Iterative and constrained algorithms to generate cloud fields with measured properties Victor Venema Clemens Simmer Susanne Crewell Bonn University R eff Surrogate

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

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

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

Iterative algorithm (Schreiber and Schmitz)

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

1D Iterative LWP surrogates

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 ] LWC Surrogate Time [hr] UT Height [km] LWC template [kg/m 3 ] LWC Surrogate

Nonlinear cells – template (Schroeter and Raasch)

Nonlinear cells - surrogate

Nonlinear cells surrogate template

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)

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

Validation RadianceReflectance Stratocumulus Cumulus

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

Evolutionary search algorithm

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

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

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

More information - Webpage  Iterative algorithms (Matlab)  Examples –Measurements –Theoretical conditions  Articles in PDF  victor/themes/surrogates/  Google: surrogate cloud fields