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Iterative and constrained algorithms to generate cloud fields with measured properties

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R### Iterative and constrained algorithms to generate cloud fields with measured properties

Surrogate

3

LWC template [kg/m

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LWC Surrogate

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Victor Venema Clemens Simmer Susanne Crewell

Bonn University

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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

- 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

- 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

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10.5

11

1.5

Time [hr] UT

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LWC template [kg/m

]

LWC Surrogate

1.5

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6

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Height [km]

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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

Constrained surrogates

- Arbitrary constraints
- Evolutionary search algorithm
- Better convergence
- Try new statistics
- Fractal geometry for cloud boundaries

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
- http://www.meteo.uni-bonn.de/ victor/themes/surrogates/
- Google: surrogate cloud fields

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