Mathematical forms of probability density functions (PDFs) of liquid water path (LWP) and total water content for marine boundary layer clouds are investigated using the homogeneity, skewness, and kurtosis of PDFs of LWP obtained from observations described in a companion paper. First, observed LWP PDF data are divided into four categories depending on the stability between 775 and 1000 hPa in order to investigate the characteristics of the PDFs of LWP depending on stability of the atmospheric boundary layer (ABL). The relationships between cloud amount and higher moments of LWP PDFs for different ABLs show different features. When the stability becomes larger, the LWP PDFs have larger homogeneity, smaller skewness, and smaller kurtosis for similar cloud amounts.

To extract useful information about the PDFs of total water content for strongly and moderately stable ABLs, the relationship between LWP PDFs and PDFs of total water content is determined by introducing a set of simple assumptions for the vertical structure of total water content in well-mixed boundary layers. By comparing the observed relationships between cloud amount and higher moments of LWP PDFs, with similar relationships deduced theoretically from various forms of PDFs of total water content, it is found that, in general, the triangular and Gaussian PDFs are a realistic approximation for PDFs of total water content in marine boundary layer clouds for strongly and moderately stable ABLs. Results concerning the correction ratio for the autoconversion rate of cloud water content to precipitation and the reduction factor for shortwave reflectance, as functions of cloud amount, are also discussed.