
\begin{equation}
\label{eqn:budget}
\rho c_p h \frac{\partial T^'}{\partial t} = R'_s + R'_l + LH' + SH' + D'_o 
\end{equation}
where primes denote the historical$-$AMIP differences; $\rho$, $c_p$, $h$ and $T$ are the sea water density, specific heat at constant pressure, mixed layer depth and mixed layer average temperature, respectively; the left hand side is the heat storage tendency and the right hand side terms are the net short wave radiation, net long wave radiation, latent flux, sensible heat flux (defined as positive into the ocean) and the three-dimensional advection and diffusion by ocean dynamics, respectively.