In order to understand whether the SST annual cycle difference between the historical and AMIP run arises from surface heat flux or ocean dynamics, we need to calculate the heat budget of the mixed layer of the ocean. %The heat budget of the mixed layer, neglecting the local tendency, can be viewed as the balance among surface short wave radiation ($R_s$), long wave radiation ($R_l$), latent flux ($LH$), sensible heat flux ($SH$) and three-dimensional advection and diffusion by ocean dynamics ($D_o$), i.e.
The historical$-$AMIP form of the ocean mixed layer heat budget can be written as: