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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
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

problem
Problem
  • Radiative transfer through clouds
    • Validation, closure experiment
    • Retrievals and parameterisations
  • Use measured cloud fields
  • Use measured cloud properties
perfectly fractal clouds
Perfectly fractal clouds
  • Clouds are well described by fractal mathematics
  • Scale free description
  • Full power spectrum
    • Scale breaks
    • Waves
  • Exact distribution
amplitude 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
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
3d surrogate clouds
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

nonlinear cells
Nonlinear cells

surrogate

template

nonlinearity testing
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
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
Validation

Reflectance

Radiance

Stratocumulus

Cumulus

constrained surrogates
Constrained surrogates
  • Arbitrary constraints
  • Evolutionary search algorithm
  • Better convergence
  • Try new statistics
  • Fractal geometry for cloud boundaries
constrained surrogates1
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
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
Outlook
  • Go from scanning measurement to Cartesian grid: fractal interpolation
  • Anisotropic power spectrum
  • More samples
  • Better decorrelation
more information webpage
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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