Iterative and constrained algorithms to generate cloud fields with measured properties
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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 schreiber and schmitz
Iterative algorithm (Schreiber and Schmitz)


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 template schroeter and raasch
Nonlinear cells – template(Schroeter and Raasch)



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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