The GFDL assimilation systems is based on the ensemble /adjustmen/t Kalman filter (EaKf; Anderson 2001), which is a deterministic variant of the ensemble Kalman filter. The EaKf estimates the probability distribution function (PDF) of climate states by combining the prior PDF derived from model dynamics and the observational PDF. It uses a two-step data assimilation procedure %Gâ%@ the first step computes ensemble increments at an observation location and the second step distributes the increments over the impacted grids - for an ensemble Kalman filter under a local least squares framework. In both systems the filtering process is implemented by a multivariate linear regression with consideration of temperature and salinity covariance (Anderson 2003). The data adjusted ensemble members are the realizations of the analysis PDF and serve as the initial conditions for the next ensemble integration.

The GFDL system consists of an EaKf applied to GFDL's fully coupled climate model CM2.1 (Delworth et al. 2006, Zhang et al. 2007), which is designed to produce a better balanced initialization as opposed to each component model using its own assimilation system. The ocean component of the ensemble coupled data assimilation (ECDA3.1) is the Modular Ocean Model version 4 (MOM4) configured with 50 vertical levels and 1° horizontal resolution, telescoping to 1/3° meridional spacing near the equator. The atmospheric component has a resolution of 2.5° x 2° with 24 vertical levels. The first guess is given by a fully coupled model where the atmosphere is constrained by an existing atmospheric analysis. Ocean observations of temperature, salinity, and SST are assimilated using covariance structures from the coupled model. Argo observations are included as they became available in the post-2000 period. The cross-interface covariance structures in the GFDL system allow for fully coupled assimilation. For the ocean component, observed temperature and salinity profiles and SST are assimilated daily (see details in http://www.gfdl.noaa.gov/ocean-data-assimilation). The atmosphere is constrained by an existing atmospheric analysis. All ECDA3.1 experiments are performed with a 12-member ensemble that is used to compute state estimation, ensemble mean, and the spread of the estimate.

Using the ECDA analysis ensembles for initial conditions, one year predictions of 10 ensemble members are produced beginning on the first of every month.

The data for this forecast system can also be obtained from: http://www.gfdl.noaa.gov/SI_Exp_Predictions.