Special cases

The above coupled equations comprise, as limiting cases, several special models treated previously in the literature.

$\bullet$Setting m=g=f=0 yields the classic stochastic SST model of [FH77], in which the ocean plays no role; the model predicts exponential decay of SST anomalies with a damping timescale $\lambda^{-1}$.

$\bullet$Setting f=0 , but $g \ne 0$, yields the stochastic gyre model of [FMZ97], in which there is no coupling between SST and windstress (cf. section 4.3).

$\bullet$Setting m=s=0 is similar to Jin [1997], who coupled ocean gyres with the atmospheric jet stream, but with no representation of the meridional overturning (cf. section 4.4).

$\bullet$Setting g=0 is similar to a stochastic thermohaline model model of Griffies [1995] (cf. section 4.4).

The following subsections focus on some possible implications for the uncoupled and the coupled problem.