Determination of Specific Rain Attenuation Using Different Total Cross Section Models for Southern Africa

20 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS Vol.105(1) March 2014 DETERMINATION OF SPECIFIC RAIN ATTENUATION USING DIFFERENT TOTAL CROSS SECTION MODELS FOR SOUTHERN AFRICA S.J. Malinga*, P.A. Owolawi** and T.J.O. Afullo*** * Dept. of Electrical Engineering, Mangosuthu University of Technology, P. O. Box 12363, Jacobs, Durban,4026, South Africa. E-mail: [email protected] ** Dept. of Electrical Engineering, Mangosuthu University of Technology, P. O. Box 12363, Jacobs, Durban,4026, South Africa. E-mail: [email protected] *** Discipline of Electrical, Electronic and Computer Engineering, University of KwaZulu-Natal, Durban, South Africa E-mail: [email protected] Abstract: In terrestrial and satellite line-of-sight links, radio waves propagating at Super High Frequency and Extremely High Frequency bands through rain undergo attenuation (absorption and scattering). In this paper, the specific attenuation due to rain is computed using different total cross section models, while the raindrop size distribution is characterised for different rain regimes in the frequency range between 1 and 100 GHz. The Method of Moments is used to model raindrop size distributions, while different extinction coefficients are used to compute the specific rain attenuation. Comparison of theoretical results of the existing models and the proposed models against experimental outcomes for horizontal and vertical polarizations at different rain rates are presented. Keywords: Method of moments, microwave attenuation, millimeter wave attenuation, rain attenuation, rainfall regimes, rain types, satellite communication, terrestrial communication, fade margin. 1. INTRODUCTION In order to account for the degree of rain attenuation or The advantages offered by Super High Frequency (SHF) rain fade in a link, two methods are often considered: the and Extremely High Frequency (EHF) bands such as direct method (which refers to direct measurements at the large bandwidth, small antenna size, and easy installation receiver using a spectrum analyzer), and the statistical or deployment have motivated the interest of researchers method (which involves rain rate and raindrop size to study various factors that prevent optimum utilization measurement). The rain rate and raindrop size of these bands. Factors such as cloud, hail, fog, snow, ice measurements allow for the estimation of rain attenuation crystals, and rain degrade terrestrial and satellite link in a cost-effective way as compared with the direct performance at these frequencies. Rain fade remains the method. Regional and global efforts have been made to dominant factor in signal fading over satellite and obtain suitable distribution functions and related terrestrial links, especially in the tropical and sub-tropical parameters for the raindrop size distribution (DSD). The regions like South Africa. In this paper, the focus is on early DSD models were based on exponential [5] signal attenuation due to absorption and scattering by distribution functions, which poorly represented the very rain. While other types of hydrometeors such as water small and very large raindrops. The other distribution vapour, snowfall, and hail are considered secondary functions that have been suggested are the Lognormal [2, deleterious factors to link design at these frequency 6], the Weibull [7, 8], and the gamma [9] distribution bands, attenuation due to rain is a fundamental quantity in functions. There are several ways of fitting measured the estimation of signal degradation in the presence of DSD data, of which the method of moments [10] and precipitation for terrestrial and satellite links. As maximum likelihood estimation [11] are the most presented in several articles, a simple power-law popularly used by many authors. While DSD relationship of specific rain attenuation as given in measurement campaigns have been reported over a equation (1) is widely used, and the values of the considerable period of time in West Africa [2, 12], less coefficient parameters k and are listed in the attention has been invested in this regard in Southern International Telecommunication Union Africa [13, 14]. Recommendation ITU-R P.838.3 [1]. One of the aims of this paper is to give a report on the (1) current DSD modelling for the South African region and its application using different extinction cross section Here R (mm/h) is the rain rate and k and are constants models. The resulting fitted DSD is integrated over the at a given frequency. It is evident from several scattering cross section to calculate the specific contributors [2, 3, 4] that k and vary with the raindrop attenuation due to rain. In order to estimate the total cross size distribution (DSD). It is observed as well that the sectional area of raindrops, the choice of rain shape is the rain DSD is location and climate dependent. key parameter. Morrison and Cross [15] fitted the drop Vol.105(1) March 2014 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 21 shape with a spheroidal model, using a least-squares 2. DISDROMETER DATA COLLECTION method. The contribution of Pruppacher and Pitter [16], presented theoretical results of raindrops at different For the purpose of this submission, two-year DSD data sizes, while Li et al. [17, 18] further simplified was collected using the Joss-Waldvogel RD-80 Pruppacher and Pitter’s model, with the expression: disdrometer (JWD) at an integration time of one minute. This equipment is placed at latitude 30 058 E and longitude 29 052 S atop the Electrical, Electronic, and Computer Engineering building, University of KwaZulu- Natal, at an altitude of 139.7 m above sea-level. It (2) measures raindrop diameters in the range of 0.3 mm to 5 mm in 20 different bins, with the accuracy of ±5%. The expression used to estimate the measured rain rate where, (mm/hr) by the equipment is presented in the JWD (3a) manual as [21]: (3b) (7) (3c) while the measured DSD, or N(D i), is given by [21]: (3d) (8) (3e) 2 Here a0 denotes the mean raindrop radius, theoretically Note that S = 5000 mm , T = 60 s, v(D i) is the terminal given as 0.25 mm to 3.00 mm with an incremental velocity, estimated using the Gunn and Kinzer approach, interval of 0.25 mm, and H( ) denotes the step function. and ni is the number of drops. With the nature of rain Equations (2) to (3) represent the spherical raindrop size distribution in Southern Africa, the rain rate is used to model. Another approach with a new formula was classify the raindrop size distribution models into four presented in reference [19] - in which case the scattered classes: electromagnetic fields were deemed due to spheroidal raindrops. Considering spheroidal raindrop scatterers, the Drizzle (R < 5mm/hr ) surface of the drops is described by: Widespread (5mm/hr R < 10 mm/hr) Shower (10 mm/hr R < 40 mm/hr) (4) Thunderstorm (R 40 mm/hr) The rain rate can be estimated from the modelled N(D i) where , and a and b represent the for each class of rain rate type, given by the expression: raindrop’s minor and major semi-axes respectively, and are measured in centimeters. In [19] Oguchi’s method (9) was used to obtain a and b from the mean drop size radius that was developed to determine the specific In the comparative studies of the measured N(D i) and rainfall attenuation. Oguchi [20] assumed that: modelled N(D ), the root mean square error (RMSE)% is i defined as: ; (5) The other method presented in [19] is that of Morrison and Cross [15], which assumes that: (10) ; (6) 3. THE METHOD OF MOMENTS The parameters obtained using the method of Morrison rd th th and Cross have shown reasonably consistent results when In this paper, the 3 , 4 , and 6 order moments are considering larger raindrops as opposed to that proposed employed to determine the three Lognormal DSD by Oguchi [20]. This paper thus uses the aforementioned parameters because of its simplicity and immediate total scattering cross section of Morrison and Cross [15], physical interpretation of the Lognormal parameters. The alongside the Pruppacher and Pitter model [16] as well as nth order moment is defined as: the Mie model, to compute the specific attenuation due to rain for Southern Africa. 22 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS Vol.105(1) March 2014 1000 approximated by x-th, y-th and z-th moments of the DSD where x, y, and z are non-integer. Then equation (11) is equivalent to: ) -3 y = 41.319x 0.625 (13) (m T N 10 My and Mz are similar to equation (13). Taking Lx to be Log NT the natural logarithm of Mx, the Lognormal DSD Power (NT) parameters are calculated as [10]: 100 40 60 80 100 120 (14a) Rain rate (mm/hr) (a) (14b) 1 (14c) Fig. 1 presents logarithmic scattergrams of Lognormal DSD parameters versus rain rate for the thunderstorm y = 0.063ln(x) + 0.298 rain type. These parameters are derived from equations 10 (13) and (14). For the other rain types such as drizzle, Log widespread and shower, Table 1 and expressions µ presented in equation (15) give details of Lognormal DSD parameters and their coefficients for the Southern African region as summarized in the expressions below: 0.1 40 50 60 70 80 90 100 110 120 130 Rain Rate(mm/hr) (15a) (15b) (b) 1 3.1 Application of Rainfall Regimes y = 0.022ln(x) + 0.013 It has been established that the raindrop size distribution varies considerably for different types of rainfall regimes or classes. These rainfall classes, as defined in section 2, 0.1 2 are: drizzle, widespread, shower and thunderstorm. The 10 corresponding parameters of their Lognormal Log distributions are shown in Table 1. A general distribution 2 model has often been used by many researchers. Log. ( 2) However, there is a notable difference in the specific 0.01 40 50 60 70 80 90 100 110 120 attenuation due to rain produced by the general model, Rain rate (mm/hr) hence the need to develop regime-specific rain attenuation models [22, 23].

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