3D cloud fields with 3D cloud fields with measured power spectra and measured power spectra and LWC height distributions for LWC height distributions for

radiative transfer calculationsradiative transfer calculations

Victor Venema, Sebastián Gimeno García, Steffen Meyer, Victor Venema, Sebastián Gimeno García, Steffen Meyer, Clemens Simmer, Susanne Crewell, Ulrich Löhnert, Clemens Simmer, Susanne Crewell, Ulrich Löhnert,

Thomas Trautmann, Andreas MackeThomas Trautmann, Andreas Macke

3D cloud fields with 3D cloud fields with measured power spectra and measured power spectra and LWC height distributions for LWC height distributions for

radiative transfer calculationsradiative transfer calculationsVictor Venema, Clemens Simmer, Susanne Crewell, Ulrich LöhnertVictor Venema, Clemens Simmer, Susanne Crewell, Ulrich Löhnert

University of BonnUniversity of Bonn

Sebastián Gimeno García, Thomas TrautmannSebastián Gimeno García, Thomas TrautmannUniversity of Leipzig / DLRUniversity of Leipzig / DLR

Steffen Meyer, Andreas MackeSteffen Meyer, Andreas MackeUniversity of KielUniversity of Kiel

3D surrogate clouds3D surrogate clouds

Time [hr] UT

Hei

ght

[km

]

LWC template [kg/m3]

10.5 11

1.4

1.6

1.8

2

2.2

0

0.1

0.2

0.3

0.4

0.5

LWC Surrogate

0 2 4 60

2

4

6

0

2

4

6

0 2 4 61.5

2

3D LWC field2D Measurement

ProblemProblem Radiative transfer through cloudsRadiative transfer through clouds

– Radiative transfer modelsRadiative transfer models– Realistic cloud fieldsRealistic cloud fields

Dynamical cloud modelsDynamical cloud models Fractal cloudsFractal clouds Empirical surrogate cloudsEmpirical surrogate clouds

– Stay closer to the measurementStay closer to the measurement

Empirical surrogate cloudsEmpirical surrogate clouds Surrogate clouds have (statistical) Surrogate clouds have (statistical)

properties of measured cloudsproperties of measured clouds

Retrievals & parameterisationsRetrievals & parameterisations– Empirical alternativeEmpirical alternative

Validation, closure experimentsValidation, closure experiments– Close to the measured cloud fieldClose to the measured cloud field

Power spectrumPower spectrum Fourier transform, square the Fourier transform, square the

coefficientscoefficients Describes the linear spatial correlations Describes the linear spatial correlations

in the fieldin the field Signal is a super positioning of sinusesSignal is a super positioning of sinuses Equivalent to an spatial autocorrelation Equivalent to an spatial autocorrelation

functionfunction Gaussian PDFGaussian PDF

Amplitude distributionAmplitude distribution Amplitude (LWP, LWC, Amplitude (LWP, LWC, ) alone is ) alone is

already good: See Independent Pixel already good: See Independent Pixel Approximation (IPA)Approximation (IPA)

Especially very important are the cloud Especially very important are the cloud free portionsfree portions

Together with power spectrum it also Together with power spectrum it also ‘defines’ the structure‘defines’ the structure

Iterative algorithm Iterative algorithm (Schreiber and Schmitz)(Schreiber and Schmitz)

Add an dimensionAdd an dimension Assume isotropyAssume isotropy Rotate and scale power spectrumRotate and scale power spectrum

1000 2000 3000 4000 5000 6000 7000 80000

100

200

300

400

500

Time (s)

LWP

(gr

/m2 )

Time (s)

Tim

e (s

)

2000 4000 6000 8000

1000

2000

3000

4000

5000

6000

7000

8000 0

100

200

300

400

500

TemplateTemplate SurrogateSurrogate

LWC profilesLWC profiles

8 8.2 8.4 8.6 8.8 9 9.2 9.4

300

400

500

600

700

800

900

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

3.6 29.5 55.1 80.7 107 132 158 184

He

igh

t (m

)

Distance (km)

Time (h)

8 8.2 8.4 8.6 8.8 9 9.2 9.4

300

400

500

600

700

800

900

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

3.6 29.5 55.1 80.7 107 132 158 184

He

igh

t (m

)

Distance (km)

Time (h)

3D surrogate clouds3D surrogate clouds

Time [hr] UT

Hei

ght [

km]

LWC template [kg/m3]

10.5 11

1.4

1.6

1.8

2

2.2

0

0.1

0.2

0.3

0.4

0.5

LWC Surrogate

0 2 4 60

2

4

6

0

2

4

6

0 2 4 61.5

2

Reff Surrogate

0 2 4 60

2

4

6

0

2

4

6

0 2 4 61.5

2

Time [hr] UT

Hei

ght [

km]

LWC template [kg/m3]

13.2 13.41

1.5

2

0

0.5

1

1.5

LWC Surrogate

0 2 4 6 80

2

4

6

8

0

2

4

6

8

0 2 4 6 81

1.52

Reff Surrogate

0 2 4 6 80

2

4

6

8

0

2

4

6

8

0 2 4 6 81

1.52

Validation surrogate cloudsValidation surrogate clouds Which statistical parameters are Which statistical parameters are

needed to describe cloud structure?needed to describe cloud structure? Does the distribution and spectrum Does the distribution and spectrum

suffice?suffice?

MethodMethod– Modelled 3D LWC fields (template)Modelled 3D LWC fields (template)– Make surrogates from their statisticsMake surrogates from their statistics– Calculate radiative propertiesCalculate radiative properties– Compare themCompare them

Surrogate stratocumulus Surrogate stratocumulus ((Duynkerke et al., FIREDuynkerke et al., FIRE))

TemplatesTemplates SurrogatesSurrogates

Surrogate stratocumulusSurrogate stratocumulus

0.3 0.4 0.5 0.6 0.7

0.3

0.4

0.5

0.6

0.7re

flect

ance

sur

roga

te

reflectance template

(a)

Rel. bias: 2 10-4,

Rel. RMS: 2 10-4

Rel. bias: < 7 10-4,

Rel. RMS: 6 10-3

0.02 0.04 0.06 0.08 0.1

0.02

0.04

0.06

0.08

0.1

radi

ance

sur

roga

te

radiance template

(b)

Surrogate cumulus Surrogate cumulus ((Brown et al., ARMBrown et al., ARM))

TemplatesTemplates SurrogatesSurrogates

Surrogate cumulusSurrogate cumulus

Rel. bias: < 1 10-2

Rel. RMS: 1 10-2

Rel. bias: < 2.3 10-2

Rel. RMS: < 4 10-2

0.05 0.1 0.15

0.02

0.04

0.06

0.08

0.1

0.12

0.14re

flect

ance

sur

roga

te

reflectance template cumulus

0.005 0.01 0.015 0.02

0.005

0.01

0.015

0.02

radiance template cumulus [W m-2 sr-1]

radi

ance

sur

roga

te [W

m-2

sr-1

]

Conclusions and outlookConclusions and outlook Validation LES: description is goodValidation LES: description is good More validation cases available?More validation cases available?

– stratocumulus with holes, dense cumulusstratocumulus with holes, dense cumulus– Raining clouds, more cloud top structure Raining clouds, more cloud top structure

Scanning measurementScanning measurement– More samplesMore samples– Better decorrelationBetter decorrelation– Anisotropic power Anisotropic power

spectrumspectrum

More information - WebpageMore information - Webpage Algorithms (Matlab)Algorithms (Matlab) ExamplesExamples

– MeasurementsMeasurements– Theoretical conditionsTheoretical conditions

Articles in PDFArticles in PDF

http://www.meteo.uni-bonn.de/ http://www.meteo.uni-bonn.de/ victor/themes/surrogates/victor/themes/surrogates/

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