## 2 Data and Methodology
### Data  
Satellite altimetry data were obtained from the Copernicus Climate Change Service (C3S). C3S provides a dataset of gridded monthly sea level anomalies from satellite altimetry measurements, where anomalies are defined as the surface height above mean sea level from 1993 to 2019. Anomalies are calculated relative to a 20-year (1993-2012) baseline. The altimetry dataset was derived using an optimal interpolation method which combined the sea level anomalies output produced by two-satellite merged constellations at any given time. The combination of two satellites provides adequate spatial sampling while optimizing stability during the interpolation process. The C3S data are considered appropriate for climate applications such as investigating the evolution of sea level change on a regional or local scale [42]. Recently updated altimetry data (DT2018) using the Data Unification and Altimeter Combination System (DUACS) were used. The DT2018 ensemble of products incorporates 25 years of observations, tidal corrections, and mean sea surface corrections to significantly improve the accuracy of altimetry estimates in coastal areas [42]. This was considered important for this study, which analyses sea level change along the coast of a small island. For more information on the processing of the altimetry data, see [42; 43]. DT2018 altimetry products do not include corrections for Global Isostatic Adjustment (GIA) nor TOPEX-A satellite instrumental drift that was characteristic of the early years of altimetry data collection. To account for GIA, the ICE-5G (VM2) model was used to correct the altimetry values [23; 44]. The instrumental drift was accounted for by using an approximation for the examined altimetry period. Details on the calculation of this approximation are provided by [18; 42]. Research quality tide gauge data for Jamaica are unavailable for the altimetry era spanning 1993 to present. Tide gauge data for nearby stations in Grenada, Puerto Rico, Dominica, Haiti, and Cuba (see Figure 1) were obtained from The University of Hawaii Sea Level Centre (see Table 1). The locations of the tide gauges, in these islands, are shown in Table 2. The tide gauge data were used to offer a simple validation of the use of the altimetry dataset in the Caribbean. To investigate ocean-atmospheric phenomena which may be linked to variations in sea levels for Jamaica and the wider Caribbean Sea, ten (10) climate/oceanic indices and variables were considered. These indices were chosen based on current understanding of Caribbean climatology, particularly rainfall, and the atmospheric/oceanic modes that influence interannual and decadal climate variability within the region. For a more fulsome discussion on Caribbean climate variability, see, for example, [45; 46; 47]. Table 1 provides details about the climate indices, including how they are derived and the data sources from which they were extracted. Table 1 also shows the information for the sea surface temperatures and surface wind datasets used in the composite analyses described in the following section. \begin{table}
\begin{tabular}{c c c c c} \hline
**(a) Data Type** & **Details** & **Length** & **Source** & **Reference** \\ \hline \multirow{4}{*}{Tide Gauge} & Station data of relative sea level & & University of Hawaii Sea Level & \\  & rise for Cuba, Haiti, Puerto Rico, & Varying Record & Centre. Retrieved from: http: & \\  & Dominica, Grenada. & & Lengths & /uhslc.soest.hawaii.edu/data/ & [23; 48] \\  & & & (accessed on 16 March 2020). & \\ \hline \multirow{4}{*}{Satellite Altimetry} & Daily Data Sea surface height & & & \\  & above mean Sea Surface (’sla’ sea & 1993–2019 & & \\  & level anomaly). \(0.25^{\circ}\times 0.25^{\circ}\) & 1993–2019 & & \\  & Gridded Dataset. & & & \\  & & & (accessed on 5 September 2019). & \\ \hline \multirow{4}{*}{Sea Surface Temperature} & Extended Reconstructed Sea & & & \\  & Surface Temperature (ERSST) v5 & 1993–2019 & & \\  & Monthly \(2.0^{\circ}\times 2.0^{\circ}\) Gridded & 1993–2019 & & \\  & Dataset.