# Description of Tropical SST Predictions

## Data Details

The current version of LIM SST forecasts is based on the NOAA Extended Reconstructed Sea Surface Temperatures, v.3b.

## Model Details

Predictions of Global Tropical Sea Surface Temperature Anomalies (SSTAs) are made using linear inverse modeling (LIM) procedure discussed in Penland, C., and T. Magorian, 1993. Anomalies are calculated relative to 1981-2010 climatology, smoothed by a three months running mean, and projected onto 20 leading EOFs containing about 90% of the SST variance in the global tropical belt. Examining the corresponding principal component (PC) time series, three of the 20 PCs were found to have significant trends. The linear trends are removed from those three PCs, leaving a 20-dimensional basis set from which the forecasts are made. The LIM forecast is made using Green functions estimated from a 1950-2010 training period. After applying the forecast procedure, the trend at the date of the forecast is replaced in the relevant PCs and the field is then transformed to geographical space.

## Description of Tropical SST Index

The prediction model was validated using a jackknifing procedure using four ten-year verification periods in the interval between 1970 and 2010. We provide prediction time series, which consist of the prediction (red lines) and verification (blue lines) corresponding to these validation periods for various tropical SST indices shown in map below:

Gaps in the prediction time series are due to the lags incurred between verification periods in the jackknifing procedure. Dotted lines are confidence intervals corresponding to one standard deviation of the expected prediction error due to stochastic forcing.

The projection onto the optimal structure (Penland and Sardeshmukh, 1995) is presented in a manner similar to those of the indices. The maps displayed on the optimal structure page are based on Green functions estimated from the 1950-2010 training period. The optimal structure index at any time is the projection of the SST map onto the optimal structure. We present the Nino 3.4 SST anomaly (blue line) together with the optimal structure index 7 months earlier (red line) and the correlation between them. Also shown is a scatter plot of these time series. The red star compares the current value of Nino 3.4 SST anomaly with the value of the optimal structure index 7 months earlier; the red arrow shows the current optimal structure index.

SSTs are consolidated onto a grid 4 degrees (latitude) by 10 degrees (longitude). Values of SST and SST anomalies represent the average value within a grid box. Numerical tables of SST predictions are presented in tabular form, with latitudes representing the center of the grid box along the left side of the table, and longitudes representing the center of the grid box along the top.