Cellular Statistical Models of Broken Cloud Fields. Part IV: Effects of Pixel Size on Idealized Satellite Observations

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

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Alexander Marshak NASA Goddard Space Flight Center, Greenbelt, Maryland

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Abstract

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF), which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud–clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

© 2019 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

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF), which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud–clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

© 2019 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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