Plane Parallel Albedo Biases from Satellite Observations. Part II: Parameterizations for Bias Removal

Abstract

Using the same satellite observations as in Part I of this paper, the authors explore ways to remove the cloud albedo bias (or plane parallel albedo bias), the difference between the plane parallel homogeneous albedo and the average albedo of independent pixels, in regions similar in size to climate model grid boxes. Scaling regional mean optical depths with the reduction factor of R. F. Cahalan et al. provides albedos close to the independent pixel values. Computed albedos approach the independent pixel values within 0.01 for ?40% of the regions tested and give standard deviations ?0.02?0.04. Fitting lognormal distributions to the observed optical depth distributions gives albedos within 0.01 of the independent pixel values more than 70% of the time, with standard deviations ?0.02?0.06. Gamma distributions are less successful than lognormal distributions, giving acceptable results (average bias ?0.01?0.02, standard deviation ?0.05?0.08) only when their parameters are estimated from the maximum likelihood estimates method. The poor performance of the gamma distribution when the method of moments is used for parameter estimation (as H. W. Barker et al. did) is attributed to the presence of high optical depth values in our retrieved fields. To apply any of the above corrections in GCMs, quantities that are not presently provided by these models are required. The reduction factor and ?gamma IP? method require the mean logarithm of optical depth, whereas the lognormal method also requires the variance. The authors suggest a parameterization of these quantities in terms of mean optical depth and cloud fraction, variables available in most GCMs. The albedos resulting from the parameterized versions of the correction methods are still much closer to the independent pixel values than the albedos of the plane parallel homogeneous assumption. Although the ?lognormal IP? gives the best overall performance, it requires knowledge of two logarithmic moments and numerical integration. It may therefore prove more appealing for observational than modeling applications.