Introduction to Introduction to cloud structure generators cloud structure generators

Victor Venema Victor Venema — — Clemens SimmerClemens Simmer

Possible cloud generatorsPossible cloud generators

Cloud model (LES)Cloud model (LES) Measured cloud structureMeasured cloud structure Fourier method (Power spectrum)Fourier method (Power spectrum) Fractal method (Power spectrum)Fractal method (Power spectrum) Evolutionary search algorithmEvolutionary search algorithm

Measured cloudMeasured cloud

Ground based measurementsGround based measurements– Measuring with different anglesMeasuring with different angles– Scanning too slowScanning too slow

Wind smearingWind smearing Non-linear and intermittent behaviourNon-linear and intermittent behaviour

Airborne or satellite measurementsAirborne or satellite measurements– Better chancesBetter chances

Measured cloud (field) statisticsMeasured cloud (field) statistics

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Fourier - introductionFourier - introduction

-5/3 Power spectrum-5/3 Power spectrum

Recipe:Recipe:

– Calculate LWP/LWC spectrumCalculate LWP/LWC spectrum

– Multiply random phaseMultiply random phase

– Inverse Fourier transform Inverse Fourier transform

– Multiple clouds Multiple clouds

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Block cloudBlock cloud

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Fourier – random phaseFourier – random phase

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Fourier – Time seriesFourier – Time series

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Fractal – IntroductionFractal – Introduction

Also: Bounded cascade modelAlso: Bounded cascade model Based on a -5/3 Power spectrumBased on a -5/3 Power spectrum R. Cahalan, A. Davis, A. Marshak, R. Cahalan, A. Davis, A. Marshak,

W. WiscombeW. Wiscombe

Recipe:Recipe:– Take homogenous cloudTake homogenous cloud– Devide it in twoDevide it in two– Redistribute LWC in random directionRedistribute LWC in random direction– And so onAnd so on

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Cascade 1Cascade 1

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Cascade 1Cascade 1

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2 Dimensional2 Dimensional

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Comparison Fourier - FractalComparison Fourier - Fractal

Both have same spectrum but have Both have same spectrum but have different structuredifferent structure

Just power spectrumJust power spectrum Need more statistical parametersNeed more statistical parameters

A search for cloudsA search for clouds

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XX·Y·Z = ·Y·Z = 256x256x64 = 2256x256x64 = 22222 = = 4.2 104.2 1066 pixels pixels

256 LWC values256 LWC values values values pixelspixels = 2 = 2352352 10 10105105

possibilitiespossibilities Search with evolutionary algorithm Search with evolutionary algorithm

& knowledge of solution& knowledge of solution

Recipe evolutionary algorithmRecipe evolutionary algorithm

Population of cloudsPopulation of clouds

Calculate their fitness / cost Calculate their fitness / cost functionfunction

Select the fittest onesSelect the fittest ones

They produce the new generation They produce the new generation with some mutationswith some mutations

And so on, until quality sufficientAnd so on, until quality sufficient

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Example – AltostratusExample – Altostratus

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Example – Input cloudExample – Input cloud

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Example – Input statisticsExample – Input statistics One-point cloud boundary statisticsOne-point cloud boundary statistics

– Histogram number of cloud layersHistogram number of cloud layers– Height histogram / profilesHeight histogram / profiles

Cloud basesCloud bases Cloud topsCloud tops Cloud coverCloud cover Cloud edgesCloud edges

Search first at large scales / low Search first at large scales / low resolutionresolution

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Example – histogramsExample – histograms

Edges

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Example – ResolutionsExample – Resolutions

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Example – searchingExample – searching

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Example – Search resultsExample – Search results

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Example – resourcesExample – resources

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ds 22256x256 = 256x256 = 2232 32 4x10 4x1099 Possibilities Possibilities

Found: 2-3 x10Found: 2-3 x1055 Attemps Attemps About 1 hour of calculation on PC About 1 hour of calculation on PC

(IDL; 700 MHz; 256 Mb)(IDL; 700 MHz; 256 Mb) Amount of attemps is linear Amount of attemps is linear

function of number of pixelfunction of number of pixel

3-Dimensional3-Dimensional

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Fitness functionFitness function Easy to computeEasy to compute Reward progressReward progress

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intermediate result 2

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wanted histogram

Population and selectionPopulation and selection Population 100 cloudsPopulation 100 clouds 9 Clouds reproduce / mutate9 Clouds reproduce / mutate Deep search: Large reproductive Deep search: Large reproductive

fraction and small populationfraction and small population Wide search: Small reproductive Wide search: Small reproductive

fraction and large populationfraction and large population

Selection is based on average Selection is based on average ranking for each fitness functionranking for each fitness function

The best cloud does not mutateThe best cloud does not mutate

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Knowledge of solutionKnowledge of solution

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– Quality criterion (next resolution)Quality criterion (next resolution)

Mutation typesMutation types LWC cloud: fractal algorithm as LWC cloud: fractal algorithm as

first guessfirst guess

OutlookOutlook 2-Point statistics2-Point statistics Liquid Water ContentLiquid Water Content Use all measurements availableUse all measurements available

– Lidar: cloud baseLidar: cloud base– Radar: cloud top / baseRadar: cloud top / base– Microwave radiometer: LWP spectrum / Microwave radiometer: LWP spectrum /

histogramhistogram– Infrared radiometer: cloud coverInfrared radiometer: cloud cover– PVM: LWC power spectra (small scales) & PVM: LWC power spectra (small scales) &

LWC profilesLWC profiles

Effective radius?Effective radius? Interpolation of direct Interpolation of direct

measurements possiblemeasurements possible

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Gedanken experimentGedanken experiment Helps to think about what kind of Helps to think about what kind of

statistics one needsstatistics one needs Little information on vertical LWC Little information on vertical LWC

variationsvariations Temporal developmentTemporal development

– Zeppelin, balloonZeppelin, balloon

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ConclusionsConclusions Multiple statistical parameters Multiple statistical parameters

needed to describe cloudsneeded to describe clouds Search algorithm seems possibleSearch algorithm seems possible Combine various statistics from Combine various statistics from

many sourcesmany sources Two-point statistics and LWCTwo-point statistics and LWC

Which statistics are needed with Which statistics are needed with what accuracy / resolution?what accuracy / resolution?

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