1. Development of a New Parameterization for Below-Cloud Scavenging of Size-Resolved Particles by Rain and Snow
Xihong Wang1, Leiming Zhang2, and Michael D. Moran2 ,
1Kellys Environmental Services 2Air Quality Research Division
Toronto, Ontario, Canada Environment Canada
Toronto, Ontario, Canada
2013 CMAS Conference Chapel Hill, North Carolina Oct. 2013

2. Outline Motivation Background and Definitions
Results from Recent Uncertainty Analyses
Methodology for Development of New Below-Cloud Scavenging Parameterization
Results for New Parameterization
Summary

3. Motivation for this Work
Wet deposition (= in-cloud + below-cloud scavenging) is often the dominant removal pathway for atmospheric particles at the global scale (e.g., Stier et al., 2005)
A significant fraction of global precipitation is solid or frozen; one global modelling study (Croft et al., 2009) estimated that ~30% of below-cloud scavenging of sulphate particles by precipitation is due to snow
Model intercomparisons have shown that precipitation scavenging parameterizations have large uncertainties (e.g., Rasch et al., 2000; Textor et al., 2006)

4. Contributing Studies
Wang, X., L. Zhang, and M.D. Moran, 2010: Uncertainty assessment of current size-resolved parameterizations for below-cloud particle scavenging by rain. Atmos. Chem. Phys., 10, , doi: /acp
Wang, X., L. Zhang, and M.D. Moran, On the discrepancies between theoretical and measured below-cloud particle scavenging coefficients for rain - a numerical investigation using a detailed one-dimensional cloud microphysics model. Atmos. Chem. Phys., 11, , doi: /acp
Zhang, L., X. Wang, M.D. Moran, and J. Feng, Review and uncertainty assessment of size-resolved scavenging coefficient formulations for snow scavenging of atmospheric aerosols. Atmos. Chem. Phys., 13, , doi: /acp
Wang, X., L. Zhang, and M.D. Moran, Development of a new semi-empirical parameterization for below-cloud scavenging of size-resolved aerosol particles by both rain and snow. Geoscientific Model Development Discuss., 6 (Submitted).

5. Types of Hydrometeors Rain (rain is “simple”)
Drops of different diameters (Dp)
Snow (snow is more complicated)
[Dm < 5 mm] snow crystals: shapes or habits include plates, columns, stars, needles, dendrites, spheres, and bullets
[Dm > 5 mm] snowflakes: aggregates of snow crystals
Rimed snow crystals, ice pellets, graupel, hail

6. Scavenging Mechanisms
Brownian diffusion
interception (size dependent)
inertial impaction (mass dependent)
thermophoresis
diffusiophoresis
electric charges
wake effects
Aerosol particle-hydrometeor collection efficiency E(dp,Dp) is a dimensionless parameter defined as the rate of collection of aerosol particles of diameter dp by the falling hydrometeor normalized by the number of upstream particles of diameter dp swept per unit time across an area equal to the effective cross-sectional area of the hydrometeor
[Figure from Slinn (1984)]

7. Definition of Scavenging Coefficient Λ
The scavenging coefficent Λ (s-1) describes the
scavenging rate or the fractional reduction per unit time
of either bulk or size-resolved aerosol particle number
concentration (below) or mass concentration
Bulk:
Size-resolved:

8. Theoretical Parameterization of Λ(dp)
where
Aeff is the hydrometeor effective cross-sectional area,
Dp and dp are the hydrometeor and aerosol-particle diameter,
V and v are the hydrometeor and aerosol-particle fall velocity,
E(dp,Dp) is hydrometeor-aerosol particle collection efficiency,
N(Dp) is the hydrometeor number size distribution.
Most theoretical parameterizations of E(dp, Dp) consider only
3 collection mechanisms: Brownian diffusion, interception,
and inertial impaction

9. Finding 1 (Wang et al., 2010): Different formulations for E(dp,Dp), N(Dp), and V(Dp) for scavenging by rain can cause uncertainties in values of Λ(dp) of up to 2 orders of magnitude. Finding 2 (Wang et al., 2010): Theoretical values for Λ(dp) for scavenging by rain are at least one order of magnitude smaller than estimates from field studies.

10. Finding 3 (Wang et al., 2011): Discrepancies between theoretical and field-derived values of Λ(dp) for scavenging by rain can largely be explained by the contribution of vertical diffusion, which is not considered in theoretical parameterizations for Λ(dp) but which does contribute to field-derived estimates.

11. Finding 4 (Zhang et al., 2013): Different formulations for E(dp,Dp), N(Dp), V(Dm), and A(Dm) for scavenging by snow can cause uncertainties in values of Λ(dp) of up to 3 orders of magnitude. Snow particle shape must also be known or assumed.

12. Starting Point for a New Parameterization for Below-Cloud Scavenging of Size-Resolved Particles Recognizing Current Limitations
Few field experiments have investigated size-resolved scavenging by rain and even fewer by snow (2?)
Field-derived values of Λ(dp) implicitly account for more processes than theoretical treatments and hence can only be expected to provide upper bounds on Λ(dp)
Theoretical parameterizations for Λ(dp) have large uncertainties but can be used; empirical schemes should not be used (to avoid process double-counting)
Scavenging by both rain and snow should be considered
A wide range of precipitation conditions and aerosol particle sizes should be considered for widest applicability
Focus should be on the higher values predicted by the available ensemble of theoretical parameterizations based on comparisons to field data (Wang et al., 2010; Zhang et al., 2013)

13. Methodology: Part 1
Develop an ensemble of theoretical parameterizations for Λ(dp) based on consideration of all available formulas for E(dp,Dp), N(Dp), V(Dm), and A(Dm) for rain and for snow
For each value of dp calculate 50th, 70th, 80th, 90th, 95th, and maximum percentile values of Λ(dp) for selected precipitation intensities R from 0.01 to 100 mm h-1 for rain and from to 10 mm h-1 for snow (as liquid water equivalent)

14. Ensemble of Λ(dp) Formulations Considered
Physical Quantity
Number of Formulas
E(d, Dp) 5
N(Dp) 10 VD 8
Λrain
400 3 4 A*
4 (habits)
Λsnow
168
*Some VD formulas for snow are specific to one snow crystal habit, so only 14 possible VD–A combinations

15. Λ(dp) Ensemble for Scavenging by Rain

16. Methodology: Part 2
Starting from a selected percentile value (90th) of Λ(dp), for each value of dp calculate a log-log best-fit line between Λ90(dp) and R for both rain and snow or
Use a least-squares polynomial curve-fitting tool to calculate 6th-order polynomial functions for A(d) and B(d) for both rain and snow; note that the accuracy is improved if fitting is performed for 2 contiguous segments
The result is 2 formulas for Λ90(dp) as a function of precipitation intensity R, one for rain and one for snow

17. Calculation and Fitting of A(d), B(d) for Snow

18. Goodness of Fit for A(d), B(d) for Snow
Original A(d) vs.
Polynomial-Fit A(d)
Relative Error as a Function of d

19. Summary
A new semi-empirical parameterization for below-cloud scavenging of size-resolved aerosol particles by both rain and snow has been developed for use in regional and global air-quality models
The results of recent uncertainty analyses of existing theoretical parameterizations for Λ(d) have been considered as well as available field-derived values ( known representativeness)
The new parameterization has a simple power-law form and only requires precipitation intensity and precipitation type to be provided as inputs ( easy to implement)