## 2 Data and Methodology
### Methodology  
The linear trend in the altimetry records was obtained using linear least-square fitting. This allowed for the trend to be determined from the timeseries by fitting it to a linear model:  
\[S=\sum_{i=1}^{n}(y_{i}-(p_{1}x_{i}+p_{2}))\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**(b)**} & \multicolumn{2}{c}{**Location**} & \multicolumn{1}{c}{**Correlation**} & \multicolumn{1}{c}{**Period of**} & \multicolumn{1}{c}{**Distance to Nearest Grid**} \\ \cline{2-5} \multicolumn{1}{c}{**Tide Gauge**} & \multicolumn{1}{c}{**Tide Gauge**} & **Altimetry Grid Box** & **Coefficient** & **Overlap** & **Corner from Tide Gauge** \\ \hline Port-au Prince, Haiti & 18.567\({}^{\circ}\) N, 72.350\({}^{\circ}\) W & 18.625\({}^{\circ}\) N, 72.625\({}^{\circ}\) W & **0.35** & 2012-2015 & 7.02 \\ \hline San Juan, Puerto Rico & 18.460\({}^{\circ}\) N, 66.117\({}^{\circ}\) W & 18.875\({}^{\circ}\) N, 66.125\({}^{\circ}\) W & **0.89** & 2000-2008 & 18.37 \\ \hline Prickley Bay, Grenada & 12.005\({}^{\circ}\) N, 61.765\({}^{\circ}\) W & 12.125\({}^{\circ}\) N, 61.875\({}^{\circ}\) W & **0.77** & 2012-2015 & 18.01 \\ \hline Roseau, Dominica & 15.313\({}^{\circ}\) N, 61.390\({}^{\circ}\) W & 15.375\({}^{\circ}\) N, 61.625\({}^{\circ}\) W & **0.74** & 2014-2016 & 27.02 \\ \hline Cabo Cruz, & 19.833\({}^{\circ}\) N, & 19.875\({}^{\circ}\) N, & **0.81** & 1993-2019 & 16.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlations between Caribbean tide gauge stations and altimetry. Significant correlations are in bold. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**(b)**} & \multicolumn{1}{c}{**Climate/Ocean**} & \multicolumn{1}{c}{**Description**} & \multicolumn{1}{c}{**Period**} & \multicolumn{1}{c}{**Source**} & \multicolumn{1}{c}{**Reference**} \\ \hline
**Variables** & & & & \\ \hline \hline \multirow{6}{*}{ \begin{tabular}{c} Sea Level \\ Pressure (SLP) \\ \end{tabular}  } & \multicolumn{1}{c}{\ \begin{tabular}{c} Reanalysis data of mean sea \\ level pressure at 17.5\({}^{\circ}\) N, 77.5\({}^{\circ}\) \\ W. Gridded monthly reanalysis \\ dataset at 2.5\({}^{\circ}\)\(\times\) 2.5\({}^{\circ}\) resolution. \\ \end{tabular}  } & \multirow{6}{*}{1949–2020} & \multicolumn{1}{c}{ \begin{tabular}{c} Extracted from US Weather \\ Service—National Met. Center’s \\ NOAAData Obtained from: \\ [[http://iridl.ldeo.columbia.edu/](http://iridl.ldeo.columbia.edu/)]([http://iridl.ldeo.columbia.edu/](http://iridl.ldeo.columbia.edu/)) \\ SOURCES/NOAA/.NCEP- \\ NCAR/.CDAS-1/.MONTHLY/ \\ Intrinsic/.MSL/.pressure/ \\ (accessed on 9 September 2021). \\ \end{tabular}  } & \multirow{6}{*}{1950–2019} & \multirow{6}{*}{1950–2019} & NOAA Database obtained from: \\  & & & \\ \cline{1-1} \cline{4-4}  & \multicolumn{1}{c}  
where \(S\) is a set of simultaneous equations with unknowns \(p_{1}\) and \(p_{2}\). The equation was solved to determine the values of \(p_{1}\) and \(p_{2}\), where the result is represented by a first-order polynomial of the form:  
\[y=p_{1}x+p_{2}\]  
The first-order differential equation gives the linear trend, where \(y\) is the sea level at time \(x\). Uncertainties in the satellite altimetry trends were obtained from analysis of the altimetry error budget and least-squared error variance-covariance assessment of the global mean sea level (GMSL) trends at a 90% confidence level [60]. The annual trend was computed for the monthly values, averaged annually. The Mann-Kendall Test was used to determine statistical significance of the trend. It is a non-parametric test of the null hypothesis that there is no monotonic trend in the tide gauge and satellite altimetry data [30]. The mean seasonal cycle of sea level change was calculated following [21; 24]. [PERSON]'s correlation coefficients were calculated between the tide gauge records for the five locations shown in Figure 1 and the closest altimetry grid point. [PERSON]'s correlation was also used for comparison.