Polarized observations for advanced atmosphere-ocean algorithms using airborne multi-spectral hyper-angular polarimetric imager

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Polarized observations for advanced atmosphere-ocean

algorithms using airborne multi-spectral hyper-angular

polarimetric imager

Ahmed El-Habashi, Jeffrey Bowles, Robert Foster, Deric Gray, Malik Chami

To cite this version:

Ahmed El-Habashi, Jeffrey Bowles, Robert Foster, Deric Gray, Malik Chami. Polarized observations

for advanced atmosphere-ocean algorithms using airborne multi-spectral hyper-angular polarimetric

imager. Journal of Quantitative Spectroscopy and Radiative Transfer, Elsevier, 2021, 262 (March),

pp.107515. �10.1016/j.jqsrt.2021.107515�. �insu-03106714v2�

ContentslistsavailableatScienceDirect

Journal

of

Quantitative

Spectroscopy

&

Radiative

Transfer

journalhomepage:www.elsevier.com/locate/jqsrt

Polarized

observations

for

advanced

atmosphere-ocean

algorithms

using

airborne

multi-spectral

hyper-angular

polarimetric

imager

Ahmed

El-Habashi

a,b,∗

_,

_Jeffrey

_Bowles

a

_,

_Robert

_Foster

a,b

_,

_Deric

_Gray

a

_,

_Malik

_Chami

c

a Remote Sensing Division,Naval Research Laboratory, Washington, DC20375, United States b National Research Council, Washington, DC, United States

c Sorbonne Université, CNRS-INSU, LaboratoireAtmosphèresMilieux Observations Spatiales (LATMOS), Boulevard de l’Observatoire, CS 34229, 06304Nice

Cedex, France

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 12 June 2020 Revised 28 December 2020 Accepted 6 January 2021 Available online 10 January 2021 Keywords:

Vector radiative transfer Remote sensing Polarimetry VICO PACE Ocean Color Retrieval algorithms Open ocean Coastal waters Scattering Bio-optics Plankton Chlorophyll-a Minerals CDOM

a

b

s

t

r

a

c

t

Airbornemeasurementsofthelinearpolarizationstateoflightwerecarriedoutovercoastaland open oceanconditionstostudyaerosolandwatercolumn propertiesandinvestigatethepossibilityofusing amulti-spectral,hyper-angularimagingpolarimeter forretrieving aerosolandhydrosoloptical proper-ties.Theinstrument,theVersatileImagerfortheCoastalOcean(VICO),isusedtosupporttheanalysis ofoceancolorpolarizedobservationsandtheirimplicationforfuturespace-bornepolarimetrysuchas thepolarimetersplannedtobedeployedwiththeNASAPlankton,Aerosol,Cloud,andoceanEcosystem (PACE)mission.Severalsetsofimagesatdifferentviewinganglesfromthevisibletothenear-infrared spectrumwerecollectedand comparedwith simulationsusingavectorradiative transfer(VRT)code. Thesimulationswereobtainedbasedonmeasuredseawaterinherentopticalpropertiesfromshipborne instrumentsandmeasuredatmosphericparametersfromtheAerosolRoboticNetwork(AERONET)anda shipbornesunphotometeratdifferentlocations. Anuncertainty methodhasbeenderived by propagat-inguncertaintiesfromthe measuredpolarizedradiances.The methoddemonstratespracticable uncer-taintyformulationsthatcanbeused toconstructameasurementuncertaintybudget forthepolarized dataproducts.ResultsfromVICOandtheVRTsimulationareconsistentforbothradianceand polariza-tionspectrumatallthemeasuredviewingangles.Thetotalandpolarizedwater-leavingreflectancesare retrievedatfourbandsand variedgeometries.Itis alsoshownthatthe polarizedremotesensing re-flectancemeasuredatvariousanglescouldbeusedtodistinguishbetweentheaerosols’andhydrosols’ opticalsignaturesbyexploitingthefactthatthepolarizedreflectanceisfairlyinsensitivetohydrosolsfor givenacquisitiongeometries.Thisstudythusprovidesanopportunitytoinvestigatevariousrelationships betweenthemicrophysicalpropertiesoftheoceanicandatmosphericparticulatessuchasrefractiveindex andparticlesizeproperties.Italsocontributestothedevelopmentofpolarization-basedinverseocean coloralgorithms.Finally,theprovidedanalysisgivesinsightsforthevalidationoftheoceancolor param-etersthatwillberetrievedfromtheforthcomingpolarimetricsatellitemissions.

© 2021 The Authors. Published by Elsevier Ltd. ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

Total and polarized light emerging from the atmosphere and oceansplaysasignificantrole intheEarth’sradiationbudget.The objective of the field of ocean color (OC) is to provide accurate monitoringofoceanicopticalpropertiesand,usingremotesensing instrumentation,understandwhatphysicaloceanconstituents pro-videthatsignature.ConventionalOCsensorsaredesignedto

mea-∗_{Corresponding author.}

E-mail address: ahmed.el-habashi.ctr@nrl.navy.mil (M. Chami).

sure the total radiances frombelow or above water, using ship-borne,airborne,orspace-borneplatforms.Thefundamental quan-tityderivedfromOCsensorsisthespectralwater-leavingradiance upwellingfrombelowthe oceansurfaceandpassingthrough the ocean-air interface. The water-leaving radiance is determined by propertiesoftheincident light andthescatteringandabsorption characteristicsoftheoceanwateranditsconstituents.These scat-tering andabsorption processes are best describedby the inher-ent optical properties (IOPs) of the seawater. Overall, it is these IOPs that determine oceanic watercolor. The total radiance mea-suredby a satellite sensoris principallycontrolled by the down-welling irradiance, the interactions of that light with the

atmo-https://doi.org/10.1016/j.jqsrt.2021.107515

sphere,theair-oceanboundary,andthewaterconstituents.To ac-curately determinewaterIOPs,andfromthemwaterconstituents, it is first necessary to compute water-leaving radiance correctly. Todosofromsatellite observations,identifyingandremovingthe non-water leaving contributions to theTop of Atmosphere (TOA) radiance is essential. This is the goal of atmospheric correction (AC) techniques. Various AC methods [1,2], along withempirical andsemi-analyticalIOPretrievalalgorithms[3-11]weredeveloped, to obtain the water optical properties and to retrieve the IOPs of thewaterconstituentsfromTOAtotal radiancemeasurements. However, thisprocess is still challengingincoastal waters where theaerosolscanbestronglyabsorbingdueto,blackcarbon,brown carbon, and/or mineral dust from the nearby cities. This condi-tionisparticularlytruewhereatmosphericcorrectionmethodsdo notworkwellforthe400-470wavelengths,whicharestrongly af-fectedbytheblueskybackgroundsignal[12,13].Consequently, al-gorithmsthatrelyonsatellitemeasurementsatthesewavelengths toretrieveIOPsarevulnerabletoretrievalinaccuracies[12]. Addi-tionally, coastalwatersexhibit overlappingabsorption spectra be-tween water constituents, as well as non-covarying components andoverlapping scatteringspectra, makingit difficultto separate individualcomponents.Thedevelopmentofinverseoceancolor al-gorithms requires an accurate retrieval of the water-leaving sig-nal andthe capabilityto determinethe fullcharacteristics ofthe aerosol and hydrosol particles. Advances in polarimetric remote sensing (PRS) provide both higher retrieval accuracy [14-16] and additional information on the determination of the optical and micro-physical properties of suspended particulates [17-19]. The use ofPRS has beenwidely recognized as a criticaltool for reli-able characterization ofaerosol andhydrosolparameters [20-22]. Several spaceborneand airbornesensors [23-26] were developed to measure the polarization state in addition to the scalar radi-ance measurements. PRSis expectedtoyieldsignificant advances inoceancolor.

The main objective of this work is to demonstrate the ca-pabilities of an operational airborne multi-spectral hyper angu-lar polarimetric imager, called Versatile Imager for the Coastal Ocean VICO [25], over open ocean and coastal water conditions. Optical closure between VICO and the vector radiative trans-fer (VRT) forward modeling wasachieved based on actual mea-surements of aerosol and seawater optical properties obtained at two different locations. Results are informative, in compari-son with the traditional total radiance imaging, suggesting fur-ther advancement ofpolarimetric retrieval over both open ocean and coastal waters should be a goal of the ocean color commu-nity. The organization ofthis paperis as follows: Section 2 pro-vides a brief review of the advancement of aerosol and hy-drosol polarimetry. Section 3 describes how the field measure-ments areanalyzed, andthe uncertainty methodology appliedin this work.Section 4 describesthe VRTmodeling approaches. Re-sults and discussions on VICO and the TOA observations with the VRT simulations at the different conditions are shown in

Section 5. Finally, a summary of the results is presented in Section6.

2. Polarimetricremotesensing

Over thelast severaldecades,the developmentofocean color instruments has been based on measurements of a single-view multi-spectralradianceofthevisiblelight.TheCoastalZoneColor ScannerExperiment(CZCS)wasthefirstsingle-viewedoceancolor instrument launched into space in 1978. Following the CZCS, a fleet ofsingle-view satellite sensorssuch asSeaWiFS,MODIS, VI-IRS, MERIS, OLCI, and GOCI was launched, providing a continu-ous data record of the global ocean over the past two decades. Thesesingle-viewinstrumentwereusedtodriveseveralstandard

oceancolorproductssuchassurfaceconcentrationsandthe inher-entopticalpropertiesofthedifferentwaterconstituents.In1999, the Multi-angleImaging SpectroRadiometer (MISR) waslaunched toobserveEarth’s climatewithcameraspointedatnine different angles. MISR wasdesigned to improve our understanding of the amountofsunlightscatteredindifferentdirectionsbytheEarth’s atmosphere,ocean,land,snow,andice.Thedevelopedsingle-view andmulti-view instrumentsutilizespectral radiance observations todriveseveralatmosphere-oceanproducts.

Whilethese instrumentsprovided awealth ofocean color in-formation, higherretrievals accuracy andadditional products are neededforbettercharacterizationoftheaerosolandhydrosol con-stituents. Polarimetry is well-suited to address these needs. Cur-rent and future planned remote sensing polarimeters can mea-sure the degree of linear polarization to an absoluteaccuracy < 0.2%.Theradiativetransfercodesusedtoanalyzethese polarimet-ric measurements can provide an accuracy that exceeds state-of-the-artpolarimeters <0.2%.Chowdharyetal.[27]provided tabu-latednumericalreflectance valuesof thetotal andlinearly polar-izedupwelling radiance justabovea rough oceansurface, andat the top ofthe atmosphere(TOA) withhighaccuracy using three independent deterministic solutions of theradiative transfer. The tabulatedreflectancevalueswerewithin10–5_-10–6_ofeachother,

for different viewing geometries, wavelengths, and atmosphere-ocean systems. The accuracy in the degree of linearpolarization waslessthan 0.1%formostsimulatedcasesandbetter than0.2% overall.Theagreementswerevalidatedthroughtheuseof stochas-tic(MonteCarlo)radiative transfercode.Similaragreementswere achievedbetweenthestochastic andprobabilistic solutionsofthe vectorradiative transfer.Regardlessofthehighaccuracyachieved betweenthe different VRT methods, it is important to note that theagreementhereisa measureofhow themodelrepresentthe physics of the different complex atmosphere-ocean systems, and doesnotnecessarilymeanthatmeasurementsofrealityshouldbe atthesamelevelofaccuracy.

Additionally,thepolarized light field showedthe capabilityof providingadditionalinformationonthemicro-physicaland macro-physicalpropertiesofaerosolandhydrosolparticles,whichare dif-ficult toinferfromthe scalarscatteredradiationobservedby the currentoceancolorinstruments[18,28,29].Polarizationissensitive totheaerosolandhydrosolparticlescomposition(complex refrac-tiveindex),size,andshape.Thepolarizedlightreflectedfromthe seasurfacecontainsusefulinformationon thesea state.It is ex-pectedthatthepolarizedremotesensingwillprovideanaccurate atmosphericcorrectionthatcanleadtoimprovedandnewaerosol andhydrosolproducts[30,31].

2.1. Space-borneandairbornepolarimeters

The first space-based polarimetric imagery was provided by the POLarization and Directionality of the Earth’s Reflectance (POLDER)missionslaunchedby theCentreNationald’Etudes Spa-tiales(CNES)to provideaccuratemonitoringofaerosolproperties

[32-35].POLDER-1 and2, onboardthe AdvancedEarthObserving Satellite (ADEOS) 1 and 2,were launched in 1996 and2002, re-spectively.BothPOLDERmissionsendedprematurelywithinnearly a yeardue to hostsatellite communication failure with POLDER-1 and satellite’s solar panel malfunctioned with POLDER-2. The longestrecord ofspace polarimetricobservationwasachievedby POLDER-3onboardthePolarizationandAnisotropyofReflectances for Atmospheric Sciences coupled with Observations from a Li-dar(PARASOL)platformwithalifespanofnineyears(2004-2013). Thepolarimetricdatasetfromtheseinstrumentsprovidedthemost detailedglobalaerosol products,such ascomposition and micro-physics of the different aerosol types.Following POLDER, several space-borneandairbornepolarimeters wereflown byvarious

na-tionalandinternationalspaceagenciesforbettercharacterizations of Earth’s atmosphere, ocean, and land. A brief summary of the current andplanned polarimeters is givenin thefollowing para-graphs.

In 2011, the National Aeronautics and Space Administration (NASA)launchedtheAerosolPolarimetrySensor(APS)ontheGlory mission [36,37]. The APS was designed to observe the out-going top-of-atmosphere (TOA) radiation at nine bands from visible to short wave infrared spectra at a spatial resolution of 5.6 km at nadir, andaswath of5.6kmcross-trackby 2200kmalong-track. The linear polarization measurements were made at all wave-lengthsandfrom250viewinganglesbetween+60° and-80° with respect to nadir. APS was expected to provide the most accu-rate data on the chemical, micro-physical, andoptical properties of aerosols andtheir spatialand temporaldistributions; unfortu-nately, the instrument did not successfully enter orbit due to a launch failure. In 2017, the Japan Aerospace Exploration Agency (JAXA) launched the Second Generation Global Imager(SGLI) on-board the Global Change Observation Mission–Climate (GCOM-C)

[38].The SGLI wasdesignedtoobserve theout-going TOA radia-tion at 19bands fromnear UltraViolet(UV) to thermalinfrared spectra at a spatialresolution of 250 m (1 km for the 763 nm band),andaswathof_±45° (1150km).Thelinearpolarization mea-surements are only available at two wavelengths (673.5 nm and 868.5 nm) at a spatial resolution of 1 km2 _{and from one}

view-ing angle,providing scattering angle directions between60° and 120°.TheChinese Space Agency (CNSA) recentlylaunched several polarimeters: the Multi-Angle Polarization Imager MAI [39] on-board the TianGong-2 (TG-2) spacecraft (2016), the Cloud and Aerosol PolarizationImagerCAPI [40]onboardofthe TanSat mis-sion(2016),andtheDirectionalPolarimetricCameraDPC[41] on-board theGaoFen-5(GF5) spacecraft (2018).The MAIis an Earth observationinstrumentprovidingmulti-channelmulti-angle polar-izationmeasurementsatsixbandsfromvisibletonear-infraredat a spatialresolution of 3 km anda swath width of770 km.The linearpolarizationmeasurementsareonlyavailableatthree wave-lengths, centeredat565,670,and865nm, andfrom12 different viewing directions.TheCAPI isa 5bands imagerfromnearultra violettoshortwaveinfraredspectraataspatialresolutionof1km andaswathof400kmx0.5km.Thelinearpolarization measure-ments are only available at two wavelengths (670 nm and1640 nm)andfromoneviewingangle.TheDPChas8channelsfrom vis-ible tonearinfraredataspatialresolutionof3.3kmandaswath of1850kmx1850km(±50° across/along-track).Thelinear polar-ization measurements areavailable at3 wavelengths,centered at 490,670,and865nm,andfrom9differentviewingdirections.

To an increasing extent,severalfuture missions arescheduled forlaunchallby2023.TheMulti-AngleImagerforAerosols(MAIA)

[42-44] planned to fly onboard of the Orbital Test Bed 2 (OTB-2) spacecraft as a part of the NASA Earth Venture Instrument program. MAIAis a targetedinstrument capable ofusing a step-and-stare or sweep viewing mode over targeted areas. It is de-signedtoobservetargetsat14bandsfromnear-ultravioletto ther-mal infrared spectra at a spatial resolution of about 200 m at nadir. Thelinearpolarizationmeasurements areavailable atthree wavelengths, centered at444, 646,and1044 nm, andfrom typi-cally 5-9viewinganglesinstep-and-staremodeandcontinuously varying viewing angles in sweep mode. NASA plans to fly a hy-perspectral imaging radiometer [45], the OceanColor Instrument (OCI), and two polarimeters [46,47] the Hyper Angular Rainbow Polarimeter-2 (HARP2), andthe Spectro-Polarimeter forPlanetary Exploration (SPEXone) onboard of the Plankton, Aerosol, Cloud, andoceanEcosystem(PACE)observatory[48].HARP2[49]was de-signedtoobservetheout-goingTOAradiationatfourwavelengths from visible to near-infrared spectra at a spatial resolution of 3 km and a wide swath of ±47° (1,556 km at nadir). The linear

polarization measurements are made at all bands and from 60 viewing angles for the 670 nm band and 20 viewing angles for other bands. HARP2 viewing angles are spaced over 114°. SPEX-one [50] was designed to observe hyperspectral linear polariza-tionfromvisibletonear-infraredspectraataspatialresolutionof 4.6× 5.4 km2_{anda narrowswath of±4° (100kmatnadir). The}

linearpolarizationmeasurements aremadeatfiveviewingangles between ±57°. The European Space Agency (ESA) planned to fly ahyperspectralimagingspectrometer,theUltra-violet,Visibleand Near-infrared Sounder (UVNS) and the Multi-View Multi-Channel Multi-Polarization Imaging (3MI) spectro-polarimeter onboard of theEUMETSATPolarSystem–Second Generation(EPS-SG)aspart ofitsSentinel-5spacemission[51].3MIisthesuccessorofPOLDER satellite series.The instrumentwasdesigned toobserve the out-goingTOAradiationat12wavelengthsfromvisibletofarinfrared spectraata spatialresolutionof4 km2 _{atnadiranda minimum}

swathof2200km.Thelinearpolarizationmeasurementsare avail-able at 9 wavelengths and at 10 to 14 viewing angles for any giventarget.TheCNSAhasapprovedtolaunchseveralspace-borne polarimeters [20]: the Particulate Observing Scanning Polarime-ter (POSP) onboard the Chinese Environmental Satellite-2 (HJ-2), theSynchronizationMonitoringAtmosphericCorrector(SMAC) on-board the High-Resolution Multi-Mode satellite-1 (GFDM-1), the PolarizationCrossFireSuite(PCF)onboardtheGaoFen-5spacecraft, and Directional Polarimetric Camera with polarized Lidar (DPC-Lidar)onboardtheCarbonMonitoringsatellite-1(CM-1).ThePOSP isanall polarizedscanningpolarimeterwithchannelsfrom near-UV toSWIR(410-2250 nm)ata spatialresolutionofabout6km anda wideswath of±32.5°.The POSPoptical design closely fol-lows the NASA APS. SMAC will provide linear polarization mea-surementsatfivewavelengths,centeredat490,670,870,1610,and 2250nm,withaspatialresolution of7× 8 kmattwoobserving pixels alongthecross-track direction. ThePCF isa synergetic de-sign of both the DPC and POSP instruments, which will allow a broadspectralandpolarization range(380-2250nm)withatleast 100viewingdirectionsintheangularrangeof_±50°.TheDPC-Lidar combines passive and active polarimetric measurements. It will provideDPC-like measurements withtwo spectral channel LIDAR centered at532(polarized) and1064 nm.The National Academy ofSciences ofUkraine(NASU)planned tolaunchtheMain Astro-nomicalObservatory(MAO)by2022[52].MAOisanallpolarized scanning polarimeter with channel from near-UV to SWIR (370-1610nm)ataspatialresolutionof6kmatnadir anda swathof +50° to-60° alongtrackand±0.25° acrosstrack.

Airbornepolarimetersimproveourabilitytomakepolarimetric spacemeasurements. Theyare developedto providehighly accu-ratecalibrated observations that can be used to verifythe space polarimetersconcept andvalidatedata processingandalgorithms performance. The majority of the developed airborne polarime-ters are designed as prototypes of current and planned orbital polarimeters. The MICROwavelengthPOLarimeter (MICROPOL)/the ObservingSystemIncludingPolaRisation(OSIRIS)[53-56],the Re-search Scanning Polarimeter (RSP) [14,17,21,57-59], the Airborne Multiangle Spectropolarimetric Imager(AirMSPI1 and 2) [60-63], the Airborne SPEX [64,65], and the Airborne HARP (AirHARP), serve as the airborne prototypes for POLDER/3MI [32-35,66,67], APS [36,37], MAIA[42-44], SPEXone [50], and HARP2 [49]space instruments, respectively [20]. The expected polarimetric accura-cies fromthesepolarimeters are 2-3%, _<0.2%, _<1%, 0.3-0.5%, and 0.3-1% in the measured degree of linear polarization (DoLP), re-spectively.Mostof thesepolarimetricaccuraciesare sufficientfor severalEarth’sremotesensingapplications.Thecurrent polarimet-ric applications are mainly focused on accurately characterizing aerosoland cloud optical and microphysicalproperties.However, animprovedaerosolandcloudcharacterizationresultsinbetter at-mosphericcorrectionsfortheoceancolorproductsandmore

accu-rateretrievals oftotalandpolarizedwater-leavingradiances. Sev-eral studies focused on developingjoint retrieval algorithms that retrieveaerosolandwater-leavingradianceusingdatafrom differ-ent multi-anglepolarization measurements. Polarimetric datasets from the RSP [21,58,68], PARASOL [69], and AirMSPI [61] were used incombinationwiththe coupledatmosphere-ocean simula-tions to retrieve the aerosol and hydrosol properties simultane-ously. The developed algorithms used different aerosol and bio-optical models withdifferent parameterizations for the joint re-trievals.The concepts of the available and planned polarimeters, their technical designs, and the accompanying algorithm devel-opment are discussed in greater detail in Dubovik et al. (2019)

[20].

2.2. Oceancolorpolarimetry

The characterization of hydrosol properties from polarimetric observations islimited. There has beenonlyone studythat used space sensors measurements [23] to show the potential of us-ing polarization todistinguishhydrosols microphysicalproperties. Loisel et al. used POLDER observations and the radiative trans-fersimulations toshowahyperbolictrendbetweenthescalar re-flectanceandthedegreeoflinearpolarization,whichcouldbe ex-plainedbychangesinthebulkassemblagesofthesuspended ma-rine particles. Nevertheless, several theoretical and in-situ based studies [15,24,29,70-79] have highlighted the importance of po-larization inretrievingoceanicconstituents.Kattawaretal.(2013)

[29] providedageneralreviewtounderstandtheevolutionof po-larizedlightintheoceanandtheroleofpolarizationasapossible tool forunderwater remote sensing. Chowdhary etal. [27] high-lightedtheabilitytosimulateandmeasurelinearpolarization sig-natures accurately and toallow forbetter characterization ofthe aerosolandhydrosolproperties.Chami(2007)[15]hasshownthat polarized reflectance could efficiently retrieve the concentration of inorganic particles regardless of the phytoplankton content in coastalwatersusinganempirical-basedinversionapproach.Chami andDefoin-Platel(2007)[16]showedthattheconsiderationof po-larization within inverse algorithm leads to a much greater in-crease of the performance of the inversion, typically by a factor of4 forthe retrievaloftheoceanicscatteringcoefficient.Tonizzo etal.(2011)[71]estimatedparticlecompositionandsize distribu-tion fromsimulatedandin-situ measuredpolarizedwater-leaving radiance. Koestner et al. (2020) [80] examined diverse seawater samples from different coastal environments to provide a thor-ough characterizationof the sizedistribution andcomposition of themarineparticlewiththeangle-resolvedpolarizedlight scatter-ing.Ibrahimetal.(2016)[74]retrievedtheratioof attenuation-to-absorptioncoefficientsfromtheobservedDoLP.Fosteretal.(2016)

[81] developedpolarized transferfunctions to determinethe un-derwaterpolarizedlightfieldfromaboveseasurfaceobservations. El-Habashietal.(2016,2017,2018)[76]were abletoretrievethe sun-induced chlorophyll-a fluorescence, which is un-polarized,in a variety of oligotrophic andeutrophic waters utilizing the frac-tional reductionin theobserved DoLPatthe fluorescenceregion. Polarimetricmeasurementsandvectorradiativetransfer(VRT) re-sultsarepotentiallypromisingforimprovedcharacterizationofthe aerosolandhydrosolparticulates.Theyareexpectedtoyield signif-icantadvancesinOCretrievalalgorithms.

Ocean polarimetry requires off-glint measurements with high polarimetric accuracyandhighspatialresolution todetect small-scale variationsof thepolarized light inthe ocean [30]. Off-glint measurements(near-principleplanemeasurements~30° to60° az-imuthangle)aremoreusefulforoceanpolarimetry toreducethe glint-contaminatedpixels whilestill havinga sufficientupwelling polarizedsignal.Simultaneously,theprincipalplanemeasurements are essential for aerosol and cloud polarimetry to maximize the

range ofscattering angles. The highpolarimetric accuracy of the APS/RSP(<0.2%)andSPEXone/SPEX(0.3-0.5%)instrumentsmakes themwellsuitedfortheoceanpolarimetryapplications;however, theirpolarimetric coveragefortheoceanicscenesare limiteddue totheiralong-trackscanningdesign.AirMSPI,theMAIAprototype instrument, can collectmulti-angle observationsof thescene be-tween _±67° usingamotorizedgimbal system,despite that AirM-SPIisdesignedtotargetland-basedpopulationswiththeobjective ofmonitoring andevaluating the public healthwith polarimetric accuracy _<1%. SPEXone and HARP2 onboard the upcoming PACE missionwillcollectmulti-anglepolarizedobservationsoverEarth’s atmosphere, land surface, andocean. SPEXone is specifically de-signedtoenablemeasurementsofopticalandmicro-physical prop-ertiesofaerosolswithunprecedenteddetail andaccuracy. HARP2 is primarily designedto measureaerosol particles andclouds,as well as properties of land and water surfaces. Although SPEX-oneandHARP2areprincipallydesignedfortheremotesensingof aerosolandcloud,respectively,thecombinedpolarimetricdatasets from both instruments are expected to provide insights for the oceanpolarimetry,yetwithalimitedspatialresolution(3-5km).

VICO, the presented instrument, is designed to collect hyper-angular linearpolarization at four visibleand NIRspectral chan-nels in an imaging mode, as done withthe HARP2/PACE instru-ment,butwithhigherpolarimetricaccuracy, similartothe SPEX-one/PACE instrument. The accuracy level in the measured VICO DoLPisbetterthan0.25%[25]withsmallsufficientangular resolu-tion(~0.12°).Inaddition,VICOisapointinginstrument(gimbaled system),whichmakesitsuitableforoceancolorapplicationsby al-lowingthemeasurementofthepolarizedlightfieldinandoff the principle-viewing plane. VICO design and specificationmake it a retrieval-capableinstrumentprovidingabettercharacterizationof the aerosoland hydrosolproperties.The polarimetric dataset ac-quiredbytheinstrumentisexpectedtobe utilizedtoverifydata processingandvalidatealgorithmperformanceforspaceborne po-larimeters such asHARP2andSPEXoneon the forthcomingPACE observatory.Theinstrumentisdiscussedinmoredetailinthe fol-lowingsectionandinBowles(2015)[25].

3. Dataanduncertainties

Inthissection,weprovidean overviewofthefield campaigns andthe instruments used inthis work. An assessment of uncer-tainty propagation forthe collected data parameters is also dis-cussedinthefollowingsubsections.

3.1. Data

Measurements from two case studies, representative of both coastal and open ocean regimes, were analyzed in this article. The first case, noted Case 1, was made on September 8, 2012, near the open ocean region of south Florida (24° 32.504’ N, -81° 2.516’ W). Coastal measurements were made on August 29, 2014,intheChesapeakeBaycoast (38° 57.917’N,-76° 23.767’W) (noted Case 2). Mapsof the geographical locations foreach case areshowninFig.1.The figureshowsatrue-color image overlaid with chlorophyll-a concentration (Chl-a) retrieved from MODIS-AquaonAugust31,2014.Chl-ainFig.1representvaluesthat are typicallyfoundineachcase.

3.1.1. Airbornemeasurements

Themainremotesensinginstrumentusedforbothcasestudies istheaircraft-basedVersatileImagerfortheCoastalOcean(VICO) developed by the Naval Research Laboratory (NRL). The design, fabrication,calibration,andairbornedeploymentmethodologiesof VICO(Table1andFig.2.)are describedinmoredetailby Bowles

Fig. 1. Maps showing the geographical locations of in situ sites corresponding to open ocean waters (noted Case 1) and coastal waters (noted Case 2) types. The aircraft flight line patterns used in this study are also shown. The figure shows a true color image as it was observed by MODIS-Aqua on August 31, 2014. The image is overlaid by the retrieved Chlorophyll-a concentrations.

Table 1

VICO Instrument Specifications. CCD, and FOV stand for Charge-Coupled Device and full angle Field-Of-View, respectively. The passband bandwidth of each of the spec- tral channels is shown in parentheses.

Property Value

Focal Plane Technology 12-bit interline transfer CCD Focal Plane Size 4872 × 3248 pixels

Spectral Channels 435 (20), 550 (10), 625 (10), 754 (10) nm

FOV 40 ° x 26 °

Max Frame Rate 3 Hz

Nominal Frame Rate 1 Hz

Fig. 2. (a) The NRL VICO instrument. (b) VICO true color image over the area of interest.

etal.[25].Tobrieflysummarize,VICOprovidesmulti-spectral radi-anceandlinearpolarizationimagesathighspatialresolutionwith agroundsampledistance (GSD)of22cm atnadirfroma height of 1525 m. Measurement of linear-polarization was obtained us-ingafour-camerasystem.The camerasarerigidlymountedonan aluminumplateautomaticallycontrolledbyarotatingstageto al-low imaging atdifferent viewingangles. A wire grid polarizer is placedovereachcamerawithorientationsat0°,45°,90° and135° relative to thevertical. The 0° filteris alignedwith the forward-to-aftaxisof theaircraft.A motorizedfilterwheelis attachedin front of each polarizing filterto providemulti-spectral measure-ments fromthe system. The filter wheel contains five-positions; fourcontainnarrow-bandspectralfilterscenteredat435,550,625, and750 nm andthelast positionwasused forthe darkcurrent measurements. Acombined globalpositioning system(GPS) with anInertialMeasurementUnit(IMU)wasmountedontherotating stagetorecordtheattitudeandpositioninformation.Theposition wasalsosuppliedbyamoreaccurate secondGPS/IMUsystem, C-miniature integratedGPS/INStacticalsystem(C-MIGITS),installed on the airframe. The attitude and position information from the rotatingstageandairframewereboth usedinthegeometric pro-cessingtodeterminethegeographicalpositionsandviewingangles ofeachpixelinthedata.Thecamerasimagedatarateofabout1.1 Hz,limitedbythespeedofthefilterwheels,toprovideradiances measured with the linear polarizersoriented in the 0°,45°, 90°, and 135° directions.The radiance values recorded from the four camerasaredonatedbyI0,I45,I90,andI135.Thecalibratedvalueof

Fig. 3. The left-hand panel shows polar plot of the viewing angles and the specular and backscattering planes in observations and simulations of the upwelling light field. The viewing angles are plotted as a function of scattering angles in units of degrees. The right-hand panel shows a polar plot of each VICO flight line for Case 1 and Case 2 sites. The solar zenith and azimuth angles are at θ0 = 44 °, and φ0 = 110 °, respectively for both cases. The anti-solar point (backscattering direction) indicated by a yellow

sun disk at θ0 = 44 °. Note that, the aircraft azimuth is relative to the Sun’s azimuth ( φv −φ0 = 0). The letters a, and b in the left-hand polar plot indicate the sunglint

region, and the anti-solar point for θ0 = 44 °, respectively. The white dash circle, indicated by the letter c, projects the underwater Snell window boundary on the viewing

geometry ( θv = 48 ° for the underwater viewing perspective).

parameters oftheincominglight observedattheaircraftaltitude asfollows(Eq.(1)): ¯Sobs₌

⎡

⎢

⎢

⎣

I Q U

⎤

⎥

⎥

⎦

obs =

⎡

⎢

⎢

⎣

0.5

(

I0+I90 + I45+I135

)

I0− I90 I45− I135

⎤

⎥

⎥

⎦

(1)

whereIisequaltothetotalradiance.QandUtogetherspecifythe state of linearpolarization tothe localmeridional plane of refer-ence. All parameters are spectrally and geometrically dependent (

θ

v,

φ

v,

λ

).

The polarangles diagram in Fig. 3 shows the viewing angles and where the specular and backscattering planes are in the observations and simulations. The figure shows a polar plot of scattering angles as a function of viewing zenith and viewing azimuth angles in units of degrees. The viewing zenith angle (

θ

v) is shown as the radial distance of the polar diagram. The

radial distance ranges from 0° at the origin point to 60° at the circumference. The viewing azimuth angle (

φ

v) is shown as the

polar angles of the diagram measuring 0° at the top moving clockwise ina 360° circle.The positionof theSunis at

θ

0= 44°

and

φ

0=110° forbothoftheVICOobservationcases.Theviewing

azimuth angles

φ

v are adjusted relative to the Sun’s azimuth

defining the solarscatteringgeometryintheprincipal plane.The diagramcanbeinterpretedbyconsideringanobserverstandingat thecenterofthepolarplot.TheviewerlooksintheSun’sazimuth direction when

φ

v = 0°. ASun disk isshown on the top of the

diagramindicatingthesolarprincipalplanedirection,thespecular directionat

φ

v=0° (top)andthebackscatteringdirectionat

φ

v=

180° (bottom).Thespecularreflectionfromthewatersurface,the direct transmission through theatmosphere fromthe Sunto the surface and from the surface to the detector, is indicated by a white starat

φ

v = 0° and

θ

v= 44°.The whitedash circleshows

theborderoftheSnellwindow(

θ

v=48°).

Theaircraftdataaretakeninwhatiscalledastarpattern.The rotation stage attempts to keep the VICO instrument pointed at the same location on the ocean surface, calledthe image center. Theaircraftthenmakesmultiplepassesoverthatpoint,witheach

passoccurringwithadifferentaircraftazimuthaldirectionrelative totheSun.Duringeachoftheseruns,theVICOistakingdata.The localzenithangle changesat aratethat scales withaltitudeand aircraftspeedandalsochangesbasedontheproximitytothe im-agecenter. That rateis slowerwhen farther away andreaches a maximumrateastheplaneoverfliestheimagecenter.Duringthe imaging,variousframesaretakenforeachcolorthatoverlapinthe zenith/azimuthspace.Theright-handpanelofFig.3showsapolar plotofVICOmultiplepassesandthesolarzenithdirectionforboth cases.

3.1.2. Shipbornemeasurements

Water optical properties were measured using Sea-Bird Sci-entific/WET Labs instruments carried out by NRL research ves-sels. Absorption and attenuation in the seawater were measured at different depths by the spectral absorption-attenuation spec-trophotometers (ac-s) and the ac-9 meter. The ac-s meter was used to measure the particulate absorption and attenuation at 83 wavelengths in the 400-750 spectral range. The ac-9 meter was used to measure the colored dissolved organic matter ab-sorption at nine wavelengths in the 412-715 nm spectral range. Thebackscatteringwasmeasuredatthreeangles(100°,125°,and 150°)andthree wavelengths(450 nm, 530nm,and650nm) us-ing the three-angles, three-wavelengths Volume Scattering Func-tionmeterECO-VSF3.Salinity,temperature, anddepth were mea-sured by the integrated Conductivity Temperature Depth (CTD) sensor(SBE49).Temperatureandsalinitywereusedwiththepure water to correct the absorption and attenuation measurements from the ac-s and ac-9 instruments. All instruments were cali-bratedbeforeandaftereachdeployment.TheleftcolumnofFig.4

showsthecorresponding in-water optical propertiesmeasured in eachcase.

FluorometricmeasurementsofChlorophyll-afluorescencewere also available from a calibrated WETStar fluorimeter. Although it is widely accepted to relate chlorophyll-a concentration to the chlorophyll-a fluorimeter measurements, the relationship suffers fromsomelimitationsduetotheinfluenceofincidentirradiance. Variations inincident irradiance influence thechlorophyll-a fluo-rescencenon-photochemicalquenching,thus leadstovariable

es-Fig. 4. The optical properties of hydrosol (left column) and aerosol (right column) for Cases 1 and 2 sites. The left column shows the spectra absorbed (orange), scattered (green), and attenuated (purple) by the seawater particles. The spectra absorbed by the Coloured Dissolved Organic Matter (CDOM) and water molecules are shown in yellow and blue, respectively, in the left column. The right column shows the spectral Single Scattering Albedo (SSA) and the aerosol size distributions as a function of radius. The aerosol and ocean optical coefficients are derived from the remote sensing aerosol network (AERONET) and the ac-s meter measurements, respectively.

timatesofchlorophyll-aconcentration[82].Becauseofthis poten-tial limitation,we estimatedthe Chl-afrommeasured absorption spectrafromtheac-smeter.Chlorophyllconcentration was deter-mined from a baseline value of the particulate absorption peak in thered waveband [82]. Themethod wasshownto be primar-ily relatedto chlorophyll-a concentrations extractedby the high-performance liquidchromatography(HPLC)overa varietyof phy-toplankton cultures and different water types, thus making it a more effectivemethod to useforthe chlorophyll-a concentration estimation.Thepeakiscomputedfromtheline-heightabsorption at 676 nm above a linear background between650 nm and 715 nm. Thebaselinebackgroundisused toremovethecontributions fromnon-algalparticlesandtheminorcontributionsbyaccessory pigments. The phytoplanktonabsorption peakis primarily associ-ated withchlorophyll-a in the red wavebanddueto much lower pigment packagingcompared to the absorption peak in theblue waveband.

Concentrations of mineral particles were also estimated from the measured absorption, and attenuation spectra based on the strongrelationshipobservedbetweeninsitumeasurementsofthe scatteringcoefficientat555nm,andtheconcentrationoftotal sus-pended solids(TSS),particulateorganicmatters(POC),and partic-ulateinorganicmatters(PIC)[83,84].Theparticulatescattering co-efficientwasobtainedfromthedifferencebetweentheparticulate attenuationandabsorptioncoefficients.

Ship-based aerosol optical depth (AOT) measurements were madeusingtheMicrotops II sunphotometer(Solar LightCo.,Inc). Microtops estimatesspectral AOT fromthe measureddirect solar irradianceatfivewavelengths,namely340nm,440 nm,675nm, 870nm,and936nm.

3.1.3. Othermeasurements

Measurementsfromtheclosestavailableground-based Aerosol Robotic NETwork, (AERONET) were used to obtain more detailed aerosolparametersforeachmeasuredsite[85].AERONETprovides estimatesofthespectralAerosolOpticalThickness(AOT),effective radius (reff), volumemedian radius (Veff),standard deviation (

σ

),

and volume concentrations (Cv) for both fine and coarse modes

ofthe aerosolsize distributions [86]. The parameters arederived fromthedirect anddiffusespectral sunradiationofthe total at-mospheric column measured by the multiband CE-318 sun pho-tometer(CIMELElectronique).WeusedthedatafromKeyBiscayne andGSFCAERONETsiteslocatedapproximately80and20nautical milesaway fromCases 1 and2sites,respectively. Asummary of the aerosol and hydrosolparameters used is shown in the right columnofFig.4andTable2.

3.2. Uncertainty

The uncertaintiesof the measured radiances andtheir conse-quentlyderivedproducts canbeestimatedusingvarious methods

Table 2

Aerosol and hydrosol parameters used for Case 1 and Case 2 sites. The wind speed is 3 m/s for both cases. Fine/Coarse is the aerosol mode fraction. m fine and m coarse are

the complex refractive indices of the fine and coarse aerosol particles, respectively. Chla, POM, and PIC are the concentrations of Chlorophyll- a ,Particulate Organic Mat- ter, and Particulate Inorganic Matter, respectively. c p and b p are the particulate at-

tenuation and scattering coefficients, respectively. a p and a g are the particulate and

dissolved absorption coefficients, respectively. AOT, SSA, and the IOPs are all given at the 440 nm band.

Parameter Units

Case 1 Case 2

(Open Ocean) (Coastal)

Aerosol Fine/Coarse % 43 69

m fine unitless 1.40 + i0.0 2 1.47 + i 0.007

m coarse unitless 1.45 + i0.0 7 1.53 + i 0.001

AOT unitless 0.094 0.057 SSA unitless 0.65 0.094 Hydrosol Chla μg L −1 _{0.01 20} POM μg L −1 _{0.25 ×10} 3 _{5.8 ×10} 3 PIM μg L −1 _{0.08 ×10} 3 _{16 ×10} 3 c p m −1 0.0715 5.62 b p m −1 0.0650 3.67 a p m −1 0.0065 1.95 a g m −1 0.0280 0.67

fromtheliterature [87-90].MonteCarlo methodprovides numer-ical estimates of theuncertainties, where the exact shape ofthe uncertaintydistributionsoftheunderlyingvariablesisconsidered. Thetechniqueiscapableofhandlingthenon-linearityand discon-tinuityincomplexderived models.Itisdeemedtobe robust,but theaddedmathematicalcomplexitycanbecomputationally inten-sive toimplementwithin thepixel-by-pixelroutine data process-ing of ocean color. In practice, the analytical law of propagation

[91] iscommonlyusedtoapproximateuncertaintiesintheocean color products [89,92,93], where propagated errors are obtained fromassumednormaluncertaintydistributions.Arecent compar-ison wasmadebetweenMonteCarlo andthelaw ofpropagation framework,showingagoodagreementinestimatinguncertainties for several ocean color products [89]. In this article,we usethe analyticallawofpropagation[87]topropagateuncertaintiesfrom the measured polarized radiance to the derived parameters. The square ofthetotaluncertaintyofeachparameter, u2

x canbe

esti-mated usingthevariance-covariancematrixofthepolarized radi-anceinputs, VL_polarized andtheJacobianmatrix,Jas:

u2x=JVLpolarized J

T ₍₂₎

Wherexis thetargetparametersuch asI, Q,andUandu2

x is

thesquareofthetotaluncertaintiesforeachofthetarget parame-teru2

I,u2Q, andu2U.Thesquareofthetotalradianceuncertainty,u2I

canthusbeestimatedfromthemeansandvariancesofmeasured polarizedradiancequantitiesas:

u2 I =



_∂

_I

∂

I0

∂

I

∂

I45

∂

I

∂

I90

∂

I

∂

I135

×

⎡

⎢

⎣

σ

2 I0

σ

I0I45

σ

I0I90

σ

I0I135

σ

I45I0

σ

2 I45

σ

I45I90

σ

I45I135

σ

I90I0

σ

I90I45

σ

2 I90

σ

I90I135

σ

I135I0

σ

I135I45

σ

I135I90

σ

2 I135

⎤

⎥

⎦

×

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

∂

I

∂

I0

∂

I

∂

I45

∂

I

∂

I90

∂

I

∂

I135

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

(3)

where thediagonal elementsof VL_polarized areequal tothe square

oftheuncertaintiesinthemeasuredpolarizedradiancequantities,

I0,I45,I90 andI135,and the off-diagonal elements are the

covari-ances betweenthem. For the total radiance calculations, we can startbycomputingthepartialderivativesinEq.(3):

J=



∂

I

∂

I0

∂

I

∂

I45

∂

I

∂

I90

∂

I

∂

I135

=



1 2 1 2 1 2 1 2

(4)

Therefore,the square of thetotal radiance uncertainty canbe calculatedas: u2 I = 1 4

σ

2 I0+

σ

2 I45+

σ

2 I90+

σ

2 I135+ 2

(

σ

I0I45+

σ

I0I90+

σ

I0I135+

σ

I45I90+

σ

I45I135+

σ

I90I135

)



(5)

Thetotal uncertaintiesofallparameters are derivedfrom cor-relatedinputquantities.Theoff-diagonalelementsofthe variance-covariance matrices are considered in the calculations. All the variance-covarianceparametersarecalculatedfromVICO measure-ments.Similarly, we cancompute thetotal uncertaintiesforeach ofthetargetparameters.Partialderivativesandtotaluncertainties ofeachtargetparameterinthisstudywerecalculatedanalytically, andaregivenintheappendix.

Severalrandomandsystematicprocessesimpactthe radiomet-ricaccuracy.Laboratoryworkwasperformedtoidentifyand quan-tify the sources of uncertainty and error in the system [25]. The typical radiometric uncertainties and errors of the system can add up to 4.5%. The radiance uncertainty and error lev-els in a single-pixel of the data can be expressed as, 1.10.022 _±

0.027

μ

Wcm−2sr−1nm−1,where1.1isthemeasuredradiancevalue atthe blue band ofCase 2 (IBlue), and± 0.027 is thesystematic

uncertainties(<_∼2.5%)associatedwiththeoutputradianceofthe in-tegratingsphere(1.5%)plustheprocess oftransferring calibration totheintegratingsphere(1%) [94].The radianceexponent,0.022, representsthephotonstatisticserrors(<_∼2%)duetostraylight,shot noise,darknoise,andfilterpositions.

Fortunately,errorsfromtherotationalpositionsofthe polariz-ing filterscan becorrected fromanymisalignment. Althoughthe polarizer’stransmissionaxeswereplacedascloselyto0°,45°,90° and 135° angles as possible, the position of the polarization fil-ters

η

1− 4were recheckedafterinstallationandcorrectedforany

misalignment errorsduring polarizersplacement. First,an exper-iment was conducted using the integrating sphere and a refer-encepolarizer withaprecisely knowntransmissionaxis.The po-larizerwasusedtocalculatethepolarizer orientationsinthe sys-tem, within the uncertainty limits of the reference polarimeter. Any offset

α

1− 4 in the polarizer’s orientationswere then

deter-mined,andacorrection methodwasusedtore-orientthesystem intotheproperreferenceplane(seechapter3Ref.[95]).The cor-rectionmatrix that re-distributetheenergy inthe VICOdetected Stokesvectorisderivedas:

C =

_{1 a b}

0 cos 2 (η1 + α1) − cos 2 (η3 + α3) sin 2 (η3 + α3) − sin 2 (η1 + α1)

0 cos 2 (η2 + α2) − cos 2 (η4 + α4) sin 2 (η4 + α4) − sin 2 (η2 + α2)

−1

(6)

whereaandbaredefinedas:

a=cos2(

η

1+

α

1)+cos2(

η

2+

α

2)+cos2(

η

3+

α

3)+cos2(

η

4+

α

4)

b=− sin2(

η

1+

α

1)− sin2(

η

2+

α

2)− sin2(

η

3+

α

3)− sin2(

η

4+

α

4)

Additionally,databinning andmultiple measurements averag-ingcansignificantlyreducethesystemuncertainties.Twobinning oraveraging steps are possible forthe collecteddata.First, since thefocal planesare high-resolution (4872×3248 pixels), thedata can be significantly binnedwhile maintaining the desired angu-larresolution. Second, thedata can be averaged across the over-lappedframesthataretakenduringthemultipleflightpasses(as describedinSec.2.1.1above).A16×16pixelbinningisusedinthe data processing. The data were also averaged across overlapping frames(fourframesonaverage)foreachviewingdirectioninthe

Fig. 5. At-sensor Stokes parameters and the corresponding uncertainty in percent derived from the 16 × 16 pixels binning for Case 1 and Case 2. Radiances are given in units of μW cm −2 nm −1 sr −1 . It is important to note that the presented uncertain-

ties in this figure come from the measuring instrument errors and uncertainties combined with several other environmental factors such as capillary ocean waves and shadowing of one facet by another, which add up to the magnitude of the quantified laboratory radiometric uncertainties and errors. The increased uncertain- ties at the longer wavelength can be primarily attributed to either an atmospheric spatial variation, and sea surface contamination (ex. sunglint, and whitecaps) in the field.

scene.Since thenadir viewingangleswere revisitedfromseveral flight lines, there were more framesto average for theseangles; however,thenumberofframestoaverageislimitedbytheflight speedattheseviewingangles.Theuseofdatabinningoraveraging providesaproperbalancebetweentheangularresolutionandthe dynamicrangeofthedatatoobservetheoceanfeatureseffectively

[25].Thedatabinningoraveragingreducestheangularresolution toasufficientdegree(~ 0.12°)whileincreasingthesignal-to-noise ratio (SNR), allowing for the reduction in the effects of random noiseandmisregistration(inanglespace)ofthefocalplanes.

The overall uncertainties experienced in the field are shown in Fig. 5. The figure shows the Stokes parameters and the cor-responding uncertainty percentageusing the 16 × 16 pixels bin-ning(ux/

μ

x∗100%,wherethe uncertaintyofeachparameterux,is

scaled by its average value

μ

x). It is important to note that the

presented uncertainties in this figure come from the measuring instrument errors anduncertaintiescombined withseveral other environmentalfactors suchascapillaryoceanwavesand shadow-ingofonefacetbyanother,whichadduptothemagnitudeofthe quantifiedlaboratoryradiometricuncertaintiesanderrors. Regard-lessofthevariabilityoftheenvironmentalcondition, thebinning improved theradiometric uncertaintyto1.4%atthe blueband of thecoastalcase.However,thisuncertaintyreductionisnotalways thecase, asseenwiththelongerwavelengthuncertaintiesofthis particularcase.Thetotalradianceuncertaintyatthe750nmband isabout5%. Theincreaseduncertaintiesatthelonger wavelength can be primarily attributedtoeitheran atmospheric spatial vari-ation,andseasurfacecontamination(ex.sunglint,andwhitecaps) inthefield.Arelativelysmallimpactofsunglintisexpectedgiven the solarzenithand viewinggeometries (

θ

0=44°,and

θ

v=0°,

re-spectively)andtheaveragewindspeed(W=3m/s)comparedtoa roughoceansurfacecase[81].Additionally,thesignallevelsatthe longer wavelength are muchlower compareto other VICO chan-nels so that thenoise levelbecomesa higherpercentance ofthe signal.

4. Theoryandmethodology

Westartwithopticalclosuresbetweentheobservedpolarized radiances by the airborne polarimeter, and the in-situ measured waterand aerosolparameters by the shipborne and the ground-based AERONET near each site. The in-situ measurements were usedintheVRTforwardmodelingtoreproducetheobserved po-larized radiances atthe aircraft level forthe different cases. The useoftheshipborneandAERONETmeasurementsinthisstudyis necessary to reach a VRT closure that relies on real-world con-ditions and not based on adjustments of many optical parame-ters.We then compute thelinear Stokes contributions of the at-mosphere andextract the water-leaving total andpolarized radi-ancesbasedontheclosureachievedbetweentheVRTmodeland theVICOobservationateachcase.Finally,weperformasensitivity studyfor the impact of thedifferent seawater conditions on the aircraftlevelandtheTOAtotalandpolarizedreflectances.

4.1. At-sensorpolarizedradianceandatmosphericcorrection The observed linear Stokes parameters, ¯Sobs _{(Eq. (1)) acquired}

fromaircraftorspacecraftovertheocean-surface-atmosphere sys-tem (AOS) can be first-approximated by the following expres-sions: ⎡ ⎢ ⎢ ⎢ ⎣ I Q U ⎤ ⎥ ⎥ ⎥ ⎦ obs ∼ = t g ⎛ ⎜ ⎜ ⎜ ⎝ ⎡ ⎢ ⎢ ⎢ ⎣ I Q U ⎤ ⎥ ⎥ ⎥ ⎦ atm+s f c (τR,τA,τRA,W) + ⎛ ⎜ ⎜ ⎜ ⎝t u ⎡ ⎢ ⎢ ⎢ ⎣ I Q U ⎤ ⎥ ⎥ ⎥ ⎦ w (τIOPs) ÷ 1 − ¯r atm ⎡ ⎢ ⎢ ⎢ ⎣ I Q U ⎤ ⎥ ⎥ ⎥ ⎦ w (τIOPs) ⎞ ⎟ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎟ ⎠ (7) Followingthenotationsdemonstratedby FraserandGaoetal.

[96,97],the atm+sfc isthe sunlight scatteredfromthe combined atmosphere andocean surface; w is the sunlight scattered from beneath the ocean surface and leaving it; tu is the direct and

diffuse upwelling transmittance through the atmosphere for the water-leavinglightvector;andtgisthetotalatmosphericgaseous

transmittance on the sun-surface sensor path, which is assumed tobeindependentinourprocess.Thedividedterm,attheendof

Eq.(7)

(

1_{− ¯r}atm

)

¯Sw,accountsfortheeffectofatmospheric

reflec-tion ofupward water-leaving light vector back to the ocean sur-face,where ¯ratm isthereflectanceoftheatmosphere.

AllthelinearStokesparametersinEq.(7)arespectrallyand ge-ometricallydependent(

θ

v,

φ

v,

θ

s,

φ

s,

λ

).The

θ

v,and

φ

varethezenith

andazimuthviewinganglesfromanaircraftoraspacecrafttothe oceansurface,respectively.The

θ

sand

φ

sarethesolarzenithand

solarazimuthangles ofthe directsunlight, respectively,and

λ

is thewavelength.TheindependentparametersineachlinearStokes vectoraredefinedasfollows:

τ

RRayleighopticalthicknessthroughtheatmosphericprofile,

τ

AAerosolopticalthicknessthroughtheatmosphericprofile,

τ

RAInteractiontermbetween

τ

Rand

τ

a,

WSurfacewindspeed,

τ

IOPs Total optical thickness through the marine profile by

cumulating the optical thickness of each component: wa-ter molecules,phytoplankton,Mineral-Like particles,yellow substance,anddetritus(InherentOpticalPropertiesofwater constituents).

Toobtain thewater-leaving radiance andits state of polariza-tion, ¯Sw_{,athoroughcalculationofradiationandpolarization}

atm+sfcradiationandpolarizationare necessarytoaccurately re-move the effects ofthe scatteringby atmosphericmolecules and aerosols, reflectionsby the air-waterinterface scattered[98], and thescatteringeffectsofsurfacefoam[99].Theseeffectscanbe de-termined basedon theRayleighcomponent,

τ

R,the aerosolload,

τ

a,aerosol type, andthe surfacewind speed,W, foreach of the

measured AOS conditions.We use theVRT model to account for theseeffects. Wecompute andremove the atm+sfccontributions fromtheobservedlinearStokesparameters usingtheVRTmodel. First,wesimulatetheatmosphere-oceansysteminaforwardsense to matchtheobservationsattheaircraftaltitudeusingthe water optical propertiesand aerosolparameters measured at each site. Then asecond setofthesimulationwasperformedtoisolatethe atm+sfccontribution, assuming the same atmosphere, andocean surface,butafullyabsorbingocean(nooceanscattering contribu-tion, ¯Sw_{= 0).Theatm+sfccontributionwasremovedfromthe}

to-talobservedradianceandpolarizationbysubtractingtheobserved and atm+sfc linearStokes parameters usingthe two sets of sim-ulation. The simulation parameters and the VRT model used are describedinthefollowingsection.

4.2. Vectorradiativetransfermodeling

The Ocean Successive Orders with Atmosphere - Advanced (OSOAA) vector radiative transfer code was used to model the field measurement. OSOAA allows the computation of the com-pleteradiancefieldandthepolarizationstate inacoupled ocean-atmospheresystem.Itcalculatestheradiativeparameters foreach component of the environment, assuming a set of plane-parallel homogeneous layersthroughouttheatmosphericandmarine pro-files [27]. The code numerically computes the contribution of each scatteringorderbasedon thesuccessiveordersofscattering method[100,101].Adetaileddescriptionofthecodeis presented in[102].

The OSOAA model was used in a forward sense to compute radiance and polarization for various viewing angles at the air-craftlevel.Scatteringandabsorptionbymoleculeswere character-ized by their optical depths anddepolarizationratio. The OSOAA modeldoesnottake intoaccountthegaseous absorption.The ef-fectsofgaseousabsorptionwerecalculatedusingthe temperature-dependent absorption cross-section data [103,104]. The transmit-tancespectraofgaseousabsorption(tg(

λ

))wascalculated

indepen-dentlybasedontheempiricalrelationship[105-107]:

tg

(

λ

,

θ

0

)

=exp

−[

τ

o3

(

λ

)

+

τ

o2

(

λ

)

+

τ

N2o

(

λ

)

+

τ

H2o

(

λ

)

] cos

θ

0



(8)

whereO3,O2,N2O,andH2Oaretheozone,oxygen,nitrogen

diox-ide and watervapor optical thicknesses, respectively, for a given solarzenithangle(

θ

0).

The radiativepropertiesofaerosolandhydrosolparticleswere describedbythesinglescatteringalbedo,opticaldepth,and single-scattering Muellermatrix. The coupledatmosphere-ocean system used inthesecomputationsisdescribedasfollows:The modeled atmosphereconsists ofairmolecules(Rayleigh) andaerosol scat-terers.Theiramounts(relatedtotheiropticalthicknesses)vary ex-ponentiallywithaltitudewithscaleheightsof8kmformolecules and 2 km for aerosols. The aerosol volume distribution is mod-eled usingabimodallognormaldistributionconsistingoffineand coarse modes. Both modesparameterized byvolumetric radii, rV,

andstandarddeviations,

σ

V,volumetricconcentrations,CV,aswell

as complex aerosolrefractive index spectra,m. The air/sea inter-facewasmodeledforaroughseadefinedby thewindspeedand thecorrelatedseasurfaceslopevarianceforanisotropicslope dis-tribution [108].The modeled oceanbody assumes ahomogenous mixture of pure seawater, particulate (phytoplankton, and NAP), anddissolved(CDOM)components.

ForrealisticMuellermatrices,ahybridmodelthatcombinesthe analytical Fournier-Forand (FF)phase function withVoss andFry (VF)reduced Muellermatrices wasusedfor theunderwater par-ticles[109].TheVFreducedMuellermatrices,withoutthe magni-tudeinformation,effectivelyprovidethe normalizedlight scatter-ingpolarization matrixbasedon realmeasurementsofthe ocean waters.TheFFanalyticalmodelcanverywellreproducetheshapes ofoceanicphase functions, especiallyat verysmallangles, based on measured IOPs [110,111]. To construct the particulate phase function,wefirst normalizedthe VFMuellermatricesby its scat-teringfunction (VFM11 (ϴ)element)ateach scatteringangle,and

then multiplied by FF scattering function (FF M11 (ϴ) element)

[68].Thevariationsinthe FFphase functionisbased onthereal indexof refraction ofthe particles (mr), and the Junge slope

pa-rameter (

γ

), foran ensemble ofparticles that havea hyperbolic particlesizedistribution(PSD).Therealpartofthebulkrefractive indexwascalculatedfromthemeasuredparticulatebackscattering ratiousingtheinversionmodelin[68,112].AlthoughFFusesonly therealpartofthe indexofrefraction,theadditionofthe imag-inarypart ofthe indexofrefraction (the amounts ofabsorption) does not significantly change the shape of the phase functions generatedby FF analyticalmodel [110].The PSDhyperbolic slope was estimated from the measured particulate attenuation spec-trum[113].Lastly,toobtainthetotalMuellermatrixofthewater body,the pure seawaterphase function, similar to Rayleigh scat-tering,is then mixedby theOSOAA withthe particulateMueller matrixtoobtainthetotalMuellermatrixofthewater.Toaccount formolecularanisotropyofwatermolecules,weusedtheRayleigh depolarizationfactorof0.039[114,115].

4.3. Observedparameters

Inthisarticle,thebi-directionalreflectance

ρ

,thedegreeof lin-ear polarization, DoLP, andthe angleof linearpolarization, AoLP, are the main parameters we use to describe the incoming light fieldsattheaircraftobservationalaltitude.Theyarecalculated us-ingthelinearStokesparametersdefinedinEq.(1)asfollows:

⎡

⎢

⎢

⎣

ρ

DoLP AoLP

⎤

⎥

⎥

⎦

Z =

⎡

⎢

⎢

⎢

⎣

ρ

u+

ρ

p



Q2_+U2_/I 0.5× tan−1

₍

_U/Q

₎

⎤

⎥

⎥

⎥

⎦

(9)

whereall parameters arespectrally andgeometrically dependent, (

θ

v,

φ

v,

λ

)andcanbecalculatedatanygivenlevel,Z,foreach

stud-iedcase. Thebi-directionalreflectance,

ρ

,is alinearcombination of the un-polarized

ρ

u and a polarized

ρ

p components. The

bi-directional reflectancecomponents arethe totalradiance andthe linearlypolarizedradiance,eachscaledbythesolarreflected radi-ation.



_ρ

u

ρ

p

=

π

r20

μ

0F0 ×



₍

_{1− DoLP}

₎

_{× I} DoLP× I

(10)

where the extraterrestrialsolar irradiance [116],F0, the cosine of

solarzenithangle,

μ

0,andtheSun-Earthdistancecorrectionfactor,

r2

0,describesthesolarradiationatthetopoftheatmosphere,TOA.

TheadvantageofusingthereflectanceandDoLPparametersis to represent the at-sensor’s incoming unpolarized and polarized light independently fromthe solarradiation,and thechoice of a referenceplaneforthe QandUparameters.Along withthat, the errorlevelinDoLPandAoLPparametersmustbe lesssincethese quantitiesare derivedfrommeasuredradiance ratiosatthesame pixel.Thiserrorreductionisonlyvalidwithpropercalibrationof the four separate camera system, thus eliminating the gain and transmissionerrorsduetopixelsdifferencesinthefinalimage.The

Fig. 6. Relative differences in the spectral and angular total ρ, DoLP and AoLP parameters for the two measured cases. The left-hand panel shows the spectra of each of these parameters at the nadir viewing direction; the right-hand panel shows the 435 nm band of each parameter as a function of viewing nadir angles and at the azimuth line of φv = 35 ° relative to the Sun. A gray line, in the middle polar diagram of the figure, indicates the flight line pattern of both cases. A Sun disk is shown on the top of the

middle polar diagram, indicating the solar principal plane direction, the specular direction at φv = 0 ° (top), and the backscattering direction at φv = 180 ° (bottom). The solar

position of the Sun was at θ0 = 44 ° and φ0 = 110 ° for both cases. Notice the large AoLP deviation between the two cases coinciding with the DoLP neutral point of Case 2

(gray dot).

systematicerrorsassociatedwithintegratingsphereradiancelevel also cancels out. Similarly, rescaled linear Stokes parameters (Q/I andU/I)areunaffected bytheseparticularerrors.TheDoLP accu-racyofVICOisbetterthan0.25%[25].

5. Resultsanddiscussion

We describe the results for VICO flying over oligotrophic and turbid water-types. The first water-type, Case 1,is representative of brightblue-likewaters found inthe large portionofthe open ocean and characterized by low Chla concentrations. Scattering and absorption are dominated by phytoplankton and the water moleculesthemselves.Thesecondwater-type,Case2,is character-izedbyhighChla,mediumnon-algalparticles,andmediumCDOM concentrations representativeofgreen-like waterstypically found inproductivephytoplanktonwaters.Theatmosphericconditionof thefirstcaseischaracterizedbyalowerSSA,indicating more ab-sorbing aerosolcompared to thesecond case. The aerosoloptical thickness, at500nm,isabouttwice lower(0.046) forCase2than for Case 1 (0.084). Differences in the measured aerosol and in-wateropticalpropertiesareshowninFig.4andTable2abovefor both cases. In thissection, we first start with theresult ofVICO

[25]observationsatdifferentconditions.Wethenshowtheresults ofVRTmatchtoVICOobservationsandtheestimatedtotaland po-larized water leavingreflectances. Lastly, we perform an analysis ofthetotalandpolarizedreflectancesvariationduetotheoceanic parameters used intheVRT modelingofthe differentconditions. This analysis is described at both the aircraft level and the TOA level.

5.1. ComparisonofVICOobservationsbetweenCases1and2sites In Fig.6, we highlight therelative differences inthe total re-flectance,DoLP,andAoLPparametersforthetwomeasuredcases. As expected, a higher blue reflectance for the first case across all the nadir viewing geometry partially pertained to the in-creasedscatteringintheopen oceancaseatthisbandin compar-ison tothe second case. The relative difference betweenthe two cases is high in the green and red bands of the DoLP (10-15%), shownin the spectral DoLP figure (left panel ofFig. 6), and rel-ativelysmallinoveralltheAoLPspectrawithin3° differences. An-other feature observed is that the DoLP crosses a neutral point for Case 2, indicated as a gray dot in the angular DoLP figure (right panel of Fig. 6), whereas that for the first case, the DoLP grazes a neutral point. Notice the corresponding AoLP disconti-nuity in the second case, marked as a gray dot in the angular AoLP figure (right panel of Fig. 6), andthe large AoLP deviation across the nadir viewing direction (0° to 90°) between the two cases.

The differences can be explained by the variation seen in aerosol and ocean optical properties at each observation, shown inFig.4above. Theresultsindicatethatsmalladjustmentstothe aerosolandocean microphysicalandopticalproperties cancause uniqueangularandspectralpatternsintheobservedtotaland po-larizedlight field. It isimportant to note that all the differences areshownatthesameviewinganglesandilluminationconditions forbothcases.

Fig. 7. Multi-spectral, and -angular VRT match with aircraft Stokes parameter ( I, Q , and U ) observations for Cases 1 and 2. The matches and residuals (i.e., measurement minus model) of the observed parameters are shown in the left and right-hand axes, respectively. The shaded red areas outline the slope of the Stokes parameter residuals across the spectral bands. Each spectral band is shown as a function of scattering angles. The values of the scattering angle 110 ° and 145 ° are indicated for each wavelength. The solar position is at θ0 = 44 ° and φ0 = 110 ° for both cases. 5.2. ComparisonofVICOmeasurementswiththeVRTsimulations

Inthissection,wepresenttheresultsfromtheVRTmodelingof VICOairborneobservationsoverthetwocases.TheVRTinput pa-rameterswereestimatedfromtheatmosphericandoceanicoptical propertiesmeasured ateachlocation, asdescribedinSection 3.2. TheopticalpropertiesofbothsitesaresummarizedinTable2and

Fig. 4 above. The multi-spectral and hyper-angular VRT matches areshowninthefollowingsubsections.

5.2.1. Multi-spectralandmulti-angularVRTmatch

Figs.7and8showthespectralVRTmatchofCase1andCase2 Stokes parametersasafunction ofscatteringangles rangingfrom 110° to145°.Case1,Case2,andtheVRTare color-codedinblue, orange, andgray, respectively.The VRT match isquite consistent with the observed VICO Stokes parameters across the spectrum and the different scattering angles. Slightly less accuracy is no-ticed in reproducing the Q and U components, probably due to the AERONET inversion performance. Indeed, adjustments in the AERONETmicrophysicalparameterforthefineaerosolmodetend to furtherimprove theVRT modelingresults atthelonger wave-lengths and viewing angles toward the Sun. As was highlighted previously[117,118],theaerosolretrievalaccuraciesfromAERONET areaffectedbythelackofusingpolarizationmeasurementsinthe AERONET inversion. A higher match accuracy could be possibly achieved by an optimizationroutine ofa complexconfigurations, howeveritisimportanttonotethat,theVRTmodelscouldbealso limited. TheVRT modelsareonly asgoodastheir internal repre-sentationofthephysicsunderlyingthemodeledatmosphere-ocean system.

Fig. 8. Multi-spectral, and -angular VRT match with aircraft ρ, DoLP , and AoLP ob- servations for Cases 1 and 2. The matches and residuals (i.e., measurement minus model) of the observed parameters are shown in the left and right-hand axes, re- spectively. The shaded red areas outline the slope for each of the observed param- eter residuals across the spectral bands. Each spectral band is shown as a function of scattering angles. The values of the scattering angle 110 ° and 145 ° are indicated for each wavelength. The solar position is at θ0 = 44 ° and φ0 = 110 ° for both cases. 5.2.2. Hyper-angularVRTmatch

AsdescribedinSec.2.1.1,theaircraftwasflowninastar-shaped patternwithmultipleflightlines tofilltheangularspaceviewed over the area of interest measured by VICO (see Fig. 3). In this flight pattern,all lines crossed astationarypoint (the area of in-terest) whereeach line defined a differentazimuthal space rela-tivetotheSun.Theinstrumentmountingstagewasrotatedduring eachflight-line,yieldingseveralsetsofimagesatdifferentviewing angles.Thetotalsamplingtimeofthestar-shapedpatternwas ap-proximately15minutes.Thevariabilityoftheseawaterand atmo-sphericconditionwasrecordedandanalyzedduringtheflighttime usingdatafromtheac-s meter,Microtops,andAERONET.No sig-nificantchangeswereobserved.We checkedthevariabilityofthe AERONET AOD measurements within ±15 minutes from the air-craftoverpass.TheAODvaluesweresimilar atthedifferent mea-surementtimes.TheAODstandarddeviationswere± 0.002and± 0.003forCases1and2,respectively.

Tovisualizethebidirectionalchanges,weillustratedtheresults using thepolar angles diagram described previously in Fig.3. In

Figs.9and11,weexploittheresultsoftheVRTmodelingandVICO observations from many different viewing angles. The radiation andthedirectionalitypatternofthelightfieldareprimarily char-acterized by the illumination condition and by the atmospheric and oceanic optical properties of the observed scenes. The total andpolarized light obtainedfrom thecoastal water observations atthe443nmbandisdescribedbytheStokesvectorcomponents I,Q,U,inFig.9,andby the

ρ

,DoLP,andAoLPinFig.11.Thetop rowsinFigs.9and11show VICOmeasurements,andthebottom rows show the corresponding result of theVRT simulations. The