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Functional box-counting and multiple elliptical dimensions in rain.

S Lovejoy, D Schertzer, A A Tsonis

    Science (New York, N.Y.)
    |February 27, 1987
    PubMed
    Summary
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    Physical systems exhibit scale invariance, where large and small scales relate by ratio. Analyzing atmospheric rain fields using elliptical dimensions revealed a fractal dimension of 2.22 +/- 0.07.

    Area of Science:

    • Geophysics
    • Atmospheric Science
    • Physics

    Background:

    • Many physical systems display scale invariance, lacking characteristic sizes.
    • Atmospheric systems, like rain, exhibit complex scaling due to stratification and variability.
    • Understanding these scaling properties is crucial for accurate modeling.

    Purpose of the Study:

    • To analyze the multi-dimensional scaling properties of atmospheric rain fields.
    • To quantify the fractal dimension of rain intensity distributions.
    • To apply advanced dimensional analysis techniques to radar data.

    Main Methods:

    • Utilized elliptical dimensional sampling to analyze scale changes.
    • Employed functional box-counting for data analysis.
    • Applied these methods to radar-derived rain data.

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    Main Results:

    • Identified multiple scaling dimensions within atmospheric rain fields.
    • Estimated the elliptical dimension (d(el)) of the rain field.
    • Obtained a quantitative estimate: d(el) = 2.22 +/- 0.07.

    Conclusions:

    • The study quantifies the complex, multi-dimensional nature of atmospheric rain fields.
    • Elliptical dimensional analysis provides a robust method for characterizing such phenomena.
    • The findings contribute to a deeper understanding of geophysical fluid dynamics and precipitation processes.