A simple model of ocean temperature re-emergence and variability

A simple stochastic one-dimensional model of interannual mid-latitude sea surface temperature (SST) variability that can be solved analytically is developed. A novel two-season approach is adopted, with the annual cycle divided into two seasons denoted summer and winter. Within each season the mixed layer depth is constant, and the transition of the mixed layer from summer to winter and vice versa is discontinuous. SST anomalies are forced by random atmospheric heat fluxes, assumed to be constant within each season for simplicity, with linear damping to represent atmospheric feedback. At the start of summer the initial SST anomaly is set equal to that at the end of the previous winter, and at the start of winter the initial temperature anomaly is found by instantaneously mixing the summer mixed layer with the heat stored below in the deeper winter mixed layer, thereby explicitly taking into account the ‘re-emergence mechanism’. Two simple auto-regressive equations for the summer and winter SST anomalies are obtained that can be easily solved. Model parameters include seasonal damping coefficients, mixed layer depths and standard deviations of the atmospheric forcing. Analytic expressions for season-to-season correlation and variability and power spectra are used to explore and illustrate the effects of the parameters quantitatively. Among the results it is found that, with regard to winter-to-winter temperature correlation, the re-emergence pathway is more influential than persistence via the summer mixed layer when the winter layer is more than twice the depth of the summer layer. With regard to winter temperature variability, the effect of a deeper winter mixed layer is to decrease the sensitivity to surface forcing and thus decrease variability, but also to increase persistence via re-emergence and thus increase variance at multidecadal scales.