Frequency Distributions of Shower Sizes

Dennis, A. S.; Fernald, F. G.

doi:10.1175/1520-0450(1963)002<0767:fdoss>2.0.co;2

Cited by 12 publications

(8 citation statements)

References 2 publications

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“…On the other hand, exponential distributions have been used empirically to describe populations of rain-cell sizes (indeed, for almost half a century, e.g. Dennis and Fernald, 1963;Sauvageot et al, 1999), although log-normal functions (e.g. Lopez, 1977) and power-law (Machado and Rossow, 1993) have also been applied successfully to statistics of cloud and rain systems.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

On the statistical distribution of dust devil diameters

Lorenz

2011

Icarus

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a b s t r a c tDust devil diameters, like many features in nature, have skewed distributions. I summarize, and present in a unified manner, literature values of dust devil optical diameters from seven terrestrial surveys, three rover-based surveys on Mars and two orbital surveys on Mars. The problems of appropriately treating these data are analogous to those for impact craters, and similar display and binning approaches are suggested. Remarkably, the Mars dust devil population remains better-known than Earth's. The theoretical justifications for possible log-normal, and (truncated) exponential and power-law descriptions of dust devil properties are discussed, and the challenges of discriminating between these candidate distributions with finite (and often, coarsely-binned) observation sets are noted: the best-sampled datasets so far appear well-described by power laws. Data required for advances in model discrimination are discussed: data binned in four or fewer ranges are useless for this purpose. Caution must be exercised in applying the notion of an 'average' dust devil and in calculating population-integral properties such as dust flux.

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Section: Theoretical Considerationsmentioning

confidence: 99%

On the statistical distribution of dust devil diameters

Lorenz

2011

Icarus

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“…[11] As part of a rain cell modeling, the choice of the physical model has to be carefully justified, for it has to account for the rain cell shape and for the rain rate horizontal distribution within the cell. From radar observations of rain field, many authors [Dennis and Fernald, 1963;Miller et al, 1975;Konrad, 1978;Goldhirsh and Musiani, 1986;Tenorio et al, 1995;Sauvageot et al, 1999] have considered that rain cells can be approximated to a circular shape. The diameter of the circular cell of equivalent area is used as a characteristic measure of the rain cell size.…”

Section: Rain Cell Definitionmentioning

confidence: 99%

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 1. Modeling of the rain cell

et al. 2003

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[1] From radar observations of rain fields at midlatitudes, a new physical model of rain cells is proposed. It strives to describe optimally the rain rate horizontal distribution within rain cells down to 1 mm h À1 . The approach is similar to that of the well-known EXCELL model. The mathematical definition of the model lies in the combination of a gaussian function and an exponential one, the cells having an elliptic horizontal cross section. Due to its hybrid structure, the new model has been named HYCELL. From a conceptual point of view, the gaussian component describes the convective-like high rain rate core of the cell, while the exponential component accounts for the surrounding stratiform-like low rain rate spreading down to 1 mm h À1 . The modeling of a rain cell with HYCELL then requires the determination of seven parameters. The latter is obtained, cell by cell, by solving a set of five fit-forcing equations completed by two continuity equations. The fit-forcing equations involve radar parameters of integral nature which refer not only to the rain cell geometry (area, ellipticity) but also to the rain rate R distribution inside the cell (mean and root mean square values of R and gradient of R). Their analytical expressions are derived from the model definition, while their values are forced to be those derived from radar measurements. Using this method, thousands of rain cells identified from radar observations in the regions of Bordeaux (southwestern France) and Karlsruhe (southwestern Germany) have been modeled. Though both sites are at midlatitude, the climatic contexts differ: oceanic for Bordeaux and continental for Karlsruhe. Results of rain rate horizontal distribution modeling within cells using HYCELL and EXCELL are compared. It is then suggested that the HYCELL model is a new tool which deserves to be considered by system designers to compute propagation parameters.

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“…[15] Many authors [Dennis and Fernald, 1963;Miller et al, 1975;Konrad, 1978;Goldhirsh and Musiani, 1986;Tenorio et al, 1995;Sauvageot et al, 1999;Mesnard and Sauvageot, 2003] have considered that rain cells can be approximated by a circular shape. The diameter of the circular cell of equivalent area is used as a characteristic measure of the rain cell size.…”

Section: Distribution Of the Rain Cell Diametermentioning

confidence: 99%

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 2. Statistical modeling of the rain rate field

et al. 2003

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[1] A methodology to simulate typical two-dimensional rain rate fields over an observation area A o of a few tens up to a few hundreds of square kilometers (i.e., the scale of a satellite telecommunication beam or a terrestrial Broadband Wireless Access network) is proposed. The scenes generated account for the climatological characteristics intrinsic to the simulation area A o . The methodology consists of the conglomeration of rain cells modeled by HYCELL and of two analytical expressions of the rain cell spatial density, both derived from the statistical distribution of the rain cell size. The scene generating requires, as an input parameter, the local Cumulative Distribution Function (CDF) of the rain rate, a meteorological data commonly available throughout the world. The rain rate field is then generated numerically, according to an iterative scheme, under the constraint of accurately reproducing the local CDF intrinsic to the simulation area A o , and following rigorously the rain cell spatial density. All the potentialities of the HYCELL model are thus used in order to generate a two-dimensional scene having a mixed composition of hybrid, gaussian, and exponential cells accounting for the local climatological characteristics. Various scenes are then simulated throughout the world, showing the ability of the method to reproduce the local CDF, with a mean error, with respect to the rain rate distribution, smaller than 1.86%, whatever the location, that is, whatever the climatology. It is suggested that this statistical modeling of the rain rate field horizontal structure be used as a tool by system designers to evaluate, at any location of the world, diversity gain, terrestrial path attenuation, or slant path attenuation for different azimuth and elevation angle directions.INDEX TERMS: 3354 Meteorology and Atmospheric Dynamics: Precipitation (1854); 3210 Mathematical Geophysics: Modeling; 3360 Meteorology and Atmospheric Dynamics: Remote sensing; 6964 Radio Science: Radio wave propagation; KEYWORDS: propagation in rain, radar meteorology, rain modeling Citation: Féral, L., H. Sauvageot, L. Castanet, and J. Lemorton, HYCELL-A new hybrid model of the rain horizontal distribution for propagation studies: 2. Statistical modeling of the rain rate field,

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Frequency Distributions of Shower Sizes

Cited by 12 publications

References 2 publications

On the statistical distribution of dust devil diameters

On the statistical distribution of dust devil diameters

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 1. Modeling of the rain cell

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 2. Statistical modeling of the rain rate field

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