Modelling of Alpha and Beta for Rain Rate Prediction for Radio Propagation Systems

The effect of rain in the design of satellite and terrestrial microwave radio links is of interest to Engineers and Scientists. It is good to have a reliable design that guarantees high level of accuracy of the rain rate distribution from the lowest rain rate value to the highest. The present work proposes a model that expresses rain rate as a function of alpha and beta obtained at 0.01% of time. When tested, the results obtained with the measurement perform well for the stations considered at a rain rated between 5mm/h to 200 mm/h. Thus, and   , the empirical models that were obtained through them could be a useful tool for the radio design engineers for high rain rate areas. Index Terms — Radio propagation, Rain Rate, Model, Attenuation, cumulative Distribution.


I INTRODUCTION 1
Attenuation due to rainfall plays significant roles in the design of earth satellite radio link at frequencies above 10GHz [1]. The increasing demand for these frequencies for telecommunication and broadcasting satellite has arouse interest in the study of radio wave attention due to rainfall on earth-satellite radio paths. Most of the attenuation studies on earth-satellite path have been carried out in the temperature regions of the world [2].
The precipitation characteristics in the tropics differ appreciably from those of the temperate regions in that empirical relationship obtained in the temperate region may not be very suitable for the system design in the tropical region. Rain attenuation can be obtained directly from rain drop size distribution [2]. It is well known that rain rates and the consequent high rain attenuation in the tropics is arguably the greatest constraint to the usability of Ku and Ka bands in the tropics [3]. However, in this work, rainfall intensity R0.01 (mm/h) exceeded for 0.01% of the time in different in different locations are studied and a model that expresses rain rate as a function of alpha and beta was proposed. '' and '  'parameters at that percentage of time are very important tools for radio wave attenuation predictions both on line-ofsight and Earth-space links. Where P (R>r) is the probability that a rain rate, R exceeds a certain threshold r, "a" and "b" are parameter depending on rain intensity for which one variant is given by:

A. Rain Distribution Models
b=8.22R -0.584 [5] proposed a prediction procedure of rainfall rate cumulative distribution which is probability law leading to a more accurate prediction of rainfall rate cumulative distribution for all climates. The rain rate data obtained using a fast rain gauge with an integration time of 10 seconds at Ile-Ife in Nigeria from September 1979 to December 1981 were used to study the dependence of rain statistics on integration time. The power law between the rain of different integration given by [2] was: Where R is the rain rate T is the integration time, at which the rain rate is available, "a" and "b" are parameters for location. [2] obtained the lognormal model using method of moment regression over a range of 0.25mm/h to 150mm/h. The model is given by: With Ile-Ife data, [2] obtained the following relation NT=108R 0.363 (6) [3] - [5] carried out an inter-comparison of raindrop size distribution models presented by [8.9.10,11].
A. O. J. Abiodun, Lead University, Nigeria. G. A. Alagbe, Ladoke Akintola University of Technology, Nigeria. @ [5] - [7] used the raindrop spectra data obtained at Ile-Ife three years to investigate the dependence of drop size distribution on rain type and location. The conclusion was that the negative exponential model is adequate for drizzle whereas, the lognormal provides a better fit for the widespread shower and thunderstorm rains.

II METHODS
In view of the above, rain data were collected at the university of Ilorin over a period of two years 1 st January 2004 to 31 st December 2005 in the physics department metrological station and cumulative distribution of rain rate computed.

A. Rain Rate Model
From the graph displayed by rain rate computed against the percentage of time, the equation 9, below was obtained. Rr=   ) (%t (9) Where (%t) can be replaced using  which gives Rr =    [6], for each station,  and  were obtained as shown in Table 1.

C. Cumulative Distribution of Rainfall
The cumulative distribution of the rainfall intensity was evaluated using the following procedure: Yearly percentage of time expressed as: Where t is the total time during which rain rate R is exec ceded and T is the overall period of interest taken to be one year in evaluating the yearly cumulative distribution for a non-leap year the percentage of time for the first minute will be: For all the stations considered, there is a good agreement between the values obtained from the predicted equations and the values obtained from the measurement.  m is measurement value and  p is predicted value of  .           For all the stations considered in this work, the consistency test conducted holds well for the measurement of about 5mm/h to about 200mm/h. In addition to the behaviour of the parameters, and  , the empirical models that were obtained through them could be a useful tool for the radio design engineers for high rain rate areas.

EJECE, European Journal of Electrical Engineering and Computer Science
Vol. 4, No. 4, July 2020