1. Development of cloud resolving model with microphysical bin model and parameterizations to predict the initial cloud droplet size distribution KUBA, Naomi Frontier Research Center for Global Change (FRCGC / JAMSTEC) kuba@jamstec.go.jp ICMW 2004, 2004, 7, 13, Hamburg

2. Contents 1.Introduction 2.Parameterizations to predict cloud droplet number 3.Parameterizations to predict cloud droplet size distribution 4.Comparison between the parameterization and particle method 5.Results of numerical experiments 6.Conclusions

3. CCN Spectrum Number of cloud droplets Rain water Generation Efficiency Updraft S max 1. Introduction Optical properties Size distribution of cloud droplets Cloud microphysical model3D non-hydrostatic regional modelPurpose

4. CCN Spectrum Number of cloud droplets Rain water Generation Efficiency Updraft S max 1. Introduction Optical properties Size distribution of cloud droplets Bin method (Eulerian framework)

5. CCN Spectrum Number of cloud droplets Rain water Generation Efficiency Updraft S max 1. Introduction Optical properties Size distribution of cloud droplets Parcel model with particle method (Lagrangian framework)

6. CCN Spectrum Number of cloud droplets Rain water Generation Efficiency Updraft S max 1. Introduction Optical properties Size distribution of cloud droplets Parameterization derived from numerical experiments using parcel model

7. Contents 1.Introduction 2.Parameterizations to predict cloud droplet number 3.Parameterizations to predict cloud droplet size distribution 4.Comparison between the parameterization and particle method 5.Results of numerical experiments 6.Conclusions

8. 2. Parameterization to predict cloud droplet number N d = A N c (S) / (N c (S) + B ) V base < 0.24 m s -1 S = 0.2 % A = 4710 V base 1.19 B = 1090 V base + 33.2

9. 2. Parameterization to predict cloud droplet number N d = A N c (S) / (N c (S) + B ) 0.24 < V base < 0.5 m s -1 S = 0.4 % A = 11700 V base - 1690 B = 10600 V base + 1480

10. 2. Parameterization to predict cloud droplet number N d = A N c (S) / (N c (S) + B ) 0.5 < V base < 1.0 m s -1 S = 0.5 % A = 4300 V base 1.05 B = 2760 V base 0.755

11. 2. Parameterization to predict cloud droplet number N d = A N c (S) / (N c (S) + B ) 1.0 < V base < 3.0 m s -1 S = 1.0 % A = 7730 - 15800 exp(-1.08V base ) B = 6030 - 24100 exp(-1.87V base )

12. 2. Parameterization to predict cloud droplet number N d = A N c (S) / (N c (S) + B ) 3.0 < V base < 10.0 m s -1 S = 2.0 % A = 1140 V base - 741 B = 909V base - 56.2

13. Relatioship between Critical supersaturation and dry radius of CCN N c ( S c R ) S (%) 0.2 0.4 0.5 1.0 2.0 R (  m) Sea Salt NaCl 0.036 0.023 0.019 0.012 0.0077 Sulfate (NH 4 ) 2 SO 4 0.048 0.031 0.027 0.017 0.011 Organic carbon ??? Black carbon ??? Dust ???

14. Relatioship between Critical supersaturation and dry radius of CCN N c ( S c R ) S (%) 0.2 0.4 0.5 1.0 2.0 R (  m) Sea Salt NaCl 0.036 0.023 0.019 0.012 0.0077 Sulfate (NH 4 ) 2 SO 4 0.048 0.031 0.027 0.017 0.011 Organic carbon 0.074 0.047 0.040 0.025 0.016 Black carbon Dust Ghan et al., 2001, J. Geophys. Res., 106, D6, 5295-5316 Table 1 density =1 hygroscopicity = 0.14

15. Contents 1.Introduction 2.Parameterizations to predict cloud droplet number 3.Parameterizations to predict cloud droplet size distribution 4.Comparison between the parameterization and particle method 5.Results of numerical experiments 6.Conclusions

16. 3. Parameterization of cloud droplet size distribution Gamma distribution. n( r ) = C r  exp(-Dr) dr C = N d ( 4  (  +3)(  +2)(  +1)N d / 3Q ) (  +1)/3 /  ! D = ( 4  (  +3)(  +2)(  +1)N d / 3Q ) 1/3 n( r ) : Number density ( cm -4 ) N d : Number of cloud droplets ( cm -3 ) Q : Cloud water ( g cm -3 ) Q adjust > Q crit

17. Contents 1.Introduction 2.Parameterizations to predict cloud droplet number 3.Parameterizations to predict cloud droplet size distribution 4.Comparison between the parameterization and particle method 5.Results of numerical experiments 6.Conclusions

18. Two schemes for microphysics particle method ( in the parcel ) bin method ( on the grid ) Framework Lagrangian Eulerlian Fixed values Number concentration of CCN Representative radius of Variable values Radius of droplets forming Number concentration of on CCN included in each class. droplets included in each bin. Activation Takeda and Kuba (1982) not considered Condensation Takeda and Kuba (1982) Coalescence not considered 0.05 s 0.5 s  t r j (t) n j (j = 1, 2,…,200) r i = r 1 2 (i-1)/3k (i = 1, 2,…,200) n i (t) included in each class droplets included in each bin. 2 - moment bin method ( Chen and Lamb, 1994 ) 2 - moment bin method ( Chen and Lamb, 1994 )

19. When relative humidity at the grid point reaches 100% for the first time Initial cloud droplets size distribution Parcel model is triggered When relative humidity at the grid point is larger than 100% and cloud water on the windward side of the point does not exist Influx of droplets from the windward Bin on the grid point

20. Two schemes for microphysics particle method ( in the parcel ) bin method ( on the grid ) Framework Lagrangian Eulerlian Fixed values Number concentration of CCN Representative radius of Variable values Radius of droplets forming Number concentration of on CCN included in each class. droplets included in each bin. Activation Takeda and Kuba (1982) not considered Condensation Takeda and Kuba (1982) Coalescence not considered 0.05 s 0.5 s  t r j (t) n j (j = 1, 2,…,200) r i = r 1 2 (i-1)/3k (i = 1, 2,…,200) n i (t) included in each class droplets included in each bin. 2 - moment bin method ( Chen and Lamb, 1994 ) 2 - moment bin method ( Chen and Lamb, 1994 ) Parameterization

21. WMO 5th Cloud Modeling Workshop 2000, Aug, 7-11 Glenwood Springs, Colorado, U.S.A. Case1-Warm Rain Development Provided by Szumowski et al. (1998) Dynamical flame flow field : 2D shallow convection (time dependent flow function) domain : 9 km wide x 3 km deep  x,  z : 50 m  t : 3 sec advection scheme: modified Smolarkiewicz (1984) CCN spectrum N CCN = fn(S) etc.

22. Wind Field (25 min )

23. Size distribution of CCN Chemical composition NaCl

24. Contents 1.Introduction 2.Parameterizations to predict cloud droplet number 3.Parameterizations to predict cloud droplet size distribution 4.Comparison between the parameterization and particle method 5.Results of numerical experiments 6.Conclusions

25. 10 0 10 2 10 4 10 6 dN/dR ( cm -4 ) Radius of droplet (  m ) Initial size distribution of cloud droplets for bin method CCN-1.0 (4.5 km,1.78km) 5.5min. Without parameterizations (with parcel model) With parameterizations gamma distr.  = 2 gamma distr.  = 4

26. 10 0 10 2 10 4 10 6 dN/dR ( cm -4 ) Radius of droplet (  m ) Size distribution of cloud droplets CCN-1.0 (4.5 km,1.93km) 8.5min. Without parameterizations (with parcel model) With parameterizations gamma distr.  = 2 gamma distr.  = 4

27. Horizontal distance ( km ) Altitude ( km ) CCN-0.5 Number concentration of cloud droplets ( cm -3 ) 25 min. without parameterization (with parcel model) with parameterization

28. Altitude ( km ) CCN-1.0 Number concentration of cloud droplets ( cm -3 ) 25 min. without parameterization (with parcel model) with parameterization Horizontal distance ( km )

29. Altitude ( km ) CCN-5 Number concentration of cloud droplets ( cm -3 ) 25 min. with parameterization without parameterization (with parcel model) Horizontal distance ( km )

30. 0 1 2 3 4 5 6 7 8 9 Accumulated Rainfall ( mm ) 5 4 3 2 1 0 without parameterization Average in a domain (mm) 1.22 1.24 1.19 CCN- 0.5 50 min. Horizontal distance ( km ) with parameterization gamma distri.  = 2  = 4

31. 0 1 2 3 4 5 6 7 8 9 Accumulated Rainfall ( mm ) 5 4 3 2 1 0 CCN- 1 50 min. Horizontal distance ( km ) without parameterization with parameterization gamma distri.  = 2  = 4 0.97 0.99 0.92 Average in a domain (mm)

32. 0 1 2 3 4 5 6 7 8 9 Accumulated Rainfall ( mm ) 5 4 3 2 1 0 CCN- 5 50 min. Horizontal distance ( km ) without parameterization with parameterization gamma distri.  = 2  = 4 0.16 0.24 0.16 Average in a domain (mm)

33. Contents 1.Introduction 2.Parameterizations to predict cloud droplet number 3.Parameterizations to predict cloud droplet size distribution 4.Comparison between the parameterization and particle method 5.Results of numerical experiments 6.Conclusions

34. Parameterizations Number Size distribution Cloud microphysical model Bin method Cloud dynamical model Rainfall Optical properties Small errorUseful to Non-hydrostatic 3D Model !

35. We are installing these parameterizations and 2-moment bin method to CReSS We plan to run it on Earth Simulator ( Simulation for Case 1 ) and to compare the results of original CReSS with that of CReSS with bin model Cloud Resolving Storm Simulator Tsuboki, K and A. Sakakibara, Large-scale parallel computing of Cloud Resolving Storm Simulator. High Performance Computing, Springer, H. P. Zima et al. Eds, 243--259. 2002

36. Issues Lack of data CCN spectrum N c ( S %) CCN counter Updraft velocity at the cloud base