Tree-based genetic programming approach to infer microphysical parameters of the DSDs from the polarization diversity measurements Tanvir Islam n , Miguel A. Rico-Ramirez,Dawei Han Department of Civil Engineering, University of Bristol, Bristol,UK a r t i c l e i n f o Article history: Received 3 March 2012 Received in revised form 23 May 2012 Accepted 24 May 2012 Available online 7 June 2012 Keywords: Drop size distribution (DSD) retrievals Polarimetric radar Dual polarization radar Disdrometer raindrop spectra Precipitation microphysics Shape and size parameters a b s t r a c t The use of polarization diversity measurements to infer the microphysical parametrization has remained an active goal in the radar remote sensing community. In view of this, the tree-based genetic programming (GP) as a novel approach has been presented for retrieving the governing microphysical parameters of a normalized gamma drop size distribution model D 0 (median drop diameter), N w (concentration parameter),and m(shape parameter)from the polarization diversity measurements.A large number of raindrop spectra acquired from a Joss–Waldvogel disdrometer has been utilized to develop the GP models, relating the microphysical parametersto the T-matrix scattering simulated polarization measurements. Several functional formulations retrieving the micro- physical parameters-D 0 [f(Z DR ), f(Z H , Z DR )], log 10 N w [f(Z H , D 0 ), f(Z H , Z DR , D 0 ), and m [f(Z DR , D 0 ), f(Z H , Z DR , D 0 )], where Z H represents reflectivity and Z DR represents differential reflectivity, have been investigated, and applied to a S-band polarimetric radar (CAMRA) for evaluation. It has been shown that the GP model retrieved microphysicalparameters from the polarization measurements are in a reasonable agreement with disdrometer observations. The calculated root mean squared errors ( RMSE) are noted as 0.23–0.25 mm for D 0 , 0.74–0.85 for log 10 N w (N w in mm 1 mm 3 ), and 3.30–3.36 for m . The GP model based microphysicalretrieval procedure is further compared with a physically based constrained gamma model for D 0 and log 10 N w estimates.The close agreement of the retrieval results between the GP and the constrained gamma models supports the suitability of the proposed genetic programming approach to infer microphysical parameterization. & 2012 Elsevier Ltd.All rights reserved. 1. Introduction The use of orthogonal polarized signals from polarimetric radar measurements propagating through the precipitation media can provide significant microphysicalinformation of raindrops, such as particle size, shape, orientation and thermodynamic state. This means, retrieval of microphysical parameters solely from the polarization diversity measurements such as reflectivity factors (Z H ), differential reflectivity (Z DR ), and specific differential phase shift (K DP ) can be possible. The studies of Seliga and Bringi(1976) and Seliga and Bringi (1978) were among the first that showed a procedure to retrieve microphysicalparameters from the orthogonal polarization mea- surements.At that time, in general,the microphysicaldrop size distributions (DSDs) were used to consider as exponential distribu- tions. The follow on studies, for example, in early eighties by Ulbrich (1983),confirm that the DSDs are better represented by gamma distribution. This gamma distribution is described by three governing parameters, N 0 as a concentration parameter, mas a shape parameter, and D as a slope parameter. Most recently,the gamma distribution has been advanced as a normalized gamma distribution with three governing parameters of N w , D 0 , and m representing the concentration parameter, median drop diameter, and shape parameter respectively (Bringi et al., 2003). Currently, it is a topic of interest in the remote sensing community to retrieve aforementioned governing gamma DSD parameters using polarization diversity measurements. Mainly, the reported works in the literature have dealt with ground based S-band (Brandes et al., 2004b; Bringi et al.,2002; Vivekanandan et al., 2004),C-band (Bringi et al., 2009; Gorgucciet al., 2001; Thurai et al.,2008),X-band (Anagnostou et al., 2008a; Gorgucci et al., 2008; Kim et al., 2010),and satellite based Ku–Ka band (Rose and Chandrasekar,2006) radar observations.At higher frequency,for example C-band and above,the path integrated attenuation hinders the successful microphysical retrievals from the polarization measurements unless the reflectivity and differ- ential reflectivity measurements are properly corrected for attenuation.In contrast, S-band has the advantage of having negligible path integrated attenuation and Mie scattering effects (Islam et al.,2012c; Testud et al., 2000). Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/cageo Computers & Geosciences 0098-3004/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cageo.2012.05.028 n Corresponding author. Tel.: þ44 1173315724; fax: þ44 1173315719. E-mail address: tanvir.islam@bristol.ac.uk (T. Islam). Computers & Geosciences 48 (2012) 20–30