On scaling aspects in cloud geometry and its relevance for Climate Modeling

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. Instead of Fractal Geometry • “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”. Benoit Mandelbrot

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

9. Instead of Area-Perimeter analyses of cloud patterns (2) • 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… 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. Surface area can be written as a function of resolution (measuring stick) l : Some Direct Consequences With L=outer scale (i.e. diameter of the cloud) and the normalizing area if measured with L, and h the Kolmogorov scale • Euclidian area SL underestimates true cloud surface area S(l=h) 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???

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

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

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

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

19. N(l) l Cloud size distributions (1) • Many observational studies: • Log-normal (Lopez 1977) • Exponential (Plank 1969, Wielicki and Welch 1986) • Power law (Cahalan and Joseph 1989, Benner and Curry 1998)

20. N(l) l • Repeat with LES. Advantages • Controlled conditions • Statistics can be made arbitrary accurate • Link with dynamics can be established Cloud size distributions (2) • 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. Cloud Size Density • Power law with b=-1.7 • Scale break in all cases • Scale break size ld case dependant (700m~1250m) Typical Domain: 128x128x128 Number of clouds sampled: 35000

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

24. Cloud Fraction density With b=-1.7 (until scale break size) • b<-2 smallest clouds dominate cloud cover • b>-2 largest clouds dominate cloud cover Dominating size 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. Representing cloud overlap in GCMs SW radiation Consider a discretized vertical column of air with partially cloudy gridboxes: 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: height amax Cloud fraction Cloud fraction Cloud fraction ap Maximum Random Maximum - Random

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

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

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

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

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

34. new stnd obs 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

35. new stnd It must be the cloud overlap obs 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!) Is this a realistic assumption? height cfmax cftot LES revisited Cloud fraction Implies : total cloud fraction cftot = cfmax cftot/cfmax = 2~3 depending on shear, depth of cloud layer

37. height cfmax Cloud fraction cftot Cloud Overlap functions: at present maximum overlap for BL-clouds (in all GCMs!) Is this a realistic assumption? height cfmax cftot LES revisited Cloud fraction Implies : total cloud fraction cftot = cfmax 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!

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

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

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: R R+ R- z x R+ R- R y x

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