Ice-Cloud effective particle size parameterization based on combined lidar, radar reflectivity, and mean Radar Doppler velocity Data Rational Brief outline of lidar/radar procedure. Theory (relationship between Doppler-vel and effective sizes) Application to ARM data. Behavior of size-dist with IWC and Temperature Conclusions

Large-scale models can not capture cloud microphysics so parameterization are necessary. For cirrus clouds: R eff =F(T) or R eff (IWC) or R eff =F(T,IWC) Previous studies have mainly used in-situ aircraft measurements Various studies have show different behavior Limited coverage Limitations of instrumentation Active remote sensing More indirect Much greater coverage/sampling ! Rational

Active (lidar/radar) cloud remote sensing Lidar Radar LidarRadar Difference in returns is a function of particle size !!   nm  3-100mm

Effective size for ice crystals Ice particles are large compared to lid (Optical scattering regime) Ice particles are small compared to rad (Rayleigh scattering regime) Exact treatment of scattering difficult (impossible?) However: Confirmed using DDA and RT calculations

Lidar/Radar Inversion Procedure Lidar+Radar Signals  /Z e =F(R' eff ) Retrieve R' eff,  Habit/size dist form info. R eff IWC Radar Reflectivity Lidar Signal Effective Radius IWC Extinction Can be problematic Can be problematic

Add Doppler Velocity....So we have. and V t is calculated using the work of Mitchell (1996) where it is a function of: D Mass(D) Area(D) Temperature Pressure V t is calculated using the work of Mitchell (1996) where it is a function of: D Mass(D) Area(D) Temperature Pressure We want to infer !

D-vs-R' eff -vs-R eff and V d (For single particles ) Habit relationships (or similar form)

Ice crystal size-dist model From aircraft measurements it is known that Ice-crystal size-distributions are generally multi-modal Model of Ivanova/Mitchel two-mode gamma with `fixed' small-mode parameters Increasing N l Increasing r l Small mode parameters 1

ARM-SGP data IWC'=IWC(R' eff /R eff ) R' eff Lidar signal Radar Z e range/time points !! range/time points !! 5 months Data Want to examine average behavior with Temperature and IWC Want to examine average behavior with Temperature and IWC

Direct point by-point inversions possible. But... Doppler is noisy (updrafts downdrafts etc..) ==> Many points can not be fit (30% to 40 % depending on habit) Results will be biased Doppler is noisy (updrafts downdrafts etc..) ==> Many points can not be fit (30% to 40 % depending on habit) Results will be biased Thus... We have binned whole data set according to IWC(') and temperature across different times, clouds etc. ==> Affects of air motions on average values should be eliminated. Thus... We have binned whole data set according to IWC(') and temperature across different times, clouds etc. ==> Affects of air motions on average values should be eliminated.

Bin by T and IWC' (not yet IWC) IWC'=IWC(R'eff/Reff) Increasing IWC' g/m 3

Fits of bi-modal model to averaged and T/IWC' binned data (Complex PC assumed) Note: Can not get a defensible fit for some habits !!! (9 IWC' intervals used-only 2 shown here) =R o +R a T (for each IWC(') interval) N l /N s =CR' eff

Comparisons (size distribution)

Average large-mode particle size

R eff -vs-Temperature

Summary+Conclusions Average behavior of ice-crystal size-dist can be well-described (in terms of observed lidar/radar effective radius and mean Doppler velocity) by a bi-modal size-dist model. Small-mode fixed. Large mode parameters function of both IWC and Temperature ! Results consistent with previous in-situ measurements. Results depend on assumed habit. However, some standard habits do not fit the data.

Differences in average R eff -vs-T behavior between previous studies may be in part due to different IWC sampled. (reanalyses of in-situ data ?) Small-mode contributions can not (in general) be ignored ! Small-mode effects most important at relatively lower IWC(Temperature) values. Results have been used to construct tables of R eff, visible extinction and mass-weighted fall-velocity-vs-T and IWC. Summary+Conclusions II

For bi-modal size distributions Compact Polycrystals (Mitchell. 1996) Mean particle radii in large mode

Results: For complex polycrystals =R o +R a T N l /N s =CR' eff R o =R o (IWC) ; R a =R a (IWC)

For bi-modal size distributions Compact Polycrystals (Mitchell. 1996) Increasing N l Non-unique relationship ! Non-unique relationship ! Unique Relationship !

Average Behavior with T and IWC ! Increasing IWC' g/m 3

Bin by IWC' (not yet IWC) IWC'=IWC(R'eff/Reff) Increasing IWC' g/m 3