Editorial Type:
Article
Article Type:
Research Article

Markovian Statistical Model of Cloud Optical Thickness. Part I: Theory and Examples

Mikhail D. Alexandrov aDepartment of Applied Physics and Applied Mathematics, Columbia University, New York, New York
bNASA Goddard Institute for Space Studies, New York, New York

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Alexander Marshak cNASA Goddard Space Flight Center, Greenbelt, Maryland

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Brian Cairns bNASA Goddard Institute for Space Studies, New York, New York

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Andrew S. Ackerman bNASA Goddard Institute for Space Studies, New York, New York

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Online Publication:
02 Dec 2022
Print Publication:
01 Dec 2022
DOI:
https://doi.org/10.1175/JAS-D-22-0125.1
Page(s):
3315–3332
Restricted access

Abstract

We present a generalization of the binary-value Markovian model previously used for statistical characterization of cloud masks to a continuous-value model describing 1D fields of cloud optical thickness (COT). This model has simple functional expressions and is specified by four parameters: the cloud fraction, the autocorrelation (scale) length, and the two parameters of the normalized probability density function of (nonzero) COT values (this PDF is assumed to have gamma-distribution form). Cloud masks derived from this model by separation between the values above and below some threshold in COT appear to have the same statistical properties as in binary-value model described in our previous publications. We demonstrate the ability of our model to generate examples of various cloud-field types by using it to statistically imitate actual cloud observations made by the Research Scanning Polarimeter (RSP) during two field experiments.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mikhail D. Alexandrov, mda14@columbia.edu

Abstract

We present a generalization of the binary-value Markovian model previously used for statistical characterization of cloud masks to a continuous-value model describing 1D fields of cloud optical thickness (COT). This model has simple functional expressions and is specified by four parameters: the cloud fraction, the autocorrelation (scale) length, and the two parameters of the normalized probability density function of (nonzero) COT values (this PDF is assumed to have gamma-distribution form). Cloud masks derived from this model by separation between the values above and below some threshold in COT appear to have the same statistical properties as in binary-value model described in our previous publications. We demonstrate the ability of our model to generate examples of various cloud-field types by using it to statistically imitate actual cloud observations made by the Research Scanning Polarimeter (RSP) during two field experiments.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mikhail D. Alexandrov, mda14@columbia.edu
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