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A propagation campaign of attenuation measurements with the 40-GHz Alphasat beacon signal is being conducted at the Universidad Politecnica de Madrid (UPM). Besides attenuation, rainfall rate data are collected with a rain gauge and a disdrometer. Rainfall rate and attenuation statistics can be used for assessment and development of attenuation prediction models for satellite radio links. In this paper, the results obtained from 5 years of rainfall rate and attenuation measurements are presented and compared with several relevant propagation models: the ITU-R P.837-6, ITU-R P.837-7 and MORSE models for rainfall rate and the ITU-R P.618-13 for attenuation. A moderate accuracy has been achieved with all models. The ITU-R P.837-7 and MORSE models improve the prediction for probabilities lower than approximately 0.01%, whereas for higher probabilities the three models show a similar performance.

Communication via satellite is still one of the most important choices in telecommunication especially for areas which are not covered by optical fiber networks. However, the radio frequency used in communication satellites is affected by rain attenuation, which is called as rain attenuation. The rain attenuation increases with increasing rainfall rate and operating frequency. Therefore, accurate estimation of 1-min rainfall rate is important for modelling rain attenuation. However, in the tropics such as Indonesia, precipitation varies in several time scales. Furthermore, climate change has increased the frequency of occurrence of extreme rain and this condition may also affect the communication system. The ITU-R model which is widely used to estimate rain attenuation assumes a stationary climate. This research analysed rainfall pattern in Indonesia. In addition, the variation in melting layer height was also investigated. The rain gauge observation in some locations in Indonesia, i.e., Kototabang, Pontianak, Manado and Biak, were analyzed. The rainfall pattern was analysed using wavelet transforms. In addition, the percentage of time exceeded of several rainfall rate which are commonly used in modeling and design of telecommunication systems was also discussed. For melting layer height, 17 years of the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data particularly TRMM PR 2A25 version 7 data were used. A 128–256 days scale band oscillation (seasonal) is observed at Kototabang, Pontianak and Biak, but it is not observed at Manado. This seasonal oscillation is an interval-independent characteristic, indicating a stationary dynamic of this signal. Intrasesonal oscillation is an interval-dependent characteristic in which the period of oscillation is not constant indicating a nonstationary dynamic of this signal. At Manado, Pontianak and Kototabang, 256–512 days scale band oscillation is also observed, but it is not clearly observed at Biak. It was also found that there is an increase of rainfall rate for small percentage of time exceeded. Furthermore, there is a slight increase of melting layer height at Kototabang, Pontianak and Biak. In Manado, linear regression shows a decrease of melting layer height with the increase of year.

Rain attenuation is the main impairment for radio communication systems operating at frequencies above 10GHz, and the rainfall rate data exceeded for 0.01% of the average year are the essential data for rain attenuation prediction. Three kinds of digital maps of rain rate (mm/h) exceeded for 0.01% of the average year in China land area have been compared and analyzed herein, which are the methods in Recommendation ITU-R P.837-7, P.837-4, and the grid data produced by using the statistical data in widely distributed station in China land area. The comparison shows that the method in P.837-7 is better than previous ITU-R method, but there are still many differences between the method in P.837-7 and the grid map obtained by the local data sources in China land area.

In this paper, we present a model for rainfall rate prediction 30 seconds ahead of time using an artificial neural network. The resultant predicted rainfall rate can then be used in determining an appropriate fade counter-measure, for instance, digital modulation scheme ahead of time, to keep the bit error rate (BER) on the link within acceptable levels to allow constant flow of data on the link during a rain event. The approach used in this paper is pattern recognition technique that considers historical rainfall rate patterns over Durban (29.8587°S, 31.0218°E). The resultant prediction model is found to predict an immediate future rain rate when given three adjacent historical rain rates. For our model validation, error analysis via root mean square (RMSE) technique on our prediction model results show that resultant errors lie within acceptable values at different rain events within different rainfall regimes.

The performance of both a recent rainfall rate model and the inter-annual variability prediction method proposed by the International Telecommunication Union has been assessed taking advantage of the availability of 16 years of rain gauge data. The above rainfall rate model produces as well monthly rainfall rate distributions that have been compared with the experimental monthly distributions achieving good results. The procedure proposed in the ITU variability prediction method has been adapted to test its usefulness to estimate monthly and seasonal variability. In some cases, fair agreement has been found between estimated and experimental variability.

Wireless communication systems operating at above 10 GHz are exposed to rain attenuation. Therefore, countries with high precipitation rate such as Malaysia, require careful planning before establishing a reliable wireless link. Signal attenuation due to rain can be measured or estimated, but it requires the knowledge of local 1-minute rainfall rate statistic. But for most part of the world, the rainfall data usually comes with higher integration time, such as 60-minute. As a result, the method to convert rainfall rate with higher integration time to 1-minute rainfall rate distribution is essential. In this study, hydrological data from five areas in East Malaysia is translated to 1-min and 60-min rainfall rate distribution. Then, five conversion models were used to convert 60-min rainfall rate to 1-min rainfall rate. From observation and conversion error analysis, this study found that Segal method performed the best when it is compared to other four conversion methods.

Malaysia is well known for its wet tropical climate and monsoon seasons which bring rainfall almost throughout the year. Therefore, designing wireless communication links above 10 GHz for Malaysian weather involves study of rainfall rate and its integration time. The knowledge of local 1-min rainfall rate statistic is the key input for the estimation of signal attenuation due to rain. Due to limitation of 1-min rain rate data availability, the conversion model is necessary to translate higher integration time rainfall rate to the required 1-min rainfall statistic. In this paper, rainfall data from six locations in the East Malaysia is acquired from a local hydrological agency and processed to a meaningful 1-min, 5-min and 10-min rainfall rate statistics. Then, four conversion models are used to convert from 5-min and 10-min rainfall rate to 1-min rainfall rate. From the conversion error analysis, it is found that the Emiliani et al conversion method performed the best for this study.

This paper presents assessments of empirical conversion methods in obtaining cumulative distribution function of rainfall rate at 1-minute integration time. From collected measured data in Kuala Lumpur, cumulative distributions of rainfall rate at various integration times were compiled. Four conversion methods were selected in the assessment namely: Segal, Burgueno, Ismail et al and Polynomial. The generated 1-minute statistics using the mentioned four empirical conversion methods are then compared with measured statistics, in order to test its validity. Based on the assessment, it can be suggested that the Ismail et al and Polynomial conversion methods seem to be capable of producing rainfall rate statistics at 1-minute integration time with close approximation to the measured values.

Precipitation plays a crucial role to the global water and energy cycle that governs the weather, climate, and ecological systems. Thorough understanding and accurate forecasting of precipitation is essential to the affairs of humans. The Tropical Rainfall Measuring Mission (TRMM), launched in 1997, is a joint space mission between NASA and the Japan Aerospace Exploration Agency (JAXA) designed to monitor and study tropical rainfall. The Precipitation Radar (PR) on board the TRMM satellite is the first space borne instrument, capable of providing high-resolution vertical profile of precipitation on a global scale. TRMM-PR operates at a single frequency of Ku- (13.6 GHz) band. The microphysical retrieval algorithms for TRMM-PR rely on the surface-reference technique (SRT) to estimate path attenuation and correct the measured Ku-band reflectivity. With the attenuation-corrected reflectivities, a modified Hitschfeld-Bordan method [1] is then used to retrieve limited drop size distribution (DSD) information, and the rainfall rate [2]. One disadvantage of single-frequency space borne radar such as TRMM-PR is that it is not easy to retrieve the DSD parameters completely. Therefore, k-Z and Z-R relationships, with their inherent assumptions, are used to estimate rainfall rate which is not sufficient to capture the variability of precipitation and has large uncertainty. Global Precipitation Measurement (GPM) mission is poised to be the next generation observations from space after the TRMM mission. GPM is a science mission with integrated applications goals for advancing the knowledge of the global water/energy cycle variability as well as improving weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of global precipitation. The GPM core satellite will be equipped with a dual-frequency precipitation radar (DPR) operating at Ku- (13.6 GHz) and Ka- (35.5 GHz) band [3]. Taking two independent sets of observation, DPR on aboard the GPM is expected to improve our knowledge of precipitation processes relative to the single-frequency (Ku- band) radar used in TRMM by providing greater dynamic range, more detailed information on microphysics. Two parameters of DSDs can be retrieved from dual-frequency observations and better accuracies in rainfall estimation can be achieved. Theoretically, rainfall rate is a function of rain drop size distribution and rain drop terminal velocity, R=0.67π∗10−3∫ v(D)D3N(D)dD. The most critical component in rainfall rate estimation is the time-space variation of drop size distribution. Le and Chandrasekar (2014) [4] developed a hybrid method to retrieve drop size distribution parameters for GPM-DPR. The hybrid method is a profile-based optimization algorithm with the philosophy to combine the attributes of forward method and linear constraints of DSDs in rain. Two of the gamma distribution parameters [5], Do and Nw, at surface are optimized when the deviation between estimates and observations are minimized. The hybrid method can be used to estimate DSDs at each space and temporal resolution of GPM-DPR observation. In this paper, rainfall rate is calculated using DSDs retrieved through the hybrid method [4] based on assumptions of particle terminal velocity. Data collected by GPM-DPR is capability to cover ±65° latitude of the earth with every 2–4 hours. Thus, a global rainfall map can be generated. In polarimetric radar system, rainfall rate can be estimated through dual-polarized radar parameter such as Zdr [6][7]. Zdr is called differential reflectivity and it is a function of particle characteristics itself. Similar of Zdr to the dual-polarization radar retrieval, there is a parameter called dual-frequency ratio (DFR) that plays an important role in the dual-frequency radar retrievals. DFR is defined as the difference of the radar reflectivity at two frequencies in decibels which carries information of single particle characteristics. In this study, we investigate potential relation between rainfall rate, reflectivity at Ku- band and DFR using theoretical simulation [8] and curve fitting. Figure 1 shows a scattergram of rainfall rate estimation from R(Zh, DFR) versus true rainfall rate. Both Zku and DFR are in linear form in this equation. This provides a direct estimation of rainfall rate without prior knowledge of drop size distribution. Since both reflectivity and dual frequency ratio are intrinsic values, attenuation correction is needed before rain rate can be estimated through R(Zh, DFR) equation. The hybrid method [4] described in previous paragraph could be one of the algorithms to perform attenuation correction. The global rainfall map generated through R(Zh, DFR) approach will be cross-compared with DSD approach described in the previous paragraph, as well as other approaches such as attenuation based rainfall rate. The comprehensive analysis of the three techniques are presented.

The accuracy of rainfall rate prediction methods must be assessed given their significant influence on the performance of rain attenuation models. Taking advantage of the large amount of rain gauge data available at UPM that can be used for model testing thanks to a recent integration conversion procedure, the predictions provided by ITU-R P.837-6 and by a newly published rainfall rate prediction method are compared.

One minute rainfall rates are a key tool for rain attenuation modeling. Availability of this data is still very scarce worldwide, especially in the tropics with insufficient propagation measurement. The scenario at the tropical and the equatorial locations is of concern due to the nature of the climate which is characterized by high rainfall intensity, enhanced frequencies of rain occurrence and the increase presence of large raindrops when compared with the temperate climates. In this work, four different rainfall rate distribution models were compared to find the best fit over the tropical stations using data from our propagation measurement — Nigeria Environmental Climatic Observatory Program (NECOP) for radio wave propagation purposes.

Various associations between radar reflectivity (Z) and rainfall rate (R), identified as Z-R relationships have been derived to facilitate the rainfall rate estimation by weather radar. Most of the previously proposed Z-R relationships were implied as too generalized and only applicable within the region that has identical climate characteristics or behavior. Based on such notion, the most accurate Z-R relationship applicable for Malaysian weather radar therefore needs to be investigated and identified. In this paper, two renowned models will be evaluated on how well they fit to Malaysian weather radar data. Preliminary comparisons between the previously proposed Z-R relationships using newly acquired radar data in Malaysia and ground-based rain gauge measurements are also presented. The use of inaccurate relationship can cause error in radar rainfall estimates. This might pose unacceptable risk for the aviation industry where accurate, dependable weather information deduced by radar system is expected at all times.

One year results of one minute rainfall rate measurement at Ota, Southwest, Nigeria (6° 42'N, 3° 14'E) from a wireless Davis Vantage Pro2 Weather Station is presented. The weather station was set at one minute integration time, and the rainfall rate data from the months of April 2012 to March 2013 have been analyzed. One minute rainfall rate at various percentages of time are needed for the modeling and prediction of rain attenuation at microwave frequencies for both terrestrial and earth space links. The measured one-minute rainfall rate events captured by the instrument for the past one year varies between 3 to 141 mm/h from 1% to 0.01% of time in an average year respectively. When the results were compared to the ITU_RP SG3 Digital Map from 1% to 0.01% (3.63 to 62.87 mm/h) the ITU-RP model underestimate rainfall rate at 0.01% exceedance by 55% and over estimate the rainfall rate at 1% exceedance by 3% respectively.

In this paper the theory of Copula functions is used for the modeling of joint exceedance probability of rain rate on two points and rain attenuation on two links. Joint statistics of rain rate and rain attenuation are employed in order to evaluate and design site diversity systems operating at frequencies above 10 GHz. Copula functions are used in order to couple the single marginal distributions of dependent variables. In this paper, four Copula functions are investigated for the modeling of joint exceedance probability of rain attenuation and rain rate for different sites and various site separation distances. It is found that the error performance of these statistics shows that they are appropriate for modeling the joint exceedance probability of rain attenuation. However, for small separation distances, it seems that other Copulas shall be used such as the Gumbel-Hoogard. Finally, some useful conclusions are drawn.

The Inverse Gaussian (IG) distribution is examined for modeling the rainfall rate and slant path and terrestrial link rain attenuation. The long-term statistics of rain rate and rain attenuation are modeled using the IG distribution. The method is validated using the recommendation of International Telecommunication Union (ITU) recommendation ITU-R. P. 837 and rain rate data from the ITU Study Group 3 database (DBSG3) database for the case of rain rate. For the modeling of rain attenuation, data which are derived from two databases of DBSG3, these of Earth-space links and line-of-sight terrestrial links are used for validating the model. The results are compared to the one using the lognormal distribution. It has been shown that IG distribution could be more appropriate for modeling rainfall rate and slant path and terrestrial link rain attenuation. Finally, some useful conclusions are derived and presented in this paper.

The study of rainfall rate integration time is important to designers of satellite communication systems. In most part of the world, long-term rain statistics are typically available for integration time of very long durations; even perhaps of one hour or more. The method and appropriate conversion of rainfall rate distribution from variable integration times to the equivalent 1-minute are indeed vital. This is due to the fact that established prediction methods for estimating the rain induced attenuation on satellite-Earth links utilize the 1-minute rainfall rate data.

In this paper, we propose a novel remote sensing method that is adequate for rainfall rate measurements in real time by means of tomographic processing applied to power attenuation measurements made across the microwave links defined by radio base station networks for mobile communication systems. A description of the tomographic algorithms we developed is presented together with some simulation results. These concern rainfall rate estimation applying such algorithms to the current radio base station arrangement over the city of Florence, Italy, while the rainfall field is simulated through weather radar data.

In this paper, the cumulative distributions of rainfall rate for 4 sites in Brazil are fitted with a mixture of 2 Weibull distributions, in an attempt to account for the joint contributions of stratiform and convective rainfall. Results, which will be presented and discussed — were considered to be very good.

This paper describes the measurement of rainfall rate at King Mongkut's Institute of Technology Ladkrabang (KMITL), Bangkok, Thailand, by using satellite signal from Thaicom5. Three years measurement of rainfall rate are presented. The experimental results indicate that the measured rainfall rate are 90mm/hr in 2005, 94 mm/hr in 2006 and 102 mm/hr in 2007. Moreover, we have developed new modify prediction model of rain attenuation by ITU-R rain attenuation model. The model provides for prediction of annual and for expected year to year variations. This model applied to collecte data compared with ITU-R model. From the results of prediction model at KMITL, we found that the highest rainfall rate 102 mm/hr in 2007 cause to signal attenuate 14.34 dB.

A semi-empirical method for the prediction of rain attenuation in terrestrial links is presented in this paper. The proposed method is simple to apply and uses the concept of an effective rainfall rate and the full rainfall rate cumulative probability distribution to predict the attenuation distribution. Test results indicate that the proposed method provides significant improvement over the current ITU-R method and other methods available in the literature.

In this paper, the statistical distribution of the rainfall rate for tropical regions is investigated based on comparisons of measured data with the rain rates obtained from calculations using the ITU-R rain maps. The rain rate distributions are compared with an empirical expression for the effective rainfall rate obtained from the cumulative distribution of measured signal attenuation in converging links with different path lengths, spatial orientations and operation frequencies. Also, a semi- empirical method for the prediction of rain attenuation in terrestrial links is presented. The proposed method is simple to apply and uses the concept of an effective rainfall and the full rainfall rate cumulative probability distribution to predict the attenuation distribution.