[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.

SUMMARYTo develop and test real-time fade mitigation techniques control algorithms, propagation time series are needed. An alternative to using real data collected from propagation experiments is to generate typical fading time-series making use of climatological characteristics as well as geometrical and radio-electrical parameters of the link. The objective of this paper is to present a rain attenuation time-series synthesizer and able to generate events on demand. The model is based on an enhanced version of the Maseng-Bakken stochastic model. In the first part of this paper, the basic principles of the enhanced Maseng-Bakken model are recalled and the parameterization of this channel model is discussed for temperate European climates. Then, the theoretical bases of the Lacoste-Carrie 'event-on-demand' model and its validation constitute the second part of this paper. The enhanced Maseng-Bakken model is fully stochastic, whereas the Lacoste-Carrie 'event-on-demand' one offers the possibility to command the maximum attenuation level and the duration of the synthesized event.

SUMMARY To reach the terabit per second of throughput, telecommunication satellites cannot make use of frequency below Ka band only. Therefore, the use of broad portion of the spectrum available at Q/V (40/50 GHz) band is foreseen for the feeder link. This study presents the evaluation of performances of different macro‐diversity schemes that may allow mitigating the deep fades experienced at Q/V bands by introducing cooperation and a limited redundancy between the different gateways of the system. Two different solutions are firstly described. The performances resulting from the use of those assumptions are derived in a second stage. Copyright © 2014 John Wiley & Sons, Ltd.

[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,

The Ka-band propagation experiments conducted by ONERA in Toulouse (43.57 • E, 1.47 • N) in the southwest of France started in 2009 and is still on-going. The equipment comprises a beacon Earth station, a profiling radiometer, and a rain gauge. The ground station measures the received beacon signal using a 10-Hz sampling rate. The profiling radiometer measures the sky brightness temperatures at five Ka-band and seven V-band channels, surface temperature, surface humidity, and surface pressure. From July 2009 to March 2011, the beacon receiver recorded the 19.7-GHz (horizontal polarization) HotBird 6 beacon signal along a slant path of 38.6 • of elevation angle. Since April 2011, the beacon receiver has been recording the 20.2-GHz (vertical polarization) Astra 3B beacon signal along a slant path of 35.1 • of elevation angle. This paper aims at providing a complete description of the ONERA Data Processing Tool (in particular the methodology followed to retrieve total attenuation) used to compute 4 years (from July 2009 to June 2013) of copolar attenuation statistics.The experimental setup and the characteristics of the Earth-space links are briefly described. The complementary cumulative distribution function (CCDF) of total attenuation for the whole period is presented and compared with ITU-R recommendations. The measured CCDF of the rainfall rate is computed and compared with ITU-R Rec. P.837 and will also be used as input for the rain attenuation model given in ITU-R Rec. P.618. The measured CCDFs of total attenuation duration and total attenuation slope are also presented.Index Terms-Astra 3B, propagation, fade duration, fade slope, HotBird 6, Ka-band, rainfall rate, satellite communication systems, total attenuation. 0018-926X

A methodology to simulate two-dimensional rain rate fields at large scale (1000 Â 1000 km 2 , the scale of a satellite telecommunication beam or a terrestrial fixed broadband wireless access network) is proposed. It relies on a rain rate field cellular decomposition. At small scale ($20 Â 20 km 2), the rain field is split up into its macroscopic components, the rain cells, described by the Hybrid Cell (HYCELL) cellular model. At midscale ($150 Â 150 km 2), the rain field results from the conglomeration of rain cells modeled by HYCELL. To account for the rain cell spatial distribution at midscale, the latter is modeled by a doubly aggregative isotropic random walk, the optimal parameterization of which is derived from radar observations at midscale. The extension of the simulation area from the midscale to the large scale (1000 Â 1000 km 2) requires the modeling of the weather frontal area. The latter is first modeled by a Gaussian field with anisotropic covariance function. The Gaussian field is then turned into a binary field, giving the large-scale locations over which it is raining. This transformation requires the definition of the rain occupation rate over large-scale areas. Its probability distribution is determined from observations by the French operational radar network ARAMIS. The coupling with the rain field modeling at midscale is immediate whenever the large-scale field is split up into midscale subareas. The rain field thus generated accounts for the local CDF at each point, defining a structure spatially correlated at small scale, midscale, and large scale. It is then suggested that this approach be used by system designers to evaluate diversity gain, terrestrial path attenuation, or slant path attenuation for different azimuth and elevation angle directions.

This set of two companion papers aims at providing a statistical framework to quantify the inter-annual variability observed on the statistics of rain attenuation or rainfall rate derived from Earth-space propagation measurements. This part I is more specifically devoted to the theoretical study of the variance of estimation of empirical complementary cumulative distribution functions (ECCDFs) derived from Earth-space rain attenuation or rainfall rate time series. To focus the analysis on the statistical variability but without loss of generality, synthetic rain attenuation time series are considered. A large variability on the ECCDFs, which depends on the duration of the synthetic data, is first put into evidence. The variance of estimation is then derived from the properties of the statistical estimator. The formulation is validated numerically, by comparison with the ECCDF variances derived from the synthetic data. The variance of the fluctuations around the CCDF is then shown to be dependent on the average of the correlation function of the time series, on the probability level and on the measurement duration. This variance of estimation is needed as a prerequisite in conjunction with the knowledge of the climatic variability to characterize the yearly fluctuations of propagation statistics computed from experimental time series. The extensions from simulations to experiments as well as the application to system planning are detailed in part II.

The design and optimization of propagation impairment techniques for space telecommunication systems operating at frequencies above 20 GHz require a precise knowledge of the propagation channel both in space and time. For that purpose, space-time channel models have to be developed. In this paper the description of a model for the simulation of long-term rain attenuation time series correlated both in space and time is described. It relies on the definition of a stochastic rain field simulator constrained by the rain amount outputs of the ERA-40 reanalysis meteorological database. With this methodology, realistic propagation conditions can be generated at the scale of satellite coverage (i.e., over Europe or USA) for many years. To increase the temporal resolution, a stochastic interpolation algorithm is used to generate spatially correlated time series sampled at 1 Hz, providing that way valuable inputs for the study of the performances of propagation impairment techniques required for adaptive SatCom systems operating at Ka band and above.