JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. D14, PAGES 16,861-16,870,JULY 27, 1997
Sensitivityof multiangleremote sensingobservations to aerosol sphericity RalphKahn,RobertWest,DuncanMcDonald,andBrianRheingans Jet Propulsion Laboratory, CaliforniaInstituteof Technology, Pasadena Michael
I. Mishchenko
NASA GoddardInstitutefor SpaceStudies,New York
Abstract. Multiangle,multispectral remotesensing observations, suchasthose anticipated fromthe EarthObserving System(EOS) multiangle imaging
spectroradiometer (MISR),candistinguish spherical fromnonspherical particles overcalm oceanfor mineral-dust-like particles with the rangeof sizesandcolumnamounts expected undernaturalconditions. The abilityto makesuchdistinctions is criticalif remotesensing of atmospheric aerosolproperties is to providesignificant newcontributions to our understanding of the global-scale, clear-sky solarradiationbalance.According to theoreticalsimulationsthe measurements can retrievecolumnopticaldepth for
nonspherical particles to an accuracy of at least0.05or 10%,whichever is larger.In addition,threeto four distinctsizegroupsbetween0.1 and 2.0 micronseffectiveradius can be identified at most latitudes.
mentswith multiangleandmultispectral capabilitiesare being built.We presentin thispapera theoretical studyof the ability In a recentpaper,Mishchenko et al. [1995]studiedthe im- of multiangleand multispectral remotesensingtechniques to plications of assuming spherical particlesin the retrievalof distinguish betweensphericalandnonspherical particles.This aerosolproperties fromremotesensing data,whennonspheri- studyispartof ourprogramto characterize theperformance of calparticlesarepresentin the atmosphere. Theydemonstrate themultiangleimagingspectroradiometer (MISR) instrument, 1.
Introduction
that for observations of dust-like aerosols over ocean, if a
which is scheduledfor launch into polar orbit on the EOS-
retrievalof total columnopticaldepthis performedbasedon an assumption of spherical particles whenin factthe particles are nonspherical, the resultscanbe seriously in error.For the casesstudied,the systematicerror in total columnoptical depthisverysensitive to the geometryof the observation and canbe arbitrarilylargewhensimulatedmonospectral satellite measurements at a singleemissionangleare usedin the retrieval, even assumingnoiselessdata. The systematic errorsdemonstrated by Mishchenko et al.
AM1 platformin June1998[Dineret al., 1991]. The MISR instrumentwill measurethe upwellingvisible radiancefrom Earth in four spectralbandscenteredat 443,
[1995]areunacceptably largefor climatechangestudies. The magnitudeof directradiativeeffectsfrom atmospheric aerosolsis asyetuncertain,but it maybe comparable to the sizeof the anticipated incremental greenhouse warmingdueto a doublingof atmospheric CO2 [Andreae, 1995;Penneret al., 1994; Kiehl and Briegleb,1993;Chadsonet al., 1992;Hansenand Lacis,1990].Dust-likeparticles,whichare likely to be nonspherical, makeimportantcontributions to the opticaldepth overlargeregionsof the planet[TegenandFung,1994].
vidinga widerangeof scattering anglecoverage for eachsur-
555, 670, and 865 nm, at each of nine emissionanglesspread out in the forward and aft directionsalong the flight path at _+70.5 ø, _+60.0 ø, _+45.6 ø, _+26.1 ø, and nadir. The spatial sam-
plingrateis 275m the cross-track directionat all angles.Over a periodof 7 mina 360-km-wide swathof Earthcomesintothe view of the camerasat each of the nine emissionangles,proface location. The data will be used to characterize aerosol
opticaldepth,aerosoltype,surfacealbedoandbidirectional reflectance, and cloudproperties.Globalcoveragewill be acquiredaboutoncein 9 daysat the equator;the nominalmission lifetime is 6 years.
2.
Modeling the Observations
For thisstudy,we usesingle-scattering phasefunctionsand Currently,satellite-based remote sensinginstrumentsproalbedos for spherical and nonspherical particlessimilar to vide our besthopeof obtainingthe spatialand temporalcovthose generated by Mishchenko et al. [1995, 1996].The noneragerequiredfor globalmonitoring of atmospheric aerosols. spherical particles are modeled as a mixture of polydisperse Althoughthe onlyglobal-scale satellite-based retrievalof total with a uniformdistributionof columnaerosolopticaldepthnowin routineoperationrelies prolateand oblatespheroids on a singlechannelof AVHRR data [Raoet al., 1989;R. B. aspectratiosrangingbetween1.4 and 2.2. (To accurately Husaret al., Satellitesensing of tropospheric aerosolsoverthe modelthe opticalpropertiesof naturallyoccurringnonspherioceanswith NOAA/AVHRR, submittedto Journal of Geo- cal particles,the criticalconditionis to have a spectrumof et al., 1996;Westet physicalResearch, 1996],new satelliteremotesensinginstru- aspectratiosasbroadasthis[Mishchenko al., thisissue].)Both sphericalandnonspherical particlesizes Copyright1997by the AmericanGeophysical Union. aregivenbypowerlawdistributions, withn(r) = C for r -< r•, Papernumber96JD01934. 0148-0227/97/96JD-01934509.00
n(r) = C(r•/r) 3 forr• -- r2.Here r is the particleradiusfor spherical particlesandthe radiusof 16,861
16,862
KAHN ET AL.: MULTIANGLE
SENSITIVITY
TO AEROSOL SPHERICITY
i
1000.00
Symbol Effective radius .........
100.00 -
spherical
0.05
I
i
0.747
non-spherical
0.7,.30
0.10
spherical
0.930
0.10
non-spherical
0.926
0.50
spherical
0.956
0.s0
non-spherical
0.941
_
i
Single scatteFing albedo
Shape
0.05
i
_
-
•'...•,,
•x,.
10.00
x,x 1.00 _
_
_
_
_
0.10
I
0.01
30
,
i
60
I
I
I
90
I
I
I
I
,
i
150
120
180
ScatteringAngle(degrees) 1000.00
I
Symbol Effective radius
.........
100.00
._•
a_
i
i
i
i
[
i
i
Single scattering albedo
Shape
0.876
1.00
spherical
1.00
non-spherical
0.883
2.00
spherical
0.794
2.00
non-spherical
0.796
10.00
1.00 --
0.10 _
_
_
_
_
_
0.01 0
30
60
90
120
150
180
ScatteringAngie(degrees)
Figure 1. Single-scattering phasefunctionsfor severalpairsof sphericaland nonsphericalparticleswith the samevaluesof reff.For all cases,ueff= 0.2, andX is 670nm. (a) For r•ff = 0.05p.m(notethat the nonspherical caseis hiddenby the sphericalcasefor thissizeparticle);r•ff = 0.1 p.m,andr•ff = 0.5 p.m;(b) r•ff - 1.0 p.m, and reff = 2.0 p.m.
a spherewith equal surfacearea for nonsphericalparticles.C is a normalizationconstantfor the distribution.The parameters r• and r 2 are selected so that the cross-sectionmeanweightedradius of the distributionas a whole is r•ff and the variance of the distribution is u•ff [Mishchenkoand Travis, 1994].For all cases,u•ffis 0.2, and the particleindexof refraction is 1.53 - 0.008i, independentof wavelength.The wavelength dependenceof single-scattering propertiesscalesasx, where x = 2 •r r/X, and X is the wavelength[Hansenand Travis, 1974]. Unless specifiedotherwise,optical properties
presentedin thispaper are for MISR band3 (670 nm); in the underlyingcalculations,opticalpropertiesare properlyscaled to accountfor wavelengthdependencein each of the MISR bands used.
Figure 1 comparesthe single-scattering phasefunctionsfor distributionsof sphericaland nonsphericalparticlesof several effective sizes.Only particleslarger than the smallestones shownin Figure 1 (r•ff = 0.05 p.m) are thoughtto contribute significantlyto the mineral dust optical depth of the atmosphere [e.g., Tegenand Fung, 1994]. The single-scattering
KAHN ET AL.: MULTIANGLE
SENSITIVITY TO AEROSOL SPHERICITY
-
41
16,863
!
-41
-82 -60
Df
Cf
Bf
Af
An
Ao
Bo
Co
Do
Comero
N
W•"E S
• 0.00
22.50
45.00
67.50
90.00
112.50
135.00
157.50
180.00
Figure 2. Range of scatteringanglesto be sampledby the nine multiangleimagingspectroradiometer (MISR) cameras,as functionsof latitude and locationin the instrumentscanline, for March 21 and the nominalEOS-AM1 platformorbit. Each scanis 360 km wide. Samplingextendsto 82ø latitude and in some seasonsfolds over toward60ø in the opposinghemisphere.The pattern remainsnearly the samebut shifts poleward,as the solsticeseasonsapproach.
phasefunctionsfor sphericaland nonsphericalparticlesat the smallestsizesare indistinguishable. Distributionswith effective radii in the 0.5-to-10tamrangeare typicalof suspendedatmospheric mineral dust aerosols[Tegenand Fung, 1994]. For theselarger aerosolsthe nonsphericalparticlesput a smaller fractionof the total scatteringinto the backscattering direction at scatteringanglesgreater than about 150ø and a larger fraction into the scatteringanglesbetween about 100ø and 150ø, comparedto sphericalparticleswith equivalentsurfacearea. The characteristics shownin Figure 1 have been reproduced for other typesof randomlyorientedaggregatesof nonspherical particles[e.g., Takanoand Liou, 1989]. The optical propertiesgiven by Mishchenkoet al. [1996] allowus to treat particleswith sizesup to about2 tam,whichis adequateto coverthe transitionin single-scattering characteristicsbetweenparticleswith x valuesin the small (Rayleigh) and large (geometricoptics)regimes.Qualitatively,the results for the largestparticleswe cantreat alsoapplyto particleswith effectiveradii between2 and 10 tam.Quantitativetreatment of the sensitivity of multiangleremotesensing to the largerparticles requiresadditionalcalculationsthat are currentlyunderway. The scatteringanglecoveragefor each of the 9 MISR cam-
oceansurface,in a cloud-free,Rayleigh-scattering atmosphere with a surfacepressureof 1.013bar and a standardmidlatitude temperatureprofile.A layercontainingeither nonspherical or sphericalparticlesis placedbetweenthe gascomponentand the surface.(Sensitivitystudiesshow that for the range of aerosoloptical depth treated here, the resultswould be unaffectedif the aerosolswere modeledas mixedwith the gasin the lowestpart of the atmosphere.)The goal is to determine the degreeto whichwe candistinguish betweenthe nonspherical and sphericalparticle casesfrom the measurements. As a measureof the sensitivityof the observationsto aerosol
properties, weusea normalized X2parameter thatweights the contributionsfrom eachobservedreflectanceaccordingto the slantpath of the observationthroughthe atmosphere.(In this paper, reflectanceis definedas the radiancemultipliedby •r and dividedby the exoatmospheric solarirradianceat normal incidence.)The slantpath weightingwaschosenbecausemeasurementstaken at steeperemissionangleshave greater sensitivityto the atmospherein proportionto this factor. We use
a X2 statisticthat includes the spectraldependence of the
measurementsbut emphasizesthe camera-to-camerageometric differences.We anticipatethat such a parameter might eras, as a function of latitude and location in the scan line, is providegoodsensitivity to particlesizeaswell asopticaldepth, shownin Figure 2 for March 21, for the nominal EOS-AM1 giventhe MISR measurements. The simplestwayto definethis platform orbit. In midlatitudes, scattering angles between statisticis to divide each spectralmeasurementby the correabout 60ø and 160ø are coveredby the nine cameras,whereas spondingspectralmeasurementin the nadir camera: at highlatitudesthe rangeis approximately40ø-150øand at low 2 __ latitudes,100ø to 160ø. With changingseasonsthe pattern of Xgeom -coverageremains nearly the samebut shifts toward the summer pole. The MISR Team has developeda radiative transfer code, 4 9 mk Lmeas(l, nadir)- Lcomp(/, nadir) based on the adding-doublingmethod [Hansenand Travis, 2 (1) k=l O'geom(/, k) 1974],to simulatetop-of-atmosphere reflectancesaswould be /--1 kCnadir observedby the MISR instrumentfor arbitrarychoiceof aerosol type and amountand variablesurfacereflectanceproper- whereL .... isthesimulated "measured" reflectance, L ½omp is ties [Diner et al., 1994]. For the presentstudywe have simu- the simulated reflectance for the "assumed" comparison lated MISR measurementsover a Fresnel-reflectingcalm model,l andk are the indicesfor wavelengthbandandcamera,
Lmeas(/, k) mcomp(/, k)]
16,864
KAHN ET AL.: MULTIANGLE
SENSITIVITY
N is the number of measurements included in the calculation,
rn•, are weights,chosento be the inverseof the cosineof the emissionangle appropriateto each camerak, (rn•,) is the averageof weightsfor all the measurements includedin the
TO AEROSOL SPHERICITY
two spectralbandsat whichthe oceansurfaceis darkest(670 and865 nm). (In somecircumstances, sunglintwill affectone or two of the MISR
cameras.
In the standard
MISR
aerosol
retrievals,signalsfrom thesecameraswill be excluded.For the calculation, andtrgco m(a dimensionless quantity) istheuncer- purposeof thissimulationstudy,we are interestedin the greattainty in the measuredchannel-to-channel reflectanceratio, est sensitivitythe instrumentcan provide, so all camerasare givenby included.)Simulations wereperformedfor an atmosphere containingnonsphericalparticleswith ratm valuesof 0.1, 0.5, 1.0,
O'r2el(/, k)
Lmeas(l k) 2 , k)o'r2el(l,
O'g2eom(/, k) = Lmeas(l, 2 4 nadir) nadir) + Lmeas(l,
(2)
and2.0/am,and'ra,at mvaluesat 670nm of 0.05,0.2, and0.8.
Appropriatescalingwasusedto simulatethe data at 865 nm, assumingthe particle index of refraction is independentof where O'r½ 1hasunits of reflectanceand is the relativecalibrawavelength. tion uncertaintyin the reflectancefor band l and camerak.
(Equation (2) is theexpansion of errors:tr2[f(x, y)] = (df/
dx)2trx 2 + (df/dy)2%2[e.g.,Bevington, 1969]. In thiscase, x isLmeas(/,k) andy isLmeas(/,nadir).) For the MISR instrument the value of trr•• is specifiedto fall between0.01 for a target with reflectanceof 100% and 0.02 for a reflectanceof 5%, in all channels[Dineret al., 1994].For thesesimulations we model trr•• as varyinglinearlywith reflectance.Note that trr•• includesthe effectsof systematiccalibrationerrors for
The•om wasthencalculated forcomparison models that
assumedistributionsof sphericalparticleswith columnoptical
depth•a,oomp ranging from0.05to 1.0in increments of 0.05, andeffective radiircomp ranging from0.1to 2.0 tam,in incre-
ments of0.1.According toPlatela, the•om criterion isable to distinguishsphericalfrom nonsphericalparticlesfor all caseschosen,exceptwhen the atmosphericparticlesare very
smalland 'ra,at m is low.We expectno discrimination for very
small particles,since the correspondingsphericaland nonsphericalsingle-scattering phasefunctionsare indistinguishinstrument noise is negligible,based on the high signal-toable(Figure1). Note that evenfor theverysmallparticlecase, noise ratio demonstratedduring MISR cameratesting. ratios of reflectance between channels. Random
error due to
forwhichthereisanacceptable match Sincethe X2 parameteris normalized to the numberof theonlyvalueof rcomp
is the corresponding equivalent-sphere radiusfor ratm,and the channelsused,a valuelessthan or aboutunityimpliesthat the acceptable •a,oomp values are within 0.05 of thecorresponding comparisonmodel is indistinguishablefrom the measurevalue of Ta,at mments.Values larger than about5 imply that the comparison Plate lb teststhe conversesituation:nonsphericalparticles model is not consistentwith the observations.In more detail, are assumedfor the comparisonmodelswhen the atmosphere X2 < 1 meansthat the averagedifference betweenthe meaactuallycontainssphericalparticles.Here againthe only case sured and comparisonquantitiesis less than the associated wherethe differencein particleshapewouldnot be detectedis measurementerror. The upper bound of 5 correspondsforparticlesareverysmalland'ra,at mislOW. mallyto an averageconfidenceof better than 95% that we are whentheatmospheric In addition,for very low atmosphericopticaldepth, some not rejectinga comparisonmodel when in fact it shouldbe cases produce twolocalminima in •com(though notlow accepted. enoughto qualifyas acceptablematches).For the ratm -' 0.5 To illustratethis in subsequent figures,we havedevelopeda isbetween 0.4and1.0tam. colorbar with three segments: a logarithmicsegmentfor values case,theminimaoccurwhenrcomp These minima arise becausethe single-scattering albedo for between10-5 and1 depicted in shades of blue,a logarithmic the comparison (spherical)particlesis slightlysmallerthanthe segment for valuesbetween 5 and104 depicted in shades of corresponding value for nonsphericalparticles.As the comred, and a linear segmentshownin light green,yellow, and parison model optical depth is increased,the comparison orangeshadesfor the intermediatevalues.Thus red shadesin model reflectanceat the scatteringanglesmeasuredby the the figuresindicatesituationswhere the model is clearlydisinstrument(60ø-160 ø) alsoincreases. For someintermediate tinguishablefrom the measurement,whereasblue shadesinvalue the differencein reflectancebetweenthe sphericaland dicate that the model is indistinguishable from the measurenonsphericalcasesreachesa local minimum. The absolute ment. Black is reservedfor exact agreementbetween model minimumand thereforethe best fit opticaldepth still falls at and measurement,which can occur in this studybecausewe the correct value. As comparisonmodel optical depth inare workingwith simulatedobservations. Note that the color creasesfurther, the distinguishability becomesgreater. table hasbeen designedso that if the colorplatesare photoSimilarresultsare obtainedat polewardgeometries.At low copied in black and white, first-orderinformation about the latitudes the range of scatteringangle coveredby MISR is ability to distinguishamongmodelsis preserved. diminished. Within about 20 ø of the subsolar latitude the scat-
teringanglecoverageonly extendsfrom 100ø to 160ø (Figure 2), limitingthe sensitivityof the retrieval.This is particularly 3. Sensitivity of Multiangle, Multispectral apparentfor both the low opticaldepthand the smallparticle Radiances to Particle Sphericity sizecases,where the reflectancedifferencesbetweenspherical In Plate la we addressthe question:If the atmosphere and nonsphericalparticlesare small to begin with. For the contains nonsphericalparticles with aerosol optical depth smallestparticlesizestestedthe retrievalis insensitiveto parTa,at m and distributionof particleswith effectiveradiusratm, ticle shapeat low latitudes.For low opticaldepththe retrieval coulda retrievalwith MISR-like multispectral,multiangledata is insensitiveto particle sizeand shapeat theselatitudes,but mistakenlyinterpretthe measuredreflectances asbeingdue to the retrievedoptical depth is still within 0.05 of the correct
spherical particles witheffective radiusrcomp andaerosol opticaldepth'ra,½omp? For aerosolretrievalsover ocean,the standardMISR algorithm usesdata from all nine emissionangles,but only in the
value.
In Plate 2a we examinethe ability of MISR-like measurementsto correctlyretrievethe propertiesof nonsphericalparticles. For this plate, both the atmosphereand comparison
Non-SphericalAtmosphere,SphericalComparison(FresnelSurface) = 0.60
A½, = 26.0
2.0
1.5
.... 104
.5
.1
2.0
.5 5.0 .1 2.0 1.0 1.5
.5
.1
2.0
1.5
1.0
10_ 5
.5
ß25
,50
,75
1.0
,25
.50
.75
1.0
,25
.50
.75
TO.comp
To.comp
To.comp
7'0,otrn=0,05
7'0,otrn=0.20
7'0,otrn=0,80
1.0
Plate la. Testsof the abilityto distinguish sphericalfromnonspherical aerosols. For eachpanel,simulatedMISR reflectances
wereproduced for anatmosphere containing nonspherical particles withthespecified ratmand•, atto'The %attoincreases to the
rightfrompaneltopanel, whereas ratmincreases frompaneltopaneltoward thetopoftheplate.'The •eom'•;asthencalculated
using thetwolongest wavelength MISRchannels inall9cameras, forcomparison models thatassume •['istributions ofspherical particles witheffective radiircomp andcolumn aerosol opticaldepth•,comp' All simulations presented arefor midlatitude geometryovera Fresnel-reflecting, calmoceansurface,and includea standardRayleighscattering contribution.(In the plate, Ix0and A•adi r are the cosineof the solarincidenceangleand the differencein azimuthbetweenthe Sun and nadir camera
directions forthecases shown.) Colors indicating thevalue of•eomareplotted ineach panel, withrcomp increasing toward the topof eachplotand•a,•omp increasing to theright.
KAHN ET AL.: MULTIANGLESENSITIVITYTO AEROSOLSPHERICITY
16,867
Non-Spherical Atmosphere, Non-Spherical Comparison (FresnelSurface) P'o= 0.60
A• = 26.0
1.5
...... 104
.5
.1
2.0
1.5
I
.5
5.0 .1
2.0
1.0
1.5
.5
.1
"
1.5
10 -s .5
.
..:
.25
ß50
.75
'7'0, comp
otm--'0.05
1.0
.25
.50
.75
1.0
.25
.50
.75
'7'a, cornp
'To,comp
'7'0, arm=0.20
'To, otm=0.80
1.0
Plate2a. Tests oftheability toconstrain nonspherical aerosols. TheX•g½orn forthesame parameter space as in Plate1, except thatthemeasured andcomparison models bothassume nonspherical particles.
KAHN ET AL.: MULTIANGLE SENSITIVITY TO AEROSOL SPHERICITY
16,867
Non-Spherical Atmosphere, Non-Spherical Comparison (FresnelSurface) ,u, ø = 0.60 2.0
A• = 26.0 -,
'
1.5
,
,10 4
'.5
.1
2.0
1.5
.5
5.0 .1
2.0
1.o
1.5
.5
.1
2.0
1.5
.5
.1
ß25
.50
.75
1"o, comp
1'o,otrn '-0'05
1.0
.25
.50
.75
1"o, comp
'/'o,otm --0'20
1.0
.25
.50
.75
1.0
?'o,comp
'r'o, otrn '-0.80
Plate2a. Tests oftheability toconstrain nonspherical aerosols. The•geom forthesame parameter space as in Plate1, exceptthatthemeasured andcomparison modelsbothassume nonspherical particles.
16,868
KAHN ET AL.: MULTIANGLE
SENSITIVITY
TO AEROSOL SPHERICITY
Non-SphericalAtmosphere,Non-SphericalComparison(FresnelSurface) P'o= 0.60 A• = 26.0 2.0
1.5 o
..... 104
• 1.0 .5
.1
I
1.5
1.0
I
.5
5.0 .1
2.0 1.0
1.5
1.o[ 5
.1 2.0
1.5
10-5 .5
.1
ß25
.50
.75
']"o,comp
•'o,ot,•=0'05
1.0
.25
.50
.75
'•'o,comp
•'o,otr=0'20
1 o0
.25
.50
.75
1.0
'•'o,comp
•'o,otr=0'80
Plate2b. Testsof theabilityto constrain nonspherical aerosols. The•bs for thesameparameter spaceas in Plate 2a.
KAHN ET AL.: MULTiANGLE
SENbittVtt
¾ t'o AEROSOL SPHERICITY
,,,,,•,,•, acceptablematchesfor all cases,with exact agreementwhen the comparisonmodel parametersequal those of the atmosphere.For low atmosphericoptical depth and midsizedto large sizedatmosphericparticles,a range of sizessatisfiesthe test. The size discriminationimproveswith increasingatmosphericoptical depth,particularlyfor midsizedparticlesß The optical depth uncertaintyis within 0.05 for small and 10% for largerparticlesizesbut is closeto 50% for the worst
16,869
,• la, gc,ß This 1•'- true ewu for caseswhere particle
shapeor sizeis not well-constrained by the retrieval.Two X2 tests,one which emphasizesthe geometricinformationin the measurementset, and one which emphasizesthe absolutereflectances,are needed to produce these constraints.Constraintson effectiveradiusvarywith columnopticaldepthand with the nature of the tests used for the retrieval.
With the two
X2testsadopted forthisstudy, threetofourdistinct sizegroups
between0.1 and 2.0 micronseffectiveradius are distinguishable over the assumedrangeof columnopticaldepths. Characterizationof the sensitivityof MISR aerosolretrievgeometricpropertiesof the scattering,which dependheavily als for a range of particle compositionsand environmental on particlesizeand shape.However,there is more information conditions,and refinement of the criteria used for choosing in the measurements that maybe usedto improvethe retrieval "best fit" models, are part of continuingwork. The MISR discriminationability. For example,we define a statisticthat Team is currently performing sensitivitystudiesfor aerosol weightsthe contributionsfrom each observedabsolutereflec- columnopticaldepth,aerosolsizedistribution,aerosolindices tance accordingto the slantpath throughthe atmosphereof of refraction,aerosolhydrationstate,mixingof particletypes, the observation: effectsof thin cirrus,fogs,stratosphericaerosols,and underlying surfacetype.
casein Plate2a.Byusing X•eom alone, wehavereduced 18 measurements to a single statistic. TheX•eom emphasizes the
2= l • : mk[Lmeas(l, k)- k) Lcømp (l,k)]2 0'2abs(/,
XabsN(m•,)
/=1
(3)
k=l
where O'abs is the absolutemeasurementerror in the reflectance;trab sis nominally3 timesthe corresponding valueof trr•l for the MISR instrument[Diner et al., 1994]. This statistic emphasizes the absolutereflectance,whichdependsheavilyon
opticaldepth.Plate2b shows•bs for the sameparameter
Acknowledgments.We thank our colleaguesD. Diner and J. Martonchik for many discussions of these topics.This researchis performedat the Jet PropulsionLaboratory,CaliforniaInstituteof Technology, under contract with the National Aeronauticsand Space Administration,and by the NASA GoddardInstitutefor SpaceStudies.
References
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4.
Conclusions
Diner, D. J., C. J. Bruegge,J. V. Martonchik,G. W. Bothwell,E. D. Danielson,E. L. Floyd, V. G. Ford, L. E. Hovland,K. L. Jones,and M. L. White, A Multi-angleImagingSpectroradiometer for terrestrial remotesensingfrom the Earth ObservingSystem,Int. J. Imaging Syst.Technol.,3, 92-107, 1991.
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A simpleX2 testis adequate to distinguish spherical from
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nonsphericalparticlesfor indicesof refractiontypicalof nat1993. ural mineral dust, and for single-scattering phase functions Mishchenko,M. I., and L. D. Travis,Lightscatteringby polydisperse, characteristic of randomlyorientedparticleswith a broadspecrotationallysymmetricnonspherical particles:Linear polarization,J. trum of sizesand shapes.The spherical-nonspherical distincQuant.Spectrosc. Radiat. Transfer,51, 759-778, 1994. tion couldnot be madefor the smallestparticlestested,which Mishchenko, M. I., A. A. Lacis, B. E. Carlson, and L. D. Travis, have effective radii of 0.1 microns or less, and for low aerosol
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