Overview of available channel models for time series generation

This document gives an overview of todays available channel models for rain fading. These channel models are time-series generators which provide a time-series which simulates rain fading where the term rain fading is used for fading caused by meteorological effects: Clouds, snow, hail, fog and rain is the main contributor to this type of fading. The first time-series generators have been presented only a few years ago and, therefore, constitute a new field in satellite communications especially at high frequencies. Time-series generators can be used in computer simulations to simulate the channel conditions in scenarios where adaptive fade countermeasures are employed. Thus, the time-series generators are essential to test and optimise fade countermeasures by computer simulations

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

A methodology to simulate typical two-dimensional rain rate fields over an observation area Ao 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 Ao. 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 Ao, 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

Influence de la diffusion des ondes électromagnétiques par les hydrométéores sur l'imagerie radiométrique du sol en ondes millimétriques

In this paper, the effects of absorption and scattering phenomenon in the atmosphere are evaluated, particularly the variations of radiometric contrasts received by a passive imager in various meteorological conditions. For that purpose, the analysis has been based on radiative transfer theory whose vectorial equation has been solved by the invariant imbedding method. Atmospheric absorption only has been studied first, then scattering effects have been taken into account. The influence on brightness temperatures has been calculated for an airborne and a spaceborne radiometer flying over uniform surfaces, either specular or lambertian, with various disturbing medium along the path. Numerical simulations have been focused on atmospheric window frequencies (35 GHz, 94 GHz and 140 GHz) in order to assess the imaging capabilities of radiometric instruments. Finally a specific method using the invariant imbedding schema and Fourier expansion along the azimuthal dependance has been developed, in order that the case of an imaging radiometer flying over non uniform surfaces composed of various parcels types could be simulated.Cet article analyse les effets de l'absorption et de la diffusion atmosphérique sur les contrastes reçus par un radiomètre imageur pour un grand nombre de conditions météorologiques. Pour cela, nous nous sommes basés sur la théorie du transfert radiatif dont nous avons résolu, l'équation matricielle à l'aide de la méthode dite de l'“invariant imbedding”. Nous avons étudié l'influence de l'absorption atmosphérique seule, puis de l'absorption et de la diffusion sur les températures radiométriques pour un radiomètre aéroporté ou sur satellite, d'abord dans le cas d'un sol uniforme spéculaire ou lambertien pour diverses perturbations atmosphériques. Nous nous sommes plus particuliérement intéressés aux fréquences correspondant aux fenêtres atmosphériques (35 GHz, 94 GHz et 140 GHz) ce qui nous a permis d'analyser les effets de l'atmosphère sur les contrastes radiométriques de scènes au sol. Afin de pouvoir appliquer notre étude au cas d'un radiomètre imageur embarqué survolant un sol non uniforme, constitué de parcelles de nature différente, nous avons développé une méthode de calcul basée sur la méthode de 1'“invariant imbedding” et la décomposition en série de Fourier suivant l'azimut, ce qui permet de prendre en compte cette non uniformité

Hycell: a new hybid model of the rain horizontal distribution for propagation studies. Part 1: Modelling of the rain cell.

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−1. 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−1. 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

Etude de la variabilité spatiale des précipitations à partir d'observations radars.

(13-15 mars 2002)

Rain cells shape and orientation distribution in south-west of France

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