NASA-CR-175154

19840008644

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NATIONALAERO;_AUTICS At|DSPACEADMINISTRATION

For the period 9/15/80 to 5/15/83

PARAIIETERIZATOFIONCLOUDEFFECTS0_|THEABSORPTION

OF SOLARRADIATION

ROGERDAVIES,PrincipalInvestigator

Departmentof Geosciences

PurdueUniversity

West Lafayette,Indiana47907

(IIASA-CR-17515q) 9ARAHETERIZATIO_I OF CLOUD 118q-16712

EFFECTS ON TIIE_BSORPTIO_IOF SOLAR RADIATIOn|

Final _eport, 15 Sep. 1980 - 15 Hay 1983

(Purdue Univ.} 99 p EC AO5/HF AO] CSCL OqB Unclas

G3/47 ! 0153

,. /Vi__/_/_
/

INTRODUCTION

As we attemptto betterunderstandthe causalmechanismsof climate

and climatechange throughthe developmentof comprehensivegeneral

circulationmodels,greaterdemandsare placedon our representationof

• the relevantphysicalprocesses. Unlikeshort term predictionmodels,

where the accumulationof biases in slowlyacting forcesmay be of

littlepracticalconsequence,climatemodels requirea carefulaccounting

of all terms that affect the energy budgetof a region. Foremostamongst

these, and the sourceof the energythat drivesthe subsequentatmospheric

motion, is the term relatedto the absorptionof solarradiation.

This final reportdescribesthe resultsof researchon the absorption

$

': of solar radiation,carriedout under grant NAG 5-I06 from the National

. Aeronauticsand Space Administration,which providedsupportof approximately$78,679over a periodof two and a half years. A numberof

connectedstudieswere performed,includingthe developmentof a new

: parameterizationscheme for the absorptionof solar radiation,experiments

with a comprehensivegeneralcirculationmodel,and developmentof a new

theoreticalmodel of the absorptionof solar radiationin clouds. The

reportis consequentlydividedinto threeparts.

Part one is an abstractof NASA TECHNICALMEMORANDUM83961 ("Document! tation of the solar radiationparameterizationin the GLAS climatemodel".

R. Davies, 1982, 57pp.),which describesthe early phase of this research

on the development,testingand implementationof a new radiationpara-

_ meterizationfor the NASA GoddardSpace FlightCenter'sclimatemodel.

Part two is a summaryof interactiveand off-lineexperimentswith

-f

the climatemodel to determinethe limitationsof the presentparaF_ meterizationscheme,culminatingin suggestionsfor future improvements.
Part three lays the theoreticalgroundworkfor one of the suggested

improvements,namelythe parameterizationof cloud absorptionin tems

of solar zenithangle, column'watervapor above the cloud top, and cloud

liquidwatercontent.Thispartdescribesresearchwhichledto a Master

of SciencedegreeforMr. Kyung-EakKim,underthesupervisionof the

PrincipalInvestigator,and forms the bulk of the report.

.o . ,

• °
3

PARTI

AbstractedfromNASATECHNICALME{,IORANDUM 83961,entitled:

DOCUMENTATIONOF THE SOLARRADIATIONPAR_4ETERIZATIONIN THE

GLASCLImaTEMODEL,

by R. Davies,June, 1982.

This documentdescribesthe parameterizationof solar radiationin the

GLAS GCM. The parameterizationis a revisionof the Lacis-Hansenpara-

: meterization;it explicitlyconsidersthe directionalnature of the

direct solar beam in treatingradiativetransferwithin clouds,and in

treatingthe effect of surfacereflection. This is accomplishedusing

delta-Eddingtonand delta-twostreammodels for the radiativetransfer " "

within isolatedatmosphericlayers,and by couplingthe individual

layerstogetherby efficientlyrepeatedapplicationsof the interaction

_ principle. . .

Off-linecomparisonswith the previousnon-directional,or diffuse,

model yield significantdifferencesin the planetaryalbedo and in the

amountsof absorbedsolar radiation• These differencesshow a systematic dependenceon latitudeand season.

i

• . . . -.
4

PARTII

PRESENTPARAHETERIZATION OF SOLARRADIATIONIN THEGODDARD

CLIMATEI,_ODEL

An enhancementto thesolarradiationparameterizationin theGoddard

climatemodel,togetherwithcomparativeresultsfromtheearlierversion

developedby LacisandHansen(1974),was describedin detailby Davies

(19B2).Briefly,thisenhancementprovidesa physicallymorerealistic

treatmentof radiativetransferwithincloudsandat theearth'ssurface,

asiverifiedby comparisonwithmorecomprehensivemodels,specifically

takingintoaccountdependenceon the directionalityof thedirectsolar

beam. ThisdependenceproduceddifSerencesin theabsorptionof solar

radiationwhichvariedmoreor lesssystematicallyfromequatorto pole, •

perturbedby cloudvariability.

Sincethen,fullyinteractivecomparisonshavebeenmadeusingthe

completeglobalclimatemodel,yieldingdifferenceswhichare generally

consistentwiththeoff-lineresults.Theirsignificance,however,is

harderto interpretdue to thepresentlyfixedseasurfacetemperatures

andunspecifiedmodelnoiseof the fullyinteractivemodel. Fig.], for j'i

example,showsdifferencesin themonthlymeangroundtB_peraturesusing

thetwoparameterizationschemes,showingthattheclimatemode]did

appearto respondto thechangein theparameterization.

• An importantconsiderationin parameterizingsolarradiationis the

questionof the requiredaccuracyof theparameterization scheme. While .

thisquestionhasyet to be seriouslyanswered,the requiredaccuracy

presumablydependson the timescaleof theapplicationandon thetype

of error,randomerrorsbeingmoretolerablethanthosewhichshow
5

persistentlatitudinalor verticalbiases. To obtaina nominalfigure

for the requiredaccuracyof the solarparameterization schemein the

Goddardclimatemodel,theatmosphericsolarabsorptiowas n systematically

perturbedduringan'interactivem0delrun,and theeffecton meanmonthly

atmospherictemperatureswasanalyzed.It wasfoundthata changein the

meanmonthly,globallyaveraged,atmospherictemperatureof 0.SKwas

producedby a systematicperturbationof _ 7 Wm"2 in absorbedsolar

radiation Thisamountwas thentakenas a nominalgoalforthe

requiredaccuracy'oftheparameterizationscheme.

The nextconsiderationwas whetheror notthe radiationparameterization

attainstheabovegoal,and a numberof off-lineexperimentswereperformed

to thisend. Forclearskycases,therewasno evidenceof systematic

errorsexceedinga fewwattspersquaremeter,theuncertaintyin the

absorbedradiationbeingmainlydueto theuncertaintyin theinput ....

variablesof surfacealbedo,watervaporandozone. Potentiallylarge

systematicerrorsappearto existfor cloudyregions,however,as

illustratedin Fig.2. Thisfigureshowsthedifferencesin monthlym_an '...

absorbedsolarenergyobtainedin an off-lineexperimentin whichthe

treatmentof cloudopticalthicknesswaschanged.

Insteadof usinga continuouscloudcoverwithconstantoptical

thicknessacrossthewholeareaof eachcloudgridelement,the

experimentaltreatmentassumeda cloudfractionof 0.45wheneverthe

climatemodelgeneratedconvectivecloudforthe gridelement.The

A

opticalthicknessof thecloudyfractionof eachrelevantlevelwas

thenincreasedto givethe samearea-averagedopticalthicknessas

before. Sincearea-averagedtransmission,in particular,dependson

opticalthicknessin a highlynon-linearmanner,andthisdependence

is alsosensitiveto solarzenithangle,thedifferencesobtainedare

L
6

not surprisingandserveto illustratethepotentialerrorsin the

presentscheme.The sensitivityto fractionalcloudeffectsis

particularlyevidentin thetropics_ndsubtropicsdueto thefrequency

of convectivecloudsandsmallsolarzenithanglesat theselatitudes.

The typicaldiscrepancyin the totalsolarabsorptionfor theselatitudes

is _ 35 Wm"2,whichis approximatelya I0%effectandwellabovethe

nominalthresholdof _ 7 Wm"2.

In termsof theevolutionof the presentparameterization, the

nextstepshouldbe a studyof thisfractionalcloudeffectin more

detailwitha vievlto reducingthe latitudinalbiasesin absorbedsolar

radiation.Sincea formalsolutionto the brokencloudprobl_,

involvingdistributionsof cloudsizes,shapes,liquidwatercontents,

I

etc.is beyondthescopeof theclimatemodel,as presentlyplanned, i

the nevlparameterizationshouldbe limitedto functionaldependenceson ..

cloudfraction,cloudt_nperatureand solarzenithangle. Theseparameterizationscouldbe obtainedin partthroughtheanalysisof more

rigorouscloudmodelingas describedin PartIll.

Forexample,Fig.3 showspreliminaryresultsfor thetotal

absorptionof solarradiationby a l km thickcloudas a functionof

cloudtopheight,assumingthedropletsize-distribution remainsconstant.

The cloudis embeddedin a tropicalmaritimeatmospherewithoverheadsun.

The totalcloudabsorptionrisesuniformlywithincreasingcloudaltitude

as thecolumnwatervaporabovetheclouddecreasesand absorbslessof

the solarinfrared.Mostof thecloudabsorptionis due to liquidwater

and not thewatervaporwithinthecloud. In factthecloudwatervapor • •

onlycontributesI0-20%of thetotalcloudabsorption,and remains

_elativelyconstantwithcloudtopaltitude.Thisis becausetheeffect

of increasedsolarinfraredat higheraltitudesis offsetby lesswater
7

vaporwithintheclouddue to coldercloudtemperatures.

Theseresultsindicatethatthepresentparameterization of the

transferof solarinfraredradiationin cloudsshouldbe substantially

revisedon physicalgroundsto reflectthedominantroleof cloud

dropletson absorption.Despitethe extensivecomputationaleffort

requiredfortheirproduction,theresultsobtaineddo not showany

especiallycomplexdependenceon cloudheight,temperatureandsolar

zenithangle. It shouldthereforebe possibleto parameterizethem

in a straightforwardmanner.

References

I. Davies,R., 1982: Documentationof thesolarradiation "-

parameterizationi theGLASclimatemodel.

NASATECH._{EM.83961. 51pp.

•2. Lacis,A.A.,andJ.E.Hansen,1974: A parameterization

forthe absorptionof solarradiationin theearth's

atmosphere.

J. Atmos.Sci., 118-133.

• °
8

FigureCaptions

Fig.I. Differences(revisedminusoriginal)in groundtemperature

•fromtwo interactiverunsof theGoddardgeneralcirculation

climatemodel,using,respectively,therevisedandoriginal

solarradiationparameterizations.Julyaverages.

Fig.2. Differences(experimentaltreatmentof cloudfractionminus

standardtreatment)in zonallyaveragedsystemabsorptionof

solarradiation.The standardtreatmentassumesI00%cloud

cover_hencloudis present.The experimentaltreatment

assumes45%cloudcoverwithgreateropticalthickness,if

convectivecloudis presentin thegridelement.Single

timestepin mid-April.

Fig.3. Resultsfroma comprehensiveradiativetransfermodelfor ".

absorbedsolarradiationas a functionof cloudtop

altitudeforconstantcloudthicknessof l km. Moist

tropicalatmospherewithoverheadsun. "'."

(a) Absorptionby watervaporwithincloud.

(b) Absorptionby clouddroplets.

(c) Totalcloudabsorption.

(d) Absorptionby watervaporabovecloud.
GROUND TEMPERATURE _..

D228 HINU513226 (c) GL_BI:ILItERN= -0.01. -_

ot 1 ,I ' ! i !,,/ ' ,';

[ :"

•i......... ;......... _......... _..... ' ...... _ .. : ....... i .... i...

-IF.O -120 -90 -K] -30 0 30 60 $0 120 150

Figure | " t2Z-'7/. !/79 TIt_:U OZ- 8/. 1/79
I

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. i

DIFFERENCES DUE TO FRACTIONAL CLOUD COVER
N

':Z

Ca) (b) C€) Cd)

o 48 B9 128 169

" ABSORBED ENERGY E_/H_2]

Figure 3 ._ ._

• °
PARTIII

. SPECTRAL ABSORPTION OF SOLAR RADIATION llj

IN HO_IOGENEOUSCLOUDS

A Thesis

Submitted to the F_:ulty

of

Purdue University

By

Kyung-Eak Kim

In Partial Fulfillment of the

Requirement for the Desree

of

_aster o_ Science

August 1989
ACKNOWLEDGEMENTS

_!i_-_-, I would IIke to express sincere gratitude and

:._:.: appreciation to my major professor, Dr. Roger Davies, for

--_!,i hisguidance andrinano_l suppor,'hrough , this_o:-_.. Hi_

::.: many helpful comments and suggestions greatly aided my

research efforts and enabled me to conduct thorough

.... _,, investigaCion._.

'):'J I am grateful to m.7committee including Dr. Phill_p d.

:¢_ Smith End Dr. Dayton G Vincent for their helpful " ;,_ •

!:_ suggestions of this manuscript. Also, my special t.han_:sare

:" extended to Dr. .Williamh. Ridgway for makin: available

:: pathlength distribution data obtained by Monte Carlo

simulation, and useful plothin_ routines. His many he:pfu|

col_Imentzand suggestions greatly improved r..yunderstandin_

in the probl._m of this thesis.

The author _ishes to express his appreciation _.oDr. W.

Wiscombe for _ copy of his computer proErara for the

calculation of _._ieoptical par-%meters.

ii.! I w,_uld _ike to express my th_nlts to my friend, Dr. i! Chsinanceg-coI bcameBaatgo Amfor ericahisin cAonugtuinstuo1980. us encouragement and help

i:i I
Ii

iii

I ap_>reciate deeply my parents and wife's parents for " ii

their many sacrifices endured to allow me to finish this

Final ly. the author wishes to express his sincere g

gratitude to his wife , Gil-Ryang Byun for her enccuragement

and help during the course of this study. :_

This research was partially supported by the National

Aeronautics and Space Administration under _rant NAG 5-106.

• o . .

: i_

. ; o

'L

0

i I.
_ iv

TABLE OF CONTENTS

PaEe

LIST OF TABLES ............................................ vi

LIST OF FIGURES .......................................... vii

ABSTRACT .................................................. ix

I. INTRODUCTION ........................................... I

If. A SURVEY OF CLOUD ABSORPTION STUDIES .................. 4

2.1 Measurements of Cloud Absorption .................. 4

2.2 Theoretical Studies of Cloud Absorption ........... 8

III. THEORY ............................................... 11

3.1 Physical Parameters Related To Cloud Absorption .11

3.2 Optical Parameters of Cloud Droplets

from Mie Theory .................................. 16

3.8 Results for Spectral Values of the Cloud

Parameters ....................................... !8

3.4 Photon Pathlength Distribution ................... 21

8.B Transmission Function of Cloud .................... _6

8.6 Spectral Cloud Absorption ........................ 2_

8.7 Summary of Cloud Absorption Model ................ 81

IV. MODEL RESULTS ........................................ 83

.4.1 Spectral Absorpt£on by Water Vapor

and Liquid Water.................................83

4.2 Comparison of the Results with a Previous Work...43

4.8 Limitations of the Model.........................4S

4.4 Dependence of Absorption on Cloud Top Aititude...4G

4.S Cloud Absorption for Different Atmospheric

Models ........................................... S8

. 4.8 ChanKe of Cloud Absorption with Cloud Thlckness..S6

" 4.7 Cloud Absorption by Different Types of CIou4 ..... B9

4.8 Dependence of Cloud Absorption on Solar" "

Zenith Angle ..................................... 8i ""

V. GLOBAL APPLICATION OF MODEL RESULTS .................. 6B
v

• Pa_e

J

VI. CONCLUSIONS .......................................... 69

, . ..

REFERENCES ........................................... 74

•li

e_ t.

"°° °_

.
• ......... • ............... o ..... ... ..... .4--..,. ° ., : /. " . ......

vi

LIST OF TABLES

Table Page

2.1 Global Absorption and Absorbed Energy by Clouds ........ 5

3.1 Cloud Drop Size Distribution Parameters ............... 13

4.1Spectrn! Cloud Absorption within and between the water

Vapor Bands ........................................... 41

4.2 Fractional Absorption of Strmtus Cloud ................ 42

4.3 Comparisons of the Present Work and Welch and Cox's

i Study................................................. _4

4.4 Cloud Absorption for Different Atmospheric _odels.....67

4.5 Cloud Absorption with Change of Cloud Thickness ....... 58

4.6 Cloud Absorption by Different Types of Cloud .......... 60

8.1 Global Application of Cloud Absorption t_odel .......... 66
: m

\

vii

LIST OF FIGURES

Figure Page

3.1 Asymmetry Factor(g), Scattering Optical Thiekness(_)

* and SinEle Scattering Albedo(_) as a function

of Wavenumber........................................20

3.2 Photon Pathlength Distribution as a Function of

Pathlength for Nimbostratus Clouds...................23 //

3.3 Photon Pathlength Distribution as a Function of

Pathlength for Stratus Cloud.........................24

3.4 Phton Pathlength Distribution as a Function of

Pathlength for Stratocumulus Cloud...................25

3._ Water Vapor Transmission Versus Wavenumber...........2T •

4.1 Fractional Cloud Absorption(solid) and Atmospheric

Water Vapor Absorption(dashed) as a Function

of Wavenumber.......................................34

4.2 Spectral Cloud Absorption(solid) _nd Atmospheric

Water Vapor Absorption above the Cloud(dashed).......36

4.3 Fractional Cloud Absorption(_olid) and Liquid _ater

Absorption(dashed) as a Function of Wavenumber.......88

4.4 Fractional Cloud Absorption(solid) and Cloud Water

Vapor Absorption(dashed) as a Function of Wavenumber.39

4.B Water Vapor Absorption(A), Droplet Absorption(B),

Total Cloud Absorption(C) and Column Vapor

Absorption(D) versus CIou4 Top Altitude .............. 47

• 4.8 Spectra] Cloud Absorption(solid) and Atmospher:[c_ater

Vapor Absorption(dashed) for Cloud Top

Altitude of _ km .....................................49

- 4.7 Spectral Cloud Absorption(solid) and Atmospheric Water

Vapor Absorption (dashed) for Cloud Top Altitude

of _ km..............................................BO
i

/

• . T ........................... .

r4

viii

I

Figure Page

4.8 Spectral Cloud Absorption(solld) and Liquid Water

" Absorption (dashed) for Cloud Top Altitude •

of 2 km..............................................52

4.9 Spectrnl'Cloud Absorption(solid) and Liquid Water

Absorption (dashed) for Cloud Top Altitude

"of 5 km.............................................. 53

4.10 Spectral Cloud Absorption(solid) and Cloud Water

Vapor Absorption(dashed)for Cloud Top Altitude

: of 2 km .............................................. 54

i 4.11 Spectral Cloud Absorption(solid) and Cloud Water

Vapor Absorption (dashed) for Cloud Top Altitude

of 5 km .............................................. 55

4.12 Fractional Cloud Absorption versus Solar

i Zenith Angle ......................................... 62

,! 4.13 Cloud Absorption versus Cosine or Solar

_ Zenith Angle ......................................... 63

_t

_ ...

D

i

• • ,

.; ....

il

t

i

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I

,1

.l
ABSTRACT

" Kim0 Kyun_-Enk. M.S., Purdue University, August 1983.

: Spectral Absorption of Solar Radiation in Homogeneous

• Clouds. Major Professor: Dr. Roger Davies.

: In order to better estimate total cloud abs._rption°

spectral cloud absorption and the relRtive role of liquid

water and _ater vapor, a theoretical model of a plane-

!

- parallel homogeneous cloud has been developed. This model

uses a photon pathlength distribution to include the effects • . . .

I of multiple scattering. The water vapor transmission

function is obtained from LOWTRAI_ _.

The results indicate that i km thick clouds absorb about

8 to 12 Z of solar radiation incident on the cloud top, and //_

cloud absorption is highly dependent upon the wavenumber.

/ Cloud absorption between leO0 em'*and 7SO0 cm_ is prim_rily z

due to liquid water while cloud absorption between II_00 cm'*

and I_000 cm'* is due to water vapor absorption. Over the ....

spectral range 7SO0 cry* to 11500 cm'*, both liquid water" and

i water vapor are responsible for cloud o.bsorption. In _'_erms

of relative absorption, liquid water contributes about 77 to . .

_I Z of total cloud absorption, depending on cl._ud type,

cloud top altitude, solar zenith angle, and atmospheric
? . . .= ......... .. . .....

x

model, while cloud water vapor contributes the remaining 9

to 23 _.

As cloud _op altitude increases, the amount of energy

absorbed by cloud and liquid water increases significantly

while the amount of energy absorbed by water vapor is nearly

constant. The absorption by atmospheric water vapor above

the cloud strongly affects the amount of energy absorbed, by

the cloud, and should not be neglected in the calculation of

cloud absorption. The fractional absorption by a cloud does

not show significant differences for different seasonal and -

zonal atmospheric models.

The application of the model results suggest that the

global average of cloud absorption is about 8 to 9 Z of the

incident solar radiation on the cloud top, based on the

global estimation of liquid water content and cloud

thickness. The global mean fractional clou_ "absorption is

about 7 Z of the global average of solar irradiance at the

top 'of the atmosphere.

ORIGINALPAG_-I_

OF POOR QUALITY
I

I

ORIGIrJAPLAG_ 13

OF POOR QUALFFY

: I. INTRODUCTION

z

Clouds are one of the most important features controlling

'! the radiation budget and climate of the earth. They cover

about 50 • of the sky on a global scale (Sas_mori, et

_' a1.,1972) and significantly modulate solar and infrared

radiation on a global scale far more than any other

constituents by their reflection and absorption of short

r_diatlon, emission of infrared radiation.

w_ve and their

In addition, the interaction of radiation _ith clouds ....

affects cloud development and microphysics

The 'primary object£Ves of this investigation are to

_ o

_) develop a theoretical model for the spectral absorption of ..

b

_: solar radiation in clouds, and to investigate the dependence

_; of cloud absorption on cloud environmental parameters The

relative contribution of liquid water and water vapor within

the cloud is also examined. For the purposes of the present

study, the clouds are assumed to be plan_-parallel

_i homogeneous media with uniform drop size distribution, and

to be embedded in a variety of atmospheric models•

_I Tropospheric absorption of solar radiation in the absence

V!

:_l of cloud takes place mainly in the water vapor absorption

bands, ranging from 0.7 Nm to 3.5 llm(orfrom about 2800 to

WD

_e
/ :

ORIGI[_L _AG_ :,J

OF POORQUALX,'DL' 2

15000 c_ 1 in wavenumbers). In the presence of clouds, the

. absorption and scattering by cloud particles substantially

modify the radiation Field of the atmosphere over this

spectral range. In addition, droplet absorption also occurs

outside o£ water vapor bands.

_n calculating the absorption of solar radiation in

clouds, one of the major problems is how to incorporate both

liquid water absorption and vapor _bsorption in the presence

of multiple scattering by cloud droplets. The task of

, accurately determining relative absorption by liquid water

and water vRpor has hitherto •remained an unanswered

question. Stephens (1978) suggested that the absorptions of

solnr radiation by liquid water and by water vapor are "l

equally significant. However, Welch and Cox (1960)

concluded that droplet absorption is primarily responsible

_or absorption of sclar radiation in thin clouds, and

roughly of equal importance to water vapor in thick clouds.

According to Slingo and Schrecker (1982), droplet absorption

\

is responsible for the •bulk of the total absorption, v/hile

i

water vapor has a only minor contribution. t

• i|

f The _ount of w_er vapor above the cloud regulates h_tal .!

cloud absorption by modifying the amount of incident solar

radiation on the top of cloud. Welch, et al. (1976) have

suggested that as the cloud top is raised, the increase in

_v_ilable energy in the water vapor absorption b_nds

outweighs decreasing water vapor concentrstion within the
/

V

i:

" ORIGII_L F_GE ;7 3

^ OF POORQUALITY

i cloud due to lower temperature, so that total cloud

; absorption may increase with height.

{

i

The model developed here therefore includes the effect o£

i

"; atmospheric water vapor above the cloud, as well as yielding

, : the relative spectral absorption by liquid water and water

i. vapor within the cloud. In addition, seasonal and zonal

ii_" variations of cloud absorption are estimated by usinE three

different cloud types and five different atmospheric models.

_-i In Chapter II, a number of papers, including both

_ measurements and theoretical studies, are reviewed in a

_! survey o£ cloud absorption studies. Chapter Ill discuss3s

'_'; the basic theory and fundamental equations used in the

_'; l

b i development of a spectral model of cloud abuorption,

_ ! including the relative absorption by liquid water and w_ter

_q_! vapor. Chapter IV presents cloud absorption res_ilts for

_t

_" three types of cloud and £_ve different atmospheric model3.

I

_" In addition, spectral cloud absorption and atmospheric wa%er

_'

_= _ vapor absorption above the cloud is also discu_;sa.4.

-_i Finally, the global application o£ the model results is

briefly discussed.

I
/

4

ORIGINAL PAG_ {_

OF POORQUALITY

II. A SURVEYOF CLOUD ABSORPTIONSTUDIES

Chapter II discusses some of the previous work on cloud

absorption, including global cloud absorption, aircraft

measurement, and theoretical studies. In addition, some

problems involved in the measurement and theoretical

calculations are discussed.

2.1 Measurements of Cloud Absorption

Although global cloud coverage is known to be about SO %

.. • . .

of the atmosphere, there are a number of different values of

global absorption by clouds. Table 2.1, as an example,

compares, the values for global cloud absorption suKfested by

a number of different authors (Lieu,1980). It is noted that •

the values of Houghton and London are for the Northern

Hemisphere, and that of Sasamori et al. is oniy for the

Southern Hemisphere. The global abscrption by Paltrid_e and

Platt(197_) is based on global and multi-annual averages.

As shown in Table 2.1, the wide range of gl_bal absorption

makes it difficult to evaluate the effect of clouds on

global radiation budget. The range of values, from 5 to 37

W/m 2, exceeds the change in the earth's heat budget due to

doubling C02 content, or to a 2 Z change • in solar constant,
5

o_

Table 2.1

^ Global Absorption and Absorbed Energy by Clouds

._ G 1oba I Absorbed

Absorption Energy ,',W/2m)

: Houghton I0 34

:" London i .6 5

:; Sasamorl, e_ ?.I. 4 14

Paltridge and Plait(1976) 11 ._37

Wittman 4 14

i"1

,.-' The above values except for Paltridge and Platt are quoted

from Lieu(1980). The global absorptien is expressed as a

_; percentage of the mean insolation at the top of the

=i atmosphere, 840 W/m =, which is _00 units.

p.

I

_L. •

P.,

g.1

B

-" .% , .

,!i.!

i!

_! •

_..:

N
,,"

• . . •

r

iJ_i - ORIGINALPAG_[_ 6

OFPOORQUALITY

!i_i which corresponds to 4-5 W/m=(Clark,1982).

iq I . • !

!_i, The extent _o which clouds absorb solar r_di_tion is

I

still _ question of some debate. Theoreti=al c_Iculations

i

of fractional absorption do not show general agreement with

t

aircraft measurements of Reynolds, et ai.(1975). According ;

to the actual msasurements of stratus clouds, the frnctional i

absorption of the incident radiation above the clouds ranges

from 0 _ to 23 _(Herman,1977). However the nechanism _

responsible for this large variability has not been clearly

explained. The v_riation may be expected becaus_ cloud_ are

,_!i_ affected by dynamical variables associated with transient

!ii!_ atmospheric processes and exhibit significant variability on ....

small scales of time and space. Furthermore, measurement

'.. 2.2 Theoretical Studies of Cloud Absorption "

For the accurate calculation of cloud absorption over a

given spectral band, we h_ve to consider the problems of

multiple scattering of photons between cloud droplets and

spectral variation of absorption by liquid water _nd w_ter

vapor. These problems are complicated by the fact that

_ multiple scattering increases the optical path oP photons in

i!-i!_" clouds, and the simple extinction law, Beer's l_w, z.pplies

" only to monochromatic radiation, Two methods are commonly

used in treating vapor absorption in the pressnce of

!ii multiple scattering. The first method is an exponential sum
I I

• i #'

• - ORIGINALPAGE I_ 7

OF POOR QUALITY

_. fit _o the transmission function, in which the broad band i

i

transmissivity is approximated by a finite sum of

exponentials (Wiscombe and Evans,%977). An alternative

:t

technique is the use of photon pathlength distributions, in {i

II

which a multiple scattering model is used to obtain the _

probability distribution of photon paths through the clouds.

t

i The cloud absorption is then found by integrating the actual

; spectral _ransmission function over the pathlength

distribution. Although the two methods differ in their

approach, Bakan et ai.(1978) showed that they are formally

.. equivalent. _,

-i A simpler approach was adopted by Lacis and Hansen (1974) ...

-. who calculated cloud absorption using a k-distribution

method to account for water vapor absorption. Their method

iS somewhat similar to the exponential sum fit of

transmission, but introduces a single probability

distribution for the absorption coefficients of water vapor.

In a different method from Lacis and Hansen(1974),

Krasnokotskaya and Romanova (19'74) used a pathlength

I'

distribution method to calculate fr_ction_l reflection.

. transmission and absorption by clouds i;%the water vapo_

absorption bands. However, they did not point out the

i

-I relative contribution by water vapor and droplets for each " " i

._ absorption band. They suggested that clouds absorb 6-12

of solar flux falling on their upper boundary and that this

range of values is weakly dependent upon the optical

:!
[

ORIGINAL PAGE !_

OF POOR _UALITY

thickness of the clouds.

Twomey (1974) calculated fractional absorption for clouds

with a thickness of 1 km by the doubling method. His values

indicate that clouds absorb 8 to 17 _ of total incoming

solar flux, depending on solar =enith angle and cloud type. P

However, there is a limitation in Twomey°s work because his

calculation is restricted to a I km thick cloud layer, and

is based on exponential absorption by water vapor. .//

,,

Following Lieu (1976), thick clouds such as nimbostrntus

and cumulonimbus reflect 80-90 _ and absorb 10-20 _ of th_

solar radiation incident upon them. For thin stratus cloudn

whose thickness is 0.1 km, the reflection is _bout 45-72

and the absorption is about 1-6 _ of the solar flux incident

on the cloud. Eis theoretical calculation suggested that

maximum cloud absorption does not exceed 20 _ of the

incident radiation on the cloud top.

By the method of exponential sum fitting of transmiosion,

Stephens (1978) calculated cloud absorption. His conclusion

is that the absorption of solar radiation by droplet and by

water vapor In cloud_ is equally significant. He also

suggested that the fractional absorption is almout r

independent of height after allowing for absorption by water ' •

vapor above the cloud.

Welch, etal. (1976) showed that droplet _bsorption in

the 2.7 and 3.3 tim water vapor bands has a significant
l [

i ........ -......

ORIGINALPAGE1_ 9

OF POORQUALITY

contribution to cloud heating rates. Using a spherical _

harmonics technique, Welch and Cox (1980) examined the

relative absorption by water vapor in cloud absorption and

its ccntrlbution to heating rates. According to their

! results, water vapor contributes approximately 20 _ of cloud

; heating near the cloud top, but up to _0 _ of cloud heating

averaged over cloud thickness of I km.

From a study on the shortwave radiative properties of

stratiform clouds, Slingo and Schrecker (1982) concluded

1

that droplets are responsible for the bulk of the

absorption, and water vapor makes a minor contribution to

total cloud _bsorption.

....

AS discussed in this section, estimation of the relative

absorption of liquid water _nd water vapor in cloud has been

quite variable, dep'ending on the authors, and it is ....

difficult to assess the range of cloud absorption and

relative absorption by liquid water and %;Bier vapor _lithin

cloud. These inconsistent conclusions may 5e due to the

lack of detailed spectral models which include the accure.te

scattering and transmission of solar radiation within cloud.

However, the main reason for this l_ck appears to be the

• computational effort required to account for both multirle

scattering effects, as well as detailed spectral

transmission in water vapor.
" 10

--" .

The present study attempts to estimate accurately the

relative absorption of liquid water and water vapor in

: clouds. The calculations are performed by using a spectral

model which takes into• account the effects of multiple

scattering and spectral absorption of water vapor in clouds.

i_.. :

:t,". ORIGINAL PAGE _"

_-' OF r--q)ORQUALITY

w.

;_-

Z

N

:':I " ° • . . ,

_ -.

°.
11

CRIGINAL PAGE [_l

OF POOR QUALITY

IIl. THEORY

In this chapter a brief discussion of optical parameters,

inc!uding drop size distribution and water vapor den=ity is

presented. In addition, the basic equations for the

calculahion of cloud absorption and computational procedure

are al_o developed.

3.1Fhysical Parameters Related to Cloud Absorption

Usually. a cloud is defined as a vi=ible aggregate of " ,

vevy small droplets, ice crystals, or a mixture of both,

with its base above the earth's surface. However, for a

more detailed description of the ._.hysicnlchuracteristics of

a cloud, it is necessary to introduce oth_:r physical

pare%meters such as; (i) shape, (_) dimensions, (.S) three

dimensional drop and ice cry_tnl size distributions, (4) t

temperature distribution, (5) cloud height from the earth's

surfg.ce, and (6) relative volume of ice crystn!s and liquid

%_._ter. The .---mounotf r'-adi_.nenerg t y which is reflected and

absorbed by a cloud is closely Feinted to all of these

fathers. In addition, cloud absorption also depends on a

few other factors, such as, surface albedo, solar zenith

//

/

angle, atmospheric water vapor content, and presence of .-/ -

/
//

-°',

....................... °

i ORIG!;;RL_ -:"

OF POOR QUALII"t"

other cloud layer(s). Among the previous factors, the drop

size distribution and water vapor content are the most

!mportnnt factors,'and'will be discussed in this sect.ion.

,o

3.1.1 Drop Size Distribution

°

The number density of cloud drops and range of drop sizes

,.: vary sii,nificantly in nature. They are not only highly

.1 dependent upon cloud type, but also cn cloud height, o

Eeometrical thickness, season, ,_ndgeographical pos'_tion.

__m- in the pre__ent study, clouds are as.sumedto be plane- -'"

,2,

parallel media which have a homogeneous liquid drop size

distribution and a uniform water vapor density in .*r

• • . .

_ saturation. This assumption allows the use of a s.implif!ed

-.,,_ cloud ncdel. For the parameterization of drop _.i,ze

_.! distribution, the. m_dified gamma distribution which was

derived from experimental data is used (Tampier and ":"

'J°

-# ........

_., Tomasi,1976). This distribution function gives the number

[; density of droplets per unit radius as a function of radius

;; in the form of _-"

ii N(r=ar exp[- r r'

_*I * where a, _ and -/ are empirically derived constants, based on

:_ the experimental drop size distribution. The parameter R

refers to the modal radius. Table 3.1 (Velch and Cox,1980)

gives the parameters for the three clouds uzed in this

il
j/ .:

/

13

TabIe 3.% ORIGINALPAGE I_

OF POOR QUALITY F

=- Cloud Drop Size Distribution Parameters

//

Cloud _ 6 _ R LWC No

Type (_m) (g/_3) (c_)

Stratocumulus .2823 5 1.19 5.33 0.141 100

(base)

Nimboshratus 1.0969 1 2.41 9.67 1.034 100

(top)

Stratus(top) .3818 3 1.30 6.75 0.3?9 100

}lore; LWC: liquid water content, No: number density or

droplet.

...-
!

GR_G:t_f-L _',,'_-" 14

i OF POOR _DAL_'_

study. The three parameters excspt for _ completely

determine the shape of the distribution curve while the

constant '_ is only related to khe total number of droplets

per unit volume.

3.1.2 Water Vapor Content

Water vapor amount within cloud is determined assuming I:

_00 • relative humidity. The saturated water vapor density

;: (_/ms) is obtained from the empirical formu'.'_used in

LOWTRAH B (Kneizys, et al., 1980), given b'!

i,t

f (t)= A exp(18.9766- 14.9595A- 2.4388Aa ) (3.2)

_i; where A=273.ib/(273.15+t), and t is the mean temperature of' 't

,._ a cloud in °C. Thi_ equation is a good aDprozimation, of

_'f_ saturated water vapor density for the tem._eraturer-.nfin_

_ from - _0 °C to + BO °C.

_.._ Since the half width and effective strength of an

absorption line are dependent and temperature.

upon pressure

_]; the water vapor density must first be scal--__to sta_',dard

pressure and temperature before being uzed in the

calculation of ,,tatevar por absorption. -h.=. _ccnled wa.ter

vapor density ;(t) is obtained through equation (3.3) /"

}_ where _ and _ indicate the mean pressure and temperature of" /
L,

•_: zs

•:- OF POOR QUALITY

,;: a cloud layer. Po and To correspond to STP(lO13 mb, 273 K).

" For the computat&on of atmospheric va@or absorption ab_ve

1

._ the cloud,..the effective ware;"vapor amount is obtained by

integrating the specific humidity q with respect to

.i

pressure, scaling as in equation (3._). That is

k_

,: y= I TdP (3.4)

f..;

[_

; where _ is _he pressure at the cloud top. g is the

;" g_avihational &cceleration of the earth. Actually, y

i

corresponds to the effective water,vapor amount above the

_l cloud, and is given in cm. This value of y may then be used

•"J to calculate atmospheric v_por absorption using LOWTRAN _. ""

,_°

"-_,, In the present work, five diffe;-ent atm,spherlc modelo

_, (McClatchey et al. 1972; Welch and Cox,__O) are used for

_i the calculation of water vapor amounts _bo'/ehha cloud. The

:I.

_; mean temperature and pressure o£ a cloud ar_ also determined

_l_. from these models. /

!

3.1.3 Cloud Size

a /

':_ The shape, size, and _h£ckne_s of cloud may be considered

I ' as continuous variables. They are dependent on season,

• geography, and atmospheric state. For the calculation of

_,. cloud 9bsorption, a homogeneous plane-parallel cloud is

assumed. The extent of the cloud is infinite in the

i_ horizontal direction. The cloud thickness is assumed to be
ORIGINALPAd_ k'-} 16 ,/

; OF POOR QUALI'{_; /

1 km as a reference thickness for the calculation of cloud

absorption. This is consistent with the typical thickness i -

_. of cumulus cloud (Paltridge and Platt,197_.).

', • 3.2 Optical Parameters of Cloud Droplets from Mie theery

__;-'. Mie theory (Zdunkowski and Strand,19691 McCa.-tney,1978

_,_ Van de Hulst.t981) has been known to give a nearly c_mplete ,

il ,

_' solution to the problem of scattering and absorption by an '

isolated sphere The theory is based on the assumption that

>_., the particIe is a homogeneous sphere with a sharp

,

_£-:: discontinuity of refractive index at its surface.

_.._'..

:_;_'." The extinction by _ spherical particle is described in .J

_. terms of its size parameter and its complex refractive

_- index• The size parameter X is defined as the ratio of the

)I:, particle radius r to wavelength X,ie, ".

.!_.

2gV (3.5)

_. To include the effect of absorption, the refractive index of _-

_k_., the medium may be expressed as a complex number. In this

;'_',_ case, the index of refraction is represented by

r,_.

,:_; _ {A) = "FIr(,a)--_[l;,(a) (3.6)

:',i_,i Here nr(X) and n_ (X) stand for the real and imaginary

"# indices of refraction, respectively. ' ' •
'%

\

!

I

i!i

Using the size parameter for a single d..-oD, let and the

i complex refractive index for pure water, the extinction ",,

! " efficiency factor Q_(×,X). scattering efficiency factor "

. Qj_(X,k), and asymmetry factor _(x,X) may be obtained u_ing

7'

! "° Mie theory. Wiscombe's computer €ode(I.979)w_s us_4 for

i'"

_-' this pu.-posetogether with data on refractive indic_s uf

t:"_ water from Irvine and Pollack(196o/^' and H_nle and

_': Querry(1973) For a cloud made up of spherical droplets

-, with drop size distribution H(r),the v_lume extinction

i. coefficient, is then found by integrat_ng over size

:, . distribution as

;,-¢.!

,:.._: _,_tx)= . r_l(r)a,_x, r)dr 0.7)

_-_, ...

._,.,

,:'_., Similarly, the volume absorption coefficient B_h(X) or the

_._. volume extinction coefficient B_ (X) may be calculated by

i;i_.'_,, replacing the Mie scattering efficiency factor by th_ _,ii_-

+i_+; efficiency factor ,'or absorption, Q._ (k,r). or extinction,

_*' _e,, (X,r)

:&

iii of The scatsingle tering stcatte o extirinncgtion,albed° <0(X)is defined a_ the ratio

w(x)= (3.8)

• 1

. The angular distribution of scattered radiation by an

element of volume, including polarization, may be determined
, r

i OF POOR QUALI_'_" 18

I

. exp:icitly using the Mie phase matrix. In the present

_ : study, it is assumed that the transfer of radiation within

:- cloud is dominated by multiple scattering so that

polarization effects .are negligible. This situation allows

the use of the Mie phase function P(O), which i: normalized

i

such that

_1".

_,,. _" --i pco)d_ = 1 (3.9)

i![ i'.!I 4g ,t_r

,_!k:. where O is the scattering angle and dQ is the solid an¢le,..

i_ The effects of multiple scattering may be further

._,;:i_ .oummarized by the asyr._metry factor, _(X,r), defined as the

_','_ solid angle average of cosO weighted by the phase function

i'_ _(X,r)= -_- pCe.x,r)(.osd((os _ o) (3.10)

!!_ The asymmetry factor for a distribution of droplet _izes is '.

i_ found by int_.grating the individual asymmetry v::lues as:

j I

ili) I "° _raNCrl_'cLx'r)(:If

!] . whe,o_'<X,r)istheas_mmetr_ r_ctorfor_sin=lo_rop'et.
_ ORIGINALPA_Z ;_

... 19

_'p_ OF POORQUALi='I_'

i_ f 3.3 Results for Spectral Values of the Cloud Parameters

i -

Figure 3.1 illustrates the asymmetry factor, optical

: thickness of scattering, and single scattering albedo as a

function of wavenumber for- the stratocumulus and

nimbostratus clouds specified in Table 3.1. The spectral

[: dependence of _ , _ and _ for stratus cl_ud is omitted from

!

<, Figure S.I for clarity as they were found to be intermediate

_t

,w

|' between the nimbostratus and stratocumulus values. The }'i

_: curves of _ and _€ do not show a large variation except in

_z the vicinity of the strong absorption band at about 3000

_ cm_. For example, the value of _ for _ nimbostratus cloud

? rfanactgesor from fromabo0.84 ut 52toto0.19038., anApard tthefromvtahis lue vof_riaa_ymm tion,ettryhe

}_ values of _ and %_are nearly constant, and remain _bout

0.88 and 100 elsewhere. For stratocumulus cloud, the value

_ of _ is between 0.77 and 0.97. The valu_ of _,.r&nges from

i i

" 14 to about 34. The highe_ variations or _ and -_are

I again re3trictod to the spectra! region between about 2000

c_thet v_nd alues4000 of c_Wa_.nd ETxclud _are aingbouttheO.eregion G an,:!o2i"8,highrespev_ri_ ctively. ti_n,

Figure 3.1 is a plotting of log(l-w)'*against w&venumber.

The \,alues of single sc_tterinE _tbedo. u, in ---io_ure G.I

increase with wavenumber, shot¢ing some oscil !ation_. The

value of log(l-u)'*changes from about 0.3 to 5.5. Hog,ever,

the value o? log(l-u)"I does not show large differences for

the three different cloud types.
• "!

i

/

j" % S . ,

_'_ \ / _ / _ .

_ " -"-'_'_ ........... i

_ " • _ "

_r_

o._. ,O"O

-,-r €-",z,

C) I • .. I . . _ II •

2000 taO00 6000 6000 10000 12000 lhO00

ttkVEto_£R I:C;_-I 3

Figure 3 o! A_y_netry factor(g), acatterln_ optical thickneas(%,), and sln_le

scatterlr_ albedo(_J) as a function of wavenumber,

Thedashedand solidlinespresentnlmbostratuasnd stratocumulusclouds, '-"

respectively. Po

o --4......

\, '/
-- ORl_!_l-.1. n_.:;i" 21

Amon_ the optical parameters of cloud droplets, the

scattering optical thickness and _ymmetry factor are used

to generate photon pathlenghh d_stribuhion of upward and

downward flux under conservative scattering. The values of

_ and _ _re selected approximately, based on c_Iculahions.

,

For the c_Ioul_tion of pathlenE_h distributions, the vmlue

of _ is fixed at 0.88 for the three type= of cloud be_ause

it does not show as much variation as the v_lue of the

scattering _ptical thickness which was normally chosen ,._28

for stratocumulus, 54 for stratus cloud _nd 100 for

nimbostratus, correspondin_ to cloud= of --i km thickness.

The variations of _ and _ around 8000 ¢S z may be neglected

because absorption dominates scattering in this _mall "''"

spectral region.

: . . 71

3,4 Photon Pathlength Distribution

!

"_e incident solar radiation is absorbed and _cattered

.thin a cloud layer by the interaction of photons with the

cloud droplets. For a moderately dense c!_ud, the direct

solar beam rapidly loses its identity' z.s a result of

multiple scattering. Therefore, the _.mounZ of abzorpziun

// and scattering is highly dependent upon the _athlength , ,

traveled by a beam of radiation rather than directly on the

geometrical thickness of the cloud.

The notion of the pathlength distribution dates back to

Fock'spaper in 192G(Van de Hulst,lSSO),and is applicable to
.s

/

.- ORIGINAL PAC_El_. 22 .'

OF POOR QUALI'i'V' ,,.

/

the cloud with multiple scattering (Irv!ne,19_4 and 1983:

.. J

Danielson et ai.,1969; Appleby and Irvine, 1973;Bakan and

[ quen=e I,1976).

When solar radiation is _cattered in the cloud, the

i'. scattered radiation leaving the cloud is composed of photons

• with different paths. The pathlen_th distribution, P(_) is

,_4. defined to be the probability per unit pathlen_th that

photons will travel n distance[ beforeemergingfrom the

cloud. The pathlength distribution, P(_) is norn_lized over

_II _ossible pathlengths such that

.' ,.

p = I (3.12) ..

_ The pathlength distribution has been obtained from a

_ Monte Carlo simuiation of the actual procesc of photon

transmission through a cloud layer with conservz,tive

scattering, using the model of Davies(197S). Th_ model wa=

run for specified @ , _€ and solar zenith an_le, e0, with

i" ICs simulations pep case.

Figure 3.2 shows an example of the photon pnthlength

_i distribution of scattering radiation in the case where 60=6,

" _=0.86, and r_ =iO0. The pathlcn_th distribution, P(4)

decreases asymptotically for large pathZength, and has a

maximum value at about 0.I km. This peak is' due to the

reflected photons from the cloud layer. The figure is

truncated at 2 km, beyond which P(_) continues to decrease
II

!

!

(;31 _ I I ,, I I_ , l t

PATI_H £NI]

Flgure 3.2 Photon pathlength distribution as a function of pathlength for

nlmbostratus cloud,

r_

t.o

• °
i

.. Ha "13_0._. '

,0 -i'3

r _;';

-_.°.

! I I ,! l I I ,

0 O.G I I .G 2 .

PATI_J._I_/FIr.lGI3

Figure 3.3 Photon pathlongth distribution a_ a function of pathlongth for _ :

stratus cloud

The distribution function is obtained under the conditions! _.= O. _ = 86, ".

\ .

\

\

_\',, , \
I | | I I O II | II I|11 I | -- • •

=,

oo

o

i V

I , ! , ! ,=,_l_ ; - * _

_0 O.B I 1.5 - _ \

'\

F'tguz'e3,h- Photon, pat,blenCh cltst,rt"butJ.on , as a funet,J.onof' 10at, h.l.en_h t'or .:

-_tractoumuluscloud-.

Thedl_trlbutlofnunctlonIs ob_alnedunder¢ho condl_ons!i_=0p .._=0.860 ..,,

aIfl. r.x.=28. .

Ix}

k.n
ORIGIH_L_;k_ 2S

.- OF POORQU,\L_

asymptotically. Figure 3.3 illustrates the typical photon

. pathlen_th distribution for n stratus cloud. The pathlength

which corresponds to the maximum value of P(1) is slightly

lazaer than that of P'(_) in Fig. 3.2. The max_rax:mvalue of

: P(9) in Figure 3.3 is about a half of the P(_) in Figure

S.2. The decrease of maximum value of P(_) is due to the

q

decrease of the scattering optical thickness. The value of ...'

6 P(_) after 0.5 km is hi_her than that or P(_) in Figure 3.2.

This higher value may be expl_ined by the higher

"

transmission due to lower scattering optical thickness. "

The pathlength distribution of stratocumulus cloud_ is .._ /

_isTlayed in Figure 8.4. The primary pe_k _t abou_ 0.25 km

k /

_ is due to the reflected photons while the secondary peak at ..... "

. ," about 1.25 km is due to the transmitted photor,s. As can be

seen in Figure 3.4, the transmitted photons are equally

_

significznt to the reflected photons for a given pathlenEth. .. "'

I A comparison of these three figures show_ tha_ as _

decreases, _he value Of P(_) for reflected photons decreases

while the va]ue of P(_) for transmitted photons increases.

/

/-

3.5 Transmission Function of Cloud /

Fizure ,_.5 presents an exampIe of water vapor

transmission, at 20 cm"t resolution obtained from LOWTP.ANB,

- and shows the very rapid change of water vapor transmission

i! with wavenumber. This figure clearly illustrates a higher
Q

Figure 3.5 Water vapor transmission versus _venumbor.

Thedashedandsolidlinesrepresentransmittanceforequivalenwtatervaporpathsof o,I \,

and I era,respectivelyThe. flgureis obtainedfromLO_TRAN5(Kneisyset ai.,1980). .,

_ e

k.
In the case of a homogeneous cloud composed of w_ter

i

vapor and liquid w_ter, the cloud transmission function can /

,j

be obtained by combining liquid water and wa_ec vapor /

.!

transmission functions. The cloud transmission fun:.ion can

be written as; / ,,

/

where the subscript CD means cloud, and T,_igj}_I . the

transmission function o£ liquid w=_ter. T?,_ t_ansmi_sion

function o£ liquid water is given in the form of

- -- _ ("

--,/£_1 - _ I -O_J_ -_W,)_,e. _u 0._5) ..

where B(Y) is the volume absorption coefficient of liquid

//
- . : _--. .-':

. . • . / ! :

'_ : i i

_. "

,/" ORrGINAKPAG-__'S 29

" OF POORQUALITY

water. The spectral interval, Av,. in equation (3. iS) should

be chosen smal I enough so that the droplet scattering

properties and 6(Y)remain relatively constant.

• /

.o

./

/ /

!. 3.6 SpectralCloud Absorption r

_,.

LI

To include the effect of water vapor absorption above the

!; cloud, the composite transmission function for photons with

pathlengzh L within the cloud may be written as;

•'.Z' T_ (..__., )co= 1,_) .(#,._,:,) (3.16)

"_: . • /

_4_I.. ,'

I_.;, The quantities _. and _ in the equation (3.18) are the ....

i't[_'_A" ' equivalent water vapor amount from the top of atmosphere to -" •

__'_,.

cloud top and the water vapor amount in cloud, respectively.

_o

_. The values of _ an_ _. are obtained through the equations

}_.i (3.3) and (3.4) 'Usingthe cloud tran_misslon function and •

i?i;

::_ A(/z_) for a !)}_ pathlength distribution, the cloud absorr.tion,

ii_., given AV is obtained from "i:"

_'_.

_iifii_ where No =COSOo and Ay=y._-P_. Ay.. is the subdivision of A_ .'

!_*:,_" and the value of Ay; is assigned as 20 c_* in the actual "" J

calculation. F_, represent_ spectral solar irradiance at the .... _

_}__ - top of the atmosphere. The values of solar spectral ;

i£! irradiance are taken from Thekaekara and Drummond(1971)
/

: ? / .

i _ / /I / I

. I • "_. ' _," , ' _ ' "

;/.

OF POORQUALITY 30

"- To determine relative _bsorption, we need the two

;

separate equations for the two Rb_orbing constituents of the

cloud. The liquid water absorption, A(ILo_ is calculnted

through

4)_ .OD

Ja']

Similarly. the cloud water vapor absorption is ziven in the

form of

In (3.17), (3.18) and (3.19), the spectral p_hhlen_th

".

distribution, _(_)'is not strongly de_enden_ ¢_. wavenumber.

Therefore, P(_) is used instead of P(_)

Dy representing the integrals in the equmtion_ (3.17) to

(3.19) as finite sums, we obtain the totai cloud absorption,

droplet absorption, snd wahe:" vapor absorption. For the

numerical integration, the trapezoid_[ ;q_th_d is u_ed, and

all values between data point3 _:relinearly interpolated

within the possible range of linearity. The vslues of step

size for wavenumber integration and pathlen_th integration '

_ are taken as 100 cff_ and O.t km, respectively.

l .
31

The value of A_ in the water ":apor transmtsoton function is

? chosen as 20 c_. The spectral resolution of droplet

1

absorption _nd scattering, and solar irradiance depends on

' the degree of variation of volume absorption coefficient,

iL i and scattering coefficient, and spectral solar irradiance

. , with wavenumber. The average value of spectral resolution

_: : of droplet absorption and scattering coefficient are about

m,, . 320 cm_ for the interval of integration. The $pecgral _, •

_ti'":i resolution of solar irradiance is about 240 cff*. Both are

!_".:

ii_:_ consistent with integration steps of lO0 c_t.

_. :

_:_., 3.7 Summary of Cloud Absorption Model

_'=..,. The numerical integration of A(Po),., . ;("o).,., and A'(.o_o

;...... require_ a number o£ input variables: (1) atmospheric model,

i_] (2) cloud type, (3) wavenumber interval and step size for

numericalintegration<4) , solarzenithangle, and

i:_ altitudes of cloud top and base. For the. given cloud type,

solar zenith angle, and wavenumber interval for integration,

the data for pathlength distribution, volume absorption

coefficient of liquid water and spectral solar irradiance

are arranged for the calculation of cloud absorption through

a main program and subroutine program_. In addition, w_ter

:_. vapor transmission is provided from LOWTRAI_ 5.

t

t[ It is noted that the volume scattering coefficient of ".

. liquid water changes with cloud type, and thus pathiength
\

p,._,..,:..E3 32

OR{GINAL """

OF POOR QUALITY

distribution is also dependent upon the type of cloud and

solar zenith angle. Therefore, the first step in the _

. application of the presen5 model he a different cloud type

is to calculate the optical parameters of the cloud usinz

Mie theory. "Secondly, the photon pathleng_h distribution

for fixed sol_r zenith angle should be generated based on

the average v_lues of scatterin_ optical thickness and

asymmetry factor of the cloud. The calculation of cloud

abzorption for different solar zenith anglec again requires

generation of the photon pahhlength distribution. The

generation of photon pathlength distribution is a major task

in the model because it is obtained through the Monte Carlo

method and requires a lot of computer time for the

simulation of physical processes within a cloud.

• . o .

The cloud absorptions with chan_es of cloud to_ _Ititude,

cloud thickness, and atmospheric model can be obtained

directl# from the'modei by assigning the altitudes of cloud

base and top, and atmospheric model. The atmospheric mo,!el

determines the mean temperature _nd pressure of cloud layer,

as well as water vapor amount above the cloud, b_sed on the

altitudes of cloud top and base.

! The present model cnn be extended for further application

. by introducing variations of cloud type and atmospheric

model, in addition, the use of pathlength distributions for

, finite clouds improve the usefulness of this model. h
:_ 33

ORIGINALPAG_[3

'_ OFPOORQUALITY

/

IV. MODEL RESULTS

€.

•_ This chapter presents results from the cloud absorption

model for three types or clouds and rive different

atmospheric models. In the calculation of cloud absorption,

the effect of solar zenith angle, cloud thickness, season,

and water vapor absorption above the cloud are examined• In

;.._. addition, a comparison against previously published results

has been made to test the present model.

4.1 Spectral Absorption by Water Vapor and Liquid Water

For the investigation of spectral variation or absorption

in stratus cloud whose thickness is I km, the cloud is

assumed to be embedded in an atmospheric model For mid- '.

latitude summer with overhead sun. Figure 4.1 shows the

:_ model results rot spectral cloud absorption and atmo_.pheric

i_" water vapor absorption expressed as fractions of the

incident solar irradianoe at the top of the atmosphere. As

illustrated in Figure 4.I, there are eight and seven

dominant _pectral bands in the profiles or _tmospheric water

vapor absorption and cloud absorption, respectively• There

are four regions of minimum cloud absorption between 1500

om"I and 8000 cm"z. These regions are mainly due to the

nearly complete absorption by -_tmosphericwater v_por above
I

i

~~~ 'u$C3

tlAVSar.·:zm CC·f-J]

Figure 4.1 Fractional cloud absorption(solid) alil atmospheric water vapor absorption

(dashed) as a function of wavenumber.

The cloud top altitudo IG 2 knI, am the Golm: zenith anglo 1s zero.

\

\

\

I

I
/

/

!_-' ORIGINALPAGe':_ /

,_ OF POORQUALITY 35 : .

the cloud. Over this spectral range, there is a general ....

" correspondence between the maximum cload absorDtion and the

: minimum atmospheric vapor absorption. The maximum c loud [.

absorption at the point of minimum atmospheric w_ter vapor

7 absorption is due to liquid water absorption, as can be seen -

:s

_- in Figure 4.8.

%_t In the spectral region of 8000 to ISO00 c_ 1 in Figure

._

.;. 4.1, the peaks of .-%tmosphericwater vnD.or absorption are

superimposed on the peaks of cloud absorption, and their

;_ values do not exceed SO _. This m__ansthat the w_.ter vapor

b

absorption bands within 8000 to 15000 c_ L are not as strong

as the water vapor absorption bands within ISO0 to 8000 cm"I.

Therefore, some cloud water vapor absorption can be expected

because of absorption

._- Incomplete by water vapor abcve the

t,,

• cloud.

p1 : ..

€ :.

_ Figure 4.2 displays the_spectral energy absorbed by cloud .//

i and atmospheric water vapor above the cloud as a function of

. wavenumber. Instead of fractional cl_.ud absorption in

_% Figure 4.I, Figure 4.2 clearly shows the rel_tive

contribution of each band to total cloud absoz-phi_n A

comparison of Figs. #4.1and 4.:> shows that there i_ good

: agreement between the patterns of l'hecurves. However, the

_ maximum fractional cloud absorption and atmospheric water . .

@ vapor absorption occurs for different wavenumbers than the

maximum values of absorbed energy due he weighting by the ....

solar spectrum. In terms of absorbed energy, the maximum

I ....
• _ • II • • f--- lill_ V iI_wj S, i • I - • Wi! t .°

Q

Figure g.2 Spectral cloud absorptlon(solld) and atmospheric water vapor absorption

above the cloud(dashed).

The same conditions in Fig. 4.1 are used.

k_
!

!

' /" /

.?

t." /

.....,j .... , /

"_t .. " ............... •....... " .

OF POORQUALITY

: cloud absorption occurs between _500 c_ t and 7000 c_ t while

the maximum atmospheric water vapor absorption t_kes place

in the range of 8000.c_ l to 8000 c_:. Two dominant cloud

-. absorption bands between 4000 c_ l and 7000 cm4 contribute

significantly to total cloud absorbed energy. Three

• absorption bands between 1500 c_ I and 7_00 c_ l are the major

components of the atmospheric water vapor absorption above t,!

the cloud. Over the spectral resion of 11500 cm_ to 15000

c_:, there are two weak bands of cloud and atmospheric water

vapor absorption. Almost all the cloud absorption is due to

the liquid water absorption between 1500 c_* and 7500 cm_.

and to water vapor between" 11000 c_ l and 15000 c_ I.

Figures 4.3 and 4.4 show the relative contributions to ....

total cloud absorption made by liquid water absorption and

absorption by water.va.por within the cloud. As ca.n be see1_

in the figures, the maximum cloud absorption over the '.

spectral range of 10000 to 15000 car* is mainly due to the

cloud water vapor absorption.

Between 7500 c_' and 10000 car', the water vapor /.

absorption is slightly larger than liquid water absorption. "...

Almost all the cloud absorption at wavenumber below about /

/

" 7000 cm'* and elsewhere between the water vapor bands, is due _

to liquid water absorption. Cloud water vapor absorption /

• dominates the total cloud absorption only in the water vapor

absorption bands above 8000 eft"I. Tlt_ only region of

equivalent absorption by liquid water is in the band

/
_a _ r_r'_,_l 7_ _:3 I I_ I_ ...

Figure t}.3Fractional cloud absorptlon(solld) and llquld water ab_orptlon(dashed)

as a f,_notlon of wavenumber,

The same conditions in Fig, 4,1 are used,
L _ 'P

J

_ oo"-n_0

-oh3

O_ "'

C r,_

g

1 ;

Figure 4.4 Fractional cloud absorptlon(eoli_) and cloud water vapor aL._orption

(dashed) as a function of wavenumber. -(

The same conditions in Fig. 4oi are used. .'\_-_

_D

i.

\

\,

• \i"-_

; '. .... ".-.. ,, \\
m

; /

/ ,I

// ; i/ ...

. OFPOORQUALrI'M / .._.

centered at 7500 cff 1. "" ;

The above results for continuously variable absorption

! may be summari=ed" dl'scretely using the conventional water __..

•, vapor absorption bands, namely: 0.7, 0.8, O_=, _, _, _, X

i / /;

_i and 3.2. Table 4.1 shows fractional absorption within and ,,_7,

l'0 ': between the water vapor absorption bands due to water vapor ,'

_i and liquid water. The U.S. standard atmosphere(196_) and /

I_I stratus cloud are used to estimate relative spectral

i /

:: absorption by water vapor and liquid water. The values in ._j

_, Table 4.1 are calculated as a percentage of incident

'_ spectral irradiance at the cloud top. The highest

fractional absorption in a water vapor band is about 97 Z in .I

the 8.2 #m band, and the lowest fractional absorption is "'

,_ about 3 • in the 0.7 #m _and. In terms of the contribution

of each band to total cloud absorption, the '_and Q bands

are very dominant in Table 4.1. These two bands constitute ".

about 3S = and together with the spectrul band between them,

make up almost 50 _ of the total cloud absorption. As

illustrated in Table 4.2. water vapor absorption is only

dominant in the 0.7, 0.8, and paz bands, while droplet

absorption dominates elsewhere. As the cloud top is rnised,

/',

the relative water vapor absorption decreases in e_ch band. 

• f

• For the cloud top with height of 1.5 |:m,the extent of the ;

l/

cloud absorption in the eiKht bands occupies 69.7 _ of total i

cloud absorption in the entire solar spectrum. For the /

[

relative absorption in the eight bands, liquid absorption

/
/t

/

/

• ,, _ ,-' i ,; ' ' "" . • ,:? " 1 /'

.. ' ... / ../"' / / f' !/ i. "° .. '_ /

"_' , ." I : / ' "' '.

_,_'_i-",,r_.'."<:"'": ............... " " . ............. -.......................... '

ORIGINAL PAGE I_

OF POOR QUALITY 41

Table 4.1

_ Spectral Cloud Absorption within and between the W_ter

Vapor _ands

Sand Band F_(abs. ) F_(abs. ) F_.(abs. ) ' ?_(ab_. )

Name Interval _X F_ Tot._ 1 abs.

(._X:Fro) (Wire2) (_t_[2Fm_) (_:) (=)

O. 20~0,70 O. 25 O, 50 O, 04 O, 20 - >J_

0.7 0.70"0.74 1.66 41.5 3.23 1.'32

0.74~0.79 0 • 27 5 • 40 O. 45 0,21

0.8 0.79~0.84 1.97 39.4 3.78 1.56

O. 84~0.86 O. 19 9.50 O. 96 O. 15

p_z 0.86~0.99 11.33 87.15 11.33 8.99

O. 99~1.0:3 1.30 3_. 50 4.44 1.0:3 /

€ I. 03_'1.23 12.31 61.55 11.9G 9.77

1.23~1.25 1.07 53.50 11.93 0.85

9 1.25~1 . 54 24.18 83.38 40.65 19.18

1.54~1.70 16.56 103.50 44.04 13.14

1.70~2.10 19.95 49.88 6:3.94 15. St3

2.10~2.27 8.77 51.G9 65.16 6.96

%P

,_ 2.27_'3.0 10.09 1:3.82 78.2G 8.01

3.2 3.0~3.57 6.31 11.C7 96.94 5.01

3.57"-7.0 9.83 2.87 92. _0 7.80

F_x(W/m2) ;Solar irradiance for a given band at the cloud

top. The cloud is assumed to have I km thickness, and is in .. ; 

". the U.S. chandard atmosphere under overhead/ sun. //'

//

t..1

.:.-.t.-
I

._ OF pOORQU,_'.',T'_: 42 ,,

Table 4.2

Fractional Absorption or" Stratus Cloud

(1) Case of Cloud Top Altitude of 1.5 km

I

: Band

!'i Ilame O. 7 O. 8 OCZ 4, 9 0 × 3. _..'

/

'-' TOABS 3.2 3.8 11.3 12.0 40.7 83.9 78.3 98.9

_j LWABS 8.g 8.8 19.€ 50.8 78.8 89.1 94.0 97.8

;'_,.!} (2) Case of Clcud Top Altitude of 5 km

_N, 1 "/

_:_ Band

;_ Name O.7 0.8 O_z € _, Q X 3.P. •

I ?'-_1.

c:_.: TOAB3 1.8 1.6 6.8 9.6 43.4 85.0 81.8 9B.8

,_:x WVAB3 82.2 77.9 62.4 34.0 20.8 10.0 A 0 1.I i_'_.. ""

!:_i LWABS 17.8 22.I 87.8 68.0 79._ 90.0 98.0 98.9

,51.

:_ i The cloud is assumed to have 1 km thickness, and is in _he % : U.3. standard atmosphere under overhead sun TOABS" cloud /

• //

L_ absorption for each band I?VABS : relative fractional wa_r : /

_.. vapor absorption in cloud. LWABS ; relative fr_c_ional .,2-

__V liquid water absorption in cloud. All values in Table 4.2 "

_ are expressed as percentages.

_.ii_ ,

!3-

I

?
• , !

/ , / ]

: • ,

_-._,,,-_..,_-_..................... _ ,_.:.........'....................................... _......-... '.................... I

" OmGtNALPAGEI_

i takes 68.3 = and water vapor absorption occupies 31.7 _.

43

OF pOORQUALITY /

i Outside the water vapor bands, liquid water contributes

_ about 30 = of total cloud absorption. 7.

• .. '.]

As the height of cloud top changes from 1.S km to 6 km,

the total cloud absorption in the eight bands is increased

about 3.1 g. This is due to greater absorption by the

droplets. Of the absorption of eight bands, the liquid

water now occupies 81,I g while water vapor takes 18.9 _.

4.2 Comparison of the Results with n Previous Work

It is desirable to compare these results obtained from

photon pakhlength distrlbution with previous york. To

examine the validity of computed results, the present work ....

is compared with Welch and Cox (1980). Table 4.3 gives a

comparison for a stratus cloud. Eefore examining the v_lues

in Table 4.3, it is importantto point out that the present ..

computation used the same type of drop size distribution and

the same atmospheric model as tha Welch and Cox study.

There appears to be a general agreement in the values of

cloud transmission and absorption. However, there exist

significant differences in the v_lues of reflection and

water vapor absorption above the cloud top. The values of

water va2or absorption above the cloud can also be examined

based on the absorptivity curve in Lacis and Hansen(1974).

According to their curve, the water vapor amount yielding n

I
,.,,_

, i ' \ l

: " ! I ; I _ " / ". i 1. 4 t ""

' ' ""

:_f<_J 1: i.... •...... " ....................................................

','I OF POORQU,a,Ll'l''l 44

Table 4.3

Comparisons of the Present ;4ork and Welch and Coz's Study

!.i Cloud Top Present llork Welch and Cox Difference

i.i HeiKht(km) (._) (_)

": T 13.9 12.8 +I. 1

1. B R 65.9 58.7 +7.2

'-. A 6.0 8.0 0.0

fi_. ATe.! 12.2 2o.s -8.€

T 14.2 13.3 +0.9

: 4 R 67.9 62.1 +5.8

'i A 9. I 10.7 -1.6

AT_ 6.8 13.9 -..'3.1

T 14.9 14.2 +0.7

i;_ _' 10 R 71. B 69.4 +2.1

:_'!_; ...

;_,_::_. A 12.6 16.4 -3.8

, ATM 1.0 O. 0 +l. 0

A stratus cloud whose thickness Is 1 km is embedded in an

!_;i' atmospheric model of GATE pha_e III with overhead sun. T;

transm£s_ion, R ;reflection, A ; absorption, ATA;.

atmospheric water vapor_ absorption above the cloud.

'.i

"[ ° .

• . .
! i

• i

ORIGINALPAGE [ZI_

OF POOR QUALITY .4S

fractional absorption of 20 _ must be larger than 10 cm of

/.1

precipitable water. It therefore appears that Welch and Cox

grossly overestimated water vapor absorption above the

cloud. This overestimation of water vapor amount _bove the

cloud directly affects tl,eir reflection values.

Unfortunmtely, there appears to be a lack of other published

results for further independent verification of the model

presented here.

4.3 Limitations of the Model

The present calculations are performed based on planeparallel homogeneous clouds, and zero reflection of solar

radiation from the earth's surface. Actually, clouds are

finite in their dimension, and their drop size distribut_cn

depends on the position within cloud. In addition, c_cud

vapor density changes with heiKht. The reflection of solar

radiation from the surface affects cloud absorption.

However, it is neglected in the present calculations because

of its small effect on cloud absorption.

For the Keneratlon of photon pathlength distribution, the

Monte C_rlo method £s used. A stochastic error is expected

from the Monte Carlo simulation of multiple scattering.

This error can be reduced by considering the number of

histories and was smnll for the cases considered here. The

stochastic error is about 0.1% in the generation of photon
46

' ORIGINA_PAG_IS

pathlength distribution. OF POORQUALITY

- The water vapor transmission function is obtained from

LOWTRAN5. The computer code of LOW_'RAI_5 calculates

atmospheric transmission averaged over 20 c_ l intervals in

steps of 5 eft t from 3_0 c_ z to 40000 c_ z. The code uses a

single parameter band model for molecular absorption. In

the case of the present calculations, some error is expected

from the estimation of the water vapor transmission function

because LOWTRAN B is incomplete. Although it is difficult

to assess _ccurately the error originated in LO_'ITR,_q_[ , the

error in the water vapor transmission function is expected

to be less than i _.

• . . .

4.4 Dependence of Absorption on Cloud Top Altitude

Figure 4.5 illustrates how the w_ter vapor a_uorptio_

above the cloud and the total cloud absorption depends on •

the cloud top altitude. A stratus cloud whose thickness is

i km is assumed to be embedded in an atmospheric model for

GATE phase III with overhead sun. The cloud toe altitude

changes from l._ to 10 km in the atmospheric model. As the

height of the cloud top increases, absorptio_ by water vapor

above the cloud decreases rapidly due to les_ column vapor

• amounts, while liquid water _bsorption and total absorption

increases steadily within the cloud due to an increase in

the solar radiation incident on the cloud top. As the cloud

top al_itudo increases, cloud temperature decreases and
CA) CD) (C) CD)

,_.-_3RDEDEI'_ERG¥C_/H:_3

Figure g,5 Water vapor absorpt.4on(A),droplet absorptlon(B), total cloud absorption(C),

and column vapor absorption(D) versus cloud top alt;ttude.
_ 48

i consequently the water amount in the cloud decreases.

v_por

_:_: Figure 4.5 does not show much decrease in cloud vapor

absorption.. This means that the reduced atmospheric water

• vapor absorption above the cloud largely compensates for the

lower vapor density within the cloud,

At a height of i0 |:m, the total cloud absorption is

increased about $7 • of its value at I km, and liquid water

absorption is about 84 • hisher, In contrast, the

atmospheric water vapor absorption above the cloud is

reduced about S2-Z from its value ah 1 km. Thus, water J "

vapor absorption above the cloud has a very important effect

on the calculation of total cloud absorption.

• • .* •

Figure 4.6 shows the spectral absorption by a stratus

• cloud and atmospheric water vapor above the cloud f_r the "

cloud'top altitude'of 2 km. The cloud whose thickness is 1 ..

km is assumed to be embedded in an atmospheric model for "

i..:i_ GATE phase IIl With overhead sun. This figure illustrates •

the spectral cloud absorption and atmospheric water v_por .\

:_!'ili_ absorption in energy per unit wavenumber. Figure 4.7 also !i:l

shows the spectral cloud absorption and _tmcspher£c

absorption above a cloud for the clou_ top altitude of S km.

• A comparison of Figures 4.8 and 4,7 shows that as the cloud

i_!_ top height increases, spectral cloud absorption increases

ii " steadily between 1500 and 7SO0 c_* while the atmospheric

_ii</ water vapor absorption above the cloud decreases

j "

"<\
!

• \

a

o i

i

ill

i.

Flb_ur4e.6Spectralcloudabsorptlon(uolldand) atnosphorlwac tervaporabsorption

(dashedfo) rcloudtopaltitude0£ 2 k_, ".

ThecloudIn embeddedin an atmosphericmodelforGATEphaseIIIwithoverheadsun, ".

4:"

/

/ /

" ..... --" ../- _ ,i , " / I

/ ;- ,/

/ / ,/
._',.

Ii i I I i • I • • LI I • -- O I I I_ I • l II i • J• I_l i I ,i_.% ,

!!At!'_'_._<•--q!:_iI,-I:i ; •

Fl_ureg.7Spectralcloudabuorpklon(_ollad)ndatmosphericw_tervaporabsorptlon

(dashed)forclo'Jdtopaltitudeof _ kin,

Thesameconditloni_n Fig.4.6are u-_efor d solarzenithan_leandatmospherlcmodel.

o

......... ", ° \ o.

"" 't , - ....... _.. ._ ...... _,.: .._.... .." "_ .A.--_
_'. _ i .° / . .

• , .

/- o t i .o

• , . ..

$

/ -

?. sl

significantly in the spectral region between 4500 and 11_00

- c_z. In the spectral region ranging from I0000 to 14000

i cm_, both cloud absorption and column vapor absorption are

: decreased. Over this spectra; range, cloud water vapor

absorption dominates over liquid water _bso_ption, and the

decrease of cloud absorption is due to the decrease of water

vapor amount within and above the cloud•

Figures 4•8 and 4.9 display liquid water absorption for

cloud top altitudes of 2 km and _ km, respectively. An

increase in liquid water absorption can be seen from the

comparision of Figures 4.8 and 4.9, as evidenced by the

broadenin_ of the Ilquid water absorption bands. A

comparison of Figure 4.10 and 4.11 shows that as the cloud ....

top altitude changes from 2 km to B km, the cloud water

vapor absorption is decreased slightly everywhere except for i_

the spectral region between about 4800 and 8000 cr.'*. For "... 4

the change of cloud top a.'titude,two major f_ctors are

• !\

related to cloud water vapor absorption: (i) decrease of

water vapor density in cloud due to the lower temperature,

(2) increase of available solar energy for cloud absorption

by the decrease of atmospheric vapor absorption abr.ve the ,-_

cloud. Thus. the increase of spectral absorption between

about 4800 and 8000 cm" may be explained by the more

.i

i•

dominant effect of (2) over the effect of (I). The net :,

effect of increase of cloud top altitude makes the cloud _

water vapor absorption decrease. ;:

|
me L g III I

i J i i

"n_,

• _ O_ :

Figure /4.8 Spectral cloud absorpt%on(soltd) ard liquid water atmorptlon(dashed)

for cloud top altitude of 2 _no

The cloud 1_ embedded in an _.t=ospheric model of GATE phase III wLth overhead sun,

• . . .\ _ \l

• .. , .: \

\ \
.........

i ] i i i i|l it i L| Ill •

\

\

_ , .

O0 :

• "_

k,

Figure4.9Spectralcloudabsorptlon(sollad)nd liquidwaterahsorptlon(dashed)

forcloudtopaltltudeof 5 kin.

The cloudIs embeddedIn a. atmosphericmodelof GATEphaseIIIwlthoverheadsun.

: \

,/

/

/
...... ! ,m

pq

t ..

• • g • • • g g : • e • • • •

Q

Q

Figure4.10Spectraclou l dabsorptlon(solaldnd)cloudwatervaporabsorption

(dashed)for cloudtop altitudeof 2 kin.

Thesamecondltlonsin Fig.4.6are usedforsolarzenithangleandatmospherLc

roodelo

.
-. f·

i

!

, '

;"

f

\

I

!

J ".

J'

~r--_--r--__-.,.-~r---r--r--__-.,.-~r--~-...,..--wo---' Q

\.

--:\:-

~,

\ -...\-

\

-_':::-..

... .../\. 76C:3 16SC3

"AVEr~;J$m CCN-IJ

Figure 4.11 Spectral cloud absorption(sol1d) am cloud Hater vapor absorption

(dashed) for cloud top altitude of 5 km.

The same conditions In Fig. 4.7 are used for solar zenith angle am atmospheric model.

n

5

tI

u

iO

m

la

m .

C)

~.

\. \ \

\\

\ '

'. '

"'--"',
./ t .

• . ,,.,

e ' . " ! /:'/

J

.- . .......... • . • .: .¢.'

m

;! _ OF POOR QUAL(r_ B8

4.5 Cloud Absorption £or Dt£ferent Atmospheric Models ./

Table 4.4 presents absorption, reflection, and

transmission by stratocumulus cloud for five different

atmospheric models. The values of cloud absorption are

nearly const=nt except for GATE phase III. This exception

can be explained by the higher moisture content or its /

atmospheric model, causing greater water vapor absorption

above the cloud than for the other atmospheric models.

Convorsely, Table 4.4 also shows the highest cloud

absorption occurs for a the mid-latitude winter atmosphere.

This is due to the lowest absorption of tha water vapor

above the cloud. In addition, the highest value of _ "

transmission and reflection for the same atmospheric model

may be explained by the same reason. In contrast, the

values in GATE phase Ill show that the lowest ones are due

to the highest water vapor absorption above the cloud.

Thus, cloud absorption does not change significantly with '/

the atmospheric models, However, the atmospheric water Z

vapor absorption is strongly dependent on the moisture

d_-stribution of atmospheric mode.ls.

4.6 Change of Cloud Absorphlon with Cloud Thickness

• Table 4.5 is an illustration of cloud absorption,

reflectlon, and transmission wlth the change of geometrical
i

!

• , / •

!

I / " ..,

• • .._

57

OF PO0|l QUPLL, T_.

Table 4.4

Cloud Absorption for DifFerent Atmospheric Models

Standard Tropical Mid-l_t. Mid-lat. GATE

"_ atmos. • atmos, summer, winter phase III

Transmission 340.2 333.6 335.5 343.9 333.0

F_fleotion 790.7 775.9 780.5 799.0 771.9

Absorption 110.4 108.2 109.8 117.7 93.7

_ Atmospheric

vapor abs. 93.9 117.8 109.5 80.4 137.1

:.I Water vapor

.... path O.20 O.45 O.34 O.12 0.83

!!_ Al! values in Table 4.5 have units of W/m 2. A stratocumulus

i'_9:':_i_ cloud is assumed to be embedded in "hhe five different

atmospheric models with overhead sun. The cloud top

altitude is 3 km, and its thickness is 1 km. The vertical

I_ wmter vapor path above the cloud is expressed in cm.

i ;_,,I ....

::.o:i •

:'J:i_.° "

".° ,

_:_i •

.

:I i

a. •

!1 '

t"

LI

'?_-! t
/

. / ./

/- . ./

/ •

.. /, ; _ / /

/ /

ORIGINALPAGEf$

, OF POOR QUALITY 58

/

Table 4.5

Cloud Absorption with Change of Cloud Thickness

AZ(km} Percent Stratocumulus Nimbostratus

i

: O._ Transmission 28._ 8.8

i,

(2.5"3) Ref I ect ion 83.9 '79.9

; Absorption 7.9 11.6 ,

-:; I Transmission 27.9 8.5

(2_-3) Ref I ect ion 63.2 79.5

"j

" Absorption 8.9 12.0

2 Transmiss ion 27.3 8.4

(1~3) Re£ I ection 62.2 78.6

;'_ Absorption I0.5 13.0

:::_: The clouds are assumed to be in the tropica! atmosphere with'.

' overhead sun.

°.

Lol i '

i
4

59

thickness of cloud. The =alculations are performed for

constant _cattering optical thickness for each cloud

- discussed in section 3.2: The total liquid water content of

clouds is kept fixed because of the uniform distribution of

cloud droplets. The cloud top altitude is also fixed at 3

km so that all clouds may have the same amount of solar flux

on their upper boundary.

Table 4.5 shows that as the cloud thickness increases,

cloud absorption increases. In addition, the reflection and

i! transmission show a slight decrease in their values as the

geometrical cloud thickness increases. Therefore, it is

obvious that the geometrical thickness of the cloud is not

an important factor for fixed water content, but the optical

thickness is a major factor in determining cloud absorption,

reflection, and transmission.

4.7 Cloud Absorption by Different Types of Cloud

The cloud absorption depends to some extent upon the

mlcrophysicnl properties and stage of developmemt of cloud.

Table 4.8 shows total absorption, reflection, and :.

transmission for three types of cloud discussed in section

[

3.2. As can be seen from Table 4.6, the highest absorption

: takes place in the nimbostratus, which has the hifhest

liquid water content ....
.o

\

_ J_11_'_°_ __':'_"TY_ _,-__-_.._:..... "

6O

_ Table 4.8 //

::i_" !... Cloud Absorption by Di_feren_ Types ot Cloud J

percent Stratus Stratocumulus Nimbostratus

.(top) (base) (top)

Absorption 10.5 8.7 11.9

Transmissicn 15.5 27.4 8.5

Reflection 74.0 63.9 79.6

\,

Note; All clouds are assumed to be embedded £n the

atmospheric model of mid-latitude summer w£hh overhead sun. /

The cloud top altitude is 2.5 k_. and the thickness of :'-

clouds is i km. All values in T_:ble 4.6 are expressed as

percentages of sclar radiation znci_enk on the cloud top. \

1__

•

!

. .. i\

°..

• .o.

- \

1!

I

,/

t t

t

/

- l
i

\

+

ORIGINALP_G_ f7 61

l OF POORQUALIT(

, It appears that the amount of liquid water has little

effect on cloud absorption. For example, the liquid water

content of nimbostratus is about seven times larger chan

that of stratocumulus, but th,_ difference ;n their

fractional absorptions is only 3.2 _. On the other hand,

the liquid water content strongly influence_ cloud

_ reflection and transmission. In the case of transmission

_' and reflection, the differences between these two cloud

types are _pproximately 19 Z and IGZ.

_ 4.8 Dependence of Cloud Absorption on Solar Zenith Angle

Based on the inc£._ent solar radiation at the top of

cloud, the fractional absorption is plotted against the

!_. solar zenith angle in Figure 4.12. The height of the cloud •

top is assumed to be 3 km. and its thichness i_ I km. The

i_It U.S. standard atmospheric model aTd stratus cloud are used

+!

• for the calculation of fractional absorption. The result.

_,t; _ to 5.7 _ as the so'lar zenith angle increases. However,

_ this range ._.squite Variable _ith the type of cloud, cloud

!_ thickness, and atmospheric state.

!]

Figure 4.1_ shows that the absorbed energy by stratu_,

clout', decreases steadily with the increase of solar zenith

!!

"_ angle _'or the same conditions as Figure 4.12. The cloud .

i':i "- absorbs about 134 W/m= under overhead sun and about 18 W/m2

iil _ for a solar zenith angle of 75°• The decrease in absorbed _;si ,,,
$ , I i . . . ,

r I

i,

• 1 /

9

• "/

, oj

:o]. ,

j.., .

II f - g I1_ II II II W I e

,/

,_ V//

I1_ /*

oo I

_ r" r t

_ ':..

I

*S/

° .

i

"...... lo_

0 20 40 60 gO ;;f

r

: o

Fl_uro g.12 F_=tton_l clou_ g_orl_Llon vorc_ 8olnr r_ntth nn31o. •

!

o .

o

/

i

• ,o.

/

t . ,/ /

/
/ - •• ;.: :.,-; ' ••,~••_..-••- ;' .- , ;."; I .' • t , ., .'

.,. or.. ' '"r..' ._....... ,'J, '~-: / ........-T··..... ....... """I~~ (fl~~,.~-...,...,r,r. ,.,..IIt....·..".,.......;"""r.·,' ·-:..•..~·'.,I"I "'''''l'lt "'r.wr·~i""·"· ..•:.: .~ .."'" " .. ':'~'l~~ ..·~-:-..~1~..-n·~.('f,...,.,r .•.~":" ".. r:;· .~. a~", ••. ' ',' :.' ..,', ~l"\,'" • " •.,.,. .~ ~,·~I'lss·,...,;.:"'~')~ ',:--. ~"',- .'. ~·.·.f.~.!.... • ~"~ .: 1,--·.,."":':' • I r

/

. .. .., ~. ''-;71~; ;'t1!

\

I

/

!

"

....__. I

I

-

(vIr!)

120

80

\.

".

'.

. j'\

, ,;

l·

coss.

Figure 4.13 Cloud absorption versus cosine of solar zenith angle

, j

o

" ,"

/' I

0.2 0.4 0.6

.- /

,

0.8 1
I \

,/ ............... . "-. _ I I _,/.,. " - ,\

• .,., J , . _°-. ..... .. ..... -.

J energy may be explained by (1) decrease of incident solar

! energy per unib, area due ho effech of angle of incidence,

i and (2) shorter pahhleng_h o£ photons due go less

._, ".

; probability of penetr_.tion into cloud, and (3) increaze of

watQr vapor path above the cloud.

! ,

t" i

&,

r.: .S

:[.

\

,

._

o

/

g7- °

o"

g2

":•iil
[i i-- :

• • ,\ t. i

e5

I! V. GLOBAL APPLICATION OF MODEL RESULTS

8 -

The results obtained in Chapter IV may be used in global

applications; for example, general circulation or climate

! models. Since the energy absorbed, reflected, and ,

"i transmitted by a cloud is not significantly dependent on the /

seasonal and zonal atmospheric models, it is possible to '"

generate cloud absorption by a simple parameterization of "

the optical properties oD cloud, based on cloud climutology.

The atnospheric water vapor absorption above the cloud can

• • " " "

also be obtained easily from the relevant atmospheric model.

The results of Figure 4.5, in particular can be used as a '_

useful guideline for the parameterization of cloud

absorption and atmospheric water vapor absorption above the

cloud. The nearly linear variation of these two curves wil!

mak_ p_rame_erization simpler. _- \

t

A range of cloud absorption under overhead sun may be

suggested for global applications. The values in T_ble

5.1.(a) are only applicable to the clouds whose liquid water

- content ranges from 0.14 to 1.0 gram/m 3 , and are given as

the fraction or solar radiation at cloud top.

An estimation of cloud absorption can be made by the

global averages of liquid water content _nd thickness of

\
66

Table S.1

Global Application of Cloud Absorption Model

(a) Range of Global Cloud Absorption for Overhead Sun

.... Cloud Thickness(km) Cloud absorption(=)

I 0.5 7 - 12

' 1 8 - 12

I

I 2 10 - 13

"1

! The values in Table S.l_(a) are expressed as a fraction of

solar radiation inciden_ on _he top of cloud.

-. |

\,

(b) Zonal Average of Cloud Absorption

"" /

Latitude zone <COSOo> (CLDABS)._ (CLDABS),_ /

(_llm2) F_<COS0O>

0 _ 10 0.634 59.2 6.9

10 ~ 20 0.61S 56.9 6.8

: 20 -- 30 0.577- 5t.6 6.6

30 ~ 40 0.$21 48.2 6.8

40 ~ 50 0.450 42.8 7.0

' SO _ 60 0.365 34.6 7.0 t

80 ~ 70 0.269 25.5 7.0 • -

. The values in the last column are expressed as percentages.

(CLDABS)_ is zonal average cloud absorption over daylength ,

based on mean cosine of solar zenith angle. The subscript ' •

• MC stands for mean cosine of Oo. Fo is solar irradiance at - " • "

" the top of the atmosphere. <COSO0> is mean cosine of solar L

zenith angle.

.:
I

[

67

clouds. The global averages of liquid water content and

cloud _hickness may be assumed to be 0.2 - 0.3 g/m° and ~1.6

I_ km. These values can be estimated approximately From a

. typical value of liquid water content of non-precipitating

cumulus clouds, 0.5 g/m s, and data on the zonal distribution

of cloud amount and thickness (Paltridge and Plat_,1976;

; Rogers,19?9) Based on these values and Table 5.1.(a), liquid

water clouds usually absorb about 8 - 9 € of the incident

/

,/

solar radiation at the top of cloud For overhead sun. / "4

"i /

, Based on the average cosine of solar zenith angle at the

vernal equinox and the zonal distribution of cloud amount

and thic|_noss (Paltridge and Plaht, 1976), Table E.l.(b)

illustrates an estimation of cloud absorption for each -'"

latitudinal zone in Northern Hemisphere. It is noted that

the present calculations exclude the data on cirrus and

altostratus clouds because these clouds are high-level

clouds and are composed of ice crystals. Therefore, the

values in Table 5.1.(b) are averaged ones due to only liquid

water clouds. Although the result Is a preliminary figure,

the values in the last column show little variation with /

!

latitude zone. This may be explained by the fact that the /

/

mean w_ter vapor path to cloud top is approximately t!

independent of the l_titudes. Approximately, _he same mean

• water vapor •path may be expected in both low and high

latltudeu since lower column vapor amount occurs at •

latitudes with higher menn solar zenith Rngle, and higher
/' I

/ . f

..~"CH'

I

" I , .

."

as

column vapor amount takes place at latitudes with lower mean

solar zenith angle.

consideration or ice crystal clouds.

Averaeing el' . a~sorption rrom th. equator to 70~N. the

~lobal average absorption is obtained and the value is

'. '

However. thi~ value may be changed by the

or the globally averaged solar irradiance at the top or the

estimated as about 47 W/m2 • Th~s value is approximately 7 %

atmosphere.

,.

...
/, ii !

_. 69

VI. CONCLUSIONS

A theoretical model of spectral absorptlc_; of solar

:

radiation in homogeneous clouds has been developed for the

purpose of the present investigations. This model is

, .'

i _ limited to plnne-paralle[ homogeneous water droplet clouds.

The model results presented in Chapter IV ind£c_te that

cloud absorption and atmospheric water vapor absorption

above the cloud are highly dependent upon the wnvenumber.

There are four principal regions of minimum cloud absorption

and three domin-_ntbands of cloud absorption between about

1BOO cm_ and 7_00 cm"l. The three dominant cloud absorption

bands exist at the points of the minimum atmospheric water

vapor absorption, and are due to nearly complete liquid"

water absorption. The minimum cloud absorption regions are

mainly _ue to the nearly complete absorption by atmospheric

water vapor above the cloud. Over this spectra" r_nge,

there is a general correspondence between the maximum cloud

absorption and the minimum atmospheric water vapor

absorption. Two cloud absorption bands between 7BOO cm"L and

_a

11500 cm'*occur at the points of the weak atmospheric water

• , .

vapor absorption, and are mainly due to both liquid water _

and cloud water vapor absorption. The cloud absorption
• / . ,.

./ ° /// i

I

70

bands between 11500 c_* and 15500 c_ I are mainly due to

water vapor absorption. Therefore. the liquid water

contributes nearly completely to cloud absorption between o_

2000 cm_ and 7500 cm_ while water vapor absorption is the

major contributor to cloud absorption between 10000 c_I

15000 c61 .

Averaged over the whole solar spectrum, total cloud

absorption, as a fraction of the incident solar radiation at

the top of the cloud, depends most strongly on liquid water

absor,tion in the wavenumber interval ranging from 1800 to

11500 €_l, and to a lesser extent on water vapor absorption

elsewhere. Thus, the most critical parameters to the model

are liquid water content and the amount of water vapor above

• . . the cloud.

For the whole spectral range of solar radiation, 1 km

thick cloud absorbs about 8 to 12 • of solar radiation

, incident on the cloud top for overhead sun. Cloud

reflection changes from 12 • to 80 _, and transmission

changes from 8.5 • to 28 _. In terms of the relative

absorption by liquid water compared with water vapor within

cloud, liquid water contributes about 77 Z to 91 • of total

cloud absorption, depending on cloud type, cloud top

altitude, and atmospheric model. The cloud water vapor

contributes the remaining 9 to 21 _ to total cloud .

absorption. This relative ratio is sensitive to the changes
i

! ,!

I

_:. of cloud top altitude within the wavenumber interval o£ 8000

to 15000 c_ 1. T -

).

i _. •

i_ Wa_er vapor absorption dominates over liquid water

• z:

:: absorption in'three, bands ie , 0.7, 0.8, and p_z The !'L ' • •

L - _,,

_,, results obtained indicate that even in the water vapor

_.

_i absorption band_ liquid water dominates over water vapor in "

i_, absorp_lon. Of the water vapor absorption bands. 3.2 _m

. _. band is the most highly saturated band, and 9 band makes the

highest contribution to total amount o£ energy absorbed by

;_: cloud.

_,_

_ For an increase in cloud top height cloud and liquid ]

i_ water absorption increase significantly, while water vapor

:_ absorption decreases slightly. The cloud _bsorption does

_t not show a significant difference for seasonal and zondl

atmospheric models.

:i_ As the physical thickness of the cloud increases for,.

i_ fixed scattering optical thickness, fractional cloud

,-, absorption increases slightly while fractional cloud

_:_ reflection and transmission show a slight decrease in their

_..i_? values.

•

i .

!! •

The amount of liquid water in a cloud does not greatly

i influence fractional absorption of cloud. However, i_ fractional transmission and reflection of cloud are highly

•

_ dependent upon the liquid water conten_. For an increase of

solar zenith angle, fractional cloud absorption and
/ i : .

72

transmission decreases steadily while cloud reflection

increases. In the case of a stratus cloud whose thickness

is 1 km. the range of fractional absorption decrease from

10.7 _ to 5.7 _. for a change of solar zenith angle from

•" zero to 7B °.

The application of model results to global average liquid

water con_ent and thickness of cloud indicates that liquid

water clouds absorb about 8 to 9 • of the incident solar

•! radiation at the top of cloud under overhead sun. There are

no strong zonal effects on fractional cloud absorption. The

global mean fractional cloud _bs_rption is about 7 _ of the

globally averaged solar irradiance at the top of atmosphere.

However. this is an approximate estimation based on the data

of liquid water clouds in the Northern Hemisphere.

/

Finally, the present results suggest that the amount of /

energy absorbed by a. cloud is mainly determined by the

liquid water content of the cloud, the atmospheric water

vapor profile above the cloud top,and solar zenith angle.

The liquid water absorption is primarily responsible for the

cloud absorption, and increases with the increase of cloud

top altitude. The cloud water vapor absorption is nearly

constant for the change of cloud top altitude. As the cloud

top altitude increases, the relative contribution of cloud
! .° ..

• . . . it.-;

_ >•

',*-: 73

_.... _,-,., wn_er vapor decreases while the liquid water absorption

_ absorption increases

i2:

": Since the present work is limlted to plane-parallel

•4. t7 homogeneous clouds t future studies on this problem should

...._.include the effects o£ fLnibe and inhomogeneous clouds, and

"-.'_ should account for the global distribution of clouds. In

,:F addition, the effect of surface albedo in the presence of

:_ broken clouds has to be considered.

_-_

.31:

;{: !

!!

b.:!:_

i'ii:)} "
°

/o.-

REFERENCES

• • ° .

.

• o .

.. ° •

\
! *

\

_'. T4

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i_"

_"

iki: o'

:!C'!

i[?i ••

_r
J
3 1176 00162 6507

I

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