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Vicarious calibration
Remote Sensing of Environment 77 (2001) 338 – 353 www.elsevier.com/locate/rse
Vicarious calibration A reflectance-based experiment with AirMISR Wedad A. Abdou*, James E. Conel, Stuart H. Pilorz, Mark C. Helmlinger, Carol J. Bruegge, Barbara J. Gaitley, William C. Ledeboer, John V. Martonchik Jet Propulsion Laboratory, California Institute of Technology, M.S. 169-237, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, USA
Abstract A vicarious reflectance-based calibration experiment for the Multiangle Imaging SpectroRadiometer (MISR) airborne simulator, AirMISR, is described as one precursor experiment of this type planned for postlaunch application to MISR itself. The experiment produces a set of multiangle near-top-of-atmosphere radiances that are compared with the multiangle AirMISR radiances, established using a laboratory calibration. The field and aircraft data were collected as part of an engineering test flight at Moffett Field, CA, on November 5, 1997. A concrete tarmac was used as the field target. Atmospheric optical depth data were collected adjacent to the target throughout the actual overflight period using a single Reagan solar radiometer. For logistical reasons, the surface hemispherical directional reflectance factor (HDRF) was determined 7 days later using the Portable Apparatus for Rapid Acquisition of Bidirectional Observation of the Land and Atmosphere III (PARABOLA III), along with the areally averaged spectral HDRF at normal incidence, obtained with an Analytical Spectral Devices (ASD) FieldSpec moderate resolution field spectrometer. AirMISR overflew the target under clear sky conditions though the aerosol turbidity was high ( 0.3 at 550 nm). Good to fair agreement has been obtained at all angles and wavelengths between the top-of-atmosphere (TOA) radiances calculated for the measured atmospheric and surface conditions and the radiances incident at AirMISR as determined from the laboratory calibration. Some systematic disagreements are present. The largest disagreements ( 15% in the blue) are found at the highest view angles and the smallest at nadir viewing ( < 5%). Possible explanations for the differences in radiances at large view angles are discussed. D 2001 Elsevier Science Inc. All rights reserved.
1. Introduction The Multiangle Imaging SpectroRadiometer (MISR) was launched on December 1999 on the Earth Observing System, EOS-AM1 spacecraft (Diner, Beckert, et al., 1998). MISR has nine CCD pushbroom cameras which will provide images of the Earth’s surface in four bands (blue, green, red, and nir at 446, 558, 672, and 866 nm, respectively) at angles of 0 (An), ± 26.1 (Af, Aa), ± 45.0 (Bf, Ba), ± 60.0 (Cf, Ca), and ± 70.5 (Df, Da), relative to nadir, both forward (+) and aftward ( ) along the direction of flight. The subscripts n, f, and a imply cameras viewing in the nadir, forward, and aftward directions, respectively. One of the major tasks of the EOS and of MISR is to provide stable well-calibrated measurements of key parameters that are crucial to a long-term assessment of temporal variations * Corresponding author. Tel.: +1-818-354-6806; fax: +1-818-3934619. E-mail address: [email protected] (W.A. Abdou).
in the Earth radiation budget especially due to clouds, aerosols, and to land surface albedo. AirMISR is an airborne MISR simulator that collects MISR-like data for the purpose of supporting the validation of MISR algorithms and calibration of the MISR instrument (Diner, Barge, et al., 1998). Radiometric calibration of AirMISR and MISR means determining an accurate relationship between reflected solar spectral radiance and instrument output. Multiple calibration pathways will be used to obtain such relationships: (1) laboratory calibration (MISR and AirMISR) (Chrien, Bruegge, & Gaitley, 1999); (2) onboard calibration involving monitoring of reflectance stability of Spectralon reference panels with absolute high quantum efficiency (HQE) photodiodes (MISR) (Bruegge et al., 1996) or terrain radiance with PIN diodes (AirMISR); (3) ground-based vicarious calibrations using natural uniform targets (MISR and AirMISR). This paper concerns pathway (3), and is the first field experiment we report that extends the vicarious calibration method, heretofore usually carried out for sensors viewing at close-to-normal inci-
0034-4257/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 0 0 3 4 - 4 2 5 7 ( 0 1 ) 0 0 2 1 3 - 9
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dence, to all angles of AirMISR instrument viewing (i.e., nadir to ± 70.5). Vicarious calibration forms a complete independent pathway for monitoring of instrument performance, including error assessment with all reflectance standards, field instruments, and atmospheric radiation measurements employed tied to National Institute of Standards and Technology (NIST)-verifiable standards. The method involves measuring either the surface reflectance or the surface-leaving radiance over the ground hemisphere at a target point, together with atmospheric scattering and absorption properties. A validated and benchmarked radiative transfer code (RTC) is used, constrained by the field measurements, to calculate the topof-atmosphere (TOA) radiance at nine view angles and four wavelengths, corresponding to the viewing directions and wavelengths of the nine MISR cameras on orbit, or to the nine view angles and four wavelengths of the gimballed single AirMISR camera. The radiances calculated from the RTC are then compared to the radiances predicted at the instrument using the laboratory and in-flight-determined calibration coefficients. Ideally, the sites of natural targets employed for vicarious calibration experiments (dry uniform lake beds in high clear remote desert areas) are chosen to minimize atmospheric scattering effects and influences of clouds. Under these conditions, TOA radiance is predominantly sensitive to the accurate measurement of surface reflectance properties. Although these ideal conditions were not met for the data acquired on November 5, 1997, valuable lessons are learned by applying the analysis tools to the observations.
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2. AirMISR instrument and observations A complete description of the AirMISR system is found in Diner, Barge, et al. (1998). AirMISR is constructed with a single camera from MISR brassboard components. The camera is mounted on a gimbal system that provides rotation about a horizontal axis into viewing directions duplicating those of MISR itself. The AirMISR package resides in the nose cone of the NASA ER-2, which flies at 20 km above sea level. AirMISR provides multiple multiangle views of nested target areas that increase in alongtrack and cross-track size with increasing view angle as shown in Fig. 1. The length of flight line required for a single pass is about 120 km. The instantaneous footprint of the camera system varies with view angle from 7 m cross-track by 6 m along-track in the nadir view to 21 55 m at the most oblique angle. Lines of image data are acquired every (Dts=) 40.8 ms. This coupled with an aircraft ground speed of (Va=) 200 m/s lead to an along-track sample spacing of (VaDts=) 8 m. While the nadir image is thus slightly undersampled, the more oblique directions are progressively increasingly oversampled, leading to an apparent smear in these images that must be accounted for in location of pixels sampled at the surface for purposes of calibration. In addition to oversampling, there is a slight systematic displacement between images of different color bands (Jovanovic, 1996) along-track at each view angle that must
Fig. 1. The view directions and nested ground fields-of-view of AirMISR for an aircraft altitude of 20 km.
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Table 1 Actual view angles of AirMISR camera during Moffett overflight Camera
An
Af/Aa
Bf/Ba
Cf/Ca
Df/Da
Angle ()
2.72
26.66/ 25.04
46.18/ 45.09
60.93/ 59.77
71.77/ 65.31
be taken into account when locating reference ground target areas in the unresampled image data. This arises because the detector line arrays for each color are displaced parallel to one another. To overcome oversampling, foreshortening, and color separation effects, homogeneous target areas are best suited to needs of the ground target calibration method. In practice, the sorting out of ground-sampled areas and differences in alignment for each band, hence actual ground location of pixels in heterogeneous areas, are accomplished using special viewing software (Chrien, 1998) that allows magnification of targets, calculation of pixel coordinates, as well as means and standard deviations of instrument responses over each sampled area and for each wavelength. Knowledge of the pointing accuracy of AirMISR relative to the local vertical is crucial for accurate assessment of the
instrument calibration, especially at higher view angles. For the aerosol and surface reflectance models, this is so because the retrieved radiance depends on absolute knowledge of the pointing direction. There are four components of the orientation: (1) the camera geometric model described above, (2) the orientation of AirMISR with respect to the ER-2 airframe, (3) the orientation of the ER-2 airframe itself with respect to the local vertical, and (4) the angular position of the gimbal on each particular forward or backward scan. Of these, the orientation of the airframe in terms of roll, pitch, and yaw, is determined from on-board navigation data to ± 0.005 in each angle. Although the gimbal housing (drum) is attached to an encoder with resolution of 2000 steps/deg, the angular position of the gimbal is presently known only from optical switch position data to ± 1 for
Fig. 2. The nadir view of Moffett Field and environs on Nov 5, 1997. Ground calibration target location (and Reagan solar radiometer station) is marked by the white arrow.
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Fig. 3. DN values from ground target area for the four AirMISR bands over the nine viewing angles. Sign convention is positive angles, forward direction (into sun), negative angles, aftward direction (away from sun). Error bars represent scatter in the DN values.
each angle. Component (2) is under study. Systematic orientation offsets have been observed as a result of ground control unit analysis, and an error of a few degrees in pitch must be taken into account. The AirMISR flight over Moffett Field, CA on November 5 took place under cloud-free but hazy atmospheric conditions at 19:27 UT (11:27 a.m., PST). The flight line was about 186 to the southwest. The solar zenith and azimuth angles were 53 and 172.6, respectively. The actual view angles of cameras with respect to the target surface normal were determined from the image data, using AirMISR navigation data and the above-mentioned viewing software, to be as given in Table 1. Fig. 2 is a nadir view image of Moffett Field showing the position of the target area located on a uniform concrete tarmac at latitude: 37420 N, longitude: 122060 W, elevation = 5 m. For analyses reported here, the raw unresampled, AirMISR image data are used. The AirMISR DN values for the ground-measured target area, located manually in the imagery using important landmarks recognized for each viewing angle and for each channel, are shown in Fig. 3.
The angle convention adopted is positive camera angles represent the forward direction, and negative angles aftward direction, corresponding to MISR cameras, Af/Aa, Bf/Ba, Cf/Ca, and Df/Da. The number of effective pixels included in the averages vary with view angle because the groundprojected field-of-view (solid angle) of AirMISR increases with viewing angle. The averages and the standard deviation bars of Fig. 3 are based on the aggregate number of pixels of the sample area as given in Table 2 for each view angle and channel. The AirMISR DN spectral response were converted into radiances using the measured AirMISR calibration coefficients. AirMISR was calibrated in the laboratory using the MISR 65-in. integrating sphere and the same light sources, procedures, and analysis tools developed for MISR (Chrien et al., 1999). The relationship between instrument response DN and incident band-averaged radiance L¯ in each band and in each pixel was developed as the quadratic form: DN DN0 ¼ g0 þ g1 L þ g2 L2
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Table 2 Number of pixels averaged in target area as function of view angle Color View
Blue
Green
Red
Near-IR
An Aa/Af Ba/Bf Ca/Cf Da/Df
64 90/72 56/72 30/36 20/35
80 80/80 56/90 35/25 42/28
99 72/70 64/64 30/30 30/40
80 72/80 56/63 30/36 24/30
where DN0 is the offset bias response, g0, g1, g2 are gain coefficients which vary with wavelength and from pixel to pixel array-averaged gain coefficients are given in Chrien et al. (1999), and L¯ is weighted by the instrument spectral response.
3. Field instruments, methodology, and observations For accurate calculations of the TOA radiance observed by AirMISR, ground measurements are used to constrain the RTC. The required input to the RTC must include: (1) the atmospheric optical depths, retrieved from the Reagan solar radiometer; (2) the surface BRF, retrieved from the Portable Apparatus for Rapid Acquisition of Bidirectional Observation of the Land and Atmosphere III (PARABOLA III) data; and describing the part of the surface in the camera’s fields-of-view; and (3) a composition and size distribution characterizing the aerosol present at the time of AirMISR flight. For logistical reasons and since this was primarily an engineering flight of AirMISR, only solar radiometer observations were obtained during the experiment. Seven days after the flight, the PARABOLA III and the Analytical Spectral Devices (ASD) measurements were collected about the same time of the day as the AirMISR flight and at the designated target area. 3.1. Reagan solar radiometer and atmospheric optical depth measurements The autotracking Reagan solar radiometer measures bottom-of-atmosphere (BOA) solar spectral irradiance and is used to determine average and instantaneous spectral optical depth in 10 channels, each about 10 nm in width near 380, 400, 440, 520, 600 670, 780, 870, 940, and 1030 nm. These instruments are calibrated (zero airmass instrument response determined) using the well-known Langley method by plotting the logarithm of instrument response vs. air mass and extrapolating to zero airmass. The Rayleigh scattering optical depth is calculated from a field measurement of atmospheric surface pressure. A residual optical depth consisting of the total instantaneous optical depth minus Rayleigh component is the starting point for simultaneous retrieval of aerosol and ozone components using a procedure due to Flittner, Herman, Thome, and Simpson (1993), which obtains the spectral aerosol optical
depth independent of any assumption about the aerosol size distribution. The Reagan radiometer was set up adjacent to a nearby hanger off the tarmac and operated continuously between 19:06 and 20:34 UT (11:06 and 12:34 PST). The spectral optical depth components for the time of overflight extracted from these records are shown in Fig. 4. The aerosol optical depth at 550 nm is near 0.3 and is a factor of three higher than would ordinarily be encountered for such calibration experiments under clear sky conditions in high desert regions. However, the relatively heavy atmospheric conditions encountered at Moffett Field provide a good test case for the sensitivity of calculated TOA radiances to aerosol compositional model, and for the relative importance of path as opposed to ground-leaving radiance in the calculations. The main source of uncertainty in the optical depths are the instrument calibration constant V0, the signal which would be obtained at zero airmass. The standard deviation of the total optical depth, st, is estimated from the relationship st tm0(sV0/V0), where m0 is cosine of the solar zenith angle and sV0 is the standard deviation of multiple V0 retrievals in the history of V0 determination. This relationship follows applying error propagation formulas (Bevington, 1969) to the Beer– Lambert law, assuming that individual measurements are error-free compared to variations introduced by atmospheric fluctuations. From this relationship, an upper limit on uncertainty in optical depth was estimated to be 0.01 in total optical depth at 380 nm. The error bars in Fig. 4 reflect that value at all wavelengths. These same magnitudes have been applied to the calculated aerosol optical depths, since no method is available to separate the combined Rayleigh, ozone, and aerosol optical depth uncertainties present. 3.2. PARABOLA III and surface BRF/HDRF The PARABOLA is a third-generation sphere-scanning radiometer built by Sensit (Mayville, ND) and represents a substantial revision in design and capability over the first version of this instrument (Deering & Leone, 1986). PARABOLA III consists of two separate sensor heads mounted at opposite ends of a center-suspended horizontal scanning arm that rotates continuously through 360 about a vertical axis. Each sensor head contains the detector assemblies for four of eight channels (443, 551, 650, 860, 944, 1028, 1652, and 400– 700 nm). Each individual head scans synchronously with the other from zenith to nadir in vertical angle. The combined synchronized motion of the heads about both axes generates a stepwise pattern of 5 circular full apex angle overlapping fields of view of sky hemisphere, and a series of 5 ellipsoidal pixels on the ground that increase in size from nadir to horizon. An entire scan of both sky and ground hemispheres generates 2664 ( = 37 72) pixels in about 3.3 min including downloading to memory. The dynamic range of the instrument is 220, enabling both the direct solar beams, sky radiance and
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Fig. 4. Total, Rayleigh, aerosol, and ozone optical depths as functions of wavelength for the November 5 calibration date for 19:27 UT. Error bars represent uncertainties taken uniformly to be 0.01 in optical depth. Based on multiple V0 determinations, this error is an overestimate.
ground-leaving radiance, to be obtained without gain changes. Details of the PARABOLA III measurements and calibration procedures will be reported elsewhere. The PARABOLA III measurements are used to retrieve the surface bidirectional reflectance factor (BRF), which is defined as the ratio between the radiance reflected from the surface to that reflected from an ideal Lambertian reflector under the same direct illumination. To obtain the BRF, Rx,y, at a point (x,y) from PARABOLA III measurements, ground-reflected radiance, direct irradiance, and diffuse sky radiance measurements are combined in a procedure developed by Martonchik (1994). A complete solution requires measurements for all solar incidence angles from horizon to zenith, but in practice, assumptions about behavior of the BRF for solar incident angles not measured (i.e., constancy or simple interpolation) can be made with little error. In the present application at Moffett Field, because of the logistics of airfield operations and because of sky conditions, PARABOLA III measurements were limited to a
period of about 45 min, on November 12, but near the time of AirMISR overpass (18:36 and 19:21 UT). Thus, a complete BRF retrieval was not possible, but use was made of the available PARABOLA III data to calculate the hemispherical directional reflectance factor (HDRF), rx,y, of the target area to approximate the BRF and to display anisotropic reflectance effects. The HDRF is defined as the ratio between the radiance reflected from the surface in a given direction (m,j) to that reflected into the same beam geometry from a perfect Lambertian surface illuminated under identical atmospheric conditions. This is expressed as: rx;y ðm; m0 ; j j0 Þ Z Z 1 1 2p ¼ Rx;y ðm; m0 ; j j0 Þ p 0 0 0 0 0 0 0 Linc x;y ðm ; m0 ; j j0 Þm dm dj Z Z 1 1 2p inc 0 =; Lx;y ðm ; m0 ; j0 j0 Þm0 dm0 dj0 p 0 0
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where m is cosine of the view zenith angle with convention < 0 upward, m0 is cosine of the Sun zenith angle, j is azimuth of the view direction measured relative to geographic north, and j0 the azimuth of the Sun. Lx,yinc is the incident total direct and diffuse radiance at point x,y. The numerator is measured by the PARABOLA III from nadir to the horizon at all azimuths. The denominator, representing the radiance reflected by a perfect Lambertian surface, is measured in the field using a Spectralon diffuse panel. During data acquisition, the Spectralon panel is placed in the southwest corner of the PARABOLA nadir field-of-view such that the radiance reflected by the panel is measured in the nadir and at 5 and 10 viewing angles from the nadir. From these measurements, and the prior laboratory measurements of the Spectralon BRF (Bruegge et al., 1999), radiances reflected by the Spectralon panel in the remaining viewing angles are determined to a good approximation. The HDRF, as expressed by the above equation, is equivalent to the BRF weighted by all sky radiance incident
angles and is a better approximation for the surface BRF than is a Lambertian assumption, as will be shown. Furthermore, the HDRF can be retrieved for given Sun incidence direction from any one complete spherical scan of the PARABOLA. The PARABOLA III instrument was set up in the center of a uniform concrete target area on a pedestal with the sensing heads 2 m above the tarmac surface. From this height, the area swept out on the surface was approximately 11 m in radius, using, as a limiting view angle, the value of 80 to avoid mixing of sky and ground pixels. The 14 scans available were used to estimate the surface HDRF. Fig. 5 shows these data interpolated into the AirMISR viewing directions from the full 5 net of retrievals. The existence of inhomogeneities in the target reflectance (most probably from few moist areas remaining from precipitation on previous day) is evident from irregularities in the HDRF observed at angles near 25(aft viewing) and at 60 (forward viewing). These irregular data were smoothed out
Fig. 5. The HDRF for target area determined by PARABOLA III on November 11, 1997. The HDRF shown are retrieved from 10 full scans and the error bars represent ± 10% of the average for the multiple determinations. The dotted horizontal lines in each panel represent the assumed lambertian reflectance obtained by the ASD determination. Width of the lines represents the 1s ( ± 1.5%) scatter in 100 samples over the target area.
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by interpolation between surrounding data points, as shown by the solid line. The error bars shown in Fig. 5 represents an upper limit of ± 10% uncertainty in the HDRF determination since the PARABOLA data were made 7 days after the AirMISR flight. For comparison, the HDRF values measured by the ASD in the nadir viewing (see below) are also shown in Fig. 5. This comparison makes evident deviations from ideal Lambertian behavior of the real surface, especially in the aftward (backscatter or negative view angle) direction. Also, the PARABOLA and ASD HDRFs should agree in the nadir direction. This is not exactly so except in the green channel. The slight disagreements, however, are within the estimated ± 10% uncertainty in the HDRF determination. 3.3. FieldSpec portable spectrometer and surface HDRF The portable spectrometer manufactured by ASD provides measurements of the surface HDRF in the nadir direction of view, rx,y ( 1; m0,j0). Traditionally, for the
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calibration of nadir viewing sensors, the target surface has often been assumed Lambertian and the nadir-viewing HDRF taken as an estimate of the Lambertian value. Thus in the present case, the ASD data were considered to be sufficient as nondirectional input to the RTC, and in the preliminary analysis, it was so assumed here. The ASD allows rapid estimation of the surface spectral HDRF between 350 and 2500 nm at an average spectral resolution of about 10 nm. The few second sampling time allows measurements over kilometer-size areas, typical of those employed in calibration exercises, to be carried out rapidly, thus minimizing possible large changes in HDRF accompanying motion of the Sun. In the field these measurements are made relative to the reflectance standard Spectralon. The latter, however, is not perfectly Lambertian and conversion of the ASD measurements to a basis of a perfectly diffuse Lambertian reflector for the current solar zenith angle is required. The correction factor is evaluated to be exactly equal to the Spectralon HDRF. Because the Spectralon is nearly a
Fig. 6. The spectral variation of surface reflectance (HDRF at normal viewing direction) obtained by the ASD FieldSpec on November, 11, 1979. Scatter on the observations (dotted lines) is 1s = ± 1.5%.
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Table 3 Components of aerosol models used in the analysis Component
rca (mm)
sb
Refractive index, n ik (550 nm)
Trophospheric sulfate Tropospheric sulfate with absorption, accumulation mode Mineral dust, accumulation mode Mineral dust, coarse mode Small ruralc Large ruralc Urban soot Sea salt, nucleation mode Sea salt, accumulation mode
0.07 0.07 0.47 1.9 0.03 0.5 0.012 0.05 0.5
1.86 1.86 2.6 2.6 2.24 2.5 2.0 2.5 2.0
1.44 i0.00 1.44 i0.005 1.53 i0.0055 1.53 i0.0055 1.53 i0.0066 1.53 i0.00 1.75 i0.44 1.5 i0.00 1.5 i0.00
a b c
Log-normal distribution characteristic radius. Log-normal distribution spread. From Shettle and Fenn (1979).
Lambertian reflector, it was found that its BRF, which is readily available from laboratory measurements (Bruegge et al., 1999), can be used as a correction factor with less than 1% errors. The average value of the spectral HDRF at normal incidence viewing from 100 samples obtained randomly
over the area, and taken at times spaced about the overflight time, is shown in Fig. 6. The range of 1s scatter for the target area is about ± 1.5% of the HDRF magnitude itself, and is almost independent of wavelength. The HDRF values from ASD spectra are averaged over the AirMISR band passes and taken to represent the magnitude of the
Fig. 7. Scattering phase function, spectral extinction coefficient, single scattering albedo, and the extinction cross-section, scaled to the aerosol spectral optical depth (dots), for the preferred aerosol model. Error bars represent an upper limit of 0.01 uncertainty in the aerosol optical depth.
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Lambertian reflectance for use in the model calculations described below. 3.4. Aerosol models and extinction cross-sections derived from solar radiometer data No direct measurements of the aerosol size distribution and composition were available for this experiment. However, since the aerosol turbidity was high (Fig. 4), it was deemed essential to investigate sensitivity of the TOA model results to choice of aerosol model. Several of the aerosol models shown in Table 3 were tried as representations of both pure forms and mixed together in various proportions. The final model selection was based on generating a spectral extinction cross-section per particle, kext, that followed the measured aerosol spectral optical depth taer through the relationship: taer kextNZ (assuming a homogeneous vertical distribution for the aerosol), where N is the effective particle number per unit volume, and Z is the height of the aerosol column in the atmosphere. The
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effective extinction cross-sections were calculated from Mie theory assuming spherical homogeneous particles and log-normal size distributions for each component. The single scattering phase functions, at 550 nm, the single scattering albedo, the extinction cross-section per particle, and the extinction coefficient scaled to the aerosol spectral optical depth are shown in Fig. 7, for the final aerosol model used in the RTC calculations presented here. This will be referred to subsequently as the preferred model. The TOA radiances calculated using this model show reasonable agreement with AirMISR’s observations, as will be shown below, and, most importantly, its extinction cross-section exhibits the same spectral behavior as the observed aerosol optical depth, compared in the lower right panel of Fig. 7. This model consists of components in the proportions (by optical depth at 550 nm) of 70% sulfate, 25% mineral dust, accumulation mode, and 5% soot. The presence of these components is climatologically reasonable for the Moffet Field area. The effective scattering properties of the
Fig. 8. Comparison of the AirMISR observed radiances (solid lines) with those calculated from the RTC (crosses) assuming the preferred aerosol model and Lambertian surface reflectance model as approximated by ASD determination. See text for analysis leading to uncertainty measures on each point.
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aerosol mixtures were calculated according to the following equations: kext;mix ðlÞ ¼
n X
Ni kext;i ðlÞ
i¼1
wmix ðlÞ ¼
n X
fi ðlÞwi ðlÞ
i¼1
pmix ðV; lÞ ¼
n X fi ðlÞwi ðlÞpi ðV; lÞ i¼1
wmix ðlÞ
where wmix, kext,mix and pmix, are the effective single scattering albedo, extinction cross-section per particle, and phase function of the aerosol mixture, and wi, kext, i, and pi are, respectively, the corresponding quantities for the ith aerosol component. The fi, and Ni are fractional content of the ith aerosol component by optical depth and by number of particles, respectively, and n is the total number of components in the mixture. The scattering angle is V.
3.5. Radiative transfer code A monochromatic, one-dimensional RTC is used to calculate multiangle upwelling TOA or near-TOA radiance as well as direct and diffuse components of the radiance fields and associated fluxes (irradiance and radiant exitance) at both the surface and an aircraft/spacecraft altitude. The code is based on the discrete ordinate matrix operator method of Grant and Hunt (1968). The associated atmosphere model is described by the number of atmospheric layers, the optical properties (aerosol and Rayleigh scattering optical depths, phase functions, and single scattering albedos) of each layer, if known or estimated. The aerosol phase function and single scattering albedo are computed from the Mie theory assuming homogeneous spherical particles, an assumed size distribution (log-normal or power law), and a complex refractive index. The surface directional reflectance characteristics can be specified either by analytical/empirical models or a BRF derived from measurements with PARABOLA. The RTC has been verified
Fig. 9. D (%) equal to 100 (Model radiance AirMISR radiance)/AirMISR radiance for the preferred aerosol model and Lambertian reflectance assumption.
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against a second code based on the Hansen– Travis (1974) adding – doubling method. The results obtained exercising the two codes agree to within 0.1%.
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ces, calculated at the same set of wavelengths, were bandaveraged and weighted by the camera spectral response at MISR’s four bands. The RTC calculations are performed for the following two cases.
4. Results and discussion Ideally, in a vicarious calibration experiment, the calculated radiances are restrained by field measurements of optical depth, aerosol composition, and size distribution, and the surface BRF. For the purpose of this experiment, the TOA radiance calculations were performed using the field measurements of the optical depths, and surface HDRF, and the above-described preferred aerosol model. The calculated radiances are then compared with AirMISR radiances, given by applying laboratory calibration coefficients to the observed DN values. The field data were interpolated at a set of 27 wavelengths in the range 380 to 1030 nm. For comparison with AirMISR observations, the TOA radian-
4.1. Nadir view HDRF approximation for surface reflectance (Lambertian assumption) Fig. 8 shows the comparison of the AirMISR-observed TOA radiances with those calculated by the RTC using the preferred aerosol model described above and assuming Lambertian surface reflectance. The percent differences for all bands are shown in Fig. 9. These represent D (%) = 100 (Model radiance AirMISR radiance)/(AirMISR radiance). The uncertainty bars, shown in Fig. 8, on the RTC-calculated values represent scatter in the ASD observations of the target area together with uncertainties in atmospheric total optical depth. For clarity, the uncer-
Fig. 10. Comparison of the AirMISR observed radiances (solid lines) with those calculated from the RTC assuming the preferred aerosol model and the surface HDRF as approximated by PARABOLA III determination. See text for analysis leading to uncertainty measures on each point.
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tainty bars on the AirMISR data points are not shown in Fig. 8 and the subsequent figures. From Figs. 8 and 9, absolute disagreements between AirMISR and RTC-calculated radiances are less than 5% in the nadir viewing and increase ( 15 to 22%) with viewing angle. Except in the nadir viewing in the blue and red channels, these disagreements are greater than the uncertainty in the RTC-calculated radiances and indicate, in this case, that the RTC calculations incorporating a Lambertian surface overestimate the radiances in the forward viewing and underestimate them in the aftward viewing. At the longer wavelengths, the contribution to the TOA radiance (see below) is dominated by the surface reflectance, mostly by radiances reaching the sensors after being reflected once by the surface (direct surface component), and to a lesser extent, by those multiply scattered by the surface (diffuse surface component). If the surface were truly Lambertian, these disagreements should diminish in the red and nir channels. The Lambertian assumption is therefore inadequate.
4.2. HDRF from PARABOLA III Fig. 10 compares calculated and measured TOA radiances using the surface HDRF estimated from PARABOLA III observations. The uncertainty bars on the RTC-calculated points are from scatter in the PARABOLA III observations of the target area and from uncertainties in aerosol optical depth. Fig. 11 shows the percent differences for all bands for this case. Adoption of the HDRF surface model leads to improvement in the agreement between model and AirMISR radiances, especially at nir wavelengths, where surface contribution to the TOA radiance is most significant. To emphasize the increasing role of surface-interacting radiance at long wavelengths, Fig. 12 depicts the percent contribution of atmosphere and surface components for each channel. Fig. 12 indicates that in the blue the majority of radiation reaching the sensor at all viewing angles fore and aft arises in the atmosphere; in the nir, however, the great predominance at most view angles is from the ground. Except in the most oblique viewing in the blue channel,
Fig. 11. D (%) equal to 100 (Model radiance AirMISR radiance)/AirMISR radiance for the preferred aerosol model and PARABOLA-calculated HDRF.
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Fig. 12. Percent contribution to the total TOA radiance of total path radiance (solid lines) and total surface-interacted radiance (dotted lines). The preferred aerosol model and the PARABOLA-calculated HDRF were used in the calculations.
most of the differences in Fig. 11 are within the uncertainty in HDRF determination. In this case also, as shown from Figs. 10 and 11, the RTC calculations generally overestimate the TOA radiances in the forward viewing, while underestimate them in the aft viewing. Three causes for these systematic differences were investigated. 4.2.1. The choice of the aerosol model These systematic differences can be reduced if we choose an aerosol model which has more large particles than the one used in the analyses. The phase function of such model is smaller in the scattering angle range of 50 to 100, correspond here to the forward viewing, and larger in the range of 150 to 170, corresponding to the aft viewing. Such an aerosol model, however, has an extinction crosssection that is not consistent with the spectral variation of optical depth measurements. Another possibility is a model with more absorption at shorter wavelengths. This, however, may resolve the discrepancy in the forward viewing but not in the aftward viewing.
4.2.2. Using the HDRF in place of the BRF From the BRF/HDRF definitions given above, the HDRF is equivalent to the BRF weighted by the diffuse sky radiance in all incident angles. This results in a smoothing effect on the BRF. The difference between the extreme values of the BRF and HDRF increases with Sun angles and with atmospheric turbidity (Martonchik et al., 1998) and therefore, is expected to be maximum at shorter wavelengths. Differences of up to 40% through 60% were reported by Martonchik et al. (1998) at a Sun angle of 65 and an optical depth of 0.4. Accordingly, the BRF, if available from the PARABOLA III data, is expected to be larger than the HDRF in the aft viewing and smaller than the HDRF in the forward viewing, resulting in offsetting some or most of the differences shown in Fig. 11. 4.2.3. Systematic changes in TOA radiances from uncertainty in camera orientation While the INS system of the aircraft reports orientation of the principal axes of the airframe to 0.005, and ground
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target points are used to help specify camera orientation, the uncertainty in orientation of the camera with respect to the airframe has not yet been determined in-flight or on the ground, and cannot be ruled out as a source of error. Can the systematic differences of calculated and measured radiances with respect to nadir direction noted previously arise from camera orientation uncertainty? To offset the differences shown in Fig. 11, a rotation of the camera about the nadir and towards the aft direction results in an increase of the aftward viewing angles and a corresponding decrease in the forward viewing angles. Such rotation will increase the atmospheric path length for the aftward viewing leading to an increase in path radiance, with an opposite effect expected for the forward viewing. Simulation of radiances, depicting the situation for a 1, 2, and 4 change in the exit angles (due to an unknown constant pitch error in orientation) was carried out to assess the magnitude of changes in TOA radiance. The corresponding values of the HDRF were calculated for the new viewing angles. Fig. 13, which illustrates the differences (%) between the simulated and
observed radiances, shows that a maximum rotation of 2 seems to improve the disagreements in the blue and green channels but does not explains all the disagreements in the aftward viewing. At 4 the differences increase in the forward direction. In the red and nir channels, any change in the viewing angles seems to increase the differences. However, in these channels, the differences are still within the 10% uncertainty of the HDRF values. The above results indicate that a combination of uncertainties in camera orientation (only 1 to 2) and in characterizing the aerosol model and the use of the HDRF in place of the BRF, may account for the disagreements, shown in Fig. 10, between observed and calculated TOA radiances. Other sources for the disagreements are under investigation. For example, the radiative transfer calculation assumes plane-parallel atmosphere conditions, and a level boundary, whereas there are buildings present around the periphery that may contribute multiple reflections to the actual measured radiances. The possible contribution of atmospheric scattering from adjacent areas (adjacency
Fig. 13. Differences (%) between observed and calculated radiances, as in Fig. 11 (solid line) and depicting a rotation of AirMISR camera by 1 (dotted line), 2 (dashed line), and 4 (dash – dotted line).
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effects) has also been neglected. In future experiments, to account for adjacency effects, a method termed radiance propagation will be used. This employs measurements by PARABOLA III of the surface-reflected radiance in the target area, which include direct beam and radiation multiply reflected between sky and ground that includes contributions from the target and surrounding surfaces. The RTC is modified to accept upward radiance incident on the lower boundary, rather than reflection of downwelling radiance. This eliminates need for measurement of the surface BRF. The optical depth and the aerosol scattering model are still required to calculate the diffuse transmittance of the atmosphere. This procedure was not possible to apply at Moffett Field because PARABOLA III measurements were delayed from time of the overflight. Future calibration experiments will include: (i) use of extended homogeneous surface targets, (ii) multiple aircraft overpasses of the target area to check on repeatability through independent determinations, (iii) sky radiance measurements at the surface and surface irradiance measurements to better constrain the aerosol model used, (iv) a more complete determination of surface BRF from the PARABOLA III instrument.
References Bevington, P. R. (1969). Data reduction and error analysis for the physical sciences. New York: McGraw-Hill (336 pp.). Bruegge, C. J., Chrien, N. L., Diner, D. J., Duval, V. G., Korechoff, R. P., & Woodhouse, R. M. (1996). Level 1 in-flight radiometric calibration and characterization algorithm theoretical basis, JPL D-13398. Jet Propulsion Laboratory, California Institute of Technology (82 pp.). Bruegge, C., Chrien, N., & Haner, D. (1999). A Spectralon BRF data base for MISR calibration applications. Remote Sensing of the Environment, (this issue).
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Chrien, N. L. (1998). Channel display user’s guide, JPL D-16283. Jet Propulsion Laboratory, California Institute of Technology (15 pp.). Chrien, N. L., Bruegge, C. J., & Gaitley, B. J. (1999). AirMISR laboratory calibration results. Remote Sensing of the Environment, (this issue). Deering, D. W., & Leone, P. (1986). Sphere-scanning radiometer for rapid directional measurements of sky and ground radiance. Remote Sensing of the Environment, 19, 1 – 24. Diner, D. J., Barge, L. M., Bruegge, C. J., Chrien, T. G., Conel, J. E., Eastwood, M. E., Garcia, J. D., Hernandez, M. A., Kurzweil, C. G., Ledeboer, W. C., Pignatano, N. D., Sarture, C. M., & Smith, B. G. (1998). The airborne multi-angle imaging spectroradiometer (AirMISR): instrument description and first results. IEEE Transactions on Geoscience Remote Sensing, 36 (4), 1339 – 1349. Diner, D. J., Beckert, J. C., Reilly, T. H., Bruegge, C. J., Conel, J. E., Martonchik, J. V., Ackerman, T. P., Davies, R., Gerstel, S. A. W., Gordon, H. R., Kahn, R. A., Muller, J.-P., Myneni, R. B., Pinty, B., Sellers, P. J., & Verstraete, M. M. (1998). Multi-angle imaging spectroradiometer (MISR) instrument description and experiment overview. IEEE Transactions on Geoscience Remote Sensing, 36 (4), 1072 – 1087. Flittner, D. E., Herman, B. M., Thome, K. J., & Simpson, J. M. (1993). Total ozone and aerosol optical depths inferred from radiometric measurements in the Chappuis absorption band. Journal of the Atmospheric Sciences, 50 (8), 1113 – 1121. Grant, I. P., & Hunt, G. E. (1968). Solution of radiative transfer problems using the invariant Sn method. Monthly Notices of the Royal Astronomical Society, 141, 27 – 41. Hansen, J. E., & Travis, L. D. (1974). Light scattering in planetary atmospheres. Space Science Reviews, 16, 527 – 610. Jovanovic, V. (1996). Level 1 in-flight geometric calibration algorithm theoretical basis, JPL D-13399. Jet Propulsion Laboratory, California Institute of Technology (58 pp.). Martonchik, J. (1994). Retrieval of surface directional reflectance properties using ground level multiangle measurements. Remote Sensing of the Environment, 50, 303 – 316. Shettle, E. P. & Fenn, R. W. (1979). Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, AFGL-TR-79-0214 (Environmental research paper No 676). Massachusetts: Air Force Geophysics Laboratory, Hanscomb AFB, 94 pp.
Vicarious calibration A reflectance-based experiment with AirMISR Wedad A. Abdou*, James E. Conel, Stuart H. Pilorz, Mark C. Helmlinger, Carol J. Bruegge, Barbara J. Gaitley, William C. Ledeboer, John V. Martonchik Jet Propulsion Laboratory, California Institute of Technology, M.S. 169-237, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, USA
Abstract A vicarious reflectance-based calibration experiment for the Multiangle Imaging SpectroRadiometer (MISR) airborne simulator, AirMISR, is described as one precursor experiment of this type planned for postlaunch application to MISR itself. The experiment produces a set of multiangle near-top-of-atmosphere radiances that are compared with the multiangle AirMISR radiances, established using a laboratory calibration. The field and aircraft data were collected as part of an engineering test flight at Moffett Field, CA, on November 5, 1997. A concrete tarmac was used as the field target. Atmospheric optical depth data were collected adjacent to the target throughout the actual overflight period using a single Reagan solar radiometer. For logistical reasons, the surface hemispherical directional reflectance factor (HDRF) was determined 7 days later using the Portable Apparatus for Rapid Acquisition of Bidirectional Observation of the Land and Atmosphere III (PARABOLA III), along with the areally averaged spectral HDRF at normal incidence, obtained with an Analytical Spectral Devices (ASD) FieldSpec moderate resolution field spectrometer. AirMISR overflew the target under clear sky conditions though the aerosol turbidity was high ( 0.3 at 550 nm). Good to fair agreement has been obtained at all angles and wavelengths between the top-of-atmosphere (TOA) radiances calculated for the measured atmospheric and surface conditions and the radiances incident at AirMISR as determined from the laboratory calibration. Some systematic disagreements are present. The largest disagreements ( 15% in the blue) are found at the highest view angles and the smallest at nadir viewing ( < 5%). Possible explanations for the differences in radiances at large view angles are discussed. D 2001 Elsevier Science Inc. All rights reserved.
1. Introduction The Multiangle Imaging SpectroRadiometer (MISR) was launched on December 1999 on the Earth Observing System, EOS-AM1 spacecraft (Diner, Beckert, et al., 1998). MISR has nine CCD pushbroom cameras which will provide images of the Earth’s surface in four bands (blue, green, red, and nir at 446, 558, 672, and 866 nm, respectively) at angles of 0 (An), ± 26.1 (Af, Aa), ± 45.0 (Bf, Ba), ± 60.0 (Cf, Ca), and ± 70.5 (Df, Da), relative to nadir, both forward (+) and aftward ( ) along the direction of flight. The subscripts n, f, and a imply cameras viewing in the nadir, forward, and aftward directions, respectively. One of the major tasks of the EOS and of MISR is to provide stable well-calibrated measurements of key parameters that are crucial to a long-term assessment of temporal variations * Corresponding author. Tel.: +1-818-354-6806; fax: +1-818-3934619. E-mail address: [email protected] (W.A. Abdou).
in the Earth radiation budget especially due to clouds, aerosols, and to land surface albedo. AirMISR is an airborne MISR simulator that collects MISR-like data for the purpose of supporting the validation of MISR algorithms and calibration of the MISR instrument (Diner, Barge, et al., 1998). Radiometric calibration of AirMISR and MISR means determining an accurate relationship between reflected solar spectral radiance and instrument output. Multiple calibration pathways will be used to obtain such relationships: (1) laboratory calibration (MISR and AirMISR) (Chrien, Bruegge, & Gaitley, 1999); (2) onboard calibration involving monitoring of reflectance stability of Spectralon reference panels with absolute high quantum efficiency (HQE) photodiodes (MISR) (Bruegge et al., 1996) or terrain radiance with PIN diodes (AirMISR); (3) ground-based vicarious calibrations using natural uniform targets (MISR and AirMISR). This paper concerns pathway (3), and is the first field experiment we report that extends the vicarious calibration method, heretofore usually carried out for sensors viewing at close-to-normal inci-
0034-4257/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved. PII: S 0 0 3 4 - 4 2 5 7 ( 0 1 ) 0 0 2 1 3 - 9
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dence, to all angles of AirMISR instrument viewing (i.e., nadir to ± 70.5). Vicarious calibration forms a complete independent pathway for monitoring of instrument performance, including error assessment with all reflectance standards, field instruments, and atmospheric radiation measurements employed tied to National Institute of Standards and Technology (NIST)-verifiable standards. The method involves measuring either the surface reflectance or the surface-leaving radiance over the ground hemisphere at a target point, together with atmospheric scattering and absorption properties. A validated and benchmarked radiative transfer code (RTC) is used, constrained by the field measurements, to calculate the topof-atmosphere (TOA) radiance at nine view angles and four wavelengths, corresponding to the viewing directions and wavelengths of the nine MISR cameras on orbit, or to the nine view angles and four wavelengths of the gimballed single AirMISR camera. The radiances calculated from the RTC are then compared to the radiances predicted at the instrument using the laboratory and in-flight-determined calibration coefficients. Ideally, the sites of natural targets employed for vicarious calibration experiments (dry uniform lake beds in high clear remote desert areas) are chosen to minimize atmospheric scattering effects and influences of clouds. Under these conditions, TOA radiance is predominantly sensitive to the accurate measurement of surface reflectance properties. Although these ideal conditions were not met for the data acquired on November 5, 1997, valuable lessons are learned by applying the analysis tools to the observations.
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2. AirMISR instrument and observations A complete description of the AirMISR system is found in Diner, Barge, et al. (1998). AirMISR is constructed with a single camera from MISR brassboard components. The camera is mounted on a gimbal system that provides rotation about a horizontal axis into viewing directions duplicating those of MISR itself. The AirMISR package resides in the nose cone of the NASA ER-2, which flies at 20 km above sea level. AirMISR provides multiple multiangle views of nested target areas that increase in alongtrack and cross-track size with increasing view angle as shown in Fig. 1. The length of flight line required for a single pass is about 120 km. The instantaneous footprint of the camera system varies with view angle from 7 m cross-track by 6 m along-track in the nadir view to 21 55 m at the most oblique angle. Lines of image data are acquired every (Dts=) 40.8 ms. This coupled with an aircraft ground speed of (Va=) 200 m/s lead to an along-track sample spacing of (VaDts=) 8 m. While the nadir image is thus slightly undersampled, the more oblique directions are progressively increasingly oversampled, leading to an apparent smear in these images that must be accounted for in location of pixels sampled at the surface for purposes of calibration. In addition to oversampling, there is a slight systematic displacement between images of different color bands (Jovanovic, 1996) along-track at each view angle that must
Fig. 1. The view directions and nested ground fields-of-view of AirMISR for an aircraft altitude of 20 km.
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Table 1 Actual view angles of AirMISR camera during Moffett overflight Camera
An
Af/Aa
Bf/Ba
Cf/Ca
Df/Da
Angle ()
2.72
26.66/ 25.04
46.18/ 45.09
60.93/ 59.77
71.77/ 65.31
be taken into account when locating reference ground target areas in the unresampled image data. This arises because the detector line arrays for each color are displaced parallel to one another. To overcome oversampling, foreshortening, and color separation effects, homogeneous target areas are best suited to needs of the ground target calibration method. In practice, the sorting out of ground-sampled areas and differences in alignment for each band, hence actual ground location of pixels in heterogeneous areas, are accomplished using special viewing software (Chrien, 1998) that allows magnification of targets, calculation of pixel coordinates, as well as means and standard deviations of instrument responses over each sampled area and for each wavelength. Knowledge of the pointing accuracy of AirMISR relative to the local vertical is crucial for accurate assessment of the
instrument calibration, especially at higher view angles. For the aerosol and surface reflectance models, this is so because the retrieved radiance depends on absolute knowledge of the pointing direction. There are four components of the orientation: (1) the camera geometric model described above, (2) the orientation of AirMISR with respect to the ER-2 airframe, (3) the orientation of the ER-2 airframe itself with respect to the local vertical, and (4) the angular position of the gimbal on each particular forward or backward scan. Of these, the orientation of the airframe in terms of roll, pitch, and yaw, is determined from on-board navigation data to ± 0.005 in each angle. Although the gimbal housing (drum) is attached to an encoder with resolution of 2000 steps/deg, the angular position of the gimbal is presently known only from optical switch position data to ± 1 for
Fig. 2. The nadir view of Moffett Field and environs on Nov 5, 1997. Ground calibration target location (and Reagan solar radiometer station) is marked by the white arrow.
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Fig. 3. DN values from ground target area for the four AirMISR bands over the nine viewing angles. Sign convention is positive angles, forward direction (into sun), negative angles, aftward direction (away from sun). Error bars represent scatter in the DN values.
each angle. Component (2) is under study. Systematic orientation offsets have been observed as a result of ground control unit analysis, and an error of a few degrees in pitch must be taken into account. The AirMISR flight over Moffett Field, CA on November 5 took place under cloud-free but hazy atmospheric conditions at 19:27 UT (11:27 a.m., PST). The flight line was about 186 to the southwest. The solar zenith and azimuth angles were 53 and 172.6, respectively. The actual view angles of cameras with respect to the target surface normal were determined from the image data, using AirMISR navigation data and the above-mentioned viewing software, to be as given in Table 1. Fig. 2 is a nadir view image of Moffett Field showing the position of the target area located on a uniform concrete tarmac at latitude: 37420 N, longitude: 122060 W, elevation = 5 m. For analyses reported here, the raw unresampled, AirMISR image data are used. The AirMISR DN values for the ground-measured target area, located manually in the imagery using important landmarks recognized for each viewing angle and for each channel, are shown in Fig. 3.
The angle convention adopted is positive camera angles represent the forward direction, and negative angles aftward direction, corresponding to MISR cameras, Af/Aa, Bf/Ba, Cf/Ca, and Df/Da. The number of effective pixels included in the averages vary with view angle because the groundprojected field-of-view (solid angle) of AirMISR increases with viewing angle. The averages and the standard deviation bars of Fig. 3 are based on the aggregate number of pixels of the sample area as given in Table 2 for each view angle and channel. The AirMISR DN spectral response were converted into radiances using the measured AirMISR calibration coefficients. AirMISR was calibrated in the laboratory using the MISR 65-in. integrating sphere and the same light sources, procedures, and analysis tools developed for MISR (Chrien et al., 1999). The relationship between instrument response DN and incident band-averaged radiance L¯ in each band and in each pixel was developed as the quadratic form: DN DN0 ¼ g0 þ g1 L þ g2 L2
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Table 2 Number of pixels averaged in target area as function of view angle Color View
Blue
Green
Red
Near-IR
An Aa/Af Ba/Bf Ca/Cf Da/Df
64 90/72 56/72 30/36 20/35
80 80/80 56/90 35/25 42/28
99 72/70 64/64 30/30 30/40
80 72/80 56/63 30/36 24/30
where DN0 is the offset bias response, g0, g1, g2 are gain coefficients which vary with wavelength and from pixel to pixel array-averaged gain coefficients are given in Chrien et al. (1999), and L¯ is weighted by the instrument spectral response.
3. Field instruments, methodology, and observations For accurate calculations of the TOA radiance observed by AirMISR, ground measurements are used to constrain the RTC. The required input to the RTC must include: (1) the atmospheric optical depths, retrieved from the Reagan solar radiometer; (2) the surface BRF, retrieved from the Portable Apparatus for Rapid Acquisition of Bidirectional Observation of the Land and Atmosphere III (PARABOLA III) data; and describing the part of the surface in the camera’s fields-of-view; and (3) a composition and size distribution characterizing the aerosol present at the time of AirMISR flight. For logistical reasons and since this was primarily an engineering flight of AirMISR, only solar radiometer observations were obtained during the experiment. Seven days after the flight, the PARABOLA III and the Analytical Spectral Devices (ASD) measurements were collected about the same time of the day as the AirMISR flight and at the designated target area. 3.1. Reagan solar radiometer and atmospheric optical depth measurements The autotracking Reagan solar radiometer measures bottom-of-atmosphere (BOA) solar spectral irradiance and is used to determine average and instantaneous spectral optical depth in 10 channels, each about 10 nm in width near 380, 400, 440, 520, 600 670, 780, 870, 940, and 1030 nm. These instruments are calibrated (zero airmass instrument response determined) using the well-known Langley method by plotting the logarithm of instrument response vs. air mass and extrapolating to zero airmass. The Rayleigh scattering optical depth is calculated from a field measurement of atmospheric surface pressure. A residual optical depth consisting of the total instantaneous optical depth minus Rayleigh component is the starting point for simultaneous retrieval of aerosol and ozone components using a procedure due to Flittner, Herman, Thome, and Simpson (1993), which obtains the spectral aerosol optical
depth independent of any assumption about the aerosol size distribution. The Reagan radiometer was set up adjacent to a nearby hanger off the tarmac and operated continuously between 19:06 and 20:34 UT (11:06 and 12:34 PST). The spectral optical depth components for the time of overflight extracted from these records are shown in Fig. 4. The aerosol optical depth at 550 nm is near 0.3 and is a factor of three higher than would ordinarily be encountered for such calibration experiments under clear sky conditions in high desert regions. However, the relatively heavy atmospheric conditions encountered at Moffett Field provide a good test case for the sensitivity of calculated TOA radiances to aerosol compositional model, and for the relative importance of path as opposed to ground-leaving radiance in the calculations. The main source of uncertainty in the optical depths are the instrument calibration constant V0, the signal which would be obtained at zero airmass. The standard deviation of the total optical depth, st, is estimated from the relationship st tm0(sV0/V0), where m0 is cosine of the solar zenith angle and sV0 is the standard deviation of multiple V0 retrievals in the history of V0 determination. This relationship follows applying error propagation formulas (Bevington, 1969) to the Beer– Lambert law, assuming that individual measurements are error-free compared to variations introduced by atmospheric fluctuations. From this relationship, an upper limit on uncertainty in optical depth was estimated to be 0.01 in total optical depth at 380 nm. The error bars in Fig. 4 reflect that value at all wavelengths. These same magnitudes have been applied to the calculated aerosol optical depths, since no method is available to separate the combined Rayleigh, ozone, and aerosol optical depth uncertainties present. 3.2. PARABOLA III and surface BRF/HDRF The PARABOLA is a third-generation sphere-scanning radiometer built by Sensit (Mayville, ND) and represents a substantial revision in design and capability over the first version of this instrument (Deering & Leone, 1986). PARABOLA III consists of two separate sensor heads mounted at opposite ends of a center-suspended horizontal scanning arm that rotates continuously through 360 about a vertical axis. Each sensor head contains the detector assemblies for four of eight channels (443, 551, 650, 860, 944, 1028, 1652, and 400– 700 nm). Each individual head scans synchronously with the other from zenith to nadir in vertical angle. The combined synchronized motion of the heads about both axes generates a stepwise pattern of 5 circular full apex angle overlapping fields of view of sky hemisphere, and a series of 5 ellipsoidal pixels on the ground that increase in size from nadir to horizon. An entire scan of both sky and ground hemispheres generates 2664 ( = 37 72) pixels in about 3.3 min including downloading to memory. The dynamic range of the instrument is 220, enabling both the direct solar beams, sky radiance and
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Fig. 4. Total, Rayleigh, aerosol, and ozone optical depths as functions of wavelength for the November 5 calibration date for 19:27 UT. Error bars represent uncertainties taken uniformly to be 0.01 in optical depth. Based on multiple V0 determinations, this error is an overestimate.
ground-leaving radiance, to be obtained without gain changes. Details of the PARABOLA III measurements and calibration procedures will be reported elsewhere. The PARABOLA III measurements are used to retrieve the surface bidirectional reflectance factor (BRF), which is defined as the ratio between the radiance reflected from the surface to that reflected from an ideal Lambertian reflector under the same direct illumination. To obtain the BRF, Rx,y, at a point (x,y) from PARABOLA III measurements, ground-reflected radiance, direct irradiance, and diffuse sky radiance measurements are combined in a procedure developed by Martonchik (1994). A complete solution requires measurements for all solar incidence angles from horizon to zenith, but in practice, assumptions about behavior of the BRF for solar incident angles not measured (i.e., constancy or simple interpolation) can be made with little error. In the present application at Moffett Field, because of the logistics of airfield operations and because of sky conditions, PARABOLA III measurements were limited to a
period of about 45 min, on November 12, but near the time of AirMISR overpass (18:36 and 19:21 UT). Thus, a complete BRF retrieval was not possible, but use was made of the available PARABOLA III data to calculate the hemispherical directional reflectance factor (HDRF), rx,y, of the target area to approximate the BRF and to display anisotropic reflectance effects. The HDRF is defined as the ratio between the radiance reflected from the surface in a given direction (m,j) to that reflected into the same beam geometry from a perfect Lambertian surface illuminated under identical atmospheric conditions. This is expressed as: rx;y ðm; m0 ; j j0 Þ Z Z 1 1 2p ¼ Rx;y ðm; m0 ; j j0 Þ p 0 0 0 0 0 0 0 Linc x;y ðm ; m0 ; j j0 Þm dm dj Z Z 1 1 2p inc 0 =; Lx;y ðm ; m0 ; j0 j0 Þm0 dm0 dj0 p 0 0
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where m is cosine of the view zenith angle with convention < 0 upward, m0 is cosine of the Sun zenith angle, j is azimuth of the view direction measured relative to geographic north, and j0 the azimuth of the Sun. Lx,yinc is the incident total direct and diffuse radiance at point x,y. The numerator is measured by the PARABOLA III from nadir to the horizon at all azimuths. The denominator, representing the radiance reflected by a perfect Lambertian surface, is measured in the field using a Spectralon diffuse panel. During data acquisition, the Spectralon panel is placed in the southwest corner of the PARABOLA nadir field-of-view such that the radiance reflected by the panel is measured in the nadir and at 5 and 10 viewing angles from the nadir. From these measurements, and the prior laboratory measurements of the Spectralon BRF (Bruegge et al., 1999), radiances reflected by the Spectralon panel in the remaining viewing angles are determined to a good approximation. The HDRF, as expressed by the above equation, is equivalent to the BRF weighted by all sky radiance incident
angles and is a better approximation for the surface BRF than is a Lambertian assumption, as will be shown. Furthermore, the HDRF can be retrieved for given Sun incidence direction from any one complete spherical scan of the PARABOLA. The PARABOLA III instrument was set up in the center of a uniform concrete target area on a pedestal with the sensing heads 2 m above the tarmac surface. From this height, the area swept out on the surface was approximately 11 m in radius, using, as a limiting view angle, the value of 80 to avoid mixing of sky and ground pixels. The 14 scans available were used to estimate the surface HDRF. Fig. 5 shows these data interpolated into the AirMISR viewing directions from the full 5 net of retrievals. The existence of inhomogeneities in the target reflectance (most probably from few moist areas remaining from precipitation on previous day) is evident from irregularities in the HDRF observed at angles near 25(aft viewing) and at 60 (forward viewing). These irregular data were smoothed out
Fig. 5. The HDRF for target area determined by PARABOLA III on November 11, 1997. The HDRF shown are retrieved from 10 full scans and the error bars represent ± 10% of the average for the multiple determinations. The dotted horizontal lines in each panel represent the assumed lambertian reflectance obtained by the ASD determination. Width of the lines represents the 1s ( ± 1.5%) scatter in 100 samples over the target area.
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by interpolation between surrounding data points, as shown by the solid line. The error bars shown in Fig. 5 represents an upper limit of ± 10% uncertainty in the HDRF determination since the PARABOLA data were made 7 days after the AirMISR flight. For comparison, the HDRF values measured by the ASD in the nadir viewing (see below) are also shown in Fig. 5. This comparison makes evident deviations from ideal Lambertian behavior of the real surface, especially in the aftward (backscatter or negative view angle) direction. Also, the PARABOLA and ASD HDRFs should agree in the nadir direction. This is not exactly so except in the green channel. The slight disagreements, however, are within the estimated ± 10% uncertainty in the HDRF determination. 3.3. FieldSpec portable spectrometer and surface HDRF The portable spectrometer manufactured by ASD provides measurements of the surface HDRF in the nadir direction of view, rx,y ( 1; m0,j0). Traditionally, for the
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calibration of nadir viewing sensors, the target surface has often been assumed Lambertian and the nadir-viewing HDRF taken as an estimate of the Lambertian value. Thus in the present case, the ASD data were considered to be sufficient as nondirectional input to the RTC, and in the preliminary analysis, it was so assumed here. The ASD allows rapid estimation of the surface spectral HDRF between 350 and 2500 nm at an average spectral resolution of about 10 nm. The few second sampling time allows measurements over kilometer-size areas, typical of those employed in calibration exercises, to be carried out rapidly, thus minimizing possible large changes in HDRF accompanying motion of the Sun. In the field these measurements are made relative to the reflectance standard Spectralon. The latter, however, is not perfectly Lambertian and conversion of the ASD measurements to a basis of a perfectly diffuse Lambertian reflector for the current solar zenith angle is required. The correction factor is evaluated to be exactly equal to the Spectralon HDRF. Because the Spectralon is nearly a
Fig. 6. The spectral variation of surface reflectance (HDRF at normal viewing direction) obtained by the ASD FieldSpec on November, 11, 1979. Scatter on the observations (dotted lines) is 1s = ± 1.5%.
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Table 3 Components of aerosol models used in the analysis Component
rca (mm)
sb
Refractive index, n ik (550 nm)
Trophospheric sulfate Tropospheric sulfate with absorption, accumulation mode Mineral dust, accumulation mode Mineral dust, coarse mode Small ruralc Large ruralc Urban soot Sea salt, nucleation mode Sea salt, accumulation mode
0.07 0.07 0.47 1.9 0.03 0.5 0.012 0.05 0.5
1.86 1.86 2.6 2.6 2.24 2.5 2.0 2.5 2.0
1.44 i0.00 1.44 i0.005 1.53 i0.0055 1.53 i0.0055 1.53 i0.0066 1.53 i0.00 1.75 i0.44 1.5 i0.00 1.5 i0.00
a b c
Log-normal distribution characteristic radius. Log-normal distribution spread. From Shettle and Fenn (1979).
Lambertian reflector, it was found that its BRF, which is readily available from laboratory measurements (Bruegge et al., 1999), can be used as a correction factor with less than 1% errors. The average value of the spectral HDRF at normal incidence viewing from 100 samples obtained randomly
over the area, and taken at times spaced about the overflight time, is shown in Fig. 6. The range of 1s scatter for the target area is about ± 1.5% of the HDRF magnitude itself, and is almost independent of wavelength. The HDRF values from ASD spectra are averaged over the AirMISR band passes and taken to represent the magnitude of the
Fig. 7. Scattering phase function, spectral extinction coefficient, single scattering albedo, and the extinction cross-section, scaled to the aerosol spectral optical depth (dots), for the preferred aerosol model. Error bars represent an upper limit of 0.01 uncertainty in the aerosol optical depth.
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Lambertian reflectance for use in the model calculations described below. 3.4. Aerosol models and extinction cross-sections derived from solar radiometer data No direct measurements of the aerosol size distribution and composition were available for this experiment. However, since the aerosol turbidity was high (Fig. 4), it was deemed essential to investigate sensitivity of the TOA model results to choice of aerosol model. Several of the aerosol models shown in Table 3 were tried as representations of both pure forms and mixed together in various proportions. The final model selection was based on generating a spectral extinction cross-section per particle, kext, that followed the measured aerosol spectral optical depth taer through the relationship: taer kextNZ (assuming a homogeneous vertical distribution for the aerosol), where N is the effective particle number per unit volume, and Z is the height of the aerosol column in the atmosphere. The
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effective extinction cross-sections were calculated from Mie theory assuming spherical homogeneous particles and log-normal size distributions for each component. The single scattering phase functions, at 550 nm, the single scattering albedo, the extinction cross-section per particle, and the extinction coefficient scaled to the aerosol spectral optical depth are shown in Fig. 7, for the final aerosol model used in the RTC calculations presented here. This will be referred to subsequently as the preferred model. The TOA radiances calculated using this model show reasonable agreement with AirMISR’s observations, as will be shown below, and, most importantly, its extinction cross-section exhibits the same spectral behavior as the observed aerosol optical depth, compared in the lower right panel of Fig. 7. This model consists of components in the proportions (by optical depth at 550 nm) of 70% sulfate, 25% mineral dust, accumulation mode, and 5% soot. The presence of these components is climatologically reasonable for the Moffet Field area. The effective scattering properties of the
Fig. 8. Comparison of the AirMISR observed radiances (solid lines) with those calculated from the RTC (crosses) assuming the preferred aerosol model and Lambertian surface reflectance model as approximated by ASD determination. See text for analysis leading to uncertainty measures on each point.
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aerosol mixtures were calculated according to the following equations: kext;mix ðlÞ ¼
n X
Ni kext;i ðlÞ
i¼1
wmix ðlÞ ¼
n X
fi ðlÞwi ðlÞ
i¼1
pmix ðV; lÞ ¼
n X fi ðlÞwi ðlÞpi ðV; lÞ i¼1
wmix ðlÞ
where wmix, kext,mix and pmix, are the effective single scattering albedo, extinction cross-section per particle, and phase function of the aerosol mixture, and wi, kext, i, and pi are, respectively, the corresponding quantities for the ith aerosol component. The fi, and Ni are fractional content of the ith aerosol component by optical depth and by number of particles, respectively, and n is the total number of components in the mixture. The scattering angle is V.
3.5. Radiative transfer code A monochromatic, one-dimensional RTC is used to calculate multiangle upwelling TOA or near-TOA radiance as well as direct and diffuse components of the radiance fields and associated fluxes (irradiance and radiant exitance) at both the surface and an aircraft/spacecraft altitude. The code is based on the discrete ordinate matrix operator method of Grant and Hunt (1968). The associated atmosphere model is described by the number of atmospheric layers, the optical properties (aerosol and Rayleigh scattering optical depths, phase functions, and single scattering albedos) of each layer, if known or estimated. The aerosol phase function and single scattering albedo are computed from the Mie theory assuming homogeneous spherical particles, an assumed size distribution (log-normal or power law), and a complex refractive index. The surface directional reflectance characteristics can be specified either by analytical/empirical models or a BRF derived from measurements with PARABOLA. The RTC has been verified
Fig. 9. D (%) equal to 100 (Model radiance AirMISR radiance)/AirMISR radiance for the preferred aerosol model and Lambertian reflectance assumption.
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against a second code based on the Hansen– Travis (1974) adding – doubling method. The results obtained exercising the two codes agree to within 0.1%.
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ces, calculated at the same set of wavelengths, were bandaveraged and weighted by the camera spectral response at MISR’s four bands. The RTC calculations are performed for the following two cases.
4. Results and discussion Ideally, in a vicarious calibration experiment, the calculated radiances are restrained by field measurements of optical depth, aerosol composition, and size distribution, and the surface BRF. For the purpose of this experiment, the TOA radiance calculations were performed using the field measurements of the optical depths, and surface HDRF, and the above-described preferred aerosol model. The calculated radiances are then compared with AirMISR radiances, given by applying laboratory calibration coefficients to the observed DN values. The field data were interpolated at a set of 27 wavelengths in the range 380 to 1030 nm. For comparison with AirMISR observations, the TOA radian-
4.1. Nadir view HDRF approximation for surface reflectance (Lambertian assumption) Fig. 8 shows the comparison of the AirMISR-observed TOA radiances with those calculated by the RTC using the preferred aerosol model described above and assuming Lambertian surface reflectance. The percent differences for all bands are shown in Fig. 9. These represent D (%) = 100 (Model radiance AirMISR radiance)/(AirMISR radiance). The uncertainty bars, shown in Fig. 8, on the RTC-calculated values represent scatter in the ASD observations of the target area together with uncertainties in atmospheric total optical depth. For clarity, the uncer-
Fig. 10. Comparison of the AirMISR observed radiances (solid lines) with those calculated from the RTC assuming the preferred aerosol model and the surface HDRF as approximated by PARABOLA III determination. See text for analysis leading to uncertainty measures on each point.
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tainty bars on the AirMISR data points are not shown in Fig. 8 and the subsequent figures. From Figs. 8 and 9, absolute disagreements between AirMISR and RTC-calculated radiances are less than 5% in the nadir viewing and increase ( 15 to 22%) with viewing angle. Except in the nadir viewing in the blue and red channels, these disagreements are greater than the uncertainty in the RTC-calculated radiances and indicate, in this case, that the RTC calculations incorporating a Lambertian surface overestimate the radiances in the forward viewing and underestimate them in the aftward viewing. At the longer wavelengths, the contribution to the TOA radiance (see below) is dominated by the surface reflectance, mostly by radiances reaching the sensors after being reflected once by the surface (direct surface component), and to a lesser extent, by those multiply scattered by the surface (diffuse surface component). If the surface were truly Lambertian, these disagreements should diminish in the red and nir channels. The Lambertian assumption is therefore inadequate.
4.2. HDRF from PARABOLA III Fig. 10 compares calculated and measured TOA radiances using the surface HDRF estimated from PARABOLA III observations. The uncertainty bars on the RTC-calculated points are from scatter in the PARABOLA III observations of the target area and from uncertainties in aerosol optical depth. Fig. 11 shows the percent differences for all bands for this case. Adoption of the HDRF surface model leads to improvement in the agreement between model and AirMISR radiances, especially at nir wavelengths, where surface contribution to the TOA radiance is most significant. To emphasize the increasing role of surface-interacting radiance at long wavelengths, Fig. 12 depicts the percent contribution of atmosphere and surface components for each channel. Fig. 12 indicates that in the blue the majority of radiation reaching the sensor at all viewing angles fore and aft arises in the atmosphere; in the nir, however, the great predominance at most view angles is from the ground. Except in the most oblique viewing in the blue channel,
Fig. 11. D (%) equal to 100 (Model radiance AirMISR radiance)/AirMISR radiance for the preferred aerosol model and PARABOLA-calculated HDRF.
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Fig. 12. Percent contribution to the total TOA radiance of total path radiance (solid lines) and total surface-interacted radiance (dotted lines). The preferred aerosol model and the PARABOLA-calculated HDRF were used in the calculations.
most of the differences in Fig. 11 are within the uncertainty in HDRF determination. In this case also, as shown from Figs. 10 and 11, the RTC calculations generally overestimate the TOA radiances in the forward viewing, while underestimate them in the aft viewing. Three causes for these systematic differences were investigated. 4.2.1. The choice of the aerosol model These systematic differences can be reduced if we choose an aerosol model which has more large particles than the one used in the analyses. The phase function of such model is smaller in the scattering angle range of 50 to 100, correspond here to the forward viewing, and larger in the range of 150 to 170, corresponding to the aft viewing. Such an aerosol model, however, has an extinction crosssection that is not consistent with the spectral variation of optical depth measurements. Another possibility is a model with more absorption at shorter wavelengths. This, however, may resolve the discrepancy in the forward viewing but not in the aftward viewing.
4.2.2. Using the HDRF in place of the BRF From the BRF/HDRF definitions given above, the HDRF is equivalent to the BRF weighted by the diffuse sky radiance in all incident angles. This results in a smoothing effect on the BRF. The difference between the extreme values of the BRF and HDRF increases with Sun angles and with atmospheric turbidity (Martonchik et al., 1998) and therefore, is expected to be maximum at shorter wavelengths. Differences of up to 40% through 60% were reported by Martonchik et al. (1998) at a Sun angle of 65 and an optical depth of 0.4. Accordingly, the BRF, if available from the PARABOLA III data, is expected to be larger than the HDRF in the aft viewing and smaller than the HDRF in the forward viewing, resulting in offsetting some or most of the differences shown in Fig. 11. 4.2.3. Systematic changes in TOA radiances from uncertainty in camera orientation While the INS system of the aircraft reports orientation of the principal axes of the airframe to 0.005, and ground
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target points are used to help specify camera orientation, the uncertainty in orientation of the camera with respect to the airframe has not yet been determined in-flight or on the ground, and cannot be ruled out as a source of error. Can the systematic differences of calculated and measured radiances with respect to nadir direction noted previously arise from camera orientation uncertainty? To offset the differences shown in Fig. 11, a rotation of the camera about the nadir and towards the aft direction results in an increase of the aftward viewing angles and a corresponding decrease in the forward viewing angles. Such rotation will increase the atmospheric path length for the aftward viewing leading to an increase in path radiance, with an opposite effect expected for the forward viewing. Simulation of radiances, depicting the situation for a 1, 2, and 4 change in the exit angles (due to an unknown constant pitch error in orientation) was carried out to assess the magnitude of changes in TOA radiance. The corresponding values of the HDRF were calculated for the new viewing angles. Fig. 13, which illustrates the differences (%) between the simulated and
observed radiances, shows that a maximum rotation of 2 seems to improve the disagreements in the blue and green channels but does not explains all the disagreements in the aftward viewing. At 4 the differences increase in the forward direction. In the red and nir channels, any change in the viewing angles seems to increase the differences. However, in these channels, the differences are still within the 10% uncertainty of the HDRF values. The above results indicate that a combination of uncertainties in camera orientation (only 1 to 2) and in characterizing the aerosol model and the use of the HDRF in place of the BRF, may account for the disagreements, shown in Fig. 10, between observed and calculated TOA radiances. Other sources for the disagreements are under investigation. For example, the radiative transfer calculation assumes plane-parallel atmosphere conditions, and a level boundary, whereas there are buildings present around the periphery that may contribute multiple reflections to the actual measured radiances. The possible contribution of atmospheric scattering from adjacent areas (adjacency
Fig. 13. Differences (%) between observed and calculated radiances, as in Fig. 11 (solid line) and depicting a rotation of AirMISR camera by 1 (dotted line), 2 (dashed line), and 4 (dash – dotted line).
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effects) has also been neglected. In future experiments, to account for adjacency effects, a method termed radiance propagation will be used. This employs measurements by PARABOLA III of the surface-reflected radiance in the target area, which include direct beam and radiation multiply reflected between sky and ground that includes contributions from the target and surrounding surfaces. The RTC is modified to accept upward radiance incident on the lower boundary, rather than reflection of downwelling radiance. This eliminates need for measurement of the surface BRF. The optical depth and the aerosol scattering model are still required to calculate the diffuse transmittance of the atmosphere. This procedure was not possible to apply at Moffett Field because PARABOLA III measurements were delayed from time of the overflight. Future calibration experiments will include: (i) use of extended homogeneous surface targets, (ii) multiple aircraft overpasses of the target area to check on repeatability through independent determinations, (iii) sky radiance measurements at the surface and surface irradiance measurements to better constrain the aerosol model used, (iv) a more complete determination of surface BRF from the PARABOLA III instrument.
References Bevington, P. R. (1969). Data reduction and error analysis for the physical sciences. New York: McGraw-Hill (336 pp.). Bruegge, C. J., Chrien, N. L., Diner, D. J., Duval, V. G., Korechoff, R. P., & Woodhouse, R. M. (1996). Level 1 in-flight radiometric calibration and characterization algorithm theoretical basis, JPL D-13398. Jet Propulsion Laboratory, California Institute of Technology (82 pp.). Bruegge, C., Chrien, N., & Haner, D. (1999). A Spectralon BRF data base for MISR calibration applications. Remote Sensing of the Environment, (this issue).
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Chrien, N. L. (1998). Channel display user’s guide, JPL D-16283. Jet Propulsion Laboratory, California Institute of Technology (15 pp.). Chrien, N. L., Bruegge, C. J., & Gaitley, B. J. (1999). AirMISR laboratory calibration results. Remote Sensing of the Environment, (this issue). Deering, D. W., & Leone, P. (1986). Sphere-scanning radiometer for rapid directional measurements of sky and ground radiance. Remote Sensing of the Environment, 19, 1 – 24. Diner, D. J., Barge, L. M., Bruegge, C. J., Chrien, T. G., Conel, J. E., Eastwood, M. E., Garcia, J. D., Hernandez, M. A., Kurzweil, C. G., Ledeboer, W. C., Pignatano, N. D., Sarture, C. M., & Smith, B. G. (1998). The airborne multi-angle imaging spectroradiometer (AirMISR): instrument description and first results. IEEE Transactions on Geoscience Remote Sensing, 36 (4), 1339 – 1349. Diner, D. J., Beckert, J. C., Reilly, T. H., Bruegge, C. J., Conel, J. E., Martonchik, J. V., Ackerman, T. P., Davies, R., Gerstel, S. A. W., Gordon, H. R., Kahn, R. A., Muller, J.-P., Myneni, R. B., Pinty, B., Sellers, P. J., & Verstraete, M. M. (1998). Multi-angle imaging spectroradiometer (MISR) instrument description and experiment overview. IEEE Transactions on Geoscience Remote Sensing, 36 (4), 1072 – 1087. Flittner, D. E., Herman, B. M., Thome, K. J., & Simpson, J. M. (1993). Total ozone and aerosol optical depths inferred from radiometric measurements in the Chappuis absorption band. Journal of the Atmospheric Sciences, 50 (8), 1113 – 1121. Grant, I. P., & Hunt, G. E. (1968). Solution of radiative transfer problems using the invariant Sn method. Monthly Notices of the Royal Astronomical Society, 141, 27 – 41. Hansen, J. E., & Travis, L. D. (1974). Light scattering in planetary atmospheres. Space Science Reviews, 16, 527 – 610. Jovanovic, V. (1996). Level 1 in-flight geometric calibration algorithm theoretical basis, JPL D-13399. Jet Propulsion Laboratory, California Institute of Technology (58 pp.). Martonchik, J. (1994). Retrieval of surface directional reflectance properties using ground level multiangle measurements. Remote Sensing of the Environment, 50, 303 – 316. Shettle, E. P. & Fenn, R. W. (1979). Models for the aerosols of the lower atmosphere and the effects of humidity variations on their optical properties, AFGL-TR-79-0214 (Environmental research paper No 676). Massachusetts: Air Force Geophysics Laboratory, Hanscomb AFB, 94 pp.