To begin with, we start by improving the most simple SOM whose governing equation is shown in the first line of the figure: *h* is the ocean mixed-layer depth that is constant in time, *c*_{p} the heat capacity, ρ the density of seawater, *T* the sea-surface temperature, *F* the surface heat fluxes (radiative + sensible + latent), and *Q* the heat flux that includes all unresolved processes such as horizontal heat transport and entrainment. The first problem with this model is that the use of a constant *h* ignores the seasonal variation in the mixed-layer depth which can exceed 50 meters over much of the ocean. Strong entrainment associated with a deepening mixed-layer during fall and winter can produce memory effect on the SST anomalies. This mechanism is thought to be essential for the generation of the Pacific Decadal Oscillation. To explore the effect of a variable mixed-layer depth we use a Niiler-Kraus mixed-layer model as our first improvement. The resulting equation is shown in the second line of figure: *w*_{e} is the entrainment velocity driven by surface fluxes, *T*_{d} the entrainment temperature. *Q’ *will be the new unresolved flux. The next unresolved process is horizontal heat transport. As a first approximation we include the horizontal transport due to Ekman flows. The resulting model is given in the last line of figure: where *v*_{ek} is the wind-driven Ekman velocity and *Q’’* is again the updated unresolved flux.

Other unresolved processes such as geostrophic flow transport, Ekman induced downwelling, wave dynamics and mesoscale systems which are still under development. Finally, full ocean model stands at the top of this hierarchy serving as the “observation” benchmark.