Radiometric cross-calibration of Gaofen-1 WFV cameras using Landsat-8 OLI images: A solution for large view angle associated problems

Remote Sensing of Environment 174 (2016) 56–68

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Radiometric cross-calibration of Gaofen-1 WFV cameras using Landsat-8 OLI images: A solution for large view angle associated problems Lian Feng a, Juan Li b, Weishu Gong c, Xi Zhao b, Xiaoling Chen a, Xiaoping Pang b,⁎ a b c

State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China Chinese Antarctic Center of Surveying and Mapping, Wuhan University, Wuhan 430079, China Department of Geographical Sciences, University of Maryland, College Park, MD 20742, USA

a r t i c l e

i n f o

Article history: Received 30 July 2015 Received in revised form 7 October 2015 Accepted 24 November 2015 Available online xxxx Keywords: Cross-calibration GF-1 Landsat-8 OLI MODIS Aerosol BRDF Radiative transfer model Remote sensing

a b s t r a c t Four wide-field-of-view (WFV) instruments are onboard the Gaofen-1 (or GF-1) satellite, providing a combined swath of ~800 km. However, observations with large view angles pose new challenges for radiometric crosscalibration with a simple image-based method when using Landsat-8 Operational Land Imager (OLI) data as a reference. Based on radiative transfer modeling, a novel radiometric cross-calibration method has been proposed in this study to solve large view angle-associated problems. The Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol products were used to simulate the top of atmosphere (TOA) signal of the reference and target instruments, and the unequal bidirectional effects were corrected using MODIS bi-directional reflectance distribution function (BRDF) products. Extensive validations with both satellite data and in situ measurements revealed an uncertainty of ~ 8% for the newly produced cross-calibration coefficients when they were used to calibrate TOA reflectance for both close-nadir and off-nadir instruments. The improvements are discernable when compared with the official provided coefficients and that were derived using the image-based crosscalibration method. This study demonstrated not only the usefulness of Landsat-8 OLI data in sensor radiometric calibration but also the impressive accuracy of the MODIS BRDF and aerosol products in radiative transfer simulations. The proposed method can be used in the future to monitor and correct potential radiometric degradations of the GF-1 WFV instruments, and it also can be easily extended to other similar satellite missions to conduct radiometric cross-calibrations. © 2015 Elsevier Inc. All rights reserved.

1. Introduction Because of the promotion of the high-definition earth observation system (HDEOS) by the Chinese government, two high-resolution satellite missions, Gaofen-1 (or GF-1, 2013–present) and Gaofen-2 (or GF-2, 2014–present), have been successfully launched into space. Another three or four satellites in HDEOS are expected to be launched in the next ten years (Xu, Gong, & Wang, 2014). Currently, the images acquired by GF-1 are available to the public after authorization. Four high spatial resolution (16 m) wide-field-of-view (WFV) cameras are onboard the GF-1 satellites, providing a revisiting period of 4 days due to their wide combined coverage (4 × 200 km). In the past two years, the GF-1 images have been used in numerous applications, including searching for evidence in criminal cases and monitoring disasters, among many others, as reported by various mass media. The potential uses for the GF-1 WFV images are not limited to these qualitative applications. The high spatial-temporal resolution and wide coverage make it possible to capture and understand biological, chemical, and physical processes on both small and large scales. Accurate ⁎ Corresponding author. E-mail addresses: [email protected] (L. Feng), [email protected] (X. Pang).

http://dx.doi.org/10.1016/j.rse.2015.11.031 0034-4257/© 2015 Elsevier Inc. All rights reserved.

radiometric calibration, however, is required before the satellite signal can be linked to any of the biophysical and biochemical parameters (Liang, 2005). Due to the lack of onboard calibrators on the GF-1 satellites, vicarious calibration efforts were made by the data operator (the China Centre for Resources Satellite Data and Application, CCRSDA) to conduct a field survey in August 2014 at the Dunhuang calibration site in China, where in situ data were measured and used for radiometric calibrations, resulting in the latest updated coefficients (updated in October 2014, http://www.cresda.com/n16/n1115/n1522/n2103/191962.html). In general, vicarious calibrations can be challenging because of their labor intensity, high cost, small dynamic range, and spatial coverage, among other factors. To overcome these limitations, cross-calibration approach has been developed using tandem images from a wellcalibrated satellite sensor as a reference; this approach has been successfully used in a number of remote-sensing instruments (Chander, Meyer, & Helder, 2004; Dinguirard & Slater, 1999; Liu, Li, Qiao, Liu, & Zhang, 2004; Teillet, Fedosejevs, Thome, & Barker, 2007; Teillet et al., 2001). A simple image-based cross-calibration method has also been proposed by Li et al. (in revision) to cross-calibrate the GF-1 WFV cameras with the rigorously calibrated Landsat-8 Operational Land Imager (OLI) data (Barsi & Markham, 2013; Roy et al., 2014). The successful use of OLI as the reference instrument was partly due to their analogous

L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

spectral bands and similar spatial resolutions between WFV (16 m) and OLI (30 m) sensors. In contrast, although the Moderate Resolution Imaging Spectroradiometer (MODIS) instruments (Terra and Aqua) have demonstrated low radiometric calibration errors, remarkable discrepancies in the ground resolutions and band configurations resulted in large calibration uncertainties (20–40%) when they were used as the references data (Li et al., in revision). The image-based method is based on the assumption that the surface and atmospheric conditions of the target and reference instruments remain unchanged during the b 30 min of overpassing time, and the top-of-atmosphere (TOA) signals of the two sensors are identical when the difference in spectral responses is adjusted. Improved radiometric performance has been demonstrated over the first version of the officially released coefficients (released in October 2013, http:// www.cresda.com/n16/n1115/n1522/n2103/191340.html). The assumption for the image-based method may not hold, however, for WFV observations with large view angles. Fig. 1a illustrates the schematic diagram of the footprints of the Landsat-8 OLI and four GF1 WFV cameras. The images collected by the Landsat-8 OLI are generally at nadir-view, with the largest sensor view zenith angle being ± 7° (Song, Woodcock, Seto, Lenney, & Macomber, 2001). In contrast, the range of the view zenith angle for the close-nadir instruments on GF-1 (WFV2 and WFV3) is 0° to 24°, and for the off-nadir instruments (WFV1 and WFV4) the range is 24°–40°. Although such ranges are less than the coarse spatial resolution satellite data (for example, 0–N55° for MODIS and the Visible Infrared Imaging Radiometer Suite (VIIRS)) (Cao, 2013; Vermote, Kotchenova, & Ray, 2011), the view zenith angle of WFVs appear much larger than the Landsat series sensors or other instruments with spatial resolutions of tens of meters. As simulated using the Second Simulation of the Satellite Signal in the Solar Spectrum model (or 6S) (Vermote, Tanré, Deuzé, Herman, & Morcette, 1997), the increase of the reflectance from the atmospheric path (ρpath) can reach N 20% for the off-nadir WFV cameras compared with nadir view (ρpath,θ = 0°). Moreover, the difference increases dramatically for larger view zenith angles (say N20°) due to the rapidly increasing distance of the atmospheric path. As such, the unequal atmospheric contributions between the target and reference sensors may lead to relatively large uncertainties when using the image-based cross-calibration method, and this is particularly true for off-nadir instruments. An additional problem associated with different satellite geometry is the anisotropic reflection of the surface targets (Barnsley, Allison, & Lewis, 1997; Franch, Vermote, Sobrino, & Fédèle, 2013; Lucht & Roujean, 2000; Lucht, Schaaf, & Strahler, 2000; Schaaf et al., 2002), which could be more significant for observations with large view angles (Jackson et al., 1990; Meyer, Verstraete, & Pinty, 1995)

57

and could lead to much more pronounced errors in the calibration coefficients. Fortunately, state-of-the-art algorithms have been developed for MODIS to create standard aerosol and bidirectional reflectance distribution function (BRDF) products (Kaufman et al., 1997; Remer, 2008; Schaaf et al., 2002). Global and regional validations and applications suggest that these products can be safely used to simulate the atmospheric contributions to the satellite signal, as well as the BRDF effects resulting from non-Lambertian surface targets in any viewing direction (Ichoku et al., 2002; Jin et al., 2003; Liang et al., 2002; Remer et al., 2005; Salomon, Schaaf, Strahler, Gao, & Jin, 2006). Thus, the MODIS atmosphere and BRDF products will be used to solve the large view anglerelated problems that cannot be handled by the image-based crosscalibration method, from which the calibration accuracy is expected to be improved. The objectives of this study are: 1. To develop a radiative transfer modeling (RTM)-based crosscalibration method for WFV instruments using the Landsat-8 OLI as a reference. In this process, MODIS aerosol products will be used to simulate the atmospheric contributions of both sensors, and MODIS BRDF products will be used to correct the different sun-view geometry between OLI and WFV images; and 2. To estimate the uncertainties of the derived cross-calibration coefficients using both satellite images and in situ data and to discuss the feasibility of the proposed method and the usefulness of the MODIS aerosol and BRDF products. 2. Data selection 2.1. Satellite datasets Both the GF-1 and the Landsat-8 are in sun-synchronous orbits with a descending node, and their overpass times are similar (~ 10:30 am local time). Four WFV cameras are onboard the GF-1 satellites with a combined swath of ~800 km. The revisiting period for GF-1 is ~4 days at the equator, which is only 1/4 of that for Landsat (16 days), enabling detection of short-term changes in land surface features. Four spectral bands covering visible to NIR spectral ranges are configured in the GF1 WFV instruments, which are quantified over 10-bit digital numbers (DN). Analogous Landsat-8 OLI bands can be found for each WFV wavelength, except for a wider bandwidth in the NIR band of the WFV. A more detailed comparison of configurations (such as wavelengths, spectral responses, etc.) between the GF-1 WFV cameras and the Landsat-8 OLI is shown in Li et al. (in revision).

Fig. 1. (a) The schematic diagram to show the positions of the Landsat-8 and GF-1 satellites and the footprints of the OLI and WFV cameras. The WFV1 and WFV4 are off-nadir instruments, and the WFV2 and WFV3 are close-nadir instruments. (b) The ratio between simulated reflectance of atmospheric path at different sensor zenith angles to that of the nadir view (zenith angle = 0°), the results for blue and NIR bands with clear (aot550 nm = 0.1) and turbid (aot550 nm = 0.3) aerosol conditions are plotted. The gray bar indicates the lower bound of the sensor zenith angle of the off-nadir instruments, which is also the upper bound of the two close-nadir cameras. θOLI and θWFV are view zenith angle of Landsat-8 OLI and WFV cameras, respectively.

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Similar spectral ranges and overpass times make it possible to conduct cross-calibration for the WFV using the OLI as the reference sensor. Carefully selected tandem WFV-OLI pairs between July 2013 and February 2014 were downloaded from the CCRSDA and the United States Geological Survey, where the image pairs were of quasi-synchronous acquisition time (b 30 min difference) and large dynamic range (with abundant land covers). All the data were collected within several months, eliminating radiometric degradation for both instruments. The selected images were visual examined to avoid contamination of thick aerosol and cloud coverage. In total, there were at least five image pairs collected to perform the cross-calibration for each WFV camera, and another two pairs were chosen for validations. The angular information (e.g. view zenith and azimuth angles) associated to the corresponding WFV images were also provided by the CCRSDA.

2.2. Aerosol data MODIS aerosol products provide daily global aerosol optical thickness (AOT or τ) and aerosol type data. As the MODIS-Terra has an overpass time similar to the GF-1 WFV cameras (descending path at ~ 10:30 am local time), the concurrent aerosol properties (e.g., MOD04_L2 products) obtained from the MODIS-Terra can be used to represent the aerosol properties of the GF images. The MODIS aerosol product has a spatial resolution of a 10 × 10 1-km (at nadir)pixel array, which can be downloaded from NASA's Goddard Space Flight Center (GSFC) (http://modis-atmos.gsfc.nasa.gov/MOD04_L2/). The aerosol types (including mixed, dust, sulfate, smoke, and heavy absorbing smoke) and the aerosol optical thickness (550 nm) contained in the products were used in the radiative transfer modeling of this study.

2.3. BRDF data The MODIS BRDF products (MCD43A1) were introduced in this study to minimize the viewing and illumination effects on the reflectance of the target and reference images. The MODIS BRDF products supply the weighting parameters associated with the Ross Thick Li Sparse Reciprocal BRDF model, which best describes the anisotropy of each pixel (Lucht et al., 2000; Schaaf et al., 2002). Three parameters provided in the products can be used in a forward version of the model to reconstruct the surface anisotropic effects and thus correct directional reflectance to a nadir view geometry. The MCD43A1 data are generated using data from both Terra and Aqua, which are distributed every 8 days with 16 days of acquisition, and the spatial resolution is 500 m. The data concurrent to the WFV-OLI image pairs were downloaded from the USGS Land Processes Distributed Active Archive Center (LP DAAC).

2.4. USGS spectral library The USGS spectral library (version of splib06a) was utilized in this study to correct the potential differences in spectral responses caused by different types of surface materials (see details below). The library was downloaded from the USGS Spectroscopy Lab (http://speclab.cr. usgs.gov/), which records more than 1300 spectra with wavelengths ranging from UV to mid-infrared. The spectral samples were collected from various surface features, including minerals, plants and manmade materials. Thus, most of the remotely detected spectral features had corresponding hyperspectral reflectance spectra features in the library. 2.5. In-situ data at the Dunhuang calibration site The Dunhuang calibration site is located in the Gobi Desert in northwest China, approximately 35 km west of the city of Dunhuang (Gansu Province). The calibration area is situated on a stabilized alluvial fan (Fig. 2a), and the surface comprises cemented gravel with no vegetation. Within an area of 20 km × 20 km in this site, measurements of more than 2000 surface reflectances showed a standard deviation of b2.0% between the visible and near-infrared spectral regions (Zhang, Zhang, & Liu, 2001) and reflectance measurements between 1999 and 2009 at this site show a small standard deviation of b3% (Hu et al., 2010). Thus, data collected in this site have been widely used for vicarious radiometric calibrations of Chinese optical satellite instruments (Chen, Hu, Xu, & Zhang, 2013; Hu et al., 2010). Field measurements were conducted by the CCRSDA in August 2014. During the field survey, spectrum measurements with the field-portable spectroradiometer (SVC HR-1024, Spectra Vista Corp.) were carried out every 30 min over a few days (see Fig. 2b). A standard plate with known reflectance was used to calibrate the measured data, and the measurements were done at nadir with a height of about 1.2 m, a detailed measurement protocol was given by (Zhang et al., 2001). Meanwhile, aerosol properties (including AOT and Angstrom coefficients) were measured automatically with a CE318 photometer (MicroAmps®) during the entire month of study. The mean bidirectional reflectance factor (BRF) of this calibration site was measured using a BRDF system, which comprises a supporting and rolling frame, a spectral radiometer, a spectral irradiance meter, and a controllingsampling unit (Hu et al., 2010). The three types of in situ data provided by the CCRSDA were used to validate the cross-calibration coefficients derived in this study. 3. Methodology The fundamental assumption of this study is that the surface reflectance, the AOT and aerosol type remain unchanged in the same location

Fig. 2. (a) WFV image and digital photography to show the features of the Dunhuang calibration site in China. (b) In situ reflectance measured by the CCRSDA on different dates of August 2014.

L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

during the 30-min time difference in the acquisition times, while the differences in cross-sensor configurations and illumination conditions are considered. The basic workflow is to perform atmospheric and BRDF corrections (with the inputs of MODIS aerosol and BRDF products) to the TOA signal of the Landsat-8 OLI data, resulting in the nadir BRDFadjusted surface reflectance. The results can be converted into the nadir BRDF-adjusted surface reflectance of the WFV cameras by applying a spectral adjustment. Then, the TOA radiance of the WFV cameras can be simulated through backward atmospheric radiation transfer modeling and BRDF modeling, where the view zenith and azimuth angles are from the WFV, and the BRDF and aerosol data are the same as those used for the OLI data. Finally, the calibration coefficients can be obtained using a linear regression between the simulated TOA radiance and the raw data (in digital number, or DN) of the WFV images. 3.1. TOA reflectance calculation The total signal received by satellite sensors (TOA signal) consists of reflectance from the surface and from the atmosphere. Assuming that the surface cover is uniform Lambertian (Vermote et al., 1997), the TOA reflectance can be expressed as ρTOA ðθs ; θv ; ϕs −ϕv Þ ¼ ρa ðθs ; θv ; ϕs −ϕv Þ þ

ρt T ðθs ÞT ðθv Þ 1−ρt S

ð1Þ

where θs and ϕv are the solar zenith and azimuth angles, respectively, θv and ϕv are the view zenith and azimuth angles, respectively, ρa is the atmospheric reflectance, S is the spherical albedo of the atmosphere, and T(θs) and T(θv) are the total downward and upward transmittances, respectively. ρt is the reflectance of the surface target. Remote sensors respond linearly to the incoming signal. Thus, the quantized standard DNs of GF-1 WFV can be converted to TOA spectral radiance LTOA(WFV,i) (wm−2·sr− 1·μm−1) using the radiance rescaling gains and bias (Chander, Markham, & Helder, 2009). For a given band i: LTOAðWFV;iÞ ¼ MWFV;i  DNWFV;i þ AWFV;i

ð2Þ

where MWFV,i is the band-specific multiplicative rescaling gain, and AWFV,i is the band-specific additive rescaling bias. The radiance is then converted to TOA reflectance by  2
ρTOAðWFV;iÞ ¼ π  LTOAðWFV;iÞ  d = EWFV;i  cosθWFV;s

ð3Þ

where θWFV,s is the solar zenith angle, d is the Earth–Sun distance in astronomical units (Chander et al., 2009), and EWFV,i is the extraatmospheric solar irradiance (wm− 2·sr− 1) based on the spectrum that can be calculated as follows: Z EWFV;i ¼

b a

Z b f ðλÞ  Si ðλÞdλ= Si ðλÞdλ a

ð4Þ

is the Landsat-8 OLI quantized and calibrated standard product pixel value, and θOLI,i is the Sun elevation angle. 3.2. Atmospheric and BRDF correction and simulation To derive the surface reflectance of OLI ρt(OLI,i), ρa, S, T(θs) and T(θv) in Eq. (1) are needed. Fortunately, these parameters can be estimated with the 6S model (Vermote et al., 1997), with necessary inputs such as the satellite geometry and aerosol data. The MODIS aerosol type and AOT data are used here, and surface targets are assumed to be of non-bidirectional effects in this step. Note that MODIS products have five aerosol types that are not identical to the convention used in the 6S model. In practice, if the aerosol type in the MODIS products is mixed or sulfate, then a continental model will be chosen in 6S, and similarly, dust corresponds to the urban model and smoke and heavy absorbing smoke correspond to the biomass burning model in 6S. Two factors may lead to disparities between the surface reflectance of the OLI and WFV: 1) viewing and illumination angle effects due to the non-Lambertian surface of the targets and 2) discrepancies of spectral responses between different instruments and surface cover types. The MODIS BRDF products, after resampling to the same spatial resolutions as the OLI and WFV cameras, can potentially be used to correct the viewing/illumination effects between the two instruments. Then the surface reflectance observed from a certain direction can be simulated by the Ross-Li BRDF model (Lucht et al., 2000; Wanner, Li, & Strahler, 1995). The theoretical basis of this semi-empirical model is that the land surface reflectance can be modeled as a sum of three kernels representing basic scattering types: isotropic scattering; radiative transfer-type volumetric scattering, as from horizontally homogeneous leaf canopies; and geometric-optical surface scattering, as from scenes containing three-dimensional objects that cast shadows and are mutually obscured from view at off-nadir angles. The equations are as follows (Roujean, Leroy, & Deschamps, 1992): ρt ðθs ; θv ; ϕs −ϕv Þ ¼ ρ0t ðθs ; θv ; ϕs −ϕv Þ  Bðθs ; θv ; φs −ϕv ; P 1 ; P 2 ; P 3 Þ   P2 P3 ¼ ρ0t ðθs ; θv ; ϕs −ϕv Þ  1 þ  K LSR ðθs ; θv ; ϕs −ϕv ; P 4 ; P 5 Þ þ  K RT ðθs ; θv ; ϕs −ϕv Þ P1 P1

ð6Þ where B is the bidirectional reflectance distribution function, and K LSR ¼

K RT ¼

1 þ secθ0v  secθ0s þ tanθ0v  tanθ0s  cosðϕs −ϕv Þ  2
 t− sint  cost −1  secθ0v þ secθ0s þ π

ð7Þ

ðπ=2−ψÞ  cosψ þ sinψ π − cosθv þ cosθs 4

ð8Þ

cosψ ¼ cosθv  cosθs þ sinθv  sinθs  cosðϕs −ϕv Þ

where Si (non-dimensional) is the normalized spectral response function of the corresponding band, f is the continuous extra-atmospheric solar irradiance (in wm−2·sr−1·μm− 1) (Thuillier et al., 2003), and a and b are the lower and upper bounds of the spectral range for band i, respectively. Theoretically, the calibration coefficients (e.g., MWFV,i and AWFV,i) can be obtained by building a linear regression between DNs and simulated TOA radiance from an accurately calibrated reference instrument, such as the Landsat-8 OLI. The TOA reflectance for the OLI data can be estimated using reflectance rescaling coefficients provided in the metadata file (MTL file):
 ρTOAðOLI;iÞ ¼ M OLI;i  DNOLI;i þ AOLI;i = sinθOLI;s

59

ð5Þ

where MOLI,i is the band-specific multiplicative rescaling factor, and AOLI,i is the band-specific additive rescaling factor from the metadata. DNOLI,i

( cos2 t ¼ min

P4 secθv þ secθs

ð9Þ

) 2 h
2
2 i  G θ0v ; θ0s ; ϕs −ϕv þ tanθ0v  tanθ0s  sinðϕs −ϕv Þ ; 1

ð10Þ
 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G θ0v ; θ0s ; ϕs −ϕv ¼ tan2 θ0v þ tan2 θ0s −2 tanθ0v  tanθ0s  cosðϕs −ϕv Þ ð11Þ tanθ0x ¼ P 5  tanθx ; x ¼ v or s:

ð12Þ

Parameter P1 (or KLamd) is the Lambertian scattering component and equal to the bidirectional reflectance for θv = 0 and θs = 0. Parameter P2 (or Kgeo) is the coefficient of the LiSparse-Reciprocal geometric scattering kernel KLSR (Wanner et al., 1995), derived for a sparse ensemble of surface objects casting shadows on a Lambertian background.

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L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

Parameter P3 (or Kvol) is the coefficient for the RossThick volume scattering kernel KRT (Roujean et al., 1992). The three critical kernel coefficients (P1, P2 and P3) are provided in MODIS BRDF products. The two constants, dimensionless crown relative height P4 and shape P5 parameters, are recommended as 2 and 1 in the model for MODIS processing (Lucht & Roujean, 2000). After removing the angular effects, the nadir ' can be obtained. BRDF-adjusted reflectance of the target ρt(OLI,i) On the other hand, the spectral responses for different surface features can be adjusted using spectral adjustment factor QE with the same method as that in Li et al. (in revision), which can be defined as: Q Ei ¼

¼

ρWFV;i ρOLI;i Z bWFV;i aWFV;i

Z

ρðλÞ  SWFV;i ðλÞ  f ðλÞdλ ,

bWFV;i aWFV;i

Z

bOLI;i aOLI;i

Z

SWFV;i ðλÞ  f ðλÞdλ

ρðλÞ  SOLI;i ðλÞ  f ðλÞdλ

bOLI;i aOLI;i

SOLI;i ðλÞ  f ðλÞdλ ð13Þ

where SWFV and SOLI (non-dimensional) are the normalized spectral response functions for WFV and OLI, respectively, and f is the continuous extra-atmospheric solar irradiance. ρ(λ) is the continuous spectral reflectance for the target, which is ideally acquired from the in situ measurements. In practice, however, it is nearly impossible to obtain sufficient data for all the calibration sites across a large area. As a compromise, the “best-matched” hyper-spectral measurements from the USGS spectral library are used in this study. The nadir BRDF-adjusted reflectance of WFV can be estimated as: ρ0t ðOLI;iÞ  Q Ei ¼ ρ0t ðWFV;iÞ

ð14Þ

3.3. Practical working steps for cross calibration As shown in Fig. 3, the calibration process of this study can be summarized as follows: 1) Geo-matched regions of interest (ROIs) are randomly selected between the Landsat-8 OLI and GF-WFV cameras. The coefficients in the MTL files are used to calculate the TOA reflectance for the OLI data, e.g., ρTOA(OLI,i). The method to select geo-matched ROIs is the same as in Li et al. (in revision). Briefly, if a randomly selected small window (or ROI) of OLI has a ratio of b1% between standard deviation and mean (stdev/mean), and the stdev/mean of the corresponding window at the same location of the WFV is also b1%, the location is then selected as the calibration site and the mean values of the two corresponding windows are used in the further calibration processes. The small variation within the windows (b 1%) is used to ensure the homogeneity of the selected calibration sites. 2) With the inputs of MODIS AOT and aerosol type products, atmospheric corrections for radiometrically calibrated ρTOA(OLI,i) are performed to obtain the surface bidirectional reflectance of OLI ρt(OLI,i), from which the nadir BRDF-adjusted OLI reflectance ρt(OLI, i)′ is derived with the assistance of MODIS BRDF products. 3) Spectral matching is carried out to find the best-matched spectra in the USGS spectral library, from which the QEs between the OLI and WFV instruments are estimated, and the nadir BRDF-adjusted reflectance of the WFV can be obtained. The method to select the matching spectra is the same as that in Li et al. (in revision), where the minimum Mahalanobis distance was used to determine the best-matched spectra in the USGS library and the atmospherically corrected OLI reflectance. 4) With the same MODIS BRDF and aerosol products, the TOA radiance of the WFV (ρTOA(WFV,i)) can be simulated using a backward atmospheric radiation transfer model.

5) Finally, the calibration coefficients can be produced through a linear regression between the simulated ρTOA(WFV,i) and the corresponding DNs of the WFV. 3.4. Methods for evaluation Two types of data were used to assess the uncertainties of the crosscalibration coefficients in this study: Landsat 8-OLI images and in situ spectrum measurements. As in the cross-calibration process, the Landsat 8-OLI images were used to derive nadir BRDF-adjusted OLI reflectance after removing the atmospheric contribution and BRDF effects with the assistant of MODIS aerosol and BRDF products. Then, spectral response differences were adjusted using a spectral adjustment factor estimated by the USGS spectral library, resulting in nadir BRDF-adjusted WFV reflectance. The same MODIS atmospheric and BRDF products were used to simulate TOA reflectance of the WFV cameras (denoted as ρSimulated) with their own satellite geometry. On the other hand, the real TOA reflectance of the WFV (denoted as ρRTM-BRDF) was calculated using the raw DN images and the newly derived calibration coefficients with Eqs. (2)–(3). The ρSimulated is considered as the ground truth, and the mean difference (MD, in percentage) and mean ratio (MR) between ρRTM-BRDF and ρSimulated are estimated, representing the uncertainties of the crosscalibration coefficients. Instead of TOA spectral radiance used in the calibration process, TOA reflectance were used here as it removes the cosine effect of different solar zenith angles and appears more often to be used in remote sensing applications (Chander et al., 2009). Note that the image pairs for validations are different from those used to derive the cross-calibration coefficients. The field survey at the Dunhuang calibration site conducted by the CCRSDA in August 2014 makes it possible to use in situ measurements to validate the calibration coefficients derived in this study. However, only six days of field reflectance measurements are available. Fortunately, the calibration site is very stable (see Fig. 2a), where reflectance collected at the acquisition time of the WFV for six days (in a span of about half a month) had negligible differences with the in situ spectrum, and the standard deviation for each WFV equivalent band (estimated using Eq. (15)) was b 2% (see Fig. 2b). Thus, a mean spectrum of the six measurements was used to validate the WFV surface reflectance, where 14 cloud-free images were taken that month, with 8 off-nadir images and 6 close-nadir images. The mean in situ surface spectrum was converted to WFV equivalent reflectance at specific bands i (ρi) using: Z ρi ¼

b a

Z b ρðλÞ  SWFV;i ðλÞ  f ðλÞdλ SWFV;i ðλÞ  f ðλÞdλ a

ð15Þ

where S is the normalized spectral response function, f is the continuous extra-atmospheric solar irradiance (in wm− 2·sr− 1·μm− 1) (Thuillier et al., 2003), and a and b are the lower and upper bounds of the spectral range, respectively. The WFV data were first calibrated into TOA reflectance using the derived calibration coefficients through Eqs. (2)–(3). Then, simulated TOA reflectance derived with the WFV equivalent reflectance, aerosol and BRF measurements was considered as ground truth to gauge the uncertainties of the calibration coefficients produced in this study. 4. Results 4.1. Results of cross-calibrations With sufficient calibration sites (N200 for any given set of bands of four WFV cameras), a linear regression between the DNs and the simulated TOA radiance (LTOA(WFV,i)) resulted in cross-calibration coefficients (both gains and offsets) for the GF-1 WFV cameras. Fig. 4 plots the

L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

simulated TOA radiance against the DNs for four spectral bands of WFV1, one of the off-nadir WFV cameras with large view angles (see Fig. 1). In addition, the results for one of the close-nadir instrument (WFV3) are shown in Fig. 5. With large dynamic ranges for both DNs and radiance, the points for all the spectral bands are aligned along the linear fitting line (with R2 N 0.9), suggesting the statistical significance of the linear fits and the validity of the regression coefficients. Note that the points are more scattered for the off-nadir instruments, which may due to the relatively larger bidirectional effects of the observations of larger view zenith angles. The cross-calibration coefficients for all four WFV cameras are tabulated in Table 1. The coefficients derived using three different cross-calibration methods are 1) radiative transfer modeling (RTM) with BRDF correction and simulation (or RTM-BRDF), 2) RTM without BRDF correction and simulation (or RTM), and 3) an imagebased method proposed in Li et al. (in revision) (or image-based). The points used to derive different versions of calibration coefficients are identical, ensuring objective comparisons between these calibration methods. As shown in Table 1, the relationships used to derive

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the calibration coefficients are highly significant for all the three methods, where the determination coefficients (eg. R2) of all the instruments and spectral bands are N 0.9. Note that slight differences exist between the image-based coefficients presented in Li et al. (in revision) and Table 1, as the points used to establish the linear regressions differed. In addition, the officially provided radiometric calibration coefficients are also listed, where a non-offset calibration method was used. The gain differences between the four versions of coefficients are estimated. When comparing the calibration gain of with and without BRDF simulation (both with RTM) (column D b in Table 1), more pronounced differences are observed for the off-nadir instruments than the close-nadir instruments. Specifically, the gain differences are generally b 5% for the two close-nadir instruments of WFV2 and WFV3. In contrast, the differences ranges between 9.42% and 16.07% for WFV1 depending on different spectral bands, and N 8% for three visible bands of WFV4, clearly suggesting the significant impact of the bi-directional effects on deriving calibration coefficients for large view zenith instruments.

Fig. 3. Flowchart of the RTM-BRDF cross-calibration method. DN represents the digital number, ρTOA is the TOA reflectance, ρt is the surface reflectance of Lambertian assumption, ρ't is the nadir adjusted surface reflectance, θs and θv are the solar and sensor zenith angles, ϕs and ϕv are the solar and sensor azimuth angles, and RSRs stand for relative spectral responses, respectively. Note that, MODIS BRDF product were used twice in the process, where the first use is to convert the atmospherically corrected surface reflectance of OLI to nadir-view, and the second is to simulate the Lambertian reflectance of WFV from nadir reflectance.

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Fig. 4. Landsat-8 OLI simulated TOA radiance against the DNs for the four spectral bands of WFV1 (off-nadir instrument) using RTM-BRDF based method. Linear fits resulted in cross-calibration coefficients.

Fig. 5. Landsat-8 OLI simulated TOA radiance against the DNs for the four spectral bands of WFV3 (close-nadir instrument) using RTM-BRDF based method. Linear fits resulted in crosscalibration coefficients.

L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

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Table 1 Calibration coefficients derived using different cross-calibration methods; the officially provided coefficients (updated in October 2014) are also listed. The coefficients derived using the proposed method of this study are shaded. The differences in gains between the four versions of coefficients are estimated. The shaded columns are the recommended calibration coefficients of this study. Sensor

Image-based

Band Gain

WFV1

WFV2

WFV3

WFV4

Offset

RTM R

2

Gain

Offset

RTM-BRDF R

2

Gain

Gain Differences * (%)

Official 2

Offset

R

Gain

a

D

b

c

D

D

d

D

Blue

0.1564

-0.5126

0.91

0.1630

7.5015

0.95

0.1892

2.5442

0.94

0.2004

20.97

16.07

21.96

5.59

Green

0.1452

-6.1533

0.97

0.1551

0.0990

0.98

0.1771

-1.3818

0.95

0.1648

21.97

14.18

11.89

7.46

Red

0.1190

-1.8138

0.97

0.1254

2.4543

0.97

0.1396

3.0544

0.95

0.1243

17.31

11.32

4.26

12.31

Nir

0.1471

-4.3431

0.96

0.1380

-2.0808

0.96

0.1510

2.6335

0.93

0.1563

2.65

9.42

5.89

3.39

Blue

0.1940

-6.9579

0.99

0.2012

-7.5161

0.99

0.2129

-6.5939

0.96

0.1733

9.74

5.82

11.94

22.85

Green

0.1590

-8.4230

0.99

0.1710

-8.0754

0.99

0.1795

-7.6358

0.95

0.1383

12.89

4.97

14.97

29.79

Red

0.1292

-5.8543

0.99

0.1386

-5.0787

0.99

0.1434

-2.9477

0.97

0.1122

10.99

3.46

15.15

27.81

21.5

Nir

0.1690

-12.4337

0.98

0.1647

-10.2854

0.98

0.1665

-8.6476

0.96

0.1391

1.48

1.09

Blue

0.1842

-1.5270

0.91

0.1905

-3.3188

0.95

0.1979

-5.0274

0.94

0.1745

7.44

3.88

Green

0.1570

0.8760

0.97

0.1745

-0.1968

0.98

0.1791

-1.3056

0.95

0.1514

14.08

Red

0.1398

-0.3268

0.97

0.1491

0.3379

0.97

0.1520

-0.0848

0.95

0.1257

8.73

Nir

0.154

-2.2783

0.96

0.1567

-2.4774

0.96

0.1572

-2.1195

0.93

0.1462

Blue

0.1892

-3.6902

0.99

0.1866

-3.1795

0.99

0.1709

-0.2750

0.98

Green

0.1772

-6.3297

0.99

0.1861

-5.8307

0.99

0.1663

-3.0948

19.70

5.56

13.41

2.64

3.70

18.30

1.95

11.22

20.92

2.08

0.32

5.34

7.52

0.1713

9.67

8.41

10.45

0.23

0.97

0.1600

6.15

10.64

10.75

3.94

Red

0.1554

-3.5839

0.99

0.1620

-2.9234

0.99

0.1471

-2.5556

0.97

0.1497

5.34

9.20

3.81

1.74

Nir

0.1745

-8.6763

0.98

0.1702

-7.1791

0.99

0.1634

-11.1482

0.96

0.1435

6.36

4.00

21.60

13.87

⁎Da is the gain differences between RTM-BRDF and image-based methods, Db is the differences between RTM-BRDF and RTM methods, Dc is the differences between image-based method and official coefficients, Dd is the differences between RTM-BRDF and official coefficients.

Relatively large gain differences (N10%) are shown between the RTM-BRDF and the image-based methods (column Da in Table 1) for three visible bands of WVF1, green and red bands of WFV2 and green

band of WFV3. While the differences are generally small for NIR bands of the four instruments, with 6.36% for WFV4 and b3% for the other three WFV sensors. Differences of 3.7–21.9% for certain bands and

Fig. 6. Evaluation of calibrated TOA reflectance of WFV1 using simulated TOA reflectance from concurrent Landsat-8 OLI. The results for three versions of calibration coefficients are plotted. MD and MR are mean relative difference and mean ratio, respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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Fig. 7. Evaluation of calibrated TOA reflectance of WFV3 using simulated TOA reflectance from concurrent Landsat-8 OLI. The results for three versions of calibration coefficients are plotted. MD and MR are mean relative difference and mean ratio, respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

instruments are revealed between the coefficients derived using the image-based method and those of the official coefficients (column Dc in Table 1), and the magnitudes for different WFV cameras and spectral bands are comparable. For the comparisons between the RTM-BRDF and official coefficients (column Dd in Table 1), evidently high differences are observed for the two close-nadir instruments, where the differences are N19.7% for four spectral bands of WFV2 and N 13% for three visible bands of WFV3. On the other hand, except for the red band of WFV1 and NIR band of WFV4, the differences are insignificant for the two off-nadir WFV cameras. 4.2. Results of evaluations The evaluation results of using Landsat-8 OLI images are shown in Fig. 6 (WFV1) and Fig. 7 (WFV3), representing the conditions for offnadir and close-nadir, respectively. For comparison, the WFV TOA reflectance calibrated using official coefficients (denoted as ρofficial, green) and that derived with the image-based cross-calibration method (denoted as ρImage-based, blue) are also plotted. To estimate the uncertainties in a statistically meaningful way, random point-pairs were generated using the ρRTM-BRDF and ρSimulated image pairs. Hundreds of valid points from homogeneous targets were selected for uncertainty estimates, where the selection criteria were the same as those used for the calibration sites (b1% of stdev/mean in a small window of both images). Clearly, ρRTM-BRDF agrees very well with ρSimulated for both the WFV1 and WFV3 cameras (red points), as the points align closely with the 1:1 line for the four spectral bands of the two instruments. Statistically, for all of the spectral bands of the two WFV cameras, the MD ranges between 2.8–6.3% and MR ranges between 0.95–0.99. Moreover, the differences between ρSimulated and ρRTM-BRDF appear much smaller than

those between ρSimulated and ρImage-based (or ρOfficial), indicating promising improvements with the proposed method. While the MD and MR of the blue and NIR bands for the WFV1 are similar between ρRTM-BRDF and ρOfficial, much better performances of ρRTM-BRDF are noticeable over other bands of this instrument and over all four bands of the WFV3. When the image-based calibration coefficients were used for the WFV1, large discrepancies occurred between ρImage-based and ρSimulated, with MD reaching 13.3% for the NIR band and N 20% for the three visible bands (Fig. 6), further confirming the problematic assumption of this method (same surface and atmospheric conditions between target and reference instruments) for large view angle instruments. In contrast, the errors of ρImage-based for the closenadir WFV3 instrument are much smaller, where the MD are ~13% for the green and red bands and b10% for the blue and NIR bands (Fig. 7), suggesting that the bidirectional effects on the close-nadir view instruments should be much smaller. Mean differences between calibrated TOA reflectance (e.g., ρRTM-BRDF, ρImage-based and ρOfficial) and ρSimulated at different reflectance ranges were estimated to further illustrate the performances of the three versions of calibration coefficients, with the results of WFV1 and WFV3 shown in Figs. 8 and 9, respectively. As in the scatter plots, the best agreements between ρ RTM-BRDF and ρSimulated are apparent for almost all the reflectance ranges of the four spectral bands, except for the comparable results of the blue and NIR bands of WFV1 between ρRTM-BRDF and ρOfficial. Meanwhile, the mean differences for ρRTM-BRDF are b10% and generally ~ 5% for any reflectance ranges, validating the impressive results obtained using the proposed cross-calibration method of this study. Fig. 10a plots the in situ simulated TOA reflectance against the calibrated TOA reflectance using different versions of calibration

L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

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Fig. 8. The mean differences between calibrated TOA reflectance of WFV1 and simulated TOA reflectance from concurrent Landsat-8 OLI for different reflectance ranges. The results for three versions of calibration coefficients are plotted. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

coefficients. The TOA reflectance calibrated using coefficients derived from the RTM-BRDF method shows favorable agreement with the in situ simulated TOA reflectance for the WFV instruments, as demonstrated by the high R2(0.72) and small MD (6.4%) and RMSD (7.7%). While most of the validation data are aligned close the 1:1 line, relatively large differences occurred in a few points of the blue and red bands. In addition, the MD and RMSD of the official coefficients are almost the same as the RTM-BRDF coefficients, with an identical MD and an even lower RMSD (7.3%), while the in situ simulated TOA reflectances were generally lower than the calibrated reflectances. Note that this could not lead to the conclusion that the performances of the official coefficients are comparable to (or even better than) those derived using the RTM-BRDF method. In fact, Fig. 10c cannot be considered an independent validation because the same in situ data were used by the CCRSDA to derive the official calibration coefficients. Yet, the performance on green and red bands are relatively lower, possibly because of that the elevated Rayleigh scattering due to the increased path length of the off-nadir instruments influence more on the blue-green bands than the longer wavelengths. On the other hand, the overall poor performances of the imaged-based coefficients are observed, with MD of 7.8% and RMSD of 10.7%, respectively. However, when only closenadir instruments were considered, the uncertainties of the imagebased coefficients are rapidly reduced to ~5%, suggesting that this method is useful for close-nadir instruments. To summarize, validations with satellite images showed MD of ~5% between calibrated WFV TOA reflectance using the newly derived calibration coefficients and simulated TOA reflectance using the Landsat-8 OLI data. Considering the calibration error of 3% for OLI in reflectance (Roy et al., 2014), the calibration uncertainty of the WFV is ~8%. Likewise, compared with the in situ simulated TOA reflectance, the

uncertainty estimates (MD and RMSD) are also b8%. As such, we can conclude that the uncertainty of the proposed calibration coefficients derived using the RTM-BRDF method is ~8%. 5. Discussion In general, it is desirable to use in situ BRDF and aerosol measurements to conduct the cross-calibration process. However, it appears to be extremely difficult to collect sufficient concurrent data for all of the image pairs and calibration sites in this study, which covers a large area of China, and this approach is further complicated by different image acquisition times. Although MODIS products (BRDF and aerosol) may introduce new sources of uncertainties to the calibration coefficients, the use of these products can be justified for the following reasons. First, the budget of the errors introduced by MODIS products can be estimated. TOA reflectance were simulated using 6S at different reflectance ranges (0.1–0.5, in BRDF-adjusted reflectance), and the relative differences between uncertainty-free and uncertainty-added TOA reflectances were estimated. For a given reflectance, the mean BRDF and AOT of the cross-calibration process were used to simulate the uncertainty-free TOA reflectance. On the other hand, uncertainties of 5% for BRDF and of ~ 0.05 ± 0.15 × τ (τ set as 0.22, representing the mean AOT of the MODIS aerosol products used in the calibration process) for AOT were added to simulate the corresponding uncertaintyadded TOA reflectance. These added uncertainties are based on comprehensive validations of previous studies (Jin et al., 2003; Liang et al., 2002; Remer et al., 2005; Salomon et al., 2006). The differences for combinations of plus and minus the uncertainties of BRDF and AOT are estimated and plotted in Fig. 11. Although the differences are relatively

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L. Feng et al. / Remote Sensing of Environment 174 (2016) 56–68

Fig. 9. The mean differences between calibrated TOA reflectance of WFV3 and simulated TOA reflectance from concurrent Landsat-8 OLI for different reflectance ranges. The results for three versions of calibration coefficients are plotted. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

larger for the NIR band (5–8%), they are b 5% for the three visible bands at any given reflectance range, which is even less than the increased atmospheric path contributions to the TOA signal (5%–N20%, Fig. 1b) for off-nadir instruments. Note that quality assurance (QA) flags were checked when using the MODIS AOT and BRDF products (Jin et al., 2003; Remer, 2008), and only the highest-quality data were used in the cross-calibration. Therefore, the uncertainties of the simulated TOA signal introduced by the MODIS AOT and BRDF products should be well below those shown in Fig. 11. This can also be interpreted as the uncertainty budget of the cross-calibration coefficients, which were derived using the relationships between simulated TOA radiance and raw digital count.

Second, when comparing the calibration coefficients derived using the RTM-BRDF and RTM methods (Table 1), obvious gain disparities (N8.4%) can be observed for WFV1 and WFV4 for the three visible bands, which should be attributed to the large view angle and its associated BRDF effects on the off-nadir instruments. The insignificant differences in NIR bands were likely due to the smaller BRDF effects on the NIR bands (Franch et al., 2013). In fact, extensive validations of this study using satellite images and in situ data show uncertainties of ~ 8% for the currently generated coefficients for both off-nadir and close-nadir cameras. Significant improvements have been made over the official calibration coefficients and those derived using the image-based cross-calibration method, suggesting the

Fig. 10. Validations of the calibrated TOA reflectance of WFV cameras using in situ reflectance and simulated TOA reflectance. The results for three versions of calibration coefficients are demonstrated. MD and RMSD are mean relative difference and root mean square difference, respectively. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

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Fig. 11. The relative differences between uncertainty-free and uncertainty-added TOA reflectance simulations for different reflectance ranges (in BRDF-adjusted reflectance). For a given reflectance, mean BRDF and AOT of the cross-calibration process were used to simulate the uncertainty-free TOA reflectance, while uncertainties of 5% for BRDF and of ~0.05 ± 0.15 × τ (τ set as 0.22, representing the mean AOT of the MODIS aerosol products used in the calibration process) for AOT were added to simulate the corresponding uncertainty-added TOA reflectance. The differences for four combinations of plus and minus the uncertainties of BRDF and AOT are estimated, representing the upper and lower bounds of the introduced calibration uncertainties by using MODIS BRDF and aerosol products. Note that, “++′” means plus the uncertainties of BRDF and AOT, “+−′” is plus the uncertainty of BRDF and minus that of AOT, “−+′” is minus BRDF and plus AOT, and “–′” is minus the uncertainties of both BRDF and AOT.

validity of the proposed method and the usefulness of the MODIS BRDF and aerosol products. Thirdly, although the BRDF products were developed using MODIS, whose spatial resolution and spectral bands are significantly different from Landsat-8 OLI and GF-1 WFV instruments, validations by previous studies proved their capability in deriving accurate nadir-view reflectance of higher resolution data, such as Landsat observations (Fuqin et al., 2010; Roy et al., 2008). Also, the calibration sites (e.g., ROIs) were only selected where the surface is homogeneous (stdev/ mean b 1%), the impacts of the spatial resolution disparity should be limited. Thus, the MODIS BRDF and AOT parameters can to be used in the WFV-OLI cross-calibration of this study. Simultaneously measured in situ hyperspectral data or hyperspectral images (such as Hyperion) are preferable to calculate QE for adjustment of spectral responses between the reference and target instruments. However, obtaining sufficient concurrent spectral measurements for randomly selected calibration sites of a large coverage is very difficult. As a solution in this study, the atmospherically corrected surface reflectance of the Landsat-8 OLI was used to find the “most approximate” spectral data in the USGS spectral library, which were then used for the QE calculations. Indeed, validations by Li et al. (in revision) showed that, for ROIs selected in WFV images, the spectral shapes and estimated QEs of either the matched USGS spectral reflectance or geo-matched hyperspectral Hyperion data (with the same acquisition date as WFV) are very consistent, suggesting that the uncertainties due to the QE estimation should be small in the calibration results. Note that, the influence of sun-view geometry on QE should be

negligible as the OLI data and in situ spectral measurements are (or close to) nadir view. The solar zenith and azimuth angles were not considered in the cross-calibration site. However, as the image-pairs of OLI and WFV were obtained across different seasons, and the calibration ROIs were selected all over China, the solar zenith angle covered a large range of 25°–60°. Thus, the calibration coefficients listed in Table 1 should be applicable to different solar zenith angles. 6. Conclusions A novel radiometric cross-calibration method has been proposed in this study to solve the problems associated with the large view angle in the cross-calibration process of the GF-1 WFV instruments. The method here is different from the previously proposed image-based crosscalibration method (Li et al., in revision) as the current approach is based on RTM. Although the RTM cross-calibration methods have been used in ocean color missions due to their much sophisticated radiometric calibration requirements (Hu, Muller-Karger, Andrefouet, & Carder, 2001; Pahlevan et al., 2014; Pan, He, & Zhu, 2004; Wang & Franz, 2000), it has been rarely used in land-based satellite missions. This may because of that the view zenith angles for the reference and target instruments are relatively small in previous studies (Chander, Coan, & Scaramuzza, 2008; Chander et al., 2004; Teillet et al., 2001), and the atmospheric path radiances are approximately the same and the BRDF effects are negligible. However, for large discrepancy in view zenith angles between the target (GF-1 WFV) and reference (Landsat-

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8 OLI) cameras of this study, these issues may cause large potential errors to the calibration coefficients. Indeed, the proposed method appears to be a good solution, with the assistant of accurate MODIS BRDF and aerosol data. The current study has demonstrated the usefulness of Landsat-8 OLI data in sensor radiometric calibration for its highly maintained accuracy, and the importance of MODIS BRDF and aerosol products should also be acknowledged. The RTM-BRDF cross-calibration methods provide a way to radiometrically calibrate the GF-1 WFV cameras with low cost and high accuracy. As long as the well-calibrated Landsat-8 OLI data are available, the method can be used to monitor and correct the potential reflectance biases caused by sensor degradations in the future. Moreover, the method may also be used to maintain accurate and consistent observations of the planning of GF missions in China or similar satellites from other countries. Acknowledgments This work was supported by the National Natural Science Foundation of China (No.: 41401388, 41331174), the Special Fund by Surveying & Mapping and Geoinformation Research in the Public Interest (No.: 201512026), the Fundamental Research Funds for the Central Universities and the open-fund projects of LIESMARS (Wuhan University). We thank the USGS for providing Landsat data and the spectral library, the MODIS Land Team for providing the aerosol and BRDF products, and the CCRSDA providing in situ spectral and other measurements. Two anonymous reviewers provided valuable comments to help improve this manuscript, whose effort is also appreciated. References Barnsley, M., Allison, D., & Lewis, P. (1997). On the information content of multiple view angle (MVA) images. International Journal of Remote Sensing, 18, 1937–1960. Barsi, J. A., & Markham, B. L. (2013). Early radiometric performance assessment of the Landsat-8 Operational Land Imager (OLI). SPIE optical engineering+ applications. International Society for Optics and Photonics (pp. 88661C-88661C-88612). Cao, C. (2013). Visible infrared imaging radiometer suite (VIIRS) sensor data record (SDR) user's guide. Version 1.2, 10 September 2013. NOAA technical report NESDIS, 142, . Chander, G., Coan, M. J., & Scaramuzza, P. L. (2008). Evaluation and comparison of the IRSP6 and the Landsat sensors. IEEE Transactions on Geoscience and Remote Sensing, 46, 209–221. Chander, G., Markham, B. L., & Helder, D. L. (2009). Summary of current radiometric calibration coefficients for Landsat MSS, TM, ETM +, and EO-1 ALI sensors. Remote Sensing of Environment, 113, 893–903. Chander, G., Meyer, D. J., & Helder, D. L. (2004). Cross calibration of the Landsat-7 ETM+ and EO-1 ALI sensor. IEEE Transactions on Geoscience and Remote Sensing, 42, 2821–2831. Chen, L., Hu, X., Xu, N., & Zhang, P. (2013). The application of deep convective clouds in the calibration and response monitoring of the reflective solar bands of FY-3A/ MERSI (medium resolution spectral imager). Remote Sensing, 5, 6958–6975. Dinguirard, M., & Slater, P. N. (1999). Calibration of space-multispectral imaging sensors: A review. Remote Sensing of Environment, 68, 194–205. Franch, B., Vermote, E., Sobrino, J., & Fédèle, E. (2013). Analysis of directional effects on atmospheric correction. Remote Sensing of Environment, 128, 276–288. Fuqin, L., Jupp, D. L. B., Reddy, S., Lymburner, L., Mueller, N., Tan, P., & Islam, A. (2010). An evaluation of the use of atmospheric and BRDF correction to standardize Landsat data. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 3, 257–270. Hu, C., Muller-Karger, F. E., Andrefouet, S., & Carder, K. L. (2001). Atmospheric correction and cross-calibration of LANDSAT-7/ETM+ imagery over aquatic environments: A multiplatform approach using SeaWiFS/MODIS. Remote Sensing of Environment, 78, 99–107. Hu, X., Liu, J., Sun, L., Rong, Z., Li, Y., Zhang, Y., ... Gu, X. (2010). Characterization of CRCS Dunhuang test site and vicarious calibration utilization for Fengyun (FY) series sensors. Canadian Journal of Remote Sensing, 36, 566–582. Ichoku, C., Chu, D. A., Mattoo, S., Kaufman, Y. J., Remer, L. A., Tanré, D., ... Holben, B. N. (2002). A spatio-temporal approach for global validation and analysis of MODIS aerosol products. Geophysical Research Letters, 29, 8006. Jackson, R. D., Teillet, P. M., Slater, P. N., Fedosejevs, G., Jasinski, M. F., Aase, J. K., & Moran, M. S. (1990). Bidirectional measurements of surface reflectance for view angle corrections of oblique imagery. Remote Sensing of Environment, 32, 189–202.

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