A model that is less sensitive to errors in the extreme small and large drop diameters, the gamma model with central moments (3, 4 and 6), is proposed to model the rain drop size distribution of Singapore. This is because, the rain rate estimated using measured drop size distribution shows that the contributions of lower drop diameters are small as compared to the central drop diameters. This is expected since the sensitivity of the Joss distrometer degrades for small drop diameters. The lower drop diameters are therefore removed from the drop size data and the gamma model is redesigned for its moments. The effects of the removal of a particular rain drop size diameter on the specific rain attenuation (in dB) and the slant-path rain attenuation calculations with forward scattering coefficients for vertical polarization are analyzed at Ku-band, Ka-band and Q-band frequencies. It is concluded that the sensitivity of the Joss distrometer although affects the rain rate estimation at low rain rates, does not affect the slant path rain attenuation on microwave links. Therefore, the small drop diameters can be ignored completely for slant path rain attenuation calculations in the tropical region of Singapore.Index Terms-dead-time problem, drop diameters, gamma distributions, rain, rain attenuation, rain drop size distribution.

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Abstract-A Z-R relation is derived using a data set which consists of nine rain events selected from Singapore's drop size distribution. Rain events are separated into convective and stratiform types of rain using two methods: the Gamache-Houze method, a simple threshold technique, and the Atlas-Ulbrich method. In the Atlas-Ulbrich method, the variability of the rain integral parameters R, Z, N w , D 0 and gamma model parameter µ are used for the classification of rain into convective, stratiform and transition. Z-R relations are derived for each type of rain after classification. The changes in the coefficients of the Z-R relations for different rain events are plotted and analyzed. The Z-R relations of the different methods using the Singapore data are compared and analyzed. It is concluded that the coefficient A of the Z-R relation is higher for the convective stage followed by the stratiform and transition stages. The coefficient b values are higher for the transition stage followed by the stratiform and convective stages. Reflectivities are extracted from RADAR data above NTU site for rain events and compared with the reflectivities derived from the distrometer data. Rain rates retrieved from RADAR data using the proposed relations from Singapore's data set are compared with the distrometer rain rates. The RADAR extracted rain rates are found to be constantly lower than the distrometer derived rain rates but matches well.

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