Mitigating predictive uncertainty in hydroclimatic forecasts: impact of uncertain inputs and model structural form

Abstract

Hydrologic and climate models predict variables through a simplification of the underlying complex natural processes. Model development involves minimising predictive uncertainty. Predictive uncertainty arises from three broad sources which are measurement error in observed responses, uncertainty of input variables and model structural error. This thesis introduces ways to improve predictive accuracy of hydroclimatic models by considering input and structural uncertainties. The specific methods developed to reduce the uncertainty because of erroneous inputs and model structural errors are outlined below.

The uncertainty in hydrological model inputs, if ignored, introduces systematic biases in the parameters estimated. This thesis presents a method, known as simulation extrapolation (SIMEX), to ascertain the extent of parameter bias. SIMEX starts by generating a series of alternate inputs by artificially adding white noise in increasing multiples of the known input error variance. The resulting alternate parameter sets allow formulation of an empirical relationship between their values and the level of noise present. SIMEX is based on the theory that the trend in alternate parameters can be extrapolated back to the notional error free zone. The case study relates to erroneous sea surface temperature anomaly (SSTA) records used as input variables of a linear model to predict the Southern Oscillation Index (SOI). SIMEX achieves a reduction in residual errors from the SOI prediction. Besides, a hydrologic application of SIMEX is demonstrated by a synthetic simulation within a three-parameter conceptual rainfall runoff model.

This thesis next advocates reductions of structural uncertainty of any single model by combining multiple alternative model responses. Current approaches for combining hydroclimatic forecasts are generally limited to using combination weights that remain static over time. This research develops a methodology for combining forecasts from multiple models in a dynamic setting as an improvement of over static weight combination. The model responses are mixed on a pair wise basis using mixing weights that vary in time reflecting the persistence of individual model skills. The concept is referred here as the pair wise dynamic weight combination. Two approaches for forecasting the dynamic weights are developed. The first of the two approaches uses a mixture of two basis distributions which are three category ordered logistic regression model and a generalised linear autoregressive model. The second approach uses a modified nearest neighbour approach to forecast the future weights. These alternatives are used to first combine a univariate response forecast, the NINO3.4 SSTA index. This is followed by a similar combination, but for the entire global gridded SSTA forecast field. Results from these applications show significant improvements being achieved due to the dynamic model combination approach. The last application demonstrating the dynamic combination logic, uses the dynamically combined multivariate SSTA forecast field as the basis of developing multi-site flow forecasts in the Namoi River catchment in eastern Australia. To further reduce structural uncertainty in the flow forecasts, three forecast models are formulated and the dynamic combination approach applied again. The study demonstrates that improved SSTA forecast (due to dynamic combination) in turn improves all three flow forecasts, while the dynamic combination of the three flow forecasts results in further improvements.