Parameterizing the difference in cloud fraction defined by area and by volume as observed with radar and lidar

Most current general circulation models (GCMs) calculate radiative fluxes through partially cloudy grid boxes by weighting clear and cloudy fluxes by the fractional area of cloud cover (C-a), but most GCM cloud schemes calculate cloud fraction as the volume of the grid box that is filled with cloud (C). In this paper, 1 yr of cloud radar and lidar observations from Chilbolton in southern England, are used to examine this discrepancy. With a vertical resolution of 300 m it is found that, on average, C-a is 20% greater than C-v, and with a vertical resolution of 1 km, C-a is greater than C-v by a factor of 2. The difference is around a factor of 2 larger for liquid water clouds than for ice clouds, and also increases with wind shear. Using C-a rather than C, calculated on an operational model grid, increases the mean total cloud cover from 53% to 63%, and so is of similar importance to the cloud overlap assumption. A simple parameterization, C-a = [1 + e((-f))(C-v(-1) - 1)](-1), is proposed to correct for this underestimate based on the observation that the observed relationship between the mean Ca and C, is symmetric about the line C-a = 1 - C-v. The parameter f is a simple function of the horizontal (H) and vertical (V) grid-box dimensions, where for ice clouds f = 0.0880 V-0.7696 H-0.2254 and for liquid clouds f = 0.1635 V-0.6694 H-0.1882. Implementing this simple parameterization, which excludes the effect of wind shear, on an independent 6-month dataset of cloud radar and lidar observations, accounts for the mean underestimate of C for all horizontal and vertical resolutions considered to within 3% of the observed C-a and reduces the rms error for each individual box from typically 100% to approximately 30%. Small biases remain for both weakly and strongly sheared cases, but this is significantly reduced by incorporating a simple shear dependence in the calculation of the parameter f, which also slightly improves the overall performance of the parameterization for all of the resolutions considered.