Size distribution models of fog and cloud droplets in terms of the modified gamma function

Size spectra of water droplets in haze, fogs and clouds of various type measured by several authors have been analyzed by a computational method in terms of the modified gamma distribution function. The preliminary results are shown on the wide ranges that result of the function parameters. These results are synthesized using a graphical method to obtain average and representative size distribution models suitable for reproducing size spectra of water droplets typical for fog and clouds in different evolutionary stages. The examination of the results in terms of skewness and kurtosis suggests typical behaviours of these two shape-parameters which can be taken into account in obtaining multimodal size distributions by the use of the properly weighted models found. The analytical expressions of skewness and kurtosis in the modified gamma distribution function are given in the Appendix. DOI: 10.1111/j.2153-3490.1976.tb00682.x

[1]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[2]  W. L. Webb PARTICULATE COUNTS IN NATURAL CLOUDS AND FOGS , 1956 .

[3]  P. Jonas,et al.  On the dispersion of the sizes of droplets growing by condensation in turbulent clouds , 1972 .

[4]  P. Squires,et al.  The Microstructure and Colloidal Stability of Warm Clouds: Part I — The Relation between Structure and Stability , 1958 .

[5]  J. A. Garland Some fog droplet size distributions obtained by an impaction method , 1971 .

[6]  L. C. Cox,et al.  A study of the contribution of pollution to visibility in a radiation fog , 1973 .

[7]  D. Deirmendjian Scattering and Polarization Properties of Water Clouds and Hazes in the Visible and Infrared , 1964 .

[8]  D. Deirmendjian Electromagnetic scattering on spherical polydispersions , 1969 .

[9]  A. Best Drop-size distribution in cloud and fog , 1951 .

[10]  W. G. Durbin Droplet sampling in cumulus clouds , 1959 .

[11]  J. Jiusto Aerosol and cloud microphysics measurements in Hawaii , 1967 .

[12]  P. Squires,et al.  The Microstructure and Colloidal Stability of Warm Clouds , 1958 .

[13]  A. Arnulf,et al.  Transmission by Haze and Fog in the Spectral Region 0.35 to 10 Microns , 1957 .

[14]  M. Kumai Arctic Fog Droplet Size Distribution and Its Effect on Light Attenuation , 1973 .

[15]  R. Eldridge Haze and Fog Aerosol Distributions , 1966 .

[16]  R. P. Leonard,et al.  Investigation of warm fog properties and fog modification concepts , 1967 .

[17]  J. Warner The Microstructure of Cumulus Cloud. Part I. General Features of the Droplet Spectrum , 1969 .

[18]  B. Kunkel Fog Drop-Size Distributions Measured with a Laser Hologram Camera , 1971 .

[19]  P N Tverskoi Physics of the Atmosphere , 1966 .

[20]  J. Warner The Microstructure of Cumulus Cloud. Part II. The Effect on Droplet Size Distribution of the Cloud Nucleus Spectrum and Updraft Velocity , 1969 .

[21]  J. W. Fitzgerald,et al.  Changes in Cloud Nucleus Concentration and Cloud Droplet Size Distribution Associated with Pollution from St. Louis , 1973 .