1. Introduction to cloud structure generators Victor Venema — Clemens Simmer

2. Possible cloud generators  Cloud model (LES)  Measured cloud structure  Fourier method (Power spectrum)  Fractal method (Power spectrum)  Evolutionary search algorithm

3. Measured cloud  Ground based measurements –Measuring with different angles –Scanning too slow  Wind smearing  Non-linear and intermittent behaviour  Airborne or satellite measurements –Better chances  Measured cloud (field) statistics Measure directly

4. Fourier - introduction  -5/3 Power spectrum  Recipe: –Calculate LWP/LWC spectrum –Multiply random phase –Inverse Fourier transform –Multiple clouds Fourier Clouds

5. Block cloud Fourier Clouds

6. Fourier – random phase Fourier Clouds

7. Fourier – Time series Fourier Clouds

8. Fractal – Introduction  Also: Bounded cascade model  Based on a -5/3 Power spectrum  R. Cahalan, A. Davis, A. Marshak, W. Wiscombe  Recipe: –Take homogenous cloud –Devide it in two –Redistribute LWC in random direction –And so on Fractal Clouds

9. Cascade 1 Fractal Clouds 1 0.8 0.64 hallo

10. Cascade 1 Fractal Clouds

11. 2 Dimensional Fractal Clouds

12. Comparison Fourier - Fractal  Both have same spectrum but have different structure  Just power spectrum  Need more statistical parameters

13. A search for clouds Living Clouds  Statistics are known  X·Y·Z = 256x256x64 = 2 22 = 4.2 10 6 pixels  256 LWC values  values pixels = 2 352  10 105 possibilities  Search with evolutionary algorithm & knowledge of solution

14. Recipe evolutionary algorithm  Population of clouds  Calculate their fitness / cost function  Select the fittest ones  They produce the new generation with some mutations  And so on, until quality sufficient Living Clouds

15. Example – Altostratus Living Clouds

16. Example – Input cloud Living Clouds

17. Example – Input statistics  One-point cloud boundary statistics –Histogram number of cloud layers –Height histogram / profiles  Cloud bases  Cloud tops  Cloud cover  Cloud edges  Search first at large scales / low resolution Living Clouds

18. Example – histograms

19. Example – Resolutions Living Clouds

20. Example – searching Living Clouds

21. Example – Search results Living Clouds

22. Example – resources Living Clouds  2 256x256 = 2 32  4x10 9 Possibilities  Found: 2-3 x10 5 Attemps  About 1 hour of calculation on PC (IDL; 700 MHz; 256 Mb)  Amount of attemps is linear function of number of pixel

23. 3-Dimensional Living Clouds

24. Fitness function  Easy to compute  Reward progress Living Clouds

25. Population and selection  Population 100 clouds  9 Clouds reproduce / mutate  Deep search: Large reproductive fraction and small population  Wide search: Small reproductive fraction and large population  Selection is based on average ranking for each fitness function  The best cloud does not mutate Living Clouds

26. Knowledge of solution Living Clouds  Start with low resolution –Quality criterion (next resolution)  Mutation types  LWC cloud: fractal algorithm as first guess

27. Outlook  2-Point statistics  Liquid Water Content  Use all measurements available –Lidar: cloud base –Radar: cloud top / base –Microwave radiometer: LWP spectrum / histogram –Infrared radiometer: cloud cover –PVM: LWC power spectra (small scales) & LWC profiles  Effective radius?  Interpolation of direct measurements possible Living Clouds

28. Gedanken experiment  Helps to think about what kind of statistics one needs  Little information on vertical LWC variations  Temporal development –Zeppelin, balloon Living Clouds

29. Conclusions  Multiple statistical parameters needed to describe clouds  Search algorithm seems possible  Combine various statistics from many sources  Two-point statistics and LWC  Which statistics are needed with what accuracy / resolution? Living Clouds