Sub-Grid Scale Variability of Clouds in the ECHAM5 Solar Radiation Scheme

Mathematics – Probability

Scientific paper

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Scientific paper

In the ECHAM5 climate model, fractional cloud cover is determined using a statistical scheme. The latter prognoses a probability density function (PDF) for the total water mixing ratio, i.e. the sum of liquid and ice water and water vapor. From this PDF, the distributions for cloud liquid and ice water content are derived and supplied to the solar radiation scheme. By weighting the radiative fluxes, computed with a standard two-stream scheme, by the corresponding probabilities, the sub-grid scale variability of cloud depth is accounted for. Related to the original scheme, planetary albedo is reduced by 0.009. Additionally, various implementations of the effective thickness approximation (ETA) are compared against the statistical approach. While for the ETA empirical parameterizations are needed, the statistical approach treats the cloud inhomogeneities consistently in the cloud and radiation scheme.

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