Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is “close” to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets. Abstract Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is “close” to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.

An increase in the planetary albedo of the earth-atmosphere system by only 10% can decrease the equilibrium surface temperature to that of the last ice age. Nevertheless, albedo biases of 10% or greater would be introduced into large regions of current climate models if clouds were given their observed liquid water amounts, because of the treatment of clouds as plane parallel. Past work has addressed the effect of cloud shape on albedo; here the focus is on the within-cloud variability of the vertically integrated liquid water. The main result is an estimate of the “plane-parallel albedo bias” using the “independent pixel approximation,” which ignores net horizontal photon transport, from a simple fractal model of marine stratocumulus clouds that ignores the cloud shape. The use of the independent pixel approximation in this context will be justified in a separate Monte Carlo study. The focus on marine stratocumulus clouds is due to their important role in cloud radiative forcing and also that, o... Abstract An increase in the planetary albedo of the earth-atmosphere system by only 10% can decrease the equilibrium surface temperature to that of the last ice age. Nevertheless, albedo biases of 10% or greater would be introduced into large regions of current climate models if clouds were given their observed liquid water amounts, because of the treatment of clouds as plane parallel. Past work has addressed the effect of cloud shape on albedo; here the focus is on the within-cloud variability of the vertically integrated liquid water. The main result is an estimate of the “plane-parallel albedo bias” using the “independent pixel approximation,” which ignores net horizontal photon transport, from a simple fractal model of marine stratocumulus clouds that ignores the cloud shape. The use of the independent pixel approximation in this context will be justified in a separate Monte Carlo study. The focus on marine stratocumulus clouds is due to their important role in cloud radiative forcing and also that, o...

The interaction of clouds with solar and terrestrial radiation is one of the most important topics of climate research. In recent years it has been recognized that only a full three-dimensional (3D) treatment of this interaction can provide answers to many climate and remote sensing problems, leading to the worldwide development of numerous 3D radiative transfer (RT) codes. The international Intercomparison of 3D Radiation Codes (I3RC), described in this paper, sprung from the natural need to compare the performance of these 3D RT codes used in a variety of current scientific work in the atmospheric sciences. I3RC supports intercomparison and development of both exact and approximate 3D methods in its effort to 1) understand and document the errors/limits of 3D algorithms and their sources; 2) provide “baseline” cases for future code development for 3D radiation; 3) promote sharing and production of 3D radiative tools; 4) derive guidelines for 3D radiative tool selection; and 5) improve atmospher... Abstract The interaction of clouds with solar and terrestrial radiation is one of the most important topics of climate research. In recent years it has been recognized that only a full three-dimensional (3D) treatment of this interaction can provide answers to many climate and remote sensing problems, leading to the worldwide development of numerous 3D radiative transfer (RT) codes. The international Intercomparison of 3D Radiation Codes (I3RC), described in this paper, sprung from the natural need to compare the performance of these 3D RT codes used in a variety of current scientific work in the atmospheric sciences. I3RC supports intercomparison and development of both exact and approximate 3D methods in its effort to 1) understand and document the errors/limits of 3D algorithms and their sources; 2) provide “baseline” cases for future code development for 3D radiation; 3) promote sharing and production of 3D radiative tools; 4) derive guidelines for 3D radiative tool selection; and 5) improve atmospher...