Phase Function (no diffraction)

on the solar radiative transfer in the cloudy atmosphere

CumulativeHabilitation Thesis

Dr. AndreasMacke

Kiel

2001

2 Single scattering atice particles in cirrus clouds 4

2.1 Scatteringtheory and iceparticlemodels . . . 5

2.2 The eect of variable cloud microphysicalproperties . . . 7

2.3 Inhomogeneousice particles . . . 9

3 Multiple scattering in inhomogeneous clouds 10

3.1 Cloudstructures . . . 12

3.2 Radiative transfer modeling . . . 12

3.3 Errorestimate ofclassicalradiative transfercodes . . . 16

3.4 Parameterizationofthesolarradiantuxdensitiesinlargescaleatmosphericmodels 18

4 Summary and Conclusion 20

1 Introduction

Cloudsarean impressivemanifestationofcomplexdynamical-thermodynamicalprocessesinthe

atmosphere (see Fig. 1). They inuence our weather and climate and are aected by anthro-

pogenic climatechanges at thesame time.

Withaglobalcoverage ofmorethan60%cloudshave aprevailingeect ontheradiationbudget

ofourplanet. Latentheatfromcondensationprocesseshelpsdrivingatmosphericcirculationcells,

whichinturninteractwiththeoceansystem(e.g. ENSO).(Negative) latentheat istransported

by cloud related condensation and evaporation processes, and the corresponding transports of

fresh water determinevegetationover landand thestabilityoftheoceanicboundarylayer.

This well recognized signicance of the cloudy atmosphere on the state of the earth's climate

standsin strongcontrastto ourquantitativeunderstanding of therelevant physicalprocesses in

clouds. The reasons for this are1) the complex macro- and microphysical properties of clouds,

2) theirfast temporaldevelopment,and 3) theirdiÆcultexperimental accessibility.

Forexample, itiswellknownthatthecloudalbedo eect dominatesthecloudgreenhouse eect,

thus clouds are cooling our climate system (Wielicki et al., 1995). However, estimations of the

globalmeanvalueofthisso-callednetradiativeforcingrangefrom-18to-30Wm 2

(Ramanathan

et al.,1989; Rossow, 1993) dependingonthe methodandtime ofobservation. The uncertainties

are muchlarger at localscales and forspecic cloudtypes.

Formany years a potential discrepancy between theoretically expected and observationally de-

rived solar broadband cloud absorption termed 'anomalous cloud absorption' ranging from 15

to 35 Wm 2

has been discussed (Fritz and MacDonald, 1951; Cess and co authors, 1995; Ra-

manathan and co authors, 1995). However, since the absorbed solar ux can only be obtained

indirectlyfrombalancingmeasurementsofreectedandtransmittedsolarradiation,andbecause

those measurements are subject to large statistical errors, the cloud anomalous absorption is

subjectto muchdebate(Stephens andTsay, 1990). Ontheother hand,thesimpliedtreatment

of cloudradiativetransferinclimatemodelsmayexplainthediscrepanciesaswell(Cairnsetal.,

2000).

Accordingto theIPCCreport\ClimateChange2001" theincreaseofCO

2

from1750 untiltoday

produces with+1.4 Wm 2

thelargest anthropogenicallyinducedchange inthe globalradiative

forcing. Comparing this number with the uncertainties of about 20 Wm 2

in cloud radiative

forcing clearlydemonstrates that a reasonableexplorationand predictionof our climatesystem

requires amuch improvedunderstanding of cloud-radiationinteractions.

The aimoftheworksummarizedinthisthesisistoaccountformostrealisticcloudpropertiesin

thedeterminationoftheradiationbalanceandintheremotesensingofclouds, asbasicresearch,

as a contributionto an improved climate modeling,and as a mandatoryconditionfor detecting

and monitoring human inuenceson thecloudy atmosphere.

In climate models the physics of radiative transfer are required for determining heating and

cooling rates for the entire climate system. For a long time practical solutions of the radiative

transferequationhavebeenavailableforplane-parallelatmosphericlayersonly. Thus,forclimate

modelingandforremotesensingapplicationscloudshavebeenandstillareidealizedbystratiform

layers. Thismayappearasareasonablesimplicationforclouddimensionsaremuchlargeralong

thehorizontalthanalong theverticaldirection. However, thespatialscales thatare relevantfor

radiative transfer, i. e.the mean thepath lengths between two successive extinction 1

processes,

1

Figure 1: \Sea of clouds". Taken from the \Karslruher Wolkenatlas" with kind permission by

Bernhard M"uhr.

canbeassmallasseveralmetersdependingonthecloudopticalthickness. Sincetherelationship

betweenradiativeandcloudpropertiesisnon-linearinmostsituations,theradiativepropertiesof

a homogeneous,i. e.spatiallyaveraged cloud,systematicallydeviates fromthedomain averaged

radiative properties of a more realistic inhomogeneous cloud. For example, the assumption of

plane-parallelcloudsleadstoasystematicoverestimationoftheamountofreectedsolarradiation

(albedo bias)(Cahalanetal., 1994).

Clouds are a global phenomenon. Therefore, cloud monitoring requires reliable satellite based

remote sensing methods. As for the radiation budget problem this impliesthe need for a most

realistic radiative transfer modeling inorder to obtain unbiasedrelationships betweenthe radi-

ances measured at the satellite radiometer and the state of the cloudy atmosphere that causes

these radiances.

Another commonly used simplication in cloud radiative transfer is the general application of

Mie-theory,i.e.theassumption ofperfectlysphericalparticles. Thisassumption iswelljustied

inthecaseofwaterclouds. However, alreadyrain dropsand inparticulariceparticlesinmixed-

phase andcirruscloudsshow pronounceddeviationsfroma sphericalshapewhichleadsto large

errorsifthescatteringandabsorptionpropertiesofthoseparticlesareapproximatedbymeansof

Mie-theory. Forexample,scatteringatnon-sphericalparticlesismore isotropiccomparedto that

of surface- and volume-equivalent spheres. Thus, theuse ofMie-theory applied to non-spherical

particlesproducesanalbedobiassimilarbutwithoppositesignto theuseofhomogeneousclouds

incase ofspatialinhomogeneous cloud elds.

Withthat thespecic goals ofmywork arefocusedon considering

1. the non-sphericity of atmospheric particles in single scattering calculations, in particular

forcirrus clouds,and

i. e. on the two major geometry eects of cloud micro- and macrophysical properties on the

radiative transferinthecloudy atmosphere.

My cumulative habilitation represents a section of my scientic work over the past seven years

that isthematicallybased on thefollowingve publications.

1. Macke, A. and Mishchenko, M. I., 1996. Applicability of regular particle shapes in light

scattering calculationsforatmosphericice particles. Appl. Opt., 35,4291{4296.

A systematic test regarding the applicabilityof idealized ice particle shapesfor

calculating thesinglescatteringand absorptionpropertiesofrealisticicecrystals

incirrusclouds.

2. Macke,A., Francis,P.N.,McFarquhar,G. M.,andKinne,S., 1998. Theroleoficeparticle

shapesand sizedistributionsinthe singlescattering propertiesof cirrusclouds. J.Atmos.

Sci,55(17),2874{2883.

A statisticalestimateof theuncertaintiesinsizedistributionaveraged scattering

and absorptionpropertiesthat arecaused bya prioriassumptionsregardingthe

sizedistributionin specicapplications.

3. Macke, A., Mishchenko, M. I., and Cairns, B., 1996a. The inuenceof inclusions on light

scattering by largeiceparticles. J. Geophys. Res., 101,23,311{23,316.

Thedevelopmentandapplicationofanewmodelthataccountsforlightscattering

and absorptionat non-sphericalinhomogeneousparticles bymeansof combining

geometric opticsand Monte Carlo radiative transfermethods.

4. Macke, A., Mitchell, D., and von Bremen, L., 1999. Monte Carlo radiative transfer calcu-

lationsforinhomogeneous mixedphase clouds. Phys. Chem. Earth (B),24(3), 237{241.

Realization of a fully 3d solar radiative transfer modelwhere all radiative prop-

erties (extinctioncoeÆcient, scattering phase function, single scattering albedo)

are spatiallyinhomogeneous.

5. Scheirer, R. and Macke, A., 2001a. On the accuracy of the independent column approxi-

mation in calculating the downward uxes inthe UV-A, UV-B and PAR spectral ranges.

J. Geophys. Res.,106(D13), 14,301{14,312.

Evaluationoftheerrorinspectralintegratedsolarirradiancesthatarecausedby

commonly usedidealizationsintherepresentation ofclouds inradiative transfer

calculations.

Except for (Scheirer and Macke, 2001a) all publications have been directed by myself. The co-

authorshavecontributedwithhelpfuldiscussions(M.I.Mishchenko,B.Cairns),byprovidingdata

(P.N. Francis, G.M. McFarquhar, S.Kinne) and resultsfrom cloud models(D. Mitchell, L. von

Bremen). The work by Scheirer and Macke (2001a) represents a continuation of (Macke et al.,

1999) and has been development under my scientic supervision. The following summary lists

Figure 2: Schematic illustration of the development of ice particle size and shape. Ice particle

replicates are plotted along a vertical prole of relative humidity with respect to water. From

Miloshevich etal. (2001).

2 Single scattering at ice particles in cirrus clouds

Our understanding of climate processes is considerably hampered by the lack of knowledge re-

garding the contribution of cirrusclouds to the radiation budget and the feedback mechanisms

associatedwiththiscloudtypewithrespecttonaturalandanthropogenicclimateuctuations(e.

g. Liou,1986). Thetheoreticaldescriptionofscatteringandabsorptionpropertiesofatmospheric

ice particles is rendered diÆcult by the strong variability in particle size and shape. However,

that knowledge is a necessary condition for the interpretation of remote sensing data and for

determiningtheradiationbudget. Ingeneral,theopticallythincirruscloudsareassociatedwith

anetwarmingdueto thelargetransmissivityforsolarirradianceand thesmallthermalemission

at the cold cloud tops. However, thenet eect critically depends on optical thickness and par-

ticle size spectra and mayrespond eitherpositive ornegative to changes inour climate (Zhang

et al., 1999). Furthermore, the net radiation budget of cirrusclouds is directly aected by the

steady increase of emissions from aircrafts resulting in larger global cirruscloud cover and in a

modicationof cirrusmicrophysicalproperties(indirect aerosoleect).

Figure2illustratesthechangesinshapeandsizeofatmosphericicecrystalsastheygrowfrommi-

crometersized"quasi-spheres"tomillimetersizeddendritesofhexagonalcolumns(bulletrosettes)

tomeltinglumpsofirregularshapediceparticles. Sincetheparticlesizesvaryalongthreeorders

of magnitudetheaveraged scattering and absorptionproperties also signicantlydependon the

2.1 Scattering theory and ice particle models

Atmospheric ice crystals are large compared to the wavelength of the incoming solar radiation

whichallows to applythegeometric optics method (GOM) to calculatetheir extinction proper-

ties. Here, the intensity and polarizationstate of a suÆciently large number of incoming rays

is traced bysimulatingthe reectionand refractionprocessesat a predened particlegeometry.

By collecting all rays that are refracted outof the particleand byaccounting for diraction at

the particles geometrical cross section it is possible to obtain the scattering, polarization, and

absorption properties of that particle. In contrast to the Mie-theory, the GOM is applicable to

arbitrary particle shapes as long as the smallest dimension of the particle is large compared to

thewavelength of theincomingradiation.

From the molecular structure of ice it is to be expected that macroscopic ice crystals have a

hexagonal shape. Despite thefactthat in-situmeasurements inmostcases reveal more complex

crystal shapes, the rst light scattering models based on the GOM have focused on hexagonal

columnsand plates. (Takano and Liou,1989, 1995). It was notuntila numberof discrepancies

arose from this approach that led to a change of mind. For example, a comparison between

modeled and observationally derived solar radiant uxdensities indicated a typical value of 0.7

to 0.75 fortheasymmetry parameter 2

,whereashexagonal symmetric crystals have valueslarger

than0.8(StackhouseandStephens,1991;Kinneetal.,1992). Furthermore,theobservedangular

dependencyofthereectedandtransmittedradianceismuchsmoothercomparedtomodelresults

based on hexagonalcrystals. (Francis,1995; Brogniez et al.,1995; Gayet et al.,1995).

The"fractalpolycrystal"introducedbyMackeetal.(1996b)providedasymmetryparameterand

radiance eldsthattted signicantlybetter to theobservations. This particletype issupposed

to representascatteringgeometrythatat thesame timehascrystallineandirregularproperties.

This geometrycorrespondsmore to anensemble ofdierentlyshapedice crystalsrather thanto

an observed particle shape. I was involved in a number of theoretical and experimental stud-

ies that have included the fractal polycrystal in their investigations (Francis, 1995; Mishchenko

et al.,1996; Mitchellet al.,1996; Mitchelland Macke, 1997; Francis et al.,1998; Chepfer et al.,

1999; McFarquhar et al., 1999; Zhang et al., 1999; Doutriaux-Boucher et al., 2000; Labonnote

et al., 2000, 2001; Zhanget al., 2001; McFarquhar et al., 2001). For thepresent mentionedare

Mishchenko et al. (1996) who layed the basis for applyingthe fractal polycrystal to the remote

sensing algorithmoftheInternational SatelliteCloudClimatologyProjectsISCCP,andMitchell

etal. (1996) who developed aparameterization of thesolarradiationbalance basedon thispar-

ticle type foruse inclimatemodels. This parameterization hasbeenintegrated into theclimate

modelsHadM3(HadleyCenter, UK)andUKMO(UKMeteorologicalOÆce),andhasledtomore

consistent calculations of the solar heating rates in the upper troposphere (Kristjansson et al.,

1999, 2000).

Since the GOM becomes less valid as the size parameter 3

decreases, its application must be

regarded as problematic for the smallest [almost all] ice crystals in the solar [thermal] spectral

range. Forthe rst time, Macke et al. (1995) quantiedthe errorof the GOM when applied to

non-spherical particles. By comparing results from the GOM and the exact T-matrix method

(Mishchenko,1993)wefoundthattheapproximationoftheGOMproducessmallererrorsincase

of non-spherical particles than in in case of surface- or volume-equivalent spheres. Thus, non-

sphericitycomestomeet theGOM!Formoderatelyabsorbingparticles,thescatteringproperties

areingoodagreementforsizeparameterabove60,thesinglescatteringalbedo 4

forsizeparameter

2

meancosineofthescatteringangle,measurefortheanisotropyofthescatteredradiation.

3

ratioofparticlesizeandwavelength

4

0 60 120 180 Scattering Angle [degree]

10 ^-2 10 ⁰ 10 ² 10 ⁴ 10 ⁶

Phase Function (no diffraction)

column plate polycrystal

Figure 3: GOM resultsfor thescattering phase function(excluding diraction) of 3d randomly

oriented columns,plates and fractalpolycrystalsat a wavelength of 0.5 m. From Macke et al.

(1998).

above 10, already. Later,Wielaard etal. (1997) andMishchenko and Macke (1999) showed that

non-absorbing particlesreacha satisfyingagreement above sizeparameterof about120.

For numerical reasons, the T-matrix method is limited to size parameter smaller than 200

(Wielaard etal., 1997). Therefore, our intercomparison studieshave shown that a combination

of GOMand T-matrixmethod provides acomplete coverage of all particlesizes orwavelengths,

respectively.

SincetheT-matrixmethodislimitedtosymmetricalparticleshapes(spheroids,circularcylinder,

...) the ndings shown above are justied when applied to those compared to real ice crystals

strongly idealized particlegeometries . The questiontherefore arises to what extendthese sim-

plicationsresemblethescattering andabsorptionpropertiesofrealiceparticles. Toanswerthis

question, Macke and Mishchenko (1996) have compared theGOM resultsfor the followingfour

particlegeometries:

hexagonal cylinder and fractal polycrystals as the two extremes of realistic ice particles,

and

geometric cross-sectional- and aspect ratio equivalent ellipsoids and circular cylinder as

possibleparticleshapesintheframework ofthe T-matrixmethod.

It turnsout thatthe use of those idealizedshapesleadsto unacceptablelarge dierences inthe

non-absorbingvisibleandthemoderatelyabsorbingnearinfraredspectralrange. Onlyatstrongly

absorbing wavelengths similarresultsarefoundforhexagonal andcircular cylinders.

In summary, however, it must be concluded that the use of idealized particle shapes does not

of GOM and T-matrixmethod isnotapplicableto simulatethe scatteringand absorptionprop-

erties of realistically shaped ice particles over the entire spectral range. The Finite Dierence

TimeDomainMethodFDTDprovidesexactsolutionsfornitehexagonalcylinder,however, this

method is limited to size parameter smaller than 15 - 20 (Yang and Liou, 1995). Therefore, a

combination of GOMand FDTD would stillleave agap inthe sizeparameterrange from 20 to

100. Untiltoday, thereis no theoryavailablethat allowsforexact solutionsforirregular shaped

particles.

2.2 The eect of variable cloud microphysical properties

At leastforthe solarspectralrange,theGOMprovidesapracticable wayto solvethescattering

problemfor the majority of particle sizes. Direct applicationsof theGOM inradiative transfer

calculationsrequirespecicchoicesregardingtheparticlegeometryandtheparticlesizedistribu-

tion. Inorder to estimatethe statistical errorsthat may resultfrom those specications, Macke

etal.(1998)havecalculatedsizedistributionaveragedscatteringphasefunctionsand singlescat-

tering albedos for a large number of observationally derived ice crystal size distributions. The

maximumnumberof available distributionsfrom US-Americanand European eld experiments

have beencollected, inorder to obtainan optimumcoverage of thenaturalvariabilityofreal ice

particlespectra.

The crystalgeometries thatwent into thecalculationsof theaveraged propertieswerehexagonal

columns, hexagonal plates, and fractal polycrystals. Fig. 3 shows thescattering phase functions

at thevisiblespectralrangeofthose essentiallydierentparticleshapes. Thehexagonalparticles

providepronouncedforwardscatteringduetotransmissionthroughplane-parallelfacets,thelarge

backscattering caused by retroreection at perpendicular facets, as well asthe 22 Æ

and 46 Æ

halos

from tranmission through 60 Æ

and 90 Æ

prisms. Hexagonal plates have larger tranmission maxima

and less side- and backscattering compared to columns. The irregular polycrystal is lacking

"typical raypaths" and thusshows a muchsmoother scatteringsignature.

Figure . 4 shows the probability density distributions of the asymmetry parameter g and the

single scattering albedo !

0

that result from the dierent particle size spectra. The asymmetry

parameter at visiblewavelengths is most responsiblefor the solarenergy budget since thesolar

irradiation is strongest and ice has negligible absorption at these wavelengths. The important

resultofthisworkisthattheg(0:5m)distributionforthedierentparticletypesdonotoverlap,

i.e. thatthechoiceoficecrystalgeometryhasastrongerinuenceonthesolarradiationbudget

than thechoice of theparticlesizedistribution.

The size of ice crystal aects the scattering and absorption properties by 1) the sizedependent

aspect ratio of hexagonal crystals (Auer and Veal, 1970) leading to stronger transmission and

smaller side- and backscattering at larger sizes, and 2) bythe less isotropic diraction at larger

geometricalcrosssections. Thelatter eectis negligible,though,ascan beseenfrom thealmost

Æ-peaked g(0;5m) distribution for theirregular polycrystal whose shape does not change with

size.

The moderate absorptionat 1.6mwavelengthaddsa furthersizedependencyleadingto broad-

ening and partly overlap of the distributions for the dierent ice particle types. Nevertheless,

the latter are still distinguishable as the standard deviation of the individual distributions are

smaller thanthedistance betweenthemodes. Thus, alsoin thesolarnear infraredthechoice of

particletype hasadominanteect compared tothechoice ofsizedistribution. Thesame istrue

fortheabsorptivityforcolumnsandplates, ascan beseenfromthe! (1:6m)-distribution. The

0.7 0.8 0.9 1.0 g(1.6µm)

polycrystals columns plates

0.7 0.8 0.9 1.0

g(0.5µm) polycrystals columns plates

0.5 0.6 0.7 0.8 0.9 1.0

ω 0 (1.6 µm) polycrystals columns plates

0.5 0.6 0.7 0.8 0.9 1.0

ω 0 (3.0 µm) polycrystals columns plates

Figure4: Frequencydistributions(arbitraryunits)oftheasymmetryparametergatawavelength

of 0.5 mand 1.6 m, and of the asymmetry parameter at a wavelength of 1.6 mand 3.0 m.

From Macke etal. (1998).

more compact shaped irregularpolycrystalabsorbs radiationmore eÆciently thanits hexagonal

counterpart, thus reacting more sensitive to dierent size distributions and yields the smallest

valuesforthesinglescatteringalbedo,whichisalsoconrmedbythedistributionat thestrongly

absorbingspectralregionat3.0 mwavelength. Here,theabsorptionis nearlysaturatedand the

variationwithsizespectra iscorrespondinglysmall.

Howdoesthevariabilityinice particleshape andsizeaect thesolarradiativetransfer incirrus

clouds? ToanswerthisquestionSchlimmeandMacke(2001)havecalculatedthesolarbroadband

cirrusradiation budgetby meansof a Monte Carlo radiative transfer code for 114 dierent size

distributions from mid-latitude cirrus clouds for hexagonal columns and fractal polycrystals,

respectively. Clouds were assumed as homogeneous and plane-parallel to focus on the eect of

microphysicalpropertiesontheradiativetransfer. Theresultingradiantuxdensitiesareshown

in Fig. 5 as a function of cloud optical thickness. As in the case for the distribution-averaged

singlescattering,theradiativeuxesdierstrongerfordierentparticleshapesthanfordierent

size distributions. However, from this results it is possible to quantify the uncertainty in the

cirrussolarradiativebudget thatis causedbyuncertaintiesintheice crystalsizedistributions.

Forirregularshaped particlesthereectivityvariesaround4%, thetransmissivityaround2 -3%

andtheabsorptionfrom9to 25%withincreasingopticalthickness. Hexagonalcolumnsaremore

sensitivetoiceparticlesizeasmentionedaboveandherereectionvariesaround7%,transmission

around 1%andabsorptionaround 20 to 6%withincreasing opticalthickness. Theuncertainties

are largest for absorption also in absolute numbers ranging from 15 to 20 Wm 2

depending on

particletype.

Evenintheunrealisticcasethattheicecrystalshapewouldbewellknowntheuncertaintiesinthe

0 5 10 0

50 100 150 200 250 300 350 400 450 500 550

upward

radiant flux density [Wm −2 ]

0 5 10

0 50 100 150 200 250 300 350 400 450 500 550

downward

optical thickness

0 5 10

0 50 100 150 200 250 300 350 400 450 500 550

absorption

Figure 5: Solarbroadbandreected, transmittedand absorbed radiative uxesfor 114 dierent

ice particlesize distributionsasa functionof cloud optical thickness. Solid (dashed)line: mean

curve for hexagonal columns (fractal polycrystal). In order to keep perspective only the mean

curve isshownforthefractal polycrystal. From Schlimmeand Macke (2001).

of this cloud type, that are one order of magnitudelarger than the discussedanthropogenically

inducedradiativeforcing.

2.3 Inhomogeneous ice particles

Acombinationofhexagonalandirregularshaped(fractalpolycrystal)iceparticlesenablesamore

or lessrealistic descriptionof theaverage scattering properties as demonstrated in McFarquhar

etal.(1999). However, thecontributionsfromthepolycrystalsprovidesan overestimation ofab-

sorption,causedbythecompactshapeofthisparticletype. Anotherwayofcombininghexagonal

symmetric andirregularicecrystalpropertiesthatbypassesthisproblemresultsfromtheMonte

Carlo GOM concept that I have developed (Macke et al., 1996a; Macke, 2000). The idea is to

allowforinternalmultiplescatteringeventsinsideacertain"hostparticle"asillustratedinFig.6.

ThismultiplescatteringisrealizedbyMonteCarloprocesses,i.e.thefreepathlengths,direction

andattenuationofapreviouslystraightlightrayaresubjectto changesdependingontheoptical

thickness and the scattering and absorption properties of internalparticles. The scattering and

absorption properties of those inclusions are determined beforehand. The following MC-GOM

resultsare basedon spherical inclusions. Ofcourse, non-sphericalparticles can beconsideredas

well,as longastheir extinction properties relative to the host mediumcan be calculated witha

suitablelight scattering method.

Examples forinclusions in atmospheric ice particles are air bubbles or scavenged aerosol parti-

cles. Otherinhomogeneitieslikemicroscopic breaksorstepsactlikelocalscatterers and maybe

accountedforbymeansof theMonte CarloGOM concept aswell.

Θ ϕ

Figure6: Illustrationoftheconsiderationofinternalscatteringprocessesinsidea hexagonalhost

particle. An incomingrayisrefractedinto theparticleand isinternallyscattered at aninclusion

around azenithangle and an azimuthangle '. From Macke (2000).

of internal conclusions is shown in Fig. 7 for three dierent types of inclusions: ammonium

sulfate, soot, and air bubbles. Ammonium sulfate and soot may origin from aircraft exhausts

and industrial emissions. Air bubbles are formed by rapid crystal growth and by spontaneous

freezing ofsupercooledwaterdroplets.

For all three types of inclusions multiple scattering inside the host particle leads to reduction

of forward and backscattering, as well as the halo peaks. In the case of the non-absorbing air

bubbles and ammonium sulfate particles side scattering increases resulting in a more isotropic

total phasefunction. Thecontributionfrom GOlightrays to thetotal scattering phasefunction

isreducedbyabsorptionat thesootinclusionssothatthestronglyforwardscattering diraction

starts to dominateleading to areducedsidescattering.

The concept oftheMC-GOM wastaken over byother researchgroupsaswelland, forexample,

serves to construct scattering phase functions that t best to satellite based measurements of

solarradianceeldsreectedfromcirrusclouds(Labonnoteet al.,2001). Contrarytothefractal

polycrystal, which is supposed to represent highly irregular shaped ice particles, the so derived

phasefunctionhasno physicalbasisanymore. However,itprovidesoptimalinputforcalculating

thecloud radiative budget andforthe remotesensing ofcloud optical thickness.

Anumberofyearswillpassbeforeitwillbecomepossibletoobtainthescatteringandabsorption

properties ofatmosphericicecrystals froma directadaptionofthedetailedcrystalstructuresto

appropriatelight scattering theories.

3 Multiple scattering in inhomogeneous clouds

Theabovediscussedicecloudsareoftenopticallythinandthesolarradiativepropertiesstrongly

dependon thesingle scattering properties of theindividual ice crystals. For deep and low level

water clouds, the situation is almost reverse with usually large values for the optical thickness

and, at least forpure water clouds, with almost constant single scattering properties. Here the

transportofthesolarradiationthroughthespatiallyinhomogeneouscloudstructurebecomesthe

0 30 60 90 120 150 180 Scattering angle [degrees]

10 ⁻² 10 ⁰ 10 ² 10 ⁴ 10 ⁶

Scattering phase function

pure ice crystal

<l> = 400 µ m

<l> = 40 µ m

<l> = 8 µ m Ammonium sulfate

Soot Air bubbles

Figure 7: Scattering phase functions of a hexagonal column with spherical inclusions made of

ammonium sulfate (multipliedby 10 4

), air bubbles (multiplied by 10 2

) and soot. From Macke

etal. (1996a).

The everyday experience that clouds appear as complex spatial structures to the unaided eye

provesthestrongrelevance ofthree-dimensionalcloud radiative transfer. A fewyears ago, prac-

ticalsolutionsoftheradiativetransferequationwererestrictedtostratiform,i.e.one-dimensional

atmospheres. A still up-to.date review of the dierent methods is given by Hansen and Travis

(1974).

Today, moderncomputer enablealmost exact calculations ofthe 3dradiative transfer bymeans

of theMonte Carlomethod (MC-RTM).Here,thescattering and absorptionofa photonbundle

startingfrom a certainsource(e.g. thesun)aretraced untilthebundleleaves thesystemunder

investigation or until it is completely absorbed. The free path length between two subsequent

extinctionprocesses,thechangeindirectionduetoascatteringeventandabsorptionareregarded

as randomprocesses that followcertain probabilitydensityfunctions determined by thevolume

extinctioncoeÆcient,thescatteringphasefunctionandthesinglescatteringalbedo(seeMarchuk

etal. (1980)).

The Spherical Harmonics Discrete Ordinate Method (SHDOM) developed by Evans (1998) di-

rectly solves for the radiative transfer equation, also in case of spatial inhomogeneous media.

SHDOMissuperiorto MonteCarlomethodswheninternaland externalradiance eldsneeds to

be calculated. The Monte Carlo approach is fasterfor calculating domainaveraged radiant ux

densities. However, the main advantage of the Monte Carlo method lies in the fact that arbi-

trary intermittentcloud structures andarbitrary anisotropic scatteringphase functionsarefully

accountedfor, whereasthenumericalexpansionof theradiativequantitiesand thelimitation to

Untiltodaylittleis known aboutthefullspatialstructureof cloudsfrom an experimental point

of view. Measurements by aircraft, cloudradar and spatiallyhigh resolved satelliteradiometers

allowforaone-and two-dimensionalprobingofclouds. Togetherwiththeoretical considerations

these measurements have revealed the multispectral nature of the spatial distribution of cloud

water (Schertzer and Lovejoy, 1987; Lovejoy and Schertzer, 1990). That means, cloud show

inhomogeneous structureson all spatialscales.

Motivatedbythefractalityofcloudsandbythelackofexperimentallyderived3dcloudstructures

3d radiative transfer calculations have been applied to artically generated cloud elds rst

(Breon, 1992; Barker and Davies, 1992; Cahalan et al., 1994; Marshak et al., 1995a,b). These

cloudsalso didnotvaryinall three directionsinspace butonlyconsideredhorizontalvariations

incloud opticalthickness.

It wasnotuntiltheavailabilityof smallscale3datmosphericcirculationmodelswithintegrated

cloudphysicsthatfull3dcloudstructurescouldbeaccountedforinradiativetransfercalculations

(Oreopoulusand Barker, 1999; Barkeret al.,1999).

Thesituationbecomesmorecomplexincaseofmixedphasecloudswherethedierentscattering

properties of water droplets, raindrops and ice particles also needto betaken into account. By

comparingsatellite-basedmeasurementsof microwave emission (sensitiveto liquidwater) and of

solarreectance(sensitivetoliquidand icewater)LinandRossow(1996)haveobtainedaglobal

mean ratioofice to liquidwater pathof 0.7fornon-precipitatingmarine clouds.

Therecentlyavailablemm-cloud-radaralsoshowalargefrequencyoficeeven forlowconvective

mid-levelsummertimeclouds(MarkusQuante, 2001;privatecommunications). Theexistence of

icephaseisdetected bythestrongdepolarizationat non-sphericalmeltingparticleswhichreveal

thetransissionregion betweensolidand liquidphase.

AsanexampleFig.8shows atimeseriesofradarreectivityand verticalvelocityobtainedfrom

theGKSScloudradarMIRACLEonAugust 2,2001. Thesuddenappearanceoflargedownward

fall velocities marks the beginning of precipitation which in turn is a result of coexisting water

and ice(Bergeron-Findeisen process) withapredominance of iceparticles above thefold.

From all those resultsit can be expected thata combinationof liquidwater and iceis more the

rulethantheexceptioninatmosphericclouds.

Inorder to generate3d mixedphase cloudsthe3d non-hydrostaticatmosphericmodel GESIMA

(Eppel et al., 1995) has been applied. The model includes a detailed cloud parameterization

developed by Levkov etal. (1992) and modied byHagedorn (1996). The cloud scheme distin-

guisheswaterdroplets,raindrops,icecrystalsandsnow. Fig.9showsanexampleoftheevolution

of aGESIMA cloudillustrated bythespatialdistributionof thevolumeextinction coeÆcientat

dierent time steps. The resolution of the model domainis 2 km horizontally and ranges from

100matthegroundto1kmat 10kmheightalongthevertical. With52x52 x26grid cells,the

wholemodeldomainroughly correspondsto asinglegrid cellina globalatmosphericcirculation

model. In order to obtainmore orlessindependent cloudrealizations from acertain model run,

cloud elds are taken every 10 minutes by an integration time step of 10 seconds. The clouds

usedinour studieshave beencalculatedbyv.Bremen etal. (2001)

3.2 Radiative transfer modeling

Thegoal ofourwork isto realizethefull3d radiative transferwhichembracestheconsideration

-60 -50 -40 -30 -20 -10 0

13:30 13:45 14:00 14:15

1 2 3 4 5 6 7 8 9 10 11 12

GKSS 95 GHz Radar BBC, Cabauw (The Netherlands) Reflectivity [dBZ]

2. August 2001

Height ASL (km)

Time (UTC)

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0

13:30 13:45 14:00 14:15

1 2 3 4 5 6 7 8 9 10 11 12

GKSS 95 GHz Radar BBC, Cabauw (The Netherlands) Velocity [m/s]

2. August 2001

Height ASL (km)

Time (UTC)

Figure 8: Time seriesof radar reectivity(top) and particle fallvelocity(bottom) derived from

theGKSScloudradarMIRACLEduringtheBBCeldcampaignoftheECprojectCLIWA-NET.

guaranteedbythe dierent contributionsof water droplets,rain, iceand snow ineach GESIMA

grid cell. Scattering and absorption at the sphericalwater dropletsis calculatedby Mie-theory.

Macke andGrossklaus(1998)havedevelopedaGOMthataccountsforthenon-sphericityofrain

drops. Snow is regarded as a highly irregular particle type and is thus realized by the fractal

polycrystal. Finally,iceparticles aretakenashexagonal columns. Each particletypeisaveraged

along a variety oftheoretical orobservationally derived sizedistributionssothat scattering and

absorption properties are availableas a functionof eective particleradius. Thisis the casefor

14 spectralbandscoveringtheentiresolarspectralrange. Thisrepresentsan extensivedatabase

thatcan beappliedto problemsinradiativebudgetcalculationsandinremotesensingofclouds.

AsanexampleFig.10 showsthescatteringphasefunctions ofthefourdierentparticletypesin

thevisiblespectralrangeasafunctionofeectiveparticleradius. Thebuilding-upoftherainbow

peakswithincreasingsizeofthesphericalwaterdroplets,thesmootheningoftheraindropphase

functionwithincreasingnon-sphericity,thesmallchangesinthephasefunctionsofthehexagonal

particles due to changing aspect ratios are clearly shown. The size-independent shape of the

fractalpolycrystaldoesnotallowformuchchangesinthescatteringphasefunctionwithchanging

eective radius.

The GESIMA quantities water content and number densities are translated into the radiative

40 Minuten

60 Minuten

80 Minuten

50 Minuten

70 Minuten

90 Minuten

Figure 9: Time seriesof GESIMA clouds. FromScheirer (2001).

(1999). Here we have investigated theinuence of dierent simplicationsin therepresentation

of clouds on the results of radiative transfer calculationsin the visible(non-absorbing) spectral

range. The followingcases have beendistinguished.

Case Description

A-SC 3dinhomogeneousextinctioncoeÆcientsandscatteringproperties,openboundaries

of themodeldomain.

A-PB as caseA-SCbutwith periodicboundaryconditions.

B as caseA-SCbutwith xedscattering andabsorptionproperties.

C as caseBbutwith constantextinction properties.

D as caseCbut horizontally.

E-W ascaseDbutwithaprioriscatteringandextinctionproperties(waterdropletswith

10 meective radius).

E-I as caseE-W butwithan ice particlesizedistributionwithan eectiveradius of30

m.

0 30 60 90 120 150 180 Scattering angle [degree]

10 ⁻² 10 ⁻¹ 10 ⁰ 10 ¹ 10 ²

Scattering phase function

nonspherical rain drops

r _eff = 200 µ m 400 µ m 600 µ m 800 µ m 10 ⁻²

10 ⁻¹ 10 ⁰ 10 ¹ 10 ²

Scattering phase function

spherical water droplets

r _eff = 5 µm 10 µ m 20 µ m 100 µ m

0 30 60 90 120 150 180

Scattering angle [degree]

irregular snow crystals

r _eff = 20 µ m 60 µ m 100 µ m 200 µ m hexagonal ice columns

r _eff = 20 µm 60 µ m 100 µ m 140 µ m

Figure 10: Scattering phase functions of spherical water droplets, oblate raindrops, irregular

shapedsnowparticlesandhexagonalicecrystalsinthevisiblespectralrangefordierenteective

radii.

cloud (A-SC) and of a cloud eld realized by horizontally periodic boundaries(A-PB). Case B

represents the commonly used situation to model 3d cloud radiative transfer by varying cloud

optical thickness only while keeping the scattering properties xed. Cases C and D stand for

completelyhomogenizedcloudseitherasanisolatedcloudblock(C) orasastratiformcloud(D).

Thelattercorrespondstotheclassicalradiativetransfer. However,inDthetruemeanscattering

phase function isused. In praxis, thescattering propertiesof the cloud particles arenot known

sothat case Emust be regardedasthemore commonlyfoundsituation.

A total of fourcloud scenarioshave beeninvestigated corresponding to convective summertime

clouds(case I),stratiformwinter clouds(case II),stratiformsummerclouds(case III),and con-

vective late summerclouds(case IV) (Hagedorn, 1996).

Fig. 11 shows the domain averaged albedo as a function of the mean optical depth for the six

representationsof cloudsinradiativetransfer. The cases EandD reecttheconvexrelationship

typical for plane parallel homogeneous clouds. Variable mean scattering properties (case D)

essentiallyprovidetwocurves,dependingonweathericeorliquidwaterdominatestheradiatively

most important upper cloud layers. Accounting for a nite cloud geometry (case C) yields a

considerablereductioninalbedobecausephotonsareabletopenetratethroughcloudsidesinthis

representation. Thisreductionstronglydependsonthecloudaspectratio(ratioofcloudvertical

tohorizontaldimension)andthusshowsanoisybehaviorinthealbedocurve. Afurtherreduction

resultsfromthespatialinhomogeneityofthevolumeextinctioncoeÆcient. Thewellknowreason

for this is the above shown non-linear dependency of cloud albedo on optical thickness. As

0 20 40 60 80 optical thickness

0.0 0.2 0.4 0.6 0.8 1.0

albedo

case D 0.0

0.2 0.4 0.6 0.8 1.0

albedo

case B 0.0

0.2 0.4 0.6 0.8

albedo

0 20 40 60 80

optical thickness case E

water cloud (E−W) ice cloud (E−I)

case C

Figure 11: Cloud albedo in the visible (non-absorbing) spectral range as a function of cloud

optical thickness for thesix cloud representations in radiative transfer. Seethe text forfurther

explanations. FromMacke et al.(1999).

Foraxedopticalthicknessthecloudaspectratiosaretheradiativelymostimportantparameters

for isolated clouds. In case of stratied clouds it is the internal cloud structure. The spatial

variabilityofthescatteringpropertiesplaysaminorrole. However,ourlatest(notyetpublished)

resultsshow thatthelatter is onlythe caseat the non-absorbingvisiblespectralregion. Spatial

inhomogeneous absorption considerably aects the radiative transfer in the solar infrared and

even showsup signicantlyinthedomainaveraged solarbroad bandradiative uxes.

3.3 Error estimate of classical radiative transfer codes

The classical and still widely used method of radiative transfer modeling simplies the spatial

cloud structureto horizontally homogeneousplane parallel(PPHOM) layers. Despite thequali-

tatively wellknown errorswhich resultfrom the PPHOM assumption thismethod is appliedto

climatemodeling,essentiallybecause of thelack ofalternativesthatcould account forsub-scale

radiativetransfer(however,seesection3.4!). Thesoobtainederrornousradiantuxdensitiesare

roughly tunedto observationally derived radiationbudget climatologies.

In order to estimate the PPHOM error Scheirer and Macke (2001a) and Scheirer and Macke

(2001b)havecomparedtheresultsfrom3dradiativetransfercalculationstothosefromequivalent

1d calculations. The followingPPHOM cases have beendistinguished:

1) Allcloudy columnsaretreated as one PPHOM cloud withhorizontally averaged cloud prop-

Upward Flux

0.2 - 4.0 microns

0 20 40 60 80 100

Optical Thickness 0

50 100 150 200 250

Homogeneous - Inhomogeneous [W m -2 ]

15 30 45 60 75

SZA [degree]

Convectiv Stratiform Multi-Layer

Atmospheric Absorption

0.2 - 4.0 microns

0 20 40 60 80 100

Optical Thickness -60

-40 -20 0 20 40

Homogeneous - Inhomogeneous [W m -2 ]

15 30 45 60 75

SZA [degree]

Convektiv Stratiform Multy-Layer

a) b)

Figure12: DierencesinthesolarbroadbandradiativeuxesbetweenPPHOM and3dradiative

transfer calculations. FromScheirer (2001).

approximation, thus produces the largest errors, and corresponds to the situation where no in-

formationon theinternalcloudstructure isavailable.

2) Each cloudy columnis treated asPPHOM case separately and the resultsof all columnsare

averaged (Independent Column Approximation ICA). This corresponds to the optimal solution

thatmakesuseof 1dradiativetransfermodels. However, theICArequiresthefullknowledge on

thespatialcloud structurewithinthedomain.

A similar study on the errors associated with those idealizations has also been performed by

Oreopoulus and Barker (1999) and by Barker et al. (1999). There, 3d radiative transfer is

restrictedtospatialinhomogeneousvolumeextinctioncoeÆcientwhereasourstudiesadditionally

accountforvariationsinscatteringandabsorptionproperties. Furthermore,thesepaperprovidea

qualitativeestimationbasedonafewexamplecloudswhereasalargenumberofcloudrealizations

is usedhereinorder toobtaina specicdependencyof theerrorson cloudoptical thicknessand

cloud type.

Fig. 12 clearly demonstrates that the assumption of homogeneous cloudiness leads to massive

overestimations of the solar broadband radiant ux densities up to 230 Wm 2

, in particular

for high sun elevation and for convective cloud types. For this situation the solar radiation is

eÆcientlytransmitted throughhorizontal cloud gaps. Comparedto the 3d results absorptionis

overestimated[underestimated)byasmuchas40Wm 2

forhigh[low]solarelevations. Averaging

overallcloudrealizationsyieldsameanoverestimationinreexionof70Wm 2

whereastheerrors

inabsorptioncancel outbychance.

Fig. 13 shows that the ICA produces much smaller errors as those resulting from assuming

completely homogeneousclouds. In fact, the dierences compared to the 3d resultsare close to

zero onaverage. Thus,theuseof1d radiative transfermodelsisacceptable fordomainaveraged

solarradiativeuxesaslongasthemodelsareappliedcolumn bycolumnto realisticsmallscale

3d cloud distributions. Thesendingsconrmthequalitative resultsby Barkeret al. (1999).

The problem remains to parameterize small scale cloud properties in large scale atmospheric

models. Furthermore, a noisy climatological value like the solar radiative ux eects the entire

0.2 - 4.0 microns

0 20 40 60 80 100

Optical Thickness -30

-20 -10 0 10 20

ICA - Inhomogeneous [W m -2 ]

15 30 45 60 75

SZA [degree]

Convektiv Stratiform Multy-Layer

0.2 - 4.0 microns

0 20 40 60 80 100

Optical Thickness -5

0 5 10

ICA - Inhomogeneous [W m -2 ]

15 30 45 60 75

SZA [degree]

Convektiv Stratiform Multy-Layer

a) b)

Figure13: DierencesinsolarbroadbandradiativeuxesbetweenICAand 3dradiative transfer

calculations. From Scheirer (2001).

acts ina non-linearwayonto theheatingratesof theearth/atmosphere system.

3.4 Parameterization of the solar radiant ux densities in large scale atmo-

spheric models

As shown in section 3.3 the assumption of homogeneous clouds leads to inacceptable errors in

the radiationuxes. Onthe other hand, if thecloud structure is known the ICA appears to be

reliableapproximationto thedomainaveraged 3dradiativetransferproblem. However, sincethe

thecloudstructureisnotknowningeneral,wedonothavethematerialathandtoapplyittothe

reliabletools. Thefollowingapproachtriestobypassthis\lackofmaterial"bysimplycorrelating

thedomainaverage radiativeuxeswiththedomainaverage cloudpropertiesforalargenumber

of3d cloudrealizations(Schewskietal.,2001;Schewski,2001). The qualityof thiscorrelation is

a measureof thefunctionaldependencybetweendomainaverage cloud and radiative properties.

Real applications of this parameterization than would also require to add some noise onto this

functionaldependencyto accountforrealisticuctuationsintheinteractionsbetweencloudsand

theother componentsof theclimatesystem.

Ourparameterizationisbasedon 168cloudeldsgeneratedwiththemesoscalemodelGESIMA.

For each cloud realization the domain average solar broad band reection R at the top of the

model domain, theabsorptionA withinthedomain,as wellasdirect T

dir

,diuseT

dif

and total

transmissionT

tot

transmission at thebottom of the domainhave beencalculatedbymeans of a

3d Monte Carloradiativetransfer model. The resultsaresummarizedinto a \radiationvector"

R

i

=[R ;A;T

tot

;T

dif

;T

dir ]

i

; i=1;168 (1)

Similarly,thedomainaverage state of thecloudyatmosphereis denedbya \cloudvector"

C =[LWP;IWP;RWP;SWP;N;H;T;Z

bot ]

i

; i=1;168 (2)

R A T

tot

T

dif

T

dir

LWP H LWP N N

0.802 0.846 0.927 0.648 0.941

LWP,N H, T LWP,SWP LWP,N LWP,N

0.929 0.899 0.957 0.945 0.979

LWP,RWP,N IWP,H,T LWP,RWP, SWP LWP,N,CH LWP,SWP,N

0.957 0.924 0.971 0.968 0.982

Table1: Optimalcloudparameterforone-, two-andthree-parameterregressionsaccordingtoeq.

(3). The resulting correlation coeÆcients between original and parameterized uxes are shown

aswell. From Schewski(2001).

whereLWP;IWP;RWP;SWP denotethewaterpaths forcloudliquidwater,ice,rainandsnow,

N the cloud cover, CH the geometrical cloud height,T CT

the cloud toptemperature and Z

Bot

thecloud bottom height.

Of course, it is possibleto construct more domain average cloud parameters like water content,

cloud coverand temperature ineach verticallayer. However,thiswould requireasimilarresolu-

tionoftheradiationvectorR

i

andthe168cloudscenesusedherewouldhardlysuÆcetoobtaina

meaningfulcorrelation. Still,thereislargepotentialinthiskindofcorrelationapproachprovided

that a suÆcientlylarge numberof cloud realizations are at hand. Inthis case a neuralnetwork

would be the method of choice to obtain the optimum nonlinear relation F

i

= f(C

i

) between

average cloudandaverageradiationproperties. Duetothelimitednumberofcloudsusedinthis

study,asimplenon-linearregression of theform

F

j

=a

j +

N

C

X

k=1 b

jk C

1

2

k +c

jk C

k +d

jk C

2

j

(3)

has beenperformed, where the a

i

;b

ij

;c

ij

;d

ij

are the regression coeÆcients and N

C

the number

of cloud parameters.

The regression hasbeenperformed fora maximumof three cloud parameters,i. e.10 regression

coeÆcients. Alargernumberwouldjustmapthesituationofthe168cloudsusedintheregression

to theexpenseofgenerality. Withasimpletrialanderrorapproachthose cloudparametershave

been selected for each radiative ux that provide the best regression. The results dividedinto

one-, two- and three-parameter regressionsareshown inTable 1.

The domain averaged cloud parameter that strongest determines the amount of reected solar

radiationiscloudliquidwater,followedbycloudcoverand rainwater path. Foracloudyregion,

the amount of cloud water basically determines the amount of radiation that is reected back

to space. The separationinto cloudy and cloud free areas considerably improves theregression.

Rainwaterpathmaypointtocloudswithstrongconvectionandthuspronouncedinhomogeneous

cloudstructurethatreducesthereectivitiescomparedtonon-precipitatingcloudswiththesame

amount of liquidwater.

Theabsorptionisbestcorrelatedwithgeometricalcloudheightwithfurtherimprovementsresult-

ing from taking cloud top temperature and ice water path into account. The strong sensitivity

to cloud height suggests that absorptionat the cloud particles happensthroughout thevertical

extensionofthecloud. Thismaybedueto the3dnatureofcloudsthatallowstheincomingpho-

from the upper cloud regions and thus cannot participate to absorption processes in the lower

cloud parts. Cloud top temperature indicates the presence of ice at cloud top, which modies

the total absorption by reecting more light from the cloud system than liquid water with the

same water path. For the same reasons, ice water path provides a further improvement in the

parameterizationof solarbroadbandabsorption.

The presence of clouds is a necessary condition for diuse transmission and usually reduces

the amount of direct transmitted light close to zero. Therefore, cloud cover shows up as the

dominantdomain averaged cloud propertyforthose two radiativequantities. Liquidwater path

addsinformationabouttheamountof radiationthat isdiuselyordirectlytransmittedthrough

the cloud eld. Cloud height is the third best parameter in the parameterization for diuse

transmission,whereasit issnow water forthedirecttransmission.

We do notintent to generalize therankingof cloud parametersdiscussedabove. It maywellbe,

thatsomeofthecorrelationsareanartefactofthespecialchoiceofcloudeldsusedinthepresent

study. However, the remarkable nding is that two- and three-parameter regressions already

produce surprisingly robust links between the domain averaged cloud and radiation properties

despite thehighlyirregular structureof theclouds. Obviously,partof theinformationofthe 3d

cloud structureis hiddeninthedomainaveragedcloud properties andthedetailedknowledge of

the3d cloud structureisnotrequiredforthe parameterization.

4 Summary and Conclusion

The work summarizedinthisthesis aims on themostrealistic modelingof solarcloud radiative

transfer to obtain the solar radiation budget of the cloudy atmosphere and to quantitatively

estimate theerrors associatedwith simpliedtreatmentsof clouds inclassicalradiative transfer

models. The focus is on the geometrical aspect, i. e. on shape, size and spatial distribution of

atmospheric hydrometeors. While for xed optical thickness the radiation properties of cirrus

clouds aremostly aected bysizeand shape of the ice particles, themacrophysicaluctuations

arechallengingthe radiative transferfordeep andlowlevelclouds.

ThesinglescatteringmodelsthatIhavedevelopedbasedontheGeometricOpticsapproximation

allowfor lightscattering calculationsfor arbitraryshaped inhomogeneous largeparticles. These

models have been approved in cirrus cloud radiative transfer modeling and serve for a wide

rangeofapplications. Presentinstrumentaltechniquesandsinglescatteringtheoriesdonotallow

to obtain scattering and absorption properties of ice particles on the basis of observationally

derivedcrystalgeometries. However,themodelsshownhereallowtodeterminerealisticscattering

propertiesfromminimizingobservedandsimulatedradianceelds. Thiswillbecomeapromising

application with regard to future satellite missions. In particular the classication of the so

obtainedscatteringpropertiesintocertainclimatologicaldomainswillprovidehelpfulinformation

formodeling theradiationbudgetand fortheremote sensing ofcirruscloudoptical thickness.

However, uncertaintieswithregardto the radiative properties willalwaysremain and thusneed

to be quantiedaswe have done incase ofthe eect of thegeneralyunknownsize distributions

on thesolarradiationbudget ofcirrusclouds.

Based on my single scattering models for non-spherical hydrometeors (ice and snow crystals,

raindrops)itwasaconsistent step towards investigatingthe full3d multiplescatteringproblem,

i. e. towards considering 3d inhomogeneous distributions of optical thickness, scattering and

radiativetransfermodelshavebeendevelopedthatcalculatedomainaveragedspectralbroadband

solarradiativeuxesat predenedcloud structureswithreasonablecomputationalexpense. The

GESIMA clouds used here are by no means representive for the global distribution of possible

atmospheric cloud elds. However, they represent a cloud subset large enough to draw some

general conclusions.

Thenon-absorbingvisiblespectralrangeisnotverysensitivetospatiallyinhomogeneousscatter-

ingproperties,whereasinhomogeneousabsorptionstrengthsstronglydeterminethesolarinfrared

whichstillshowupinthesolarbroadbanduxes(notshown). Asshowninpreviousworkonpure

waterclouds, theICA providesa reasonableapproximationto the3d radiativetransfer problem

in case of domainaveraged radiative quantitiesforthe more complex mixed phase clouds. This

renders itpossibleto continueusingclassical1dradiativetransfer codesinclimate modelsofin-

formationofthesub-scaleclouddistributionisathand. However, aswecouldshow,itispossible

to t domain average radiative quantities to domain average cloud properties with acceptable

accuracy. This opens a door to a more statistically based parameterization of cloud radiative

uxesbased ona considerablylargerand more representative collection of3d cloud realizations.

After all, the numerical ndings summarized here need to be veried both qualitatively and

quantitatively against observations. Despite the diÆculties in obtaining the instantaneous 3d

cloudeldandthedomainaverage radiativequantitiesatthesame time,futuretechniquesbased

on combinationsof active and passivecloud remotesensing (Lohnert etal.,2001), aswellasthe

combinationofgroundbasedandsatellitebasedcloudremotesensing(vanLammerenetal.,2000)

will unfold the relationship betweencloud and radiative properties at least for some exemplary

cases. This will provide the touchstones for the modeling of cloud physics and cloud radiative

transfer and willleadto a stronger collaborationbetweenthe two research areas.

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