Differential Rotation and Cloud Texture: Analysis Using Generalized Scale Invariance

K. Pflug Department of Physics, McGill University, Montreal, Quebec, Canada

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S. Lovejoy Department of Physics, McGill University, Montreal, Quebec, Canada

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D. Schertzer Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, Paris, France

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Abstract

The standard picture of atmospheric dynamics is that of an isotropic two-dimensional large scale and an isotropic three-dimensional small scale, the two separated by a dimensional transition called the “mesoscale gap.” Evidence now suggests that, on the contrary, atmospheric fields, while strongly anisotropic, are nonetheless scale invariant right through the mesoscale. Using visible and infrared satellite cloud images and the formalism of generalized scale invariance (GSI), the authors attempt to quantify the anisotropy for cloud radiance fields in the range 1–1000 km. To do this, the statistical translational invariance of the fields is exploited by studying the anisotropic scaling of lines of constant Fourier amplitude. This allows the investigation of the change in shape and orientation of average structures with scale.

For the three texturally—and meteorologically—very different images analyzed, three different generators of anisotropy are found that generally reproduce well the Fourier space anisotropy. Although three cases are a small number from which to infer ensemble-averaged properties, the authors conclude that while cloud radiances are not isotropic (self-similar), they are nonetheless scaling. Since elsewhere (with the help of simulations) it is shown that the generator of the anisotropy is related to the texture, it is argued here that GSI could potentially provide a quantitative basis for cloud classification and modeling.

Abstract

The standard picture of atmospheric dynamics is that of an isotropic two-dimensional large scale and an isotropic three-dimensional small scale, the two separated by a dimensional transition called the “mesoscale gap.” Evidence now suggests that, on the contrary, atmospheric fields, while strongly anisotropic, are nonetheless scale invariant right through the mesoscale. Using visible and infrared satellite cloud images and the formalism of generalized scale invariance (GSI), the authors attempt to quantify the anisotropy for cloud radiance fields in the range 1–1000 km. To do this, the statistical translational invariance of the fields is exploited by studying the anisotropic scaling of lines of constant Fourier amplitude. This allows the investigation of the change in shape and orientation of average structures with scale.

For the three texturally—and meteorologically—very different images analyzed, three different generators of anisotropy are found that generally reproduce well the Fourier space anisotropy. Although three cases are a small number from which to infer ensemble-averaged properties, the authors conclude that while cloud radiances are not isotropic (self-similar), they are nonetheless scaling. Since elsewhere (with the help of simulations) it is shown that the generator of the anisotropy is related to the texture, it is argued here that GSI could potentially provide a quantitative basis for cloud classification and modeling.

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