1. Parametric representation of the hydrometeor spectra for LES warm bulk microphysical schemes. Olivier Geoffroy, Pier Siebesma (KNMI), Jean-Louis Brenguier, Frederic Burnet (Météo-France) I.Problematic, methodology and measurements II.Cloud spectrum: results III.Rain spectrum: results IV.Sensitivity tests in shallow cumulus simulations. V.Z-R relationship

2. To derive other moments from M 0 & M 3, M 0 & M 3 it is necessary to make an assumption about the shape of the CDSD and the RDSD Cloud Sedim: Radar reflectivity: Interaction with radiative transfert: τ~M2τ~M2 Rain Sedim Problematic Rain evap: ~M 1 & M 2 autoconversion: Radar reflectivity: N c (M 0 ) & q c (~M 3 ), N r (M 0 ) & q r (~M 3 ) Microphysical processes / variables Cond/evap: Bulk prognostics variables = ~SM 1 =M 6

3. Generalized Gamma Lognormal Are Lognormal, Gamma, Gamma in mass suitable ? With which value of the width parameter σ g or ν? Common distributions ν =1 ν =6 ν =11 α=1 Size distri = Gamma α=3 Mass distri = Gamma = Marshall Palmer σ g =? ν =? 3 parameters M 0, M 3 = prognostics 4 parameters M 0, M 3 = prognostics α =1 or 3

4. Observationnal data Data = particule counters in situ Measurements at 1Hz resolution (~ 100 m). -Sc and Cu spectra - Measurements at each levels in the BL - ~100 m resolution - Complete hydrometeors spectra : 1 µm to 10 mm flight plan RICO : 7 cases of Cu ACE-2 : 8 cases of Sc Fast FSSP : ~2  ~50 µm OAP-260-X : 5  635 µm 2DP-200X: 245  12645 µm Fast FSSP : ~2  ~40 µm OAP-200-X : 35  310 µm Instruments campaign

5. CloudRain D0 D0 Methodology For each spectrum: D 0 = 75 µm Cloud: ACE-2 : 19000 spectra RICO : 8500 spectra

6. q c, N c CloudRain D0 D0 Methodology For each spectrum: D 0 = 75 µm Cloud: ACE-2 : 19000 spectra RICO : 8500 spectra σ g Lognormal M1M1

7. q c, N c CloudRain D0 D0 Methodology For each spectrum: D 0 = 75 µm Cloud: ACE-2 : 19000 spectra RICO : 8500 spectra σ g Lognormal M1M1 M2M2 M5M5 M6M6 σ g

8. ν1ν1 q c, N c CloudRain D0 D0 Methodology For each spectrum: D 0 = 75 µm Cloud: ACE-2 : 19000 spectra RICO : 8500 spectra σ g Gamma Lognormal M1M1 M2M2 M5M5 M6M6 ν1ν1 σ g ν1ν1 ν1ν1

9. ν1ν1 q c, N c CloudRain Methodology For each spectrum: D 0 = 75 µm Cloud: ACE-2 : 19000 spectra RICO : 8500 spectra σ g Gamma in mass Gamma Lognormal M1M1 M2M2 M5M5 M6M6 ν1ν1 σ g ν1ν1 ν1ν1 ν3ν3 ν3ν3 ν3ν3 ν3ν3 D0 D0

10. ν1ν1 q c, N c CloudRain D0 D0 Methodology For each spectrum: D 0 = 75 µm Rain: ACE-2 : not used RICO : 2860 spectra Cloud: ACE-2 : 19000 spectra RICO : 8500 spectra σ g Gamma in mass Gamma Lognormal M1M1 M2M2 M5M5 M6M6 ν1ν1 σ g ν1ν1 ν1ν1 ν3ν3 ν3ν3 ν3ν3 ν3ν3 M1M1 M2M2 M4M4 M6M6 q r, N r ν1ν1 σ g ν1ν1 ν1ν1 ν1ν1 ν3ν3 ν3ν3 ν3ν3 ν3ν3

11. Plan I.Methodology and measurements II.Cloud spectrum: results III.Rain spectrum: results IV.Sensitivity tests in shallow cumulus simulations.

12. Cloud, width parameter=f(M 1 ) Grey points = value of σ g that best represent M 1 for each spectrum Circles = value that minimize the standard deviation of the absolute errors M measure -M analytic in each moment class Triangles = value that minimize the standard deviation of the relative errors M measure / M analytic in each moment class

13. Cloud, width parameter=f(M p ) Circles = value that minimize the standard deviation of the absolute errors M measure -M analytic in each moment class Triangles = value that minimize the standard deviation of the relative errors M measure / M analytic in each moment class Value of the width parameter: Lognormal: Gamma: Gamma in mass:

14. Lognormal: Gamma: Gamma in mass: Cloud, width parameter=f(q c ) Parameterization formulation : Circles = value that minimize the standard deviation of the absolute errors M measure -M analytic in each LWC class Triangles = value that minimize the standard deviation of the relative errors M measure / M analytic in each LWC class

15. Gamma in mass: Gamma: Lognormal: Cloud, relative error=f(M p ) Value of the width parameter:

16. Cloud, relative error = f(q c ) Lognormal: Gamma: Gamma in mass: Parameterizations:

17. Gamma in mass: Gamma: Lognormal: Cloud, relative error=f(M p ) Value of the width parameter:

18. Cloud, relative error = f(q c ) Lognormal: Gamma: Gamma in mass: Parameterizations:

19. Plan I.Methodology and measurements II.Cloud spectrum: results III.Rain spectrum: results IV.Sensitivity tests in shallow cumulus simulations.

20. Rain: Gamma, ν=f(D v ) Seifert (2008) ν=f(D v ) Measurements vs Seifert (2008) results: - Some distributions larger than Marshall Palmer at low D v - Less narrow distributions at high D v 1 16 13 10 7 4 Differences: - Measurements at every levels in cloud region - Seifert (2008): distribution at the surface, no condensation Marshall and Palmer (1948) Stevens and Seifert (2008) ν=f(D v )

21. Rain : free parameter=f(q r ) Dependance in function of qr  Better results Lognormal: Gamma: Gamma in mass: Parameterizations : Circles = value that minimize the standard deviation of the absolute errors M measure -M analytic in each RWC class Triangles = value that minimize the standard deviation of the relative errors M measure / M analytic in each RWC class

22. Rain : relative errors Dependance in function of qr  Better results Lognormal: Gamma: Gamma in mass: Parameterizations: Marshall Palmer

23. Plan I.Problematic, methodology and measurements II.Cloud spectrum: results III.Rain spectrum: results IV.Sensitivity tests in shallow cumulus simulations. V.Z-R relationship

24. Sensivity test: RICO case LWP (g m -2 ) RWP (g m -2 ) R surface (W m -2 ) Ensemble of models DALES simulations Models of the intercomparison exercise (black) ν 3c =1, ν r =1 ν 3c =f(lwc), ν r =f(lwc)

25. Deeper BL based on RICO θlθl qtqt -0.6 K + 2.5 g kg -1 + 0.5 g kg -1 Colder Moister -0.6 K Averaged profiles restart

26. Sensitivity to ν 3c ν 3c 1f(qc) LWP (g m -2 )14.817.1 RWP (g m -2 )8.94.3 υ c =1  A=8 υ c =2  A=3.75 υ c =3  A= 2.7 Autoconversion rate : =A 3 10 -8 (Seifert and Beheng, 2006)

27. Sensitivity to ν r νrνr 1 f(q c ) ( ) ν SS08 ( ) 611 LWP (g m -2 )15.014.816.018.319.0 RWP (g m -2 )7.68.912.520.323.1 CB CT Processes depending on ν r : rain sedim, evap, self-collection and break-up width

28. Plan I.Problematic, methodology and measurements II.Cloud spectrum: results III.Rain spectrum: results IV.Sensitivity tests in shallow cumulus simulations. V.Z-R relationship

29. Z-R Snodgrass (2009) Z=68 R 2

30. Summary -Development of a parameterization of the width parameter of the cloud droplet spectra as a function of the LWC. -Development of a parameterization of the width parameter of the rain drop spectra as a function of the RWC Lognormal: Gamma: Gamma in mass: Lognormal: Gamma:

31. Z-R Snodgrass: red TRMM: green Only 2dp

32. Z-R

33. Sensitivity to ν r νrνr 1 f(q c ) ( ) ν SS08 ( ) 611 LWP (g m -2 )15.014.816.018.319.0 RWP (g m -2 )7.68.912.520.323.1 Without rain evaporation - Sensivity to ν r in sedim process  similar results as Stevens and Seifert (2008) - Main sensitivity : sedimentation process. ν r in sedim  RWP ν r in sedim  V qr  evap  LWP  RWP ν r in evap  evap  LWP νrνr 1f(q c ) ν SS0 8 611 LWP (g m -2 )12.4/13.313.212.8 RWP (g m -2 )9.5/15.119.221.9 CB CT Processes depending on ν r : rain sedim, evap, self-collection and break-up width Flux precip

34. Observational data ACE-2 : not used RICO : 2860 spectra ACE-2 : 19000 spectra RICO : 8500 spectra Scatterplot all q c -N c values Scatterplot all q r -N r values  Large number of spectra typical of Sc and Cu (RF07, RF08, RF11, RF13)

35. Measured spectra ACE-2 : 8 cases of Sc Fast FSSP : ~2  ~50 µm, 266 bins OAP-260-X : 5  635 µm, 63 bins, Δ bin ~ 10 µm 2DP-200X: 45  12645 µm, 63 bins, Δ bin ~ 200 µm Fast FSSP : ~2  ~40 µm, 266 bins OAP-200-X : 15  310 µm, 15 bins, Δ bin ~ 20 µm RICO : 7 cases of Cu - Complete hydrometeors spectra : 1 µm to 10 mm

36. Parameterization formulation : Cloud, absolute error=f(M p ) Normalization: M 1 : 100 µm cm -3 M 2 :1000 µm 2 cm -3 M 5 :10 7 µm 5 cm -3 M 6 :10 9 µm 6 cm -3 σ: 1 µm

37. Cloud, absolute error =f(q c ) Parameterization formulation : Normalization: M 1 : 100 µm cm -3 M 2 :1000 µm 2 cm -3 M 5 :10 7 µm 5 cm -3 M 6 :10 9 µm 6 cm -3 σ: 1 µm

38. ACE 2 - RICO

39. Only ACE 2

41. Only RICO

43. Rain sedimentation Terminal velocities parameterization (Stevens and Seifert, 2008) : V qr > V Nr V=f(D v ), ν r =1V=f(D v ), ν r =6V=f(D v ), ν r =11 V qr V Nr V qr -V Nr V qr V Nr V qr -V Nr V qr V Nr V qr -V Nr broader : ν r  V qr,V Nr distribution V qr -V Nr  Size sorting

44. Rain sedimentation (averaged profiles) ν  width  V qr  R surf  dRWP /dt  RWP ν  width  RWP  evap  LWP (positive feedback) sc / b-up : low impact Evap : low impact µ  evap but larger droplets  R surf Sedim  LWP  RWP (peaks)  RWP, R surf (large drops)

45. Rain evaporation C evap = 1  D v = constant during evaporation (happens if preence of little drops) C evap = 0  N r = constant during evaporation (happens if only large drops) Rain mixing ratio r r Rain concentration N r C evap = 0.7 – 1 (A. Seifert personal com)

46. C evap sensitivity C evap = 0.7 – 1 (A. Seifert personal com) C evap =1 C evap =0.7 C evap =0 ~2 mm j -1 C evap = 1  D v = constant, N r C evap = 0  N r = constant, D v  evap  LWP and RWP

47. Autoconversion, sensitivity = 8 (υ c =1) = 3.75 (υ c =2) = 2.7 (υ c =3) k cc = 4.44 E9 m 3 kg -2 s -1 10.44 E9 m 3 kg-2 s -1 Autoconversion rate : (Cloud droplet width) Collection efficiency ~2 mm j -1 Sensitivity to the coefficients υ c (cloud droplet spectra width)

48. The rain drop distribution Gamma law :  1 free parameter : ν r Gamma law (r r = 0.2 g kg -1, N r = 10000 m -3 ) ν r = 1 ν r =6 ν r =11 with : D v  ν r ν  Narrower distribution Seifert (2008) ν ν=f(D v ) 1 16 13 10 7 4 1-D bin model spectra : = Marshall Palmer

49. ν r sensivity ν r =1 ν r =f(Dv) ν r =6 ν r =11 ~2 mm j -1 ν Width Size sorting V qr R surf dRWP /dt RWP ν RWP evap LWP Impact due to sedimention (acrr ~ cste)

50. Precipitating flights : RF07, RF08, RF12 (low vlues and low number of points, 0.10 g m-3), RF13, RF11

51. Explicit (bin) scheme 50 – 100 variables  High numerical cost Bulk scheme : only 2 bins cloud rain D 0 ~ 40 - 100 µm 1 - 5 variables  Numerical cost  Parameterisations of the microphysical processes D ~ 40 µm n(D) ~ 1 µm~ 8 mm D n(D) ~ 1 µm~ 8 mm Warm cloud Bulk parameterisation

52. Sensivity test: RICO case LWP (g m -2 ) RWP (g m -2 ) P surface (W m -2 ) DALES simulations

53. Rain: Gamma, ν=f(D v ) Seifert (2008) ν=f(D v ) Measurements vs Seifert (2008) results: - Some distributions larger than Marshall Palmer at low D v - Less narrow distributions at high D v 1 16 13 10 7 4 Differences: - Measurements at every levels in cloud region - Seifert (2008): distribution at the surface, no condensation Marshall and Palmer (1948) Stevens and Seifert (2008) ν=f(D v )

54. Sensitivity to ν r νrνr 1 f(q c ) ( ) ν SS08 ( ) 611 LWP (g m -2 )15.014.816.018.319.0 RWP (g m -2 )7.68.912.520.323.1 CB CT Processes depending on ν r : rain sedim, evap, self-collection and break-up width