We propose and evaluate several improvements to the accuracy of the shooting and bouncing ray (SBR) method for ray-tracing (RT) electromagnetic modeling. We propose per-ray cone angle calculation, with the maximum separation angle between rays calculated for every individual ray, based on a set of local neighbors rather than a single global maximum. This allows the smallest theoretical error of the SBR method, adaptive ray spawning procedures, and a unique analysis of the effect of ray cone sizes on the accuracy of the method. For the conventional uniform angular distribution of rays, a less general and versatile but more expeditious approach, we derive an analytical expression for the optimal choice of cone angle to again maximize the overall accuracy of the SBR computation. Both approaches are derived using icosahedral ray spawning geometry and adjacent ray sets, which are also used for our double counted rays identification and removal technique that avoids complicated ray path searches. The results demonstrate that the advanced shooting and bouncing RT method--using both proposed ray cone generation approaches--can perform wireless propagation modeling of tunnel environments with the same accuracy as image theory RT, a dramatically less efficient but traditionally considerably more accurate solver.

This article proposes and presents a novel approach to the characterization of winter precipitation and modeling of radar observables through a synergistic use of advanced optical disdrometers for microphysical and geometrical measurements of ice and snow particles (in particular, a multi-angle snowflake camera—MASC), image processing methodology, advanced method-of-moments scattering computations, and state-of-the-art polarimetric radars. The article also describes the newly built and established MASCRAD (MASC + Radar) in-situ measurement site, under the umbrella of CSU-CHILL Radar, as well as the MASCRAD project and 2014/2015 winter campaign. We apply a visual hull method to reconstruct 3D shapes of ice particles based on high-resolution MASC images, and perform “particle-by-particle” scattering computations to obtain polarimetric radar observables. The article also presents and discusses selected illustrative observation data, results, and analyses for three cases with widely-differing meteorological settings that involve contrasting hydrometeor forms. Illustrative results of scattering calculations based on MASC images captured during these events, in comparison with radar data, as well as selected comparative studies of snow habits from MASC, 2D video-disdrometer, and CHILL radar data, are presented, along with the analysis of microphysical characteristics of particles. In the longer term, this work has potential to significantly improve the radar-based quantitative winter-precipitation estimation.

Taking advantage of the recent developments in machine learning, we propose an approach to automatic winter hydrometeor classification based on utilization of convolutional neural networks (CNNs). We describe the development, implementation, and evaluation of a method and tool for classification of snowflakes based on geometric characteristics and riming degree, respectively, obtained using CNNs from high-resolution images by a Multi-Angle Snowflake Camera (MASC). These networks are optimal for image classification of winter precipitation particles due to their high accuracy, computational efficiency, automatic feature extraction, and application versatility. They require little initial preparation, enable the use of smaller training sets through transfer learning techniques, come with large supporting communities and a wealth of resources available, and can be applied and operated by nonexperts. We illustrate both the ease of implementation and the usefulness of operation the CNN architecture offers as a tool for researchers and practitioners utilizing in situ optical observational devices. A training dataset containing 1450 MASC images is developed primarily from two storm events in December 2014 and February 2015 in Greeley, Colorado, by visual inspection of recognizable snowflake geometries. Defined geometric classes are aggregate, columnar crystal, planar crystal, small particle, and graupel. The CNN trained on this dataset achieves a mean accuracy of 93.4% and displays excellent generalization (ability to classify new data). In addition, a separate training dataset is developed by sorting snowflakes into three classes and showcasing distinct degrees of riming. The CNN riming degree estimator yields promising initial results but would benefit from larger training sets.

A visual hull method for reconstruction of realistic 3D shapes of snowflakes and other hydrometeors based on high-resolution photographs of particles in free fall from multiple views captured by a multiangle snowflake camera (MASC), or another similar instrument, is proposed and presented. The visual hull of an object is the maximal domain that gives the same silhouettes as the object from a certain set of viewpoints. From the measured fall speed and the particle shape reconstruction, the particle density and dielectric constant are estimated. This is the first time 3D shape reconstructions based on multiple high-resolution photographs of real (measured) snowflakes are performed. The results are clearly much better than any similar data in the literature. They demonstrate—in experiments involved in real snowstorm observations and those with simulated and fake 3D-printed snowflakes—sufficient silhouette information from the five cameras of the expanded MASC system and excellent performance of the implemented mechanical calibration and software self-calibration of the system. In addition to enabling realistic “particle by particle” computations of polarimetric radar measurables for winter precipitation, the visual hull 3D shape reconstructions of hydrometeors can be used for microphysical characteristics analyses, hydrometeor classification, and improvement of radar-based estimations of liquid-equivalent snow rates.

A new full-wave computational electromagnetics (CEM) approach to precipitation particle scattering analysis based primarily on a higher order method of moments (MoM) for solving surface integral equations (SIEs) is proposed, as an alternative and addition to the conventionally used tools in this area. This is a well-established CEM approach that has not been applied, evaluated, discussed, and compared with other approaches in the scattering analysis of precipitation particles so far. Several characteristic examples of scattering from precipitation particles of various shapes demonstrate the capabilities and potential of the presented numerical methodology, and discuss its advantages over both discrete dipole approximation (DDA) and T-matrix methods – in cases considered. In particular, it is shown that the higher order MoM-SIE approach is much faster, more accurate and robust than the DDA method, and much more general and versatile than the T-matrix method. In addition, the paper illustrates probl...

We present the application of adjoint analysis to 3-D finite-element method scattering problems for a posteriori error estimation and adaptive refinement. Adjoint-based methodologies, though underutilized in computational electromagnetics (CEM), enable significant improvements for both efficiency and accuracy. We first formulate the adjoint problem of the 3-D double-curl wave equation and the error estimates for the construction of novel accelerated adaptive refinement algorithms. We demonstrate adaptive error control for a customizable quantity of interest (QoI) resulting in targeted refinement and improved resource allocation through the application of automatic global and local error tolerance heuristics that accelerate the refinement process. The proposed refinement algorithms rapidly refine even extremely coarse initial discretizations to high accuracy, eliminating or substantially reducing manual intervention in the generation of computationally efficient and accurate simulations. Moreover, comparisons with analytical results validate our approach to accelerating automatic refinement to fine tolerances.