The Distribution of Atmospheric Ice Particle Shapes and Their Observations PDF Download

Author: Edwin Lee Dunnavan
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Languages : en
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Book Description
This dissertation develops methodological and mathematical techniques for describing the distribution of various ice particle geometries and their 2D observations. It is common for models and observations to integrate both types of distributions when estimating key microphysical properties related to growth and depletion of ice particles. However, much of what is known about the actual 3D ice particle shapes is derived from 2D images or projections of each particle. Ice particle orientations therefore can distort the observed 2D geometry in a way that obscures the underlying 3D structure. A major discovery of this dissertation is that various transformations of ice particle distributions and their projections are represented in closed-form as univariate and bivariate H-functions. The properties of H-functions are based heavily on the Mellin integral transform. The concepts, notations, and properties of these functions might seem foreign to many in the meteorology and atmospheric science community. Therefore, chapter 2 of this dissertation provides an overview of the relevant math that surrounds H-functions as well as their various properties. Chapter 3 develops an integral transform method for projecting distributions of ice particle habits (approximated as spheroids) onto a 2D plane. This projection process is geometrically analogous to how in situ observations capture ice particle shapes as well as how projected areas are used in microphysical fall speed calculations. Distribution transformations using mapping equations and numerical integration of projection kernels show that both truncation of size distributions and changes in Gaussian dispersion can alter the modality and shape of projection distributions. As a result, the projection process can more than triple the relative entropy between the spheroidal and projection distributions for commonly assumed model and orientation parameters. This shape uncertainty is maximized for distributions of highly eccentric particles and for particles like aggregates that are thought to fall with large canting-angle deviations. The integral transform methodology is used to propose an in situ approach for estimating model parameters that govern ice particle shape from distribution moments of observed in situ ellipse fit eccentricity or second eccentricity.Chapter 4 utilizes two separate datasets of best-fit ellipsoid estimates derived from Multi-Angle Snowflake Camera (MASC) observations to construct a bivariate beta distribution for capturing snow aggregate shapes. This mathematical model is used along with Monte Carlo simulated aggregates to study how combinations of monomer properties affect aggregate shape evolution. Plate aggregates of any aspect ratio produce a consistent ellipsoid shape evolution, whereas thin column aggregates evolve to become more spherical. However, thin column aggregates yield fractal dimensions much less than the often assumed value of 2.0. This discovery suggests that aggregates formed in cirrus clouds could exhibit significantly different physical properties than those formed in mixed-phase clouds. Simulated aggregate ellipsoid densities and fractal analogs of density (lacunarity) are much more variable depending on combinations of monomer size and shape. The inconsistent relationship between shape and density suggests that mass-dimensional prefactors should be rescaled in a more physical manner. Both simulations and observations prove aggregates are rarely oblate. These results therefore contradict much of the current literature on snow aggregate shapes, since many models and radar forward simulators assume homogeneous oblate spheroids. Chapter 5 investigates the effect of convolving particle property distributions when using the bivariate beta distribution from chapter 4. Idealized tests show that the number weighted mean fallspeed for ellipsoidal aggregates is more than 90% less than that of sphere/fractal aggregates, while mass-weighted fallspeeds for ellipsoid aggregates are approximately 60% of sphere/fractal aggregates. The distribution ranges produced by ellipsoidal aggregates is shown to be much more consistent with observed fall speed ranges than using a mass-dimensional relationship alone. This implies that current microphysics models systematically overestimate mass and number sedimentation fluxes but underestimate size sorting anywhere from 8% to 20%. Properties of the H-function are used to develop a spectral bulk modeling methodology that can utilize any number of distribution moments in the estimation of distribution parameters. The use of this spectral bulk microphysics methodology in numerical weather prediction models can therefore provide the computational simplicity of bulk microphysics models while still exhibiting the numerical complexity of bin microphysics models.