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Ann M. Fridlind
and
Andrew S. Ackerman

Abstract

A proposed objective of the planned Aerosol–Cloud–Ecosystem (ACE) satellite mission is to provide constraints on climate model representation of aerosol effects on clouds by retrieving profiles of aerosol number concentration, effective variance, and effective radius over the 0.1–1-μm radius range under humidified ambient conditions with 500-m vertical resolution and uncertainties of 100%, 50%, and 10%, respectively. Shallow, broken marine clouds provide an example of conditions where boundary layer aerosol properties would be retrieved in clear-sky gaps. To quantify the degree of constraint that proposed retrievals might provide on cloud radiative forcing (CRF) simulated by climate models under such conditions, dry aerosol size distribution parameters are independently varied here in large-eddy simulations of three well-established modeling case studies. Using the rudimentary available aerosol specifications, it is found that relative changes of total dry aerosol properties in simulations can be used as a proxy for relative changes of ambient aerosol properties targeted by ACE retrievals. The sensitivity of simulated daytime shortwave CRF to the proposed uncertainty in retrieved aerosol number concentration is −15 W m−2 in the overcast limit, roughly a factor of 2 smaller than a simple analytic estimate owing primarily to aerosol-induced reductions in simulated liquid water path across this particular set of case studies. The CRF sensitivity to proposed uncertainties in retrieved aerosol effective variance and effective radius is typically far smaller, with no corresponding analytic estimate. Generalization of the results obtained here using only three case studies would require statistical analysis of relevant meteorological and aerosol observations and quantification of observational and model uncertainties and biases.

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Ann M. Fridlind
and
Andrew S. Ackerman
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David E. Stevens
,
Andrew S. Ackerman
, and
Christopher S. Bretherton

Abstract

The authors present three-dimensional numerical simulations of oceanic trade cumulus clouds underlying stratocumulus clouds. The case studied is a Global Energy and Water Experiment (GEWEX) Cloud System Study (GCSS) model intercomparison that is loosely based on observed conditions during the Atlantic Trade Cumulus Experiment (ATEX). It is motivated by the importance of this cloud type to global cloud radiative forcing, and their role as a feeder system for deep convection in the Tropics. This study focuses on the sensitivity of the modeled cloud field to the domain size and the grid spacing. Domain widths from 6.5 to 20 km and horizontal grid spacings ranging from 10 to 80 m, with corresponding vertical grid spacing ranging from 5 to 40 m, are studied, involving massively parallel computations on up to 2.5 billion grid cells. The combination of large domain size and small grid resolution provides an unprecedented perspective on this type of convection.

The mean stratocumulus cloud fraction, optical depth, and vertical fluxes of heat, moisture, and momentum are found to be quite sensitive to both the domain size and the resolution. The sensitivities are associated with a strong feedback between cloud fraction, cloud-top radiative cooling, and entrainment. The properties of individual cumulus clouds rising into the stratocumulus are less affected than the stratocumulus clouds. The simulations with 80-m horizontal by 40-m vertical resolution are clearly under-resolved, with distinctly different distributions of liquid water within the clouds. Increasing the resolution to finer than 40 m horizontal/20 m vertical affects the inversion structure and entrainment processes somewhat, but has less impact on the structure of individual clouds. Large-domain simulations exhibit mesoscale structure in the cloud organization and liquid water path. This mesoscale variability feeds back on the domain-mean properties through the cloud-radiative feedback. These simulations suggest that very large computations are required to obtain meaningful cloud statistics for this case.

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Bastiaan van Diedenhoven
,
Ann M. Fridlind
, and
Andrew S. Ackerman

Abstract

Lidar measurements obtained during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment under a mixed-phase stratus cloud that was lightly precipitating ice show a range of surprisingly low depolarization ratios (4%–23%), despite an absence of cloud droplets there. These depolarization ratios are much lower than the range of theoretical values obtained for various ice habits. The depolarization ratios correlate well with radar reflectivity, suggesting that the variation in depolarization ratios results from variations in ice water content, rather than variation in ice habits or orientation. By calculating lidar depolarization based on (i) large-eddy simulations and (ii) in situ ice size distribution measurements, it is shown that the presence of humidified aerosol particles in addition to the ice precipitation can explain the distribution and vertical profile of the observed depolarization ratios, although uncertainties related to the aerosol size distributions are substantial. These calculations show that humidified aerosol must be taken into account when interpreting lidar depolarization measurements for cloud and precipitation phase discrimination or ice habit classification, at least under conditions similar to those observed during SHEBA.

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Bastiaan van Diedenhoven
,
Andrew S. Ackerman
,
Brian Cairns
, and
Ann M. Fridlind

Abstract

A parameterization is presented that provides extinction cross section σ e , single-scattering albedo ω, and asymmetry parameter g of ice crystals for any combination of volume, projected area, aspect ratio, and crystal distortion at any wavelength in the shortwave. Similar to previous parameterizations, the scheme makes use of geometric optics approximations and the observation that optical properties of complex, aggregated ice crystals can be well approximated by those of single hexagonal crystals with varying size, aspect ratio, and distortion levels. In the standard geometric optics implementation used here, σ e is always twice the particle projected area. It is shown that ω is largely determined by the newly defined absorption size parameter and the particle aspect ratio. These dependences are parameterized using a combination of exponential, lognormal, and polynomial functions. The variation of g with aspect ratio and crystal distortion is parameterized for one reference wavelength using a combination of several polynomials. The dependences of g on refractive index and ω are investigated and factors are determined to scale the parameterized g to provide values appropriate for other wavelengths. The parameterization scheme consists of only 88 coefficients. The scheme is tested for a large variety of hexagonal crystals in several wavelength bands from 0.2 to 4 μm, revealing absolute differences with reference calculations of ω and g that are both generally below 0.015. Over a large variety of cloud conditions, the resulting root-mean-squared differences with reference calculations of cloud reflectance, transmittance, and absorptance are 1.4%, 1.1%, and 3.4%, respectively. Some practical applications of the parameterization in atmospheric models are highlighted.

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Bastiaan van Diedenhoven
,
Ann M. Fridlind
,
Andrew S. Ackerman
, and
Brian Cairns

Abstract

Satellite measurements are used to evaluate the glaciation, particle shape, and effective radius in cloud-resolving model simulations of tropical deep convection. Multidirectional polarized reflectances constrain the ice crystal geometry and the thermodynamic phase of the cloud tops, which in turn are used to calculate near-infrared reflectances so as to constrain the simulated ice effective radius, thereby avoiding inconsistencies between retrieval algorithms and model simulations. Liquid index values derived from Polarization and Directionality of the Earth’s Reflectances (POLDER) measurements indicate only ice-topped clouds at brightness temperatures (BTs) lower than −40°C, only liquid clouds at BT > −20°C, and both phases occurring at temperatures in between. Liquid index values calculated from model simulations generally reveal too many ice-topped clouds at BT > −20°C. The model assumption of platelike ice crystals with an aspect ratio of 0.7 is found consistent with POLDER measurements for BT < −40°C when very rough ice crystals are assumed, leading to an asymmetry parameter of 0.74, whereas measurements indicate more extreme aspect ratios of ~0.15 at higher temperatures, yielding an asymmetry parameter of 0.84. MODIS-retrieved ice effective radii are found to be 18–28 μm at BT < −40°C, but biased low by about 5 μm owing primarily to the assumption of pristine crystals in the retrieval. Simulated 2.13-μm reflectances at BT < −40°C are found to be about 0.05–0.1 too large compared to measurements, suggesting that model-simulated effective radii are 7–15 μm too small. Two simulations with contrasting ice nucleation schemes showed little difference in simulated effective radii at BT < −40°C, indicating that homogeneous nucleation is dominating in the simulations. Changes around −40°C in satellite observations suggest a change in cloud-top ice shape and/or size in natural deep convection possibly related to a change in the freezing mechanism.

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Mikhail D. Alexandrov
,
Alexander Marshak
, and
Andrew S. Ackerman

Abstract

A new analytical statistical model describing the structure of broken cloud fields is presented. It depends on two parameters (cell size and occupancy probability) and provides chord distributions of clouds and gaps between them by length, as well as the cloud fraction distribution. This approach is based on the assumption that the structure of a cloud field is determined by a semiregular grid of cells (an abstraction of the atmospheric convective cells), which are filled with cloud with some probability. First, a simple discrete model is introduced, where clouds and gaps can occupy an integer number of cells, and then a continuous analog is developed, allowing for arbitrary cloud and gap sizes. The influence of a finite sample size on the retrieved statistics is also described.

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Mikhail D. Alexandrov
,
Andrew S. Ackerman
, and
Alexander Marshak

Abstract

Cellular statistical models are designed to provide a simple two-parameter characterization of the structure of broken cloud fields described through distributions of cloud fraction and of chord lengths for clouds and clear gaps. In these analytical models cloud fields are assumed to occur on a semiregular grid of cells (which can be vaguely interpreted as atmospheric convective cells). In a simple, discrete cell model, cell size is fixed and each cell can either be completely filled with cloud with some probability or remain empty. Extending the discrete model to a continuous case provides more realism by allowing arbitrary cloud and gap sizes. Here the continuous cellular model is tested by comparing its statistics with those from large-eddy simulations (LES) of marine boundary layer clouds based on case studies from three trade-cumulus field projects. The statistics largely agree with some differences in small sizes approaching the LES model grid spacing. Exponential chord-length distributions follow from the assumption that the probability of any cell being cloudy is constant, appropriate for a given meteorological state (narrow sampling). Relaxing that assumption, and instead allowing this probability to have its own distribution, leads to a power-law distribution of chord lengths, appropriate to a broader sample of meteorological states (diverse sampling).

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Bastiaan van Diedenhoven
,
Andrew S. Ackerman
,
Ann M. Fridlind
, and
Brian Cairns

Abstract

The use of ensemble-average values of aspect ratio and distortion parameter of hexagonal ice prisms for the estimation of ensemble-average scattering asymmetry parameters is evaluated. Using crystal aspect ratios greater than unity generally leads to ensemble-average values of aspect ratio that are inconsistent with the ensemble-average asymmetry parameters. When a definition of aspect ratio is used that limits the aspect ratio to below unity for both hexagonal plates and columns, the effective asymmetry parameters calculated using ensemble-average aspect ratios are generally consistent with ensemble-average asymmetry parameters, especially if aspect ratios are geometrically averaged. Ensemble-average distortion parameters generally also yield effective asymmetry parameters that are largely consistent with ensemble-average asymmetry parameters. In the case of mixtures of plates and columns, it is recommended to geometrically average the aspect ratios and to subsequently calculate the effective asymmetry parameter using a column or plate geometry when the contribution by columns to a given mixture’s total projected area is greater or less than 50%, respectively. In addition, it is shown that ensemble-average aspect ratios, distortion parameters, and asymmetry parameters can generally be retrieved accurately from simulated multidirectional polarization measurements based on mixtures of varying columns and plates. However, such retrievals tend to be somewhat biased toward yielding columnlike aspect ratios. Furthermore, generally large retrieval errors can occur for mixtures with approximately equal contributions of columns and plates and for ensembles with strong contributions of thin plates.

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Xiaoli Zhou
,
Andrew S. Ackerman
,
Ann M. Fridlind
, and
Pavlos Kollias
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