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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength

Rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles are calculated by the T-matrix method, as extended to randomly oriented scatterers. The computational scheme is described along with a newly developed convergence procedure that makes it possible to substantially reduce computer time and storage requirements. The elements of the Stokes scattering matrix for a power-law size distribution of randomly oriented moderately aspherical spheroids are shown to be much smoother than and differ substantially from those of equivalent monodisperse spheroids; averaging over orientations does not eliminate the necessity of averaging over particle sizes. The angular-scattering behavior of the ensembles of nonspherical particles is found to be significantly different from that of the equivalent polydisperse spheres.

Mishchenko, Michael I.↗
DOE OSTI2021

Consideration of Initial Cloud Droplet Size Distribution Shapes in Quantifying Different Entrainment-Mixing Mechanisms

Entrainment-mixing process significantly affects cloud micro/macrophysics and the evaluation of aerosol indirect effects. However, it remains an open question as to how to quantify entrainment-mixing mechanism for broad cloud droplet size distributions (CDSDs). Here, CDSDs with different spectral widths are used to initialize the Explicit Mixing Parcel Model to address this problem, and microphysical properties are compared for different CDSD widths. For relatively broad CDSDs, as the number concentration and liquid water content decrease, the volume-mean radius and mean radius increase, which is opposite to the scenario for relatively narrow CDSDs and the homogeneous/inhomogeneous conceptual model. For the relatively broad CDSDs, such relationships could be mistaken as inhomogeneous mixing with subsequent ascent in analysis of the conventional microphysical mixing diagram. This then causes traditional homogenous mixing degrees to be unrealistically negative and not applicable for relatively broad CDSDs. New measures are introduced to explicitly account for the effect of CDSD spectral shapes on quantifying entrainment-mixing mechanism. The new measures yield reasonable ranges of values that conform to the dynamical measures such as the Damköhler and transitional scale numbers, and their temporal variation can be explained physically. This study extends the measures of homogeneous mixing degrees from narrow to broad CDSDs, and sheds new light on the consideration of CDSD shapes in parameterizations of entrainment-mixing mechanism.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1992

Titan's aerosols. I - Laboratory investigations of shapes, size distributions, and aggregation of particles produced by UV photolysis of model Titan atmospheres

Experiments in which C2H2, C2H4, and HCN were photolyzed separately and as a mixture in UV light have been conducted in order to ascertain the physical properties of model Titan atmosphere aerosols. Aerosols formed from photolysis of C2H4 were physically similar to those formed from C2H2; protolysis of HCN rapidly generated particles that did not grow to sizes greater than 0.09 microns. While the formation of particles from C4H2 was observed within minutes, formation was slowed by a factor of 4 when C2H2 and HCN were added.

Scattergood, Thomas W.↗
DOE OSTI2022

Size-dependent shape distributions of platinum nanoparticles

Transmission electron microscopy revealed size-dependent shape distributions in platinum nanoparticles, which were consistent with trends observed by applying Boltzmann statistics to the energy computed with atomistic models.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Shape, size, and distribution of magnetic particles in Bjurbole chondrules

Chondrules from the Bjurbole chondritic meteorite (L4) exhibit saturation remanence magnetization (SIRM) values which vary over three orders of magnitude. REM values (Natural Remanence Magnetization/SIRM) for Allende (C3V) and Chainpur (LL3) are less than 0.01 but in Bjurbole some chondrules were found to have REM values greater than 0.1 with several greater than 0.2. REM values greater than 0.1 are abnormal and cannot be acquired during weak field cooling. If exposure to a strong field (whatever the source) during the chondrules' history is responsible for the high REM values, was such history associated with a different processing which might have resulted in different shape, size, and distribution of metal particles compared to chondrules having REM values of less than 0.01? Furthermore, magnetic hysteresis results show a broad range of magnetic hardness and other intrinsic magnetic properties. These features must be related to (1) size and amount of metal; and (2) properties of, and amount of, tetrataenite in the chondrules (all chondrules thus far subjected to thermomagnetic analysis show the presence of tetrataenite). A scanning electron microscopy (SEM) study is underway to determine the relationship between the shape, size, and distribution of metal particles within individual chondrules and the magnetic properties of these chondrules. Results from the SEM study in conjunction with magnetic property data may also help to discern effects from possible lightning strikes in the nebula prior to incorporation of the chondrules into the parent body.

Nava, David F.↗
NASA NTRS2010

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.

Lane, John E.↗
NASA NTRSDate not supplied

Characterizing Detailed Grain Shape and Size Distribution Properties of Lunar Regolith

Introduction: As the nation prepares to return to the Moon, there is an increasing need for testing tools, instruments, and equipment in simulated environments on Earth to ensure successful operations during lunar missions. Regolith will affect all aspects of future lunar missions, from plume interactions during landing to space suit and tool design [1]. Because of this, it is important to understand the grain shape and size properties of lunar regolith and how those influence regolith behavior in order to prepare for these missions. This knowledge is also vital to create more accurate lunar regolith simulants for testing equipment in a lunar environment. While particle size analyses have been performed on most Apollo soils using simple sieving, shape has only been crudely addressed [2]. This work analyzes 4 lunar regolith samples to provide a better understanding of these size and shape parameters and will provide a more accurate baseline of data to create high-fidelity lunar regolith simulants. Methods: New technologies exist today that are capable of measuring size and shape simultaneously for hundreds of thousands of particles in a single measurement. We conducted a rigorous analysis of the particle size distribution (PSD) as well as the size-dependent 2D and 3D shape parameters of lunar regolith samples of different compositions and maturity levels. This analysis was done using a Microtrac SYNC which provides a unique combination of tri-laser diffraction and Dynamic Image Analysis (DIA). Sample Selection. Four regolith samples were selected for analysis based on maturity level and lunar terrain type: • 10084 – Mature high-Ti mare regolith • 15601 – Immature low-Ti mare regolith • 64501 – Mature highland regolith • 67461 – Immature highland regolith Sample Analysis. After receiving the samples, each sample was imaged with an optical microscope (Figure 1). To obtain 2D and 3D particle size and shape, 0.1 g of each sample was then added to the SYNC for analysis, which outputs more than 30 size and shape parameters for each individual grain as well as the complete size distribution from 0.01-2000 μm by blending laser diffraction and DIA together. For the 0.1 g sample masses requested, ~100,000 grains per sample were captured by DIA. Results: From the PSD analysis, it can be seen that the average particle size of 10084 is ~24.5 µm which is much smaller than the average particle size of the Apollo sample collection (~72 µm) [3], while the average particle size of samples 15601, 64501, and 67461 are larger than the Apollo sample average at ~106 µm, ~103 µm, and ~118.5 µm respectively. The size and shape measurements for the samples output ~30 parameters, four of which were focused on for this study: sphericity, aspect ratio, roundness, and concavity (Figure 3). However, after analyzing the plots it was found that only sphericity and aspect ratio showed differences between the samples. These two parameters are measured on a scale from 0 to 1, with 1 being a perfect sphere with equal dimensions. The results show that the sphericity values are slightly high-er for the mature samples 10084 and 64501 (~0.96) than they are for samples 15601 and 67461 (~0.95) (Figure 4). The aspect ratio values are slightly lower for samples 64501 (~0.7) and 67461 (~0.74) than they are for samples 10084 (~0.76) and 15601 (~0.8) (Figure 5). Discussion: Mature regoliths are those that have been exposed to micrometeorite and solar wind bombardment for long periods of time, breaking up particles and causing them to become more rounded [4]. Therefore, the smaller particle sizes and higher sphericity values for samples 10084 and 64501 are expected due to their higher maturity level compared to 15601 and 67461. However, the aspect ratio values are not dependent on maturity and are instead dependent on terrain type. The lower aspect ratio values for the high-land samples is potentially due to the higher plagioclase content, which occurs in elongated particles and does not break down as easily as the pyroxenes or olivines that are present in the mare. Conclusion and Future Work: The results of this work provide a baseline of high-quality data that will contribute to the creation of high-fidelity lunar simulants and will greatly benefit NASA’s efforts of establishing a human presence on the Moon. Future work includes performing unsupervised image classification on the ~105 particle images per sample in order to identify different classes of grains. These grain classes can then be linked to detailed shape properties, and the relative abundance of each class in the samples can be compared. Acknowledgments: We would like to thank the Extraterrestrial Materials Analysis Group (ExMAG) and the Astromaterials Allocation Review Board (AARB) for allocating lunar regolith samples 10084,9010, 15601,365, 64501,249, and 67461,171 for this work. References: [1] Taylor, L. A. et al. (2005) AIAA #2510. [2] Katagiri et al. (2015) ASCE. [3] Carrier III, W. D. (2005) Lunar Geotech Institute Tech Report. [4] McKay, D. S. et al. (1991) The Lunar Sourcebook, Chapter 7.

S R Deitrick↗
NASA NTRS2016

Polarized View of Supercooled Liquid Water Clouds

Supercooled liquid water (SLW) clouds, where liquid droplets exist at temperatures below 0 C present a well known aviation hazard through aircraft icing, in which SLW accretes on the airframe. SLW clouds are common over the Southern Ocean, and climate-induced changes in their occurrence is thought to constitute a strong cloud feedback on global climate. The two recent NASA field campaigns POlarimeter Definition EXperiment (PODEX, based in Palmdale, California, January-February 2013) and Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS, based in Houston, Texas in August- September 2013) provided a unique opportunity to observe SLW clouds from the high-altitude airborne platform of NASA's ER-2 aircraft. We present an analysis of measurements made by the Research Scanning Polarimeter (RSP) during these experiments accompanied by correlative retrievals from other sensors. The RSP measures both polarized and total reflectance in 9 spectral channels with wavelengths ranging from 410 to 2250 nm. It is a scanning sensor taking samples at 0.8deg intervals within 60deg from nadir in both forward and backward directions. This unique angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135deg and 165deg. Simple parametric fitting algorithms applied to the polarized reflectance provide retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT),which allows retrieval of the droplet size distribution without assuming a size distribution shape. We present an overview of the RSP campaign datasets available from the NASA GISS website, as well as two detailed examples of the retrievals. In these case studies we focus on cloud fields with spatial features varying between glaciated and liquid phases at altitudes as high as 10 km, which correspond to temperatures close to the homogeneous freezing temperature of pure water drops (about -35 C or colder). The multimodal droplet size distributions retrieved from RSP data in these cases are consistent with the multi-layer cloud structure observed by correlative Cloud Physics Lidar (CPL) measurements.

Clouds↗
DOE OSTI2023

Deducing subnanometer cluster size and shape distributions of heterogeneous supported catalysts

Abstract Infrared (IR) spectra of adsorbate vibrational modes are sensitive to adsorbate/metal interactions, accurate, and easily obtainable in-situ or operando. While they are the gold standards for characterizing single-crystals and large nanoparticles, analogous spectra for highly dispersed heterogeneous catalysts consisting of single-atoms and ultra-small clusters are lacking. Here, we combine data-based approaches with physics-driven surrogate models to generate synthetic IR spectra from first-principles. We bypass the vast combinatorial space of clusters by determining viable, low-energy structures using machine-learned Hamiltonians, genetic algorithm optimization, and grand canonical Monte Carlo calculations. We obtain first-principles vibrations on this tractable ensemble and generate single-cluster primary spectra analogous to pure component gas-phase IR spectra. With such spectra as standards, we predict cluster size distributions from computational and experimental data, demonstrated in the case of CO adsorption on Pd/CeO 2 (111) catalysts, and quantify uncertainty using Bayesian Inference. We discuss extensions for characterizing complex materials towards closing the materials gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Entrainment and aerosol effects on marine boundary-layer clouds: An investigation using ACE-ENA data from HOLODEC, G1, Pico and ACTOS (Final Report on Project Activities)

Marine boundary-layer clouds cover large regions of the globe and are known to strongly influence radiative balances. The microphysical properties and persistence of these clouds are tightly coupled with cloud-top entrainment and aerosol properties within both the boundary layer and the overlying free troposphere. This work addressed the microphysical response to entrainment and aerosol properties in marine stratocumulus clouds, using data from the Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) project. Specifically, emphasis was placed on 1. extensive in situ measurements taken with the Atmospheric Radiation Measurement (ARM) G1 aircraft using the Holographic Detector for Clouds (Holodec) instrument; 2. airborne measurements obtained with the helicopter-borne Airborne Cloud Turbulence Observation System (ACTOS) operated by the Leibniz Institute for Tropospheric Research (TROPOS) during the first phase of ACE-ENA; and 3. above-boundary-layer, mountain-top measurements taken at the Pico Mountain Observatory (OMP) by the research group of the co-investigator and scientists from TROPOS during the first phase of ACE-ENA. The work is aligned with the topic “Warm Boundary-Layer Atmospheric Processes.” Key results include the following. Data from the Holographic Detector for Clouds (Holodec) were reprocessed, refined, and validated through a careful instrument intercomparison, resulting in a high-quality dataset available on the ARM archive for ACE-ENA. High-resolution ACTOS measurements of thermodynamics, microphysical, and turbulence properties were analyzed to explore the behavior of the entrainment velocity at cloud top. Analysis of the vertical variability of cloud droplet size distribution shape suggests that mixing is more inhomogeneous near cloud top, and more homogeneous deeper into the cloud. Analysis of aerosol measurements from OMP explored the mixing state and cloud condensation nucleus properties, as well as the implications for radiative forcing. Finally, a machine learning algorithm was developed for identifying characteristic cloud droplet size distributions, and was employed to explore microphysical regimes in stratocumulus clouds observed during ACE-ENA. The characteristic size distributions are narrow, and only when spatially averaged do they produce the broad “gamma” distributions typically assumed in models. This implies that precipitation development should account for variability and correlations in the distribution shape as well as the number concentration of cloud droplets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Surface-mediated spontaneous emulsification of the acylated peptide, semaglutide

Acylated peptides composed of glucagon-like peptide-1 receptor agonists modified with a fatty acid side chain are an important class of therapeutics for type 2 diabetes and obesity but are susceptible to an unusual physical instability in the presence of hydrophobic surfaces, i.e., spontaneous emulsification, also known as ouzo formation in practice. In this work, light scattering, small-angle X-ray scattering, and circular dichroism measurements are used to characterize the physical properties of the semaglutide colloidal phase, including size distribution, shape, secondary structure, internal structure, and internal composition, as a function of solution physico-chemical conditions. The existence and size of the colloids formed are successfully predicted by a classical Rayleigh model, which identifies the parameters controlling their size and formation. Colloid formation is found to be catalyzed by hydrophobic surfaces, and formation rates are modeled as an autocatalytic reaction, enabling the formation of a master curve for various surfaces that elucidates the mechanism. Surfaces differ due to differences in surface wettability, which can be correlated with Hansen solubility parameters. This work provides insights into this unusual colloidal phenomenon and guides the peptide synthesis process and drug product formulation in the pharmaceutical industry.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2016

Retrievals of Cloud Droplet Size from the RSP Data: Validation Using in Situ Measurements

We present comparisons of cloud droplet size distributions retrieved from the Research Scanning Polarimeter (RSP) data with correlative in situ measurements made during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). This field experiment was based at St. Johns airport, Newfoundland, Canada with the latest deployment in May - June 2016. RSP was onboard the NASA C-130 aircraft together with an array of in situ and other remote sensing instrumentation. The RSP is an along-track scanner measuring polarized and total reflectances in9 spectral channels. Its unique high angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135 and 165 degrees. A parametric fitting algorithm applied to the polarized reflectances provides retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT), which allows us to retrieve the droplet size distribution (DSD) itself. The latter is important in the case of clouds with complex structure, which results in multi-modal DSDs. During NAAMES the aircraft performed a number of flight patterns specifically designed for comparison of remote sensing retrievals and in situ measurements. These patterns consisted of two flight segments above the same straight ground track. One of these segments was flown above clouds allowing for remote sensing measurements, while the other was at the cloud top where cloud droplets were sampled. We compare the DSDs retrieved from the RSP data with in situ measurements made by the Cloud Droplet Probe (CDP). The comparisons show generally good agreement with deviations explainable by the position of the aircraft within cloud and by presence of additional cloud layers in RSP view that do not contribute to the in situ DSDs. In the latter case the distributions retrieved from the RSP data were consistent with the multi-layer cloud structures observed in the correlative High Spectral Resolution Lidar (HSRL) profiles. The comparison results provide a rare validation of polarimetric droplet size retrieval techniques, which can be used for analysis of satellite data on global scale.

cloud droplets↗
NASA NTRS2018

Retrievals of Cloud Droplet Size from the Research Scanning Polarimeter Data: Validation Using In Situ Measurements

We present comparisons of cloud droplet size distributions (DSDs) retrieved from the research scanning polarimeter (RSP) data with correlative in situ measurements made during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). The airborne portion of this field experiment was based out of St. John's airport, Newfoundland, Canada with the focus of this paper being on the deployment in May - June 2016. RSP was onboard the NASA C-130 aircraft together with an array of in situ and other remote sensing instrumentation. The RSP is an along-track scanner measuring the polarized and total reflectance in 9 spectral channels. Its uniquely high angular resolution allows for characterization of liquid water droplet sizes using the rainbow structure observed in the polarized reflectance over the scattering angle range from 135 to 165.degrees The rainbow is dominated by single scattering of light by cloud droplets, so its structure is characteristic specifically of the droplet sizes at cloud top (within unit optical depth into the cloud, equivalent to approximately 50m). A parametric fitting algorithm applied to the polarized reflectance provides retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, the Rainbow Fourier Transform (RFT), which allows us to retrieve the droplet size distribution itself. The latter is important in the case of clouds with complex microphysical structure, or multiple layers of cloud, which result in multi-modal DSDs. During NAAMES the aircraft performed a number of flight patterns specifically designed for comparisons between remote sensing retrievals and in situ measurements. These patterns consisted of two flight segments above the same straight ground track. One of these segments was flown above clouds allowing for remote sensing measurements, while the other was near the cloud top where cloud droplets were sampled. We compare the DSDs retrieved from the RSP data with in situ measurements made by the Cloud Droplet Probe (CDP). The comparisons generally show good agreement (better than 1 micron for effective radius and in most cases better than 0.02 for effective variance) with deviations explainable by the position of the aircraft within the cloud, or by the presence of additional cloud layers between the cloud being sampled by the in situ instrumentation and the altitude of the remote sensing segment. In the latter case, the multi-modal DSDs retrieved from the RSP data were consistent with the multi-layer cloud structures observed in the correlative High Spectral Resolution Lidar (HSRL) profiles. The results of these comparisons provide a rare validation of polarimetric droplet size retrieval techniques, demonstrating their accuracy and robustness and the potential of satellite data of this kind on a global scale.

Remote Sensing↗
DOE OSTI2023

Bead–Spring Simulation of Ionomer Melts—Studying the Effects of Chain-Length and Associating Group Fraction on Equilibrium Structure and Extensional Flow Behavior

Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system’s mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters’ size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups’ fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer–Grest type bead–spring model and perform large-scale MD simulations to explore the effect of polymer chain-length (l) and fraction (f s ) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by ‘sticky’ beads) between 5 and 20%, and a fixed sticky–sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S(q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing f s and l. The average cluster size Nc increases with f s . However, the effect of chain-length on Nc appears to be pronounced only at higher values of f s . Under extensional flows, the computed stress (and viscosity) is higher at higher f s and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Evaluating the Performance of Single and Double Moment Microphysics Schemes During a Synoptic-Scale Snowfall Event

Increases in computing resources have allowed for the utilization of high-resolution weather forecast models capable of resolving cloud microphysical and precipitation processes among varying numbers of hydrometeor categories. Several microphysics schemes are currently available within the Weather Research and Forecasting (WRF) model, ranging from single-moment predictions of precipitation content to double-moment predictions that include a prediction of particle number concentrations. Each scheme incorporates several assumptions related to the size distribution, shape, and fall speed relationships of ice crystals in order to simulate cold-cloud processes and resulting precipitation. Field campaign data offer a means of evaluating the assumptions present within each scheme. The Canadian CloudSat/CALIPSO Validation Project (C3VP) represented collaboration among the CloudSat, CALIPSO, and NASA Global Precipitation Measurement mission communities, to observe cold season precipitation processes relevant to forecast model evaluation and the eventual development of satellite retrievals of cloud properties and precipitation rates. During the C3VP campaign, widespread snowfall occurred on 22 January 2007, sampled by aircraft and surface instrumentation that provided particle size distributions, ice water content, and fall speed estimations along with traditional surface measurements of temperature and precipitation. In this study, four single-moment and two double-moment microphysics schemes were utilized to generate hypothetical WRF forecasts of the event, with C3VP data used in evaluation of their varying assumptions. Schemes that incorporate flexibility in size distribution parameters and density assumptions are shown to be preferable to fixed constants, and that a double-moment representation of the snow category may be beneficial when representing the effects of aggregation. These results may guide forecast centers in optimal configurations of their forecast models for winter weather and identify best practices present within these various schemes.

Molthan, Andrew L.↗