4.7 Parameterization of Cloud Fraction

Cloud amount (or cloud fraction), and the associated optical properties, are evaluated via a diagnostic method in CAM 3.0. The basic approach is similar to that employed in the CCM2 and CCM3. The diagnosis of cloud fraction is a generalization of the scheme introduced by Slingo [161], with variations described in Kiehl et al. [91]; Hack et al. [66], and Rasch and Kristjánsson [144]. Cloud fraction depends on relative humidity, atmospheric stability and convective mass fluxes. Three types of cloud are diagnosed by the scheme: low-level marine stratus ( $\cfrac _{st}$), convective cloud ( $\cfrac _{cir}$), and layered cloud ($\cfrac _c$). Layered clouds form when the relative humidity exceeds a threshold value which varies according to pressure. The diagnoses of these cloud types are described in more detail in the following paragraphs.

Marine stratocumulus clouds are diagnosed using an empirical relationship between marine stratocumulus cloud fraction and the stratification between the surface and 700mb derived by Klein and Hartmann [95]. The CCM3 parameterization for stratus cloud fraction over oceans has been replaced with

$$\cfrac _{st} = \min\biggl\lbrace 1., \max\bigl[0., (\theta_{700}-\theta_s)*.057-.5573 \bigr] \biggr\rbrace$$ (4.169)

$\theta_{700}$ and $\theta_s$ are the potential temperatures at 700 mb and the surface, respectively. The cloud is assumed to be located in the model layer below the strongest stability jump between 750 mb and the surface. If no two layers present a stability in excess of -0.125 K/mb, no cloud is diagnosed. In areas where terrain filtering has produced non-zero ocean elevations, the sea surface temperature used for this computation is reduced from the true sea surface elevation to the model surface elevation according to the lapse rate of the U.S. Standard Atmosphere (-6.5 $^\circ$C/km).

Convective cloud fraction in the model is related to updraft mass flux in the deep and shallow cumulus schemes according to a functional form suggested by Xu and Krueger [192]:

$$\cfrac _{shallow} = k_{1,shallow} ln(1.0+k_2 M_{c,shallow})$$ (4.170)

$$\cfrac _{deep} = k_{1_deep} ln(1.0+k_2 M_{c,deep})$$ (4.171)

where $k_{1,shallow}$ and $k_{1_deep}$ are adjustable parameters given in Appendix C, $k_2 = 500$, and $M_c$ is the convective mass flux at the given model level.

The remaining cloud types are diagnosed on the basis of relative humidity, according to

$$\cfrac _c = \left( \frac{RH - RH_{\min}} {1 - RH_{\min}} \right)^{2}$$ (4.172)

The threshold relative humidity $RH_{\min}$ is set according to pressure $p$ as

$$RH_{\min} = \begin{cases}RH_{\min}^{low} & p > 750 mb \ RH_{\min... ...d}-750 mb} & p_{mid} < p < 750 mb \ RH_{\min}^{high} & p < p_{mid} \end{cases}$$ (4.173)

where $p_{mid}$ in an adjustable parameter denoting the minimum pressure for a linear ramp from the low cloud threshold to the high cloud threshold. At present this ramp is implemented only in one configuration of the model; other versions have a step function achieved by setting $p_{mid} = 750$ mb. $RH_{\min}^{low}$, $RH_{\min}^{high}$, and $p_{mid}$ are specified as in Appendix C. Also, the parameter $RH_{\min}^{low}$ is adjusted over land by $-0.10$. This distinction is made to account for the increased sub-grid-scale variability of the water vapor field due to inhomogeneities in the land surface properties and subgrid orographic effects.

The total cloud $\cfrac _{tot}$ within each volume is then diagnosed as

$$\cfrac _{tot} = \max(\cfrac _{c}, \cfrac _{cir}, \cfrac _{st}),$$

This is equivalent to a maximum overlap assumption of cloud types within each gridbox. The condensate value is assumed uniform within any and all types of cloud within each grid box.