iterative and constrained algorithms to generate cloud fields with measured properties
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Iterative and constrained Iterative and constrained algorithms to generate algorithms to generate
cloud fields with cloud fields with measured propertiesmeasured properties
Victor Venema Victor Venema Clemens Simmer Clemens Simmer Susanne CrewellSusanne Crewell
Bonn UniversityBonn UniversityTime [hr] UT
Hei
ght [
km]
LWC template [kg/m 3]
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/m 3]
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
ProblemProblem Radiative transfer through cloudsRadiative transfer through clouds
– Validation, closure experimentValidation, closure experiment– Retrievals and parameterisationsRetrievals and parameterisations
Use measured cloud fieldsUse measured cloud fields Use measured cloud propertiesUse measured cloud properties
Perfectly fractal cloudsPerfectly fractal clouds Clouds are well described by fractal Clouds are well described by fractal
mathematicsmathematics Scale free descriptionScale free description
Full power spectrumFull power spectrum– Scale breaksScale breaks– WavesWaves
Exact distributionExact distribution
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)
Iterative algorithmIterative algorithm Spectral adaptation Spectral adaptation
– Calculate spectrum iterate time series Calculate spectrum iterate time series – Replace magnitudes by those from the Replace magnitudes by those from the
original time seriesoriginal time series– The phases are kept unalteredThe phases are kept unaltered
Amplitudes adaptationAmplitudes adaptation– By rankingBy ranking– Replace values by the original values with Replace values by the original values with
same rankingsame ranking– E.g. largest iterate value is replace by E.g. largest iterate value is replace by
largest values of templatelargest values of template
1D Iterative LWP surrogates1D Iterative LWP surrogates
1000 2000 3000 4000 5000 6000 7000 80000
100
200
300
400
500
Time (s)
LWP
(gr/m
2 )
1000 2000 3000 4000 5000 6000 7000 80000
100
200
300
400
500
Time or space
LWP
or L
WC
0 500 1000 1500 2000 2500 3000 35000
100
200
300
400
500
600
Number
LWP
(gr/m
2 )
MeasuredSurrogate
10-3
10-2
10-1
10-5
100
105
k (Hz)
Pow
er
MeasuredSurrogate
3D surrogate clouds3D surrogate clouds Made Made
surrogates surrogates routinely for the routinely for the BBC campaign BBC campaign
2 3D-examples2 3D-examples 2D LWP fields2D LWP fields
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
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
Nonlinear cells – templateNonlinear cells – template((Schroeter and RaaschSchroeter and Raasch))
Template LES stratocumulus
10 20 30 40 50 60 70
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70
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10 20 30 40 50 60 701.522.533.5
Nonlinear cells - surrogateNonlinear cells - surrogateSurrogate stratocumulus
10 20 30 40 50 60 70
10
20
30
40
50
60
70
10
20
30
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10 20 30 40 50 60 701.522.533.5
Nonlinear cellsNonlinear cellsTemplate LES stratocumulus
10 20 30 40 50 60 70
10
20
30
40
50
60
70
10
20
30
40
50
60
70
10 20 30 40 50 60 701.522.533.5
Surrogate stratocumulus
10 20 30 40 50 60 70
10
20
30
40
50
60
70
10
20
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50
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10 20 30 40 50 60 701.522.533.5
surrogate
template
Nonlinearity testingNonlinearity testing Cells stratocumulusCells stratocumulus Fall streaksFall streaks
– Also in low LWP sectionsAlso in low LWP sections– Less clear in LWC fieldsLess clear in LWC fields
Cloud top and base structureCloud top and base structure– ConvergenceConvergence
Phase space of LWC (in situ)Phase space of LWC (in situ)
Validation surrogate cloudsValidation surrogate clouds 3D LWC fields from LES modelling3D LWC fields from LES modelling
– Cumulus: Brown et al., ARMCumulus: Brown et al., ARM– Stratocumulus: Stratocumulus: Duynkerke et al., FIREDuynkerke et al., FIRE
Make surrogates from their statisticsMake surrogates from their statistics Calculate radiative propertiesCalculate radiative properties Compare all pairsCompare all pairs
0.3 0.4 0.5 0.6 0.7
0.3
0.4
0.5
0.6
0.7
refle
ctan
ce s
urro
gate
reflectance template
(a)
ValidationValidation
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)
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)
RadianceReflectanceS
trato
cum
ulus
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
]
0.05 0.1 0.15
0.02
0.04
0.06
0.08
0.1
0.12
0.14
refle
ctan
ce s
urro
gate
reflectance template cumulus
Cum
ulus
Constrained surrogatesConstrained surrogates Arbitrary constraintsArbitrary constraints Evolutionary search algorithmEvolutionary search algorithm
Better convergenceBetter convergence Try new statisticsTry new statistics Fractal geometry for cloud boundariesFractal geometry for cloud boundaries
Evolutionary search algorithmEvolutionary search algorithm
Constrained surrogatesConstrained surrogates height profilesheight profiles
– cloud basecloud base– cloud topcloud top– cloud covercloud cover– average LWCaverage LWC
HistogramsHistograms– LWPLWP– LWCLWC– number of layersnumber of layers
Power spectra & lengthPower spectra & length– LWPLWP– Highest cloud topHighest cloud top– Lowest cloud baseLowest cloud base
Conclusions and outlookConclusions and outlook Iterative surrogate clouds have good Iterative surrogate clouds have good
radiative propertiesradiative properties Generate 3D LWC field from a measurementGenerate 3D LWC field from a measurement Investigate which statistics are needed to Investigate which statistics are needed to
describe structuredescribe structure
Iterative wavelet surrogatesIterative wavelet surrogates Constrained surrogates to try different Constrained surrogates to try different
statistical propertiesstatistical properties– ‘‘Fractal’ cloud boundariesFractal’ cloud boundaries– ‘‘Multifractal’ liquid waterMultifractal’ liquid water– No periodic boundary conditionsNo periodic boundary conditions
OutlookOutlook Go from scanning measurement to Go from scanning measurement to
Cartesian grid: fractal interpolationCartesian grid: fractal interpolation Anisotropic power spectrumAnisotropic power spectrum More samplesMore samples Better Better
decorrelationdecorrelation
More information - WebpageMore information - Webpage Iterative algorithms (Matlab)Iterative 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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