Comparison of probability density functions for total speci c humidity and saturation de cit humidity , and consequences for cloud parametrization

Various models which predict cloud variables use probability density functions of either speciŽ c humidity or saturation deŽ cit humidity to represent subgrid-scale variations. Using the former is considered to be an approximation since it does not allow variation of dew-point across the grid. In this paper the validity of that approximation is investigated and typical errors incurred are stated. Aircraft data from subtropical regions and tethered-balloon data from midlatitudes are examined to compare differences between the two types of distribution. The average relative error in cloud fraction introduced by assuming a constant value of saturation across a grid is found to be approximately half an okta. However, results suggest that there is a Ž xed relation between the widths of both distributions allowing easy conversion between the two.