We have developed and discussed the theory and applications of a physical-mathematical model of the dynamics of rain attenuation and have tested it as a rain attenuation prediction model in slant paths. Other parameters, however, such as fade durations and rates of change of fades, can be calculated. The main physical input is the 1-min rain rate time series of a site, which is converted to a rain rate space series along horizontal or slant paths by using an estimate of the storm translation speed v method known as “synthetic storm technique.” However, the long-term predictions are found to be insensitive to v. The vertical structure of precipitation is modeled with two layers. The model was tested against the probability distributions of rain long-term 11.6-GHz attenuation collected at the three Italian stations (Fucino, Gera Lario, and Spino d'Adda) during the SIRIO propagation experiment (13 years of data) for which concurrent rain rate time series are available. In the outage probability range 10−1 to 5×10−3% defined the prediction error e = ( Ap − Am) / Am (where Am and Ap are respectively, the measured and predicted rain attenuations, dB), = −10.6%, σ=7.6% and rms=13%. Compared to nine other well-known prediction methods, the present model surmounts all of them in the three sites tested.

Physical-mathematical model of the dynamics of rain attenuation based on rain rate time series and a two-layer vertical structure of precipitation

The quality of satellite communication systems can be seriously affected by variable climatic phenomena such as rain and turbulence. For the design of communication systems with a required availability, statistical knowledge of climatic propagation effects is essential. In this thesis three climatic propagation effects are studied: • the fade slope (rate of change) of attenuation due to rain; • scintillation due to tropospheric turbulence; • depolarisation due to rain and ice crystals. For the study, experimental satellite signal measurements are analysed, received from the satellite Olympus at Eindhoven University of Technology and Helsinki University of Technology. The statistical behaviour of the propagation effects is studied in relation with the theoretical background. The results obtained are compared with results from many other measurement sites. This way, relations with link parameters (among which the frequency) and with meteorological parameters are studied. New prediction models for the propagation effects are developed, as well as improvements to existing models. The main conclusions obtained are the following: The rain fade slope is found to have, conditional for a rain attenuation level, a symmetrical distribution. The standard deviation of this distribution is proportional with attenuation, independent of frequency, and dependent on filter bandwidth. It is likely to depend on elevation angle and on the relative contribution of different rain types. The signal level due to tropospheric scintillation is found to have an asymmetrical distribution; the asymmetry increases with scintillation intensity. The frequency dependence of scintillation shows strong variability between different measurement sites; several possible explanations for this observation are given. For global long-term prediction of scintillation, current models use only the wet term of refractivity as a meteorological input, however it is found that the water content of heavy clouds is necessary as an additional meteorological input parameter. An improved prediction model of tropospheric scintillation is presented, based on the conclusions found. The relation between depolarisation and attenuation due to rain is studied using measurements from many different sites; the different dependencies of this relation on link parameters are empirically quantified and the model for this relation is updated. For the case of depolarisation caused by simultaneous rain and ice, a calculation method is developed to separate the contributions of both partial media. The conclusions obtained and the new prediction models developed in this thesis can improve the prediction of propagation effects, which is essential for satellite communication system design in general and for adaptive link control systems in particular.

Climatic radiowave propagation models for the design of satellite communication systems

The paper presents a new prediction model of rain attenuation in slant paths; it models the precipitation with two layers of constant vertical precipitation rate. The relationship between the rain-rate in the first layer above the ground (layer A) and the apparent precipitation rate (defined in the paper) in the second layer (layer B, which models the melting layer) is theoretically derived: assuming a log-normal probability distribution for the rain-rate in layer A (measured at ground), the apparent rain-rate in layer B is also log-normal with the same standard deviation, but with its median value 3.134 times the median value of the ground rain-rate. The rain-rate statistical process in space is assumed to be also log-normal with a correlation function determined from radar measurements. Assuming that the path attenuation (expressed in decibels) is also log-normal, its average and standard deviation are then derived. The model is tested against the large CCIR data bank of slant path attenuation with or without concurrent rain-rate, frequency ranges between 6 and 34.5 GHz, in the latitude range between 1.3 and 67.4 degrees. In the probability range 10−3-10−3 the root mean square (RMS) log-error of the Long Term data bank (single experiments of about 5 years) is about 26%, with average ( ) log-error close to zero. For data banks of single experiments of shorter duration the RMS increases while decreases. The model is not significantly biased with attenuation, frequency of the experiment or latitude of the station. The distributions of the overall log-error and that of the log-error conditioned on given probabilities are both Gaussian. Sensitivity to different theoretical assumptions about the calculation of the specific attenuation kRα and to different numerical values of the snow density is also tested.

Rain attenuation predicted with a two-layer rain model

We present annual/seasonal rainfall rate statistics derived from a 29-month data bank of 1 sample/min, measured by a disdrometer located inside the National Technical University of Athens Campus. We discuss both the inaccuracy and the unavailability of the measuring equipment, as well as the statistical reliability of the rainfall rate sample. Additionally, after applying the Synthetic Storm Technique on the measured rainfall rate time series, we present the first long term simulated annual/seasonal and diurnal rain attenuation statistics, at 12 GHz for a hypothetical downlink from Hellas Sat 2 to Athens. According to the results, we predict that communication downlinks working in the afternoon and early evening hours must be given an extra power margin, to compensate for high rain attenuation

Annual and diurnal slant path rain attenuation statistics in Athens obtained with the synthetic storm technique

A comparison of measured attenuation series with the attenuation series obtained from rain rate measurement by using synthetic storm technique is made for Ku band signal at a tropical location. Validity of the model is tested for the long-term statistics in terms of the cumulative distribution of attenuation occurrence and fade duration. Applicability of the model is also shown to be valid event-wise. It has been demonstrated that the long term statistics of predicted rain attenuation are insensitive to storm translation speed. No significant differences are found when cumulative distributions of predicted attenuation values are compared for different data sampling intervals. It has been observed that there exists a good correlation between the predicted and measured values of attenuation for at least 80% of the events.

D. Maggiori

Papers

Computed transmission through rain in the 1-400 GHz frequency range for spherical and elliptical drops and any polarization