### Methodology for ESRL 2-Category, 2-Tier Seasonal Forecast Tool

The tropical SST forecasts are derived from 5 different sources, as described below. The atmospheric predictions are based on a statistical analysis relating each tropical SST forecast to atmospheric general circulation model (GCM) data of global precipitation and 500-mb height.

### SST Predictions

We use the linear combination of the first 28 seasonal EOFs of tropical SST (explaining 98% of the seasonal SST variance within 20N-20S) as the predictor set that maximize the correlation with an identical 28 EOFs of the SST predictand. These structures are linearly combined to yield the forecast of the spatial distribution of total SST anomaly within 20N-20S. Predictions are made for lags of 1-season through lags of 4-seasons. A total of 12 sets of EOF bases have been calculated that correspond to each of the 12 overlapping seasons. The CCA model has been trained on the 1950-99 period using the National Centers for Environmental Prediction (NCEP) SST data (Smith et al. 1996, JCLIM).

(2) NCEP Operational SST forecastNCEP's Climate Modeling Branch (CMB) SST forecast is based on a combination of damped persistance of initial tropical SSTs anomalies with the NCEP coupled model forecast (Ji et al. 1994, BAMS). For short leads, the SST forecast is largely damped persistance, and at longer leads it is strongly weighted to the coupled model prediction of tropical Pacific SST anomalies. These are effectively the SST anomalies used in the two-tierred climate prediction system at NCEP, whose predictions are available at http://www.emc.ncep.noaa.gov/research/cmb/atm_forecast/. The NCEP SST forecasts are kindly provided to us by Dr. A. Kumar.

(3) IRI blended SST forecast.The International Research Institute's (IRI) forecast of tropical SSTs combines the NCEP coupled model forecast for the tropical Pacific basin with statistical CCA predictions for the Indian ocean and tropical Atlantic basins. The CCA prediction in the Atlantic is provided by CPTEC of Brazil. These are the SST forecasts used in the IRI's two-tierred prediction system, available at http://iri.ldeo.columbia.edu/climate/forecast/. The SST forecasts are kindly provided by Dr. L. Goddard of the IRI forecast division.

(4) ESRL Linear Inverse Model forecastThe SST anomaly pattern is forecast using the method of linear inverse modeling (LIM) as described in Penland and Magorian (1993, J Clim), and Penland and Matrosova (1998, J Clim). The method uses global tropical SST anomalies (30N-30S) as predictors. The LIM has been trained on COADS SST data for 1951-2000, retaining the leading 20 EOFs. The SST forecasts are kindly provided by Dr. C. Penland and L. Matrosova of ESRL.

(5) NSIPP Model (NASA Goddard)NSIPP runs its fully coupled global ocean-atmosphere-land model initialized with NSIPP analyzed ocean states to produce 12-month forecasts of the coupled system. The ocean assimilation/analyses are currently restricted to the tropical Pacific, so the main product from these forecasts, referred to here as Tier 1 forecasts, is tropical Pacific sea-surface temperature (SST) anomalies. The SST forecasts are kindly provided by Dr. M. Suarez of NASA.

### Seasonal Atmospheric Predictions

A CCA model is constructed that relates the first 10 EOFs of tropical SSTs to a similar 10 EOF basis of an atmospheric predictand. The predictands are seasonal tropical precipitation anomalies (20N-20S), Pacific-North American seasonal precipitation anomalies (20N-70N, 120E-30W), and Pacific-North American seasonal 500-mb height (20N-70N, 120E-30W). Separate CCA models are constructed for each predictand, and 12 CCA models have been made, one for each of the 12 overlapping seasons. The models are for the zero-lag (simultaneous) relation of tropical SSTs with the predictand during a 1950-99 training period.

The predictand data are derived from atmospheric GCM simulations that have been run for 1950-99 and forced with the monthly varying global SSTs. Four different GCMs are included in the analysis:

(1) NCEP MRF9The NCEP climate model is T40, L18 and is described in Kumar et al. (1996, JCLIM). A 12 member ensemble has been performed for 1950-99. The data have been kindly provided by Dr. A. Kumar of NCEP's Climate Modeling Branch.

(2) ECHAM3The European Centre-Hamburg Model (ECHAM3) is T42, L18 and is described in Roeckner et al. (1992). A 10-member ensemble has been performed for 1950-99. The data have been kindly provided by Dr. L. Goddard of the IRI forecast division

(3) CCM3The National Centre for Atmospheric Research (NCAR) Community Climate Model (CCM3) is T42, L18 and is described in Hack et al. (1998, JCLIM). A 12-member ensemble has been performed for 1950-99. The data have been kindly provided by Dr. J. Hurrell, Dr. M. Blackmon and J. Lee of NCAR's Climate and Global Dynamics Division.

(4) GFDL-R30This model of the Geophysical Fluid Dynamics Laboratory (GFDL) is R30, L18 and is described further in Broccoli and Manabe (1992, JCLIM). A 12-member ensemble has been performed for 1950-99. Four members used globally prescribed SST anomalies, 4 members used only tropical Pacific SSTs anomalies, and 4 members used tropical Pacific prescribed SST anomalies coupled to a 50-meter ocean mixed layer model in the remaining world oceans. The data were kindly provided by Dr. G. Lau and M. Nath of GFDL.

(5) NSIPPA single data set is constructed by combining the 4 GCM ensembles. The ensemble mean seasonal anomaly for each of the 4 GCMs is calculated, with anomalies computed relative to the respective model's 1950-99 climatology. Because these models possess different sensitivities to identical SST boundary forcing (e.g., Hoerling et al. 2001, JCLIM), we standardized the ensemble anomaly of each GCM by its own "external" variance, also calculated for the 1950-99 period. The external variance is simply the variance of the model's ensemble mean anomalies. These are then averaged across the 4 GCMs to yield a grand, standardized ensemble mean anomaly consisting of 46 realizations. Actual anomalies are recovered by multiplying the standardized anomaly of each season by the 4-model averaged external variance. The CCA model is trained on this grand GCM data set.

#### Making the predictions

The atmospheric prediction is made by first projecting the predicted tropical SST anomalies onto the 10 EOF SST basis set for 1950-99. The CCA model, based on zero-lag relations of this SST and the individual atmospheric predictands gotten from the GCM, is then used to predict seasonal precipitation anomalies and atmospheric circulation.

The fields of the forecast variables are in terms of standardized anomalies rather than the total anomaly itself. They are standardized by the total seasonal variability of the particular variable for each season as estimated from the 4 GCMs. The forecast so displayed allows for a meaningfull assessment of the strength of the expected SST forced signal relative to the total GCM seasonal variability, and thus provides a measure of signal-to-noise ratio at each grid point. The larger the standardized anomaly, the more likely it is that the GCM (or nature) would yield an anomaly of that sign.