Spatio-temporal models of Australian rainfall and temperature data

Abstract

This thesis presents three essays on the analysis of historical meteorological data in Australia. The Australian Bureau of Meteorology has established a network of more than one thousand stations across Australia that have recordings dating from early last century, resulting in a large dataset of meteorological records. These data provide important information on the dynamics of the Australian climate system and systematic investigation using these data can help us to better understand our climate and prepare for possible changes. The purpose of this thesis is to develop models and methods to analyse such meteorological data from a statistical perspective.

In Chapter 2, a spatia-temporal model is developed based on monthly average temperature data at 177 locations in south-eastern Australia over 40 years. Guided by a preliminary analysis, a model with components dealing with spatial varying mean and seasonality, short-term and long-term temporal trends is built, and the space-time interaction is modelled by the kernel-convolution method. It is shown that the temperature has become warmer in most of the south-eastern Australia during the period under investigation.

In Chapter 3, a new duration-dependent Hidden Markov Model is proposed as an extension to the Hidden Markov Model (HMM) and Non-homogeneous Hidden Markov Model (NHMM) which assumes that the transition probabilities are either constant or only depend on some independent variables. The possibility of duration-dependent effects is formally considered in this chapter where the transition probabilities are allowed to be explicitly correlated to duration - how long the hidden system has been in the current state. This approach is used to model the amount of daily rainfall amount at 5 locations in Darwin, Northern Territory.

For data arising from climate phenomenon, such as the temperature and rainfall data considered here, it is common for outliers to be present. The presence of outliers could unduly influence the results of any analysis that are conducted and make conclusion non-robust. But it is often difficult to detect them simultaneously because of the masking effect. Motivated by this problem, a general method is proposed in Chapter 4 for identifying multiple influential observations in regression models. The ability of this method is tested and illustrated by both a thorough simulation and several examples.