1. Iterative and constrained algorithms to generate cloud fields with measured properties Victor Venema Clemens Simmer Susanne Crewell Bonn University 1 1.5 2 R eff Surrogate 02468 0 2 4 6 8 0 2 4 6 8 02468 1 1.5 2

2. Problem  Radiative transfer through clouds –Validation, closure experiment –Retrievals and parameterisations  Use measured cloud fields  Use measured cloud properties

3. Perfectly fractal clouds  Clouds are well described by fractal mathematics  Scale free description  Full power spectrum –Scale breaks –Waves  Exact distribution

4. Amplitude distribution  Amplitude (LWP, LWC,  ) alone is already good: See Independent Pixel Approximation (IPA)  Especially very important are the cloud free portions  Together with power spectrum it also ‘defines’ the structure

5. Iterative algorithm (Schreiber and Schmitz)

6. Iterative algorithm  Spectral adaptation –Calculate spectrum iterate time series –Replace magnitudes by those from the original time series –The phases are kept unaltered  Amplitudes adaptation –By ranking –Replace values by the original values with same ranking –E.g. largest iterate value is replace by largest values of template

7. 1D Iterative LWP surrogates

8. 3D surrogate clouds  Made surrogates routinely for the BBC campaign  2 3D-examples  2D LWP fields Time [hr] UT Height [km] LWC template [kg/m 3 ] 10.511 1.4 1.6 1.8 2 2.2 0 0.1 0.2 0.3 0.4 0.5 LWC Surrogate 0246 0 2 4 6 0 2 4 6 0246 1.5 2 Time [hr] UT Height [km] LWC template [kg/m 3 ] 13.213.4 1 1.5 2 0 0.5 1 1.5 LWC Surrogate 02468 0 2 4 6 8 0 2 4 6 8 02468 1 1.5 2

9. Nonlinear cells – template (Schroeter and Raasch)

10. Nonlinear cells - surrogate

11. Nonlinear cells surrogate template

12. Nonlinearity testing  Cells stratocumulus  Fall streaks –Also in low LWP sections –Less clear in LWC fields  Cloud top and base structure –Convergence  Phase space of LWC (in situ)

13. Validation surrogate clouds  3D LWC fields from LES modelling –Cumulus: Brown et al., ARM –Stratocumulus: Duynkerke et al., FIRE  Make surrogates from their statistics  Calculate radiative properties  Compare all pairs

14. Validation RadianceReflectance Stratocumulus Cumulus

15. Constrained surrogates  Arbitrary constraints  Evolutionary search algorithm  Better convergence  Try new statistics  Fractal geometry for cloud boundaries

16. Evolutionary search algorithm

17. Constrained surrogates  height profiles –cloud base –cloud top –cloud cover –average LWC  Histograms –LWP –LWC –number of layers  Power spectra & length –LWP –Highest cloud top –Lowest cloud base

18. Conclusions and outlook  Iterative surrogate clouds have good radiative properties  Generate 3D LWC field from a measurement  Investigate which statistics are needed to describe structure  Iterative wavelet surrogates  Constrained surrogates to try different statistical properties –‘Fractal’ cloud boundaries –‘Multifractal’ liquid water –No periodic boundary conditions

19. Outlook  Go from scanning measurement to Cartesian grid: fractal interpolation  Anisotropic power spectrum  More samples  Better decorrelation

20. More information - Webpage  Iterative algorithms (Matlab)  Examples –Measurements –Theoretical conditions  Articles in PDF  http://www.meteo.uni-bonn.de/ victor/themes/surrogates/  Google: surrogate cloud fields