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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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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

A Moderate Resolution View of the Spectral Absorption of Clouds

Some of the first evidence of a cloud absorption anomaly came from retrievals of cloud droplet size using measured multispectral cloud reflectance and in situ microphysical measurements. It was found that spectra computed from the measured droplet size or, equivalently, effective radius inverted from the reflectance measurements disagreed in such a way that suggested there was more absorption in cloud than predicted by theory. During the past decade new evidence of a cloud absorption anomaly has emerged from broadband solar flux measurements from above and below clouds. Based on these findings new field campaigns were devised to specifically address this problem. The most recent of these, the Atmospheric Radiation Measurement (ARM) Enhanced Shortwave Experiment II (ARESEII), included measurements of upwelling and downwelling moderate resolution (10 nm) solar irradiance spectra from above and below cloud. During this talk we will briefly summarize the advantages and limitations of these spectrally resolved measurements compared to the more standard broadband flux. We will focus on cloudy atmosphere results from the ARESEII field study and compare them to theoretical spectra from three independent models.

Pilewskie, Peter↗
NASA NTRS2013

Vertical Structure of Ice Cloud Layers From CloudSat and CALIPSO Measurements and Comparison to NICAM Simulations

The shape of the vertical profile of ice cloud layers is examined using 4 months of CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) global measurements taken on January, April, July, and October 2007. Ice clouds are selected using temperature profiles when the cloud base is located above the 253K temperature level. The obtained ice water content (IWC), effective radius, or extinction coefficient profiles are normalized by their layer mean values and are expressed in the normalized vertical coordinate, which is defined as 0 and 1 at the cloud base and top heights, respectively. Both CloudSat and CALIPSO observations show that the maximum in the IWC and extinction profiles shifts toward the cloud bottom, as the cloud depth increases. In addition, clouds with a base reaching the surface in a high-latitude region show that the maximum peak of the IWC and extinction profiles occurs near the surface, which is presumably due to snow precipitation. CloudSat measurements show that the seasonal difference in normalized cloud vertical profiles is not significant, whereas the normalized cloud vertical profile significantly varies depending on the cloud type and the presence of precipitation. It is further examined if the 7 day Nonhydrostatic Icosahedral Atmospheric Model (NICAM) simulation results from 25 December 2006 to 1 January 2007 generate similar cloud profile shapes. NICAM IWC profiles also show maximum peaks near the cloud bottom for thick cloud layers and maximum peaks at the cloud bottom for low-level clouds near the surface. It is inferred that oversized snow particles in the NICAM cloud scheme produce a more vertically inhomogeneous IWC profile than observations due to quick sedimentation.

Ham, Seung-Hee↗
NASA NTRS1989

The 27-28 October 1986 FIRE IFO Cirrus case study: Comparison of radiative transfer theory with observations by satellite and aircraft

Observations of cirrus and altocumulus clouds during the First International Satellite Cloud Climatology Project Regional Experiment (FIRE) are compared to theoretical models of cloud radiative properties. Three tests are performed. First, LANDSAT radiances are used to compare the relationship between nadir reflectance ot 0.83 micron and beam emittance at 11.5 microns with that predicted for model calculations using spherical and nonspherical phase functions. Good agreement is found between observations and theory when water droplets dominate. Poor agreement is found when ice particles dominate, especially using scattering phase functions for spherical particles. Even when compared to a laboratory measured ice particle phase function, the observations show increased side scattered radiation relative to the theoretical calculations. Second, the anisotropy of conservatively scattered radiation is examined using simultaneous multiple angle views of the cirrus from LANDSAT and ER-2 aircraft radiometers. Observed anisotropy gives good agreement with theoretical calculations using the laboratory measured ice particle phase function and poor agreement with a spherical particle phase function. Third, Landsat radiances at 0.83, 1.65, and 2.21 microns are used to infer particle phase and particle size. For water droplets, good agreement is found with King Air FSSP particle probe measurements in the cloud. For ice particles, the LANDSAT radiance observations predict an effective radius of 60 microns versus aircraft observations of about 200 microns. It is suggested that this descrepancy may be explained by uncertainty in the imaginary index of ice and by inadequate measurements of small ice particles by microphysical probes.

Wielicki, Bruce A.↗
NASA NTRS1990

The 27-28 October 1986 FIRE IFO cirrus case study - Comparison of radiative transfer theory with observations by satellite and aircraft

Observations of cirrus and altocumulus clouds during the FIRE are compared to theoretical models of cloud radiative properties. Three tests are performed. First, radiances are used to compare the relationship between nadir reflectance ot 0.83 micron and beam emittance at 11.5 microns with that predicted for model calculations using spherical and nonspherical phase functions. Good agreement is found between observations and theory when water droplets dominate. Poor agreement is found when ice particles dominate, especially using spherical-particle phase functions (SPPFs). Even when compared to a laboratory-measured ice-particle phase function (IPPF), the observations show great side-scattered radiation than the theoretical calculations. Second, the anisotropy of conservatively scattered radiation is examined using simultaneous multiple angle views of the cirrus from Landsat and ER-2 aircraft radiometers. Observed anisotropy gives good agreement with theoretical calculations using the laboratory IPPF and poor agreement with an SPPF. Third, Landsat radiances at 0.83, 1.65, and 2.21 microns are used to infer particle phase and size. For water droplets, good agreement is found with particle-probe measurements in the cloud. For ice particles, the Landsat radiance observations predict an effective radius of 60 microns versus aircraft observations of about 200 microns. It is suggested that this discrepancy may be explained by uncertainty in the imaginary index of ice and by inadequate measurements of small ice particles by microphysical probes.

Wielicki, Bruce A.↗
DOE OSTI2024

Neutrino charge radius and additional one-loop radiative corrections at ultranear reactor experiments

We scrutinize the potential of upcoming ultranear reactor neutrino experiments to detect radiative corrections in the elastic neutrino-electron scattering channel, focusing on the JUNO-TAO and CLOUD detectors, which employ advanced scintillator detection technologies. Previous reactor experiments have already constrained the electron neutrino charge radius, which is a neutrino property associated with a certain subset of the total radiative corrections, and have achieved limits that are only about an order of magnitude away from the Standard Model prediction. Our study demonstrates that JUNO-TAO and CLOUD could discover the neutrino charge radius in the near future, considering the established treatment of the charge radius. However, we show that it is necessary to go beyond this standard treatment. By including the complete set of one-loop level radiative corrections, we find a partial cancellation with the charge radius effect, reducing the experimental sensitivity to this quantity. Nevertheless, JUNO-TAO and CLOUD still have the potential to achieve a 5 σ discovery but over longer timescales within a reasonable operational time frame. Published by the American Physical Society 2024

Brdar, Vedran (ORCID:0000000170275104)↗
NASA NTRS2000

Aerosol Radiative Forcing in Asian Continental Outflow

Aerosols in elevated layers were sampled with FSSP-probes and wire impactors over the Pacific ocean aboard the NASA DC-8 aircraft. Analyses of particle size and morphology identifies two distinctly different aerosol types for cases when the mid-visible extinctions exceed 0.2/km. Smaller sizes (effective radii of 0.2 um) and moderate absorption (mid-visible single scattering albedo of.935) are typical for urban-industrial pollution. Larger sizes (effective radii of 0.7 um) and weak absorption (mid-visible single scattering albedo of 0.985) identify dust. This aerosol classification is in agreement with its origin as determined by airmass back trajectory analysis. Based on lidar vertical profiling, aerosol dominated by dust and urban-industrial pollution above 3km were assigned mid-visible optical depths of 0.50 and 0.27, respectively. Radiative transfer simulations, considering a 50% cloud-cover below the aerosol layers, suggest (on a daily tP C)C> basis) small reductions (-4W/m2) to the energy budget at the top of the atmosphere for both aerosol types. For c' 0 dust, more backscattering of sunlight (weaker solar absorption) is compensated by a stronger greenhouse effect due to larger sizes. Forced reductions to the energy budget at the surface are 12W/m2 for both aerosol types. In contrast, impacts on heating rates within the aerosol layers are quite different: While urban-industrial aerosol warms the layer (at +0.6K/day as solar heating dominates), dust cools (at -0.5K/day as infrared cooling dominates). Sensitivity tests show the dependence of the aerosol climatic impact on the optical depth, particle size, absorptivity, and altitude of the layers, as well as clouds and surface properties. Climatic cooling can be eliminated (1) for the urban-industrial aerosol if absorption is increased to yield a mid-visible single scattering albedo of 0.89, or if the ocean is replaced by a land surface; (2) for the dust aerosol if the effective radius is increased from 0.7 to 1.2 um. The removal of low-level clouds doubles the cooling at the top of the atmosphere to about -8W/m2.

Pueschel, R.↗
NASA NTRS2006

What does Reflection from Cloud Sides tell us about Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from CloudSat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3-D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimentional(3-D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 microns) and one with liquid water efficient absorption of solar radiation (2.1 microns). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3-D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, A.↗
NASA NTRS2005

What Does Reflection from Cloud Sides Tell Us About Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from Cloudsat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimensional (3D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 micrometers) and one with liquid water efficient absorption of solar radiation (2.1 micrometers). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, Alexander↗
NASA NTRS2019

Seasonal Variation in Martian Water Ice Cloud Particle Size

We employ the complete record of Mars limb-viewing observations by the Compact Reconnaissance Imaging Spectrometer, totaling 922 successful retrievals, to chart the seasonal variation in water ice cloud particle size. Low-latitude clouds exhibit particle size sorting with altitude at all seasons, with particles ranging from >3.0 m in effective radius to 1.01.5 m. However, at a given altitude, the ice particle size often varies through the year. Ice particle sizes in the tropics follow a different seasonal cycle than ice mixing ratio. North polar clouds have a complex seasonal cycle, with a sloped size profile with altitude as the polar hood cloud forms in early fall trending to a roughly uniform 1.5 m profile by the end of winter. These data are an important metric to validate and improve general circulation model microphysical routines and to better understand how martian water ice clouds influence the atmospheric radiative budget.

Scott D. Guzewich↗
NASA NTRS2006

Aerosol Indirect Effect Studies at Southern Great Plains During the May 2003 Intensive Operations Period

During May 2003 the Department of Energy's Atmospheric Radiation Measurement Program conducted an Intensive Operations Period (IOP) to measure the radiative effects of aerosol and clouds. A suite of both in situ and remote sensing measurements were available to measure aerosol and cloud parameters. This paper has three main goals: First, it focuses on comparison between in situ retrievals of the radiatively important drop effective radius r(sub e) and various satellite, airborne, and surface remote sensing retrievals of the same parameter. On 17 May 2003, there was a fortuitous, near-simultaneous sampling of a stratus cloud by five different methods. The retrievals of r(sub e) agree with one another to within approx.20%, which is approximately the error estimate for most methods. Second, a methodology for deriving a best estimate of r(sub e) from these different instruments, with their different physical properties and sampling volumes, is proposed and applied to the 17 May event. Third, the paper examines the response of r(sub e) to changes in aerosol on 3 days during the experiment and examines the consistency of remote sensing and in situ measurements of the effect of aerosol on r(sub e). It is shown that in spite of the generally good agreement in derived r(sub e), the magnitude of the response of r(sub e), to changes in aerosol is quite sensitive to the method of retrieving r(sub e) and to the aerosol proxy for cloud condensation nuclei. Nonphysical responses are sometimes noted, and it is suggested that further work needs to be done to refine these techniques.

Feingold, Graham↗
NASA NTRS1977

The evaporation of spherical clouds in a hot gas. II - Effects of radiation

The effects of radiation on the evaporation of spherical clouds in a hot medium are considered. The critical cloud radius at which radiative losses balance conductive heating is determined as a function of the external temperature and density. Smaller clouds evaporate, and larger clouds condense. The conditions under which the surfaces of the clouds may be detected are discussed. Net radiative losses for evaporating clouds are calculated, and an effective cooling function for a cloudy medium is obtained. The results may be applied to clouds in supernova remnants, in the interstellar medium, and in clusters of galaxies.

Mckee, C. F.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-27314-DND

The NASA Langley Research Center airborne High Spectral Resolution Lidar (HSRL-2) provided extensive measurements of smoke above shallow marine clouds while deployed from the NASA ER-2 aircraft during the NASA EV-S Observations of Aerosols above Clouds and their Interactions (ORACLES) mission. During the first ORACLES field campaign in September 2016, the ER-2 was deployed from Walvis Bay, Namibia and conducted flights over the southeastern Atlantic Ocean. HSRL-2 measured profiles of aerosol backscattering, depolarization, extinction and aerosol optical depth (AOD) at 355 and 532 nm and aerosol backscattering and depolarization at 1064 nm and so provided an excellent characterization of the wide-spread smoke layers above shallow marine clouds. We present profiles of aerosol microphysical properties such as concentration and effective radius that are derived from the HSRL-2 multiwavelength measurements of backscatter and extinction.

Detlef Müller↗
NASA NTRS1974

Interpretation of the polarization of Venus

The linear polarization of sunlight reflected by Venus is analyzed by comparing observations with extensive multiple scattering computations. The analysis establishes that Venus is veiled by a cloud or haze layer of spherical particles. The refractive index of the particles is about 1.44 at 0.55 microns with a normal dispersion, the refractive index decreasing from about 1.46 at 0.365 microns to 1.43 at 0.99 microns. The cloud particles have a narrow size distribution with a mean radius of about 1 micron; specifically, the effective radius of the size distribution is approximately 1.05 microns and the effective variance is about 0.07. The particles exist at a high level in the atmosphere, with the optical thickness unity occurring where the pressure is about 50 mb. The particle properties deduced from the polarization eliminate all but one of the cloud compositions which have been proposed for Venus. A concentrated solution of sulfuric acid provides good agreement with the polarization data.

Hansen, J. E.↗
NASA NTRS2017

Global Statistics of Microphysical Properties of Cloud-Top Ice Crystals

Ice crystals in clouds are highly complex. Their sizes, macroscale shape (i.e., habit), mesoscale shape (i.e., aspect ratio of components) and microscale shape (i.e., surface roughness) determine optical properties and affect physical properties such as fall speeds, growth rates and aggregation efficiency. Our current understanding on the formation and evolution of ice crystals under various conditions can be considered poor. Commonly, ice crystal size and shape are related to ambient temperature and humidity, but global observational statistics on the variation of ice crystal size and particularly shape have not been available. Here we show results of a project aiming to infer ice crystal size, shape and scattering properties from a combination of MODIS measurements and POLDER-PARASOL multi-angle polarimetry. The shape retrieval procedure infers the mean aspect ratios of components of ice crystals and the mean microscale surface roughness levels, which are quantifiable parameters that mostly affect the scattering properties, in contrast to a habit. We present global statistics on the variation of ice effective radius, component aspect ratio, microscale surface roughness and scattering asymmetry parameter as a function of cloud top temperature, latitude, location, cloud type, season, etc. Generally, with increasing height, sizes decrease, roughness increases, asymmetry parameters decrease and aspect ratios increase towards unity. Some systematic differences are observed for clouds warmer and colder than the homogeneous freezing level. Uncertainties in the retrievals will be discussed. These statistics can be used as observational targets for modeling efforts and to better constrain other satellite remote sensing applications and their uncertainties.

Van Diedenhoven, Bastiaan↗
NASA NTRS1990

Cloud optical parameters as derived from the multispectral cloud radiometer

Here, researchers analyze the data taken in the marine stratocumulus intensive field observation component of the First ISCCP Regional Experiment (FIRE), conducted off the California coast in July, 1987 using the Multispectral Cloud Radiometer (MCR). Researchers installed an efficient retrieval scheme for deriving the cloud optical thickness and droplet mode radius, and have described the behavior of the retrieval error. Generally the scheme can retrieve the optical thickness and mode radius adequately unless they are too small; the use of the forward scattering region is more sound than the use of the backscattering portion. Applying the method to real data, researchers derived the two-dimensional distribution of optical thickness and mode radius for a portion of one of the FIRE marine stratocumulus missions. In this case study, the droplet size showed a more uniform distribution than optical thickness with some correlation between large droplet size and small optical thickness. Although researchers can find microphysical reasons for these tendencies, they suspect that the remotely sensed droplet size may be overestimated. As a future problem, they will compare results with in situ data of the droplet size distribution. Also it will be very important to check several reasons why the droplet radius might be overestimated, e.g., soot contamination, effect of escaping photons from the lateral sides of broken clouds, and so on.

Nakajima, Eruyuki↗
NASA NTRS1998

Galileo Probe Measurements of Thermal and Solar Radiation Fluxes in the Jovian Atmosphere

The Galileo probe net flux radiometer (NFR) measured radiation fluxes in Jupiter's atmosphere from about 0.44 to 14 bars, using five spectral channels to separate solar and thermal components. Onboard calibration results confirm that the NFR responded to radiation approximately as expected. NFR channels also responded to a superimposed thermal perturbation, which can be approximately removed using blind channel measurements and physical constraints. Evidence for the expected NH3 cloud was seen in the spectral character of spin-induced modulations of the direct solar beam signals. These results are consistent with an overlying cloud of small NH3 ice particles (0.5-0.75 microns in radius) of optical depth 1.5-2 at 0.5 microns. Such a cloud would have so little effect on thermal fluxes that NFR thermal channels provide no additional constraints on its properties. However, evidence for heating near 0.45 bar in the NFR thermal channels would seem to require either an additional opacity source beyond this small-particle cloud, implying a heterogeneous cloud structure to avoid conflicts with solar modulation results, or a change in temperature lapse rate just above the probe measurements. The large thermal flux levels imply water vapor mixing ratios that are only 6% of solar at 10 bars, but possibly increasing with depth, and significantly subsaturated ammonia at pressures less than 3 bars. If deep NH3 mixing ratios at the probe entry site are 3-4 times ground-based inferences, as suggested by probe radio signal attenuation, then only half as much water is needed to match NFR observations. No evidence of a water cloud was seen near the 5-bar level. The 5-microns thermal channel detected the presumed NH4SH cloud base near 1.35 bars. Effects of this cloud were also seen in the solar channel upflux measurements but not in the solar net fluxes, implying that the cloud is a conservative scatterer of sunlight. The minor thermal signature of this cloud is compatible with particle radii near 3 gm, but it cannot rule out smaller particles. Deeper than about 3 bars, solar channels indicate unexpectedly large absorption of sunlight at wavelengths longer than 0.6 microns, which might be due to unaccounted-for absorption by NH3 between 0.65 and 1.5 microns.

Sromovsky, L. A.↗
NASA NTRS1998

Galileo Probe Measurements of Thermal and Solar Radiation Fluxes in the Jovian Atmosphere

The Galileo probe net flux radiometer (NFR) measured radiation fluxes in Jupiter's atmosphere from about 0.44 to 14 bars, using five spectral channels to separate solar and thermal components. Onboard calibration results confirm that the NFR responded to radiation approximately as expected. NFR channels also responded to a superimposed thermal perturbation, which can be approximately removed using blind channel measurements and physical constraints. Evidence for the expected NH3 cloud was seen in the spectral character of spin-induced modulations of the direct solar beam signals. These results are consistent with an overlying cloud of small NH3 ice particles (0.5-0.75 microns in radius) of optical depth 1.5-2 at 0.5 microns. Such a cloud would have so little effect on thermal fluxes that NFR thermal channels provide no additional constraints on its properties. However, evidence for heating near 0.45 bar in the NFR thermal channels would seem to require either an additional opacity source beyond this small-particle cloud, implying a heterogeneous-cloud structure to avoid conflicts with solar modulation results, or a change in temperature lapse rate just above the probe measurements. The large thermal flux levels imply water vapor mixing ratios that are only 6% of solar at 10 bars, but possibly increasing with depth, and significantly subsaturated ammonia at pressures less than 3 bars. If deep NH3 mixing ratios at the probe entry site are 3-4 times ground-based inferences, as suggested by probe radio signal attenuation, then only half as much water is needed to match NFR observations. No evidence of a water cloud was seen near the 5-bar level. The 5 microns thermal channel detected the presumed NH4SH cloud base near 1.35 bars. Effects of this cloud were also seen in the solar channel upflux measurements but not in the solar net fluxes, implying that the cloud is a conservative scatterer of sunlight. The minor thermal signature of this cloud is compatible with particle radii near 3 microns, but it cannot rule out smaller particles. Deeper than about 3 bars, solar channels indicate unexpectedly large absorption of sunlight at wavelengths longer than 0.6 microns, which might be due to unaccounted-for absorption by NH3 between 0.65 and 1.5 microns.

Sromovsky, L. A.↗
NASA NTRS1995

Laboratory Investigation of Direct Measurement of Ice Water Content, Ice Surface Area, and Effective Radius of Ice Crystals Using a Laser-Diffraction Instrument

The aircraft microphysics probe, PVM-100A, was tested in the Colorado State University dynamic cloud chamber to establish its ability to measure ice water content (IWC), PSA, and Re in ice clouds. Its response was compared to other means of measuring those ice-cloud parameters that included using FSSP-100 and 230-X 1-D optical probes for ice-crystal concentrations, a film-loop microscope for ice-crystal habits and dimensions, and an in-situ microscope for determining ice-crystal orientation. Intercomparisons were made in ice clouds containing ice crystals ranging in size from about 10 microns to 150 microns diameter, and ice crystals with plate, columnar, dendritic, and spherical shapes. It was not possible to determine conclusively that the PVM accurately measures IWC, PSA, and Re of ice crystals, because heat from the PVM evaporated in part the crystals in its vicinity in the chamber thus affecting its measurements. Similarities in the operating principle of the FSSP and PVM, and a comparison between Re measured by both instruments, suggest, however, that the PVM can make those measurements. The resolution limit of the PVM for IWC measurements was found to be on the order of 0.001 g/cubic m. Algorithms for correcting IWC measured by FSSP and PVM were developed.

Gerber, H.↗