Lagrangian representation of microphysics in numerical models. Formulation and application to cloud geo-engineering problem

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Tobias Henry
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1 Lagrangian representation of microphysics in numerical models. Formulation and application to cloud geo-engineering problem M. Andrejczuk and A. Gadian University of Oxford University of Leeds

2 Outline Microphysics parametrizations Lagrangian formulation Cloud geo-engeneering Application of Lagrangian microphysics Conclusions

3 Microphysics parametrizations Microphysics parametrization is still unresolved problem! Bulk models: qc=qv-qvs (if qv > qvs) No information (limited) about droplet spectrum Bin models f r dr = f r t r dt Problem with representing aerosol and numerical diffusion (i-1,j+1) (i,j+1) Lagrangian approach dr i A = S S eq r,r a,... dt r i To many droplets! ~108 m-3 (i-1,j) (i,j)

models f r dr = f r t r dt Problem with representing aerosol and numerical diffusion

4 Stochastic particle approach Track (artificial) parcels representing real aerosol particle For typical LES grid (40m x 40m x 10m) instead 16 x physical aerosol track 100, each representing 16 x 109 identical aerosol. Spectrum for each grid can be composed from these parcels No problems with numerical diffusion when solving growth equation Sub-grid scale information available Only one additional information to keep number of physical particles parcel represents (i-1,j+1) (i,j+1) Problems? Sampling error How to treat coalescence (i-1,j) (i,j)

Spectrum for each grid can be composed from these parcels No problems with numerical diffusion when solving growth equation Sub-grid

5 Coalescence representation Kinetic collection equation (descrite representaion): Ni N = i t V i j K i, j N j Problem with limiting the number of parcels Collision of two parcels results in 3 (two old, representing less droplets and one new - bigger) 100 parcels initially (n(n-1)/2 collisions on each timestep) 1-th timestep nd timestep 12 million There are approximate solutions to this problem - transfer of droplets between parcels (Shima 2009)

droplets and one new - bigger) 100 parcels initially (n(n-1)/2 collisions on each timestep) 1-th timestep 5050

6 Coalescence representation Mapping on the Eulerian grid: Existing: (N1,r1,ra1), (N2,r2,ra2), (N3,r3,ra3)... Old:(N1-N12-N13-...,r1,ra1), (N2-N12-N23-...,r2,ra2), (N3-N13-N23-...,r3,ra3)... New: (N12,r12,ra12), (N13,r13,ra13), (N23,r23,ra23)... N(ri,raj)= Nkl W(ri,raj)= Nkl(r3k,l-r3akl) A(ri,raj)= Nklr3akl, IF (N(ri,raj) > TL) create new parcel: Nm= N(ri,raj) ram=(a(ri,raj)/nm)1/3 rm=(ram3+w(ri,raj)/nm)1/3 ra r

.. N(ri,raj)= Nkl W(ri,raj)= Nkl(r3k,l-r3akl) A(ri,raj)= Nklr3akl, IF (N(ri,raj) > TL) create new

7 Coalescence representation Merging parcels having similar properties Existing: (N1,r1,ra1), (N2,r2,ra2), (N3,r3,ra3)... Old:(N1-N12-N13-...,r1,ra1), (N2-N12-N23-...,r2,ra2), (N3-N13-N23-...,r3,ra3)... New: (N12,r12,ra12), (N13,r13,ra13), (N23,r23,ra23)... ra new parcel: Nm= N(ri,raj) ram=(a(ri,raj)/nm)1/3 rm=(ram3w(ri,raj)/nm)1/3 Merge conserving water aerosol and number r

..,r3,ra3)... New: (N12,r12,ra12), (N13,r13,ra13), (N23,r23,ra23).

8 Coalescence validation Lagrangian - solid Eulerian - dashed Solutions after 200, 800, 1400, and 2000 s for hydrodynamic kernel with Long collision efficiency for Bott scheme and Lagrangian scheme 30 bins 60 bins 120 bins 240 bins

hydrodynamic kernel with Long collision efficiency for

9 Model Formulation Dynamics/thermodynamics (Eulerian) du = 1/ P i,3 B D u F pu dt d = C d dt d L =D C d dt cp dq v =D qv C d dt Microphysics (Lagrangian) du p 1 = u u p i,3 g dt p dr p A = S Seq r p, r pa dt r p N p N = p t V dx p =u p dt p j K p, j N j

dt Microphysics (Lagrangian) du p 1 = u u p i,3 g dt p dr p A

10 Cloud geo-engineering Adding aerosol to increase cloud albedo less Solar radiation more Stratocumulus cloud Aerosol source

11 Model setup Model 2D domain 80x200 (dx=40, dz=10) Periodic boundary conditions Radiative cooling near the cloud top Setup similar to Stevens cases from VOCALS observations HIGH cloud droplet number (250 cm-3) MED cloud droplet number (120 cm-3) LOW cloud droplet number (65 cm-3) 200 m Additional aerosol Initial conditions (dynamics, thermodynamics and aerosol) from VOCALS observations. Each case have different aerosol distribution, temperature, qv and velocity profiles

number (120 cm-3) LOW cloud droplet number (65 cm-3) 200 m Additional aerosol Initial conditions (dynamics,

12 Model Location and size of parcels with r > 1 um 1<r<10 10<r<20 20<r<50 50<r<100 r>100 Diagnosed qc qc [g/kg]

13 Model Validation How cloud albedo and cloud droplet concentration responds to additional aerosol? How additional aerosol affects droplet and aerosol spectrum? How additional aerosol affects activation of cloud droplets? Perturbations run REFERENCE RUN 2h no coalescence END 2h coalescence 6 hours

How additional aerosol affects droplet and aerosol spectrum?

14 Cloud Albedo Reference +100 cm cm cm cm-3 Statistically insignificant increase Solid ra=0.1μm Dashed ra=0.5 μm Last 1 hour ra=0.1 ra=0.5 RUN HIGH MED REF σ LOW Cloud Albedo: A=0.75(1-g)τ/(1+0.75(1-g)τ) asymmetry factor(0.85) Statistically significant decrease optical thickness t = b [2 n r r dr ]dz 2 Ap>Ar ΔA Ap>Ar ΔA Hp100 N 0.4 N* -2.5 Hp200 N 0.1 N* -2.0 Hp Hp Mp Mp Mp Mp Lp Lp Lp Lp

85) Statistically significant decrease optical thickness t = b [2 n r r dr ]dz 2 Ap>Ar ΔA Ap>Ar ΔA Hp100 N 0.4 N* -2.5 Hp200 N 0.

15 Bulk changes da=(<ap>-<ar>) - ra=0.5μm - ra=0.1μm HIGH MED LOW Strong dependence on specific case Sensitivity for MED aerosol O - Aerosol MED profiles LOW X - Aerosol MED profiles HIGH Different REF runs! Aerosol properties more important than dynamics and thermodynamics HIGH MED LOW θ [k] qv [g/kg] u [m/s] Within BL

Aerosol MED profiles LOW X - Aerosol MED profiles HIGH Different REF runs!

16 Aerosol/Droplet Spectra Reference +100 cm cm cm cm-3 Cloud droplet Increase in concentration of the small droplets HIGH MED LOW Aerosol Formed in the coalescence process

17 Aerosol activation HIGH MED LOW ra = 0.5 dashed ra = 0.1 solid Reference +100 cm cm cm cm-3 Aerosol competing effect strong only when seeding with large aerosol! But does not affect the number significantly.

18 Conclusions Cloud albedo may increase when stratocumulus clouds are seeded with the aerosol (must be big enough to activate) Best results when seeding clouds with low/moderate droplet concentration For high cloud droplet concentration seeding may not affect albedo (but albedo for these clouds already increases with time) Strong effect of the aerosol properties on da dn Key is to deliver aerosol into the cloud! Perturbation run Mp m below cloud base 400m 600m 700m MED ref run

seeding may not affect albedo (but albedo for these clouds already increases with time) Strong effect of the aerosol

PHYSICAL-CHEMICAL PROCESSES OF CLOUD ACTIVATION STUDIED WITH A DESKTOP CLOUD MODEL

PHYSICAL-CHEMICAL PROCESSES OF CLOUD ACTIVATION STUDIED WITH A DESKTOP CLOUD MODEL Stephen E. Schwartz [email protected] Brookhaven National Laboratory Upton NY USA 11973 6th International Conference Air-Surface