- 1 - 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

- 2 - Motivation for Study 1.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. 2.Satellite retrievals of IWP are sensitive to many microphysical properties. The above knowledge would characterize and likely reduce uncertainties in IWP retrievals.

- 3 - 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

- 4 - 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

- 5 - Impact of ice particle fall velocities – continued % difference in high-level cloud coverage, tropical – ML PSD scheme

- 6 - CAM simulations for tropical anvil & synoptic cirrus PSD Tropical ML PSD SW cloud forcing LW cloud forcing

- 7 - Temperature Differences: Tropical anvil minus synoptic cirrus PSD simulations

- 8 - 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, Also available at:  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.

- 9 - N(D) = N o D ν exp(-λD) 60 μm Small mode Large mode -30 < T < -34 o C

The diffusional growth dependence of the PSD on β can be inferred by differentiating the ice particle mass expression: m = α D β dD -1 1-β dm ____ = (αβ) D ____ dt dt b(β+2-σ)-1 Aggregation 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 depends on β. Ice Particle Mass Expressions Representative for the Large Mode PSD

Sensitivity of large mode PSD fit to β β = 2.1β = < T < -44 C (2β )  D - D Z ν = ________________________ D Z -  D

Calculation of α and β, 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 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).

Results: Gamma function fits to observed PSD β = 1.6β = 2.1β = 1.6 β = 1.9β = < T < -39 C-40 < T < -44 C -45 < T < -49 C -50 < T < -54 C-55 < T < -59 C-60 < T < -64 C

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 ν and  D from each mode to temperature. The PSD λ is determined from ν and  D. N o 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 N o. The IWC ratio is related to temperature. Input for the PSD scheme is temperature and IWC.

Extrapolated using Ivanova et al. (2001)

small mode large mode

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This scheme reproduces the time-weighted mean PSD for each 5 o C 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 ,000 km sampling distance. ● The sampling was done on 14 different days in different clouds. Testing of the PSD Scheme

Testing the PSD scheme at -50 to -55 o C, where single leg PSD variability was the greatest, as shown below:

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 < 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 D eff. These power laws yield the total measured PSD area when applied to the PSD: A obs = ∫ γD σ N(D)dD

N = 2.34 cm -3 IWC sm /IWC t = 0.88 Samp. time = 14 min. D eff = 10 μm Predicted D eff = 13 μm 3 IWC D eff = _______ 2 ρ i A

N = 0.64 cm -3 IWC sm /IWC t = 0.98 Samp. time = 3 min. D eff = 10 μm Predicted D eff = 13 μm

N = 0.21 cm -3 IWC sm /IWC t = 0.23 Samp. time = 3 min. D eff = 31 μm Predicted D eff = 13 μm

N = 0.37 cm -3 IWC sm /IWC t = 0.68 Samp. time = 14 min. D eff = 17 μm Predicted D eff = 13 μm

N = 0.56 cm -3 IWC sm /IWC t = 0.69 Samp. time = 10 min. D eff = 17 μm Predicted D eff = 13 μm

N = 1.89 cm -3 IWC sm /IWC t = 0.99 Samp. time = 12 min. D eff = 9.3 μm Predicted D eff = 13 μm

N = cm -3 IWC sm /IWC t = 0.45 Samp. time = 10 min. D eff = 17 μm

N = 0.28 cm -3 IWC sm /IWC t = 0.96 Samp. time = 6 min. D eff = 10 μm

N = 3.65 cm -3 IWC sm /IWC t = 0.85 Samp. time = 6 min. D eff = 16 μm

N = cm -3 IWC sm /IWC t = 0.89 Samp. time = 13 min. D eff = 10 μm

N = 0.71 cm -3 IWC sm /IWC t = 0.91 Samp. time = 4 min. D eff = 11 μm

N = 1.50 cm -3 IWC sm /IWC t = 0.78 Samp. time = 18 min. D eff = 10 μm

N = 0.33 cm -3 IWC sm /IWC t = 0.33 Samp. time = 4 min. D eff = 25 μm

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

N = 1.96 cm -3 IWC sm /IWC t = 0.11 Samp. time = 9 min. D eff = 68 μm Predicted D eff = 59 μm

N = 0.50 cm -3 IWC sm /IWC t = 0.15 Samp. time = 10 min. D eff = 57 μm Predicted D eff = 60 μm

N = 3.12 cm -3 IWC sm /IWC t = 0.39 Samp. time = 5 min. D eff = 28 μm Predicted D eff = 60 μm

N = 0.91 cm -3 IWC sm /IWC t = 0.12 Samp. time = 16 min. D eff = 60 μm Predicted D eff = 59 μm

N = 0.94 cm -3 IWC sm /IWC t = 0.06 Samp. time = 20 min. D eff = 86 μm Predicted D eff = 59 μm

N = 4.47 cm -3 IWC sm /IWC t = 0.44 Samp. time = 6 min. D eff = 26 μm Predicted D eff = 60 μm

N = 0.54 cm -3 IWC sm /IWC t = 0.05 Samp. time = 19 min. D eff = 93 μm

N = 1.32 cm -3 IWC sm /IWC t = 0.34 Samp. time = 7 min. D eff = 33 μm

N = 0.65 cm -3 IWC sm /IWC t = 0.08 Samp. time = 3 min. D eff = 82 μm

N = 0.16 cm -3 IWC sm /IWC t = 0.15 Samp. time = 6 min. D eff = 52 μm

N = 0.10 cm -3 IWC sm /IWC t = 0.05 Samp. time = 3 min. D eff = 109 μm

N = 1.08 cm -3 IWC sm /IWC t = 0.06 Samp. time = 19 min. D eff = 90 μm

N = 0.96 cm -3 IWC sm /IWC t = 0.34 Samp. time = 9 min. D eff = 30 μm

Measured vs. Predicted D eff -40 < T < -35 o C: Measured D eff = 63 ± 28 μm Predicted D eff = 60 μm -55 < T < -50 o C: Measured D eff = 15 ± 7 μm Predicted D eff = 13 μm

Temperature Dependence of D eff TemperatureD eff ( o C) (µm) If these D eff are representative of cirrus, what will be the sign and the magnitude of the cirrus feedback on climate? See Stephens et al. (JAS, 1990).

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. β m = α D σ A = γ D b Re = a X(5 flow regimes for a and b) 2 α gb b (β + 2 –σ ) – 1 V t = a υ ( ____________ ) D ρ a υ 2 γ Accurate to within 20% of observed fall velocities

Ice Mass Sedimentation Rates (cont.) Mass removal rate = R = v sm IWC sm + v l IWC l Median mass dimension = D m = (β + ν +0.67)/λ ν where N(D) = N o D exp(-λD) for each mode. B B V sm = A D m,sm V l = A D m,l

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 law relationship 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 D eff well although D eff varies by about ± 45%. Due to the small D eff values, the sign and magnitude of the cirrus climate feedback should 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 of mid-latitude cirrus. Conclusions

JJ. Atmospheric and Oceanic Technology Adjusting 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

A = fraction of the “original” concentration to total concentration of ice particles. From Field et al. 2003, J. Atmos. Ocean. Tech., 20,

Small Mode PSD Adjustments for Large Particle Shattering At FSSP Inlet Cloud temperaturePercent Artifacts ( o C)(relative to total N)

N = 3.05 cm -3 IWC sm /IWC t = 0.68 Samp. time = 12 min. Can shattering explain small mode PSD between -30 & -35 o C where homogeneous freezing nucleation is not active?

N = cm -3 IWC sm /IWC t = 0.07 Samp. time = 12 min. Can shattering explain small mode PSD between -30 & -35 o C where homogeneous freezing nucleation is not active?