Description of C-LIM Tropical SST and OLR Predictions
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 1982-2007. (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 two details: it is based on a slightly longer dataset, and the model state variable consists of SST and OLR 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 5 degree grid boxes that contain no fewer than 50% ocean points. 7-day running means are then calculated and the data are otherwise used as in Newman et al.; resulting differences are minor.
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 7-day running means and also area-averaged onto the same 5 degree 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 7-day running means but using a simple linear weighting for missing values.
Both OLR and SST fields are put onto a grid with 5 degree spacing in both latitude and longitude. Anomalies are weekly averaged and are relative to a 1982-2007 daily climatology (smoothed with a 31-day running mean). Values of OLR and SST anomalies represent the average value within a grid box. Similar to Newman et al., the leading 22 SST EOFs (representing about 70% of the domain-integrated variance) are retained. For this real-time C-LIM, the leading 35 OLR EOFs (representing about 65% of the variance) are retained; in contrast, Newman et al. retained only about 36% of the weekly heating variance but also two thirds of the weekly velocity potential variance.
Due to data availability limitations, forecast initializations are one day behind. Therefore, the most up-to-date weekly mean is constructed from data for days n-7 through n-1, so that the "Week 1" forecast is a weekly mean centered on day n+3, the "Week 2" forecast is centered on day n+10, and so on.
Forecast skill:
The prediction model was validated using a jackknifing procedure in which one year is removed at a time to serve as independent data. Maps of the resulting cross-validated forecast skill for both tropical SST and OLR are shown for forecast leads of 1-5 weeks and 12, 16, 20, 24, and 28 weeks. Anomaly correlation skill scores are between predictions and verifications; note that forecast verifications used in this measure of skill are not truncated in EOF space. 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). Such an analysis is planned for these webpages at a later date.