‘Where the Creeks Run Dry or Ten Feet High’: A Probabilistic Approach to Stage Height Forecasting in Australia

Abstract Streamflow prediction is a challenging but important task as it affects many processes in the environment. In Australia, the task is particularly complex because the transition from low to high flows can be rapid, and the overall variability is high. Accurate water resource management in Australia requires models that can accommodate these unique characteristics. Complicating matters further, streamflow is not directly measured but inferred from stage height measurements using rating curves. To address the challenges posed by the unique Australian hydrological features mentioned above, the present work proposes a model that: (a) directly predicts stage height rather than streamflow, (b) is sufficiently complex to learn the high variability of stage heights and (c) quantifies epistemic and aleatoric uncertainty by using a Bayesian framework. Our model is a Bayesian Hierarchical Mixture of Experts (BHME) model, with two mixture components. The two components are gamma densities in which the mean and variance are parameterized to depend on upstream stage height and rainfall from the previous day. The mixture weights are also parameterized to depend on the previous day's upstream stage height and rainfall through a logit link function. The method was tested on three gauging stations in the Orara and Richmond rivers. The BHME model provides better fit to the data and better predictive densities compared to a single component model. Notably, the BHME model excels in forecasting less frequent, high stage heights, crucial for managing high flow events. Additionally, transitions between mixture components offer insights into sudden stage height regime changes.