Comparison of probability density functions for total specific humidity and saturation deficit humidity, and consequences for cloud parametrization

Various models which predict cloud variables use probability density functions of either specific humidity or saturation deficit 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 fixed relation between the widths of both distributions allowing easy conversion between the two.