1. 1 Cloud Boundaries 2 Cloud Sizes 3 Cloud Overlap On scaling aspects in cloud geometry and its relevance for Climate Modeling Pier Siebesma, Harm Jonker, Roel Neggers and Olivier Geoffroy KNMI RK-Lunch (without food), 20100427

2. Tools Satellites Ground based remote sensing High Resolution Modeling (LES)

3. What it’s not about……….. Mesoscale organisation, cold pools etc………..

4. Instead………..

5. 1 Cloud Boundaries Siebesma and Jonker Phys. Rev Letters (2000)

6. Is this a Cloud?? ….and, how to answer this question?

7. “Shapes, which are not fractal, are the exception. I love Euclidean geometry, but it is quite clear that it does not give a reasonable presentation of the world. Mountains are not cones, clouds are not spheres, trees are not cylinders, neither does lightning travel in a straight line. Almost everything around us is non- Euclidean”. Fractal Geometry Benoit Mandelbrot Instead of

8. Area-Perimeter analyses of cloud patterns (1) Procedure: Measure the projected cloud area A p and the perimeter L p of each cloud Define a linear size through Perimeter dimension define through: Slope: D p = 1 For “ordinary” Euclidean objects:

9. Pioneered by Lovejoy (Science 1982) Area-perimeter analyses of projected cloud patterns using satellite and radar data Suggest a perimeter dimension Dp=4/3 of projected clouds!!!!! Confirmed in many other studies since then… Area-Perimeter analyses of cloud patterns (2) Instead of Consequences: Cloud perimeter is fractal and hence self-similar in a non-trivial way. Makes it possible to ascribe a (quantitative) number that characterizes the structure Provides a critical test for the realism of the geometrical shape of the LES simulated clouds!!!! Slope 4/3

10. Similar analysis with LES clouds Measure Surface As and linear size of each cloud Plot in a log-log plot Assuming isotropy, observations would suggest Ds=Dp+1=7/3

11. Result of one cloud field

12. Repeat over 6000 clouds

13. Some Direct Consequences Surface area can be written as a function of resolution (measuring stick) l : Euclidian area SL underestimates true cloud surface area S(l=  ) by a factor LES model resolution of l=50m underestimates cloud surface area still by a factor 5!!! Does this have consequences for the mixing between clouds and the environment??? With L=outer scale (i.e. diameter of the cloud) and the normalizing area if measured with L, and  the Kolmogorov scale

14. Transport = Contact area x Flux turbulence diffusive flux Resolution dependence for transport over cloud boundary (1) resolved advection Subgrid diffusion

15. Consequences for transport over cloud boundary (2) (Richardson Law) No resolution dependancy for Ds=7/3!!

16. Is this shear luck ???? Not really: Repeat the previous arguments for Boundary flux T only Reynolds independent if which completes a heuristic “proof” why clouds are fractal with a surface dimension of 7/3.

17. Gradient Percolation A stronger underlying mechanism ? (Peters et al JAS 2009) Dp=4/3

18. 2 Cloud Sizes Neggers, Jonker and Siebesma JAS (2003)

19. Cloud size distributions (1) Many observational studies: Log-normal ( Lopez1977) Exponential (Plank 1969, Wielicki and Welch 1986) Power law (Cahalan and Joseph 1989, Benner and Curry 1998) N(l) l

20. Cloud size distributions (2) Repeat with LES. Advantages Controlled conditions Statistics can be made arbitrary accurate Link with dynamics can be established N(l) l Specific Questions: What is the functional form of the pdf? What is the dominating size for the cloud cover? Which clouds dominate the vertical transport?

21. Definitions: Projection area of cloud n: Size : Total number of clouds: Cloud fraction: Related through:

22. Typical Domain: 128x128x128 Number of clouds sampled: 35000 Power law with b=-1.7 Scale break in all cases Scale break size l d case dependant ( 700m~1250m) Cloud Size Density

23. Cloud size density (2) Universal pdf when rescaled with scale- break size l d

24. Cloud Fraction density Dominating size With b=-1.7 (until scale break size) b<-2 smallest clouds dominate cloud cover b>-2 largest clouds dominate cloud cover Due to scale break there is a intermediate dominating size

25. Conclusions Cloud size distribution: with b=-1.7 Non-universal scale break size beyond which the number density falls off stronger. (Only free parameter left) No resolution dependency has been found Intermediate cloud size has been found which dominates the cloud fraction (Similar for mass flux)

26. Open Questions: What is the physics behind the power law of the cloud density distribution? What is causing the scale break?

27. 3 Cloud Overlap Neggers, Siebesma and Heus, submitted to BAMS (observational evidence) Neggers and Siebesma, to be submitted to GRL (parameterization not treated here) Jonker, Siebesma and Geoffroy, in Progress (exploring the geometrical causes)

28. Consider a discretized vertical column of air with partially cloudy gridboxes: Representing cloud overlap in GCMs Problem: where to position the part containing cloud relative to the other levels Very important for vertical radiative transfer GCMs can not resolve overlap themselves, so parameterization is required. Existing functions: Cloud fraction a max apap height Cloud fraction MaximumRandomMaximum - Random SW radiation

29. Different tendency to form cumulus anvils is caused by differences in the vertical structure of model mass flux: MM Non-mixing; Fixed structure Mixing; Flexible structure Tiedtke (1989) in IFSEDMF-DualM

30. ECMWF IFS difference in summertime diurnal cloud cover between CY32R3 + EDMF-DualM and CY32R3 Thanks to Martin Köhler, ECMWF 1 The GCM problem free climate run, June-July 2008 new stnd

31. Along with a daily mean 2m temperature bias over land……… free climate run, June-July 2008

32. Suggesting: 1. less PBL clouds 2. larger SW down 3. larger H 4. low level warming SW

33. stnd new Tiedtke (1989) stnd M Constant mass flux; Fixed structure M Mixing; Flexible structure EDMF-DualM (new)

34. New scheme has more realistic mixing New scheme has a better cloud fraction profile But……. Systematic too low cloud cover?? And a positive bias in the T_2m stnd new obs stnd new

35. stnd new obs It must be the cloud overlap stnd new New scheme has more realistic mixing New scheme has a better cloud fraction profile But……. Systematic too low cloud cover?? And a positive bias in the T_2m

36. Cloud Overlap functions: at present maximum overlap for BL-clouds (in all GCMs!) height Cloud fraction cf max Implies : total cloud fraction cf tot = cf max Is this a realistic assumption? LES revisited cftot/cfmax = 2~3 depending on shear, depth of cloud layer cf tot

37. Cloud Overlap functions: at present maximum overlap for BL-clouds (in all GCMs!) height Cloud fraction cf max Implies : total cloud fraction cf tot = cf max Is this a realistic assumption? LES revisited cftot/cfmax = 2~3 depending on shear, depth of cloud layer Even without shear! This number is enough to correct the bias in cloud cover and short wave radiation ! cf tot Cloud fraction height cf max

38. z acac dz=40m LES z acac Climate Model dz=300m Would this be a good verification of the Cloud fraction profile of the climate model?

39. z acac dz=40m LES z acac Climate Model dz=300m z acac Coarse grained LES dz=300m

40. Large Eddy Simulation Shallow Cumulus Convection (BOMEX) No Shear Blue: Ab: maximum cloud fraction (near cloud base) Red: Ap: projected cloud fraction

41. Ratio between projected cloudy area and average cloudy area for individual clouds What is causing this high ratio?

42. Procedure: Bin all clouds according to their height Determine the cloudy area as a function of height for all subsets h Determine the projected cloudy area as a function of height for all subsets h

43. Hypotheses: x z R-R- R+R+ R x y R-R- R+R+ R

46. x z R-R- R+R+ R x y R-R- R+R+ R

51. x z R-R- R+R+ R x y R-R- R+R+ R

56. 4/3 !?

57. Hypotheses: x z R-R- R+R+ R x y R-R- R+R+ R

59. x z R-R- R+R+ R x y R-R- R+R+ R

60. Recenter the centre of mass at each level. An unsolved riddle!

61. Maximum overlap assumption in GCMs underestimates the total cloud fraction by a factor 2~3 (even without shear). This gives rise to systematic overestimation of surface temperature in GCMs. Projected cloudy area scales with cloud thickness with a 4/3 power. (Probably) mainly due to a random walk of the centre of mass of the clouds. A simple parameterization (not treated here) can be derived that takes into account shear and irregularity. Summary Supergrid-scale (organized structures, shear)  z ~ 100-200m Subgrid-Scale (irregularity)