A simple conceptual model of cirrus horizontal inhomogeneity and cloud fraction

A simple conceptual model of horizontal inhomogeneity and cloud amount in cirrus clouds has been formulated on the basis that internal horizontal inhomogeneity in the ice mixing ratio is due to variations in the cloud depth, which are assumed to be Gaussian. The use of such a model was justified by the observed relationship between the normalized variability of cloud depth and both the cloud amount and the normalized variability of the ice‐water mixing ratio (and extinction). Using radar cloud‐depth data as input, the model reproduced well the in‐cloud ice‐water mixing ratio histograms obtained from horizontal aircraft runs during the FIRE‐II cirrus campaign. For totally overcast cases the histograms were almost Gaussian, but changed as cloud amount decreased to distributions which peaked at the lowest non‐zero ice value and decreased rapidly and monotonically towards higher ice values for cloud amounts below 90%. Cloud amounts and average ice‐water mixing ratios for cases with observed distributions of cloud depth were predicted by the model to within 15% and 31% of the observed values. This model could be used as a starting point in the development of a GCM parametrization of the ice mixing‐ratio probability distribution function and cloud amount, if a means of diagnosing the depth of the saturated layer and the standard deviation of cloud depth from basic large‐scale meteorological parameters could be determined. Copyright © 2002 Royal Meteorological Society.