Towards parameterization of cloud drop size distribution for large scale models Wei-Chun Hsieh Athanasios Nenes Image source: NCAR

Motivation Current General Circulation Models (GCMs) treat cloud microphysics as bulk properties, i.e., one-single size Ignore cloud drop size distribution would bias the estimate of indirect effect which is subject to the largest uncertainty in climatic forcing assessment (IPCC 2007) The estimated indirect decrease % as considering size distribution effect, i.e., droplet dispersion [Liu and Daum, NATURE, 2002] Uncertainty in estimate of indirect effect is related to cloud microphysical schemes, especially autoconversion parameterization

More CCN Less CCN Indirect effect Effective radius (μm) West coast (California) Aerosol act as Cloud Condensation Nuclei (CCN). Anthropogenic emissions increase their levels  Decreases cloud droplet size  more reflection of sunlight (“first” indirect effect)  cloud precipitation decreases (“second” indirect effect) Rosenfeld, Kaufman, and Koren, ACPD, 2005 Estimate of Indirect effect is subject to the largest uncertainty for climatic forcing assessment (IPCC, 2007)

Objective Developing parameterization to explicitly compute droplet growth (i.e., evolution of droplet size distribution properties). Then important cloud microphysical properties such as LWC, effective radius, droplet spectrum width can be obtained With these droplet size distribution characteristics, we can also compute autoconversion rates with existing parameterizations

Based on Fountoukis and Nenes, 2005 We assume that the droplets ascend in an updraft and evolve within a Lagrangian frame of reference. The model explicitly computes growth of droplet population by condensation of excess water vapor generated by cooling as raising air parcel adiabatically. The Framework

Algorithm for computing droplet size distribution. Input: P, T, updraft velocity, aerosol & gas phase characteristics. Initial conditions at s max : Droplet Size Distribution, DSD, n d (D p ) The rate change of supersaturation ds/dt is given by = W’ ?? Droplets growth is continuously computed until the integrated LWC reach LWC W’ predicted from large scale model. Photo source: CSTRIPE imagery V: updraft velocity dW/dt: rate change of liquid water content (LWC), W The equation of droplet growth Output: DSD as a function of time (height) n d (D p ) = f(t) D pi : droplet size of section i; G: growth factor s eq is the equilibrium s of the droplet

Evaluation of droplet growth parameterization  clouds sampled during NASA CRYSTAL-FACE and CSTRIPE (Meskhidze et al., 2005).  CRYSTAL-FACE is for cumulus clouds in Key West, Florida (2002).  CSTRIPE is for stratecumulus clouds in Monterey, California (2003). Evaluation of droplet growth parameterization The framework is evaluated by comparing predicted size distribution with those computed from a numerical parcel model (Nenes et al., 2001) for clouds sampled during NASA CRYSTAL-FACE and CSTRIPE (Meskhidze et al., 2005). CRYSTAL-FACE is for cumulus clouds in Key West, Florida (2002). CSTRIPE is for stratecumulus clouds in Monterey, California (2003). The majority of data are within 15% of the parcel model predictions; lower relative dispersion predicted by parameterization is mainly due to the underestimation of spectrum width and not mean droplet size (Figure on the right). This deviation is small suggesting that using the activation parameterization provides a good boundary condition for subsequent growth. Evaluation with parcel model

Evaluation of droplet growth parameterization Lower relative dispersion predicted by parameterization is mainly due to the underestimation of spectrum width and not mean droplet size This deviation is small suggesting that using the activation parameterization provides a good boundary condition for subsequent growth.

Evaluation with in-situ observations We focus on spectra without drizzle and are relatively narrow to avoid entrainment effect The narrow spectrum observed in near adiabatic regions is still broader than the predicted adiabatic spectrum

Spectra Broadening 0.32    0.1 Average ratios Broadening of the DSD is in part from variability of updraft in clouds This variability is accounted for by averaging spectra over the PDF of updraft velocity relative dispersion (defined as standard deviation over mean radius of cloud drop distribution)

Prediction of autoconversion Liu and Daum (2004) R 6 and R 6c : mean and critical radius of 6 th moment of cloud droplet distribution k 2 and  6 : Stokes constant and coefficient related to cloud drop dispersion. N and L: cloud drop number and cloud liquid water content. H: threshold function which specifies the onset of autoconversion when R 6 > R 6c  : relative dispersion (  =  /r m ) cloud drop number cloud liquid water content

Linking growth with autoconversion Autoconversion rates are computed using the P 6 formulation of Liu and Daum (2004): Underestimation of Autoconversion rates by parcel model and parameterization is mainly due to the underprediction of relative dispersion. (Left) Agreement of autoconversion rates between predicted and measured is improved by adjusting (increasing) the relative dispersion by a factor of 5. (Right) P 6 autoconversion rates (Predicted relative dispersion) P 6 autoconversion rates (Adjusted relative dispersion)

Uncertainty of autoconversion rates Autoconversion errors come from errors in droplet number and relative dispersion. Errors in droplet number tend to partially cancel errors from relative dispersion. On average, autoconversion uncertainty was -41.1% and +3.4% from the predicted relative dispersion and cloud drop number concentration for CRYSTAL-FACE and -58.4% and +5.6% in CSTRIPE.

Summary I The growth parameterization framework links drop activation with collision-coalescence and predicts evolution of cloud droplet distributions Good agreement between parameterization and detail numerical model indicates the framework is capable to provide cloud microphysics and is feasible to implement in general circulation models (GCMs). Evaluation of framework with in-situ observations show an underestimation of spectrum dispersion. Considering PDF updrafts has the effect to broaden the droplet distribution. However, we still systematically underpredict spectrum dispersion; this suggests we are in the “right direction” but still need to include additional broadening mechanisms. For the time being, we can apply the framework with the systematic correction of spectral dispersion.

Summary II This underestimation would cause 50% underestimation of computed autoconversion rates and this uncertainty may amplify due to errors in predicting cloud drop number concentration. Our study shows drop spectra has significant influence in predicting autoconversion rates and this may have crucial impacts in assessment of second aerosol indirect effect and distribution of precipitation.

Thank you Questions?

Overall, underestimation of relative dispersion by framework is seen for majority of the data and this is due to adiabatic assumption in the framework. We only consider droplets whose growth is controlled by diffusion of water vapor which tend to narrow the droplet spectra. The underestimation is about a factor of 5.