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.

Analytical Solutions to the Stochastic Kinetic Equation for Liquid and Ice Particle Size Spectra. Part I: Small-Size Fraction

2008 ◽  
Vol 65 (7) ◽  
pp. 2025-2043 ◽  
Author(s):  
Vitaly I. Khvorostyanov ◽  
Judith A. Curry
Keyword(s):  
Water Content ◽  
Analytical Solutions ◽  
Climate Models ◽  
Size Fraction ◽  
Size Spectra ◽  
Cloud Liquid Water ◽  
Gamma Distributions ◽  
Ice Water Content ◽  
Cloud Ice ◽  
Ice Water

Abstract The kinetic equation of stochastic condensation for cloud drop size spectra is extended to account for crystalline clouds and also to include the accretion–aggregation process. The size spectra are separated into small and large size fractions that correspond to cloud drops (ice) and rain (snow). In Part I of this two-part paper, analytical solutions are derived for the small-size fractions of the spectra that correspond to cloud drops and cloud ice particles that can be identified with cloud liquid water or cloud ice water content, and used in bulk microphysical schemes employed in cloud and climate models. Solutions for the small-size fraction have the form of generalized gamma distributions. Simple analytical expressions are found for parameters of the gamma distributions that are functions of quantities that are available in cloud and climate models: liquid or ice water content and its vertical gradient, mean particle radius or concentration, and supersaturation or vertical velocities. Equations for the gamma distribution parameters provide an explanation of the dependence of the observed spectra on atmospheric dynamics, cloud temperature, and cloud liquid water or ice water content. The results are illustrated with example calculations for a crystalline cloud. The analytical solutions and expressions for the parameters presented here can be used for parameterization of the small-size fraction size spectra in liquid and crystalline clouds and related quantities (e.g., optical properties, lidar, and radar reflectivities).

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 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 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 A two-channel, tunable diode laser-based hygrometer for measurement of water vapor and cirrus cloud ice water content in the upper troposphere and lower stratosphere

2015 ◽  
Vol 8 (1) ◽  
pp. 211-224 ◽  
Author(s):  
T. D. Thornberry ◽  
A. W. Rollins ◽  
R. S. Gao ◽  
L. A. Watts ◽  
S. J. Ciciora ◽  
...  
Keyword(s):  
Water Vapor ◽  
Water Content ◽  
Lower Stratosphere ◽  
Tunable Diode Laser ◽  
Cirrus Cloud ◽  
Total Water ◽  
Cloud Particle ◽  
Upper Troposphere ◽  
Ice Water Content ◽  
Ice Water

Abstract. The recently developed NOAA Water instrument is a two-channel, closed-path, tunable diode laser absorption spectrometer designed for the measurement of upper troposphere/lower stratosphere water vapor and enhanced total water (vapor + inertially enhanced condensed phase) from the NASA Global Hawk unmanned aircraft system (UAS) or other high-altitude research aircraft. The instrument utilizes wavelength-modulated spectroscopy with second harmonic detection near 2694 nm to achieve high precision with a 79 cm double-pass optical path. The detection cells are operated under constant temperature, pressure, and flow conditions to maintain a constant sensitivity to H2O independent of the ambient sampling environment. An onboard calibration system is used to perform periodic in situ calibrations to verify the stability of the instrument sensitivity during flight. For the water vapor channel, ambient air is sampled perpendicular to the flow past the aircraft in order to reject cloud particles, while the total water channel uses a heated, forward-facing inlet to sample both water vapor and cloud particles. The total water inlet operates subisokinetically, thereby inertially enhancing cloud particle number in the sample flow and affording increased cloud water content sensitivity. The NOAA Water instrument was flown for the first time during the second deployment of the Airborne Tropical TRopopause EXperiment (ATTREX) in February–March 2013 on the NASA Global Hawk UAS. The instrument demonstrated a typical in-flight precision (1 s, 1σ) of better than 0.17 parts per million (ppm, 10−6 mol mol−1), with an overall H2O vapor measurement uncertainty of 5% ± 0.23 ppm. The inertial enhancement for cirrus cloud particle sampling under ATTREX flight conditions ranged from 33 to 48 for ice particles larger than 8 μm in diameter, depending primarily on aircraft altitude. The resulting ice water content detection limit (2σ) was 0.023–0.013 ppm, corresponding to approximately 2 μg m−3, with an estimated overall uncertainty of 20%.

scholarly journals A two-channel, tunable diode laser-based hygrometer for measurement of water vapor and cirrus cloud ice water content in the upper troposphere and lower stratosphere

2014 ◽  
Vol 7 (8) ◽  
pp. 8271-8309 ◽  
Author(s):  
T. D. Thornberry ◽  
A. W. Rollins ◽  
R. S. Gao ◽  
L. A. Watts ◽  
S. J. Ciciora ◽  
...  
Keyword(s):  
Water Vapor ◽  
Water Content ◽  
Lower Stratosphere ◽  
Tunable Diode Laser ◽  
Cirrus Cloud ◽  
Total Water ◽  
Cloud Particle ◽  
Upper Troposphere ◽  
Ice Water Content ◽  
Ice Water

Abstract. The recently developed NOAA Water instrument is a two-channel, closed-path, tunable diode laser absorption spectrometer designed for the measurement of water vapor and enhanced total water (vapor + inertially enhanced condensed-phase) in the upper troposphere/lower stratosphere from the NASA Global Hawk unmanned aircraft system (UAS) or other high-altitude research aircraft. The instrument utilizes wavelength-modulated spectroscopy with second harmonic detection near 2694 nm to achieve high precision with a 79 cm double-pass optical path. The detection cells are operated under constant temperature, pressure and flow conditions to maintain a constant sensitivity to H2O independent of the ambient sampling environment. An on-board calibration system is used to perform periodic in situ calibrations to verify the stability of the instrument sensitivity during flight. For the water vapor channel, ambient air is sampled perpendicular to the flow past the aircraft in order to reject cloud particles, while the total water channel uses a heated, forward-facing inlet to sample both water vapor and cloud particles. The total water inlet operates subisokinetically, thereby inertially enhancing cloud particle number in the sample flow and affording increased cloud water content sensitivity. The NOAA Water instrument was flown for the first time during the second deployment of the Airborne Tropical TRopopause EXperiment (ATTREX) in February–March 2013 on board the Global Hawk UAS. The instrument demonstrated a typical in-flight precision (1 s, 1σ) of better than 0.17 parts per million (ppm, 10−6 mol mol−1), with an overall H2O vapor measurement uncertainty of 5% ± 0.23 ppm. The inertial enhancement for cirrus cloud particle sampling under ATTREX flight conditions ranged from 33–48 for ice particles larger than 8 μm in diameter, depending primarily on aircraft altitude. The resulting ice water content detection limit (2σ) was 0.023–0.013 ppm, corresponding to approximately 2 μg m−3, with an estimated overall uncertainty of 20%.

The impact of ice cloud particle microphysics on the uncertainty of ice water content retrievals

2011 ◽  
Vol 112 (2) ◽  
pp. 189-196 ◽  
Author(s):  
Wenbo Sun ◽  
Yongxiang Hu ◽  
Bing Lin ◽  
Zhaoyan Liu ◽  
Gorden Videen
Keyword(s):  
Water Content ◽  
Cloud Particle ◽  
Ice Cloud ◽  
Ice Water Content ◽  
Ice Water ◽  
The Impact

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.

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