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A novel higher order finite-element technique based on generalized curvilinear hexahedra with hierarchical curl-conforming polynomial vector basis functions is proposed for microwave modeling. The finite elements are implemented for geometrical orders from 1 to 4 and field-approximation orders from 1 to 10 in the same Galerkin-type finite-element method and applied to eigenvalue analysis of arbitrary electromagnetic cavities. Individual curved hexahedra in the model can be as large as approximately 2 2 2 , which is 20 times the traditional low-order modeling discretization limit of 10 in each dimension. The examples show excellent flexibility and efficiency of the higher order (more precisely, low-to-high order) method at modeling of both field variation and geometrical curvature, and its excellent properties in the context of-refinement of solutions, for models with both flat and curved surfaces. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.

Analysis of drop size distributions (DSD) measured by collocated Meteorological Particle Spectrometer (MPS) and a third-generation, low-profile, 2D-video disdrometer (2DVD) are presented. Two events from two different regions (Greeley, Colorado, and Huntsville, Alabama) are analyzed. While the MPS, with its 50-μm resolution, enabled measurements of small drops, typically for drop diameters below about 1.1 mm, the 2DVD provided accurate measurements for drop diameters above 0.7 mm. Drop concentrations in the 0.7–1.1-mm overlap region were found to be in excellent agreement between the two instruments. Examination of the combined spectra clearly reveals a drizzle mode and a precipitation mode. The combined spectra were analyzed in terms of the DSD parameters, namely, the normalized intercept parameter NW, the mass-weighted mean diameter Dm, and the standard deviation of mass spectrum σM. The inclusion of small drops significantly affected the NW and the ratio σM/Dm toward higher values relative to using the 2DVD-based spectra alone. For each of the two events, polarimetric radar data were used to characterize the variation of radar-measured reflectivity Zh and differential reflectivity Zdr with Dm from the combined spectra. In the Greeley event, this variation at S band was well captured for small values of Dm (<0.5 mm) where measured Zdr tended to 0 dB but Zh showed a noticeable decrease with decreasing Dm. For the Huntsville event, an overpass of the Global Precipitation Measurement mission Core Observatory satellite enabled comparison of satellite-based dual-frequency radar retrievals of Dm with ground-based DSD measurements. Small differences were found between the satellite-based radar retrievals and disdrometers.

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