regulated catchments to evaluate the effects on both the water users and the environment. These models include a representation of the physical system with modules such as flow routing, rainfall-runoff modelling or groundwater/surface water interactions, as well as management components to take into account infrastructure such as dams, canals or extraction points. Water allocation models can be complex modelling structures with a large number of parameters to be calibrated on limited datasets, especially regarding the management aspects. Additionally, these models are used as a tool in the making of long-term decisions with important social and environmental impacts. As a result, the assessment of uncertainty becomes a critical task to inform the decision-makers about the likely robustness of the model analysis and predictions. Calibration of these models is currently problematic. In particular, the errors affecting system observations are often not properly accounted for, which is a concern since these errors may be quite large. Furthermore, calibration is often performed separately on various components of the system, resulting in inconsistencies when the components are linked. These deficiencies make it difficult to quantify the uncertainty in the predictions of the entire system performance. The Bayesian approach provides a platform to directly address the sources of uncertainty (input, output, and model error) in the model calibration and prediction process. This study seeks to develop a Bayesian multi- response method for use with river system models, allowing joint calibration to all sources of information available in a particular application. Unlike the traditional approach, joint calibration forces consistency in performance across the entire system. Moreover, the Bayesian approach provides a framework for a proper accounting of uncertainty both in the inferred parameters and in the model predictions. This study illustrates the application of the Bayesian multi-response calibration approach to the STICKMAN model, a simplified river system model which describes key aspects of complex river basin models such as IQQM but is computationally less demanding. The model was calibrated using a Weighted Least Squares method in a synthetic data study. Model calibration used both single and multiple response data (eg. streamflow at the outlet and at internal system nodes, reservoir time series, etc.) to investigate the improvements in parameter estimation associated with the inclusion of additional responses. The use of multiple response data during model calibration was generally found to reduce parameter uncertainty. However, the extent of reductions in uncertainty depended on which responses were included, highlighting that some sources of data are more informative than others. This supports the findings of Kuczera and Mroczkowski's (1998), who conclude that the value of new sources of response data should be assessed a priori before embarking on (potentially expensive) field campaigns. This study reports the first findings in this project. Future work will explore the effects of multiple response data on model predictive performance, further develop the STICKMAN model to better represent processes and errors, and finally consider IQQM case studies.