The Effects of the Quasi-Liquid Layer on Ice Crystal Scattering

It is now well known that there exists a so-called Quasi-Liquid Layer (QLL) on the surface of ice, sometimes referred to as the premelting layer. The QQL consists of a thin water-like layer that exists at a temperature below the bulk melting point for a given pressure. The thickness of this QLL has been reported as being a few nanometers up to 100 nm and larger. It is thought that the QLL plays an important role in the slipperiness of ice, recrystallization and coarsening of ice grains, regelation (pressure-induced change in freezing), and electrification of thunderclouds. Recently Sazaki et al. (2011) showed direct visualization of the QLL via advanced optical microscopy, which can visualize the individual 0.37-nm-thick elementary steps on ice crystal surfaces. Their results show two distinctly different QLLs existing simultaneously. Work by Furukawa et al. (1987) show that the QLL can have a dielectric constant close to that of water. This then precipitates the question: can the QLL significantly affect the scattering characteristics of ice crystals in storms?

In order to investigate the QLL, a numerically rigorous full-wave computational electromagnetics technique based on the higher order method of moments (MoM) in the surface integral equation (SIE) formulation (Notaros, 2008) is used. According to this method, the external (between QLL and air) and internal (between ice and QLL) dielectric boundary surfaces of a QLL-coated ice crystal are modeled by generalized quadrilateral patches. Electric and magnetic equivalent surface current density vectors over the patches are approximated using hierarchical polynomial vector basis functions. The unknown current-distribution expansion coefficients in the polynomials are determined by a Galerkin-type direct solution to the surface integral equations (SIEs) based on boundary conditions for tangential components of total (incident plus scattered) electric and magnetic fields on all dielectric surfaces in particle models.

We model small ice columns and plates, such as columns and plates of hexagonal prism shapes, with various QLL thicknesses and calculate the polarimetric variables of specific differential phase, Kdp, and differential reflectivity, Zdr, on a “particle-by-particle” basis. We also use similar particle size distributions as in Hubbert et al. 2014 and calculate Kdp and Zdr for exponentially or otherwise distributed sizes of rigorously defined shapes by the MoM-SIE method. We address the question of how large must the QQL be to influence the scattering calculations. In addition, we perform comprehensive simulation study varying the dielectric constant and the axis ratio for the QLL-coated small ice columns and plates. The results are related to the potential effects on radar measurements in convective storms.