Effective cloud fraction Directory UMM :Data Elmu:jurnal:A:Atmospheric Research:Vol55.Issue2.Oct2000:

Ž . clouds in the model Slingo, 1987; Tiedtke, 1993 . The coverage of a grid box by clouds Ž . can be termed the Aextrinsic fractional cloudinessB Randall, 1989 and all current models use a weighting of overcast and clear radiation computation to calculate the grid averaged radiation field. The weighting is determined by the cloud fraction and assumptions regarding the overlap between cloud layers in fractionally cloudy grid Ž . boxes Harshvardhan et al., 1987; Ridout et al., 1994 . The separation of a model grid box into clear and cloudy regions does not solve the problem completely since some assumptions need to be made regarding the distribution of optical thickness in the cloudy region. Since the typical climate model is incapable of generating these distributions as yet, some methods have been proposed to calculate Ž effective optical thickness to represent such cloud inhomogeneities Cahalan et al., . 1994a,b; Barker, 1996 . There is yet another problem associated with the transfer function that relates simulated clouds and the radiation field. This is the issue of geometrical effects. All radiation parameterizations rely on plane parallel computations as their basis. The diagnosed cloud fraction in a numerical model grid box, of course, does not incorporate any geometric effects. Traditionally, it has been accepted that the cloud fraction provided to the radiation parameterization is an AeffectiveB cloud fraction, which Ž . includes geometric effects. Loeb et al. 1998 have modeled conservatively scattering cloud fields that have both horizontal variations in extinction coefficient and structure at cloud top. However, they did not attempt to develop a parameterization that could be used in atmospheric models. In this note, we revisit the concept of effective cloud fraction because past studies have always considered outgoing fluxes in both the reflected shortwave and emitted longwave when defining the effective cloud fraction for radiation parameterizations. The recent renewed interest in atmospheric solar absorption, in particular, the role of Ž . geometrical effects in interpreting measurements Valero et al., 1997 , and computing Ž . solar absorption O’Hirok and Gautier, 1998 has brought the issue to the fore again after a long period of dormancy.

2. Effective cloud fraction

The effective cloud fraction, N , is defined for an array of finite clouds but the e arguments presented here can be applied as well to any edge effects that may be Ž . observed. As defined by Weinman and Harshvardhan 1982 and Welch and Wielicki Ž . 1984 , N is the equivalent cloud fraction of a planiform field of clouds with the same e vertical optical thickness required to give the same flux as that reflected from the finite cloud array, i.e., F ≠sN F ≠ t 1 Ž . Ž . e pp Where F ≠ is the total flux escaping to space from the array, F ≠ is the corresponding pp plane-parallel quantity, and t is the optical depth of the plane-parallel cloud. It is assumed that the finite cloud elements have the same vertical optical depth as the plane-parallel cloud and that the properties are for an isolated layer. In practice, such a layer would be embedded in a multi-layer atmospheric model. The concept of an Ž effective cloud fraction has also been used for longwave radiation Harshvardhan, 1982; . Ellingson, 1982; Takara and Ellingson, 1996 but here we will restrict ourselves to shortwave radiation only. Ž . Note from Eq. 1 that N is defined in terms of the reflected flux. There is no reason e to believe that the same effective cloud fraction will be applicable to the computation of layer absorption or solar transmission to the surface. For the purpose of this study we therefore define the following. The normal cloud fraction, or earth cover, N, is the fraction of earth covered by clouds when the clouds are projected vertically. However, this in not the cloud fraction observed from the surface which is the fractional sky cover Ž . Ž . Warren et al., 1988 . We can further refine the definition of N given in Eq. 1 as e follows N s R N rR N 2 Ž . Ž . Ž . e R pp and N s A N rA N 3 Ž . Ž . Ž . e A pp Ž . Where R and A are the actual reflectance and absorptance of the partly cloudy layer; R and A are the corresponding quantities when the cloud in the layer is considered pp pp to be plane-parallel and homogeneous. All quantities refer to the properties of the entire layer including the clear portions.

3. Cloud model