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SP lunar reflectance model for radiometric calibration of hyperspectral and multispectral sensors
Planetary and Space Science 124 (2016) 76–83
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Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Development of an application scheme for the SELENE/SP lunar reflectance model for radiometric calibration of hyperspectral and multispectral sensors Toru Kouyama a,n, Yasuhiro Yokota b, Yoshiaki Ishihara c, Ryosuke Nakamura a, Satoru Yamamoto d, Tsuneo Matsunaga d a
National Institute of Advanced Industrial Science and Technology, Japan Tusukuba Planetary Science Group, Japan Institute of Space and Astronautical Science/Japan Aerospace Exploration Agency, Japan d National Institute for Environmental Studies, Japan b c
art ic l e i nf o
a b s t r a c t
Article history: Received 13 November 2015 Received in revised form 3 February 2016 Accepted 11 February 2016 Available online 19 February 2016
We have developed an application scheme for conducting lunar calibration, one of the radiometric calibration methods for optical instruments onboard Earth-orbiting satellites and planetary explorers, with a newly developed hyperspectral lunar reflectance model based on SELENE/SP data. Because the model considers photometric properties (lunar surface reflectance and its dependences on incident, emission, and phase angles) with high spectral and spatial resolution (6–8 nm wavelength intervals and 0.5° grid meshes in lunar latitude and longitude), it enables us to simulate disk-resolved Moon radiance observed by not only multispectral but also hyperspectral sensors in space. Simulations of Moon observations conducted by ASTER with its three visible and near infrared bands, produced brightness profiles of simulated Moon images that show high correlation (more than 0.99) with the observed images in all bands, and the relative brightness of each pixel can be evaluated with 5% uncertainty. Consistency of dependence on phase angle and the libration effect between the SP model and another lunar reflectance model, ROLO, was also confirmed. The SP model will therefore be useful for evaluating the relative degradation of sensors in space. & 2016 Elsevier Ltd. All rights reserved.
keywords: Radiometric calibration Lunar calibration Moon Hyperspectral sensor
1. Introduction Radiometric calibration is one of the most important issues for multi-spectral and hyper-spectral sensors in space, because instrument performances are continuously degrading during orbits owing to the harsh environmental conditions during and after launch. Long-term radiometric calibration is indispensable for reliable and stable quality control of satellite data products. Several on-orbit calibration methods have been applied to earlier and existing satellites, such as onboard calibration using equipped onboard lamps or solar diffusers as reference light sources (cf. Sakuma et al., 2005 for Advanced Spaceborne Thermal Emission and Reflection radiometer (ASTER)), vicarious calibration comparing brightness of terrestrial targets with ground in-situ n Correspondence to: Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology, Umezono 1-1-1, 305-8568, Tsukuba, Japan. E-mail address: [email protected] (T. Kouyama).
http://dx.doi.org/10.1016/j.pss.2016.02.003 0032-0633/& 2016 Elsevier Ltd. All rights reserved.
measurements (cf. Thome et al., 2008), cross calibration comparing observed brightness from the same target’s with different satellite sensors (cf. Yamamoto et al., 2011a), and lunar calibration using the Moon as a known brightness target (Eplee et al., 2004; Kieffer and Stone, 2005). Since the Moon can be considered to be an extremely long-term photometrically stable object (Kieffer, 1997), for example more than one million years are needed for just 1% variation in the lunar surface reflectance, we can treat the Moon as an ideal target with known-brightness during mission lifetimes, which are much shorter than the relevant time scale for the Moon. There have been Earth observation missions that have adopted lunar calibration. During the SeaWIFS mission, the relative degradations of its multi-spectral sensors were confirmed with small uncertainties on the order of 0.1% (Eplee et al., 2004). Today, several hyperspectral imaging satellite missions (typical spectral interval: 5–10 nm) have been proposed, such as Hyperspectral Imager Suite (HISUI), which is a future Japanese hyperspectral mission comprising a hyperspectral imager and a multispectral imager (Matsunaga et al., 2013). The HISUI hyper-spectral
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imager will continuously obtain images with a spectral range from 400 nm to 2500 nm (186 channels with a spectral interval of 5– 10 nm). For the hyper spectral sensors, lunar calibration is an ideal method for hyperspectral radiometric calibration, because the sensors can observe the Moon without any atmospheric absorption and scattering which could cause large uncertainties, especially in the spectral regions where strong water absorption exists. The hyperspectral lunar surface reflectance model (Yokota et al., 2011) based on hyper-spectral observation data taken with Spectral Profiler (SP) onboard SELENE, a Japanese Lunar Explorer operated from 2007 to 2009. SP covered the visible (VIS: 512.6– 1010.7 nm) and near infrared wavelength regions (NIR1: 883.5– 1676.0 nm and NIR2: 1702.1–2578.9 nm) with a spectral sampling interval of 6–8 nm and 500 500 m2 footprint scale (Matsunaga et al., 2001; Haruyama et al., 2008; Matsunaga et al., 2008; Yamamoto et al., 2011b), and it observed whole lunar surface repeatedly with various solar incident and phase angles during the SELENE operation period. To establish a lunar calibration method based on the hyperspectral lunar reflectance model, we propose an application scheme for simulating the observation of the Moon with an SP model, as described in Section 2. To evaluate the consistency of the scheme, we show a simulation of a previous Moon observation and results from comparisons between the simulated and observed radiance in Section 3. In Section 3, we also discuss the consistency between SP model and another lunar reflectance model. Conclusions and remarks are included in Section 4.
2. Simulation of observations of the Moon with the SELENE/SP lunar reflectance model 2.1. SELENE/SP lunar reflectance model Yokota et al. (2011) proposed a disk-resolved lunar reflectance model based on SP hyperspectral data with a resolution of 1° 1° in lunar latitude and longitude. The model provides radiance factor which corresponds to reflectance standardized with the specified solar incident angle (i), emission angle (e) and phase angle (α) of 30°, 0° and 30°, respectively. In this study, we used a model with a higher resolution of 0.5° 0.5° generated by the same procedure as that for the 1° 1° model of Yokota et al. (2011). The model also describes the photometric dependencies of the reflectance on incident, emission and phase angles for each wavelength band. The spatial resolution of the map (0.5°, approximately 30 km at the equator of the Moon) corresponds to solid angle of one pixel of the HISUI hyper-spectral imager, considering its Moon observations from its Earth-orbit position. Fig. 1 shows the lunar reflectance map of the SP model at 752.8 nm (as in Yokota et al., 2011), and an example of the reflectance spectrum at a grid point of longitude 0° and latitude 0°. 2.2. Simulating observations of the Moon Following Eq. (11) in Yokota et al. (2011), we can simulate the instantaneous lunar surface reflectance (or radiance factor) at each grid point when we provide i, e and α at each map grid. The radiance factor rsim at a grid point is estimated from r sim λ; i; e; α ¼ r corr λ; 301; 01; 301
X L ði; e; αÞ f ðα Þ ; X L ð301; 01; 301Þ f ð301Þ
ð1Þ
where λ represents the wavelength and rcorr is the photometrically corrected reflectance provided in the SP model. XL is the linear combination of the Lommel–Seeliger and Lambert scattering laws
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Fig. 1. (a) Radiance factor map on a 0.5° 0.5° grid at 752.8 nm (as in Yokota et al., 2011). (b) Spectrum of radiance factor at (0°, 0°) latitude and longitude (marked with “ þ” in (a)).
given by (McEwen, 1991, 1996; McEwen et al., 1998): X L ði; e; αÞ ¼ 2LðαÞ
cos i þ ½1 LðαÞ cos i; cos i þ cos e
ð2Þ
where L is a function describing the limb darkness whose phase angle dependence is described by a third order polynomial: LðαÞ ¼ 1:0 þ c1 α þ c2 α2 þ c3 α3 ;
ð3Þ
where c1, c2 and c3 are empirical coefficients, c1 ¼ 0.019, c2 ¼0.242 10 3 and c3 ¼ 1.46 10 6 in this study, following McEwen (1996). f is an empirical function for describing the phase angle dependency defined in Yokota et al. (2011) as: f ðαÞ ¼ 1 þ B α; hλ ; B0λ P α; cλ ; g λ ; ð4Þ B α; hλ ; B0λ ¼
B0λ ; 1 þ tanh α=2 =hλ
ð5Þ
1 cλ 1 þcλ P HG α; g λ þ P HG α; g λ ; P α; cλ ; g λ ¼ 2 2
ð6Þ
1 gλ 2 P HG α; g λ ¼ 3=2 ; 2 1 þ g λ 2g λ cos α
ð7Þ
where hλ, B0λ cλ, and gλ are parameters that are empirically determined for every wavelength from SP observation and are provided by Yokota et al. (2011). We divided the lunar surface into three albedo groups (bright highland, dark mare and middle) with the same classification proposed in Yokota et al. (2011) to calculate XL and f in Eq. (1). In this study SPICE toolkit (Acton, 1996), distributed by NASA, was used to calculate the geometry parameters of i, e, and α at every map grid point. The distance between the Sun and the Moon and the distance between the Moon and an observer were also calculated with the tool based on epoch J2000. After calculating rsim, the lunar surface radiance Rsp (W m 2 μm 1 sr 1) when the moon is a distance D from the sun was obtained by multiplying rsim by the solar irradiance and correcting for the distance between the Sun and the Moon, I Sun λ D 2 RSP λ ¼ r sim λ; i; e; α ; ð8Þ 1AU π where ISun is the solar irradiance (W m 2 μm 1) at a distance 1 AU and D represents the distance in units of AU. We adapted the
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Newkur data (Gueymard, 2004) as a solar irradiance model which was used to construct the SP model from the SP observation data (Yamamoto et al., 2011a), and thus the uncertainty of the solar irradiance model is canceled out in Eq. (8). Fig. 2 shows an example of a map of the simulated lunar surface radiance obtained with a possible geometry condition seen from Earth. Next, to project the simulated Moon’s brightness onto a detector plane, a ray tracing procedure introduced by Ogohara et al. (2012) was used to obtain the lunar latitude and longitude of each pixel. For each pixel, we calculated an intersection point on the surface of a spherical target (the Moon with radius 1737.4 km) using an eye vector from each pixel of a detector onboard satellite. Since the location on the Moon's surface indicated by a pixel does not generally correspond to an exact grid point location on the map, we used bilinear interpolation to estimate the radiance observed at each pixel. In addition, since the SP model describes both the near side and the far side of the Moon, it also allows us to simulate the expected lunar image including the far side of the Moon which can never be seen from the Earth. Fig. 3 shows examples of predicted images of both the nearside and the farside Moon seen from the Earth on April 18 of 2003 and seen from the position above the anti-Earth point on the Moon on 3 May 2003, respectively. This is an advantage of using the SP model for radiometric calibration of planetary explorers which may observe both sides of the Moon. It should be noted that there could be unexpected image distortion in observed images because of the variation of thermal environment in space, which could result in changes in the optical calibration parameters of the sensors and lead to misregistration
Fig. 2. An example of a simulated lunar surface radiance map (752.8 nm). “þ ” and “ ” represent the assumed sub-observer and sub-solar points, respectively.
of the lunar latitude and longitude of pixels between the observed and simulated images. Therefore, as a final step, to reduce possible misregistration, lunar latitude and longitude for each pixel in a simulated image are obtained again using an image-matching technique based on the method proposed by Matsuoka and Kodama (2011). This technique considers the cross correlation between the simulated image obtained in the previous step and the observed lunar image; it then distorts the simulated image with an affine transformation to fit the observed image to the subpixel order based on the maximum position of correlation.
3. Consistency of simulated Moon image 3.1. Comparison of observed and simulated Moon images To evaluate the precision of the scheme introduced in Section 2, we simulated a prior Moon observation conducted on April 14, 2003 with a phase angle of 27.7° (the negative sign indicates the waxing phase) by ASTER, which is a constellation of visible and near infrared (VNIR, Band 1 3), short (SWIR, Band 4 9) and thermal infrared (TIR, Band 10 14) pushbroom optical sensors onboard Terra (Yamaguchi et al., 1998). In this study, we used observation data from the VNIR bands (Band 1: 520 600 nm, Band 2: 630 690 nm and Band 3: 760 860 nm) whose wavelengths are included in the wavelength range described in the SP model. The data were corrected using radiometric correction coefficients from onboard calibration results (Sakuma et al., 2005; Arai et al., 2011). To construct the simulated image, we integrated the hyperspectral radiance of the simulated Moon images with the band spectral response functions from ASTER (https://asterweb.jpl.nasa. gov/characteristics.asp) as follows: R W SRF λ RSP λ dλ R Rband ¼ W SRF λ dλ; ð9Þ where Rband represents the radiance of the integrated image (Band image), and wsrf is the spectral response function of a band. Then we compared the observed and the simulated radiance at every pixel to evaluate the statistical consistency of the simulation. Fig. 4 shows an example of a pair of observed (ASTER Band 2) and simulated Moon images. Because the spatial distance of the scan
Fig. 3. Examples of simulated Moon images (left) seen from Earth position on April 18, 2003 and (right) seen from the position above the anti-Earth point on the Moon on May 3, 2003.
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Fig. 4. An example of a pair of (a) observed and (b) simulated Moon images. The observed Moon image was taken by ASTER (Band 2) on April 14, 2003.
Fig. 5. Radiance ratios between the simulated images and the images observed by ASTER normalized with each mean ratio shown in Table 1. The regions bounded by black lines (i¼ 60° and e¼ 45°) indicate the regions to be used for the pixel-based comparison in this study. Dashed lines represent latitudes and longitudes with an interval of 30°.
interval on the lunar surface by ASTER, a pushbroom sensor, was shorter than the length corresponding to the field of view of a pixel when ASTER observed the Moon, the Moon shape is an ellipse in the image; this is so called oversampling effect. The oversampling effect was corrected using an ellipse fitting technique (Kanatani and Sugaya, 2007) to give the circular lunar disk shown in Fig. 4. Since SP observed the lunar surface exclusively under nadir conditions, the accuracy of the emission angle dependency of the reflectance has been unclear at high emission angles (Yokota et al., 2011). In addition, the accuracy of the incident angle dependency has also been unclear in high latitude regions because the solar incident angle is always high there. We have confirmed large variations in the radiance ratio between the simulated and observed images in the high-incident angle region (near terminator) and high-emission angle region (near Moon disk limb). Therefore, to avoid unexpected radiance bias in the simulation, we decided to make pixel-based comparisons only in the region where the solar incident angle is less than 60° and the emission angle is less than 45° (Fig. 5). Averaging radiance ratios in every 1 degree bins for incident (Fig. 6a) and emission angles (Fig. 6b) in this limited region in Band 2, it is confirmed that radiance ratios
show smaller dependencies on both the incident and emission angles, and have standard deviations less than 5% in all bins. Frequency distributions of the radiance for Bands 1, 2, and 3 are obtained by comparing the simulated and the observed radiances (Fig. 7). Correlation coefficients, ratios and standard deviations of the ratios from the comparison are listed in Table 1. The results from the comparison without the limitation of incident and emission angles (i.e. io90° and eo90°) are also provided in Table 1. Correlation coefficients for the unlimited case are lower, and standard deviations are two or three times larger than in the limited case (io60° and e o45°). In the case of i o90° and eo90°, less than 0.3% of the pixels, whose ratios are more than 3, are excluded from the comparison to avoid including ratios divided by near zero values. Because the correlation coefficients exceed 0.99 for all bands, the simulated Moon image accurately describes the Moon's features (brightness patterns) seen in observation, although simulated radiance in Band 1 is 27% darker and that in Band 3 is 5% brighter than the observed radiance (Fig. 5 and Table 1). One possible reason for these discrepancies is the calibration tendency of SP. According to a study investigating SP consistency (Ohtake et al., 2013), observed radiance from SP appears darker than that
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Fig. 6. Profiles of the radiance ratio (Band 2) for (a) solar incident and (b) emission angles estimated from pixels included in the limited incident and emission angle region. Error bars represent the standard deviations at each angle.
Fig. 7. Frequency distributions of simulated radiance and observed radiance of the Moon for Bands 1, 2, and 3. The gray scale represents the normalized frequency in each plot.
Table 1 Correlation coefficients, ratios between observed and simulated Moon images, and standard deviations of the ratio. Results from the comparison without i and e limitations are also listed below the limited values in parentheses. Band 1 (520– 600 nm)
Band 2 (630– 690 nm)
Band 3 (760– 860 nm)
Correlation coefficient (without i and e limitations)
0.992 (0.982)
0.993 (0.983)
0.993 (0.985)
Ratio: Observation/SP model
1.267
1.011
0.947
(1.284)
(1.025)
(0.948)
0.049 (0.111)
0.039 (0.102)
0.035 (0.094)
Standard deviation
from Multi-band Imager, which was also onboard SELENE, in the wavelength range of Band 1 where the shortest wavelength region in the visible band sensor of SP is located. Detailed studies of the calibration of the absolute radiance of SP will be done in the future.
In contrast, the standard deviations of all bands are less than 5%, which indicates that the relative magnitude of the observed brightness to the simulated brightness can be determined with small uncertainty (o5%) at each pixel. Considering the statistical summation of errors from the two observations, it is expected that the evaluation of the relative degradation of a pixel between two individual observations could be achieved with an accuracy of √(52 þ52), approximately 7%, since relative degradation of a sensor’s sensitivity can be measured by combining a set of comparison results between simulations and observations conducted at different periods. In addition, if we focus on the mean relative degradation of a sensor, we may determine the magnitude of the mean degradation more accurate than for evaluating each individual pixel's degradation, because the uncertainty of the mean degradation is expected to reduce according to the square root of the number of pixels used in the comparison. It should be noted that since in Moon observation we can ignore absorption and scattering effects from terrestrial atmosphere and aerosols which cause large uncertainty in observations, the other candidates causing uncertainty in observations except for sensor degradation are such as thermal noise of a sensor, misregistration of a pixel and uncertainty of determining dark
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level. Because the thermal noise and the misregistration are considered to provide random noise, both components should be included in the standard deviation of ratios of observation and simulation. Therefore if the uncertainty of dark level remains negligible, the standard deviation can be used as an indication of error range for the comparison. 3.2. Comparison of disk integrated irradiance between the SP model and the ROLO model Consistency among different lunar reflectance models based on different observations can be useful to test the models. Investigations of consistency among several observations and lunar reflectance models at specified locations (e.g. the Apollo landing sites) have been reported (Besse et al., 2013; Ohtake et al., 2013). In this study, a disk-integrated reflectance model developed from the RObotic Lunar Observatory (ROLO), a ground-based telescopic system (Kieffer and Wildey, 1996; Stone and Kieffer, 2002; Kieffer and Stone, 2005), is used to investigate SP model’s characteristics such as dependencies on wavelength, phase angle and libratoin effect comparing with other lunar reflectance model, so that we understand what properties are consistent among different lunar reflectance models. Both models can describe the disk-integrated Moon irradiance (W m 2 μm 1) at various wavelengths and various phase angle conditions and thus comparison of these models provides a useful understandings of the models for observations with various wavelength and phase angle conditions. Irradiance from the SP model, ISP, is evaluated from X I SP λ ¼ Rsp;i λ δΩpixel ; ð10Þ
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estimated with its orbit information distributed from North American Aerospace Defense Command. Similar to the result shown in Section 3.1, the ratio of the ROLO model to the SP model shows a decreasing trend with wavelength, and the ratio is larger than 1 (up to 1.2) at shorter wavelength and smaller at longer wavelengths. Again the calibration issue for SP observation is one possible candidate for this discrepancy. Accordingly, we may consider modifying the absolute magnitude of the SP model using other lunar reflectance models, in this study the ROLO model is considered. Fig. 8 also shows a fitted cubic function for the ratios, which runs smoothly between the SP model and the ROLO model. The function is described as: 2 3 p λ ¼ a0 þ a1 λ þa2 λ þ a3 λ ; ð11Þ where a0, a1, a2, and a3 are the fitting coefficients (for the case of
α ¼–27.7°, a0 ¼1.885, a1 ¼ 1.891 10 3, a2 ¼ 1.257 10–6, and
a3 ¼ –2.984 10–10). Using this fitted function as a radiometric correction function for the SP model, we can describe corrected reflectance, r 0sim , ð12Þ r 0sim λ; i; e; α ¼ r 0sim λ; i; e; α p λ ;
where Rsp,i is the radiance at a pixel of positon i in the projected Moon disk in a simulated image and δΩpixel is the solid angle of a pixel; large incident and emission angle regions may cause an up to 2% bias of irradiance (see Table 1). In this study we used 4.569 10 10 (str) for δΩpixel based on the specification of ASTER VNIR (Yamaguchi et al., 1998). Irradiance from the ROLO model is evaluated from the disk-averaged reflectance with the solar irradiance model used for generating the ROLO model as shown in Kieffer and Stone (2005). Irradiance ratios between the two models are estimated at 18 wavelengths (544.0–1633.6 nm) which are described in the ROLO model and the SP model covers. Fig. 8 shows a comparison of the two models averaging simulated Moon images assuming the images were taken by ASTER every time when the phase angle of Sun, Moon and Terra was 27.7° 71° from January 2000 to December 2015. In these simulations Terra’s positions were
and we can re-estimate the SP radiance at each pixel and at each wavelength using r 0sim instead of rsim in Eq. (8). Following the procedure described in Section 2, we can simulate the lunar observation again as shown in Section 3.1 with the corrected radiance. The mean radiance ratios between observations and simulations shown in Table 1 are notably changed to 1.085 from 1.267, 0.921 from 1.011 and 0.927 from 0.947 in Bands 1, 2, and 3, respectively, as shown in Stone and Kieffer (2006). This indicates that, through the correction with the ROLO model, the precision of the corrected radiance of the SP model could be considered traceable to the precision of the standard star observations which are basis for the ROLO model. A detailed study of possible collaboration between different models will be conducted in the future. As lunar observations can be conducted in various phase angles and libration conditions, dependencies on the phase angle and the libration effect (varying sub-observer latitude and longitude) should be investigated in addition to the wavelength dependency. Fig. 9 displays a comparison of the phase angle dependencies of the SP and ROLO models for a wavelength of 754.3 nm using the ratio of the two models. The ratio shows a clear phase angle dependence in the small phase angle region (|α| o20°) resulting from the different descriptions of phase angle dependencies in the two models, whereas variation of the ratio is within a 71% range from its mean value in the larger phase angle regions (|α| 420°). The tendency in the small phase angle region may be explained by different magnitudes of a backscatter opposition effect, which
Fig. 8. Ratio of disk integrated irradiance estimated from the SP and ROLO models at the phase angle of –27.7° (black circles). The dashed line is a fitted cubic function. Diamonds are the results from the comparisons of the SP model and ASTER observations.
Fig. 9. Ratio of the disk-integrated irradiance between the SP model and the ROLO model at 745.3 nm estimated from January 2000 to December 2015. Error bars represent the standard deviations at each phase angle. Negative values of the phase angle indicate lunar waxing phases.
i
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Fig. 10. Same as Fig. 9 but for (a) sub-observer latitude and (b) sub-observer longitude.
causes rapid variation in the observed radiance with a decreasing phase angle (Hapke, 1993), between the dark mare (low albedo) regions and the highland (high albedo) regions. When |α| o 20° the magnitude of f in (1) for low albedo regions reaches more than 2% larger than that for high albedo regions (Yokota et al., 2011). Since the different albedo groups are integrated into one fitting model which covers whole phase angle range in the ROLO model, this could result in a discrepancy between the results based on the ROLO and SP models in the small phase angle region where the different magnitude of the opposition effect could be considered. In contrast, radiance ratio profiles do not show any clear dependency on of the sub-observer latitude and longitude (Fig. 10), which means that both models consistently describe the libration effect of the Moon on the reflectance. In addition, SP model shows the consistent phase angle dependency with ROLO model in a phase angle range from |30°| to |60°| where the ratio varies only 0.5%. This implies one can reach more consolidating conclusion of radiometric calibration combining different lunar calibration results based on different models in this phase angle range. Future lunar observations conducted with various phase angles in a sufficient short period would be helpful to determine the phase angle dependency among lunar reflectance models, especially in the small angle range (o |20°|). Because of the great variation in the opposition effect at small phase angles of |α| o5° (e.g., Hapke, 1993; Buratti et al., 1996; Helfenstein et al., 1997; Shkuratov et al., 1999; Shkuratov and Helfenstein, 2001), the small phase angle range has been excluded in the SP model (Yokota et al., 2011). In addition, at large phase angles (|α| 4 75°), the magnitude of the observed radiance decreases rapidly with increasing phase angle and thus the large phase angles were also excluded from this study.
infrared bands, resulted in high correlation coefficients (more than 0.99) for all bands indicating that lunar surface brightness patterns were well simulated, although the absolute magnitude of the simulated radiance shows 27% discrepancy with that of the observed in ASTER Band 1. Considering that observed Moon radiance from different observations can be compared with the simulated Moon radiance, the SP model is useful for evaluating the relative degradation of sensors with small uncertainty, several percent for pixel-based calibration and more accurate evaluation could be expected for mean sensor degradation. Consistency between the SP and ROLO models was also investigated to evaluate the plausibility of lunar reflectance models. A discrepancy in absolute irradiance was confirmed in the comparison of the simulations from the SP and ROLO models. Although both models show a consistent dependency on the libration effect of the Moon, the SP model shows different phase angle dependency than the ROLO model in the small phase angle range (o|20°|). Future lunar observations conducted with various phase angles in a sufficient short period would be helpful to determine the phase angle dependency among the models. Additionally in the phase angle range of 30–60°, both models are expected to provide consistent evaluations of relative degradation of a sensor, because in this phase angle range we may avoid possible difference of phase angle dependencies among the models. Finally, Moon observations acquired by a hyperspectral sensor, such as EO-1 Hyperion (Pearlman and Member., 2003), would provide additional observational perspective for investigating the characteristics of SP model. Future hyperspectral missions, which will provide valuable Earth observation data for environmental monitoring, forestry, and global energy and resource issues, have increased the importance of hyperspectral radiometric calibration. Lunar calibration based on the SP model will be useful for the radiometric calibration of future hyper and multi-spectral sensors.
4. Conclusions and remarks We have developed an application scheme for conducting lunar calibration with a hyperspectral lunar reflectance model based on SELENE/SP data. Since the model includes photometric properties with high spectral and spatial resolution, it enabled us to simulate any Moon observation conducted by not only by multispectral but also hyperspectral sensors of optical instruments onboard Earth orbiting satellites and planetary explorers. Simulations of a previous Moon observation by ASTER, with its three visible and near
Acknowledgment This study was conducted using the SELENE/SP data distributed from JAXA. The authors appreciate the open data policy of the SELENE project. The authors also thank Dr. F. Sakuma, Dr. A. Iwasaki, Dr. T. Tachikawa, Dr. Kodama and ASTER Science team for providing ASTER Luna observation data. The authors greatly appreciate Dr. Stone, Dr. Tsuchida, Dr. Yamamoto, Dr. Kato
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and Dr. Obata for their valuable comments and supports. The authors also thank the two anonymous reviewers for providing valuable comments on the draft of the paper.
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Matsunaga, T., Ohtake, M., Hirahara, Y., 2001. Haruyama, development of a visible and near infrared spectrometer for Selenological and Engineering Explorer (SELENE). Proc. SPIE Int. Soc. Opt. Eng. 4151, 32–39. Matsunaga, T., Ohtake, M., Haruyama, J., Ogawa, Y., Nakamura, R., Yokota, Y., Morota, T., Honda, C., Torii, M., Arai, T., Saiki, K., Takeda, H., Hirata, N., Kodata, S., Sugihara, T., Demura, H., Asada, N., Terazono, J., Otake, H., 2008. Discoveries on the lithology of lunar crater central peaks by SELENE Spectral Profiler. Geophys. Res. Lett. 35, L23201. Matsunaga, T., Iwasaki, A., Tsuchida, S., Tanii, J., Kashimura, O., Nakamura, R., Yamamoto, H., Tachikawa, T., Rokugawa, S., 2013. Current status of Hyperspectral Imager Suite (HISUI), Proc. Geoscience and Remote Sensing Symposium (IGARSS), 2013 International, p.p. 3510–3513. Ogohara, K., Kouyama, T., Yamamoto, H., Sato, N., Takagi, M., Imamura, T., 2012. Automated cloud tracking system for the Akatsuski Venus climate orbiter data. Icarus 217, 661–668. Ohtake, M., Pieters, C.M., Isaacson, P., Besse, S., Yokota, Y., Matsunaga, T., Boardman, J., Yamomoto, S., Haruyama, J., Staid, M., Mall, U., Green, R.O., 2013. One Moon, many measurements 3: spectral reflectance. Icarus 226, 364–374. Pearlman, S.J., Member, S., 2003. Hyperion, a space-based imaging spectrometer. IEEE Trans. Geosci. Remote Sens. 41, 1160–1173. Sakuma, F., Ono, A., Tsuchida, S., Ohgi, N., Inada, H., Akagi, S., Ono, H., 2005. Onboard calibration of the ASTER instrument. IEEE Trans. Geoscience and Remote Sensing 43, 2715–2724. Shkuratov, Y.G., Helfenstein, P., 2001. The opposition effect and the quasi-fractal structure of regolith: I. theory. Icarus 152, 96–116. Shkuratov, Y.G., Kreslavsky, M.A., Ovcharenko, A.A., Stankevich, D.G., Zubko, E.S., Pieters, C., Arnold, G., 1999. Opposition effect from clementine data and mechanisms of backscatter. Icarus 141, 132–155. Stone, T.C., Kieffer, H.H., 2002. Absolute irradiance of the Moon for on-orbit calibration. Proc. SPIE Int. Soc. Opt. Eng. 4814, 211–221. Stone, T.C., Kieffer, H.H., 2006. Use of the Moon to support on-orbit sensor calibration for climate change measurements. Proc. SPIE Int. Soc. Opt. Eng. 6296, 62960Y. Thome, K., Arai, K., Tsuchida, S., Biggar, S., 2008. Vicarious calibration of ASTER via reflectance-based approach. IEEE Trans. Geosci. Remote Sens. 46, 3285–3295. Yamaguchi, Y., Kahle, A.B., Tsu, H., Kawakami, T., Pniel, M., 1998. Overview of advanced spaceborne thermal emission and reflection radiometer (ASTER). IEEE Trans. Geosci. Remote Sens. 36, 1062–1071. Yamamoto, H., Kamei, A., Nakamura, R., Tsuchida, S., 2011a. Long-term cross-calibration of the Terra ASTER and MODIS over the CEOS calibration sites Earth Observing Systems XVI, 815318. Proc. SPIE Int. Soc. Opt. Eng. 8153. Yamamoto, S., Matsunaga, T., Ogawa, Y., Nakamura, R., Yokota, Y., Ohtake, M., Haruyama, J., Morota, T., Honda, C., Hiroi, T., Kodama, S., 2011b. Preflight and inflight calibration of the Spectral Profiler on board SELENE (Kaguya). IEEE Trans. Geosci. Remote Sens. 49, 4660–4676. Yokota, Y., Matsunaga, T., Ohtake, M., Haruyama, J., Nakamura, R., Yamamoto, S., Ogawa, Y., Morota, T., Honda, C., Saiki, K., Nagasawa, K., Kitazato, K., Sasaki, S., Iwasaki, A., Demura, H., Hirata, N., Hiroi, T., Honda, R., Iijima, Y., Mizutani, H., 2011. Lunar photometric properties at wavelengths 0.5–1.6 μm acquired by SELENE Spectral Profiler and their dependency on local albedo and latitudinal zones. Icarus 215, 639–660.
Contents lists available at ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Development of an application scheme for the SELENE/SP lunar reflectance model for radiometric calibration of hyperspectral and multispectral sensors Toru Kouyama a,n, Yasuhiro Yokota b, Yoshiaki Ishihara c, Ryosuke Nakamura a, Satoru Yamamoto d, Tsuneo Matsunaga d a
National Institute of Advanced Industrial Science and Technology, Japan Tusukuba Planetary Science Group, Japan Institute of Space and Astronautical Science/Japan Aerospace Exploration Agency, Japan d National Institute for Environmental Studies, Japan b c
art ic l e i nf o
a b s t r a c t
Article history: Received 13 November 2015 Received in revised form 3 February 2016 Accepted 11 February 2016 Available online 19 February 2016
We have developed an application scheme for conducting lunar calibration, one of the radiometric calibration methods for optical instruments onboard Earth-orbiting satellites and planetary explorers, with a newly developed hyperspectral lunar reflectance model based on SELENE/SP data. Because the model considers photometric properties (lunar surface reflectance and its dependences on incident, emission, and phase angles) with high spectral and spatial resolution (6–8 nm wavelength intervals and 0.5° grid meshes in lunar latitude and longitude), it enables us to simulate disk-resolved Moon radiance observed by not only multispectral but also hyperspectral sensors in space. Simulations of Moon observations conducted by ASTER with its three visible and near infrared bands, produced brightness profiles of simulated Moon images that show high correlation (more than 0.99) with the observed images in all bands, and the relative brightness of each pixel can be evaluated with 5% uncertainty. Consistency of dependence on phase angle and the libration effect between the SP model and another lunar reflectance model, ROLO, was also confirmed. The SP model will therefore be useful for evaluating the relative degradation of sensors in space. & 2016 Elsevier Ltd. All rights reserved.
keywords: Radiometric calibration Lunar calibration Moon Hyperspectral sensor
1. Introduction Radiometric calibration is one of the most important issues for multi-spectral and hyper-spectral sensors in space, because instrument performances are continuously degrading during orbits owing to the harsh environmental conditions during and after launch. Long-term radiometric calibration is indispensable for reliable and stable quality control of satellite data products. Several on-orbit calibration methods have been applied to earlier and existing satellites, such as onboard calibration using equipped onboard lamps or solar diffusers as reference light sources (cf. Sakuma et al., 2005 for Advanced Spaceborne Thermal Emission and Reflection radiometer (ASTER)), vicarious calibration comparing brightness of terrestrial targets with ground in-situ n Correspondence to: Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology, Umezono 1-1-1, 305-8568, Tsukuba, Japan. E-mail address: [email protected] (T. Kouyama).
http://dx.doi.org/10.1016/j.pss.2016.02.003 0032-0633/& 2016 Elsevier Ltd. All rights reserved.
measurements (cf. Thome et al., 2008), cross calibration comparing observed brightness from the same target’s with different satellite sensors (cf. Yamamoto et al., 2011a), and lunar calibration using the Moon as a known brightness target (Eplee et al., 2004; Kieffer and Stone, 2005). Since the Moon can be considered to be an extremely long-term photometrically stable object (Kieffer, 1997), for example more than one million years are needed for just 1% variation in the lunar surface reflectance, we can treat the Moon as an ideal target with known-brightness during mission lifetimes, which are much shorter than the relevant time scale for the Moon. There have been Earth observation missions that have adopted lunar calibration. During the SeaWIFS mission, the relative degradations of its multi-spectral sensors were confirmed with small uncertainties on the order of 0.1% (Eplee et al., 2004). Today, several hyperspectral imaging satellite missions (typical spectral interval: 5–10 nm) have been proposed, such as Hyperspectral Imager Suite (HISUI), which is a future Japanese hyperspectral mission comprising a hyperspectral imager and a multispectral imager (Matsunaga et al., 2013). The HISUI hyper-spectral
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imager will continuously obtain images with a spectral range from 400 nm to 2500 nm (186 channels with a spectral interval of 5– 10 nm). For the hyper spectral sensors, lunar calibration is an ideal method for hyperspectral radiometric calibration, because the sensors can observe the Moon without any atmospheric absorption and scattering which could cause large uncertainties, especially in the spectral regions where strong water absorption exists. The hyperspectral lunar surface reflectance model (Yokota et al., 2011) based on hyper-spectral observation data taken with Spectral Profiler (SP) onboard SELENE, a Japanese Lunar Explorer operated from 2007 to 2009. SP covered the visible (VIS: 512.6– 1010.7 nm) and near infrared wavelength regions (NIR1: 883.5– 1676.0 nm and NIR2: 1702.1–2578.9 nm) with a spectral sampling interval of 6–8 nm and 500 500 m2 footprint scale (Matsunaga et al., 2001; Haruyama et al., 2008; Matsunaga et al., 2008; Yamamoto et al., 2011b), and it observed whole lunar surface repeatedly with various solar incident and phase angles during the SELENE operation period. To establish a lunar calibration method based on the hyperspectral lunar reflectance model, we propose an application scheme for simulating the observation of the Moon with an SP model, as described in Section 2. To evaluate the consistency of the scheme, we show a simulation of a previous Moon observation and results from comparisons between the simulated and observed radiance in Section 3. In Section 3, we also discuss the consistency between SP model and another lunar reflectance model. Conclusions and remarks are included in Section 4.
2. Simulation of observations of the Moon with the SELENE/SP lunar reflectance model 2.1. SELENE/SP lunar reflectance model Yokota et al. (2011) proposed a disk-resolved lunar reflectance model based on SP hyperspectral data with a resolution of 1° 1° in lunar latitude and longitude. The model provides radiance factor which corresponds to reflectance standardized with the specified solar incident angle (i), emission angle (e) and phase angle (α) of 30°, 0° and 30°, respectively. In this study, we used a model with a higher resolution of 0.5° 0.5° generated by the same procedure as that for the 1° 1° model of Yokota et al. (2011). The model also describes the photometric dependencies of the reflectance on incident, emission and phase angles for each wavelength band. The spatial resolution of the map (0.5°, approximately 30 km at the equator of the Moon) corresponds to solid angle of one pixel of the HISUI hyper-spectral imager, considering its Moon observations from its Earth-orbit position. Fig. 1 shows the lunar reflectance map of the SP model at 752.8 nm (as in Yokota et al., 2011), and an example of the reflectance spectrum at a grid point of longitude 0° and latitude 0°. 2.2. Simulating observations of the Moon Following Eq. (11) in Yokota et al. (2011), we can simulate the instantaneous lunar surface reflectance (or radiance factor) at each grid point when we provide i, e and α at each map grid. The radiance factor rsim at a grid point is estimated from r sim λ; i; e; α ¼ r corr λ; 301; 01; 301
X L ði; e; αÞ f ðα Þ ; X L ð301; 01; 301Þ f ð301Þ
ð1Þ
where λ represents the wavelength and rcorr is the photometrically corrected reflectance provided in the SP model. XL is the linear combination of the Lommel–Seeliger and Lambert scattering laws
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Fig. 1. (a) Radiance factor map on a 0.5° 0.5° grid at 752.8 nm (as in Yokota et al., 2011). (b) Spectrum of radiance factor at (0°, 0°) latitude and longitude (marked with “ þ” in (a)).
given by (McEwen, 1991, 1996; McEwen et al., 1998): X L ði; e; αÞ ¼ 2LðαÞ
cos i þ ½1 LðαÞ cos i; cos i þ cos e
ð2Þ
where L is a function describing the limb darkness whose phase angle dependence is described by a third order polynomial: LðαÞ ¼ 1:0 þ c1 α þ c2 α2 þ c3 α3 ;
ð3Þ
where c1, c2 and c3 are empirical coefficients, c1 ¼ 0.019, c2 ¼0.242 10 3 and c3 ¼ 1.46 10 6 in this study, following McEwen (1996). f is an empirical function for describing the phase angle dependency defined in Yokota et al. (2011) as: f ðαÞ ¼ 1 þ B α; hλ ; B0λ P α; cλ ; g λ ; ð4Þ B α; hλ ; B0λ ¼
B0λ ; 1 þ tanh α=2 =hλ
ð5Þ
1 cλ 1 þcλ P HG α; g λ þ P HG α; g λ ; P α; cλ ; g λ ¼ 2 2
ð6Þ
1 gλ 2 P HG α; g λ ¼ 3=2 ; 2 1 þ g λ 2g λ cos α
ð7Þ
where hλ, B0λ cλ, and gλ are parameters that are empirically determined for every wavelength from SP observation and are provided by Yokota et al. (2011). We divided the lunar surface into three albedo groups (bright highland, dark mare and middle) with the same classification proposed in Yokota et al. (2011) to calculate XL and f in Eq. (1). In this study SPICE toolkit (Acton, 1996), distributed by NASA, was used to calculate the geometry parameters of i, e, and α at every map grid point. The distance between the Sun and the Moon and the distance between the Moon and an observer were also calculated with the tool based on epoch J2000. After calculating rsim, the lunar surface radiance Rsp (W m 2 μm 1 sr 1) when the moon is a distance D from the sun was obtained by multiplying rsim by the solar irradiance and correcting for the distance between the Sun and the Moon, I Sun λ D 2 RSP λ ¼ r sim λ; i; e; α ; ð8Þ 1AU π where ISun is the solar irradiance (W m 2 μm 1) at a distance 1 AU and D represents the distance in units of AU. We adapted the
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Newkur data (Gueymard, 2004) as a solar irradiance model which was used to construct the SP model from the SP observation data (Yamamoto et al., 2011a), and thus the uncertainty of the solar irradiance model is canceled out in Eq. (8). Fig. 2 shows an example of a map of the simulated lunar surface radiance obtained with a possible geometry condition seen from Earth. Next, to project the simulated Moon’s brightness onto a detector plane, a ray tracing procedure introduced by Ogohara et al. (2012) was used to obtain the lunar latitude and longitude of each pixel. For each pixel, we calculated an intersection point on the surface of a spherical target (the Moon with radius 1737.4 km) using an eye vector from each pixel of a detector onboard satellite. Since the location on the Moon's surface indicated by a pixel does not generally correspond to an exact grid point location on the map, we used bilinear interpolation to estimate the radiance observed at each pixel. In addition, since the SP model describes both the near side and the far side of the Moon, it also allows us to simulate the expected lunar image including the far side of the Moon which can never be seen from the Earth. Fig. 3 shows examples of predicted images of both the nearside and the farside Moon seen from the Earth on April 18 of 2003 and seen from the position above the anti-Earth point on the Moon on 3 May 2003, respectively. This is an advantage of using the SP model for radiometric calibration of planetary explorers which may observe both sides of the Moon. It should be noted that there could be unexpected image distortion in observed images because of the variation of thermal environment in space, which could result in changes in the optical calibration parameters of the sensors and lead to misregistration
Fig. 2. An example of a simulated lunar surface radiance map (752.8 nm). “þ ” and “ ” represent the assumed sub-observer and sub-solar points, respectively.
of the lunar latitude and longitude of pixels between the observed and simulated images. Therefore, as a final step, to reduce possible misregistration, lunar latitude and longitude for each pixel in a simulated image are obtained again using an image-matching technique based on the method proposed by Matsuoka and Kodama (2011). This technique considers the cross correlation between the simulated image obtained in the previous step and the observed lunar image; it then distorts the simulated image with an affine transformation to fit the observed image to the subpixel order based on the maximum position of correlation.
3. Consistency of simulated Moon image 3.1. Comparison of observed and simulated Moon images To evaluate the precision of the scheme introduced in Section 2, we simulated a prior Moon observation conducted on April 14, 2003 with a phase angle of 27.7° (the negative sign indicates the waxing phase) by ASTER, which is a constellation of visible and near infrared (VNIR, Band 1 3), short (SWIR, Band 4 9) and thermal infrared (TIR, Band 10 14) pushbroom optical sensors onboard Terra (Yamaguchi et al., 1998). In this study, we used observation data from the VNIR bands (Band 1: 520 600 nm, Band 2: 630 690 nm and Band 3: 760 860 nm) whose wavelengths are included in the wavelength range described in the SP model. The data were corrected using radiometric correction coefficients from onboard calibration results (Sakuma et al., 2005; Arai et al., 2011). To construct the simulated image, we integrated the hyperspectral radiance of the simulated Moon images with the band spectral response functions from ASTER (https://asterweb.jpl.nasa. gov/characteristics.asp) as follows: R W SRF λ RSP λ dλ R Rband ¼ W SRF λ dλ; ð9Þ where Rband represents the radiance of the integrated image (Band image), and wsrf is the spectral response function of a band. Then we compared the observed and the simulated radiance at every pixel to evaluate the statistical consistency of the simulation. Fig. 4 shows an example of a pair of observed (ASTER Band 2) and simulated Moon images. Because the spatial distance of the scan
Fig. 3. Examples of simulated Moon images (left) seen from Earth position on April 18, 2003 and (right) seen from the position above the anti-Earth point on the Moon on May 3, 2003.
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Fig. 4. An example of a pair of (a) observed and (b) simulated Moon images. The observed Moon image was taken by ASTER (Band 2) on April 14, 2003.
Fig. 5. Radiance ratios between the simulated images and the images observed by ASTER normalized with each mean ratio shown in Table 1. The regions bounded by black lines (i¼ 60° and e¼ 45°) indicate the regions to be used for the pixel-based comparison in this study. Dashed lines represent latitudes and longitudes with an interval of 30°.
interval on the lunar surface by ASTER, a pushbroom sensor, was shorter than the length corresponding to the field of view of a pixel when ASTER observed the Moon, the Moon shape is an ellipse in the image; this is so called oversampling effect. The oversampling effect was corrected using an ellipse fitting technique (Kanatani and Sugaya, 2007) to give the circular lunar disk shown in Fig. 4. Since SP observed the lunar surface exclusively under nadir conditions, the accuracy of the emission angle dependency of the reflectance has been unclear at high emission angles (Yokota et al., 2011). In addition, the accuracy of the incident angle dependency has also been unclear in high latitude regions because the solar incident angle is always high there. We have confirmed large variations in the radiance ratio between the simulated and observed images in the high-incident angle region (near terminator) and high-emission angle region (near Moon disk limb). Therefore, to avoid unexpected radiance bias in the simulation, we decided to make pixel-based comparisons only in the region where the solar incident angle is less than 60° and the emission angle is less than 45° (Fig. 5). Averaging radiance ratios in every 1 degree bins for incident (Fig. 6a) and emission angles (Fig. 6b) in this limited region in Band 2, it is confirmed that radiance ratios
show smaller dependencies on both the incident and emission angles, and have standard deviations less than 5% in all bins. Frequency distributions of the radiance for Bands 1, 2, and 3 are obtained by comparing the simulated and the observed radiances (Fig. 7). Correlation coefficients, ratios and standard deviations of the ratios from the comparison are listed in Table 1. The results from the comparison without the limitation of incident and emission angles (i.e. io90° and eo90°) are also provided in Table 1. Correlation coefficients for the unlimited case are lower, and standard deviations are two or three times larger than in the limited case (io60° and e o45°). In the case of i o90° and eo90°, less than 0.3% of the pixels, whose ratios are more than 3, are excluded from the comparison to avoid including ratios divided by near zero values. Because the correlation coefficients exceed 0.99 for all bands, the simulated Moon image accurately describes the Moon's features (brightness patterns) seen in observation, although simulated radiance in Band 1 is 27% darker and that in Band 3 is 5% brighter than the observed radiance (Fig. 5 and Table 1). One possible reason for these discrepancies is the calibration tendency of SP. According to a study investigating SP consistency (Ohtake et al., 2013), observed radiance from SP appears darker than that
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Fig. 6. Profiles of the radiance ratio (Band 2) for (a) solar incident and (b) emission angles estimated from pixels included in the limited incident and emission angle region. Error bars represent the standard deviations at each angle.
Fig. 7. Frequency distributions of simulated radiance and observed radiance of the Moon for Bands 1, 2, and 3. The gray scale represents the normalized frequency in each plot.
Table 1 Correlation coefficients, ratios between observed and simulated Moon images, and standard deviations of the ratio. Results from the comparison without i and e limitations are also listed below the limited values in parentheses. Band 1 (520– 600 nm)
Band 2 (630– 690 nm)
Band 3 (760– 860 nm)
Correlation coefficient (without i and e limitations)
0.992 (0.982)
0.993 (0.983)
0.993 (0.985)
Ratio: Observation/SP model
1.267
1.011
0.947
(1.284)
(1.025)
(0.948)
0.049 (0.111)
0.039 (0.102)
0.035 (0.094)
Standard deviation
from Multi-band Imager, which was also onboard SELENE, in the wavelength range of Band 1 where the shortest wavelength region in the visible band sensor of SP is located. Detailed studies of the calibration of the absolute radiance of SP will be done in the future.
In contrast, the standard deviations of all bands are less than 5%, which indicates that the relative magnitude of the observed brightness to the simulated brightness can be determined with small uncertainty (o5%) at each pixel. Considering the statistical summation of errors from the two observations, it is expected that the evaluation of the relative degradation of a pixel between two individual observations could be achieved with an accuracy of √(52 þ52), approximately 7%, since relative degradation of a sensor’s sensitivity can be measured by combining a set of comparison results between simulations and observations conducted at different periods. In addition, if we focus on the mean relative degradation of a sensor, we may determine the magnitude of the mean degradation more accurate than for evaluating each individual pixel's degradation, because the uncertainty of the mean degradation is expected to reduce according to the square root of the number of pixels used in the comparison. It should be noted that since in Moon observation we can ignore absorption and scattering effects from terrestrial atmosphere and aerosols which cause large uncertainty in observations, the other candidates causing uncertainty in observations except for sensor degradation are such as thermal noise of a sensor, misregistration of a pixel and uncertainty of determining dark
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level. Because the thermal noise and the misregistration are considered to provide random noise, both components should be included in the standard deviation of ratios of observation and simulation. Therefore if the uncertainty of dark level remains negligible, the standard deviation can be used as an indication of error range for the comparison. 3.2. Comparison of disk integrated irradiance between the SP model and the ROLO model Consistency among different lunar reflectance models based on different observations can be useful to test the models. Investigations of consistency among several observations and lunar reflectance models at specified locations (e.g. the Apollo landing sites) have been reported (Besse et al., 2013; Ohtake et al., 2013). In this study, a disk-integrated reflectance model developed from the RObotic Lunar Observatory (ROLO), a ground-based telescopic system (Kieffer and Wildey, 1996; Stone and Kieffer, 2002; Kieffer and Stone, 2005), is used to investigate SP model’s characteristics such as dependencies on wavelength, phase angle and libratoin effect comparing with other lunar reflectance model, so that we understand what properties are consistent among different lunar reflectance models. Both models can describe the disk-integrated Moon irradiance (W m 2 μm 1) at various wavelengths and various phase angle conditions and thus comparison of these models provides a useful understandings of the models for observations with various wavelength and phase angle conditions. Irradiance from the SP model, ISP, is evaluated from X I SP λ ¼ Rsp;i λ δΩpixel ; ð10Þ
81
estimated with its orbit information distributed from North American Aerospace Defense Command. Similar to the result shown in Section 3.1, the ratio of the ROLO model to the SP model shows a decreasing trend with wavelength, and the ratio is larger than 1 (up to 1.2) at shorter wavelength and smaller at longer wavelengths. Again the calibration issue for SP observation is one possible candidate for this discrepancy. Accordingly, we may consider modifying the absolute magnitude of the SP model using other lunar reflectance models, in this study the ROLO model is considered. Fig. 8 also shows a fitted cubic function for the ratios, which runs smoothly between the SP model and the ROLO model. The function is described as: 2 3 p λ ¼ a0 þ a1 λ þa2 λ þ a3 λ ; ð11Þ where a0, a1, a2, and a3 are the fitting coefficients (for the case of
α ¼–27.7°, a0 ¼1.885, a1 ¼ 1.891 10 3, a2 ¼ 1.257 10–6, and
a3 ¼ –2.984 10–10). Using this fitted function as a radiometric correction function for the SP model, we can describe corrected reflectance, r 0sim , ð12Þ r 0sim λ; i; e; α ¼ r 0sim λ; i; e; α p λ ;
where Rsp,i is the radiance at a pixel of positon i in the projected Moon disk in a simulated image and δΩpixel is the solid angle of a pixel; large incident and emission angle regions may cause an up to 2% bias of irradiance (see Table 1). In this study we used 4.569 10 10 (str) for δΩpixel based on the specification of ASTER VNIR (Yamaguchi et al., 1998). Irradiance from the ROLO model is evaluated from the disk-averaged reflectance with the solar irradiance model used for generating the ROLO model as shown in Kieffer and Stone (2005). Irradiance ratios between the two models are estimated at 18 wavelengths (544.0–1633.6 nm) which are described in the ROLO model and the SP model covers. Fig. 8 shows a comparison of the two models averaging simulated Moon images assuming the images were taken by ASTER every time when the phase angle of Sun, Moon and Terra was 27.7° 71° from January 2000 to December 2015. In these simulations Terra’s positions were
and we can re-estimate the SP radiance at each pixel and at each wavelength using r 0sim instead of rsim in Eq. (8). Following the procedure described in Section 2, we can simulate the lunar observation again as shown in Section 3.1 with the corrected radiance. The mean radiance ratios between observations and simulations shown in Table 1 are notably changed to 1.085 from 1.267, 0.921 from 1.011 and 0.927 from 0.947 in Bands 1, 2, and 3, respectively, as shown in Stone and Kieffer (2006). This indicates that, through the correction with the ROLO model, the precision of the corrected radiance of the SP model could be considered traceable to the precision of the standard star observations which are basis for the ROLO model. A detailed study of possible collaboration between different models will be conducted in the future. As lunar observations can be conducted in various phase angles and libration conditions, dependencies on the phase angle and the libration effect (varying sub-observer latitude and longitude) should be investigated in addition to the wavelength dependency. Fig. 9 displays a comparison of the phase angle dependencies of the SP and ROLO models for a wavelength of 754.3 nm using the ratio of the two models. The ratio shows a clear phase angle dependence in the small phase angle region (|α| o20°) resulting from the different descriptions of phase angle dependencies in the two models, whereas variation of the ratio is within a 71% range from its mean value in the larger phase angle regions (|α| 420°). The tendency in the small phase angle region may be explained by different magnitudes of a backscatter opposition effect, which
Fig. 8. Ratio of disk integrated irradiance estimated from the SP and ROLO models at the phase angle of –27.7° (black circles). The dashed line is a fitted cubic function. Diamonds are the results from the comparisons of the SP model and ASTER observations.
Fig. 9. Ratio of the disk-integrated irradiance between the SP model and the ROLO model at 745.3 nm estimated from January 2000 to December 2015. Error bars represent the standard deviations at each phase angle. Negative values of the phase angle indicate lunar waxing phases.
i
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Fig. 10. Same as Fig. 9 but for (a) sub-observer latitude and (b) sub-observer longitude.
causes rapid variation in the observed radiance with a decreasing phase angle (Hapke, 1993), between the dark mare (low albedo) regions and the highland (high albedo) regions. When |α| o 20° the magnitude of f in (1) for low albedo regions reaches more than 2% larger than that for high albedo regions (Yokota et al., 2011). Since the different albedo groups are integrated into one fitting model which covers whole phase angle range in the ROLO model, this could result in a discrepancy between the results based on the ROLO and SP models in the small phase angle region where the different magnitude of the opposition effect could be considered. In contrast, radiance ratio profiles do not show any clear dependency on of the sub-observer latitude and longitude (Fig. 10), which means that both models consistently describe the libration effect of the Moon on the reflectance. In addition, SP model shows the consistent phase angle dependency with ROLO model in a phase angle range from |30°| to |60°| where the ratio varies only 0.5%. This implies one can reach more consolidating conclusion of radiometric calibration combining different lunar calibration results based on different models in this phase angle range. Future lunar observations conducted with various phase angles in a sufficient short period would be helpful to determine the phase angle dependency among lunar reflectance models, especially in the small angle range (o |20°|). Because of the great variation in the opposition effect at small phase angles of |α| o5° (e.g., Hapke, 1993; Buratti et al., 1996; Helfenstein et al., 1997; Shkuratov et al., 1999; Shkuratov and Helfenstein, 2001), the small phase angle range has been excluded in the SP model (Yokota et al., 2011). In addition, at large phase angles (|α| 4 75°), the magnitude of the observed radiance decreases rapidly with increasing phase angle and thus the large phase angles were also excluded from this study.
infrared bands, resulted in high correlation coefficients (more than 0.99) for all bands indicating that lunar surface brightness patterns were well simulated, although the absolute magnitude of the simulated radiance shows 27% discrepancy with that of the observed in ASTER Band 1. Considering that observed Moon radiance from different observations can be compared with the simulated Moon radiance, the SP model is useful for evaluating the relative degradation of sensors with small uncertainty, several percent for pixel-based calibration and more accurate evaluation could be expected for mean sensor degradation. Consistency between the SP and ROLO models was also investigated to evaluate the plausibility of lunar reflectance models. A discrepancy in absolute irradiance was confirmed in the comparison of the simulations from the SP and ROLO models. Although both models show a consistent dependency on the libration effect of the Moon, the SP model shows different phase angle dependency than the ROLO model in the small phase angle range (o|20°|). Future lunar observations conducted with various phase angles in a sufficient short period would be helpful to determine the phase angle dependency among the models. Additionally in the phase angle range of 30–60°, both models are expected to provide consistent evaluations of relative degradation of a sensor, because in this phase angle range we may avoid possible difference of phase angle dependencies among the models. Finally, Moon observations acquired by a hyperspectral sensor, such as EO-1 Hyperion (Pearlman and Member., 2003), would provide additional observational perspective for investigating the characteristics of SP model. Future hyperspectral missions, which will provide valuable Earth observation data for environmental monitoring, forestry, and global energy and resource issues, have increased the importance of hyperspectral radiometric calibration. Lunar calibration based on the SP model will be useful for the radiometric calibration of future hyper and multi-spectral sensors.
4. Conclusions and remarks We have developed an application scheme for conducting lunar calibration with a hyperspectral lunar reflectance model based on SELENE/SP data. Since the model includes photometric properties with high spectral and spatial resolution, it enabled us to simulate any Moon observation conducted by not only by multispectral but also hyperspectral sensors of optical instruments onboard Earth orbiting satellites and planetary explorers. Simulations of a previous Moon observation by ASTER, with its three visible and near
Acknowledgment This study was conducted using the SELENE/SP data distributed from JAXA. The authors appreciate the open data policy of the SELENE project. The authors also thank Dr. F. Sakuma, Dr. A. Iwasaki, Dr. T. Tachikawa, Dr. Kodama and ASTER Science team for providing ASTER Luna observation data. The authors greatly appreciate Dr. Stone, Dr. Tsuchida, Dr. Yamamoto, Dr. Kato
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and Dr. Obata for their valuable comments and supports. The authors also thank the two anonymous reviewers for providing valuable comments on the draft of the paper.
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