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A Simple Parameterization For Mid-latitude Cirrus Cloud

Ice Particle Size SpectraAnd 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

1. CAM performance has been shown to be sensitive to the representationof the ice particle size distribution (PSD) when the PSD is coupled with icesedimentation rates and cloud optical properties (Mitchell and Rasch 2006).To drive down CAM uncertainties, the cirrus PSD should be represented inthe CAM as accurately as possible. A big advantage in using the PSD instead of effective diameter is a realistic assessment of ice sedimentationrates, which GCM simulations are very sensitive to.

a. In addition to the PSD, ice cloud sedimentation rates and radiativeproperties depend on the ice particle area- and mass-dimension relationships. More accurate information on these relationships would be helpful.

2. 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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Small mode enhancement with decreasing T for tropical anvil cirrus; Opposite for mid-latitude cirrus. PSDs coupled with ice sedimentation and cirrus optical properties.

CAM Experiment Using Two PSD Schemes

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Impact of ice particle fall velocities

IWP zonal means for in-cloud conditions,

tropical & mid-latitude

PSD schemes

Difference in IWP,tropical – ML PSD scheme

Tropical

M L PSD

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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

Tropical

ML PSD

SW cloud forcing LW cloud forcing

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Temperature Differences: Tropical anvil minussynoptic 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.htm

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 < D < 30 μm*, CPI for 30 μm < D < 200 μm*, and 2DC for 200 μm < D < 2000 μm

* Note: Size breakpoints shown here are nominal and are adjusted slightly for best fit.

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N(D) = No Dν exp(-λD)

60 μmSmall mode

Large mode

-30 < T < -34oC

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The diffusional growth dependence of the PSD on β can be inferred by differentiating the ice particle mass expression: m = α Dβ

dD -1 1-β dm____ = (αβ) D ____ dt dt

b(β+2-σ)-1Aggregation growth also depends on β: v = a D

In practice, β is determined for the large mode by optimizing the large mode gamma-fit with the observed PSD. Note ν dependson β.

Ice Particle Mass Expressions Representative for the Large Mode PSD

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Sensitivity of large mode PSD fit to β

β = 2.1 β = 1.6

-40 < T < -44 C -40 < T < -44 C

(2β + 0.67)D - DZν = ________________________ DZ - D

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Calculation of α and β, small mode: The m-D relationship forthe small mode is not too uncertain since the ice particles arequasi-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 α and β, large mode: β for the large mode was estimated from the PSD shape, while corresponding α 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 β values were generally consistent with those suggested in Heymsfield et al. (2007).

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Results: Gamma function fits to observed PSD

β = 1.6 β = 2.1 β = 1.6

β = 1.9 β = 2.1

-35 < T < -39 C -40 < T < -44 C -45 < T < -49 C

-50 < T < -54 C -55 < T < -59 C -60 < T < -64 C

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Developing a PSD SchemeDiagnosed Through Temperature and IWC

Strategy: Now that all the gamma parameters are knownfor each temperature interval, use polynomial fits to relateν andD from each mode to temperature. The PSD λ is determined from ν andD. No for each mode is calculatedfrom the IWC ratio; small mode to total PSD IWC. Theincomplete gamma function is used to account for the change in mass relationship across the PSD when calculatingNo. The IWC ratio is related to temperature.

Input for the PSD scheme is temperature and IWC.

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Extrapolatedusing Ivanova et al. (2001)

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small mode

large mode

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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.

Testing of the PSD Scheme

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Testing the PSD scheme at -50 to -55 oC, where single leg PSDvariability was the greatest, as shown below:

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Testing of the PSD Scheme (continued)

The next slides compare the single measured PSD withthe parameterized PSD, given by the red-dashed curve.The small mode of the measured PSD is in blue (D < 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 concentrationN and the IWC ratio (small mode to total PSD) are basedon the measurements.● Area-dimensional power laws for each mode wereused to calculate Deff. These power laws yield the total measured PSD area when applied to the PSD:

Aobs = ∫ γDσ N(D)dD

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N = 2.34 cm-3

IWCsm/IWCt = 0.88Samp. time = 14 min.Deff = 10 μmPredicted Deff = 13 μm

3 IWCDeff = _______

2 ρi A

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N = 0.64 cm-3

IWCsm/IWCt = 0.98Samp. time = 3 min.Deff = 10 μmPredicted Deff = 13 μm

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N = 0.21 cm-3

IWCsm/IWCt = 0.23Samp. time = 3 min.Deff = 31 μmPredicted Deff = 13 μm

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N = 0.37 cm-3

IWCsm/IWCt = 0.68Samp. time = 14 min.Deff = 17 μmPredicted Deff = 13 μm

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N = 0.56 cm-3

IWCsm/IWCt = 0.69Samp. time = 10 min.Deff = 17 μmPredicted Deff = 13 μm

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N = 1.89 cm-3

IWCsm/IWCt = 0.99Samp. time = 12 min.Deff = 9.3 μm Predicted Deff = 13 μm

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N = 0.148 cm-3

IWCsm/IWCt = 0.45Samp. time = 10 min.Deff = 17 μm

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N = 0.28 cm-3

IWCsm/IWCt = 0.96Samp. time = 6 min.Deff = 10 μm

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N = 3.65 cm-3

IWCsm/IWCt = 0.85Samp. time = 6 min.Deff = 16 μm

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N = 0.068 cm-3

IWCsm/IWCt = 0.89Samp. time = 13 min.Deff = 10 μm

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N = 0.71 cm-3

IWCsm/IWCt = 0.91Samp. time = 4 min.Deff = 11 μm

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N = 1.50 cm-3

IWCsm/IWCt = 0.78Samp. time = 18 min.Deff = 10 μm

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N = 0.33 cm-3

IWCsm/IWCt = 0.33Samp. time = 4 min.Deff = 25 μm

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Testing the PSD scheme at -35 to -40 oC, where single leg PSDvariability was 2nd greatest, as shown below:

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N = 1.96 cm-3

IWCsm/IWCt = 0.11Samp. time = 9 min.Deff = 68 μmPredicted Deff = 59 μm

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N = 0.50 cm-3

IWCsm/IWCt = 0.15Samp. time = 10 min.Deff = 57 μmPredicted Deff = 60 μm

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N = 3.12 cm-3

IWCsm/IWCt = 0.39Samp. time = 5 min.Deff = 28 μmPredicted Deff = 60 μm

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N = 0.91 cm-3

IWCsm/IWCt = 0.12Samp. time = 16 min.Deff = 60 μmPredicted Deff = 59 μm

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N = 0.94 cm-3

IWCsm/IWCt = 0.06Samp. time = 20 min.Deff = 86 μmPredicted Deff = 59 μm

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N = 4.47 cm-3

IWCsm/IWCt = 0.44Samp. time = 6 min.Deff = 26 μmPredicted Deff = 60 μm

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N = 0.54 cm-3

IWCsm/IWCt = 0.05Samp. time = 19 min.Deff = 93 μm

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N = 1.32 cm-3

IWCsm/IWCt = 0.34Samp. time = 7 min.Deff = 33 μm

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N = 0.65 cm-3

IWCsm/IWCt = 0.08Samp. time = 3 min.Deff = 82 μm

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N = 0.16 cm-3

IWCsm/IWCt = 0.15Samp. time = 6 min.Deff = 52 μm

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N = 0.10 cm-3

IWCsm/IWCt = 0.05Samp. time = 3 min.Deff = 109 μm

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N = 1.08 cm-3

IWCsm/IWCt = 0.06Samp. time = 19 min.Deff = 90 μm

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N = 0.96 cm-3

IWCsm/IWCt = 0.34Samp. time = 9 min.Deff = 30 μm

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Measured vs. Predicted Deff

-40 < T < -35 oC: Measured Deff = 63 ± 28 μmPredicted Deff = 60 μm

-55 < T < -50 oC: Measured Deff = 15 ± 7 μmPredicted 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 arerepresentative ofcirrus, what will bethe sign and themagnitude of the cirrus feedback onclimate? SeeStephens et al.(JAS, 1990).

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Treatment of Ice Sedimentation Rates

From Mitchell 1996: Use of mass- and area-dimensional power laws fordetermining precipitation particle terminal velocities. J. Atmos. Sci.

βm = α D

σA = γ D

bRe = a X (5 flow regimes for a and b)

2 α g b b (β + 2 –σ ) – 1Vt = a υ ( ____________ ) D ρa υ2 γ

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 = (β + ν +0.67)/λ

νwhere N(D) = No D exp(-λD) for each mode.

B BVsm = A Dm,sm

Vl = A Dm,l

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1. 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.

2. In combination with the results of Heymsfield et al. (2007), this methodology

provides a way for estimating the ice particle mass-dimension power lawrelationship that is representative of the large mode.

3. 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 feedbackshould be revisited.

4. The PSD scheme provides the needed information to realistically estimate

ice mass sedimentation rates, something critical to GCM performance.

5. 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 ofmid-latitude cirrus.

Conclusions

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JJ. Atmospheric and Oceanic TechnologyAdjusting the Small Mode to Account for

Ice Particle Shattering at FSSP

Inlet•From Field et al. 2003,

J. Atmos. Oceanic Tech.

•FSSP interarrival times reveal 2 modes, one mode possibly due to shattering

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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 ShatteringAt FSSP Inlet

Cloud temperature Percent Artifacts(oC) (relative to total N)

-57 0-52 11-47 13-42 14-37 20-32 22-27 51-22 55

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N = 3.05 cm-3

IWCsm/IWCt = 0.68Samp. time = 12 min.

Can shattering explain small mode PSD between -30 & -35 oCwhere homogeneous freezing nucleation is not active?

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N = 0.857 cm-3

IWCsm/IWCt = 0.07Samp. time = 12 min.

Can shattering explain small mode PSD between -30 & -35 oCwhere homogeneous freezing nucleation is not active?