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).

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.

scholarly journals Changes in the shape of cloud ice water content vertical structure due to aerosol variations

2016 ◽  
Vol 16 (10) ◽  
pp. 6091-6105 ◽  
Author(s):  
Steven T. Massie ◽  
Julien Delanoë ◽  
Charles G. Bardeen ◽  
Jonathan H. Jiang ◽  
Lei Huang
Keyword(s):  
Water Content ◽  
Vertical Structure ◽  
Distribution Functions ◽  
Ozone Monitoring Instrument ◽  
Modis Aod ◽  
Ice Water Content ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
Cloud Ice ◽  
Ice Water ◽  
Derivatives Of

Abstract. Changes in the shape of cloud ice water content (IWC) vertical structure due to variations in Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depths (AODs), Ozone Monitoring Instrument (OMI) absorptive aerosol optical depths (AAODs), and Microwave Limb Sounder (MLS) CO (an absorptive aerosol proxy) at 215 hPa are calculated in the Tropics during 2007–2010 based upon an analysis of DARDAR IWC profiles for deep convective clouds. DARDAR profiles are a joint retrieval of CloudSat-CALIPSO data. Analysis is performed for 12 separate regions over land and ocean, and carried out applying MODIS AOD fields that attempt to correct for 3-D cloud adjacency effects. The 3-D cloud adjacency effects have a small impact upon our particular calculations of aerosol–cloud indirect effects. IWC profiles are averaged for three AOD bins individually for the 12 regions. The IWC average profiles are also normalized to unity at 5 km altitude in order to study changes in the shape of the average IWC profiles as AOD increases. Derivatives of the IWC average profiles, and derivatives of the IWC shape profiles, in percent change per 0.1 change in MODIS AOD units, are calculated separately for each region. Means of altitude-specific probability distribution functions, which include both ocean and land IWC shape regional derivatives, are modest, near 5 %, and positive to the 2σ level between 11 and 15 km altitude. Similar analyses are carried out for three AAOD and three CO bins. On average, the vertical profiles of the means of the derivatives based upon the profile shapes over land and ocean are smaller for the profiles binned according to AAOD and CO values, than for the MODIS AODs, which include both scattering and absorptive aerosol. This difference in character supports the assertion that absorptive aerosol can inhibit cloud development.

scholarly journals Changes in the shape of cloud ice water content vertical structure due to aerosol variations

2016 ◽  
Author(s):  
Steven T. Massie ◽  
Julien Delanoe ◽  
Charles G. Bardeen
Keyword(s):  
Water Content ◽  
Vertical Structure ◽  
Distribution Functions ◽  
Convective Clouds ◽  
Modis Aod ◽  
Ice Water Content ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
Cloud Ice ◽  
Ice Water ◽  
Derivatives Of

Abstract. Changes in the shape of cloud ice water content vertical structure due to aerosol variations are calculated in the Tropics during 2007–2010 based upon an analysis of DARDAR ice water content (IWC) profiles for deep convective clouds. DARDAR profiles are a joint retrieval of CloudSat-CALIPSO data. Our analysis is performed for 12 separate regions over land and ocean, and carried out applying Moderate-Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD) fields that attempt to correct for 3D cloud adjacency effects. The 3D cloud adjacency effects have a small impact upon our calculations of aerosol-cloud indirect effects. IWC profiles are averaged for three AOD bins individually for the 12 regions. The IWC average profiles are also normalized to unity at 5 km altitude in order to study changes in the shape of the average IWC profiles as AOD increases. Derivatives of the IWC average profiles, and derivatives of the IWC shape profiles, in percent change per 0.1 change in MODIS AOD units, are calculated separately for each region. Means of altitude-specific probability distribution functions, which include both ocean and land IWC shape regional derivatives, are modest, near 5 %, and positive to the 2σ level between 11 and 15 km altitude.

scholarly journals Ice water content of arctic, midlatitude, and tropical cirrus – Part 2: Extension of the database and new statistical analysis

2012 ◽  
Vol 12 (11) ◽  
pp. 29443-29474 ◽  
Author(s):  
A. E. Luebke ◽  
L. M. Avallone ◽  
C. Schiller ◽  
C. Rolf ◽  
M. Krämer
Keyword(s):  
Water Content ◽  
Radiative Forcing ◽  
Climate Models ◽  
Distribution Functions ◽  
Formation Mechanisms ◽  
Mean Values ◽  
Microphysical Properties ◽  
Ice Water Content ◽  
Ground Based Lidar ◽  
Ice Water

Abstract. Ice clouds are known to be major contributors to radiative forcing in the Earth's atmosphere, yet describing their microphysical properties in climate models remains challenging. Among these properties, the ice water content (IWC) of cirrus clouds is of particular interest both because it is measurable and because it can be directly related to a number of other radiatively important variables such as extinction and effective radius. This study expands upon the work of Schiller et al. (2008), extending a climatology of IWC by combining datasets from several European and US airborne campaigns and ground-based lidar measurements over Jülich, Germany. The relationship between IWC and temperature is further investigated using the new merged dataset and probability distribution functions (PDFs). A PDF-based formulation allows for representation of not only the mean values of IWC, but also the variability of IWC within a temperature band. The IWC-PDFs are found to be bimodal over the whole cirrus temperature range, which might be attributed to different cirrus formation mechanisms such as heterogeneous and homogeneous freezing. The PDFs of IWC are further compared to distributions of cirrus ice crystal number and mass mean radius, which show that the general relationship between IWC and temperature appears to be influenced much more by particle number than by particle size.

scholarly journals Cloud ice water content retrieved from the CALIOP space-based lidar

2012 ◽  
Vol 39 (5) ◽  
pp. n/a-n/a ◽  
Author(s):  
Melody Avery ◽  
David Winker ◽  
Andrew Heymsfield ◽  
Mark Vaughan ◽  
Stuart Young ◽  
...  
Keyword(s):  
Water Content ◽  
Ice Water Content ◽  
Cloud Ice ◽  
Ice Water

scholarly journals Relationships between Ice Water Content and Volume Extinction Coefficient from In Situ Observations for Temperatures from 0° to −86°C: Implications for Spaceborne Lidar Retrievals

2014 ◽  
Vol 53 (2) ◽  
pp. 479-505 ◽  
Author(s):  
Andrew Heymsfield ◽  
Dave Winker ◽  
Melody Avery ◽  
Mark Vaughan ◽  
Glenn Diskin ◽  
...  
Keyword(s):  
Water Content ◽  
Extinction Coefficient ◽  
Climate Models ◽  
Detection Threshold ◽  
The Arctic ◽  
Effective Diameter ◽  
Ice Clouds ◽  
Ice Water Content ◽  
Ice Water ◽  
Volume Extinction Coefficient

AbstractAn examination of 2 yr of Cloud–Aerosol Lidar Infrared Pathfinder Satellite Observations (CALIPSO) lidar observations and CloudSat cloud radar observations shows that ice clouds at temperatures below about −45°C frequently fall below the CloudSat radar’s detection threshold yet are readily detectable by the lidar. The CALIPSO ice water content (IWC) detection threshold is about 0.1 versus 5 mg m−3 for CloudSat. This comparison emphasizes the need for developing a lidar-only IWC retrieval method that is reliable for high-altitude ice clouds at these temperatures in this climatically important zone of the upper troposphere. Microphysical measurements from 10 aircraft field programs, spanning latitudes from the Arctic to the tropics and temperatures from −86° to 0°C, are used to develop relationships between the IWC and volume extinction coefficient σ in visible wavelengths. Relationships used to derive a radiatively important ice cloud property, the ice effective diameter De, from σ are also developed. Particle size distributions (PSDs) and direct IWC measurements, together with evaluations of the ice particle shapes and comparisons with semidirect extinction measurements, are used in this analysis. Temperature-dependent De(σ) and IWC–σ relationships developed empirically facilitate the retrieval of IWC from lidar-derived σ and De values and for comparison with other IWC observations. This suite of empirically derived relationships can be expressed analytically. These relationships can be used to derive IWC and De from σ and are developed for use in climate models to derive σ from prognosed values of IWC and specified PSD properties.

scholarly journals Diagnosing the average spatio-temporal impact of convective systems – Part 1: A methodology for evaluating climate models

2013 ◽  
Vol 13 (23) ◽  
pp. 12043-12058 ◽  
Author(s):  
M. S. Johnston ◽  
S. Eliasson ◽  
P. Eriksson ◽  
R. M. Forbes ◽  
K. Wyser ◽  
...  
Keyword(s):  
Water Content ◽  
Outgoing Longwave Radiation ◽  
Longwave Radiation ◽  
Cloud Fraction ◽  
Convective Systems ◽  
Ice Water Content ◽  
The Mean ◽  
Spatio Temporal ◽  
Cloud Ice ◽  
Ice Water

Abstract. An earlier method to determine the mean response of upper-tropospheric water to localised deep convective systems (DC systems) is improved and applied to the EC-Earth climate model. Following Zelinka and Hartmann (2009), several fields related to moist processes and radiation from various satellites are composited with respect to the local maxima in rain rate to determine their spatio-temporal evolution with deep convection in the central Pacific Ocean. Major improvements to the earlier study are the isolation of DC systems in time so as to prevent multiple sampling of the same event, and a revised definition of the mean background state that allows for better characterisation of the DC-system-induced anomalies. The observed DC systems in this study propagate westward at ~4 m s−1. Both the upper-tropospheric relative humidity and the outgoing longwave radiation are substantially perturbed over a broad horizontal extent and for periods >30 h. The cloud fraction anomaly is fairly constant with height but small maximum can be seen around 200 hPa. The cloud ice water content anomaly is mostly confined to pressures greater than 150 hPa and reaches its maximum around 450 hPa, a few hours after the peak convection. Consistent with the large increase in upper-tropospheric cloud ice water content, albedo increases dramatically and persists about 30 h after peak convection. Applying the compositing technique to EC-Earth allows an assessment of the model representation of DC systems. The model captures the large-scale responses, most notably for outgoing longwave radiation, but there are a number of important differences. DC systems appear to propagate eastward in the model, suggesting a strong link to Kelvin waves instead of equatorial Rossby waves. The diurnal cycle in the model is more pronounced and appears to trigger new convection further to the west each time. Finally, the modelled ice water content anomaly peaks at pressures greater than 500 hPa and in the upper troposphere between 250 hPa and 500 hPa, there is less ice than the observations and it does not persist as long after peak convection. The modelled upper-tropospheric cloud fraction anomaly, however, is of a comparable magnitude and exhibits a similar longevity as the observations.

scholarly journals UARS/MLS Cloud Ice Measurements: Implications for H2O Transport near the Tropopause

2005 ◽  
Vol 62 (2) ◽  
pp. 518-530 ◽  
Author(s):  
D. L. Wu ◽  
W. G. Read ◽  
A. E. Dessler ◽  
S. C. Sherwood ◽  
J. H. Jiang
Keyword(s):  
Water Content ◽  
Total Water ◽  
Ice Clouds ◽  
Clear Sky ◽  
Ice Water Content ◽  
Satellite Microwave ◽  
Cold Point ◽  
Cloud Ice ◽  
Ice Water

Abstract A technique for detecting large hydrometeors at high altitudes is described here and applied to the Upper Atmosphere Research Satellite/Microwave Limb Sounder (UARS/MLS) 203-GHz radiance measurements at tangent pressures between 200 and 46 hPa. At these tangent pressures the radiances remain optically thin and cloudy-sky radiances are brighter than normal clear-sky cases. Unlike infrared/visible cloud observations, the 203-GHz radiances can penetrate most ice clouds and are sensitive to ice crystals of convective origin. Rough ice water content (IWC) retrievals are made near the tropopause using estimated size distributions from in situ convective studies. The seasonal mean IWC observed at 100 hPa reaches vapor-equivalent 20 ppmv or more over convective centers, dominating the total water content. Convectively lofted ice, therefore, appears to be hydrologically significant at the tropical cold point. IWC is well correlated spatially with relative humidity with respect to ice (RHi) at 100 hPa during both the dry (January–March) and moist (July–September) periods.

scholarly journals Evaluation of the Lidar–Radar Cloud Ice Water Content Retrievals Using Collocated in Situ Measurements

2015 ◽  
Vol 54 (10) ◽  
pp. 2087-2097 ◽  
Author(s):  
Sujan Khanal ◽  
Zhien Wang
Keyword(s):  
Remote Sensing ◽  
Water Content ◽  
Cloud Microphysics ◽  
In Situ Measurements ◽  
Ice Water Content ◽  
Flight Level ◽  
The Mean ◽  
Cloud Ice ◽  
Ice Water

AbstractRemote sensing and in situ measurements made during the Colorado Airborne Multiphase Cloud Study, 2010–2011 (CAMPS) with instruments aboard the University of Wyoming King Air aircraft are used to evaluate lidar–radar-retrieved cloud ice water content (IWC). The collocated remote sensing and in situ measurements provide a unique dataset for evaluation studies. Near-flight-level IWC retrieval is compared with an in situ probe: the Colorado closed-path tunable diode laser hygrometer (CLH). Statistical analysis showed that the mean radar–lidar IWC is within 26% of the mean in situ measurements for pure ice clouds and within 9% for liquid-topped mixed-phase clouds. Considering their different measurement techniques and different sample volumes, the comparison shows a statistically good agreement and is close to the measurement uncertainty of the CLH, which is around 20%. It is shown that ice cloud microphysics including ice crystal shape and orientation has a significant impact on IWC retrievals. These results indicate that the vertical profile of the retrieved lidar–radar IWC can be reliably combined with the flight-level measurements made by the in situ probes to provide a more complete picture of the cloud microphysics.

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