Spheroidal Approximation Research Articles

Invalid spheroidal geopotential approximation and non-decomposable centrifugal acceleration from gravity – Reply to: Comments on “Horizontal gravity disturbance vector in atmospheric dynamics” by Chang, Wolfe, Stewart, McWilliams

Chang, Wolfe, Stewart, and McWilliams commented on my recent work regarding the horizontal gravity disturbance vector in atmospheric and oceanic dynamics. Their comments are incorrect. They ignored the horizontal pressure gradient error, claimed the validity of the spheroidal geopotential approximation subjectively based only on small metric error, and decomposed gravity into gravitational and centrifugal accelerations, which should never have been done. Here, I explain further why the spheroidal geopotential approximation is invalid and why gravity cannot be decomposed into gravitational and centrifugal accelerations in atmospheric and oceanic dynamics. Physically, the horizontal gravity disturbance vector vanishes in the horizontal momentum equation using the true gravity gt in the true geopotential coordinates but does occur in the horizontal momentum equation using the true gravity gt in the spheroidal geopotential coordinates due to the horizontal pressure gradient error in the coordinate transformation. The error of horizontal pressure gradient force in transforming true geopotential to spheroidal geopotential coordinates equals to the horizontal gravity disturbance vector. The spheroidal geopotential approximation claimed by Chang, Wolfe, Stewart, and McWilliams is invalid.

Mapping the morphological identifiers of distinct conformations via the protein translocation current in nanopores

Conformational changes of proteins play a vital role in implementing their functions and revealing the underlying mechanisms in various biological processes. It is still challenging to monitor protein conformations with temporal fingerprints of current-resistance pulses in the nanopore technique. Here the low-resolution morphologies of different conformations of a typical integrin, αxβ2, were estimated via relative blockade currents simulated from all-atom molecular dynamics (MD). Distinct conformational states of αxβ2 were directly explained by the volume and shape identifiers. Protein modulation in ionic current was analyzed from the conductivity distribution inside the protein-blocked nanopore. Combining a discrete model with spheroidal approximation, a MD-based approach was developed to theoretically predict the volume and shape of the nanopore for sensing αxβ2. This method was also applicable in specifying morphological identifiers of six other proteins, and the theoretical predictions are in good agreement with the experimental measurements. These results potentiated the validity of this method for the conformational identification of proteins in nanopores.

Magnetic (electric) drop deformation in uniform external fields: Volume averaged methods and formation of static and dynamic conical tips

Analytical relationships describing droplet deformation in external magnetic (electric) fields rely on spheroidal and ellipsoidal shape approximations. We show that the ellipsoidal shape approximations that assume a uniform internal magnetic field are only valid for small deformations (aspect ratio a/b ≈ 4). For large droplet deformations, the non-uniformity in the field within the droplet becomes substantial, rendering such approximations to be invalid. To overcome the limitations of ellipsoidal theory, we perform numerical simulations to determine volume averaged demagnetization factor and fields. Based on the numerical simulations, we propose semi-analytical relationships to describe small and large deformations for magnetic droplets using volume averaged methods. We test and validate our results with the existing experimental results and find an excellent agreement between our model and experimental studies. We extend our analysis and investigate static and dynamic droplets with conical tips. We show that droplets with conical tips could be defined solely by the characteristic half cone angle. We analyze unstable droplets with extremely high susceptibility χ → ∞ and find that conical tips with a half cone angle of θc ≈ 30° and an aspect ratio of ≈3.7 are formed prior to breakup, in agreement with the prior experimental studies of charged electric droplet breakup. We show that the volume averaged methods derived for droplets with finite tip curvature are also valid and in good agreement with the computational and previous experimental studies of magnetic droplets with conical tips.

Computational fluid dynamic simulations of thermochemical conversion of pulverized biomass in a dilute flow using spheroidal approximation

A drag force model for spheroids, referred as the spheroid model, was implemented in OpenFOAM, in order to better predict the thermochemical conversion of pulverized biomass. Our previous work has found that the spheroid model predicts more dispersed results in terms of particle velocities and local concentrations comparing to other conventional particle models under non-reactive conditions. This work takes the spheroid model one step further, by validating against experiments performed under reactive conditions with a newly implemented heat transfer model for spheroids as well as updated devolatilization kinetic parameters. In addition, simulations were conducted in a configuration similar to a pilot-scale entrained flow gasifier for more realistic scenarios. Particle mass and axial velocity development were compared accordingly using four different modelling approaches with increasing complexity. When compared with models of spheroidal shape assumptions, the sphere and simplified non-sphere model predict 61% and 43% longer residence times, respectively. The combination of the spheroid shape assumption with the heat transfer model for spheroids tends to promote drying and devolatilization. On the other hand, the traditional spherical approach leads to longer particle residence times. These opposing effects are believed to be a major contributing factor to the fact that no significant differences among modelling approaches were found in terms of syngas production at the outlet. Furthermore, particle orientation information was reported in both experiments and simulations under reactive conditions. Its dependency on gas velocity gradient under reactive conditions is similar to what was reported under non-reactive conditions.

Spheroidal approximation for finite-amplitude highly viscous axisymmetric drop/bubble free shape relaxation.

A common simplification used in different physical contexts by both experimentalists and theoreticians when dealing with essentially non-spherical drops is treating them as ellipsoids or, in the axisymmetric case, spheroids. In the present theoretical study, we are concerned with such a spheroidal approximation for free viscous shape relaxation of strongly deformed axisymmetric drops towards a sphere. A general case of a drop in an immiscible fluid medium is considered, which includes the particular cases of high and low inside-to-outside viscosity ratios (e.g., liquid drops in air and bubbles in liquid, respectively). The analysis involves solving for the accompanying Stokes (creeping) flow inside and outside a spheroid of an evolving aspect ratio. Here this is accomplished by an analytical solution in the form of infinite series whose coefficients are evaluated numerically. The study aims at the aspect ratios up to about 3 at most in both the oblate and prolate domains. The inconsistency of the spheroidal approximation and the associated non-spheroidal tendencies are quantified from within the approach. The spheroidal approach turns out to work remarkably well for the relaxation of drops of relatively very low viscosity (e.g., bubbles). It is somewhat less accurate for drops in air. A semi-heuristic result encountered in the literature, according to which the difference of the squares of the two axes keeps following the near-spherical linear evolution law even for appreciable deformations, is put into context and verified against the present results.

Comparisons of Electromagnetic Scattering Properties of Real Hailstones and Spheroids

AbstractSevere (>2.5 cm) hail causes >$5 billion in damage annually in the United States. However, radar sizing of hail remains challenging. Typically, spheroids are used to represent hailstones in radar forward operators and to inform radar hail-sizing algorithms. However, natural hailstones can have irregular shapes and lobes; these details significantly influence the hailstone’s scattering properties. The high-resolution 3D structure of real hailstones was obtained using a laser scanner for hail collected during the 2016–17 Insurance Institute for Business and Home Safety (IBHS) Hail Field Study. Plaster casts of several record hailstones (e.g., Vivian, South Dakota, 2010) were also scanned. The S-band scattering properties of these hailstones were calculated with the discrete dipole approximation (DDA). For comparison, scattering properties of spheroidal approximations of each hailstone (with identical maximum and minimum dimensions and mass) were calculated with the T matrix. The polarimetric radar variables have errors when using spheroids, even for small hail. Spheroids generally have smaller variations in the polarimetric variables than the real hailstones. This increased variability is one reason why the correlation coefficienttends to be lower in observations than in forward-simulated cases using spheroids. Backscatter differential phaseδalso is found to have large variance, particularly for large hailstones. Irregular hailstones with a thin liquid layer produce enhanced and more variable values for reflectivity factor at horizontal polarizationZHH, differential reflectivityZDR, specific differential phaseKDP, linear depolarization ratio (LDR), andδcompared with dry hailstones;is also significantly reduced.

Eulerian-Lagrangian simulation of pulverized biomass jet using spheroidal particle approximation

Pulverized biomass has great potential to replace coal in many industrial systems such as suspension-firing furnaces and entrained-flow gasifiers. The shape of pulverized biomass deviates significantly from the quasi-spherical coal particle, however, it is common to simulate pulverized biomass particles as spheres as most biomass models are developed based on coal models. With the aim of obtaining a more realistic simulation of pulverized biomass, this work extends the treatment of pulverized biomass to spheroids. A spheroid model that accounts for spheroidal particle drag force and torque was implemented into an Eulerian-Lagrange computational fluid dynamic solver. Comprehensive verifications and validations were performed by comparing with experiments and direct numerical simulations. Furthermore, non-reactive simulations of a lab-scale entrained flow gasifier were carried out using a conventional spherical particle model, a simplified non-sphere model, and the implemented detailed spheroidal particle model. By studying the simulation results of particle and fluid velocities in axial, radial and tangential directions, differences were observed when comparing the sphere model, the simplified non-sphere model, and the spheroid model. The spheroid model shows that particle orientation, which is ignored in the sphere model and the simplified non-sphere model, plays a role in the behavior of the particle dynamics. It was also found that, under such conditions, the spheroid model, compared to the sphere model, yields a more dispersed distribution regarding the particle residence time and local concentration. These non-reactive simulation results imply that shortcomings may exist in the common practice of simulating conversion of pulverized biomass in which the sphere model or the simplified non-sphere model is applied.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Gravitational waves and core-collapse supernovae

A mechanism of formation of gravitational waves in the Universe is considered for a nonspherical collapse of matter. Nonspherical collapse results are presented for a uniform spheroid of dust and a finite-entropy spheroid. Numerical simulation results on core-collapse supernova explosions are presented for the neutrino and magneto-rotational models. These results are used to estimate the dimensionless amplitude of the gravitational wave with a frequency ν ~ 1300 Hz, radiated during the collapse of the rotating core of a pre-supernova with a mass of 1.2 M⊙ (calculated by the authors in 2D). This estimate agrees well with many other calculations (presented in this paper) that have been done in 2D and 3D settings and which rely on more exact and sophisticated calculations of the gravitational wave amplitude. The formation of the large-scale structure of the Universe in the Zel’dovich pancake model involves the emission of very long-wavelength gravitational waves. The average amplitude of these waves is calculated from the simulation, in the uniform spheroid approximation, of the nonspherical collapse of noncollisional dust matter, which imitates dark matter. It is noted that a gravitational wave radiated during a core-collapse supernova explosion in our Galaxy has a sufficient amplitude to be detected by existing gravitational wave telescopes.

Comparison between acoustic measurements of brass instruments and one-dimensional models with curved wavefronts and transformed axial coordinates.

A progressive spherical or spheroidal wavefront approximation has previously been found to be a necessary step for a more accurate application of Webster's wave equation to rapidly flaring horns. This leads to a necessary transformation of the horn area function, from the usual flat cross-sectional area in terms of the axial coordinate, into a curved cap-like wavefront area as a function of either the axial coordinate, the arc-length coordinate along the horn profile, the leading curved wavefront coordinate, or still other possible longitudinal coordinates. In this article, horn functions, and related frequency potential functions are calculated from the measured horn profiles of a trombone and a trumpet for several of the above parameterizations. From them, cutoff frequencies and effective lengths are determined. A comparison is drawn between theoretical results using different parameterizations, results calculated via transfer-matrix models, and experimental measurements of the acoustical input impedance and reflection function of both instruments. Results indicate that one-dimensional models accurately predict the effective lengths, and consequently the fundamental resonance frequency of the instruments within ±25 cents, but fail noticeably in predicting cutoff frequencies, leading to what is probably an inaccurate representation of perceived timbre.

Spheroidal and ellipsoidal harmonic expansions of the gravitational potential of small Solar System bodies. Case study: Comet 67P/Churyumov‐Gerasimenko

AbstractGravitational features are a fundamental source of information to learn more about the interior structure and composition of planets, moons, asteroids, and comets. Gravitational field modeling typically approximates the target body with a sphere, leading to a representation in spherical harmonics. However, small celestial bodies are often irregular in shape and hence poorly approximated by a sphere. A much better suited geometrical fit is achieved by a triaxial ellipsoid. This is also mirrored in the fact that the associated harmonic expansion (ellipsoidal harmonics) shows a significantly better convergence behavior as opposed to spherical harmonics. Unfortunately, complex mathematics and numerical problems (arithmetic overflow) so far severely limited the applicability of ellipsoidal harmonics. In this paper, we present a method that allows expanding ellipsoidal harmonics to a considerably higher degree compared to existing techniques. We apply this novel approach to model the gravitational field of comet 67P, the final target of the Rosetta mission. The comparison of results based on the ellipsoidal parameterization with those based on the spheroidal and spherical approximations reveals that the latter is clearly inferior; the spheroidal solution, on the other hand, is virtually just as accurate as the ellipsoidal one. Finally, in order to generalize our findings, we assess the gravitational field modeling performance for some 400 small bodies in the Solar System. From this investigation we generally conclude that the spheroidal representation is an attractive alternative to the complex ellipsoidal parameterization, on the one hand, and the inadequate spherical representation, on the other hand.

Rapid and Accurate MRI Segmentation of Peritumoral Brain Edema in Meningiomas.

The extent of peritumoral brain edema (PTBE) in meningiomas commonly affects the clinical outcome. Despite its importance, edema volume is usually highly inaccurately approximated to a spheroid shape. We tested the accuracy and the reproducibility of semiautomatic lesion management software for the analysis of PTBE in a homogeneous case series of surgically confirmed intracranial meningiomas. PTBE volume was calculated on magnetic resonance images in 50 patients with intracranial meningiomas using commercial lesion management software (Vue PACS Livewire, Carestream, Rochester, NY, USA). Inter and intraobserver agreement evaluation and a comparison between manual volume calculation, the semiautomatic software and spheroid approximation were performed in 22 randomly selected patients. The calculation of edema volume was possible in all cases irrespective of the extent of the signal changes. The median time for each calculation was 3min. Interobserver and intraobserver agreement confirmed the reproducibility of the method. Comparison with standard (fully manual) calculation confirmed the accuracy of this software. Our study showed a high level of reproducibility of this semiautomatic computational method for peritumoral brain edema. It is rapid and easy to use after relatively short training and is suitable for implementation in clinical practice.

Role of spheroidal particles in closure studies for aerosol microphysical–optical properties

A study has been carried out to assess the discrepancies between computed and observed aerosol scattering and backscattering properties in the atmosphere. The goals were: (i) to analyse the uncertainty associated with computed optical properties when spherical and spheroidal approximations are used, and (ii) to estimate nephelometry errors due to angular truncation and non‐Lambertian illumination of the light source in terms of size range, particle shape and aerosol chemical compounds. Mie and T‐matrix theories were used for computing light optical properties for spherical and spheroidal particles, respectively, from observed particle size distributions. The scattering coefficient of the fine mode was not much influenced by the particle shape. However, computed backscattering values underestimated the observed values by ∼15%. For the coarse mode, the spheroidal approximation yielded better results than that for spherical particles, especially for backscattering properties. Even after applying the spheroidal approximation, computed scattering and backscattering values within the coarse mode underestimated the observed values by ∼49% and ∼11%, respectively. The angular correction most widely used to correct the nephelometer data was discussed to explore its uncertainty. In the case of the scattering properties within the coarse mode, the change of the computed optical parameter is ∼+8% and for the scattering and backscattering values within the fine mode it is lower than ∼±4% for spherical and spheroidal particles. Additionally, if the spheroidal particles are used to evaluate the aerosol optical properties, the correction must be reconsidered with the aim of reducing the uncertainty found for scattering within the coarse mode. This is recommended for sites with desert dust influence; then the deviation of the computed scattering can be up to 13%.

Analytical mean Green operators/Eshelby tensors for patterns of coaxial finite long or flat cylinders in isotropic matrices

Recently, an analytical solution has been provided for mean and axial Green operators (GO) of circular cylindrical inclusions with finite length in 3D isotropic (elastic-like and dielectric-like) materials, from long rods to truly penny-shaped ones. This result provides a situation for examining the commonly used “shape spheroidal approximation” of same aspect ratio as well as possibly more appropriate alternatives. For cases when such a spheroidal approximation would remain needed, we propose and compare an “operator spheroidal approximation” in terms of best matching GO, which is exactly operator-identical for dielectric-like properties and nearly identical for elastic-like ones. Next, a simple analytical solution is explicated for the mean isotropic GO of all patterns of coaxial circular long or flat cylinders with same radii, obtained from solving the coaxial cylinder pair interaction problem. These patterns can be seen as either fragmented cylinders or as cylinder alignments. The obtained GO solution form is further shown to formally hold for similar patterns of domains having more general shapes. The established general property of such patterns is that the interaction part of their mean GO can be expressed as a linear combination of the mean GO of all the pattern sub-domains. The mean GO solution for one such pattern is further proved to be valid as well for the domains – of the double inclusion type – obtained in connecting the pattern elements by their outer envelop of zero thickness, thanks to the GO blindness to connectivity differences. This GO equivalency is finally used to define a global operator spheroidal approximation in terms of best matching GO for any such coaxial cylinder pattern. Effective properties for an isotropic matrix reinforced by congruent cylinders or patterns are estimated within a mean field approximation context.

Characterization of Dust Particles’ 3D Shape and Roughness with Nanometer Resolution

Mineral dust particles in the atmosphere are often aspherical and their shape is important for a multitude of processes. Yet, measurements of the true shape in three dimensions are rare, even in a laboratory setting. Here, we employ atomic force microscopy to determine the 3D shape and surface roughness for two dusts commonly used in laboratory experiments, Arizona test dust (ATD) and kaolinite. Our major finding is that both are thin and remarkably smooth. An oblate spheroidal description is an excellent fit to these data. We use correlation analysis to further examine the surface properties of the dusts and find essentially no features at horizontal spatial scales between ∼10 and 100 nm. This surprising result is supported by the agreement between our specific surface area and BET surface area measurements. The thin, smooth, spheroidal approximation has many implications for physical processes in the atmosphere, including dust transport and radiative transfer.Copyright 2015 American Association for Aero...

Consistent quasi‐shallow models of the global atmosphere in non‐spherical geopotential coordinates with complete Coriolis force

A pair of dynamically consistent quasi‐shallow equation sets has recently been developed for global spherical atmospheres and oceans in spherical polar coordinates, using the standard spherical geopotential approximation. This pair is of intermediate complexity between two standard known pairs (one shallow, one deep). A surprising feature of this new pair is that the fluid is assumed to be of essentially shallow depth, yet the Coriolis force is completely represented. This is in contradistinction to the traditional shallow pair, where the Coriolis force is incompletely represented in order to achieve dynamical consistency.However, the Earth is better represented by a spheroid than by a sphere. It is shown herein that the aforementioned work can be generalised by making the weaker spheroidal geopotential approximation to obtain an analogous pair of quasi‐shallow equation sets using axisymmetric curvilinear orthogonal coordinates. This pair is derived in two different, but complementary, ways: via the traditional Eulerian approach, and via Hamilton's principle of least action.

Mean and axial green and Eshelby tensors for an inclusion with finite cylindrical 3D shape

Inclusions with the shape of a finite cylinder are generally approximated by a spheroid of same aspect ratio in order to take benefit of the simple and often analytical form of the Eshelby tensor for ellipsoids. Although mathematically advantageous, such an approximation is worse than considering the mean tensor related to the true inclusion shape. Using the Radon transform method, we give an exact formal expression of the mean shape function for a finite cylinder of general aspect ratio in any media and of the related mean Green and Eshelby tensors in isotropic elastic media, a 3D case which to the author knowledge has no reported solution in the literature so far. Thanks to this mean shape function we provide analytical forms for the fundamental integrals to compare with those of the spheroidal approximation. Noticeable differences show up which are discussed in terms of best spheroidal approximation. Since these tensors, as their fundamental integrals, are not uniform in non ellipsoidal inclusions, we also provide a simple exact solution for the fundamental integrals at any point of the finite fibre axis, so allowing analytical check of property variations along a long cylinder, what is not possible in the ellipsoidal approximation context. Case examinations and comparisons will be the purpose of a forthcoming paper.

Spheroidal and spherical geopotential approximations

It is customary in atmospheric modelling to approximate the equi‐geopotential surfaces of apparent gravity as spheres, and to use spherical polar coordinates to represent the global atmosphere. However Earth's mean surface is more accurately approximated by a spheroid of revolution than by a sphere, and therefore the geopotential surfaces are better represented as spheroidal surfaces than spherical ones. Several authors have considered how to develop a spheroidal coordinate system. The keystone for this is a sufficiently accurate, yet simple and flexible, mathematical approximation of the geopotential for a spheroidal Earth. Geopotential approximation is a compromise between the extremes of being either too simple, with deficient representation of the essentials of the underlying physics, or too complicated, leading to overly complicated coordinate systems.A new spheroidal geopotential approximation is proposed herein. It is relatively simple, and analytically tractable, yet properly represents the underlying physics. Using this new approximation, a new, relatively simple, quasi‐orthogonal spheroidal coordinate system is developed. It is then straightforward to obtain the customary spherical geopotential approximation, with its associated use of spherical polar coordinates, as an asymptotic limit of this new formulation. This confirms a previous finding, obtained using a different quasi‐orthogonal coordinate system. The spheroidal geopotential approximation, and quasi‐orthogonal coordinate system, proposed herein are however much simpler, yet no less accurate. They thereby lead to a much simpler, more direct, yet equally rigorous, justification for the spherical geopotential approximation. Copyright © 2010 Royal Meteorological Society

Interfacial Susceptibilities in Nanoplasmonics via Inversion of Fresnel Coefficients

The reflection coefficients of a nanoparticle film are driven to a large extent by perpendicular and parallel interfacial susceptibilities that have the meaning of “dielectric thicknesses” which combine the actual geometry of the film and its dielectric properties. The direct determination of these parameters faces the long-standing issue of the derivation of complex optical constants from Fresnel coefficients via a unique spectroscopic measurement. The present work sets up an iterative algorithm based on inversion of the reflection coefficients recorded in the UV–visible range for two polarization states s and p and Kramers–Kronig (KK) analysis. To calculate the KK integrals over a limited energy window, the strategy was to complement measurements by spectra calculated in the framework of the spheroidal dipole approximation. The algorithm has been successfully tested on synthetic data of differential reflectivity for supported truncated spheres. These were chosen to span different dielectric behaviors, involving (a) for the particles, metals whose optical response is dominated by plasmonic excitations with a noticeable Drude behavior (Ag and Au) and (b) for the substrate, either nonabsorbing wide bandgap (alumina) or semiconducting (zincite and titania) oxides. Unlike the thin plate model, the approach was proven to apply to “dielectric thicknesses” of several tens of nanometres in cases in which, even for geometric sizes of the order of the nanometer, the classical long-wavelength dielectric approximation fails because of strong plasmon resonances. Therefore, the disentanglement of dielectric behaviors along the parallel and perpendicular directions simplifies the understanding on the interface polarization process by removing substrate contribution. The present work that deals with plasmonics in nanoparticles can be easily generalized to different morphologies as well as to other combinations of Fresnel coefficients.

Modeling the microwave single‐scattering properties of aggregate snowflakes

AbstractA new snowflake aggregation model is developed to study single‐scattering properties of aggregate snowflakes. Snowflakes are generated by random aggregation of six‐bullet rosettes constrained by size‐density relationships derived from previous field observations. Due to random generation, aggregates may have the same size or mass, yet different morphology allowing for a study into how shape influences their scattering. Single‐scattering properties of the aggregates were investigated using discrete dipole approximation (DDA) at 10 frequencies. Results were compared to those of Mie theory for solid and soft spheres (density 10% that of solid ice) and to T‐matrix results for solid and soft spheroidal cases with aspect ratios of 0.8. Above size parameter 0.75, neither the solid nor the soft sphere and spheroidal approximations accurately represented the DDA results for aggregates. Asymmetry and the normalized scattering and backscattering cross sections of the aggregates fell between the soft and solid spherical and spheroidal approximations. This implies that evaluating snow scattering properties using realistic shapes, such as the aggregates created in this study, is of paramount importance. Concerning the morphology of the aggregate snowflakes created in this study, the dependence of their single‐scattering properties on each aggregate's detailed structure seemed of secondary importance. Using normalized standard deviation as a measure of relative uncertainty, it is found that the relative uncertainty in backscattering arising from the different morphologies caused by random aggregation is typically ~15% for individual particles and ~18% when integrated over size distributions. Relative uncertainties for other single‐scattering parameters are less.