Identification and modelling of hydrological persistence with hidden Markov models

Abstract

Hydrological observations are characterised by wet and dry cycles, a characteristic that is termed hydrological persistence. Interactions between global climate phenomena and the hydrological cycle result in rainfall and streamflow data clustering into wetter and drier states. These states have implications for the management and planning of water resources. Statistical tests constructed from the theory of wet and dry spells indicate that evidence for persistence in monthly observations is more compelling than at an annual scale. This thesis demonstrates that examination of monthly data yields spatially - consistent patterns of persistence across a range of hydrological variables. It is imperative that time series models for rainfall and streamflow replicate the observed fluctuations between the climate regimes. Monthly time series are generally represented with linear models such as ARMA variants ; however simulations from such models may underestimate the magnitude and frequency of persistence. A different approach to modelling these data is to incorporate shifting levels in the broader climate with a tendency to persist within these regimes. Hidden Markov models ( HMMs ) provide a strong conceptual basis for describing hydrological persistence, and are shown to provide accurate descriptions of fluctuating climate states. These models are calibrated here with a full Bayesian approach to quantify parameter uncertainty. A range of novel variations to standard HMMs are introduced, in particular Autoregressive HMMs and hidden semi - Markov models which have rarely been used to model monthly rainfall totals. The former model combines temporal persistence within observations with fluctuations between persistent climate states, and is particularly appropriate for modelling streamflow time series. The latter model extends the modelling capability of HMMs by fitting explicit probability distributions for state durations. These models have received little attention for modelling persistence at monthly scale. A non - parametric ( NP ) HMM, which overcomes the major shortcomings of standard parametric HMMs, is also described. Through removing the requirement to assume parametric forms of conditional distributions prior to model calibration, the innovative NP HMM framework provides an improved estimation of persistence in discrete and continuous data that remains unaffected by incorrect parametric assumptions about the state distributions. Spatially - consistent persistence is identified across Australia with the NP HMM, showing a tendency toward stronger persistence in low-rainfall regions. Coherent signatures of persistence are also identified across time series of total monthly rainfall, numbers of rain - days each month, and the intensities of the most extreme rain events recorded each month over various short durations, illustrating that persistent climate states modulate both the numbers of rain events and the amount of moisture contained within these events. These results provide a new interpretation of the climatic interactions that underlie hydrological persistence. The value of HMMs to water resource management is illustrated with the accurate simulation of a range of hydrologic data, which in each case preserves statistics and spell properties over a range of aggregations. Catchment - scale rainfall for the Warragamba Reservoir is simulated accurately with HMMs, and rainfall - runoff transformations from these simulations provide reservoir inflows of lower drought risk than provided from ARMA models.