An improved algorithm based on the self-consistent principle for rain attenuation correction of reflectivity Z H and differential reflectivity Z DR are presented for X-band radar. The proposed algorithm calculates the optimum coefficients for the relation between the specific attenuation coefficient and the specific differential phase, every 1 km along a slant range. The attenuation-corrected Z DR is calculated from reflectivity at horizontal polarization and from reflectivity at vertical polarization after attenuation correction. The improved rain attenuation correction algorithm is applied to the range-height indicator (RHI) scans as well as the plan position indicator (PPI) volume scan data observed by X-band wavelength (MP-X) radar, as operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) in Japan. The corrected Z H and Z DR values are in good agreement with those calculated from the drop size distribution (DSD) measured by disdrometers.The two governing parameters of a normalized gamma DSD, normalized number concentration N W , and drop median diameter D 0 are estimated from the corrected Z H and Z DR , and specific differential phase K DP values based on the ''constrained-gamma'' method. The method is applied to PPI and RHI data of a typhoon rainband to retrieve the three-dimensional distribution of DSD. The retrieved DSD parameters show reasonable agreement with disdrometer data. The present results demonstrate that high-quality correction and retrieval DSDs can be derived from X-band polarimetric radar data.

No abstract

We consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several sufficient optimality conditions under various (generalized) invexity assumptions and certain regularity conditions are presented. In addition, we introduce a Wolfetype dual and Mond-Weir-type dual and establish duality relations under various (generalized) invexity and regularity conditions.

No abstract

No abstract

No abstract

No abstract

No abstract