## Description of C-LIM Tropical Forecasts

Inspired by the success of linear inverse model (LIM) predictions of seasonal tropical SST anomalies (Penland and Magorian 1993) and of weekly extratropical atmospheric circulation anomalies (Newman et al. 2003), we have constructed a coupled LIM (C-LIM) to make weekly tropical forecasts of both oceanic and atmospheric variables, a procedure described in great detail in Newman et al. (2009). In the C-LIM, the dynamical evolution operator is estimated from the observed statistics of weekly-averaged tropical variations over the years 1982-2011. (Also see Penland and Sardeshmukh 1995 for a complete treatment of LIM and its construction, and Winkler et al. 2001 for more detail on the atmospheric LIM.)

The version of the C-LIM used in these web pages differs from the Newman et al. (2009) C-LIM in a few key details: it is based on a slightly longer dataset, the model state variable consists of SST, 20 degC isotherm depth in the ocean, OLR, and 200/850 mb winds rather than SST, diabatic heating and atmospheric circulation. This latter change is made so that forecasts can be initialized in near real-time. All qualitative (and generally quantitative) aspects of the model remain the same.

### Data details:

Newman et al. obtained weekly SSTs from the NOAA OI V2 dataset. However, since this dataset is generally unavailable in near real-time, we instead use the NOAA High-resolution Blended Analysis of Daily SST and Ice dataset (AVHRR-only) (version 2). This dataset has 0.25 degree resolution, but to produce the coarse-graining necessary for a LIM we area-average in 2 degree latitude x 5 degree longitude grid boxes that contain no fewer than 50% ocean points. 5-day running means are then calculated instead of the 7-day running means used in Newman et al.; resulting differences are consistent with the somewhat higher resolution and will be described in an upcoming paper.

To construct the C-LIM used on this website we also use the daily interpolated OLR dataset [Liebmann and Smith (Bulletin of the American Meteorological Society 1996)], averaged into 5-day running means and also area-averaged onto the same grid used for the SST field. To initialize our forecasts, however, since this dataset is not available in real-time we instead use un-interpolated OLR data, also averaged into 5-day running means but using a simple linear weighting for missing values. Winds are obtained from the NCEP-NCAR Reanalysis in near realtime and are again averaged onto the same grid.

Daily anomalies are averaged with a 5-day running mean (misleadingly termed pentad here) and are determined relative to a 1982-2011 daily climatology (smoothed with a 31-day running mean). Values of anomalies represent the average value within a grid box. Similar to Newman et al., the leading 19 SST EOFs (representing about 65% of the domain-integrated pentad variance) are retained. Also, for this real-time C-LIM, the leading 44 OLR EOFs (representing about 65% of the variance) and leading 26 combined wind EOFs (representing about 40% of the variance) are retained; in contrast, Newman et al. retained only about 36% of the weekly heating variance, and 44% of the weekly streamfunction variance but also two thirds of the weekly velocity potential variance. Additionally, this C-LIM includes the leading 2 Z20 EOFS, which represent 34% of the variance.

Due to data availability limitations, forecast initializations are usually 1-2 days behind. So, for example, the most up-to-date pentad mean may be constructed from data for days n-5 through n-1, so that the "Pentad 1" forecast is a 5-day mean centered on day n+2, the "Pentad 2" forecast is centered on day n+7, and so on.

### Forecast skill:

The prediction model was validated using a jackknifing procedure in which three years (10% of the dataset) are removed at a time to serve as independent data. Maps of the resulting cross-validated forecast skill for tropical SST, winds, and OLR are shown for forecast leads of 1-8 pentads and 12, 18, 24, 30, 36, 42, 48, and 54 pentads. Cross validation is carried out as follows: We sub-sampled the data record by sequentially removing one three-year period, determined the model for the remaining years, and then generated forecasts for the independent years. This procedure was repeated for the entire period. Forecast skill is then determined by comparing the local anomaly correlation between the cross-validated model predictions and gridded untruncated (that is, not truncated in EOF space) verifications. The most recent forecast verification map displayed here, however, is truncated in EOF space.

All LIM forecasts on these webpages represent ensemble mean forecasts. Also, LIM not only produces forecasts but also allows for an a priori estimate of forecast skill (Newman et al. 2003). The expected skill, measured as the mean forecast skill of an infinite member ensemble of forecasts, is indicated for each forecast. This prediction of the actual skill is good on average for skill > 0.4.