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Iterative and constrained algorithms to generate cloud fields with measured properties

R. Surrogate. 3. LWC template [kg/m. ]. LWC Surrogate. e. f. f. 2.2. 0.5. 6. 6. 6. 6. 0.4. 2. 4. 4. 4. 4. 0.3. 1.8. Height [km]. 2. 2. 2. 2. 0.2. 1.6. 0.1. 0. 0. 0. 0. 1.4. 0. 2. 4. 6. 0. 2. 4. 6. 0. 2. 2. 10.5. 11. 1.5. 1.5. Time [hr] UT. 0. 2.

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Iterative and constrained algorithms to generate cloud fields with measured properties

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  1. R Surrogate 3 LWC template [kg/m ] LWC Surrogate e f f 2.2 0.5 6 6 6 6 0.4 2 4 4 4 4 0.3 1.8 Height [km] 2 2 2 2 0.2 1.6 0.1 0 0 0 0 1.4 0 2 4 6 0 2 4 6 0 2 2 10.5 11 1.5 1.5 Time [hr] UT 0 2 4 6 0 2 4 6 3 LWC template [kg/m ] LWC Surrogate 1.5 8 8 2 6 6 1 4 4 Height [km] 1.5 2 2 0.5 0 0 0 2 4 6 8 1 0 13.2 13.4 Time [hr] UT 0 2 4 6 8 Iterative and constrained algorithms to generate cloud fields with measured properties Victor Venema Clemens Simmer Susanne Crewell Bonn University R Surrogate e f f 8 8 6 6 4 4 2 2 0 0 0 2 4 6 8 2 2 1.5 1.5 1 1 0 2 4 6 8

  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 3 LWC template [kg/m ] LWC Surrogate 2.2 0.5 6 6 0.4 2 4 4 0.3 1.8 Height [km] 2 2 0.2 1.6 0.1 0 0 1.4 0 2 4 6 0 2 10.5 11 1.5 Time [hr] UT 0 2 4 6 3 LWC template [kg/m ] LWC Surrogate 1.5 8 8 2 6 6 1 4 4 Height [km] 1.5 2 2 0.5 0 0 0 2 4 6 8 1 2 0 1.5 13.2 13.4 1 Time [hr] UT 0 2 4 6 8

  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 Reflectance Radiance 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

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