Cumulus Clouds from the rough surface perspective

Document Type : Research Article

Authors

1 Ph.D. Student, Department of physics, University of Mohaghegh Ardabili, Ardabil, Iran

2 Associate Professor, Department of physics, University of Mohaghegh Ardabili, Ardabil, Iran

3 Assistant Professor, Department of physics, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

Although it is well-known the clouds show a fractal geometry for a long time, their detailed analysis is missing in the literature yet. Within scattering of the received radiation from the sun, clouds play a very important role in the energy budget in the earth atmosphere. It was shown that the surface fluctuations and generally the statistics of the clouds has a very important impact on the scattering and the absorption of the radiation of the sun. In this paper we first study the relation between the visible light intensity and the width of the cumulus clouds. To this end, we find that the received intensity is , where ,  and  To this end we supposed that the transmitted intensity of light from a column of cloud is proportional to where (summation of the absorbed and the scattered contributions). Using this relation, we find a one to one relation between the cloud width and the intensity of the received visible light in low intensity regime. By calculating the Mie scattering cross sections for the physical parameters of the clouds, we argue that this correspondence works for thin enough clouds, and also the width of the clouds is proportional to the logarithm of the intensity. The Mie cross section is shown to behave almost like  for large enough s, where  is the angle of radiation of sun with respect to earth’s surface, or equivalently the cloud’s base. This allows us to map the system to two-dimensional rough media. Then exploiting the rough surface techniques, we study the statistical properties of the clouds. We first study the roughness, defined for rough surfaces as . This study on the local and global roughness exponents (α_l and α_g respectively) show that the system is self-similar. We also consider the fractal properties of the clouds. Importantly by least square fitting of the roughness we show numerically that the exponents are and . We study also the other statistical observables and their distributions. By studying the distribution of the local curvature (for various scales) and the height variable we conclude that these functions, and consequently the system is not Gaussian. Especially the distribution of the height profile follows the Weibull distribution, defined via the relation  for  and zero otherwise. The reasoning of how this relation arises is out of scope of the present work, and is postponed to our future studies. The studies on the local curvature, defined via  reveals the same behaviors and structure. All of these show that the problem of the width of cumulus clouds maps to a non-Gaussian self-similar rough surface. Also we show that the system is mono-fractal, which requires  . Given these results, the authors think that the top of the clouds are anomalous random rough surfaces that affect the albedo of cloud fields.

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References

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Journal of the Earth and Space Physics
Volume 47, Issue 1
April 2021
Pages 175-186

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