Single-crystal images collected in mid-latitude cirrus are analyzed to
provide internally consistent ice physical and optical properties for a
size-resolved cloud microphysics model, including single-particle mass,
projected area, fall speed, capacitance, single-scattering albedo, and
asymmetry parameter. Using measurements gathered during two flights through a
widespread synoptic cirrus shield, bullet rosettes are found to be the
dominant identifiable habit among ice crystals with maximum dimension
(

It is well known that cirrus clouds substantially impact radiative fluxes and
climate in a manner that depends upon their microphysical and macrophysical
properties

It is also well known that ice crystals in the atmosphere exhibit a profound
degree of diversity in morphology that impacts microphysical process
rates and radiative properties

In very detailed modeling studies of ice evolution, if habit geometry is well
defined, precise calculations can be made for capacitance and other
microphysical parameters

Currently, based on CPI imagery, automated identification of ice habit is
relatively commonly reported

Perhaps not yet as widely considered in models are the difficulties of
consistently assigning ice crystal component aspect ratio, roundness, and
microscale surface roughness for accurate calculation of radiative properties

Here we analyze single-crystal ice crystal field data with the primary
objective of deriving physically continuous ice microphysical and
optical properties over the size range required (1–3000

In situ observations are analyzed from a well-sampled cirrus system observed
during 1 April (flight B) and 2 April (flight A) during the 2010 Small
Particles in Cirrus (SPARTICUS) field campaign

GOES composite image at 23:39 UTC on 1 April 2010. Black circle indicates the Southern Great Plains long-term measurement site in Oklahoma.

Previous studies using SPARTICUS data can be considered in at least five
general categories: characterization of the environmental properties observed

To provide context for parcel simulations, we also use Learjet ice particle
size distributions derived from a 2-D Stereo Probe (2DS) equipped with tips
that reduce effects of shattering

The overall objective of this study is to use analyzed CPI image data to derive
consistent representations of ice physical and optical properties for a
size-resolved ice microphysics scheme, and to compare results with existing
literature. The target microphysics scheme is based on the Community
Aerosol-Radiation-Microphysics Application (CARMA) code

In this work the ice crystal properties in each ice mass bin are represented
using the approach developed by

In each ice mass bin, quantities that are not considered in the Böhm
scheme but that should ideally be specified in an integrated manner are
capacitance and radiative scattering and absorption coefficients. For a given
crystal, the capacitance can be either specified from the literature in the
case of a pristine habit or else estimated from prolate or oblate spheroids

Scattering and absorption properties assuming randomly oriented ice crystals
in each mass bin are computed following

Parcel simulations are used to test ice properties in a simplified framework,
following

Fraction of ice by habit class for all crystals imaged

Considering all CPI images collected during the 1–2 April flights, automated
analysis places roughly half of all ice crystals in the small quasi-sphere
category, and remaining crystals are primarily unclassified
(Fig.

Bullet rosettes imaged on 1 April with

For each bullet rosette measured with the ICR software,
Fig.

Bullet model: measured and calculated properties of imaged bullet
rosettes with six arms (black symbols), fewer than six arms (blue symbols),
and more than six arms (red symbols). Line types indicate derived ice
properties as follows (see legend in panel

For the same crystals, Fig.

Because we seek a continuous description of ice
properties across all sizes, here we take the approach of adopting a physical
model of crystal geometry to extrapolate measured properties
smoothly to sizes smaller than measured. A similar
approach was taken by

Figure

The

The bullet model described above now allows calculation of crystal surface
area (

Mass–dimensional and area–dimensional power law coefficients for

Bullet model: measured and calculated properties of imaged ice
crystals (red symbols) emphasizing the transition to the smallest sizes.
Effective density and projected area for bullet rosettes with ICR
measurements

In Fig.

The difference between our calculated

Our calculated

Whereas our calculated

Figure

Although

As in Fig.

As in Fig.

To consider uncertainty in the geometry of the smallest crystals, we next
consider an alternative proposed model for early bullet rosette shape:
budding Bucky balls

However, using this simplified Bucky ball model, a developing six-arm rosette
has a systematically smaller

Fraction of imaged ice crystals with

We return now to the distribution of habits during the 1–2 April flights,
and consider the properties of crystals in the observed cirrus deck that are
not identified as bullet rosettes. The rosettes are most common in the upper
cloud regions at temperatures colder than

Aggregate model: measured and calculated properties of aggregates of
bullet rosettes with 12 arms (black symbols), fewer than 12 arms
(blue symbols), and more than 12 arms (red symbols). Line types indicate
derived ice properties as follows (see legend in panel

However, aggregates of pristine rosettes also represent a small fraction of
ice crystals observed in this case, at least on a number basis. CPI images
show that some rosettes reach a plate growth regime (Fig.

Bullet rosettes and unclassified crystals with radiating growth imaged on 1 April.

For the purposes of considering how plate-like growth impacts rosette
single-crystal properties, it is notable from the SPARTICUS images in this case
that radiating side plane elements appear to increasingly fill the space
between the arms of rosettes and rosette aggregates, giving the impression of
cobwebs that lead to blocky ice particle shapes (e.g., Fig.

We next consider an approximate model for the physical and optical properties
of these more common, irregular crystals. In the data set examined here, we
are unable to find a consistent increase in projected area ratio with
increasing temperature that would be expected if rosettes are modified by side
plane growth during sedimentation from colder to warmer temperatures, but we do
find that unclassified crystals at all temperatures exhibit consistently larger
area ratios than rosette crystals (Fig.

Unclassified ice crystals with sublimated edges imaged on 1 April.

Ratio of measured

We first calculate the additional projected area that can be attributed to
side plane growth. Considering all unclassified crystals, a fit of measured

Polycrystal model: measured and calculated properties of
unclassified ice crystals (red symbols). Line types indicate derived ice
properties as follows (see legends in panels

The foregoing results for this polycrystal model are dependent upon the
underlying bullet model assumed, the assumed ratio of

Ice crystal fall speeds at 350 mb and 233 K for derived ice
properties as follows (see legend): a sphere, six-arm rosettes following the
bullet and Bucky ball models, 12-arm aggregates following the bullet
model, the polycrystal model, five-arm rosettes from

Figure

Given literature ice properties, using our model to calculate crystal fall
speed as detailed in

Owing to the dependence of parameterized capacitance on bullet arm aspect
ratio alone (see Sect.

To grossly evaluate the potential effect of different model ice properties on
ice crystal nucleation and growth, we first consider parcel simulations
without the complication of sedimentation. Since aggregation is neglected,
aggregate ice properties are not considered. As described in
Sect.

Ice crystal capacitance normalized by maximum dimension at 350 mb
and 233 K for derived ice properties as in Fig.

Figure

The strongest

In summary, in the simple case of a non-sedimenting parcel, differing ice
property assumptions lead to a factor of 2 difference in

Vertical wind speeds retrieved from 19:06 UTC on 1 April to 02:23 UTC on 2 April at elevations of 6.1–12.0 km, from a sample size of 123 469 retrievals obtained in 47 layers at 10 s resolution.

When sedimentation is included with an assumed parcel depth of 100 m
following

Ice particle size distributions (PSDs) simulated at

Simulated ice crystal number concentration as a function of parcel
distance from initiation at

As in Fig.

As in Fig.

As in Fig.

Although sedimentation only reduces parcel

At the greatest

Ice single-crystal optical properties as a function of maximum
dimension for the bullet, Bucky ball, aggregate, and polycrystal models, and
for

Extinction cross sections, scattering asymmetry parameters, and
single-scattering albedos that are consistent with the derived crystal
geometries are needed for interactive radiative calculations in
cloud-resolving simulations and for calculation of diagnostic fluxes and
radiances to be compared with measurements

The

The single-scattering albedo (

The asymmetry parameter (

Calculated

Figure

In preparation for large-eddy simulations with size-resolved microphysics for
a case study of mid-latitude synoptic cirrus observed on 1–2 April 2010
during the SPARTICUS campaign

Our results using a typical bullet model of rosettes give

In parcel simulations with and without sedimentation, differing ice
properties lead to factors of 2–4 difference in crystal number concentration

Overall, it appears that the main differences between our models and past
literature arise from differences in bullet rosette geometry (i.e.,
single-particle mass) or its representation (i.e., definition of

Ice single-crystal effective diameter as a function of maximum
dimension for the bullet, Bucky ball, aggregate, and polycrystal models,

Optical properties of ice crystal size distributions shown in
Fig.

Evolution of newly nucleated ice crystals may proceed from amorphous shapes
to more defined habits

It may be the case that uncertainties in ice crystal

With respect to classification of morphological properties, it also appears
to be the case that classification algorithms may give substantially
differing results. For instance, whereas here roughly 80 % of crystals with

Overall, the results obtained here motivate the use of our derived ice properties in comparison with more widely used values in 3-D simulations of the 1–2 April SPARTICUS conditions, which can in turn be compared with in situ ice size distribution observations.

A fundamental geometric element of all ice models considered below is the
regular hexagonal column with length

Since branch length measurements extend from crystal center to the outermost
edge of projected randomly oriented branches, the true mean total branch
length (including cap or core contributions, depending on the model) is taken
as the mean of the measured lengths less one-half of the mean of the measured
widths times

All non-aggregate models (bullet, Bucky ball, and polycrystal) assume six branches, consistent with mean and median number found over all bullet rosettes measurable with the ICR software.

Derived ice properties are supplied as the Supplement.

The bullet model assumes that each hexagonal column has a single cap, and
that the six caps meet at a point in the center of the crystal. If the cap is
a hexagonal pyramid with a fixed angle

Thus, wider branches have longer caps.
Here we assume fixed

For the bullet model, total true branch length includes both hexagonal column
length

A least squares fit of mean branch width

In the limit of zero

With crystal geometry now defined using the bullet model, it is
straightforward to calculate the aspect ratio

However, the randomly oriented projected area

If the cap angle

The Bucky ball model assumes that each hexagonal column grows initially from
a Bucky ball face. The core is approximated as a sphere with diameter

Similarly, in order to insure a branch width of

With crystal geometry now defined using the Bucky ball model, it is
straightforward to calculate the branch aspect ratio (

Rigorous calculation of

Relative to the bullet model, the Bucky ball model exhibits a stronger
increase of

The “aggregate model” is an extension of the bullet model. A least squares
fit of mean branch length

The mean and median measured number of arms is 12, consistent with
aggregates primarily of two typical single rosettes. The roughly 30 %
reduction in slope compared with single rosettes can be attributed to the
overlap of aggregate arms, compounded by random orientation when two crystals
create a linearly aligned pair that will be rarely normal to the viewing
angle. A least squares fit of mean branch width

To handle unphysical branch widths in the limit of zero

Using this model for aggregates, mass and projected area are simply twice that of bullet rosettes,

Using Eq. (

The polycrystal model is derived for unclassified crystals using plate growth
on the bullet model as a basis. When the unclassified crystals are initially
assumed to follow the bullet model, and measured

Based on trial and error, taking the foregoing assumptions as a recipe, the
following prescription was found to match effective density from

Plate thickness

In the limit of zero plate size,

Plate contribution to polycrystal mass can be calculated as

Total mass is then

This work was supported by the NASA Radiation Sciences Program and the Office of Science (BER), U.S. Department of Energy under agreements DE-SC0006988, DE-SC0008500, and DE-SC0014065. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Resources supporting this work were also provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. We thank the SPARTICUS science team for collecting and archiving all data sets referenced. Edited by: H. Grothe