scholarly journals The Dimensional Characteristics of Ice Crystal Aggregates from Fractal Geometry

2010 ◽  
Vol 67 (5) ◽  
pp. 1605-1616 ◽  
Author(s):  
C. G. Schmitt ◽  
A. J. Heymsfield
Keyword(s):  
Fractal Dimension ◽  
Water Content ◽  
Fractal Geometry ◽  
Ice Crystal ◽  
Temperature Dependent ◽  
Projected Area ◽  
Cloud Particle ◽  
Self Consistent ◽  
Ice Water Content ◽  
Ice Water

Abstract Ice crystal aggregates imaged by aircraft particle imaging probes often appear to be fractal in nature. As such, their dimensional properties, mass, and projected area can be related using fractal geometry. In cloud microphysics, power-law mass (m)– and area (A)–dimensional (D) relationships (e.g., m = aDb) incorporate different manifestations of the fractal dimension as the exponent (b). In this study a self-consistent technique is derived for determining the mass and projected area properties of ice particles from fractal geometry. A computer program was developed to simulate the crystal aggregation process. The fractal dimension of the simulated aggregates was estimated using the box counting method in three dimensions as well as for two-dimensional projected images of the aggregates. The two- and three-dimensional fractal dimension values were found to be simply related. This relationship enabled the development of mass–dimensional relationships analytically from cloud particle images. This technique was applied to data collected during two field projects. The exponent in the mass–dimensional relationship, the fractal dimension, was found to be between 2.0 and 2.3 with a dependence on temperature noted for both datasets. The coefficient a in the mass–dimensional relationships was derived in a self-consistent manner. Temperature-dependent mass–dimensional relationships have been developed. Cloud ice water content estimated using the temperature-dependent relationship and particle size distributions agreed well with directly measured ice water content values. The results are appropriate for characterizing cloud particle properties in clouds with high concentrations of ice crystal aggregates.

scholarly journals Understanding effective diameter and its application to terrestrial radiation in ice clouds

2011 ◽  
Vol 11 (7) ◽  
pp. 3417-3429 ◽  
Author(s):  
D. L. Mitchell ◽  
R. P. Lawson ◽  
B. Baker
Keyword(s):  
Water Content ◽  
Climate Modeling ◽  
Effective Diameter ◽  
Projected Area ◽  
Cloud Particle ◽  
Ice Clouds ◽  
Wave Resonance ◽  
Cloud Water Content ◽  
Ice Water Content ◽  
Ice Water

Abstract. The cloud property known as "effective diameter" or "effective radius", which in essence is the cloud particle size distribution (PSD) volume at bulk density divided by its projected area, is used extensively in atmospheric radiation transfer, climate modeling and remote sensing. This derives from the assumption that PSD optical properties can be uniquely described in terms of their effective diameter, De, and their cloud water content (CWC), henceforth referred to as the De-CWC assumption. This study challenges this assumption, showing that while the De-CWC assumption appears generally valid for liquid water clouds, it appears less valid for ice clouds in regions where (1) absorption is not primarily a function of either the PSD ice water content (IWC) or the PSD projected area, and (2) where wave resonance (i.e. photon tunneling) contributes significantly to absorption. These two regions often strongly coincide at terrestrial wavelengths when De

scholarly journals Understanding effective diameter and its application to terrestrial radiation in ice clouds

2010 ◽  
Vol 10 (12) ◽  
pp. 29405-29447
Author(s):  
D. L. Mitchell ◽  
R. P. Lawson ◽  
B. Baker
Keyword(s):  
Water Content ◽  
Climate Modeling ◽  
Effective Diameter ◽  
Projected Area ◽  
Cloud Particle ◽  
Ice Clouds ◽  
Wave Resonance ◽  
Cloud Water Content ◽  
Ice Water Content ◽  
Ice Water

Abstract. The cloud property known as "effective diameter" or "effective radius", which in essence is the cloud particle size distribution (PSD) volume at bulk density divided by its projected area, is used extensively in atmospheric radiation transfer, climate modeling and remote sensing. This derives from the assumption that PSD optical properties can be uniquely described in terms of their effective diameter, De, and their cloud water content (CWC), henceforth referred to as the De–CWC assumption. This study challenges this assumption, showing that while the De–CWC assumption appears generally valid for liquid water clouds, it appears less valid for ice clouds in regions where (1) absorption is not primarily a function of either the PSD ice water content (IWC) or the PSD projected area, and (2) where wave resonance (i.e. photon tunneling) contributes significantly to absorption. These two regions often strongly coincide at terrestrial wavelengths when De

scholarly journals In-situ measurements of tropical cloud properties in the West African monsoon: upper tropospheric ice clouds, mesoscale convective system outflow, and subvisual cirrus

2011 ◽  
Vol 11 (1) ◽  
pp. 745-812 ◽  
Author(s):  
W. Frey ◽  
S. Borrmann ◽  
D. Kunkel ◽  
R. Weigel ◽  
M. de Reus ◽  
...  
Keyword(s):  
Water Content ◽  
Potential Temperature ◽  
In Situ Measurements ◽  
Size Distributions ◽  
Ice Crystal ◽  
Cloud Particle ◽  
Ice Particles ◽  
Ice Water Content ◽  
Ice Water

Abstract. In-situ measurements of ice crystal size distributions in tropical upper troposphere/lower stratosphere (UT/LS) clouds were performed during the SCOUT-AMMA campaign over West Africa in August 2006. The cloud properties were measured with a Forward Scattering Spectrometer Probe (FSSP-100) and a Cloud Imaging Probe (CIP) operated aboard the Russian high altitude research aircraft M-55 ''Geophysica'' with the mission base in Ouagadougou, Burkina Faso. A total of 117 ice particle size distributions were obtained from the measurements in the vicinity of Mesoscale Convective Systems (MCS). Two or three modal lognormal size distributions were fitted to the average size distributions for different potential temperature bins. The measurements showed proportionate more large ice particles compared to former measurements above maritime regions. With the help of trace gas measurements of NO, NOy, CO2, CO, and O3, and satellite images clouds in young and aged MCS outflow were identified. These events were observed at altitudes of 11.0 km to 14.2 km corresponding to potential temperature levels of 346 K to 356 K. In a young outflow (developing MCS) ice crystal number concentrations of up to 8.3 cm−3 and rimed ice particles with maximum dimensions exceeding 1.5 mm were found. A maximum ice water content of 0.05 g m−3 was observed and an effective radius of about 90 μm. In contrast the aged outflow events were more diluted and showed a maximum number concentration of 0.03 cm−3, an ice water content of 2.3 × 10−4 g m−3, an effective radius of about 18 μm, while the largest particles had a maximum dimension of 61 μm. Close to the tropopause subvisual cirrus were encountered four times at altitudes of 15 km to 16.4 km. The mean ice particle number concentration of these encounters was 0.01 cm−3 with maximum particle sizes of 130 μm, and the mean ice water content was about 1.4 × 10−4 g m−3. All known in-situ measurements of subvisual tropopause cirrus are compared and an exponential fit on the size distributions is established in order to give a parameterisation for modelling. A comparison of aerosol to ice crystal number concentrations, in order to obtain an estimate on how many ice particles result from activation of the present aerosol, yielded low activation ratios for the subvisual cirrus cases of roughly one cloud particle per 30 000 aerosol particles, while for the MCS outflow cases this resulted in a high ratio of one cloud particle per 300 aerosol particles.

scholarly journals In situ measurements of tropical cloud properties in the West African Monsoon: upper tropospheric ice clouds, Mesoscale Convective System outflow, and subvisual cirrus

2011 ◽  
Vol 11 (12) ◽  
pp. 5569-5590 ◽  
Author(s):  
W. Frey ◽  
S. Borrmann ◽  
D. Kunkel ◽  
R. Weigel ◽  
M. de Reus ◽  
...  
Keyword(s):  
Water Content ◽  
Potential Temperature ◽  
In Situ Measurements ◽  
Size Distributions ◽  
Ice Crystal ◽  
Cloud Particle ◽  
Ice Particles ◽  
Ice Water Content ◽  
Ice Water

Abstract. In situ measurements of ice crystal size distributions in tropical upper troposphere/lower stratosphere (UT/LS) clouds were performed during the SCOUT-AMMA campaign over West Africa in August 2006. The cloud properties were measured with a Forward Scattering Spectrometer Probe (FSSP-100) and a Cloud Imaging Probe (CIP) operated aboard the Russian high altitude research aircraft M-55 Geophysica with the mission base in Ouagadougou, Burkina Faso. A total of 117 ice particle size distributions were obtained from the measurements in the vicinity of Mesoscale Convective Systems (MCS). Two to four modal lognormal size distributions were fitted to the average size distributions for different potential temperature bins. The measurements showed proportionately more large ice particles compared to former measurements above maritime regions. With the help of trace gas measurements of NO, NOy, CO2, CO, and O3 and satellite images, clouds in young and aged MCS outflow were identified. These events were observed at altitudes of 11.0 km to 14.2 km corresponding to potential temperature levels of 346 K to 356 K. In a young outflow from a developing MCS ice crystal number concentrations of up to (8.3 ± 1.6) cm−3 and rimed ice particles with maximum dimensions exceeding 1.5 mm were found. A maximum ice water content of 0.05 g m−3 was observed and an effective radius of about 90 μm. In contrast the aged outflow events were more diluted and showed a maximum number concentration of 0.03 cm−3, an ice water content of 2.3 × 10−4 g m−3, an effective radius of about 18 μm, while the largest particles had a maximum dimension of 61 μm. Close to the tropopause subvisual cirrus were encountered four times at altitudes of 15 km to 16.4 km. The mean ice particle number concentration of these encounters was 0.01 cm−3 with maximum particle sizes of 130 μm, and the mean ice water content was about 1.4 × 10−4 g m−3. All known in situ measurements of subvisual tropopause cirrus are compared and an exponential fit on the size distributions is established for modelling purposes. A comparison of aerosol to ice crystal number concentrations, in order to obtain an estimate on how many ice particles may result from activation of the present aerosol, yielded low ratios for the subvisual cirrus cases of roughly one cloud particle per 30 000 aerosol particles, while for the MCS outflow cases this resulted in a high ratio of one cloud particle per 300 aerosol particles.

scholarly journals Ice particle sampling from aircraft – influence of the probing position on the ice water content

2017 ◽  
Author(s):  
Armin Afchine ◽  
Christian Rolf ◽  
Anja Costa ◽  
Nicole Spelten ◽  
Martin Riese ◽  
...  
Keyword(s):  
Water Content ◽  
Radiative Properties ◽  
Closed Path ◽  
Ice Crystal ◽  
Aircraft Wing ◽  
Cloud Particle ◽  
Particle Sampling ◽  
Ice Water Content ◽  
The Mean ◽  
Ice Water

Abstract. The ice water content (IWC) of cirrus clouds is an essential parameter determining their radiative properties and thus is important for climate simulations. Therefore, for a reliable measurement of IWC on board of research aircraft, it is important to carefully design the ice crystal sampling and measuring devices. During the HALO field campaign ML-CIRRUS in 2014, IWC was recorded by three closed path total water together with one gas phase water instrument. The hygrometers were supplied by inlets mounted on the roof of the aircraft fuselage. Simultaneously, the IWC is determined by a cloud particle spectrometer attached under an aircraft wing. Two more examples of simultaneous IWC measurements by hygrometers and cloud spectrometers are presented, but the inlets of the hygrometers were mounted at the fuselage side (Geophysica, StratoClim campaign 2017) and bottom (WB57, MacPex 2011). This combination of instruments and inlet positions provides the opportunity to experimentally study the influence of the ice particle sampling position on the IWC. As expected from theoretical considerations, we found that the IWCs provided by the roof inlets deviate from those measured under the aircraft wing. Caused by the inlet position in the shadow-zone behind the aircraft cockpit, ice particles populations with mean mass sizes larger than about 25 μm radius are subject to losses, which lead to strongly underestimated IWCs. On the other hand, cloud populations with mean mass sizes smaller than about 12 μm are dominated by particle enrichment and thus overestimated IWCs. In the range of mean mass sizes between 12 and 25 μm, both enrichment and losses of ice crystal can occur, depending on whether the ice crystal mass peak of the – in these cases bimodal – size distribution is on the smaller or larger mass mode. The resulting deviations of the IWC reach factors of up to 10 or even more for losses as well as for enrichment. Since the mean mass size of ice crystals increases with temperature, losses are more pronounced at higher temperatures while at lower temperatures IWC is more affected by enrichment. In contrast, in the cases where the hygrometer inlets were mounted at the fuselage side or bottom, the agreement of IWCs is – due to undisturbed ice particle sampling, as expected from theory – most frequently within a factor of 2.5, independently of the mean ice crystal sizes. Summarizing, in case IWC needs to be detected solely by measurements from closed path hygrometers, it is crucial for a solid measurement to mount the respective inlets at the aircraft’s side or bottom.

Analytical Solutions to the Stochastic Kinetic Equation for Liquid and Ice Particle Size Spectra. Part II: Large-Size Fraction in Precipitating Clouds

2008 ◽  
Vol 65 (7) ◽  
pp. 2044-2063 ◽  
Author(s):  
Vitaly I. Khvorostyanov ◽  
Judith A. Curry
Keyword(s):  
Kinetic Equation ◽  
Water Content ◽  
Analytical Solutions ◽  
Algebraic Function ◽  
Size Fraction ◽  
Cloud Particle ◽  
Size Spectra ◽  
Large Size ◽  
Ice Water Content ◽  
Ice Water

Abstract The stochastic kinetic equation is solved analytically for precipitating particles that can be identified as rain, snow, and graupel. The general solution for the size spectra of the large-size particles is represented by the product of an exponential term and a term that is an algebraic function of radius. The slope of the exponent consists of the Marshall–Palmer slope and an additional integral that is a function of the radius. Both the integral and algebraic terms depend on the condensation and accretion rates, vertical velocity, turbulence coefficient, terminal velocity of the particles, and the vertical gradient of the liquid (ice) water content. At sufficiently large radii, the radius dependence of the algebraic term is a power law, and the spectra have the form of gamma distributions. Simple analytical expressions are derived for the slopes and indices of the size distributions. These solutions provide explanations of the observed dependencies of the cloud particle spectra in different phases and size regimes on temperature, height, turbulence, vertical velocities, liquid or ice water content, and other cloud properties. These analytical solutions and expressions for the slopes and shape parameters can be used for parameterization of the spectra of precipitating particles and related quantities (e.g., optical properties, radar reflectivities) in bulk cloud microphysical parameterizations and in remote sensing techniques.

Evaluation of Collocated Measurements of Radar Reflectivity and Particle Sizes in Ice Clouds

2011 ◽  
Vol 50 (10) ◽  
pp. 2104-2119 ◽  
Author(s):  
Binod Pokharel ◽  
Gabor Vali
Keyword(s):  
Water Content ◽  
Particle Density ◽  
Radar Data ◽  
Precipitation Rate ◽  
Ice Crystal ◽  
Ice Clouds ◽  
Sampling Locations ◽  
Ice Water Content ◽  
Particle Imaging ◽  
Ice Water

AbstractMeasured 94-GHz reflectivity in midlevel, stratiform ice clouds was compared with reflectivity calculated from size distributions determined with a particle imaging probe. The radar and the particle probe were carried on the same aircraft, the Wyoming King Air, ensuring close spatial correspondence between the two measurements. Good overall agreement was found within the range from −18 to +16 dBZ, but there is an important degree of scatter in the results. Two different assumptions about particle density led to calculated values that bracket the observations. The agreement found for reflectivity supports the use of the data for establishing relationships between the measured reflectivity and ice water content and between precipitation rate and reflectivity. The resulting equation for ice water content (IWC vs Z) agrees with the results of Liu and Illingworth within a factor of 2 over the range of overlap between the two datasets. The equation here reported for precipitation rate (PR vs Z) has a shallower slope in the power-law relationship than that reported by Matrosov as a consequence of sampling particles of greater densities. Because the radar and the particle probe were collocated on the same platform, errors arising from differences in sampling locations and volumes were minimized. Therefore it is concluded that the roughly factor-of-10 spread in IWC and in PR for given Z is, primarily, a result of variations in ice crystal shape and density. Retrievals of IWC and PR from cloud radar data can be expected to have that level of uncertainty.

Improvement in Determination of Ice Water Content from Two-Dimensional Particle Imagery. Part II: Applications to Collected Data

2006 ◽  
Vol 45 (9) ◽  
pp. 1291-1303 ◽  
Author(s):  
R. Paul Lawson ◽  
Brad A. Baker
Keyword(s):  
Particle Size ◽  
Water Content ◽  
Particle Mass ◽  
Two Dimensional ◽  
Projected Area ◽  
Ice Water Content ◽  
Rms Error ◽  
Particle Size And Shape ◽  
Ice Water

Abstract In Part I of this two-part series, a new relationship for ice particle mass M was derived based on an expanded dataset of photographed ice particles and melted drops. The new relationship resulted in a reduction of nearly 50% in the rms error in M. In this paper, new relationships for computing particle mass and ice water content from 2D particle imagery are compared with other relationships previously used in the literature. Comparison of the old and new relationships, when applied to data collected in natural clouds, shows that results using the old relationships differ from the new relationships by up to a factor of 3, depending on particle size and shape. One of the new relationships can be applied to existing (archived) datasets of two-dimensional images, provided that the number of occulted pixels in each image (i.e., projected area) is available.

scholarly journals Ice Crystal Sizes in High Ice Water Content Clouds. Part II: Statistics of Mass Diameter Percentiles in Tropical Convection Observed during the HAIC/HIWC Project

2017 ◽  
Vol 34 (1) ◽  
pp. 117-136 ◽  
Author(s):  
D. Leroy ◽  
E. Fontaine ◽  
A. Schwarzenboeck ◽  
J. W. Strapp ◽  
A. Korolev ◽  
...  
Keyword(s):  
Water Content ◽  
Ice Crystals ◽  
Ice Crystal ◽  
Potential Threat ◽  
Convective Systems ◽  
Imaging Probes ◽  
Ice Water Content ◽  
The Individual ◽  
Particle Imaging ◽  
Ice Water

AbstractHigh ice water content (IWC) regions in mesoscale convective systems (MCSs) are a potential threat to commercial aviation, as they are suspected to cause in-service engine power-loss events and air data probe malfunctions. To investigate this, the high-altitude ice crystals (HAIC)/high ice water content (HIWC) projects set up a first field campaign in Darwin (Australia) in 2014. The airborne instrumentation was selected to provide the most accurate measurements of both the bulk total water content (TWC), using a specially developed isokinetic evaporator, and the individual ice crystals properties, using particle imaging probes.This study focuses on determining the size ranges of ice crystals responsible for the mass in high IWC regions, defined here as cloud regions with IWC greater than 1.5 g m−3. It is shown that for high IWC areas in most of the encountered MCSs, median mass diameters (MMDs) of ice crystals range from 250 to 500 μm and decrease with increasing TWC and decreasing temperature. At the same time, the mass contribution of the smallest crystals (below 100 μm) remains generally low (below 15%).In contrast, data from two flight missions in a long-lasting quasi-stationary tropical storm reveal that high IWC values can also be associated with MMDs in the range 400–800 μm and peak values of up to 2 mm. Ice crystal images suggest a major growth contribution by vapor deposition (columns, capped columns) even for such larger MMD values.

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