Degree Name

Master of Philosophy


School of Mathematics and Applied Statistics


Sea surface temperature (SST) in the Pacific Ocean is a key component of many global climate models and of the El Ni~no Southern Oscillation (ENSO) phenomenon. We analyse SST for the period November 1981 { December 2014. To study the temporal variability of the ENSO phenomenon, we have selected a subregion of the tropical Pacific Ocean, namely the Ni~no 3.4 region, as it is thought to be the area where SST anomalies indicate most clearly ENSO's in uence on the global atmosphere. SST anomalies, obtained by subtracting the appropriate monthly averages from the data, are the focus of the majority of previous analyses of the Pacific and other oceans' SSTs. Preliminary data analysis showed that not only Ni~no 3.4 spatial means but also Ni~no 3.4 spatial variances varied with month of the year. In this thesis, we conduct an analysis of the raw SST data and introduce diagnostic plots (here, plots of variability versus central tendency). These plots show strong negative dependence between the spatial standard deviation and the spatial mean. Outliers are present, so we use robust regression to obtain intercept and slope estimates for the twelve individual months and for all-months-combined. Based on this meanstandard deviation relationship, we define a variance-stabilising transformation. The transformation we derive is logarithmic, monotonic, nonlinear, and it respects the variability seen in SSTs from month to-month during the year. On the raw SST and transformed scales, we describe the Ni~no 3.4 SST time series with statistical models that are linear, heteroskedastic, and dynamical. We also derive a back-transform to take our forecasts on the transformed scale back to degrees Celsius. We compare the two forecasting methods via in-sample forecasting the data the model was trained on, November 1981 { December 2014, and then out-of-sample forecasting from January 2015 { December 2017. Our results indicate that the forecasts on the transformed scale perform better when predicting up to and into boreal spring, while the forecasts on the original scale perform better when predicting across and from boreal spring into summer. We also provide visualisations of the forecast error bias and variance which can be used to better identify and understand the (boreal) spring barrier.