vicarious calibration of the gosat sensors using the railroad valley desert playa

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011 1781 Vicarious Calibration of the GOSAT Sensors Using the Railroad Valley Desert Playa Akihiko Kuze, D. M. O’Brien, T. E. Taylor, Jason O. Day, Christopher W. O’Dell, Fumie Kataoka, Mayumi Yoshida, Yasushi Mitomi, Carol J. Bruegge, Harold Pollock, Ralph Basilio, Mark Helmlinger, Tsuneo Matsunaga, Shuji Kawakami, Kei Shiomi, Tomoyuki Urabe, and Hiroshi Suto Abstract—Japan’s Greenhouse Gases Observing Satellite (GOSAT) was successfully launched into a sun-synchronous orbit on January 23, 2009 to monitor global distributions of carbon dioxide (CO 2 ) and methane (CH 4 ). GOSAT carries two instru- ments. The Thermal And Near-infrared Sensor for carbon Obser- vation Fourier-Transform Spectrometer (TANSO-FTS) measures reflected radiances in the 0.76 μm oxygen band and in the weak and strong CO 2 bands at 1.6 and 2.0 μm. The TANSO Cloud and Aerosol Imager (TANSO-CAI) uses four spectral bands at 0.380, 0.674, 0.870, and 1.60 μm to identify clear soundings and to provide cloud and aerosol optical properties. Vicarious calibration was performed at Railroad Valley, Nevada, in the summer of 2009. The site was chosen for its flat surface and high spectral reflectance. In situ measurements of geophysical parameters, such as surface reflectance, aerosol optical thickness, and profiles of temperature, pressure, and humidity, were acquired at the overpass times. Because the instantaneous field of view of TANSO-FTS is large (10.5 km at nadir), the spatially limited reflectance measurements at the field sites were extrapolated to the entire footprint using independent satellite data. During the campaign, six days of measurements were acquired from two different orbit paths. Spectral radiances at the top of the atmosphere were calculated using vector radiative transfer models coupled with ground in situ data. The agreement of the modeled radiance spectra with those measured by the TANSO-FTS is within 7%. Significant degradations in responsivity since launch have been detected in the short-wavelength bands of both TANSO-FTS and TANSO-CAI. Manuscript received April 15, 2010; revised September 24, 2010; accepted October 17, 2010. Date of publication December 6, 2010; date of current version April 22, 2011. The work at Colorado State University was supported by the National Aeronautics and Space Administration under Contract 1280999 and Contract NNX06AC76G. A. Kuze, S. Kawakami, K. Shiomi, T. Urabe, and H. Suto are with the Japan Aerospace Exploration Agency, Tsukuba 305-8505, Japan (e-mail: kuze. [email protected]). D. M. O’Brien and C. W. O’Dell are with the Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, CO 80523-1375 USA. T. E. Taylor is with the Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371 USA. J. O. Day was with the Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371 USA. He is now with the National Science Foundation, Washington, DC 20006-4403 USA. F. Kataoka, M. Yoshida, and Y. Mitomi are with the Remote Sensing Technology Center of Japan, Tsukuba 305-0032, Japan. C. J. Bruegge, H. Pollock, and R. Basilio are with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109-8099 USA. M. Helmlinger is with the Northrop Grumman Aerospace Systems, Redondo Beach, CA 90278 USA. T. Matsunaga is with the National Institute for Environment Studies, Tsukuba 305-8506, Japan. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2010.2089527 Index Terms—Carbon dioxide (CO 2 ), Greenhouse Gases Ob- serving Satellite (GOSAT), thermal and near-infrared sensor for carbon observation (TANSO), vicarious calibration. I. I NTRODUCTION G REENHOUSE Gases Observing Satellite (GOSAT) is designed to retrieve highly accurate column-averaged mixing ratios of carbon dioxide (CO 2 ) and methane (CH 4 ) from space. GOSAT is a joint project of the Japan Aerospace Exploration Agency (JAXA), the Ministry of the Environ- ment, and the National Institute for Environmental Studies (NIES). There are two instruments aboard GOSAT. The Ther- mal And Near-infrared Sensor for carbon Observation Fourier- Transform Spectrometer (TANSO-FTS) detects short-wave infrared (SWIR) radiation reflected by the Earth’s surface as well as thermal infrared radiation from the ground and the atmosphere [1]. TANSO-FTS measures three narrow bands (0.76, 1.6, and 2.0 μm) and one wide band (5.5–14.3 μm) with 0.2-cm 1 spectral resolution. The specifications of TANSO- FTS are listed in [1, Table II]. The instantaneous field of view (IFOV) of TANSO-FTS is captured via a simple in-line optical camera (CAM) with specifications described in [1, Table III]. The second instrument aboard GOSAT is the TANSO Cloud and Aerosol Imager (TANSO-CAI), which is a radiometer with ultraviolet (UV), visible, and SWIR bands (summarized in [1, Table IV]), used to detect and correct for cloud and aerosol contamination [2]. In this paper, TANSO-CAI appears in two roles: it is used to map spatial variations of reflectance across the Railroad Valley (RRV) playa when calibrating TANSO- FTS, and it is also the subject of vicarious calibration. Many details related to each instrument design, hardware perfor- mance, on-orbit operation, and data processing are provided in [1]. GOSAT was successfully launched on January 23, 2009, from Tanegashima Space Center, Japan. The function and performance of all systems were verified to meet operating standards during the initial three-month checkout phase [3]. The second three-month phase (May–July, 2009) includes the initial calibration requirement. JAXA’s GOSAT team is responsible for the development of the TANSO instruments, the satellite launch and operation, and the level-1 data processing. The National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory (JPL) launched its Orbiting Carbon Ob- servatory (OCO) [4] a month later on February 24, but OCO failed to reach orbit. Subsequently, NASA JPL’s Atmospheric CO 2 Observations from Space (ACOS) team has been involved 0196-2892/$26.00 © 2010 IEEE

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011 1781

Vicarious Calibration of the GOSAT SensorsUsing the Railroad Valley Desert Playa

Akihiko Kuze, D. M. O’Brien, T. E. Taylor, Jason O. Day, Christopher W. O’Dell, Fumie Kataoka,Mayumi Yoshida, Yasushi Mitomi, Carol J. Bruegge, Harold Pollock, Ralph Basilio, Mark Helmlinger,

Tsuneo Matsunaga, Shuji Kawakami, Kei Shiomi, Tomoyuki Urabe, and Hiroshi Suto

Abstract—Japan’s Greenhouse Gases Observing Satellite(GOSAT) was successfully launched into a sun-synchronous orbiton January 23, 2009 to monitor global distributions of carbondioxide (CO2) and methane (CH4). GOSAT carries two instru-ments. The Thermal And Near-infrared Sensor for carbon Obser-vation Fourier-Transform Spectrometer (TANSO-FTS) measuresreflected radiances in the 0.76 μm oxygen band and in the weakand strong CO2 bands at 1.6 and 2.0 μm. The TANSO Cloudand Aerosol Imager (TANSO-CAI) uses four spectral bands at0.380, 0.674, 0.870, and 1.60 μm to identify clear soundings and toprovide cloud and aerosol optical properties. Vicarious calibrationwas performed at Railroad Valley, Nevada, in the summer of2009. The site was chosen for its flat surface and high spectralreflectance. In situ measurements of geophysical parameters,such as surface reflectance, aerosol optical thickness, and profilesof temperature, pressure, and humidity, were acquired at theoverpass times. Because the instantaneous field of view ofTANSO-FTS is large (10.5 km at nadir), the spatially limitedreflectance measurements at the field sites were extrapolatedto the entire footprint using independent satellite data. Duringthe campaign, six days of measurements were acquired fromtwo different orbit paths. Spectral radiances at the top of theatmosphere were calculated using vector radiative transfer modelscoupled with ground in situ data. The agreement of the modeledradiance spectra with those measured by the TANSO-FTSis within 7%. Significant degradations in responsivity sincelaunch have been detected in the short-wavelength bands of bothTANSO-FTS and TANSO-CAI.

Manuscript received April 15, 2010; revised September 24, 2010; acceptedOctober 17, 2010. Date of publication December 6, 2010; date of currentversion April 22, 2011. The work at Colorado State University was supportedby the National Aeronautics and Space Administration under Contract 1280999and Contract NNX06AC76G.

A. Kuze, S. Kawakami, K. Shiomi, T. Urabe, and H. Suto are with theJapan Aerospace Exploration Agency, Tsukuba 305-8505, Japan (e-mail: [email protected]).

D. M. O’Brien and C. W. O’Dell are with the Cooperative Institute forResearch in the Atmosphere, Colorado State University, Fort Collins, CO80523-1375 USA.

T. E. Taylor is with the Department of Atmospheric Science, Colorado StateUniversity, Fort Collins, CO 80523-1371 USA.

J. O. Day was with the Department of Atmospheric Science, Colorado StateUniversity, Fort Collins, CO 80523-1371 USA. He is now with the NationalScience Foundation, Washington, DC 20006-4403 USA.

F. Kataoka, M. Yoshida, and Y. Mitomi are with the Remote SensingTechnology Center of Japan, Tsukuba 305-0032, Japan.

C. J. Bruegge, H. Pollock, and R. Basilio are with the Jet PropulsionLaboratory, California Institute of Technology, Pasadena, CA 91109-8099USA.

M. Helmlinger is with the Northrop Grumman Aerospace Systems, RedondoBeach, CA 90278 USA.

T. Matsunaga is with the National Institute for Environment Studies,Tsukuba 305-8506, Japan.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2010.2089527

Index Terms—Carbon dioxide (CO2), Greenhouse Gases Ob-serving Satellite (GOSAT), thermal and near-infrared sensor forcarbon observation (TANSO), vicarious calibration.

I. INTRODUCTION

GREENHOUSE Gases Observing Satellite (GOSAT) isdesigned to retrieve highly accurate column-averaged

mixing ratios of carbon dioxide (CO2) and methane (CH4)from space. GOSAT is a joint project of the Japan AerospaceExploration Agency (JAXA), the Ministry of the Environ-ment, and the National Institute for Environmental Studies(NIES). There are two instruments aboard GOSAT. The Ther-mal And Near-infrared Sensor for carbon Observation Fourier-Transform Spectrometer (TANSO-FTS) detects short-waveinfrared (SWIR) radiation reflected by the Earth’s surface aswell as thermal infrared radiation from the ground and theatmosphere [1]. TANSO-FTS measures three narrow bands(0.76, 1.6, and 2.0 μm) and one wide band (5.5–14.3 μm) with0.2-cm−1 spectral resolution. The specifications of TANSO-FTS are listed in [1, Table II]. The instantaneous field of view(IFOV) of TANSO-FTS is captured via a simple in-line opticalcamera (CAM) with specifications described in [1, Table III].The second instrument aboard GOSAT is the TANSO Cloudand Aerosol Imager (TANSO-CAI), which is a radiometer withultraviolet (UV), visible, and SWIR bands (summarized in[1, Table IV]), used to detect and correct for cloud and aerosolcontamination [2]. In this paper, TANSO-CAI appears in tworoles: it is used to map spatial variations of reflectance acrossthe Railroad Valley (RRV) playa when calibrating TANSO-FTS, and it is also the subject of vicarious calibration. Manydetails related to each instrument design, hardware perfor-mance, on-orbit operation, and data processing are providedin [1].

GOSAT was successfully launched on January 23, 2009,from Tanegashima Space Center, Japan. The function andperformance of all systems were verified to meet operatingstandards during the initial three-month checkout phase [3]. Thesecond three-month phase (May–July, 2009) includes the initialcalibration requirement. JAXA’s GOSAT team is responsiblefor the development of the TANSO instruments, the satellitelaunch and operation, and the level-1 data processing. TheNational Aeronautics and Space Administration (NASA) JetPropulsion Laboratory (JPL) launched its Orbiting Carbon Ob-servatory (OCO) [4] a month later on February 24, but OCOfailed to reach orbit. Subsequently, NASA JPL’s AtmosphericCO2 Observations from Space (ACOS) team has been involved

0196-2892/$26.00 © 2010 IEEE

1782 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

in the vicarious calibration of GOSAT and the retrieval of CO2

and related geophysical parameters from GOSAT level-1 data.Although CO2 is determined from GOSAT radiance spectra

via a differential absorption method that minimizes systematicerrors in the measurements, the GOSAT operational retrievalalgorithm requires an absolute radiometric calibration. Theinversion algorithm first computes spectral radiances at the topof the atmosphere (TOA) with likely scenarios of the surfaceand atmospheric state for scenes determined to be relativelyfree of cloud and aerosol [5]. Perturbations are made in theassumptions until the modeled and measured absolute radiancesagree. Accurate radiometric calibration therefore is essential forthe retrieval of state parameters, such as the surface reflectanceand the aerosol amount, which impact the observed radiancesignature. One of the mission requirements was to achievean absolute radiometric accuracy of better than ±5% prior tolaunch to achieve 1 ppm accuracy of column-averaged mixingratios of CO2. The laboratory calibrations used integratingspheres, which were cross calibrated with GOSAT and OCOstandard radiometers. The cross-calibration results agree tobetter than 1.8% at 0.76 μm, 1.6% at 1.6 μm, and 1.4% at2.0 μm, confirming that the required calibration standard of 5%uncertainty has been surpassed [6].

In orbit, two routine onboard calibrations are performed forTANSO-FTS SWIR bands 1, 2, and 3. The solar irradiancecalibration uses an onboard diffuser plate made of Spectralon.Direct solar light is reflected from the plate and directed tothe FTS optics, providing a well-known calibration source.The front side of the diffuser plate is exposed on every orbit,whereas the back of the plate is illuminated only once permonth by rotating the plate. The second on-orbit calibration isa lunar calibration, in which the GOSAT is rotated and pointedat the lunar surface, which has stable reflectance. For TANSO-CAI, only the lunar calibration is performed. However, there areuncertainties in the on-orbit calibrations. First, the diffuser plateshows degradation in its reflectivity caused by exposure to UVradiation. Second, there is some uncertainty in the lunar surfacereflectance database. These issues highlight the importance ofperforming a vicarious calibration after launch of the satellite.

As stated in the JAXA/NIES requirements for GOSAT, thefirst vicarious calibration campaign has to be performed duringthe initial calibration phase (within six months of launch).Although the vicarious campaign described here has largeruncertainties than those from the prelaunch calibration, thefollowing requirements have been met by the field campaign:an accuracy of better than 10% and at least three good datasets measured by TANSO-FTS (bands 1, 2, and 3) and TANSO-CAI, each supported by ground-based in situ data.

II. VICARIOUS CALIBRATION EXPERIMENT

A. Overview

The vicarious calibration campaign was performed in theRRV desert playa, Nevada (38.497◦ N, 115.691◦ W, height1437 m), by the JAXA GOSAT and NASA ACOS teams.The field sites from where ground measurements were takenlie on a dry lake bed within the Great Basin desert and are

Fig. 1. GOSAT paths 36 and 37 that pass close to RRV.

Fig. 2. TANSO-FTS observation geometry for RRV from GOSAT paths 36and 37.

characterized by loose sandy soil with virtually no vegetation.The measurement campaign took place during the dry seasonfrom June 23 to July 5, 2009. Unfortunately, in the summer of2009, the weather throughout the American west was unusuallywet, so there were several days with clear skies, some withcloud, and a short period of heavy rain during the campaign.

GOSAT is in a sun-synchronous orbit at an altitude of666 km with an inclination of 98◦. The local nadir overpasstime is approximately 12:47 PM, and the ground speed of6.8 km/s produces a three-day repeat cycle with a total of44 paths. Since RRV is located between paths 36 and 37, asshown in Fig. 1, it is not observed by TANSO-FTS in its nor-mal scanning mode. However, by uploading tables containingcross-track (CT) and along-track (AT) pointing angles, and byspecifying the observation start time in advance, TANSO-FTScan view RRV in target mode. Fig. 2 shows the geometry forviewing RRV from paths 36 and 37, which have viewing timesof 20:44 and 21:16 UTC, respectively. Unlike TANSO-FTS,TANSO-CAI has a wide swath of ±36.1◦ for bands 1, 2, and3 with 500-m spatial resolution and ±30.0◦ for band 4 with1500-m spatial resolution. Therefore, from path 36, all fourbands lie within the instrument field of view (FOV), whereasfrom path 37, only bands 1, 2, and 3 cover RRV.

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1783

Fig. 3. Selected base camp and observation sites superimposed on an imagefrom CAM bore sighted with TANSO-FTS. The ellipses represent typicalTANSO-FTS footprints from paths 36 and 37.

B. Selection of the Sites

In nadir viewing mode, the IFOV of TANSO-FTS is15.8 mrad, which projects to a footprint with a 10.5 km di-ameter at the Earth’s surface. This is a large IFOV comparedwith many space-borne instruments. Since it is not feasibleto measure the reflectance of the entire footprint from theground with fine spatial resolution, a site that is approximatelyuniform over the TANSO-FTS IFOV must be chosen for thevicarious calibration. In addition, the probabilities of clearsky and low aerosol optical thickness should be high. Severalcandidates were considered, including Tinga Tingana, Australia(28◦ S, 139◦ E), RRV, and the Sahara Desert. Ultimately, RRVwas chosen for its relatively good accessibility as well asprevious experience at that site [7]–[9].

Using data measured in band 3 of the TANSO-CAI prior tothe field experiment on May 15, 2009, when no precipitationwas detected, 60 sites within RRV were selected for spatialuniformity of the reflectance over 3 × 3 TANSO-CAI pixels.Each site is designated with a number and a letter, the latterbased on the measured reflectance in TANSO-CAI band 3. Theletter H represents high estimated reflectance (39%–50%), Mrepresents medium reflectance (37%–39%), and L representslow reflectance (30%–37%). The final selection of seven sitesfrom the 60 sites, shown in Fig. 3, was based on ease of accessfrom local roads for logistical reasons.

C. Aerosol and Meteorological Measurements

During the field campaign, a base camp was establishedon the RRV playa at 38.5044◦ N, 115.6925◦ W, closeto the AErosol RObotic NETwork (AERONET) site [10].The AERONET cloud-screened (L1.5) aerosol optical depths(AOD) at 1020 and 500 nm at the approximate overpass times

TABLE IRRV AOD AT 1020 AND 500 nm AFTER CLOUD SCREENING AT THE

APPROXIMATE OVERPASS TIMES OF GOSAT

Fig. 4. Profiles of temperature (solid line) and relative humidity (bold line)measured with a Vaisala sonde on 2009-06-27.

of GOSAT are shown in Table I. In addition, included arethe values of the Ångström exponent from the cloud-screeneddata, which provides information about the aerosol size andtype [11]. During the field campaign, relatively large values ofthe Ångström exponent (between 1.5 and 1.9) indicate smallparticles, consistent with background aerosol.

To provide vertical profiles of pressure, temperature andrelative humidity needed for the radiative transfer calculations,a model RS92-SGP Vaisala sonde was launched over the playafrom the base camp at the time of each GOSAT overpass.The horizontal drift during the sonde flight was small. As anexample, Fig. 4 shows the measured profiles from the June 27launch, which reached a height above the tropopause of about24 km in 100 min.

D. Surface Reflectance Measurements

In an attempt to determine representative values of the sur-face reflectance of the TANSO-FTS and TANSO-CAI foot-prints, the surface reflectance was measured from the ground atseveral locations on the playa around the times of the GOSAToverpasses. These measurements were made by field crews us-ing commercial Analytical Spectral Devices Inc. (ASD) Field-Spec spectrometers, specifications for which are summarized inTable II. These units contain three detectors that operate in threewavebands from 350 to 2500 nm. This covers both the TANSO-FTS SWIR bands 1, 2, and 3, and also the TANSO-CAIbands 1, 2, 3, and 4.

Surface reflectance measurements were made at the sevenselected sites shown in Fig. 3. Fig. 5 illustrates the configurationof a typical measurement grid, whose area is equal to that ofthe TANSO-CAI footprints in bands 1, 2, and 3. During each

1784 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

TABLE IISPECIFICATIONS OF THE ASD FIELDSPEC SPECTROMETERS

Fig. 5. Grid on which the surface reflectance was measured with ASDspectrometers. Large circles show the locations of the Spectralon targets usedfor calibration.

Fig. 6. Measurement configuration showing the ASD spectrometer and theSpectralon reference panel used for calibration. The spectralon panel wascarefully leveled so as to be plane parallel to the regional surface.

GOSAT overpass, the field crew carried the ASD spectrometerand controlling computer at steady speed from point 1 topoint 21 (Fig. 5) in ascending order. Measurements of thesurface reflectance were acquired continuously along the path.The fore optics of the ASD were mounted at the end of a1 meter pole, with the observer holding the other end of the poleto avoid shadowing the ASD target, as depicted in Fig. 6. Whenthe field operator reached each corner of the central square, i.e.,points 1, 6, 11, 16, and 21 in Fig. 5, several reference spectrafrom a Spectralon panel were acquired. The gain was set at the

Fig. 7. Surface reflectance measured with an ASD spectrometer for site L08on 2009-06-27. The bold line shows the mean reflectance, whereas the dottedlines lie one standard deviation from the mean.

beginning, point 1 of Fig. 5, and as required during the sequenceto adjust for sensor saturation. In addition, dark current wasmeasured at each Spectralon panel.

During the field measurements, seven Spectralon diffuserpanels were available for use. Three were selected as refer-ences, only to be used at the base camp for intercomparisonof all the panels. Therefore, those units were not exposed asfrequently to the harsh desert conditions. The remaining fourpanels were deployed to the field measurement grids to performthe calibrations described above. A quick intercomparison wasperformed between all panels, and no significant difference be-tween the seven panels was detected, except for the wavelengthregion much shorter than TANSO-FTS band 1.

After the initial data processing, including accumulatingspectra, performing gain correction, and removing outliers fromthe time series, the counts (digital numbers) are converted intomeasured reflectance via

rsurface =

(Rsurface

Rspectralon

)BRDFspectralon ρspectralon

where Rsurface is the response in counts measured by theASD over the desert surface, and Rspectralon is the responsemeasured by the ASD over the Spectralon panels, the latterinterpolated to the time of the surface measurement. The valueof BRDFspectralon is calculated for the particular geometry ofthe measurement, and ρspectralon is the hemispheric reflectanceof Spectralon as reported by the manufacturer.

The interpolation of the Spectralon reflectance to the time ofthe surface measurements is an important step. Simple interpo-lation is problematic because the Spectralon signals are subjectto systematic variations, principally caused by movement of thesun, and unpredictable variations, such as imperfect levelingof the tripod-mounted Spectralon panel by the operator. Thesystematic trends are removed by normalizing each Spectralonmeasurement by the cosine of the solar zenith angle and theBidirectional Reflectance Distribution Function (BRDF) of theSpectralon for the geometry prevailing at the time of the mea-surement. The resulting signals are then averaged to eliminatethe remaining random variations. Finally, the Spectralon signalis reconstructed as the product of the average, the cosine of thesolar zenith angle, and the BRDF.

Fig. 7 shows the mean of the reflectance samples acquiredon June 27 at site L08. The dotted curves are one standard

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1785

Fig. 8. Images of RRV by CAM that is aligned with TANSO-FTS. Superimposed on the CAM images are the actual TANSO-FTS footprints taken from path 36(left) and path 37 (right) estimated from the CAM data.

deviation from the mean, indicating the uncertainty in the meanreflectance. The gaps at 1340–1440 and 1800–1950 nm arecaused by water vapor absorption. These reflectances mustbe extrapolated to the large footprint of TANSO-FTS via themethod outlined in Section III.

E. Footprint Registration

Level-1 data contain the latitude and longitude of the cen-ter and corners of the IFOV of TANSO-FTS. The CT andAT angles of the pointing mechanism are recorded by theonboard resolver, which might have a slight offset on orbit.Consequently, footprint locations in level-1 data, which arecalculated from the resolver and satellite position, possibly havesmall errors that must be corrected using independent data.For this purpose, CAM was rigidly mounted on the opticalbench and carefully aligned with TANSO-FTS before launch.Because the mounting is rigid, it is reasonable to assume thatthe alignment was not changed by the launch. CAM has a largerFOV than TANSO-FTS, allowing features in the FOV to beidentified, thereby fixing the true position of the TANSO-FTSfootprints. Fig. 8 shows CAM images of RRV on which aresuperimposed the actual footprints of TANSO-FTS from paths36 and 37, which are accurately registered using the positionsof the surrounding mountains.

III. CORRECTIONS FOR PLAYA INHOMOGENEITY

Because the area of the playa sampled by the field crew(∼0.25 km2) is much smaller than the TANSO-FTS footprint(∼80 km2), a method had to be devised to extrapolate from thereflectance measured at the field site to the whole TANSO-FTSfootprint. Several techniques were tried.

The first involved using the simultaneous TANSO-CAI im-age of the playa. TANSO-CAI has wide and continuous spatialcoverage with 500-m resolution in bands 1, 2, and 3 at 0.380,0.674, and 0.870 μm, and 1500 m in band 4 at 1.600 μm. Theentire area of the TANSO-FTS IFOV is about 320 TANSO-CAI 500 m pixels. By averaging the radiances of these pixels,the average reflectance over the TANSO-FTS footprint can beestimated as follows. If Ci0,j0(λ) denotes the reflectance at

wavelength λ measured with the ASD spectrometer at TANSO-CAI pixel (i0, j0) on the playa, then the IFOV-averaged re-flectance C(λ) may be approximated by

C(λ) =

(L(λm)

Li0,j0(λm)

)Ci0,j0(λ) (1)

where Li0,j0(λm) is the TANSO-CAI radiance for pixel (i0, j0)in the band whose central wavelength λm is closest to λ,and L(λm) is the average radiance measured by TANSO-CAI over the TANSO-FTS footprint. This calculation does notrequire absolute calibration of TANSO-CAI; it suffices that theTANSO-CAI signal be proportional to the radiance.

Although TANSO-CAI and TANSO-FTS are on the samesatellite and view the playa from the same direction, thisapproach does not eliminate BRDF effects, because the ASDviewed the surface from directly above. Consequently, thecalibration results derived using path 36 observations to theeast were systematically different from those for path 37 tothe west. An additional complication is that TANSO-CAI doesnot have a channel near 2.0 μm, so TANSO-CAI could not actas a transfer standard for reflectance in band 3 of TANSO-FTS.Finally, because the pixels in the 1.6 μm band of TANSO-CAIare larger (1500 m), this band of TANSO-CAI was not able toobserve the playa from path 37.

In view of these difficulties, an alternative method to ex-trapolate the measured surface reflectance to the full TANSO-FTS footprint was developed using the MODerate resolutionImaging Spectroradiometer (MODIS). The mathematical for-mulation is relegated to the appendix, but the ideas behind themethod are straightforward and are summarized here. First, asingle MODIS radiance image (MYD02) for a cloud-free dayis used to provide the relative brightness of all pixels on theRRV playa. Thus, if the field crew measured the reflectance attarget H03 (for example), then it is assumed that they wouldhave obtained the spectrum

Spectrum at P =MODIS radiance at P

MODIS radiance at H03×Spectrum at H03

if they had been able to measure simultaneously at pixel P. TheMODIS radiance measurements are made with geometry (both

1786 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

TABLE IIIQUALITY OF THE DATA SETS

sun and satellite) different from GOSAT; but nonetheless, itis assumed that the spectra scale as indicated above. Second,MODIS BRDF data [12], [13] are used to compensate for thedifferent directions of observation, downwards for the ASDand obliquely for GOSAT. This method leads to a BRDF withstandard MODIS kernels (basis functions for the BRDF) butscaled to be consistent with the field measurements at the testsite. All results presented in this paper use this method.

IV. DATA ANALYSIS

A. Measured Radiance From Prelaunch Calibration Data

TANSO-FTS level-1B files contain raw spectra in units ofV/cm−1 with 0.2-cm−1 spectral interval. TANSO-CAI level-1A files contain raw counts. Together with level-1 data, radi-ance conversion tables for TANSO-FTS and TANSO-CAI areprovided. These tables are based on the prelaunch calibrationperformed with the integrating spheres at JAXA. Before apply-ing the TANSO-CAI radiance conversion, the dark offset mustbe subtracted, and the counts must be divided by the integrationtime. Finally, spectral radiances in units of W/cm2/sr/cm−1 forTANSO-FTS and in units of W/m2/sr/μm for TANSO-CAI areobtained simply by multiplying the calibration factors from thetables.

B. Polarization Model

As the surface of the playa is assumed to be weakly po-larizing, the atmosphere over RRV has low scattering opticalthickness, and the observation geometry is not far from nadir,polarization is not critical for vicarious calibration. Neverthe-less, because TANSO-FTS simultaneously measures two linearpolarizations, the radiative transfer calculations took polariza-tion into account using the model outlined in [1] and [14]. TheStokes vectors incident upon the P and S channel detectors of

TANSO-FTS, denoted SP,output and SS,output, are related tothe incident Stokes vector Sinput by

SP,output =MPpMoptMr(−2ΘCT)

×Mm(ΘAT)Mp(ΘAT)Mr(2ΘCT)Sinput

SS,output =MSpMoptMr(−2ΘCT)

×Mm(ΘAT)Mp(ΘAT)Mr(2ΘCT)Sinput

where MPp and MSp are the Mueller matrices of the polar-ization beam splitters, Mopt represents the optical efficiencyof the FTS mechanism and after optics, which consist of tele-scopes, band separation optics, and collecting optics, Mr(Θ)represents a rotation through angle Θ, Mm represents reflectionat the pointing mirror, and Mp represents the phase differenceintroduced by the optical coating on the pointing mirror. Finally,ΘCT and ΘAT denote the CT and AT scan angles.

In practice, vector radiative transfer codes were used tocompute the Stokes vector at the TOA using as inputs theoptical properties of the atmosphere and surface, which arederived from meteorological, aerosol, and ASD observations, asdescribed above. Two linear polarizations were computed andcompared with the measured values.

C. Data Quality

A summary of the weather conditions and the ASD datacollected at the time of the six GOSAT overpasses during thefield campaign is given in Table III. There were nine days ofGOSAT overpasses but three were cloudy. During each over-pass, two ASD teams were deployed, providing simultaneousground reflectance information at sites with different surfacecharacteristics. Two of the ASD data sets were rejected fromthe final GOSAT calibration analysis (site H03 on 2009-06-23and site H03 on 2009-07-03) due to high standard deviationsin the measured responses. Four of the remaining ten data sets

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1787

were considered passable but not ideal due to such issues ascomplications with incorrect setting of the ASD internal clock,high standard deviations in the measured counts, a late start dueto failed ASD battery, and in one case erratic measurementsaround Spectralon panel references. Ultimately, ten data setswere retained for calibration of the TANSO-FTS, as will bediscussed in Section V.

D. Models for Calculating TOA Radiances

To calibrate the spectral radiance measured by TANSO-FTS and TANSO-CAI, the polarized radiance at the TOAis simulated with a radiative transfer model. The input datafor the model are the IFOV-averaged surface reflectance (orBRDF), the vertical profiles of pressure, the relative humidityand temperature from the radiosonde, and the aerosol opticalthickness estimated from the Cimel sun photometer at the RRVAERONET site.

For the TANSO-FTS simulations, the radiative transfer codeis that used by the GOSAT simulator at Colorado State Uni-versity [14]. The scalar radiance is computed using the suc-cessive order of interaction model [15], [16], with accelerationprovided by the low-stream interpolator [17]. Calculation ofthe polarized radiance employs a second-order-of-scatteringapproximation to reach accurate results in optically thin media[18]. Because the optical thickness of aerosol is low at RRV,a simple model for its vertical distribution suffices. If theÅngström coefficient is large, indicating small particles, thenthe aerosol is assumed to be continental aerosol, and it islocated in layers near the surface. Conversely, if the Ångströmcoefficient is small, indicating large particles, then the aerosolis assumed to be thin cirrus, the optical properties of whichare derived from a temperature-dependent size distribution [19]with phase matrices based partly on observation and partly onmodeling of scattering by ice crystals [20], [21]. In practice,the Ångström coefficient was large throughout the campaign.The model also accounts for the dispersion, instrument lineshape function and Mueller matrix of the GOSAT FTS, soseparate spectra for the P and S polarizations are computed. Anempirically determined spectral shift is included to representalignment drift with time of the FTS.

For the TANSO-CAI simulations, the radiative transfer wasperformed using the RSTAR/PSTAR code [22] with HITRAN2008 providing the spectroscopy. In simulating spectra forTANSO-CAI, 12 spectral points were used in bands 1 and 4,and ten points were used in bands 2 and 3. Again, the meteo-rology was derived from the radiosonde ascent, and the aerosolproperties were inferred from AERONET. The atmosphere wasdivided into layers 0–2, 2–3, 3–5, and 5–120 km. The surfacewas assumed to be Lambertian.

The model of the solar irradiance spectrum developed byToon (private communication) is the default for this paper.

V. CALIBRATION OF TANSO-FTS

Figs. 9 and 10 compare the calculated and measured spectrafor one day of the campaign (June 27), one site (L08), and onepolarization (P). Plots for other days, sites, and polarizations

Fig. 9. Calculated and measured spectra for P polarization, the latter deter-mined with the preflight calibration. Field measurements at site L08 on 2009-06-27 were used for the surface properties.

are similar and, therefore, omitted. Fig. 9 shows the spectraas functions of frequency, whereas Fig. 10 is a scatter plot ofthe preflight calibrated radiance against the calculated radiance.The measured spectra were obtained from the GOSAT L1B fileby applying the preflight radiometric calibration coefficients forall the SWIR bands. In the scatter plots, the slope of the line ofbest fit passing through the origin gives the relative calibration,measured versus calculated. Table IV shows the slopes for theSWIR bands and both polarizations derived using data from thecloud-free days and the measurement sites selected in Table III.Although there is scatter within the columns of the table, it isat least a factor of 2 smaller than when TANSO-CAI is usedto map the reflectance across the footprint and the BRDF ofthe surface is ignored. The standard deviations of the selectedobservations are 2.6%, 2.8%, and 3.6% for the P-polarizationin bands 1, 2, and 3. The results for the S-polarization aresimilar.

1788 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

Fig. 10. Scatter plots of calculated versus measured P polarization, the latterdetermined with the preflight calibration. Field measurements at site L08 on2009-06-27 were used for the surface properties.

VI. CALIBRATION OF TANSO-CAI

Radiometric calibration of TANSO-CAI is simpler than forTANSO-FTS because the area of the TANSO-CAI footprintis approximately the same as that sampled by the field crew.Therefore, the TOA radiance calculated using the reflectancederived from the ASD spectrum may be compared directly withthe TANSO-CAI radiance for the pixel covering the field site.The only refinement needed is a convolution of the simulatedhigh-resolution radiance spectrum with filter transfer functionsfor the TANSO-CAI bands. In principle, a BRDF correctionshould also be applied because the ASD measured the nadirreflectance, whereas TANSO-CAI viewed the target from anoblique angle. This correction will be applied in future work.To minimize the BRDF effect of bands 1, 2, and 3, the resultsfrom equal numbers of path 36 and 37 observations can be av-eraged, because TANSO-CAI measures forward and backwardreflections on paths 36 and 37, respectively.

TABLE IVSLOPE OF THE LINEAR RELATION BETWEEN THE

PREFLIGHT-CALIBRATED RADIANCE AND THE CALCULATED

RADIANCE FOR THE SELECTED DATA SETS

Fig. 11. Comparison between TOA-measured radiance and simulated radi-ance in the TANSO-CAI bands, the former using the preflight calibration. Theupper and lower panels are for paths 36 and 37, respectively. The simulationsfor TANSO-CAI bands 1 and 2 used the solar model from [25], whereas thosefor bands 3 and 4 used Toon’s model.

Daily comparisons between the simulated and measuredTOA radiances from TANSO-CAI are shown in Fig. 11. Theradiances measured from orbit path 37 are significantly higherin TANSO-CAI bands 2 and 3, possibly due to the surfaceBRDF. Finally, Table V compares the TANSO-CAI-measuredradiance with the simulated radiance at the TOA for June 27and July 2. It is clear that there has been large degradation(exceeding 10%) in TANSO-CAI bands 1 and 4 compared withthe preflight calibration. Observations over other targets alsoindicate degradation in bands 1 and 4.

In band 1, the most likely cause of reduction in responseis deterioration of the optics. In band 4, there are three

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1789

TABLE VCOMPARISON BETWEEN TANSO-CAI-MEASURED RADIANCE AT THE

TOA AND RADIATIVE TRANSFER MODEL CALCULATIONS

FOR 2009-06-27 AND 2009-07-02

TABLE VIAPPROXIMATE ERROR BUDGET FOR THE VICARIOUS

CALIBRATION OF TANSO-FTS

plausible reasons. The first, and most likely, is degradation ofthe optics. The second is related to the IFOV and the out-of-pixel response. The TANSO-CAI pixels were specified tobe square, but the masking of the detector was not perfect.Consequently, TANSO-CAI band 4 might be detecting straylight from a few kilometers away from the target. At RRV,that stray light could come from areas with low reflectance,such as the vegetated regions south of the playa. The thirdreason is possible contamination (such as ice) on the surfaceof the cooled InGaAs detector. However, the probability is low,because the InGaAs detector array is installed in a package andhermetically sealed.

VII. DISCUSSION

A. Approximate Error Budget

Estimates of errors from the major sources of uncertainty inthe vicarious calibration are summarized in Table VI. As thesurface of the playa is diffusive and the polarization sensitivityis small, the largest error sources are related to the reflectancemeasurements, the averaging over the TANSO-FTS footprint,and the solar irradiance model.

The differences between the P and S polarizations measuredby TANSO-FTS were very small; typically, the ratio

〈IP − IS〉/〈IP + IS〉

was less than 0.5%, where the angular brackets denote the meanvalue over the set of frequencies where the total intensity I =IP + IS exceeds a threshold well above the noise. This figurewas adopted as an estimate of the relative error caused by usinga nonpolarizing model of the surface.

To assess the sensitivity to aerosol, TOA radiances were sim-ulated for 2009-06-27 with the aerosol modeled as describedearlier and also with the aerosol optical thickness set to zero.The continuum intensities in the O2 A-band at 13190 cm−1

differed by 0.8%. This was taken as a rough measure of theerror that might be caused by incorrect vertical distribution ofaerosol or incorrect assignment of its optical properties.

The error due to BRDF was estimated by using differentBRDF releases for RRV. Provided that the lake bed was notcovered by snow or flooded between the BRDF releases, thepredicted reflectances for the sun-target-satellite geometry dif-fered by less than 1%.

The pointing instability is much smaller than 1 km at thesurface. As TANSO-FTS has only a single pixel and usesaspherical optics, the optical aberrations are small. Therefore,the radiance error due to IFOV estimation is likely to be lessthan 2%.

The method to extrapolate the reflectance measured at thefield sites to the TANSO-FTS IFOV appears to be robust. Thestandard deviations of the measurements on the selected daysare 2.6%, 2.7%, and 3.6% in bands 1, 2, and 3, respectively. InTable VI, a figure of 3% has been assumed for all bands. Thisfigure includes both the error in the ASD spectra and the errorin extrapolating from the field site to the TANSO-FTS footprint.

Assuming that several sources of error are independent, thecombined error for the vicarious calibration of TANSO-FTS isapproximately 7%.

B. Instrument Degradation After Launch

Fig. 12 shows the monthly solar calibration data for TANSO-FTS using the back side of the diffuser plate. The upper panelshows the ratio of the radiance from the front and back sides ofthe diffuser plate, whereas the lower panel shows the radiancefrom the back side after correction for the distance between thesatellite and the sun and the angle of incidence of the solar beamupon the diffuser. The back side of the diffuser is exposed todirect solar radiation only once a month by rotating the diffuserduring the solar calibration, whereas the front side is exposedall the time. The ratio in the upper panel indicates that the frontsurface of the diffuser has degraded in proportion to the expo-sure time. Assuming that the back side of the diffuser has notdegraded after a year in orbit and that the TANSO-FTS responseis common to both front and back side measurements, then thereflectivity of the front side has decreased by approximately7% in band 1 after one year in orbit. In contrast, no significantdegradation is observed in bands 2 and 3 for the front side incomparison with the back side.

1790 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

Fig. 12. Solar irradiance monthly calibration data from the onboard Spec-tralon diffuser. The upper panel shows the ratio of the radiance from the frontand back sides of the diffuser. The lower panel shows the change from thefirst measurement in space from the back side after correction for the distancebetween the satellite and the sun and the angle of incidence of the solarbeam upon the diffuser. The vertical lines represent the time of the vicariouscalibration.

The combination of the reflectance of the back side andthe responsivity of TANSO-FTS appears to have decreased byabout 2.7% in band 1 and by less than 1% in bands 2 and 3 atthe time of the vicarious calibration campaign. Again, assumingthat the reflectivity of the back side is stable, because it is rela-tively protected from UV radiation, these measurements appearto place an upper bound upon the degradation in responsivityof TANSO-FTS, 3% in band 1 and 1% in bands 2 and 3.These figures are relative to the first measurements in space onMarch 4, 2009.

In contrast, the observations at RRV suggest that theTANSO-FTS responsivities have changed by 11% ± 7%, 2%± 7%, and 3% ± 7% compared with the preflight calibration,whose accuracy is estimated to be 3%. The cross-calibrationcheck between JAXA and NASA suggests consistency of thepreflight calibration to within 1.8%, 1.6%, and 1.4%. Recon-ciling the different measurements seems to require that thevicarious calibration in band 1 is low, and perhaps that thepreflight calibration is high. Nevertheless, the requirement ofbetter than 10% accuracy from the vicarious calibration hasbeen met.

Assuming that the degradation is due to contaminationof the on-orbit satellite environment and that it depends onwavelength, the UV band 1 of TANSO-CAI is likely to have

larger degradation. This is consistent with the observationsfrom the vicarious calibration and also from modeling [23].The TANSO-CAI responsivities have changed by −17% ±6%, +4% ± 6%, 0% ± 6%, and −18% ± 6%, respectively.The approximate error budget for the TANSO-CAI vicariouscalibration is similar to that for TANSO-FTS except for errorsof IFOV-averaged reflectance and errors in IFOV estimation.

The estimated degradations of responsivity for TANSO-FTSand TANSO-CAI are summarized in Table VII.

C. Solar Irradiance Model

The accuracy of the solar irradiance model directly affectsthe accuracy of the spectral radiance calculated at the TOA.There are several solar models available for use in the radiativetransfer; for example, Chance and Kurucz [24], Toon (privatecommunication), Thuillier [25], and World Radiation Center[26]. The first two databases have high spectral resolution.The solar model used in this paper (Toon’s model) representsthe irradiance as the product of the solar continuum and thetransmittance of the solar photosphere, the continuum modeledby a ninth-order polynomial fit to SOLSPEC observations,and the transmittance based on a compilation of solar lineswhose parameters are derived from Kitt Peak observations.As shown in Fig. 13, the maximum discrepancy between thesolar irradiance spectra is approximately 2%. Kurucz’s model is2.0% lower than Toon’s data in band 2; the difference is smallerin bands 1 and 3.

D. Planned Improvements for Future Calibration Campaigns

To monitor the day-to-day variations of reflectivity of theplaya, it was decided to measure the reflectance of site H03 ev-ery day of the campaign. Unfortunately, frequent observationsdisturbed the surface of the playa with footsteps and tracks,which meant that some of the H03 data have large errors. Inaddition, there were problems with computer hardware andoperation. Under the hot desert environment, the PCs requireproper cooling and shielding from thermal radiation whenoperated for extended periods of time.

Another practical problem of the field campaign was theinterval between acquiring reflectance spectra of the Spectralonpanels. Generally, the time was in excess of 20 min, whichmeant that changes in the solar zenith angle had to be taken intoaccount. More frequent observations of the Spectralon panelswould increase the accuracy of the calibration. The mission lifeof GOSAT is five years, and the vicarious calibration is plannedthroughout the mission to monitor degradation of the responseof the TANSO instruments. However, as the surface reflectancemeasurements with ASD spectrometers are labor intensive, analternative using an airborne reference is under consideration.As a trial, a formation flight with the well-calibrated airbornevisible/infrared imaging spectrometer (AVIRIS) [27] was per-formed on October 9, 2009. The airborne imaging spectrom-eter has the advantage that the IFOV-averaged radiance canbe interpolated (using a radiative transfer model) to TANSO-FTS wavelengths at high spatial resolution. Furthermore, thedependence upon an accurate solar model is reduced.

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1791

TABLE VIIESTIMATED DEGRADATIONS OF RESPONSIVITY FOR TANSO-FTS AND TANSO-CAI

Fig. 13. Comparison of solar irradiance models. Kurucz’s model [24] isshown in blue (solid), the model from Thuillier et al. [25] is in green (dashed),and Toon’s model is in red (dotted).

VIII. CONCLUSION

A vicarious calibration of GOSAT’s TANSO-FTS andTANSO-CAI sensors has been performed in the summer of2009 per the JAXA/NIES mission statement. The measurementcampaign was conducted using as target a dry lake bed in RRV,Nevada, which has a reasonably well characterized level surfacewith relatively high spectral homogeneity. During the fieldcampaign, six days of ground and satellite measurements wereobtained in an attempt to fully characterize the atmosphere andsurface at the time of the satellite overpasses. In situ measure-ments of ground properties and atmospheric column profileswere used as inputs to radiative transfer codes to simulate TOAradiances.

The reflectances measured at the field sites with ASD spec-trometers were extrapolated to the TANSO-FTS footprints us-ing MODIS radiance data, whereas corrections for the differentviewing geometries were derived from MODIS BRDF data.The agreement between the satellite measured radiances withprelaunch calibration and simulated TOA radiances from aradiative transfer model is approximately 7%. The largest errorsources for the vicarious calibration are the reflectance mea-surements, their extrapolation to the TANSO-FTS footprint,and the uncertainties in the solar models.

The solar irradiance calibration data derived from the so-lar diffuser also indicate degradations of TANSO-FTS andTANSO-CAI. Consequently, it is recommended that users ofGOSAT data use the results of this paper to model the degra-dation with time and to correct the prelaunch calibration.

Assuming that the electronic units (such as amplifier andanalog–digital converter) have not changed, then the degra-dations in responsivity must be associated with reductions inthe pointing mirror reflectivity, FTS modulation efficiency, andafter optics transmittance.

To monitor the degradation with time, additional vicariouscalibrations are planned throughout the nominal operating life-time of GOSAT, with the next scheduled to take place at RRVin the summer of 2010. It is hoped that implementation ofseveral changes to the methodology discussed in this paper willyield improved results. In addition, simultaneous overflights byAVIRIS, BRDF measurement, and ground-based measurementsof CO2 and CH4 should provide a more complete validation ofthe calibration.

APPENDIX

CORRECTION FOR SPATIAL VARIABILITY OF THE PLAYA

Consider a grid of MODIS pixels centered on the target.Let Mk

ij denote the MODIS radiance in band k for pixel(i, j) observed in a MODIS overflight close to the time of thevicarious calibration. Ideally, the MODIS observations shouldbe close to nadir. The overpass should be very clear, so carefulscreening for cloud and aerosol is essential. We chose theMODIS overpass on day 190 of 2009 (July 9) with 500-mspatial resolution. Not only was the sky clear at the time of theoverpass, as judged visually and by the MODIS cloud flags,which showed only a small trace of cirrus, but also the scanangle at the satellite was approximately 7◦, meaning that theobservations were close to nadir and the MODIS footprintswere small.

Let

Ci0j0(λ,Θsun, ϕsun,Θobs, ϕobs)

denote the spectrum measured with the ASD device. Here,(i0, j0) is the index of the MODIS pixel in which the fieldmeasurements are made; Θsun and ϕsun are the zenith angleand the azimuth of the sun at the time of the field measurements;Θobs and ϕobs are the zenith angle and the azimuth of the fieldmeasurements; and λ denotes wavelength. In practice, most ofthe observations are toward nadir, in which case Θobs = 0 andϕobs = 0.1

1We assume that the movement of the sun during the observations may beneglected. Since the field campaign was close to the summer solstice, the errorincurred by neglecting the movement of the sun over the hour or so duringwhich the field data were acquired is likely to be small. Nevertheless, it wouldbe easy to adjust these formulas to allow for the exact time of observation.

1792 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

Because the field crew cannot cover the whole playa, weassume that, had they been able to measure on pixel (i, j) andnot just pixel (i0, j0), they would have obtained the reflectancespectrum

Cij(λ,Θsun, ϕsun,Θobs, ϕobs)

= Ci0j0(λ,Θsun, ϕsun,Θobs, ϕobs)

(Mk

ij

Mki0j0

).

For each GOSAT band, we choose a single MODIS band toperform the scaling; no attempt is made to interpolate betweenthe MODIS bands. The rationale (assumption) is that the spec-tra from different parts of the playa are multiples of a commonspectrum. For GOSAT bands 1, 2, and 3, we choose MODISbands with central wavelengths at 860, 1640, and 2130 nm toperform the scaling.

To calculate the radiance at the TOA, the surface BRDF isrequired. This is taken from the MODIS (MCD43B1 product)but scaled so that the reflectance in the experimentally observeddirection (Θobs, ϕobs) agrees with the measurements. LetKr(Θsun, ϕsun,Θ, ϕ), r = 1, 2, 3, denote the MODIS kernelsfor a black sky with incident beam from direction (Θsun, ϕsun)and radiance reflected into the TANSO viewing direction(Θ, ϕ). The BRDF in MODIS band k for pixel (i, j), whichis denoted Rk

ij , is the linear combination

Rkij(Θsun, ϕsun,Θ, ϕ) =

3∑r=1

αkijrKr(Θsun, ϕsun,Θ, ϕ) (2)

where the coefficients αkijr are provided by the MODIS BRDF

product MCD43B1. For the pixel indexed by (i, j), we definethe indicatrix

Ikij(Θsun, ϕsun,Θ, ϕ) =Rk

ij(Θsun, ϕsun,Θ, ϕ)

Rkij(Θsun, ϕsun,Θobs, ϕobs)

.

This function captures the angular distribution of the reflectedradiance but not the overall scaling. Next, we assume that theBRDF for pixel (i, j) takes the form

Bij(λ,Θsun, ϕsun,Θ, ϕ)

= Cij(λ,Θsun, ϕsun,Θobs, ϕobs)Ikij(Θsun, ϕsun,Θ, ϕ).

This model combines the angular distribution inferred fromthe MODIS BRDF with the absolute scaling measured by thefield crew. Again, we associate the indicatrices for MODISbands with central wavelengths at 860, 1640, and 2130 nm withGOSAT bands 1, 2, and 3. If we substitute the expression for theindicatrix in terms of the BRDF kernels, then we obtain

Bij(λ,Θsun, ϕsun,Θ, ϕ)

= Cij(λ,Θsun, ϕsun,Θobs, ϕobs)

×3∑

r=1

Θkijr

Kr(Θsun, ϕsun,Θ, ϕ)

Rkij(Θsun, ϕsun,Θobs, ϕobs)

.

Let wij denote the weight associated with pixel (i, j), normal-ized so that ∑

ij

wij = 1.

Because the MODIS pixels are small compared with theGOSAT footprint, we assume that wij = 1/N if pixel (i, j)lies inside the GOSAT footprint and wij = 0 otherwise, whereN is the number of MODIS pixels falling within the GOSATfootprint. We define the area-weighted BRDF to be

B(λ,Θsun, ϕsun,Θ, ϕ) =∑i,j

wijBij(λ,Θsun, ϕsun,Θ, ϕ)

(3)which reduces to

B(λ,Θsun, ϕsun,Θ, ϕ) =

3∑r=1

βr(λ)Kr(Θsun, ϕsun,Θ, ϕ)

(4)where the coefficient βr(λ) is given by

βr(λ) =∑i,j

wijαkCij(λ,Θsun, ϕsun,Θobs, ϕobs)

Rkij(Θsun, ϕsun,Θobs, ϕobs)

.

As the scattering optical thickness of the atmosphere overRRV is very small, the radiance at the TOA varies almostlinearly with the surface reflectance. Consequently, performinga single radiative transfer calculation with the average surfacereflectance is equivalent to performing separate radiance cal-culations for all the reflectance pixels and then averaging theradiances. Replacing the “ghost” measurements by the truemeasurements and the MODIS radiance scaling factors, weobtain

βr(λ) = Ci0j0(λ,Θsun, ϕsun,Θobs, ϕobs)

×∑i,j

(Mk

ij

Mki0j0

)wijα

kijr

Rkij(Θsun, ϕsun,Θobs, ϕobs)

.

This may be written more compactly as follows:

βr(λ) = γkrCi0j0(λ,Θsun, ϕsun,Θobs, ϕobs)

where

γkr =

∑i,j

(Mk

ij

Mki0j0

)wijα

kijr

Rkij(Θsun, ϕsun,Θobs, ϕobs)

.

Thus, the area-weighted BRDF has the same form as thestandard MODIS BRDF, except that the coefficients at anywavelength λ are obtained by multiplying the field-measuredspectrum Ci0j0(λ,Θsun, ϕsun,Θobs, ϕobs) by factors γk

r , thelatter derived from both MODIS radiance and MODIS BRDFmeasurements.

In practice, the MODIS BRDF product MCD43B1 for day185 of 2009 (July 4) was chosen. Because each BRDF release

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1793

is derived from MODIS radiance observations over a 16-dayinterval, the BRDF should not be significantly compromisedby the early morning rain reported by the field crew onJuly 3.

ACKNOWLEDGMENT

The authors would like to thank T. Takeda, H. Ohyama,K. Yotsumoto, M. Kasuya of JAXA, H. Tan and L. Chapskyfrom NASA’s Jet Propulsion Laboratory, and B. Cherian fromthe California Institute of Technology for helping with theplanning and measurements. The ACOS contribution to thispaper was carried out at the Jet Propulsion Laboratory and atColorado State University. A portion of the research describedin this paper was carried out at the Jet Propulsion Laboratory,California Institute of Technology, under a contract with theNational Aeronautics and Space Administration.

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Akihiko Kuze was born in 1963. He received theB.S. and M.S. degrees in geophysics and the D.S.degree in earth and planetary science from the Uni-versity of Tokyo, Tokyo, Japan, in 1986, 1988,and 2003.

He was previously with the Space Systems Di-vision, NEC Corporation, Yokohama, Japan, andthe Harvard-Smithsonian Center for Astrophysics,Cambridge, MA. He is currently with the JapanAerospace Exploration Agency, Tsukuba, Japan. Hehas been a member of the GOSAT project team

since 2003.

D. M. O’Brien received the M.Sc. degree in the-oretical physics from the Australian National Uni-versity, Canberra, Australia, and the Ph.D. degreein mathematical physics from the University ofAdelaide, Adelaide, Australia.

After postdoctoral positions in Scotland andAustralia, he joined the Commonwealth Scientificand Industrial Research Organization of Australia,where his focus was radiation, remote sensing, andinstrumentation. Since 2004, he has been a SeniorResearch Scientist with Colorado State University,

Fort Collins. He is a member of the OCO and ACOS science teams.

1794 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 49, NO. 5, MAY 2011

T. E. Taylor received the B.S. degree in physicsfrom the University of Georgia, Atlanta, in1997 and the M.S. degree in atmospheric sci-ence from Colorado State University, Fort Collins,in 2005.

He was with the EPA’s National UV MonitoringCenter for a number of years. Since 2006, he hasbeen with NASA’s OCO and ACOS projects. Heis currently with the Department of AtmosphericScience, Colorado State University.

Jason O. Day received the Ph.D. degree in atomicphysics from the University of Wisconsin-Madison.

From 2008 to 2009, he was a Postdoctoral Fellowwith the OCO team. He is currently serving as anAAAS Science and Technology Policy Fellow withthe Division of Atmospheric and Geospace Sciences,National Science Foundation.

Christopher W. O’Dell received the Ph.D. degree inphysics from the University of Wisconsin-Madison,in 2001.

After postdoctoral positions in both astronomyand microwave remote sensing, in 2007, he joinedthe research staff at Colorado State University, FortCollins, where he is currently a member of the Coop-erative Institute on Research in the Atmosphere. Hisresearch concerns the remote sensing of climaticallyimportant atmospheric variables such as water vaporand carbon dioxide.

Fumie Kataoka received the B.S. and M.S. de-grees in earth science from Okayama University,Okayama, Japan, in 2003 and 2005, respectively.

Since 2005, she has been with the Remote Sens-ing Technology Center of Japan, Tsukuba, Japan.Her current research theme is atmospheric remotesensing.

Mayumi Yoshida received the B.S. and M.S. de-grees in earth and planetary science from HokkaidoUniversity, Sapporo, Japan, in 1998 and 2000, re-spectively.

Since 2000, she has been with the Remote Sens-ing Technology Center of Japan, Tsukuba, Japan.Her current research theme is atmospheric remotesensing.

Yasushi Mitomi received the B.E. and M.E. degreesin ocean engineering from Tokai University, Tokyo,Japan, in 1991 and 1993, respectively.

Since 1993, he has been with the Remote SensingTechnology Center of Japan, Tsukuba, Japan. Hiscurrent research theme is the development of atmo-spheric correction methods for ocean color remotesensing.

Carol J. (Kastner) Bruegge received the Ph.D.degree in optical sciences from the University ofArizona, Tucson, in 1985.

She is currently with the Jet Propulsion Lab-oratory, NASA, Pasadena, CA, and is a memberof the OCO science team. From 1988 to 2003,she was a member of the Earth Observing Sys-tem (EOS) Multi-angle Imaging SpectroRadiometer(MISR) team. She has been a Principal Investigatorof the LSpec (LED Spectrometer) automatic vicar-ious calibration facility, and also the First Interna-

tional Satellite Land Surface Climatology Program (ISLSCP) Field Experiment(FIFE), a ground-truth hydrology experiment conducted from 1987 to 1992.

Harold Pollock received the B.S. degree in engineer-ing and applied science from the California Instituteof Technology, Pasadena, in 1991.

He is currently an Instrument Architect with OCO,Jet Propulsion Laboratory, NASA, Pasadena.

Ralph Basilio received the Ph.D. and M.S. degreesin aerospace engineering from the University ofSouthern California, Los Angeles, and the B.S. de-gree in aerospace engineering from the CaliforniaState Polytechnic University, Pomona. He is alsoa graduate of the Engineering Management Pro-gram with the California Institute of Technology,Pasadena.

He is currently the Deputy Project Manager ofthe OCO project with the Jet Propulsion Laboratory,California Institute of Technology.

Mark Helmlinger received the B.S. degree inphysics from the California State Polytechnic Uni-versity, Pomona, in 1991.

He is currently with Northrop GrummanAerospace Systems, Redondo Beach, CA. He hasparticipated in the Boreal Ecosystem-AtmosphereStudy (BOREAS) and the Southern AfricanRegional Science Initiative (SAFARI 2000)international intensive field campaigns and hasalso lead several deployments to Rail Road Valleyand other playas. He is uniquely experienced

with the operation, methodology, maintenance, and analysis of most of theinstrumentation used in vicarious calibration and product validation activities,including JPL’s Portable Apparatus for Rapid Acquisition of BidirectionalObservation of the Land and Atmosphere (PARABOLA) instrument.

Tsuneo Matsunaga received the Doctor of Engi-neering degree from the University of Tokyo, Tokyo,Japan, in 1997.

He is currently the Chief of Office for GlobalEnvironmental Database with the Center for GlobalEnvironmental Research, National Institute for Envi-ronmental Studies (NIES), Tsukuba, Japan. He is amember of the NIES GOSAT project and Japan-USASTER Science Team, and the PI of Spectral Profilerinstrument onboard Japanese lunar explorer Kaguya.

KUZE et al.: VICARIOUS CALIBRATION OF THE GOSAT SENSOR 1795

Shuji Kawakami received the Doctor of Sciencedegree from Nagoya University, Nagoya, Japan,in 1997.

He is currently with the Earth Observation Re-search Center, Japan Aerospace Exploration Agency(JAXA), Tsukuba, Japan, where he is a member ofthe GOSAT calibration team. He worked on sev-eral aircraft campaigns for measurements of tropo-spheric ozone and its precursors and ozonesondeobservations.

Kei Shiomi received the Doctor of Science degreein earth and planetary science from the University ofTokyo, Tokyo, Japan, in 2001.

He has worked for AMSR and AMSR-E data re-search with the Remote Sensing Technology Centerof Japan. He is currently with the Earth Observa-tion Research Center, Japan Aerospace ExplorationAgency (JAXA), Tsukuba, Japan, where he is incharge of GOSAT calibration and data processing.

Tomoyuki Urabe received the B.S. and M.S. de-grees from Tokyo Institute of Technology, Tokyo,Japan, in 2002 and 2004, respectively.

From 2001 to 2004, he was a member of theCubeSat Project Team with the Laboratory for SpaceSystems (LSS), Tokyo Institute of Technology. Since2004, he has been an Engineer with the GOSATproject team, Japan Aerospace Exploration Agency(JAXA), Tsukuba, Japan. His research interests in-clude small satellites, electrical power subsystems ofspacecraft, and contamination control.

Hiroshi Suto received the Ph.D. degree from TohokuUniversity, Sendai, Japan, in 2002.

Between 2002 and 2006, he was a Postdoc-toral Fellow with the National Institute for En-vironmental Studies. Since 2006, he has been incharge of the development of TANSO instrumentsas an Aerospace Project Research Associate withthe Japan Aerospace Exploration Agency (JAXA),Tsukuba, Japan.