A Simple Parameterization

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A Simple Parameterization For Mid-latitude
Cirrus Cloud Ice Particle Size Spectra And Ice
Sedimentation Rates David L.
Mitchell Desert Research Institute, Reno,
Nevada Brad Baker, R. Paul Lawson, Bryan
Pilson and Qixu Mo SPEC, Inc., Boulder,
Colorado
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Motivation for Study

• CAM performance has been shown to be sensitive to
  the representation
• of the ice particle size distribution (PSD) when
  the PSD is coupled with ice
• sedimentation rates and cloud optical properties
  (Mitchell and Rasch 2006).
• To drive down CAM uncertainties, the cirrus PSD
  should be represented in
• the CAM as accurately as possible. A big
  advantage in using the PSD
• instead of effective diameter is a realistic
  assessment of ice sedimentation
• rates, which GCM simulations are very sensitive
  to.
• a. In addition to the PSD, ice cloud
  sedimentation rates and radiative
• properties depend on the ice particle area- and
  mass-dimension
• relationships. More accurate information on
  these relationships would
• be helpful.
• Satellite retrievals of IWP are sensitive to many
  microphysical properties.
• The above knowledge would characterize and likely
  reduce uncertainties
• in IWP retrievals.

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CAM Experiment Using Two PSD Schemes
Small mode enhancement with decreasing T for
tropical anvil cirrus Opposite for mid-latitude
cirrus. PSDs coupled with ice sedimentation and
cirrus optical properties.
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Impact of ice particle fall velocities
IWP zonal means for in-cloud conditions, tropical
mid-latitude PSD schemes
M L PSD
Tropical
Difference in IWP, tropical ML PSD scheme
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Impact of ice particle fall velocities continued
difference in high-level cloud
coverage, tropical ML PSD scheme
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CAM simulations for tropical anvil synoptic
cirrus PSD
ML PSD
Tropical
LW cloud forcing
SW cloud forcing
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Temperature Differences Tropical anvil
minus synoptic cirrus PSD simulations
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• Improving the PSD Treatment for Synoptic Cirrus
• PSD from Lawson et al. (2006) In situ
  observations of the microphysical properties of
  wave, cirrus and anvil clouds. Part II Cirrus
  Clouds. J. of Atmos. Sci. Vol. 63, 3186-3203
  Also available at www.specinc.com/publications.ht
  m
• Mid-latitude (non-convective) cirrus PSD obtained
  during 22 Learjet flight missions, 104 horizontal
  legs
• (1 PSD per leg) and over 15,000 km of in-cloud
  sampling, -28C ? T ? -61C
• Measured by
• FSSP for 2 µm lt D lt 30 µm,
• CPI for 30 µm lt D lt 200 µm, and
• 2DC for 200 µm lt D lt 2000 µm
• Note Size breakpoints shown here are nominal
  and are adjusted slightly for best fit.

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-30 lt T lt -34oC
60 µm
Small mode
Large mode
N(D) No D? exp(-?D)
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Ice Particle Mass Expressions Representative for
the Large Mode PSD
The diffusional growth dependence of the PSD on ß
can be inferred by differentiating the ice
particle mass expression m a Dß dD -1
1-ß dm ____ (aß) D ____ dt
dt b(ß2-s)-1 Aggregation growth
also depends on ß v a D In practice, ß is
determined for the large mode by optimizing the
large mode gamma-fit with the observed PSD.
Note ? depends on ß.
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Sensitivity of large mode PSD fit to ß
-40 lt T lt -44 C
-40 lt T lt -44 C
ß 2.1
ß 1.6
(2ß 0.67)?D - DZ ? ____________________
____ DZ - ?D
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Calculation of a and ß, small mode The m-D
relationship for the small mode is not too
uncertain since the ice particles
are quasi-spherical or compact. An m-D
relationship developed by Nousiainen and
McFarquhar, based on detailed mathematical
analysis of small quasi-spherical CPI images,
was used. Small mode IWC uncertainty
15. Calculation of a and ß, large mode ß for
the large mode was estimated from the PSD shape,
while corresponding a values were obtained from
Heymsfield et al. (2007, JAS, Refinements to Ice
Particle Mass Dimensional and Terminal Velocity
Relationships for Ice Clouds. Part I
Temperature Dependence). The PSD shape derived ß
values were generally consistent with those
suggested in Heymsfield et al. (2007).
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Results Gamma function fits to observed PSD
-35 lt T lt -39 C
-40 lt T lt -44 C
-45 lt T lt -49 C
ß 1.6
ß 2.1
ß 1.6
-50 lt T lt -54 C
-55 lt T lt -59 C
-60 lt T lt -64 C
ß 1.9
ß 2.1
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Developing a PSD Scheme Diagnosed
Through Temperature and IWC
Strategy Now that all the gamma parameters are
known for each temperature interval, use
polynomial fits to relate ? and?D from each mode
to temperature. The PSD ? is determined from ?
and?D. No for each mode is calculated from the
IWC ratio small mode to total PSD IWC.
The incomplete gamma function is used to account
for the change in mass relationship across the
PSD when calculating No. The IWC ratio is
related to temperature. Input for the PSD scheme
is temperature and IWC.
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Extrapolated using Ivanova et al. (2001)
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large mode
small mode
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Testing of the PSD Scheme
This scheme reproduces the time-weighted mean PSD
for each 5 oC temperature interval very well,
but the real test is whether it can approximate
reasonably well the single leg PSD that were
averaged to produce the time-weighted mean PSD.
? These single PSD were sampled over about
3-20 min., corresponding to about 30-200,000 km
sampling distance. ? The sampling was done on
14 different days in different clouds.
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Testing the PSD scheme at -50 to -55 oC, where
single leg PSD variability was the greatest, as
shown below
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Testing of the PSD Scheme (continued)
The next slides compare the single measured PSD
with the parameterized PSD, given by the
red-dashed curve. The small mode of the measured
PSD is in blue (D lt 60 µm), while the large mode
is in green. There are 13 comparisons. All PSD
(measured and parameterized) are having the same
IWC. The number concentration N and the IWC
ratio (small mode to total PSD) are based on the
measurements. ? Area-dimensional power laws for
each mode were used to calculate Deff. These
power laws yield the total measured PSD area
when applied to the PSD Aobs ? ?Ds N(D)dD
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N 2.34 cm-3 IWCsm/IWCt 0.88 Samp. time 14
min. Deff 10 µm Predicted Deff 13 µm
3 IWC Deff _______ 2 ?i A
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N 0.64 cm-3 IWCsm/IWCt 0.98 Samp. time 3
min. Deff 10 µm Predicted Deff 13 µm
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N 0.21 cm-3 IWCsm/IWCt 0.23 Samp. time 3
min. Deff 31 µm Predicted Deff 13 µm
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N 0.37 cm-3 IWCsm/IWCt 0.68 Samp. time 14
min. Deff 17 µm Predicted Deff 13 µm
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N 0.56 cm-3 IWCsm/IWCt 0.69 Samp. time 10
min. Deff 17 µm Predicted Deff 13 µm
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N 1.89 cm-3 IWCsm/IWCt 0.99 Samp. time 12
min. Deff 9.3 µm Predicted Deff 13 µm
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N 0.148 cm-3 IWCsm/IWCt 0.45 Samp. time 10
min. Deff 17 µm
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N 0.28 cm-3 IWCsm/IWCt 0.96 Samp. time 6
min. Deff 10 µm
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N 3.65 cm-3 IWCsm/IWCt 0.85 Samp. time 6
min. Deff 16 µm
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N 0.068 cm-3 IWCsm/IWCt 0.89 Samp. time 13
min. Deff 10 µm
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N 0.71 cm-3 IWCsm/IWCt 0.91 Samp. time 4
min. Deff 11 µm
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N 1.50 cm-3 IWCsm/IWCt 0.78 Samp. time 18
min. Deff 10 µm
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N 0.33 cm-3 IWCsm/IWCt 0.33 Samp. time 4
min. Deff 25 µm
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Testing the PSD scheme at -35 to -40 oC, where
single leg PSD variability was 2nd greatest, as
shown below
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N 1.96 cm-3 IWCsm/IWCt 0.11 Samp. time 9
min. Deff 68 µm Predicted Deff 59 µm
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N 0.50 cm-3 IWCsm/IWCt 0.15 Samp. time 10
min. Deff 57 µm Predicted Deff 60 µm
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N 3.12 cm-3 IWCsm/IWCt 0.39 Samp. time 5
min. Deff 28 µm Predicted Deff 60 µm
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N 0.91 cm-3 IWCsm/IWCt 0.12 Samp. time 16
min. Deff 60 µm Predicted Deff 59 µm
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N 0.94 cm-3 IWCsm/IWCt 0.06 Samp. time 20
min. Deff 86 µm Predicted Deff 59 µm
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N 4.47 cm-3 IWCsm/IWCt 0.44 Samp. time 6
min. Deff 26 µm Predicted Deff 60 µm
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N 0.54 cm-3 IWCsm/IWCt 0.05 Samp. time 19
min. Deff 93 µm
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N 1.32 cm-3 IWCsm/IWCt 0.34 Samp. time 7
min. Deff 33 µm
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N 0.65 cm-3 IWCsm/IWCt 0.08 Samp. time 3
min. Deff 82 µm
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N 0.16 cm-3 IWCsm/IWCt 0.15 Samp. time 6
min. Deff 52 µm
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N 0.10 cm-3 IWCsm/IWCt 0.05 Samp. time 3
min. Deff 109 µm
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N 1.08 cm-3 IWCsm/IWCt 0.06 Samp. time 19
min. Deff 90 µm
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N 0.96 cm-3 IWCsm/IWCt 0.34 Samp. time 9
min. Deff 30 µm
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Measured vs. Predicted Deff
-40 lt T lt -35 oC Measured Deff 63 28
µm Predicted Deff 60 µm -55 lt T lt -50 oC
Measured Deff 15 7 µm Predicted Deff 13
µm
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Temperature Dependence of Deff
Temperature Deff (oC) (µm)
-22 33 -27 32 -32 30
-37 60 -42 22 -47 23
-52 13 -57 10 -62 10
If these Deff are representative of cirrus, what
will be the sign and the magnitude of the cirrus
feedback on climate? See Stephens et al. (JAS,
1990).
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Treatment of Ice Sedimentation Rates From
Mitchell 1996 Use of mass- and area-dimensional
power laws for determining precipitation particle
terminal velocities. J. Atmos. Sci. ß m
a D s A ? D b Re a X (5 flow
regimes for a and b)
2 a g b b (ß 2 s ) 1 Vt a ? (
____________ ) D ?a ?2
? Accurate to within 20 of observed fall
velocities
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Ice Mass Sedimentation Rates (cont.) Mass
removal rate R vsm IWCsm vl IWCl Median
mass dimension Dm (ß ? 0.67)/?
? where N(D) No D exp(-?D) for each mode.
B B Vsm A Dm,sm Vl A Dm,l
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Conclusions

• A method has been developed for fitting two gamma
  functions to the measured
• PSD in ice clouds based primarily on the mean,
  median mass, and median radar
• reflectivity dimensions of the PSD. The results
  suggest natural PSD can be described
• as two populations of particles having different
  mass-dimension relationships.
• In combination with the results of Heymsfield et
  al. (2007), this methodology
• provides a way for estimating the ice particle
  mass-dimension power law
• relationship that is representative of the large
  mode.
• A method for diagnosing the PSD based on T and
  IWC was developed. The PSD
• scheme estimates the mean Deff well although Deff
  varies by about 45. Due to
• the small Deff values, the sign and magnitude of
  the cirrus climate feedback
• should be revisited.
• The PSD scheme provides the needed information to
  realistically estimate
• ice mass sedimentation rates, something critical
  to GCM performance.
• This PSD scheme could be (1) used in GCMs or (2)
  used along with the PSD
• database to compare PSDs predicted by GCMs with
  PSDs representative of

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JJ. Atmospheric and Oceanic Technology
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A fraction of the original concentration to
total concentration of ice particles. From Field
et al. 2003, J. Atmos. Ocean. Tech., 20, 249-261.
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Small Mode PSD Adjustments for Large Particle
Shattering At FSSP Inlet
Cloud temperature Percent Artifacts (oC) (rela
tive to total N) -57 0 -52 11 -47 13
-42 14 -37 20 -32 22 -27 51 -22
55
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Can shattering explain small mode PSD between -30
-35 oC where homogeneous freezing nucleation is
not active?
N 3.05 cm-3 IWCsm/IWCt 0.68 Samp. time 12
min.
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Can shattering explain small mode PSD between -30
-35 oC where homogeneous freezing nucleation is
not active?
N 0.857 cm-3 IWCsm/IWCt 0.07 Samp. time 12
min.