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Cellular Statistical Models of Broken Cloud Fields. Part I: Theory

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  • 1 Department of Applied Physics and Applied Mathematics, Columbia University, and NASA Goddard Institute for Space Studies, New York, New York
  • | 2 NASA Goddard Space Flight Center, Greenbelt, Maryland
  • | 3 NASA Goddard Institute for Space Studies, New York, New York
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Abstract

A new analytical statistical model describing the structure of broken cloud fields is presented. It depends on two parameters (cell size and occupancy probability) and provides chord distributions of clouds and gaps between them by length, as well as the cloud fraction distribution. This approach is based on the assumption that the structure of a cloud field is determined by a semiregular grid of cells (an abstraction of the atmospheric convective cells), which are filled with cloud with some probability. First, a simple discrete model is introduced, where clouds and gaps can occupy an integer number of cells, and then a continuous analog is developed, allowing for arbitrary cloud and gap sizes. The influence of a finite sample size on the retrieved statistics is also described.

Corresponding author address: Mikhail Alexandrov, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025. Email: malexandrov@giss.nasa.gov

Abstract

A new analytical statistical model describing the structure of broken cloud fields is presented. It depends on two parameters (cell size and occupancy probability) and provides chord distributions of clouds and gaps between them by length, as well as the cloud fraction distribution. This approach is based on the assumption that the structure of a cloud field is determined by a semiregular grid of cells (an abstraction of the atmospheric convective cells), which are filled with cloud with some probability. First, a simple discrete model is introduced, where clouds and gaps can occupy an integer number of cells, and then a continuous analog is developed, allowing for arbitrary cloud and gap sizes. The influence of a finite sample size on the retrieved statistics is also described.

Corresponding author address: Mikhail Alexandrov, NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025. Email: malexandrov@giss.nasa.gov

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