‘Where the creeks run dry or ten feet high’ Bayesian models for hydrology in Australia

Abstract

This thesis tackles the complex challenge of water management in Australia, where climate change intensifies variability in water availability, creating significant challenges in accurate hydrological forecasting. Reliable predictions of water resource ecosystems require models that account for diverse data sources and the complexities of natural systems, making uncertainty quantification essential for informed decision-making. Using a Bayesian approach, this thesis develops methods to provide probabilistic hydrological predictions with quantified uncertainties. The first contribution of this thesis is the development of a Bayesian Hierarchical Mixture of Experts (BHME) model that captures rapid changes and variability in river stage heights, crucial for anticipating high-flow events. To address the variability in stage-discharge relationships, a novel method named’ AdaptRatin’ is proposed. AdaptRatin partitions gauging data into locally stationary segments and models the stage- discharge relationship non-parametrically by placing a Gaussian process prior over it. This approach can capture changes over time and reliably estimate both stationary and non-stationary stage discharge relationships. Building on these insights, a framework for generating probabilistic streamflow forecasts tailored to Australian river systems is introduced, combining stage height predictions from the BHME model with stage-discharge relationships estimated by AdaptRatin. This combined approach uses observed data alone, providing robust, data-driven, probabilistic streamflow forecasts to support water management decisions.