Effects of uncertainty in hydrologic model calibration on extreme event simulation

Computer models representing the hydrologic cycle as a simplified system have become a preferred tool for estimating floods. However, scientific understanding of the uncertainty inherent in these models has not kept pace with their development and application. In many cases it is incorrectly assumed that all uncertainty in model structure, input data, and parameters is minimized or eliminated through calibration. The end result is a ubiquitous but unknowable degree of model predictive uncertainty that may or may not significantly affect the outcome of any given application. Extrapolation o f a model beyond its calibration range (i.e., for extreme event simulation) invariably results in a substantial increase in this uncertainty. This work aims to promote qualitative and quantitative understanding of model predictive uncertainty in extreme event simulation. It therefore begins with a review of the many sources contributing to model predictive uncertainty, an analysis of their origins and interdependencies, and a synthesis of various methods for analyzing uncertainty. As a pre-requisite step towards the larger goal of reducing overall model predictive uncertainty, this work investigates the variability in estimates of extreme floods (e.g., peak flow, timing, and volume) introduced by subjective decisions made during calibration. Multiple automatic calibrations of a conceptual hydrologic model are conducted using different objective functions to evaluate calibration performance, resulting in a collection of non-inferior parameter sets. Each parameter set is then used to simulate an extreme event based on hydrologic data for the Coquitlam Lake watershed in British Columbia, which is developed for hydropower by BC Hydro. The combined output of these extreme event simulations characterizes the relative variability in the hydrographs. Simulations are conducted using the University of British Columbia Watershed Model (UBCWM), which is widely used to describe and forecast watershed behaviour in mountainous areas of British Columbia. Calibrations of the UBCWM utilize the Shuffled Complex Evolution Algorithm (SCE-UA), an effective and efficient optimization-based automatic calibration routine. Because automatic calibrations fail to capture the different kinds of expert knowledge inherent in a manual calibration, extreme event hydrographs obtained using calibrated parameter sets are compared on a relative rather than absolute basis. Results show that automatic calibration may provide a straightforward method o f identifying potential areas where subject models are over-parameterized with respect to the calibration data. More importantly, preliminary results show that the variability is relatively constrained amongst simulations based on a Probable Maximum Flood (PMF) scenario, with coefficient of variation for peak flow, event volume, and time to peak of 4%, 1%, and 1% respectively. This value is negligible in comparison with other uncertainties that dominate extreme events like the PMF. Thus, the PMF-based simulations are relatively insensitive to the different measures of calibration performance used. Similar trials using other models would permit an estimate of the extent to which one could expect to resolve divergent estimates through implementing different but equally valid calibrations. Observations of this work are applicable for the management of hydropower production and flood control for these watersheds. These observations will provide insights into uncertainty in extreme event simulation and may contribute to the improved management of water, hydropower systems, and public safety in Canada and around the world.

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