Recent work by a number of climate modelers has suggested that modest changes in atmospheric forcing can lead to radical changes in oceanic circulation that could have a dramatic impact on the global heat balance. The pioneering study of Stommel (1961) was apparently the first to suggest that the ocean's thermohaline circulation could exist in different, but stable, states. A spate of recent work with more complex models has confirmed that early work (see the comprehensive review of Weaver et al., 1993) and revealed many of the properties of the state transitions, as well as the sensitivity of the model results to subtle changes in the specification of the forcing—in these cases the flux of fresh-water into and out of the oceans.

Most of the work to date has been done with simplified ocean models or steady-state fluxes of fresh-water. The important work of Mikolajewicz and Maier-Reimer (1990, 1991) added a stochastic forcing term in the fresh-water flux and also used a full three-dimensional ocean general-circulation model (OGCM). Their result showed a quasi-periodic fluctuation in the thermohaline circulation; it had a time scale of the order of 300 years, and was most apparent in the Atlantic Ocean. Stocker and Mysak (1992) find significant spectral peaks in paleoclimate data with about the same period. Recently, Weaver et al. (1993) and Mysak et al. (1993) repeated that experiment (with a more simplified OGCM and rather arbitrarily defined flux fields) and described the relative importance of the stochastic term to the general model behavior.

The current paper expands on these earlier studies by examining the response of a realistic OGCM to different types of stochastic forcing. The model response to purely climatological forcing is compared to the additional response induced by stochastic forcing that is (1) white in both space and time, (2) red in space and white in time, and (3) red in both space and time, with the degree of redness determined by the coupling coefficients between the sea-surface temperature (SST) and SST gradients and the fresh-water flux field. This represents a coupled ocean-atmosphere model of a type that does not seem to have been previously explored.

This section describes the ocean and stochastic atmospheric models used in this study. It also describes briefly how the coupled ocean-atmosphere model with feedback was constructed.

The OGCM used here is identical to that used by Mikolajewicz and Maier-Reimer (1990, 1991; MMR hereafter), which is described in detail by Maier-Reimer et al. (1993). It is a linear, primitive-equation model with a horizontal resolution of approximately 3.5° (an E-type grid) and 11 levels in the vertical. Unlike most of the modeling studies discussed above, this OGCM uses realistic geometry and ocean bathymetry. This is an important characteristic if one wishes to infer that the model results have relevance to the real world. The numerics are handled in such a way as to allow a time step of 30 days, thereby making extended integration feasible even on a workstation. At the surface (only) the heat-balance equation has a seasonally varying Newtonian damping to observed surface air temperature climatology, while the salt balance uses a seasonally varying fresh-water flux to give realistic surface salinity fields (mixed boundary conditions). Seasonally varying wind stress (Hellerman and Rosenstein, 1983) is also used to force the model.

Again unlike most of the modeling work discussed above, the OGCM includes a simplified thermodynamic sea-ice model wherein the heat flux through the ice is proportional to the temperature difference between the underlying water and air temperature, and inversely proportional to the thickness of the ice. If one is interested in forcing an OGCM with fresh-water flux, then some representation of sea ice seems mandatory for a realistic simulation. In addition, the full UNESCO equation of state for seawater (see UNESCO, 1981) is used by the model to help properly represent the large-scale density changes associated with mixing. More details on the model and its construction can be found in the references above. These references also show that the model does a reasonable job of reproducing the major features of the ocean's general circulation as well as the distribution of temperature and salinity in the deep ocean.

The basis for constructing several of the atmospheric models is a 10-year integration of the Hamburg climate model (ECHAM3. T42 resolution; see Roeckner et al., 1992) forced by anomalous global SSTs. This integration was conducted as part of the Atmospheric Model Intercomparison Project (AMIP). The results, made available to us courtesy of L. Bengtsson, give monthly, globally gridded anomalies of fresh-water flux from the model and the observed SST and SST gradients that produced them. The distribution of the long-term mean and standard deviations of the fresh-water flux (E - P) are shown on Figure 1. In another study, we show that the flux and atmospheric moisture fields produced by this model compare well with observations of these same quantities where such comparisons are possible (Pierce et al. (unpublished manuscript, 1994)). The following atmospheric "models" were derived from this basic data set.