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.
This set of two companion papers aims at providing a model for the inter-annual variability of earth-space propagation statistics and for the inherent risk and CIs. In part I, it was proposed to model the yearly variance σ² of empirical complementary CDFs so that σ 2 p ð ÞC the inter-annual climatic variance and p the long-term probability. Particularly, an analytical formulation of σ 2 E was derived and parameterized from synthetic rain attenuation data. Considering the statistical framework developed in part I, this part II is specifically devoted to the parameterization of the variance of estimation σ 2 E from experimental data of rain attenuation and rainfall rate. Then, a methodology to model and parameterize worldwide the inter-annual climatic variance σ 2 C is presented. The model of yearly variance of the empirical complementary CDFs σ 2 ¼ σ 2 C þ σ 2 E is finally compared against yearly experimental variances derived from data collected worldwide. The knowledge of this variability is very useful for system design as it allows the risk on a required availability and associated with a given propagation margin to be quantified.
This paper presents the analysis on two weather radar datasets, collected at Spino d’Adda (Italy) and Bordeaux (France), for the simulation and the performance evaluation of a site diversity system. Results from the two locations are compared and the impact of different factors such as the baseline and link orientation is assessed and related to the local climatologic characteristics. The results obtained are then compared with the model currently recommended by the ITU-R for the estimation of the site diversity performance. A linkage is then established between the preferable baseline orientation and the predominant direction of the rain field advection. The rain field displacement is finally shown to be well approximated by the wind speed and direction relative to the 700 hPa isobar extracted from the ECMWF ERA-40 meteorological database
In Recommendation ITU-R P.1853-1, a stochastic approach is proposed to generate long-term rain attenuation time series , including rain and no rain periods anywhere in the world. Nevertheless, its dynamic properties have been validated so far from experimental rain attenuation time series collected at mid-latitudes only. In the present paper, an effort is conducted to derive analytically the first-and second-order statistical properties of the ITU rain attenuation time-series synthesizer. It is then shown that the ITU synthesizer does not reproduce the first-order statistics (particularly the rain attenuation cumulative distribution function CDF), however, given as input parameters. It also prevents any rain attenuation correlation function other than exponential to be reproduced, which could be penalizing if a worldwide synthesizer that accounts for the local climatology has to be defined. Therefore, a new rain attenuation time-series synthesizer is proposed. It assumes a mixed Dirac-lognormal modeling of the absolute rain attenuation CDF and relies on a stochastic generation in the Fourier plane. It is then shown analytically that the new synthesizer reproduces much better the first-order statistics given as input parameters and enables any rain attenuation correlation function to be reproduced. The ability of each synthesizer to reproduce absolute rain attenuation CDFs given by Recommendation ITU-R P.618 is finally compared on a worldwide basis. It is then concluded that the new rain attenuation time-series synthesizer reproduces the rain attenuation CDF much better, preserves the rain attenuation dynamics of the current ITU synthesizer for simulations at mid-latitudes, and, if it proves to be necessary for worldwide applications, is able to reproduce any rain attenuation correlation function.
This paper describes a methodology to model the propagation conditions for Earth observation data downlink operating at Ka band. It relies on the use of numerical weather forecast models to perform local high resolution reanalysis of the meteorological conditions on which the propagation effects can be computed. From the meteorological simulations spanning long durations, time series representative of attenuation between an orbiting satellite and a ground station are extracted, knowing orbital and RF characteristics of the system. Index Terms-Earth observation data downlink, ka band, attenuation ground station, rain, numerical weather forecast models.I.
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