3D Shape Reconstruction of Snowflakes from Multiple Images, Meshing, Dielectric Constant Estimation, Scattering Analysis, and Validation by Radar Measurements

A multi-angle snowflake camera (MASC), which simultaneously captures multiple different high-resolution views of a snowflake in free-fall, along with the snowflake's fallspeed, is used in conjunction with the visual hull geometrical method for reconstruction of three-dimensional (3D) shapes, to perform snowflake scattering analysis. For various winter snow events, the scattering analysis of these individual flakes is used to compute the radar observables Zh, Zdr, LDR, Kdp, and ρhv that are compared against the corresponding data collected above the site of the MASC by two state-of-the-art polarimetric weather radars, CSU-CHILL Radar and NCAR SPOL Radar.

This paper presents and discusses visual hull 3D shape reconstruction of snowflakes and ice particles using the high-resolution MASC photographs of a hydrometeor from multiple angles and the corresponding 2D silhouettes of the object. Results appear to be much more accurate than any other available snowflake shape reconstruction examples in literature and are thus indicative of a good potential of this approach. The paper also presents and discusses conversion of these shapes into meshes of quadrilateral patches suitable for electromagnetic scattering modeling and analysis, calculation of the scattering matrices to obtain realistic simulations of the radar observables, and validation by radar measurements.

The visual hull of an object can be interpreted as the maximal domain that gives the same silhouettes as the object from a set of viewpoints. The 3D reconstructed snowflakes are represented by surface meshes of flat triangular patches, which capture a large amount of detail about the shape of the free-falling snowflakes, representative of the flakes that the two radars are viewing. In order to improve the 3D reconstruction obtained from the visual hull method, two additional cameras were added to the MASC, “externally,” to provide additional views. They are on an elevated plane with respect to the original three, at about a 55-degree angle above horizon. All five cameras trigger simultaneously and collect images at a 2-Hz rate. We perform 5-camera software self-calibration of the MASC, to obtain a correction matrix that is then used as an input to the visual hull code to correct for a non-perfect mechanical calibration. Without this, the visual hull fails to create 3D reconstructions for many snowflakes. It also allows images with more than one snowflake per image to be used. In addition, we use a meshing software, ANSYS ICEM CFD, controlled by a TCL script, to convert the triangular mesh into a quadrilateral mesh, which is input to the scattering analysis code. Finally, we use the fall speed from the MASC and the horizontal cross-sectional projected area of the 3D reconstruction of the particle, along with state parameters measured at the MASC site, to estimate the particle mass (Böhm's method). From the mass and volume of the meshed flake, we estimate the density, and then the dielectric constant of each snowflake, based on a Maxwell-Garnet formula.

The process is almost completely automatized and streamlined from the handling of the MASC images, to the visual hull method and the creation of meshes that adequately represent features of the geometry, to the estimation of the dielectric constant, and finally the scattering analysis. This gives us a representative data set, of different particle types, to compare with CHILL and SPOL radar data.