A Fractal Dimensional Analysis on the Cloud Shape Parameters of Cumulus over Land

Gotoh, Kazuo; Fujii, Yasuhiko

doi:10.1175/1520-0450(1998)037<1283:afdaot>2.0.co;2

Cited by 24 publications

(17 citation statements)

References 19 publications

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“…[6] Cumulus cloud size distribution, in the size range of $100 m to 15 km, have been reported by, e.g., Wielicki and Welch [1986], Welch and Wielicki [1986], Welch et al [1988], Cahalan and Joseph [1989], Joseph and Cahalan [1990], Sengupta et al [1990], Weger et al [1992], , Kuo et al [1993], Benner and Curry [1998], and Gotoh and Fujii [1998]. The cloud-size parameter considered in most of these works is the diameter of the equivalent circular area D, i.e., D = (4A/p) 1/2 , where A is the cloud horizontal area.…”

Section: Brief Review Of the Literaturementioning

confidence: 99%

Structural characteristics of rain fields

Mesnard

Sauvageot

2003

J. Geophys. Res.

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[1] This paper analyzes the shape of rain area size distributions (RASDs) observed by radar in tropical and midlatitude regions. The rain area is defined, with respect to a rain threshold t, as the area, inside a contour, where the rain rate is higher than t. The size considered is the diameter of the equivalent circular area D. The reflectivity peaks inside the rain areas are numbered and the rain areas put together by classes having the same peak number. The size distributions of the rain areas containing the same number of peaks p are well fitted by lognormal functions, the parameters of which, m p and s p , are weakly dependent on the conditions of the peak determination. The parameters m p and s p are found to be linked by a power relation. For D < 6 km most of the rain areas are single peaked. The RASD without peak number distinction is a lognormal mixture. Using the relations obtained for m p , s p , and the rain area number as functions of p enables one to simulate RASDs with results in good agreement with the observations. Because of the limitation in the radar sampling at both ends of the RASD and the decrease of area number with increasing size, the radar-observed RASDs are severely truncated. The possibility of an approximate fitting of the truncated RASD with diverse functions is discussed. At the intermediary values of the threshold, i.e., for t ranging between 3 and 12 mm h À1 , where the RASD is easiest to compute, the slope of these truncated distributions is not strongly dependent on the threshold. This slope appears not to be very sensitive to the minimum and maximum distances bounding the domain where the rain field is observed. The RASD is found to be sloping more over sea than over land. The slope of the RASDs shows a small diurnal variation but no significant annual variation. The ''perimeter to area'' (fractal) dimension of the rain area for the sample without peak number distinction is around 1.35. Single-peaked and multipeaked rain areas have different perimeter to area dimensions, $1.23 and 1.38, respectively. These values are almost independent from the threshold and from the location of the domain observed.

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Section: Brief Review Of the Literaturementioning

confidence: 99%

Structural characteristics of rain fields

Mesnard

Sauvageot

2003

J. Geophys. Res.

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“…In this section, we focus on the special case of self similar processes, i.e., signals which exhibit monofractal scale invariance [21]. Such processes have been used as a satisfying first approximation to model or describe very various phenomena, such as ionic transport [22], fluid turbulence [23], climate [24], river flows [25], cloud structure [26] or earthquakes [27], as well as neural signals [28], stock markets [29,30], texture patterns [31] or internet traffic [32]. A process X t is monofractal scale-invariant if there exists a real number H such that for all a ∈ R + * , the probability density functions of x at and a H x t are equivalent.…”

Section: Self-similar Processesmentioning

confidence: 99%

Information Theory for Non-Stationary Processes with Stationary Increments

Granero-Belinchon

Roux

Garnier

2019

Entropy

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We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allow us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process but also offers a new way to quantify the multi-fractality.

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“…Por otra parte, la propia estructura de las nubes se define como fractal, y diferentes estudios han caracterizado la naturaleza fractal de estas estructuras (Mandelbrot, 1983;Peitgen et al, 1992;Carvalho y Silva Dias, 1998;Gotoh y Fujii, 1998).…”

Section: Aplicaciones Al Estudio De La Cubierta Nubosaunclassified

Aplicación del análisis fractal al estudio de las estructuras dinámicas de fluidos medioambientales

Platónov

Barceló²,

Apraiz

2008

ing.agua

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Resumen: La aparición de múltiples escalas, que interactúan entre si en diversos fenómenos físicos medioambientales, especialmente cuando el régimen fluido es turbulento, exige métodos de análisis nuevos. El análisis multi-fractal permite cuantificar el nivel de complejidad geométrico y en algunos casos a partir de una caracterización geométrica se pueden predecir algunos aspectos dinámicos del fluido. Se aplica el método de Box-Counting (conteo de cajas) para calcular la dimensión fractal o capacidad de Kolmogorov a observaciones de nubes obtenidas mediante las imágenes de satélite de la Atmósfera (Infrarrojo IR y Visible) y de superficie del Océano (Radar de Apertura Sintética SAR). En todos los casos las diferencias en complejidad entre los distintos tonos de gris detectados en las imágenes de satélites de estructuras atmosféricas, derrames de crudo o penachos de aguas contaminadas en la superficie marina son un reflejo de las condiciones físicas ambientales del medio fluido atmosférico u oceánico y nos permiten entender mejor los procesos dinámicos y de transporte de energía a distintas escalas del flujo analizado. INTRODUCCIÓNEl estudio de la atmósfera y del océano está fuertemente ligado a la teledetección y a las herramientas de procesado de información utilizadas. En ambos casos se estudian flujos complejos con un número de Reynolds elevado. Debido a la no-linealidad de las interacciones fluidas se generan múltiples escalas, observables tanto en las velocidades como en la estructura de los campos escalares, entre ellos la temperatura, la velocidad, la concentración de trazadores, la densidad, etc. Es interesante poder relacionar de alguna forma las características geométricas de observaciones de imágenes del flujo en estudio con sus propiedades físicas y su dinámica.En este estudio se analizan estructuras nubosas utilizando imágenes Meteosat en el canal visible y en el IR térmico. Con el IR térmico se obtiene información de la temperatura de la parte superior de las nubes y esta está correlacionada con la altura, obteniendo una estructura tridimensional a caracterizar. Por otra parte también se caracterizan estructuras en el mar formadas por la dispersión de derrames de hidrocarburos, se utilizan para este trabajo las imágenes de Radar de Apertura Sintética (SAR). El nexo común de ambas aplicaciones es la utilización de la caracterización fractal y la presentación y versatilidad de la herramienta de cálculo ImaCalc.Las entidades fractales se caracterizan por presentar autosemejanza a diferentes rangos de escalas de observación, cuando se trabaja con en-© Fundación para el Fomento de la Ingeniería del Agua

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A Fractal Dimensional Analysis on the Cloud Shape Parameters of Cumulus over Land

Cited by 24 publications

References 19 publications

Structural characteristics of rain fields

Structural characteristics of rain fields

Information Theory for Non-Stationary Processes with Stationary Increments

Aplicación del análisis fractal al estudio de las estructuras dinámicas de fluidos medioambientales

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