5.3 Evaluation of the Ocean $Q$ Flux

The ocean $Q$ flux is generally evaluated using a CAM 3.0 control simulation driven by prescribed sea surface temperature and sea ice distributions. Let

$$F_{net} = FS - FL - LH - SH$$ (5.12)

over ocean (regardless of whether the ocean surface is open or ice covered), for each of 12 ensemble mean months (n=1,...,12). The Q flux distribution for each month n is then evaluated: (note that here we use the CAM 3.0 sign convention on the Q flux).

$$Q = Q_{ocean} - Q_{ice} - F_{net}$$ (5.13)

where:

$$Q_{ocean} = (\rho_o C_o h_o/\texttt{daysmonth}(m)) {\{(1-A(m+1)) T_o(m+1) - (1-A(m-1)) T_o(m-1)\}}$$ (5.14)

$$Q_{ice} = L_i {\{A(m+1)h_i(m+1) - A(m-1)h_i(m-1)\}}/\texttt{daysmonth}(m)$$ (5.15)

where $\texttt{daysmonth}$ is the number of days in each month, $L_i$ is the latent heat of fusion for ice, and $h_i$ is the regionally specified ice thickness. We then define an annual average using the monthly mean data:

$$\overline{Q} = \sum_{m=1,12} \texttt{daysmonth}(m) Q(m)/365$$ (5.16)

By definition

$$\overline{Q_{ocean}} = 0$$ (5.17)

$$\overline{Q_{ice}} = 0$$ (5.18)

so that

$$\overline{Q} = -\overline{F_{net}}$$ (5.19)

Since $F_{net}$ is the monthly mean flux into the ocean directly from the control, $Q$ must be constrained to ensure that the actual $Q$ applied in the SOM configuration has the same annual mean as $-\overline{F_{net}}$. Otherwise, the application of the $Q$ flux would introduce a source or sink of heat with respect to the control.

The actual $Q$ applied in the SOM configuration is based on linear interpolation between monthly means, taken as midpoints. Since the months have different lengths, in general the annual mean of the $Q$ flux applied to the SOM will not equal $-\overline{F_{net}}$. Thus, we must define another annual mean, based on the time interpolated $Q$, to ensure that the SOM applied Q has the identical annual mean as the fluxes $F_{net}$ from the control run.