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NASA/TM–2016-217551Atmospheric Correction for Satellite Ocean Color RadiometryCurtis D. Mobley, Jeremy Werdell, Bryan Franz, Ziauddin Ahmad, and Sean BaileyNational Aeronautics andSpace AdministrationGoddard Space Flight CenterGreenbelt, Maryland 20771June 2016

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NASA/TM–2016-217551Atmospheric Correction for Satellite Ocean Color RadiometryCurtis D. MobleySequoia Scientific, Inc., Bellevue, WAJeremy WerdellNASA’s Goddard Space Flight Center, Greenbelt, MDBryan FranzNASA’s Goddard Space Flight Center, Greenbelt, MDZiauddin AhmadNASA’s Goddard Space Flight Center, Greenbelt, MDSean BaileyNASA’s Goddard Space Flight Center, Greenbelt, MDNational Aeronautics andSpace AdministrationGoddard Space Flight CenterGreenbelt, Maryland 20771June 2016

Notice for Copyrighted InformationThis manuscript has been authored by employees of Sequoia Scientific, Inc. with the NationalAeronautics and Space Administration. The United States Government has a non-exclusive,irrevocable, worldwide license to prepare derivative works, publish, or reproduce this manuscript, and allow others to do so, for United States Government purposes. Any publisheraccepting this manuscript for publication acknowledges that the United States Governmentretains such a license in any published form of this manuscript. All other rights are retainedby the copyright owner.Trade names and trademarks are used in this report for identification only. Their usage does notconstitute an official endorsement, either expressed or implied, by the National Aeronautics andSpace Administration.Level of Review: This material has been technically reviewed by technical management

AbstractThis tutorial is an introduction to atmospheric correction in general and also documentation of theatmospheric correction algorithms currently implemented by the NASA Ocean Biology ProcessingGroup (OBPG) for processing ocean color data from satellite-borne sensors such as MODIS andVIIRS. The intended audience is graduate students or others who are encountering this topic for thefirst time. The tutorial is in two parts. Part I discusses the generic atmospheric correction problem.The magnitude and nature of the problem are first illustrated with numerical results generated bya coupled ocean-atmosphere radiative transfer model. That code allow the various contributions(Rayleigh and aerosol path radiance, surface reflectance, water-leaving radiance, etc.) to the topof-the-atmosphere (TOA) radiance to be separated out. Particular attention is then paid to thedefinition, calculation, and interpretation of the so-called “exact normalized water-leaving radiance”and its equivalent reflectance. Part I ends with chapters on the calculation of direct and diffuseatmospheric transmittances, and on how vicarious calibration is performed. Part II then describesone by one the particular algorithms currently used by the OBPG to effect the various steps ofthe atmospheric correction process, viz. the corrections for absorption and scattering by gases andaerosols, Sun and sky reflectance by the sea surface and whitecaps, and finally corrections for sensorout-of-band response and polarization effects. One goal of the tutorial—guided by teaching needs—is to distill the results of dozens of papers published over several decades of research in atmosphericcorrection for ocean color remote sensing. Any subsequent modifications to the originally publishedtechniques are noted in the documentation. This content of this tutorial is available online asthe Atmospheric Correction chapter of the Ocean Optics Web Book, beginning at correction/chapter overview. A pdf version ofthe report can be downloaded as Mobley et al. (2016) in the publications section of the OceanOptics Web Book.AcknowledgmentsThis work was supported by NASA Grant NNX14AQ49G to author C.D.M. titled Documentationof NASA Ocean Color Atmospheric Correction Algorithms in Preparation for the 2015 SummerClass in Optical Oceanography and Ocean Color Remote Sensing. This report constitutes partof the final report on that grant. Howard Gordon made useful comments on the computation ofdiffuse attenuation, and he and David Antoine helped with the formulation and interpretation ofnormalized reflectances.

ContentsList of FiguresivList of TablesviIThe Atmospheric Correction Problem11 Problem Formulation42 Example Radiances83 Normalized Reflectances3.1 Normalized Radiances and Reflectances . . . . . . . . . . . . . . . . . . . . . . . . .3.2 The BRDF Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131317234 Atmospheric Transmittances254.1 Direct Transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Diffuse Transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Vicarious Calibration29II34The NASA OBPG Algorithms6 Gases6.1 Nonabsorbing Gases . . . . . .6.1.1 Wind Speed and Surface6.1.2 Pressure Effects . . . . .6.2 Absorbing Gases . . . . . . . .6.2.1 Absorption by Ozone . .6.2.2 Absorption by NO2 . . . . . . . . .Reflectance. . . . . . . . . . . . . . . . . . . . . . . . . . . .Effects. . . . . . . . . . . . .383838404042437 Sun Glint468 Whitecaps48ii

9 Aerosols9.1 Aerosol Properties . . . . . .9.2 Black-pixel Calculations . . .9.3 Non-black-pixel Calculations9.4 Strongly Absorbing Aerosols .505053575910 Spectral Out-of-band Correction6011 Polarization Correction66References70iii

List of Figures1.1Processes contributing to the TOA radiance . . . . . . . . . . . . . . . . . . . . . . . for example calculations . . . . . . . . . . . . . . . . .Example radiances contributing to the TOA radiance . . . . . . .Fractional contributions to the TOA radiance . . . . . . . . . . .TOA radiances for various environmental and viewing conditions3.13.23.3Comparisons of Lu and Lw for a zenith Sun, with and without an atmosphere . . . . 15Comparison of exact normalized and unnormalized water-leaving reflectances . . . . 22Example reflectances contributing to the TOA reflectance . . . . . . . . . . . . . . . 224.1Direct and diffuse transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.1Flowchart of the atmospheric correction process . . . . . . . . . . . . . . . . . . . . . 366. optical thickness and depolarization ratioTransmittance by O2 and H2 O . . . . . . . . . . .Transmittance by O3 . . . . . . . . . . . . . . . . .Transmittance by NO2 . . . . . . . . . . . . . . . .Band-averaged optical depth and cross sections . .8.1Whitecap reflectance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499. of aerosol volume, number, and particle size distributions. . . . .Relative humidity effects on an aerosol volume and particle size distributions.Dependence of (λ, 865) on aerosol model . . . . . . . . . . . . . . . . . . . .Remote-sensing reflectances in the NIR . . . . . . . . . . . . . . . . . . . . .Qualitative behavior of (λ, 865) for blue-absorbing aerosols . . . . . . . . . .Ocean regions for non-black-pixel corrections . . . . . . . . . . . . . . . . . . sensor response; linear ordinate . . . . . . . . . . . . . . . . . . . .MODIS sensor response; logarithmic ordinate . . . . . . . . . . . . . . . . .MODIS 412 nm sensor response vs. an idealized 10 nm FWHM response. .Rrs spectra as functions of the chlorophyll concentration . . . . . . . . . . .Rrs responses for the SeaWiFS 555 nm band vs. an idealized 11 nm FWHMExample out-of-band correction factor . . . . . . . . . . . . . . . . . . . . .iv.6. 9. 10. 11. 12.3941414143.515255565659. . . . . . . . . . . . .sensor. . . .616162636465

11.1 Geometry for polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67v

List of Tables1.1Radiance notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.15.2Processing Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Ancillary data needed for atmospheric correction . . . . . . . . . . . . . . . . . . . . 379.1NIR bands used for aerosol correction . . . . . . . . . . . . . . . . . . . . . . . . . . 54vi5

Part IThe Atmospheric Correction Problem1

In several recent years the NASA Ocean Biology and Biogeochemistry Program supported anintensive summer course, “Ocean Optics Summer Class: Calibration and Validation in Support ofOcean Color Remote Sensing,” at the University of Maine ( Those graduate-level classes covered both theory and instrumentation for opticaloceanography and ocean color remote sensing. During those courses, Jeremy Werdell of the NASAGoddard Space Flight Center, Ocean Biology Processing Group (OBPG) gave lectures on how theOBPG calibrates, validates, and processes ocean color data from sensors such as SeaWiFS, MODIS,and VIIRS (Werdell, 2015). His lectures outlined the many complicated steps used for atmosphericcorrection of measured at-sensor radiances and inspired this tutorial.The purpose of this tutorial is to expand upon Werdell’s lectures and review and summarizein one document the entire process of atmospheric correction as currently implemented by OBPG.The algorithms and equations presented here rest on several decades of research going all the wayback to the Coastal Zone Color Scanner (CZCS), which was launched in 1978. References aregiven to the original literature, which can be consulted for historical perspective and the scientificunderpinnings and details of the current algorithms.There are many other sources with additional information about atmospheric correction. TheNASA ocean color web site at contains a wealth ofinformation about how NASA collects, processes, calibrates, validates, archives and distributesocean color data from a variety of satellite sensors. That web site has many pages with linksto various technical memos and other information about ocean color, and many of the data filesunderlying the atmospheric correction process can be downloaded there.There are also many non-NASA sources of information on atmospheric correction. The OceanOptics Web Book ( presents basic information on opticaloceanography and ocean-color remote sensing needed to understand the present tutorial. The University of Maine website given above links to PowerPoint presentations of lectures given at the University of Maine summer courses, and to videos of the 2015 lectures. The International Ocean ColorCoordinating Group (IOCCG) has hosted summer lecture series during which the lectures werevideoed. The IOCCG lectures delivered by Menghua Wang in 2012 and 2014 ( and cover much of thematerial presented here. IOCCG report 10 s the SeaWiFS-MODIS vs. MERIS vs. OCTS-GLI vs. POLDER atmospheric correction algorithms, but assumes that the reader is already familiar with the general process.This tutorial is organized as follows. Part I first formulates the atmospheric correction problemin terms of the various contributions to the top-of-the-atmosphere (TOA) radiance measured bya satellite-borne sensor. Those contributions come from solar radiance scattered by atmosphericmolecules and aerosols, Sun and sky radiance reflected by the sea surface (either by the watersurface itself or by foam from whitecaps), and finally from water-leaving radiance. The nature andmagnitude of these contributions is then illustrated using numerical simulations from a coupledocean-atmosphere radiative transfer model. The computations of various reflectances and atmospheric transmittances are then discussed in detail. Part II then treats the various contributionsin turn, showing how each undesired contribution is estimated so that it can be removed from themeasured TOA value. The end result is an estimate of the water-leaving radiance, or its corresponding exact normalized water-leaving reflectance, which carries information about the water-column2

itself.Once obtained, the normalized water-leaving reflectance is the input to algorithms for retrievalof various quantities of scientific interest. These ocean-color products include—among others—theChlorophyll a concentration, the water-column diffuse attenuation for downwelling plane irradiance at 490 nm (Kd490, which is a proxy for water transparency), water-column absorption andbackscatter coefficients, and particulate organic and inorganic Carbon. The algorithms for retrieval of specific products, given the normalized reflectance, are given in a series of reports foundat Those retrieval algorithms are not discussedhere.3

CHAPTER1Problem FormulationThe total radiance Lt measured by a satellite-borne sensor at the top of the atmosphere (TOA)comes from contributions by atmospheric scattering, Latm ; Sun and sky radiance reflected backupward by the sea-surface and reaching the TOA, LTOAsurf ; and water-leaving radiance that reachesthe TOA, LTOA:wTOALt Latm LTOA.(1.1)surf LwFor brevity, the viewing direction (θv , φv ) and wavelength λ are not shown. Expanding this equationinto further levels of detail requires the definition of many different radiances, and precise notationis needed to minimise confusion. The atmospheric contribution Latm is always considered to beat the TOA. However, the surface-reflected radiance and water-leaving radiance can be formulatedeither at the sea surface or at the TOA. For these radiances, a superscript TOA will be used tospecify the TOA value. Thus Lw will denote the water-leaving radiance just above the sea surface,and LTOAwill denote how much of Lw reaches the TOA. Table 1.1 summarizes the various radianceswintroduced in this chapter and used throughout this report.The atmospheric contribution in Eq. (1.1), usually called atmospheric path radiance, comesfrom scattering by atmospheric gases and aerosols, including multiple scattering between gases andaerosols. The path radiance that comes solely from scattering by atmospheric gas molecules isusually called the Rayleigh radiance, LR , because scattering by molecules is well described by theRayleigh mathematical model of scattering by particles that are much smaller than the wavelengthof light. In the absence of any aerosols, the atmospheric path radiance would equal the Rayleighradiance. Let La denote the aerosol contribution, which is the path radiance that would occur ifthe atmosphere consisted only of aerosol particles. Let LaR denote the contribution resulting frommultiple scattering between aerosols and gases. The total surface reflectance can be separated intoa contribution due to direct Sun glint from the water surface, LTOA; by background sky radiancegreflected by the water surface, LTOA;andbySunandskyradiancereflected by whitecaps andskyTOAfoam, Lwc . Thus Eq. (1.1) can be further partitioned intoTOALt LR [La LaR ] LTOA LTOA LTOA.gwsky Lwc(1.2)In practice, the aerosol and aerosol-gas contributions are usually grouped together and treated asone contribution, sometimes denoted LA La LaR and often called just the aerosol contribution.4

Table 1.1: Radiance notation. Spectral radiance L has SI units of W m 2 nm 1 sr 1 ; in practicemW cm 2 µm 1 sr 1 is often used.Symbol DefinitionLttotal upwelling radiance at the top of the atmosphereLatmtotal contribution of atmospheric scattering to the TOA radianceLTOAsurftotal contribution of surface-reflected radiance to the TOA radianceLRtotal Rayleigh radiance at the TOALr“standardardized” Rayleigh radiance at the TOALaTOA radiance due to scattering by aerosols onlyLaRTOA radiance due to aerosol-molecule scatteringLALa LaR ; total aerosol radiance at the TOALwwater-leaving radiance just above the sea surfaceLTOAwthe part of the water-leaving radiance Lw that reaches the TOALgdirect Sun glint radiance just above the sea surfaceLTOAgthe part of the direct Sun glint radiance Lg that reaches the TOALskysurface-reflected background sky radiance at the sea surfaceLTOAskythe part of the surface-reflected background sky radiance Lsky thatreaches the TOALwcradiance due to whitecaps and foam just above the sea surfaceLTOAwcthe part of the whitecap radiance Lwc that reaches the TOALuupwelling underwater radiance just beneath the sea surfaceThe sky reflectance term is accounted for as part of the Rayleigh correction, which incorporatesreflectance by the sea surface. For some sensors that were specifically optimized for ocean color(e.g., CZCS and SeaWiFS), the strongest part of the Sun glint (the Sun’s glitter pattern) is avoidedby pointing the sensor in a direction away from the Sun so that almost no direct glint is presentin the image. However, there is still a correction for residual amounts of Sun glint. Figure 1.1illustrates these contributions to the TOA radiance.Most papers (e.g., Wang and Bailey, 2001; Wang, 2002) rewrite Eq. (1.2) asLt LR [La LRa ] T Lg tLwc tLw ,(1.3)or something very similar. Now, however, Lg , Lwc , and Lw are all measured at sea level. T is thedirect transmittance between the sea surface and the TOA along the viewing direction, and t isdiffuse transmittance in the viewing direction. These transmittances are discussed in §4.Yet a third formulation can be found in the literature (e.g., Franz et al., 2007, Eq. 1): Lt Lr [La Lra ] tdv Lwc tdv Lw tgv tgs fp .(1.4)5

Figure 1.1: Qualitative illustrations of the various processes contributing to the total TOA radiance.The notation corresponds to Table 1.1 and colors correspond to the spectra of Fig. 2.2. The blueN-N represents a nitrogen (N2 ) molecule, or any other atmospheric gas molecule; the brown blobrepresents an aerosol particle. The red glint terms are discussed in §2.Here tdv is the diffuse transmittance along the viewing path of the sensor. tgv is the transmittanceby atmospheric gases in the viewing direction, and tgs is the transmittance by atmospheric gases inthe Sun’s direction; these transmittances are usually called gaseous transmittances. fp is a knowninstrument polarization-correction factor. Comparison of Eqs. (1.3) and (1.4) shows, for example,thatLR Lr tgv tgs fp .Thus the total TOA Rayleigh contribution LR has been factored into a product of terms involvinga Rayleigh term times gaseous transmittances and a polarization-correction factor. The differencebetween Eqs. (1.3) and (1.4) is primarily a matter of simplification for presentation purposes. Thefp term came into the nomenclature because MODIS has large polarization sensitivity and thisrequires correction. Earlier papers by Gordon and Wang often ignored the gaseous transmissionterms because they were only considering ozone, which could be “taken off the top,” so to speak,with the remaining problem being effectively formulated below the ozone layer. The Lr term iscomputed using a standard atmosphere and only non-absorbing gases N2 and O2 . This allows“standard” Rayleigh radiances Lr to be computed as a function of Sun and viewing geometry. Thegaseous transmittances are computed by use of absorption coefficients, computed path lengths, and6

gas concentrations for the various gases. The fp term is computed for each image pixel as a functionof atmosphere and surface polarization states (modeled Rayleigh and glint Stokes vectors) and thesensor-specific polarization sensitivity with viewing direction.All of Eqs. (1.2), (1.3), and (1.4) can be found in the literature. They all give the same TOAtotal radiance Lt . Which form is used in a particular instance is determined by convenience. Forms(1.2), (1.3) are often convenient for discussions of theory, whereas form (1.4) is convenient foroperational atmospheric correction algorithms.The goal of atmospheric correction is to convert a measured top-of-the-atmosphere radiance Ltinto the corresponding sea-level water-leaving radiance Lw . Since only Lt is measured, this requiresestimation of the various atmospheric and surface-reflectance terms seen in Eqs. (1.3) or (1.4) sothat they can be subtracted from Lt in order to arrive at Lw . How this is done is the subject ofPart II of this report.7

CHAPTER2Example RadiancesLet us illustrate the magnitudes of the various radiances in Eqs. (1.2) and (1.3) with a specific example. The orbital characteristics of the proposed NASA HyspIRI (Hyperspectral InfraredImager; satellite were used to obtain the Sun zenith and azimuthal angles at the time the sensor would fly over a point at (latitude, longitude) (28.75N, 158.00 W) on June 21. This point is north of the island of Oahu in Hawaii and is knownas Station ALOHA (A Long-term Oligotrophic Habitat Assessment). Figure 2.1 shows the relevant angles needed for the simulation. A coupled HydroLight-MODTRAN ocean-atmosphereradiative transfer code was used to compute the in-water and atmospheric radiances both justabove the sea surface and at the top of the atmosphere. (HydroLight is an underwater radiative transfer code; MODTRAN is an atmospheric code; Both are widely used for radiative transfer calculationsin their respective geophysical domains.) That code can separate the Rayleigh vs. [aerosol aerosol-Rayleigh] contributions, but cannot separate the pure aerosol from the aerosol-Rayleighcontributions. Like wise, it does not normally separate Sun glint and sky glint contributions, although that separation can be effected with some extra effort (explained below). (The partitioningof atmospheric radiance contributions in the model simulations is not exactly the same as is doneoperationally, but the model simulations can still illustrate the various contributions to the TOAradiance.)A simulation was done for the following environmental conditions: The water was homogeneous and infinitely deep. The water IOPs were simulated using a chlorophyll concentration of Chl 0.05 mg m 3 inthe “new Case 1” IOP model in HydroLight. This IOP model is based on Bricaud et al. (1998)for absorption and Morel et al. (2002) for scattering. (This IOP model is described in detail at constituents of the ocean/level 2/a new iop model for case 1 water.) The Sun zenith angle was θSun 17.99 deg and the Sun’s azimuthal angle was east of thenadir point at 84.34 deg from true north.8

Figure 2.1: Sun and viewing geometry for a mid-dayHyspIRI pass over StationALOHA on 21 June. The off-nadir viewing angle was θv 30 deg, φv 281.12 deg, which is at right angles tothe satellite’s orbital direction and looking to the west side of the orbit, away from the Sun’sdirection. The atmospheric conditions (temperature profile, water vapor, ozone, etc.) were typical of atropical marine atmosphere (defined via MODTRAN’s “Tropical Atmosphere” option). Thesky conditions were clear. The aerosols were for an open-ocean marine atmosphere. The wind speed was 10 m s 1 . The wavelength resolution was 10 nm from 350 to 1500 nm.Figure 2.2 shows various radiances and irradiances obtained from this simulation. The solidcurves are values at the TOA, and the dotted curves are the corresponding quantities just abovethe sea surface. The Ed TOA curve (the solid purple line) is the extraterrestrial solar irradiance (averaged over 10 nm bands) on a surface parallel to the mean sea surface. The dips in thecurve below 700 nm are due to absorption by various elements in the Sun’s photosphere; these areFraunhofer lines averaged over the 10 nm bands of this simulation. Above 700 nm, the Sun’s irradiance is close to a blackbody spectrum (see radiometry/level 2/light from the sun). The purple dotted line shows how much of theTOA solar irradiance reaches the sea surface. There are large dips in the TOA irradiance thatreached the sea surface in the regions around 940 and 1130; these are due to absorption by watervapor, as are the smaller dips near 720 and 820 nm. The large opaque region between 1350 and1450 nm is due to water vapor and carbon dioxide. The dip at 760 nm is due to absorption byatmospheric oxygen. These absorption features of the Earth’s atmosphere will affect any radiationpassing through the atmosphere.The solid blue line shows the TOA radiance Lt that would be measured by a satellite lookingin the direction 30 deg West of the nadir point. The orange curve shows how much of the totalis atmospheric path radiance, Latm . The aqua and gray curves respectively show how much of9

Figure 2.2: Example radiances contributing to the TOA radiance. Solid lines are radiances at theTOA; dotted lines are at the sea surface (SFC). The geometric, atmospheric, and water conditionsare described in the text.the path radiance is due to Rayleigh scattering by atmospheric gases and by aerosols (includingaerosol-gas interactions). The green curves in Fig. 2.2 show that the water-leaving radiance at theTOA (the solid curve) is less than the water-leaving radiance just above the sea surface (the dottedcurve). This makes intuitive sense, because part of the water-leaving radiance would be lost toatmospheric absorption or scattering into other directions before that radiance reaches the TOA.The red curves show the total radiances due to surface reflectance, i.e., the sum of the background sky reflectance and the direct Sun glint. However, the red curves show that the surfacereflectance contribution is greater at the TOA than at the surface. This seems counterintuitive andrequires explanation. In Fig. 1.1 the arrow labeled Lg represents Sun glint due to the occasionalwave facet that is tilted in just the right direction to create glint that is seen by the sensor. Thearrow labeled Lgs represents the very bright glint in the Sun’s specular direction; the sensor is looking in the direction away from the Sun’s azimuthal direction in order to avoid viewing this specularglint. However, the specular glint gives a strong reflected radiance, some of which is being scatteredby the atmosphere into the sensor viewing direction; this is illustrated by the Lgs2 arrow in Fig.1.1. The surface contribution in Fig. 2.2 is the sum of the Lsky , Lg , and Lgs2 contributions. If theocean is viewed from just above the sea surface (the red dotted line), the surface-reflected radiancecomes only from reflected sky radiance Lsky and a small amount of direct Sun glint Lg from wavefacets that are tilted in just the right way to reflect the Sun’s direct beam into the direction ofthe sensor. (This direct Sun glint Lg is minimal because of the choice of viewing direction.) Thesesurface-reflected sky and Sun radiances decrease between the su

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