## 2 Data and Methodology
### Methodology
Empirical Orthogonal Functions (EOFs) were used to investigate seasonal, interannual, and long-term sea level variability for the wider Caribbean Sea in which Jamaica is located. EOF analysis is commonly used in atmospheric sciences to identify spatial patterns in data over time by isolating statistically independent modes in the data [61]. EOF analysis was first applied to the unaltered ('raw') satellite altimetry data of sea level anomalies for the Caribbean region (10-24\({}^{\circ}\) N, 59-89\({}^{\circ}\) W). The linear trend was then removed (i.e., the altimetry data was 'detrended') and EOF analysis re-performed to investigate seasonal and interannual signals [23; 30]. Likewise, to investigate the interannual and long-term trends, the seasonal signal identified in the altimetry data (i.e., by averaging for each month in the year over the entire record) was subtracted from the altimetry record so that a non-seasonal altimetry dataset was obtained (i.e., the data was 'deseasoned') and EOFs determined. Finally, to investigate the interannual variability, the data were detrended and deseasoned, and a 13-month running mean applied before EOF analysis was carried out. The application of the running mean was to account for the eddy-rich nature of the Caribbean Sea [23]. Because summer (June-July-August) is climatologically when the highest sea levels occur for southeastern Jamaica (see Section 3.2), variability in this period was also investigated. Extracted sea level anomalies for June to August (JJA) were averaged for each year, and the EOF analyses previously described were repeated for the summer dataset. Correlation analysis was used to investigate possible connections between the dominant EOF modes and (i) large scale climate phenomenon such as ENSO, (ii) climate and ocean indices capturing variability in sea level pressures, sea surface temperatures (SSTs), and near surface wind in the Caribbean, and (iii) the SST gradient between the tropical north Atlantic and tropical Pacific oceans, which is a known influence on the strength of the Caribbean low level jet (CLLJ) [55]. See again Table 1 for a detailed description of the indices. [PERSON]'s correlation analysis is non-parametric and can reveal non-linear trends and relationships between two variables which may not be captured by [PERSON]'s correlation [62; 63; 64]. This was used to calculate correlation coefficients between the leading principal components and the climate indices. Finally, composite analysis was performed to examine the extent to which surface wind variability and SSTs act as potential drivers of sea level change in the region and, specifically, for the south coast of Jamaica. The analysis was restricted to the summer season. To derive the composites, the summer (averaged over JJAS) sea level anomalies timeseries for Jamaica was divided into quartiles, and high (upper quartile) and low (bottom quartile) sea level years isolated. Composite maps of mean summer SST and near surface wind anomalies were created for the high versus low sea level years, as well as for the difference between high and low sea level years. A Student's \(t\)-test with confidence interval 0.95 was used to determine regions of statistically significant difference [65; 66].