White-White (WW) Atmospheric Model
At a given ocean-model grid point the anomalous freshwater flux for each time step was obtained from a set of normally distributed random numbers with zero mean and standard deviation of s mm/day. Values of s in the range 1 to 3 mm/day are approximately equal to the amplitude of the seasonal cycle of fresh-water flux that forces the OGCM. These values are also approximately equal to rms values obtained from the AMIP run, and to an independent estimate obtained by Roads et al. (1992) from the National Meteorological Center (NMC) analysis. The same procedure was used at each individual ocean-model grid point, so that the anomalous fresh-water flux that drove the OGCM had no spatial correlation in its covariance field and was uncorrelated in both space and time, i.e., white in both wave-number and frequency space. We refer to this as the white-white or WW model.
Red-White (RW) Atmospheric Model
The AMIP fresh-water flux anomaly field was represented as a series of empirical orthogonal functions (EOFs). The first 15 of these spatial functions en(x) and their associated eigenvalues ln were retained. At each time step of the OGCM, an anomalous global fresh-water flux field was constructed as the linear combination of products of the en(x) and n-random number with zero mean and standard deviation ln. This model had the spatial structure of the freshwater flux field from the T42, which was highly spatially correlated (red in wave-number space) while being random in time (white in frequency space). Note that each EOF mode carried the same variance, ln, as in the AMIP run. This type of stochastic atmospheric model is conceptually similar to but quantitatively different from that employed by MMR, and we refer to it here as the RW model.
Red-Red (RR) Atmospheric Model with Feedback
The AMIP data were used to develop a regression model relating the SST and SST gradients to the anomalous freshwater flux. The model used the 15 leading EOFs of the AMIP fresh-water flux and SST fields. The regression model was nearly global in nature, covering all ocean points where sea ice never occurred. In most regions it captured 80 to 90 percent of the variance in the original AMIP fresh-water flux data set (only 15 EOFs).5 However, the interesting fact was that the regression model captured a minimum of 96 percent of the variance associated with the first 15 EOFs. This result in turn suggests the highly linear relation between the SST and SST gradients and fresh-water flux. The basic approach to constructing such an atmospheric model can be found in Barnett et al. (1993).
Incorporation of the SST and SST gradient into the model obviously allows for a feedback between the ocean and pseudo-atmosphere and represents a type of coupled model not previously attempted on a global scale (although such a coupled model has produced good simulations of El Niño events (Barnett et al., 1993)). The relatively slow changes in SST ensure that the atmospheric model will be red in frequency space. The large-scale spatial correlations in both SST and fresh-water flux produce a wave-number dependence that is also red, so this model was called the red-red or RR model.
The basic model was run for 4000 years of simulated time forced only by the seasonal cycle. The state of the ocean at that time was taken as the initial condition for all subsequent runs. Four different basic simulations were