Single-site point process-based rainfall models in a nonstationary climate
Long series of simulated rainfall are required at point locations for a range of applications, including hydrological studies. Clustered point-process based rainfall models have been used for generating such simulations for many decades. One of their main advantages is the fact that they generate simulations in continuous time, allowing aggregation to different timescales in a consistent way, and such models generally perform well in representing rainfall at hourly to daily timescales. An important disadvantage, however, is their stationarity. Although seasonality can be allowed for by fitting separate models for each calendar month or season, the models are unsuitable in their basic form for climate impact studies. In this thesis we develop new methodology to address this limitation. We extend the current fitting approach by replacing the discrete covariate, calendar month, with continuous covariates which are more directly related to the incidence and nature of rainfall. The covariate-dependent model parameters are estimated for each time interval using a kernel-based nonparametric approach within a Generalised Method of Moments framework. An empirical study using the new methodology is undertaken using a time series of five-minute rainfall data. In addition to addressing the need for temporal non-stationarity, which is our main focus, we also carry out a systematic comparison of a number of key variants of the basic model, in order to identify which features are required for an optimal fit at sub-hourly resolution. This generates some new insights into the models, leading to the development of a new model extension, which introduces dependence between rainfall intensity and duration in a simple way. The new model retains the “rectangular pulses” (i.e. rain cells with a constant intensity) of the original clustered point-process model, which had previously been considered inappropriate for fine-scale data, obviating the need for a computationally more intensive “instantaneous pulse” model.