Ž .
Atmospheric Research 55 2000 115–129 www.elsevier.comrlocateratmos
Geometrically effective cloud fraction for solar radiation
Michael Batey
1
, Harshvardhan , Robert Green
Department of Earth and Atmospheric Sciences, Purdue UniÕersity, West Lafayette, IN 47907-1397, USA Received 10 April 2000; accepted 27 June 2000
Abstract
It has been suggested in the past that an AeffectiveB cloud fraction can be used to take into account cloud geometry effects in solar radiation parameterizations. All such models have been
based on the reflected flux from non-plane-parallel cloud fields. In this study, it is shown that the Ž
. AeffectiveB cloud fraction based on absorption or transmission could differ considerably from
that based on reflection and, moreover, is not constant throughout the solar spectrum even for fixed cloud geometry. Furthermore, the representation of cloud radiative forcing at the surface and
at the top of the atmosphere in terms of cloud fractions are based on different AeffectiveB cloud fractions. Therefore, a simple interpretation of measured values of the forcing ratio is not possible
when geometric effects are present. q 2000 Elsevier Science B.V. All rights reserved.
Keywords: Albedo; Atmosphere; Climate; Clouds
1. Introduction
Numerical weather prediction and climate models have always had to grapple with the issue of representing the cloud coverage of grid boxes for purposes of the radiation
parameterization. In general, in order to compute the radiation field, one requires information on the physical coverage of the grid box by clouds and the optical properties
of the clouds. This is true irrespective of the technique used to generate the simulated
Corresponding author. Ž
. E-mail address: harshpurdue.edu Harshvardhan .
1
Current affliation: TRW, Aurora, CO, USA 0169-8095r00r - see front matter q 2000 Elsevier Science B.V. All rights reserved.
Ž .
PII: S 0 1 6 9 - 8 0 9 5 0 0 0 0 0 6 0 - 0
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
