(IJARAI) International Journal of Advanced Research in Artificial Intelligence, Vol. 2, No. 8, 2013 1 | Page www.ijarai.thesai.org Comparison between Rayleigh and Mie Scattering Assumptions for Z-R Relation and Rainfall Rate Estimation with TRMM/PR Data Kohei Arai Graduate School of Science and Engineering Saga University Saga City, Japan Abstract— Comparison of the rain rate estimated with the assumptions of Rayleighand Mie scattering is made. We analyzed the different relationships between the radar reflective factor and rain rate (so-called Z-R relationship) with both scattering models for different DSD (droplet size distribution) and rainfall types as the wavelength is 2.2cm which is in accord with the band of TRMM/PR. Meanwhile we introduced a discrete ordinates method to retrieve the Z-R relationship for Mie scattering assumption. It is found that the retrieval result can be represented as the sum of some simple Z-R relationships. By the analysis of the Z-R relationships estimated from Rayleigh and Mie scattering assumptions in the rain types, we found that the difference of Z-R relationships between Rayleigh and Mie scattering in the thunderstorm that represents the larger raindrop size is larger than that in the drizzle that represent the smaller raindrop size. Keywords-TRMM/PR; Precipitation; Z-R Relation; Rainfall Rate; Rayleigh scattering; Mie scattering; Droplet size distribution; RadarReflectivity Factor; I. INTRODUCTION Rainfall rate estimation of the Tropical Rainfall Measuring Mission: TRMM carries Precipitation Radar: PR is based on Z-R Relation (Z denotes radar reflectance factor, while R denotes rainfall rate)[1]. In order to estimate Z factor, attenuation due to rainfall and scattering due to raindrops is taken into account. Scattering due to raindrops depends on droplet size distribution under Rayleigh or Mie scattering assumptions. If the droplet size is greater than λ/8 (λdenotes wavelength), then Mie scattering assumption is appropriate while that is less thanλ/8, then Rayleigh scattering is assumed. Usually, Rayleigh scattering is assumed for rainfall rate estimation of TRMM/PR empirically [2], [3], [4]. It is reported that Mie scattering based Z factor estimation is better than that of Rayleigh scattering based estimation [5],[6]. Although these reports deal with influence due to different assumptions, Rayleigh and Mie scattering on Z factor estimation, there is no report which discuss the influence on rainfall rate estimation. The reason for this is difficulty on definition of Z-R Relation which is taken into account rainfall types [10], atmospheric conditions, topological effect, etc. There is a paper related to radar meteorology which deals with Z-R Relation based on empirical exponential law of 69 of different rainfall types, weather conditions, written by Battan [7]. Also difficulty is caused by complicated computations of backscattered reflection factor based on Mie scattering assumption. In this paper, rainfall rate estimation method based on Mie scattering is proposed together with some experimental background data for validation of the proposed method. Firstly, Z-R Relation based on Rayleigh and Mie scattering assumptions for three rainfall types, stratiform, drizzling, and thunder storm theoretically. Then both influences of the different scattering assumptions on Z-R Relation and rainfall rate estimations. There is mm order of droplet size according to Marshall and Palmer [9]. Wavelength of TRMM/PR is 22mm [8] so that Rayleigh limitation is situated at 2.75 mm. Therefore, it is better to adopt Mie scattering assumption for rainfall rate estimation for such large droplet size of rainfall. The following section describes theoretical background of rainfall estimation followed by experimental data for validation of the proposed method. Then conclusion is described together with some discussions. II. THEORETICAL BACKGROUND A. Estimation of Rayleigh and Mie Scattering Based Z-R Relations Averaged received reflectance can be represented as equation (1),     max 0 6 2 4 5 ) ( | | ) ( D vol b dD D N D K dD D N     (1) where K denotes abruption coefficient of water and ice crystal while D denotes droplet radius, N(D) denotes size distribution and σdenotes backscattering cross section. Radar reflection factor, Z, then is represented in equation (2), dD D N D Z D ) ( max 0 6   (2) On the other hand, Mie scattering based Z factor is expressed as equation (3), dD D N K Z D Mie Mie ) ( | | max 0 2 5 4      (3) Then rainfall rate can be written in equation (4), dD D D N D R D ) ( ) ( 10 * 6 max 0 3 4      (4)