Engineering topics

Mitchell, David L.

Publications and source records attributed to Mitchell, David L..

At least 19 records

DOE OSTI2021

Version 4 CALIPSO Imaging Infrared Radiometer ice and liquid water cloud microphysical properties – Part I: The retrieval algorithms

Following the release of the version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version (version 4; V4) of the CALIPSO Imaging Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter and ice or liquid water path estimates. Dedicated retrievals for water clouds were added in V4, taking advantage of the high sensitivity of the IIR retrieval technique to small particle sizes. This paper (Part I) describes the improvements in the V4 algorithms compared to those used in the version 3 (V3) release, while results will be presented in a companion (Part II) paper. The IIR Level 2 algorithm has been modified in the V4 data release to improve the accuracy of the retrievals in clouds of very small (close to 0) and very large (close to 1) effective emissivities. To reduce biases at very small emissivities that were made evident in V3, the radiative transfer model used to compute clear-sky brightness temperatures over oceans has been updated and tuned for the simulations using Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) data to match IIR observations in clear-sky conditions. Furthermore, the clear-sky mask has been refined compared to V3 by taking advantage of additional information now available in the V4 CALIOP 5 km layer products used as an input to the IIR algorithm. After sea surface emissivity adjustments, observed and computed brightness temperatures differ by less than ±0.2 K at night for the three IIR channels centered at 08.65, 10.6, and 12.05 µm, and inter-channel biases are reduced from several tens of Kelvin in V3 to less than 0.1 K in V4. We have also improved retrievals in ice clouds having large emissivity by refining the determination of the radiative temperature needed for emissivity computation. The initial V3 estimate, namely the cloud centroid temperature derived from CALIOP, is corrected using a parameterized function of temperature difference between cloud base and top altitudes, cloud absorption optical depth, and CALIOP multiple scattering correction factor. As shown in Part II, this improvement reduces the low biases at large optical depths that were seen in V3 and increases the number of retrievals. As in V3, the IIR microphysical retrievals use the concept of microphysical indices applied to the pairs of IIR channels at 12.05 and 10.6 µm and at 12.05 and 08.65 µm. The V4 algorithm uses ice look-up tables (LUTs) built using two ice habit models from the recent “TAMUice2016” database, namely the single-hexagonal-column model and the eight-element column aggregate model, from which bulk properties are synthesized using a gamma size distribution. Four sets of effective diameters derived from a second approach are also reported in V4. Here, the LUTs are analytical functions relating microphysical index applied to IIR channels 12.05 and 10.6 µm and effective diameter as derived from in situ measurements at tropical and midlatitudes during the Tropical Composition, Cloud, and Climate Coupling (TC4) and Small Particles in Cirrus Science and Operations Plan (SPARTICUS) field experiments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Superthermal Electron Deposition on the Mars Nightside During ICMEs

Superthermal electron precipitation is one of the main sources supporting the Mars nightside ionosphere. It is expected that solar wind electron fluxes are to increase significantly during interplanetary coronal mass ejections (ICMEs) and therefore an enhanced nightside ionospheric density. This study is to quantify the variation of the precipitating and deposited electron fluxes during five extreme ICMEs encountered by Mars Global Surveyor (MGS). We find that energy fluxes correlate better with the upstream dynamic pressure proxy than number fluxes and electron fluxes increase more at high energies, which means that electrons tend to have a lower peak production altitude during storm times. The precipitating and net/deposited fluxes are increased up to an order of magnitude from low to high dynamic pressures. The estimated total electron content (TEC) is a few times of 10 14 m -2 for quiet times and on the order of 1015 m -2 for storm times, with an enhancement up to an order of magnitude locally near strong crustal fields. Crustal magnetic fields have an effect on the deposited fluxes with more prominent magnetic reflection over strong magnetic fields during quiet periods, which is significantly reduced during storm times. Lastly, we estimate a global energy input from downward fluxes of 1.1 × 10 8 and 5.5 × 10 8 W and the globally deposited energy from net fluxes of 2.0 × 10 7 and 1.6 × 10 8 W for quiet and storm time periods, a factor of 5 and 8 enhancement globally, respectively, but up to an order of magnitude locally near strong crustal fields.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Characterizing Mars's Magnetotail Topology With Respect to the Upstream Interplanetary Magnetic Fields

The canonical picture of the magnetotail of unmagnetized planets consists of draped interplanetary magnetic fields (IMFs) forming opposite-directed lobes, separated by the current sheet. DiBraccio et al. (2018, https://doi.org/10.1029/2018GL077251) showed that Mars's magnetotail has a twist departing from this picture. Magnetohydrodynamic (MHD) results suggest that the asymmetry in how open field lines connected to the planet populate the tail causes the apparent twist. To validate this interpretation, we compare the tail topology determined from MHD simulations to that inferred from data collected by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft, in particular, how each topology responds to the upstream IMF orientation. The occurrence rates for open topology from both data and MHD vary with IMF polarities in a similar fashion as the tail twisting. This suggests that Mars's crustal fields have a global effect on the magnetosphere configuration, supporting the picture of a “hybrid” magnetotail that is partly induced/draped and partly intrinsic/planetary in origin.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2018

MAVEN Case Studies of Plasma Dynamics in Low‐Altitude Crustal Magnetic Field at Mars 1: Dayside Ion Spikes Associated With Radial Crustal Magnetic Fields

We report for the first time, simultaneous ion, electron, magnetic field vector and electric field wave measurements made possible by Mars Atmosphere and Volatile EvolutioN, during ion energy flux spikes in low‐altitude radial crustal magnetic fields on the Mars dayside. Observations show energetic electrons and ions (E > 25 eV) precipitating on magnetic field lines assumed as closed. Ions (E < 1.4 keV) display broad velocity distributions toward Mars, showing ions flowing from higher altitude possibly after magnetic reconnection or loss cone filling from pitch angle scattering effects. Precipitating ions (E < 1.4 keV) show nonadiabatic features depending on ion mass and energy and returning ions (E < 1.4 keV) show evidence of conserving the first adiabatic invariant in a mirror field. We observe magnetic field perturbations up to 60 nT, electric field wave amplitudes up to 38 mV/m, and brief periods of peaked electron spectra. At ∼175 km and at times Mars Atmosphere and Volatile EvolutioN is below the mirroring altitude of electrons, we observe mirroring and transverse heating of H+ ions alongside increased electric field wave amplitude fluctuations. It suggests field aligned potential drops result from different mirror altitudes of ions and electrons. Ions E > 1.4 keV (O+) occur as injected accelerated ion beams and ions heated after energization or deceleration. Energy dispersed kilo‐electron‐volt ions suggest a selection effect in radial magnetic fields for lower‐energy Marsward ions, compared to reflection of higher‐energy anti‐Sunward ions. Precipitating kilo‐electron‐volt ions show energy deposition rates of 3.6 ×10(exp -6) W/sq m and sputtering escape rates from precipitating O+ ions of 1.5 ×10(exp 5)/(sq cm.s) and 2.1 ×10(exp 6)/(sq cm.s) are calculated.

Plasma Dynamics↗

NASA NTRS2018

The Three-Dimensional Bow Shock of Mars as Observed by MAVEN

The Martian magnetosphere is a product of the interaction of Mars with the interplanetary magnetic field and the supersonic solar wind. The location of the bow shock has been previously modeled as conic sections using data from spacecraft such as Phobos 2, Mars Global Surveyor, and Mars Express. The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission spacecraft arrived in orbit about Mars in November 2014 resulting in thousands of crossings to date. We identify over 1,000 bow shock crossings. We model the bow shock as a three-dimensional surface accommodating asymmetry caused by crustal magnetic fields. By separating MAVEN's bow shock encounters based on solar condition, we also investigate the variability of the surface. We find that the shock surface varies in shape and location in response to changes in the solar radiation, the solar wind Mach number, dynamic pressure of the solar wind, and the relative local time location of the strong crustal magnetic fields (i.e., whether they are on the dayside or on the nightside).

Supersonic↗

NASA NTRS2018

The Twisted Configuration of the Martian Magnetotail: MAVEN Observations

Measurements provided by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft are analyzed to investigate the Martian magnetotail configuration as a function of interplanetary magnetic field (IMF) BY. We find that the magnetotail lobes exhibit a ~45deg twist, either clockwise or counterclockwise from the ecliptic plane, up to a few Mars radii downstream. Moreover, the associated cross-tail current sheet is rotated away from the expected location for a Venus-like induced magnetotail based on nominal IMF draping. Data-model comparisons using magnetohydrodynamic simulations are in good agreement with the observed tail twist. Model field line tracings indicate that a majority of the twisted tail lobes are composed of open field lines, surrounded by draped IMF. We infer that dayside magnetic reconnection between the crustal fields and draped IMF creates these open fields and may be responsible for the twisted tail configuration, similar to what is observed at Earth.

Martian↗

NASA NTRS2016

Calipso Observations of the Dependence of Homo- and Heterogeneous Ice Nucleation in Cirrus Clouds on Latitude, Season and Surface Condition

There are two fundamental mechanisms through which cirrus clouds form; homo- and heterogeneous ice nucleation (henceforth hom and het). The relative contribution of each mechanism to ice crystal production often determines the microphysical and radiative properties of a cirrus cloud. A new satellite remote sensing method is described in this study to estimate cirrus cloud ice particle number concentration and the relative contribution of hom and het to cirrus cloud formation as a function of altitude, latitude, season and surface type (e.g. land vs. ocean). This method uses co-located observations from the Infrared Imaging Radiometer (IIR) and from the CALIOP (Cloud and Aerosol Lidar with Orthogonal Polarization) lidar aboard the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation) polar orbiting satellite, employing IIR channels at 10.6 μm and 12.05 μm. The method is applied here to single-layered clouds of visible optical depth between about 0.3 and 3. Two years of Version 3 data have been analyzed for the years 2008 and 2013, with each season characterized in terms of 532 nm cirrus cloud centroid altitude and temperature, the cirrus cloud ice particle number concentration, effective diameter, layer-average ice water content and visible optical depth. Using a conservative criterion for hom cirrus, on average, the sampled cirrus clouds formed through hom occur about 43% of the time in the Arctic and 50% of the time in the Antarctic, and during winter at mid-latitudes in the Northern Hemisphere, hom cirrus occur 37% of the time. Elsewhere (and during other seasons in the Northern Hemisphere mid-latitudes), this hom cirrus fraction is lower. Processes that could potentially explain these observations are discussed, as well as the potential relevancy of these results to ice nucleation studies, climate modeling and jet-stream dynamics.

Mitchell, David L.↗

NASA NTRS2016

Electron Energetics in the Martian Dayside Ionosphere: Model Comparisons with MAVEN Data

This paper presents a study of the energetics of the dayside ionosphere of Mars using models and data from several instruments on board the Mars Atmosphere and Volatile EvolutioN spacecraft. In particular, calculated photoelectron fluxes are compared with suprathermal electron fluxes measured by the Solar Wind Electron Analyzer, and calculated electron temperatures are compared with temperatures measured by the Langmuir Probe and Waves experiment. The major heat source for the thermal electrons is Coulomb heating from the suprathermal electron population, and cooling due to collisional rotational and vibrational CO2 dominates the energy loss. The models used in this study were largely able to reproduce the observed high topside ionosphere electron temperatures (e.g., 3000 K at 300 km altitude) without using a topside heat flux when magnetic field topologies consistent with the measured magnetic field were adopted. Magnetic topology affects both suprathermal electron transport and thermal electron heat conduction. The effects of using two different solar irradiance models were also investigated. In particular, photoelectron fluxes and electron temperatures found using the Heliospheric Environment Solar Spectrum Radiation irradiance were higher than those with the Flare Irradiance Spectrum Model-Mars. The electron temperature is shown to affect the O2(+) dissociative recombination rate coefficient, which in turn affects photochemical escape of oxygen from Mars.

magnetic topology↗

NASA NTRS2016

Contributions of the ARM Program to Radiative Transfer Modeling for Climate and Weather Applications

Accurate climate and weather simulations must account for all relevant physical processes and their complex interactions. Each of these atmospheric, ocean, and land processes must be considered on an appropriate spatial and temporal scale, which leads these simulations to require a substantial computational burden. One especially critical physical process is the flow of solar and thermal radiant energy through the atmosphere, which controls planetary heating and cooling and drives the large-scale dynamics that moves energy from the tropics toward the poles. Radiation calculations are therefore essential for climate and weather simulations, but are themselves quite complex even without considering the effects of variable and inhomogeneous clouds. Clear-sky radiative transfer calculations have to account for thousands of absorption lines due to water vapor, carbon dioxide, and other gases, which are irregularly distributed across the spectrum and have shapes dependent on pressure and temperature. The line-by-line (LBL) codes that treat these details have a far greater computational cost than can be afforded by global models. Therefore, the crucial requirement for accurate radiation calculations in climate and weather prediction models must be satisfied by fast solar and thermal radiation parameterizations with a high level of accuracy that has been demonstrated through extensive comparisons with LBL codes. See attachment for continuation.

climatology↗

NASA NTRS2016

MAVEN Observations of Magnetic Flux Ropes with a Strong Field Amplitude in the Martian Magnetosheath During the ICME Passage on 8 March 2015

We present initial results of strong field amplitude flux ropes observed by Mars Atmosphere and Volatile EvolutioN (MAVEN) mission around Mars during the interplanetary coronal mass ejection (ICME) passage on 8 March 2015. The observed durations were shorter than 5 s and the magnetic field magnitudes peaked above 80 nT, which is a few times stronger than those usually seen in the magnetosheath barrier. These are the first unique observations that MAVEN detected such flux ropes with a strong field at high altitudes (greater than 5000 km). Across these structures, MAVEN coincidentally measured planetary heavy ions with energies higher than a few keV. The spatial properties inferred from the Grad-Shafranov equation suggest that the speed of the structure can be estimated at least an order of magnitude faster than those previously reported quiet-time counterparts. Hence, the space weather event like the ICME passage can be responsible for generating the observed strong field, fast-traveling flux ropes.

8 March 2015↗

NASA NTRS2004

MGS MAG/ER Data Analysis Using a Time and Magnetic Field Dependent Electron Transport Model

The goal of that project was to examine certain details about the dayside electron environment at Mars as seen by the Mars Global Surveyor (MGS) magnetometer/electron reflectometer (MAG/ER) instrument. Specifically, we stated that we would use the Khazanov and Liemohn (K&L) kinetic electron transport model to analyze features in the observations. This code includes a non-uniform magnetic field and time-dependence in the result (different from most other models of this type). It was originally developed for electron motion along field lines in the Earth's magnetosphere (between conjugate ionospheres), and is thus quite appropriate for application to the Mars magnetic field scenario. Numerous code developments were implemented and the Mars version of the K&L model is fully operational. Initial results from this code have focused on the examination of MGS MAG/ER observations in the crustal field region when it is on the dayside. After several presentations at scientific meetings, this study culminated in a JGR publication last year.

Liemohn, Michael W.↗

NASA NTRS1996

Radar Observations of Asteroid 1620 Geographos

Goldstone radar observations of Geographos from August 28 through September 2, 1994 yield over 400 delay-Doppler images whose linear spatial resolutions range from approx. 75 to approx. 151 in, and 138 pairs of dual-polarization (OC, SC) spectra with one-dimensional resolution of 103 m. Each data type provides thorough rotational coverage. The images contain an intrinsic north/south ambiguity, but the equatorial view allows accurate determination of the shape of the radar-facing part of the asteroid's pole-on silhouette at any rotation phase. Sums of co-registered images that cover nearly a full rotation have defined the extremely elongated shape of that silhouette. Here we present individual images and co-registered sums over approx. 30 deg of rotation phase that show the silhouette's structural characteristics in finer detail and also reveal numerous contrast features "inside" the silhouette. Those features include several candidate craters as well as indications of other sorts of large-scale topographic relief, including a prominent central indentation. Protuberances at the asteroid's ends may be related to the pattern of ejecta removal and deposition caused by the asteroid's gravity field. The asteroid's surface is homogeneous and displays only modest roughness at centimeter-to-meter scales. Our estimates of radar cross section and the currently available constraints on the asteroid's dimensions are consistent with a near-surface bulk density between 2 and 3 g/cu cm. The delay-Doppler trajectory of Geographos' center of mass has been determined to about 200 m on August 28 and to about 100 m on August 31, an improvement of two orders of magnitude over pre-observation ephemerides.

Ostro, Steven J.↗

NASA NTRS1996

Radar Observations of Asteroids 1 Ceres, 2 Pallas, and 4 Vesta

Asteroids 1 Ceres, 2 Pallas, and 4 Vesta were observed with the 13-cm Arecibo radar and the 3.5-cm Goldstone radar during several apparitions between 1981 and 1995. These observations help to characterize the objects' surface properties. Echoes from Ceres and Pallas are approximately 95% polarized (muon(sub C) = sigm(sub SC)/sigma(sub OC) equivalent to 0.05) in the sense expected for specular (mirror) reflection yet broadly distributed in Doppler frequency, thus revealing surfaces that are smoother than the Moon at decimeter scales but much rougher (rms slopes > 20 deg) on larger scales. Slopes on Ceres appear to be somewhat higher when viewed with the 3.5-cm wavelength, a trend that is observed for the terrestrial planets and the Moon. In contrast, echoes from Vesta are significantly depolarized, indicating substantial near-surface complexity at scales near 13 cm (muon(sub C) = 0.24 +/- 0.04) and 3.5 cm (muon(sub C) = 0.32 +/- 0.04), which is probably a consequence of Vesta's relatively strong basaltic surface material and may be a signature of large impact features inferred to be present on the surface. The low radar albedos of Ceres (circumflex-sigma(sub C) = 0.042 +/- 0.006) and Pallas (circumfle-sigma(sub C) = 0.075 +/- 0.011) are in the range expected for surfaces with a carbonaceous chondrite mineralogy. Pallas' distinctly higher albedo implies a approximately 35% higher surface density, which could result from a lower regolith porosity and/or a higher specific gravity (zero-porosity density). Given a porosity of 45%, the specific gravities of the surface materials on Ceres and Pallas would be approximately 2.3 and approximately 3.0 g/cc, respectively, which would be consistent with (1) the presence of an additional silicate component on Pallas' surface (as inferred from spectroscopic observations) and (2) recent mass estimates, which suggest a higher mean (volume-averaged) density for Pallas than for Ceres.

Mitchell, David L.↗

NASA NTRS1995

Radar Observations of Asteroids 7 Iris, 9 Metis, 12 Victoria, 216 Kleopatra, and 654 Zelinda

We report 13-cm wavelength radar observations of the main-belt asteroids 7 Iris, 9 Metis, 12 Victoria, 216 Kleopatra, and 654 Zelinda obtained at Arecibo between 1980 and 1989. The echoes are highly polarized yet broadly distributed in Doppler frequency, indicating that our targets are smooth on decimeter scales but very rough on some scale(s) larger than about I m. The echo spectra are generally consistent with existing size, shape, and spin information based on radiometric, lightcurve, and occultation data. All of our targets possess distinctive radar signatures that reveal large- scale topography. Reflectivity spikes within narrow ranges of rotation phase suggest large flat regions on Iris, Metis, and Zelinda, while bimodal spectra imply nonconvex, possibly bifurcated shapes for Kleopatra and Victoria. Kleopatra has the highest radar albedo yet measured for a main-belt asteroid, indicating a high metal concentration and making Kleopatra the best main-belt candidate for a core remnant of a differentiated and subsequently disrupted parent body. Upon completion of the Arecibo telescope upgrade, there will be several opportunities per year to resolve main-belt asteroids with hundreds of delay-Doppler cells, which can be inverted to provide estimates of both three-dimensional shape and radar scattering properties.

Mitchell, David L.↗

NASA NTRS1995

Radar Observations of Asteroids 7 Iris, 9 Metis, 12 Victoria, 216 Kleopatra, and 654 Zelinda

asteroids↗

NASA NTRS1994

Radar aperture synthesis observations of asteroids

We report of Goldstone-VLA, radar aperture-synthesis observations of the mainbelt asteroids 324 Bamberga and 7 Iris and the near-Earth asteroids 1991 EE and 4179 Toutatis. Simultaneous resolution of echoes in both angle and Doppler frequency provide new constraints on the mainbelt asteroids' pole directions: Bamberga's spin vector is within 40 deg of the south ecliptic pole, and the twofold ambiguity in Iris' pole direction (P. Magnusson, 1989) is resolved in favor of the ecliptic coordinates lambda = 15 deg, beta = +25 deg. For Bamberga, monostatic and bistatic radar echoes and VLA thermal-emission measurements, also reported here, are consistent with radiometric estimates of Bamberga's size and with the hypothesis that the asteroid is overlain by a regolith having a porosity of approximately 50%. Our near-Earth asteroid measurements required the development of new on-line VLA software that allows imaging of objects that are in the telescope's `near field.' This software has been successfully tested on Toutatis at a distance of 0.06 AU and will be essential for VLA observations of Earth-approaching comets.

De Pater, Imke↗

NASA NTRS1994

A model predicting the evolution of ice particle size spectra and radiative properties of cirrus clouds. Part 2: Dependence of absorption and extinction on ice crystal morphology

This study builds upon the microphysical modeling described in Part 1 by deriving formulations for the extinction and absorption coefficients in terms of the size distribution parameters predicted from the micro-physical model. The optical depth and single scatter albedo of a cirrus cloud can then be determined, which, along with the asymmetry parameter, are the input parameters needed by cloud radiation models. Through the use of anomalous diffraction theory, analytical expressions were developed describing the absorption and extinction coefficients and the single scatter albedo as functions of size distribution parameters, ice crystal shapes (or habits), wavelength, and refractive index. The extinction coefficient was formulated in terms of the projected area of the size distribution, while the absorption coefficient was formulated in terms of both the projected area and mass of the size distribution. These properties were formulated as explicit functions of ice crystal geometry and were not based on an 'effective radius.' Based on simulations of the second cirrus case study described in Part 1, absorption coefficients predicted in the near infrared for hexagonal columns and rosettes were up to 47% and 71% lower, respectively, than absorption coefficients predicted by using equivalent area spheres. This resulted in single scatter albedos in the near-infrared that were considerably greater than those predicted by the equivalent area sphere method. Reflectances in this region should therefore be underestimated using the equivalent area sphere approach. Cloud optical depth was found to depend on ice crystal habit. When the simulated cirrus cloud contained only bullet rosettes, the optical depth was 142% greater than when the cloud contained only hexagonal columns. This increase produced a doubling in cloud albedo. In the near-infrared (IR), the single scatter albedo also exhibited a significant dependence on ice crystal habit. More research is needed on the geometrical properties of ice crystals before the influence of ice crystal shape on cirrus radiative properties can be adequately understood. This study provides a way of coupling the radiative properties of absorption, extinction, and single scatter albedo to the microphysical properties of cirrus clouds. The dependence of extinction and absorption on ice crystal shape was not just due to geometrical differences between crystal types, but was also due to the effect these differences had on the evolution of ice particle size spectra. The ice particle growth model in Part 1 and the radiative properties treated here are based on analytical formulations, and thus represent a computationally efficient means of modeling the microphysical and radiative properties of cirrus clouds.

Mitchell, David L.↗

NASA NTRS1993

Importance of aggregation and small ice crystals in cirrus clouds, based on observations and an ice particle growth model

The 1 November 1986 FIRE I case study was used to test an ice particle growth model which predicts bimodal size spectra in cirrus clouds. The model was developed from an analytically based model which predicts the height evolution of monomodal ice particle size spectra from the measured ice water content (IWC). Size spectra from the monomodal model are represented by a gamma distribution, N(D) = N(sub o)D(exp nu)exp(-lambda D), where D = ice particle maximum dimension. The slope parameter, lambda, and the parameter N(sub o) are predicted from the IWC through the growth processes of vapor diffusion and aggregation. The model formulation is analytical, computationally efficient, and well suited for incorporation into larger models. The monomodal model has been validated against two other cirrus cloud case studies. From the monomodal size spectra, the size distributions which determine concentrations of ice particles less than about 150 mu m are predicted.

Mitchell, David L.↗