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Abstract
On-orbit radiometric calibration of the optical sensors on-board SuperView-1 satellites is the foundation for further quantitative applications. A field calibration campaign was orchestrated to radiometrically calibrate the SuperView-1 optical sensors at the Baotou calibration site in China during September 2018. Based on the collected datasets, three independent methods (reflectance-based, radiance-based, and cross-calibration) were used to determine the radiometric calibration coefficients of the SuperView-1 optical sensors with multiple permanent artificial calibration targets. Comparisons of the desert top-of-atmosphere radiance calculated based on the coefficients determined with independent methods were analyzed. Comparison results show that the minimum and maximum relative differences of the radiometrically-calibrated desert TOA radiance between the reflectance-based and radiance-based methods are 1.26% and 4.23% for SV0102 and SV0104, respectively. While, the minimum and maximum relative differences of the radiometrically-calibrated desert TOA radiance between the reflectance-based and radiance-based methods are 0.82% and 6.83% for SV0101 and SV0103, respectively. The reasonably good agreement of the radiometrically calibrated coefficients of the SuperView-1 on-board sensors between these independent methods is encouraging. An uncertainty analysis was also discussed, and the results suggest that the overall uncertainties of the predicted TOA radiance are less than 4.5%, 4.0%, and 5.15% for the reflectance-based, radiance-based, and cross-calibration methods, respectively.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, an increasing number of remote sensing satellites equipped with high spatial resolution sensors have been launched in China. SuperView-1 is a set of launched Chinese civilian remote sensing satellites operated by the Beijing Space View Tech Co Ltd. SuperView-1 includes four satellites, namely, SuperView-1 01(SV0101), SuperView-1 02 (SV0102), SuperView-1 03(SV0103), and SuperView-1 04(SV0104). SV0101 and SV0102 were launched on 28 December 2016, whereas SV0103 and SV0104 were launched on 9 January 2018. In fact, the four sensors are designed almost the same even though they were carried on four SuperView-1 satellites. For each sensors, there are four CCD detectors arranged in a linear array way. The lifetime of the four SuperView-1 satellites and sensors were designed for eight years. Currently, the four SuperView-1 satellite operate at an altitude of 530 km in a Sun-synchronous orbit. Each SuperView-1 satellites can revisit the same location of the earth within 1 days, and the scan swath is approximately 12 km. Each satellite collects images with 0.5 m resolution for the panchromatic channel, and 2 m resolution for the blue, green, red, and NIR multispectral channels, respectively. So far, the SuperView-1 is the highest spatial resolution commercial Earth-observation satellite designed in China.
The objective of the SuperView-1 satellite constellation is to provide commercial earth observation and remote sensing data with high spatial resolutions. Since its launch, SuperView-1 has collected a considerable number of images, which can be widely used in high-accuracy mapping and land-use, land-cover, agriculture, vegetation, and environmental monitoring, along with other applications. However, the on-orbit radiometric calibration coefficients should be determined for further quantitative applications. For example, classification of land use and land cover changes depends on an accurate radiometric characterization of the instruments [1]. Therefore, accurate radiometric calibration is the foundation to ensuring the quality of the SuperView-1 images. Post-launch radiometric calibration approach using a satellite-equipped calibrator (e.g., solar, lamp, or blackbody) has been used to calibrate on-orbit optical sensors. For example, it has been successfully used to calibrate optical sensors carried on the satellites of Landsat [2–4], the Suomi National Polar-Orbiting Partnership Visible Infrared Imaging Radiometer Suite (S-NPP VIIRS) [5], the Moderate Resolution Imaging Spectroradiometer (MODIS) [6], and Sentinel-2 (S2) [7]. However, as is well-known, recently-launched Chinese satellites, such as the HuanJing- (HJ), ZiYuan- (ZY), and GaoFen- (GF) series satellites, have no on-board calibration system. Hence, alternative calibration approaches must be developed to calibrate the radiometric performance of these space-borne sensors.
Vicarious calibration has been proven to be an effective method for calibrating the radiometric performance of on-orbit satellite optical sensors since its use by the Remote Sensing Group (RSG) at the University of Arizona in the 1980s [8]. These vicarious methods can be categorized as reflectance-based, radiance-based, and irradiance-based calibration methods [8–12]. In China, the HJ-, ZY-, and GF-series satellites are usually vicariously calibrated during July to August each year by the CCRSDA, and the resultant radiometric calibration coefficients are published on the official website. Cross-calibration is another important alternative method, and is based on a well-calibrated radiometric reference sensor (e.g., S2, Landsat operational land imager (OLI), or MODIS). Owing to the reliability and low cost of cross-calibration, it has been widely used to calibrate the radiometric performance of Chinese satellites launched without on-board calibrator systems, such as the Beijing-1 and GF-series optical sensors [13–16].
This study aims to calibrate the radiometric performance of the high spatial resolution sensors on-board SuperView-1 satellites with multiple ground permanent artificial targets using three independent methods: reflectance-based, radiance-based, and cross-calibration. This paper is organized as follows. Section 2 describes the calibration site and the datasets collected during the field campaign. Section 3 describes the multiple permanent artificial targets-based radiometric calibration method. Section 4 describes the results of the radiometric calibration coefficients determined with multiple ground permanent artificial calibration targets using the three independent methods. Section 4 also describes the comparison results between the calculated desert TOA radiance with the radiometric calibration coefficients determined by the independent methods. Section 5 and Section 6 provides a detailed discussion on the uncertainty and validation analysis. Finally, conclusions are drawn in Section 7.
2. Calibration site and datasets
2.1 Calibration site description
In this study, the Baotou calibration site was selected as our vicarious radiometric calibration site. The Baotou calibration site (40.88 °N, 109.53 °E) is located at Urad Qianqi of Inner Mongolia in north China, with an average elevation of approximately 1270 m above sea level. The semi-desert, clear sky, and uniform surface of Urad Qianqi have been deemed ideal for calibration experiments. There are two categories of targets at the Baotou calibration site for vicarious radiometric calibration. One includes four permanent artificial reflectance targets (namely, one black, one grey, and two white targets), which are suitable for airborne and high spatial resolution sensors (e.g., within 10 m). The artificial reflectance panels are made of black, grey, and white gravels with relative smooth spectrum. The gravels were exploited and collected by a mine company in the mountain located at the Inner Mongolia of north China and the particle size of the gravels is about 0.5 cm to 1.5 cm. The other category comprises a large area of desert target with an average reflectance of approximately 30%, for moderate spatial resolution satellites (e.g., Landsat series satellite optical sensors at 30 m). Figure 1 shows the permanent artificial calibration targets and natural desert targets at the Baotou calibration site. The distance between the desert target and artificial targets is approximately 2 km.
Fig. 1. Calibration targets at the Baotou calibration site, Inner Mongolia, China. (a) Permanent artificial calibration targets; (b) Desert calibration target.
2.2 Airborne hyperspectral data
Airborne hyperspectral data with a spatial resolution of 0.48 m were acquired by an airborne visible and NIR hyperspectrometer (abbreviated as Air-VNIR) at approximately the same time and in approximately the same viewing geometry as in the SuperView-1 satellite overpass of the Baotou calibration site on 23 September 2018. The acquisition information of the Air-VNIR images at the Baotou calibration site are listed in Table 1. The Air-VNIR was equipped on a manned vehicle flying at an altitude of approximately 3.27 km. The Air-VNIR was designed by the Shanghai Institute of Technical Physics (SITP) at the Chinese Academy of Sciences (CAS). The Air-VNIR data covered the visible and near-infrared (VNIR) spectral region from 400 nm to 1050 nm, with 300 near-contiguous spectral bands at 3.5 nm spectral resolution. The radiometric and spectral characteristics of the Air-VNIR were well-calibrated in the laboratory. The collected airborne hyperspectral images were used to calibrate the on-orbit radiometric performance of the SuperView-1 satellite-equipped optical sensors, using a radiance-based method based on multiple permanent artificial targets. Figure 2 shows a hyperspectral 3D cube of the permanent artificial targets and the desert target at the Baotou calibration site from the collected Air-VNIR images on 23 September 2018.
Fig. 2. Hyperspectral 3D cube of the calibration targets at the Baotou calibration site with collected Air-VNIR image on 23 September 2018. (a) Permanent artificial targets; (b) desert target.
Table 1. Acquisition information of Air-VNIR, SuperView-1, and Sentient-2 images at Baotou calibration site.
2.3 Sentinel-2 and SuperView-1 satellite images
The S2 mission includes two satellites, namely, Sentinel-2A (S2A) and Sentinel-2B (S2B), which were launched on 23 June 2015 and 7 March 2017, respectively. Each satellite is equipped with a multi-spectral instrument (MSI), which can acquire images with a high revisit capability (5 days with two satellites), high resolution (10 m, 20 m, and 60 m), and multispectral imagery (13 spectral bands in the visible, NIR, and short-wavelength infrared domains) [7]. The S2 satellites include an on-board diffuser to monitor radiometric changes in performance throughout the mission duration. The on-board calibration accuracy of the S2 MSI sensor is reported to be better than 5% [7,17]. The VNIR bands have been stable to within 1% since launch, and within 0.1% since April 2016, as reported by Gascon et al. [17]. Therefore, the radiometric stability of the S2 MSI makes it a good reference sensor for cross-calibration of the SuperView-1 on-board sensors. In this study, the bands 2, 3, 4, and 8, with 10 m spatial resolution, were used to cross-calibrate the blue, green, red, and VNIR bands of the SuperView-1 on-board sensors. As listed in Table 1, S2A and S2B data were acquired on 29 and 21 September 2018, and were used to cross-calibrate the SV0101 and SV0103 data acquired on 29 and 20 September 2018. Figure 3(a) shows a subset of RGB composite images of the Baotou calibration site obtained by SV0103 on 20 September. Figure 3(b) shows the subset of RGB composite images of the Baotou calibration site, as obtained by S2B on 21 September. Figure 4 illustrates the relative spectral responses of SuperView-1 and the corresponding S2 MSI bands in the laboratory before launch. It should be pointed out that the S2B MSI and SV0103 images were not acquired on the same day. However, the difference in overpass time of the S2B and SV0103 satellites is within a half an hour, and the values of aerosol optical thickness (AOT) at 550 nm and columnar water vapor (CWV) are very close. In addition, the solar and viewing geometry are very similar, as listed in Table 1.
Fig. 3. Subset of RGB composite images of the Baotou calibration site obtained by (a) SV0103 on 20 September, (b) Sentinel-2B (S2B) on 21 September (the red box indicates the permanent artificial calibration targets, and the orange box indicates the desert target).
Fig. 4. Relative spectral responses of SuperView-1 and the corresponding S2 multi-spectral instrument (MSI) band in the laboratory before launch: (a) Sentinel-2A (S2A) vs. SV0101; (b) S2B vs. SV0103.
2.4 In situ measurements
During the field campaign, the surface reflectance of the permanent black, grey, and white artificial calibration targets and that of the desert target were collected using a field portable spectroradiometer with nadir view, one half-hour before and after the airborne SuperView-1 and S2 satellite overpasses of our calibration site on 20, 21, 23, and 29 September 2018. The reflectance measurement were performed from side-center-center of the artificial target. And, thirty reflectance measurements were carried for each artificial target. Figure 5(a) shows the averaged ground measured surface reflectance corresponding to the black, grey, and white permanent artificial calibration targets and the natural desert target at the Baotou calibration site. Atmospheric datasets including the AOT at 550 nm, CWV, and atmospheric vertical profiles were also collected. An automatic sun tracking photometer was deployed at the Baotou calibration site, and a member of AErosol RObotic NETwork (AERONET) was used to measure the solar irradiance before and after the airborne SuperView-1 and S2 satellite overpasses of the calibration site. The AOT at 440 nm, 670 nm, 870 nm, and 1020 nm channels and CWV data could then be downloaded directly from the AERONET website after processing of the collected data. The linearly-interpolated AOT at 550 nm and the CWV values at the time of overpasses of the calibration site are listed in Table 1. It should be pointed out that the aerosol type used in this study is the default rural type provide by the MODTRAN-5 model instead of user defined based on the retrieved AOT data. In addition, atmospheric vertical profiles including temperature, humidity, and pressure were also collected at every 200 m from ground to a 10 km height with a radiosonde balloon, near the time of the SV0102 and SV0104 satellites overpassing the calibration site on 23 September 2018. Figure 5(b) shows the atmospheric vertical profiles collected on 23 September 2018.
Fig. 5. In situ measurements of surface reflectance and atmospheric vertical profiles. (a) Averaged ground measured reflectance corresponding to the black, grey, and white permanent artificial calibration targets and desert target at Baotou calibration site. (b) The atmospheric vertical profiles collected with radiosonde balloon near the time of SV0102 and SV0104 satellites overpassing the Baotou calibration site on 23 September 2018.
3. Methodology
As is well-known, absolute radiometric calibration enables a relationship for converting the digital numbers (DNs) of the images to radiance images with physical units. Currently, ground natural target with single reflectance characteristic in middle reflectance (e.g. desert) were current widely selected to vicarious radiometrically calibrate the onboard optical sensors. However, it cannot well characterize the radiometric performance over the entire dynamic range of the onboard optical sensors. Therefore, it is preferable to characterize the radiometric performance over the entire dynamic range using multiple ground calibration targets with several reflectance steps (e.g., 0.05, 0.20, 0.30, and 0.50). (e.g., 0.05, 0.20, 0.30, and 0.50). This study introduces a multiple permanent artificial targets-based radiometric calibration approach for high spatial resolution space-borne sensors. The TOA band radiance (${L_{TOA,i}}$) of the space-borne sensors corresponding to the multiple permanent artificial targets are predicted and linearly-fitted using the corresponding DN values observed by the space-borne sensors, as expressed by Eq. (1). Then, the radiometric calibration coefficients of the space-borne sensors can be determined according to Eq. (1).
Here, $Gai{n_i}$ and $Bia{s_i}$ are the radiometric calibration coefficients of the space-borne high spatial resolution sensor at the corresponding i band. According to Eq. (1), the TOA band radiance of the space-borne sensors corresponding to the multiple permanent artificial targets should be predicted first. In this study, three independent methods (namely, reflectance-based, radiance-based, and cross-calibration) were introduced to predict the TOA band radiance.
3.1 Reflectance-based method
The first step of reflectance-based method is to predict the TOA radiance retrieved by the sensors based on the radiative transfer theory. Assuming that the land surface is uniform Lambertian and under a horizontally-homogeneous atmosphere, the TOA radiance can be expressed as Eq. (2) [18]:
Here, ${L_{TOA}}(\lambda )$ is the spectral radiance retrieved by the sensor to be calibrated; ${L_{path}}(\lambda )$ is the path radiance; ${\rho _t}(\lambda )$ is the surface reflectance; ${E_\textrm{s}}(\lambda )$ is the exoatmospheric solar irradiance; $\tau ({\mu _s},\lambda )$ is the total transmittance from the sun to the surface; $\tau ({\mu _v},\lambda )$ is the total transmittance from the surface to the sensor; ${\mu _s}$ and ${\mu _v}$ are the cosine values of the sun and viewing zenith angles, respectively; and $S(\lambda )$ is the atmospheric spherical albedo.
According to Eq. (2), the TOA radiance can be predicted by using a radiative transfer code once the surface reflectance and atmospheric conditions are known. Thus, the reflectance-based method requires an accurate ground-measured reflectance of the calibration target before and after the satellite overpasses the calibration site (within 30 minutes). The reflectance-based method uses the measured reflectance of the calibration target as an input to the radiative transfer code, which calculates the radiance at the top of the atmosphere. The MODerate resolution atmospheric TRANsmission (MODTRAN) 5 code was used in this study, owing to its high accuracy [19]. The other key atmospheric inputs characterizing the molecular scattering and absorption as required by the radiative transfer code are the AOT at 550 nm and CWV, which are always measured by a photometer. Based on the predicted spectral TOA radiance, the TOA band radiance of the Superview-1 sensor can then be calculated by convoluting the spectral TOA radiance with the spectral response function of the corresponding channels, as described by Eq. (3).
In Eq. (3), ${L_{TOA,i}}$ is the TOA radiance in band i; ${R_i}(\lambda )$ is the relative spectral response function of the corresponding bands; ${L_{TOA}}(\lambda )$ is the continuous TOA spectral radiance; and ${\lambda _1}$ and ${\lambda _2}$ are the lower and upper wavelengths of the spectral range in band i, respectively.
3.2 Airborne radiance-based method
The radiance-based method is an improvement upon reflectance-based method, and was proposed to reduce the atmospheric effects on TOA radiance prediction. It uses a well-calibrated radiometer to measure the radiance of a calibration target at approximately the same time and in approximately the same viewing geometry as the sensor to be calibrated [9]. The well-calibrated radiometer usually flies at an altitude above 3 km to maximize atmospheric effects under the plane. Then, the TOA radiance retrieved by the sensor to be calibrated can be calculated after having been corrected for the effects of the atmosphere from the air to the satellite. Therefore, the TOA radiance retrieved by sensor to be calibrated in Eq. (1) can be rewritten as Eq. (4):
Here, ${L_{TOA}}(\lambda )$ is the spectral radiance retrieved by sensor to be calibrated. ${L_{path}}(\lambda )$ is the path radiance. $S(\lambda )$ is the atmospheric spherical albedo. ${L_t}(\lambda )$ is the observed radiance of calibration target by the airborne radiometer. $\tau ({\mu _v},\lambda )$ is the total transmittance from the airborne radiometer to the calibrated sensor. ${\mu _v}$ is the cosine value of the zenith viewing angle. As expressed in Eq. (4), the spectral TOA radiance can be calculated once the radiance of the calibration targets, the path radiance, and the total transmittance in the view direction from the airborne radiometer to the satellite are determined. In this study, the radiance of the calibration targets were measured by a strictly radiometric and spectrally-calibrated spectrometer mounted on a plane, at the time when the satellite payload with the sensors to be calibrated passed over the Baotou calibration site. In addition, the path radiance and total transmittance in the view direction were simulated with the MODTRAN 5 radiative transfer code, using the atmospheric datasets from the Baotou AERONET station. Then, the TOA band radiance of the space-borne sensor could be calculated by convoluting the spectral TOA radiance with the relative spectral response function of the corresponding channels using Eq. (3).
3.3 Cross-calibration method
Cross-calibration is another important alternative method based on a well-calibrated radiometric reference sensor (e.g. Landsat OLI, MODIS, or S2 MSI). Owing to the reliability and low cost of cross-calibration, it has been widely used to calibrate the radiometric performance of sensors in launched Chinese satellites without on-board calibration systems, such as the Beijing-1, Huangjing-1, and GF-series optical sensors [13–16]. In this study, the cross-calibration method is also used to radiometrically calibrate the SuperView-1 sensors with well-calibrated S2 MSI sensor. The band TOA reflectance of the SuperView-1 can be determined from the band TOA reflectance of the well-calibrated S2 MSI and spectral band adjustment factors (SBAFs), according to Eq. (5).
Here, $\rho _{SV,i}^\ast $ is the band TOA reflectance of the SuperView-1. $\rho _{MSI,i}^\ast $ is the band TOA reflectance of the well-calibrated S2 MSI, and can be directly extracted from the level 1C (L1C) product. ${K_{SV - MSI,i}}$ is a SBAF of the TOA reflectance, and is used to compensate for the differences in spectral response and sun-target-sensor geometries between the SuperView-1 and S2 MSI sensors. The SBAF approach has been widely used in on-board satellite sensor cross-calibration [20]. The SBAF of the TOA reflectance between the SuperView-1 and S2 MSI sensors is defined as in Eq. (6).
Here, $\rho _{SV,i}^{sim}$ is the TOA reflectance of the SuperView-1 satellite sensor, as simulated by the MODTRAN 5 transfer radiative code using the ground-measured artificial targets’ reflectance at Baotou calibration site, spectral response of SuperView-1 satellite sensor, AOT, CWV, and sun-target-sensor geometries. $\rho _{MSI,i}^{sim}$ is the TOA reflectance of the S2 MSI sensor as simulated by MODTRAN 5 transfer radiative code with the same inputs, except for the relative spectral response.
Then, the corresponding band TOA reflectance of SuperView-1 satellite sensor (${L_{TOA,i}}$) can be converted to the TOA band radiance using Eq. (7).
Here ${E_{s,i}}$ is the exoatmospheric solar irradiance at 1 AU, ${\theta _s}$ is the solar zenith angle, and d is the earth-sun distance in AU.
4. Results
4.1 Radiometric calibration results with reflectance-based method
According to the description of the reflectance-based method in Section 3.1, the radiometric calibration coefficients of SV0101, SV0102, SV0103, and SV0104 were determined by linearly-fitting the TOA band radiance with averaged DNs corresponding to the three permanent artificial calibration targets, using Eq. (1). Figure 6 shows plots of the TOA band radiance versus the DNs corresponding to the three permanent artificial calibration targets in the blue, green, red, and NIR channels for SV0101, SV0102, SV0103, and SV0104, respectively. The radiometric calibration coefficients (W/m2/sr/µm) of SV0101, SV0102, SV0103, and SV0104 are listed in Table 2. It can be seen from the results that there are similar linear relationships and trends for the NIR bands of SV0101, SV0102, SV0103, and SV0104. The linear relationships and trends for the blue, green, and red channels are also very consistent, except for those of SV0101 sensor. It is interesting to note that the DN values of the SV0101 blue, green, and red channels are apparently smaller than the other three SuperView-1 sensors’ corresponding channels. However, the predicted TOA radiance for the blue, green and red channels are close to each other for all four of the SuperView-1 sensors. The small differences in predicting TOA band radiance between all SuperView-1 sensors may be due to differences in ground measurements of surface reflectance, atmospheric data and the relative spectral response. But the DN value difference seems to be the main reason causing the difference in the linear relationship between the predicted TOA band radiance and the DN values in the blue, green, and red channels of SV0101 as compared to other three SuperView-1 sensors. It may also indicate that the radiometric performance of SV0101 has apparently changed in the blue, green, red, and NIR channels as compared to the corresponding channels of the other three sensors.
Fig. 6. Plots of the simulated top-of-atmosphere (TOA) band radiance with reflectance-based method versus the digital number (DN) values of multiple permanent artificial calibration targets in the blue, green, red, and NIR channels, respectively. (a) SV0101 on 29 September 2018, (b) SV0102 on 23 September 2018, (c) SV0103 on 20 September 2018, (d) SV0104 on 23 September 2018.
Table 2. Determined radiometric calibration coefficients of SV0101, SV0102, SV0103 and SV0104 with reflectance-based method using multiple permanent artificial calibration targets in the Baotou calibration site.
4.2 Radiometric calibration results with radiance-based method
Owing to the high cost of an airborne campaign, we only collected hyperspectral data with the Air-VNIR once, at approximately the same time and viewing geometry as when the SV0102 and SV0104 satellites passed over the Baotou site on 23 September 2018. Therefore, only the SV0102 and SV0104 on-board sensors were radiometrically-calibrated with the radiance-based method. According to the method described in Section 3.2, the total transmittance and path radiance from the airborne height to the satellite flight height when the SV0102 and SV0104 satellites passed over the Baotou site were initially simulated based on the simultaneously-acquired atmospheric parameters and profile. Then, the radiance of the permanent artificial targets were extracted from the hyperspectral images collected by the Air-VNIR. Using the transmittance, path radiance, and airborne radiance, the TOA band radiance of the permanent artificial targets were calculated according to Eq. (4). Then, the TOA band radiance were scattered with the corresponding DNs of the permanent artificial targets extracted from the SV0102 and SV0104 images collected on 23 September 2018, as shown in Fig. 7. The absolute radiometric calibration coefficients (W/m2/sr/µm) of SV0102 and SV0104 were also determined, and are listed in Table 3. It can be found from the results that the linear trends in all four channels are very consistent when comparing these two sensors. The coefficients of determination between the predicted TOA band radiance and the DN values are larger than 0.999, i.e., better than in the reflectance-based method. For each artificial target, the predicted TOA band radiance of SV0102 is close to that of SV0104 in all four channels. The slight gaps in the predicted TOA band radiance and DNs may be caused by the atmosphere, surface characteristics, viewing geometries, or the relative spectral response between SV0102 and SV0104. Overall, the gains and bias between SV0102 and SV0104 are close to each other in all four multispectral channels.
Fig. 7. Plots of the simulated TOA band radiance with radiance-based method versus the DN values of multiple permanent artificial calibration targets in the blue, green, red, and NIR channels, respectively. (a) SV0102 on 23 September 2018, (b) SV0104 23 September 2018.
Table 3. Determined radiometric calibration coefficients of SV0102 and SV0104 with radiance-based method using multiple permanent artificial calibration targets in the Baotou calibration site.
4.3 Radiometric calibration results with cross-calibration method
As described in Section 2.3, the SV0101 data acquired on 29 September 2018 was cross-calibrated with the S2A images acquired on the same day and at approximately the same time. The SV0103 data acquired on 20 September 2018 was cross-calibrated with the S2B MSI image acquired on 21 September 2018. According to the cross-calibration method introduced in Section 3.3, the SBAFs of the TOA reflectance between SuperView-1 and the S2 MSI sensor were initially determined based on the in situ data sets listed in Table 4. Then, the band TOA reflectance of the black, grey, and white artificial targets in the blue, green, red, and NIR channels of the SV0101 and SV0103 were calculated with the TOA reflectance SBAFs. Next, the TOA band reflectance were converted to TOA band radiance, using Eq. (7). Finally, the TOA band radiance of the three permanent artificial targets for each channel of SV0101 and SV0103 were scattered with the corresponding DN values of the same permanent artificial targets, as shown in Fig. 8. Similar to the case with the reflectance-based method, the cross-calibrated TOA band radiance of the three artificial targets for each channel between SV0101 and SV0103 have good agreement. However, the linear trend of the SV0101 channels is different from that of the SV0103 channels, except for the NIR channel. The main reason is that the DN values in the blue, red, and NIR channels of the corresponding three artificial targets as observed by SV0101 are apparently smaller than those as observed by SV0103. Using the linear relationship shown in Fig. 8, the absolute radiometric calibration coefficients (W/m2/sr/µm) of SV0101 and SV0103 were determined with the cross-calibration method, and are listed in Table 5. The coefficients of determination between the predicted TOA band radiance and DN values are also larger than 0.999, i.e., close to the radiance-based method, and better than the reflectance-based method.
Fig. 8. Plots of the simulated TOA band radiance with cross-calibration method versus the DN values of multiple permanent artificial calibration targets in the blue, green, red, and NIR channels, respectively. (a) SV0101 on 29 September 2018, (c) SV0103 on 20 September 2018.
Table 4. Spectral band adjustment factors (SBAFs) of top-of-atmosphere (TOA) reflectance corresponding to the black, grey, and white artificial calibration targets.
Table 5. Determined radiometric calibration coefficients (W/m2/sr/µm) of SV0101 and SV0103 with cross-calibration method using multiple permanent artificial calibration targets in the Baotou calibration site.
4.4 Comparison of radiometric calibration results with independent methods
To validate the reliability of the calibration results, the DN values for the desert site, extracted from SV0102 and SV0104, were converted to TOA band radiance using the calibration coefficients determined independently with reflectance-based and radiance-based methods. Figure 9 compares the calibrated desert TOA band radiance in all four multi-spectral channels of SV0102 and SV0104 with coefficients determined from the reflectance-based and radiance-based methods. The error bars are the uncertainties discussed in Section 5. Overall, the TOA band radiance for the desert site using the calibration coefficients computed with the reflectance-based method in the four channels are quite consistent with those from the radiance-based method for both SV0102 and SV0104. However, the TOA band radiance for the desert site using the calibration coefficients computed with the reflectance-based method are slightly lower than those from the radiance-based method for both SV0102 and SV0104, in all four multi-spectral channels. Unfortunately, the explanation for the appearance is not known for the moment. As an improvement upon the reflectance-based method, the radiance-based method only needs to correct the atmospheric effects between the airborne radiometer and the spaceborne sensor, which can reduce the errors in the aerosol-type assumption [21]. The relative differences between these two methods were also calculated, as shown in Fig. 9. The relative difference is 1.26%, 3.20%, 2.31%, and 1.41% respect to the blue, green, red, and NIR channels of SV0102, respectively. In contrast, the relative difference is 2.29%, 4.23%, 3.34%, and 2.42% in the blue, green, red, and NIR channels of SV0104, respectively. The results also indicate that the calibrated coefficients of SV0102 and SV0104 are reliable, after comparing the results with the two independent methods.
Fig. 9. Comparison as well as relative difference of the desert TOA band radiance between reflectance-based and radiance-based method in the blue, green, red, and NIR channels of the (a) SV0102 and (b) SV0104 on 23 September 2018, respectively.
Similarly, the absolute radiometric calibration coefficients were used to convert the desert DN values extracted from SV0101 and SV0103 to TOA band radiance, which were compared with the results based on the cross-calibration method. Figure 10 shows a comparison of the desert TOA band radiance calculated with the absolute radiometric calibration coefficients by the reflectance-based and cross-calibration methods in the blue, green, red, and NIR channels of the SV0101 and SV0103, respectively. The error bars are the uncertainties discussed in Section 5. In contrast to the comparison results between the reflectance-based and radiance-based methods for SV0102 and SV0104, the results of the reflectance-based method are slightly higher than those of the cross-calibrated method, especially in the green and red channels, for both SV0101 and SV0103. Explanation on larger error for SV0103 may be due to larger AOT and date difference. The relative differences in the blue, green, red, and NIR channels of SV0101 between these two methods are 1.69%, 5.93%, 6.83%, and 3.18%, respectively. While, the relative differences in the blue, green, red, and NIR channels of SV0103 between these two methods are 1.42%, 4.93%, 5.81%, and 0.82%, respectively. Generally, the relative differences of the SV0101 between the reflectance-based and cross-calibration methods are larger than those of the corresponding channels of SV0103, which may be due to the relative spectral response and/or an acquisition geometry difference. However, the trends of the relative differences in all four channels of SV0101 and SV0103 are very similar. Therefore, two conclusions can be drawn according to the results. Firstly, the determined absolute radiometric calibration coefficients for both SV0101 and SV0103 are relatively reliable, as the largest relative difference is less than 7% between the two compared independent methods. Secondly, the on-orbit radiometric performances of SV0101 and SV0103 have similar changes in all four channels after being launched.
Fig. 10. Comparison as well as relative difference of the desert band TOA radiance between reflectance-based and cross-calibration method in the blue, green, red, and NIR channels of the (a) SV0101 and (b) SV0103, respectively.
5. Uncertainty analysis
Theoretically, the TOA band radiance used to determine the radiometric calibration should be the same or at least approximately equal when predicted with different methods. However, it is inevitable that various uncertainty errors in the data collection and processing, and those inherent in the selected calibration method, may consequently affect the final vicarious radiometric calibration accuracy. A combination of different and independent methods for TOA band radiance prediction not only provides a comprehensive way to characterize the radiometric performance of on-board sensors, but also allows for the detection of possible systematic errors in any of the methods [22,23]. Therefore, it is crucial to analyse the various uncertainty sources of the different methods, which may be reflected in the final radiometric calibration coefficients. In this study, the relative difference of simulated TOA radiance between with and without error is defined as the uncertainty for each uncertainty source.
5.1 Uncertainty analysis of the reflectance-based method
As to the uncertainty of the predicted TOA radiance with the reflectance-based method, six uncertainty sources were analyzed in this study: the ground reflectance measurement, bidirectional reflectance distribution function (BRDF) characteristics, aerosol type, AOT at 550 nm, CWV, and MODTRAN 5 radiative transfer code. The uncertainty for the reference panel is was estimated to be approximately 0.25% over the VNIR spectral range due to the directional (8°)-hemispheric reflectance of the reference panel, according to a panel report by the Labsphere Company. In natural conditions, the reference panel is not perfectly Lambertian. Therefore, the uncertainty of the reference panel’s directional-directional reflectance should be considered technically. However, it was ignored in this study due to relevant report on the bidirectional effect were not officially provided by the Labsphere Company. In addition, the radiance of the reference panel were measured by a spectroradiometer in nadir view and the bidirectional effect of the reference panel can be reduced to minimum to some extent. Measurement error in the field campaign may affect the surface reflectance and was estimated as 1%, and other error sources, including variations on environmental temperature, wind, other factors, and transportation effects were estimated as 1% by referring to previously-reported studies [21–25]. Therefore, the combined error of the surface reflectance is a quadratic sum with approximately 1.45%, which contributes to the uncertainty of the TOA radiance simulation with the MODTRAN 5 radiative code by less than 2.5% over all of the VNIR channels for SuperView-1, as listed in Table 6. The view zenith angles of the SuperView-1 satellites were basically less than 10 degrees, as listed in Table 1. However, we do not consider the BRDF effects of the artificial calibration targets during the radiometric calibration in this study. The BRDF effects of the artificial targets were analyzed with a Ross-Li model [26,27]. The results suggest that the uncertainty of the TOA radiance as simulated by the MODTRAN 5 radiative transfer code was estimated to be less than 1.5% over all of the VNIR channels for SV0101 and SV0102, with a view zenith angle of approximately 6 degrees. In contrast, the uncertainty of the simulated TOA radiance of SV0103 and SV0104 was estimated to be less than 2.75%, with a view zenith angle of approximately 10 degrees.
Table 6. Errors sources and uncertainties in simulated TOA radiance of reflectance-based method.
Atmospheric characterization is another primary error source in the reflectance-based method, especially the error contribution owing to choice of the complex index of refraction of the aerosols and the determination of the size distribution of the aerosol particles [21]. Therefore, it very important to determine the aerosol type during the vicarious calibration campaigns. However, it is hard to estimate the aerosol properties used to characterize the aerosol type in a field experiment. In our study, we chose a standard rural aerosol type of in the MODTRAN 5 radiative transfer code, which may not well-characterize the real aerosol type. These differences in inappropriately-chosen aerosol types may result in systematic uncertainties in the calibration results, as reported by a previous study [13]. Thus, the desert aerosol type was chosen to replace the rural aerosol type used in this study, and the MODTRAN5 radiative transfer code was run again to approximate the errors contributed to the TOA radiance from the inappropriately-chosen aerosol type. Table 6 lists the relative differences due to the inappropriately-chosen aerosol type for SV0101, SV0102, SV0103, and SV0104, respectively. It can be seen that the relative differences in the TOA radiance for SV0101, SV0102, and SV0104 are very similar, owing to the very low AOT at 550 nm, meaning that the reflectance-based method is insensitive to the aerosol type for very low AOT at 550 nm values, i.e., less than 0.1. However, there is an evident relative difference in the simulated TOA radiance of SV0103 owing to the inappropriately-chosen aerosol type, which is mainly caused by the relative high value of AOT at 550 nm at approximately 0.2. The results suggest that the aerosol type should be selected carefully or determined with accurate aerosol properties when AOT at 550 nm is at 0.2 or higher. As to the uncertainty in the AOT at 550 nm and CWV retrieval, as reported by AERONET [28], they would result in uncertainties of TOA radiance generally less than 0.5% and 0.4%, respectively, as listed in Table 6. In addition, the uncertainty of the MODTRAN 5 radiative transfer code is ±2% in radiance simulation [19].
We assumed that all of the analyzed uncertainty sources above are independent [24]. Then, a root sum square approach was used to calculate the overall uncertainty in the TOA radiance in the reflectance-based method, as listed in Table 6. Generally, the overall uncertainty in the TOA radiance in the reflectance-based method is less than 4.5% for all of the SuperView-1 satellites. The uncertainty values of the TOA radiance for SV0103 and SV0104 are slightly larger than those of SV0101 and SV0102, primarily owing to the errors from the chosen aerosol type and BRDF effect.
5.2 Uncertainty analysis of the radiance-based method
There are several uncertainty sources for the radiance-based method, including the hyperspectrometer radiometric calibration, measurement errors during the flying campaign, and atmospheric corrections from the altitude of the airplane to the TOA. The hyperspectrometer radiometric calibration in the laboratory causes the largest error in the radiance-based method. The hyperspectrometer used in this study was calibrated against a radiance source consisting of a lamp-illuminated diffuse reflectance panel. Therefore, there are uncertainties associated with the lamp-diffuser panel radiance source, the uniformity of the source, hyperspectrometer nonlinearity, hyperspectrometer noise during calibration, and so on. The total uncertainty of the hyperspectrometer radiometric calibration in the laboratory is estimated to be less than 2%, according to the report of the hyperspectrometer designer from the SITP of CAS.
With regard to the measurement errors during the flying campaign, they may be associated with the data logger, radiometer stability, and the view angle difference between the hyperspectrometer and SuperView-1. The contribution of error from radiometer stability to the TOA radiance uncertainty is mainly due to temperature drift and vibration during the airplane flying, and is estimated to be less than 1% according to the report from the SITP of CAS. However, the error from the data logger is not given by the SITP of CAS. Therefore, we merely estimated the contribution error from the data logger to the TOA radiance uncertainty as less than 0.5, by referring to the error estimation by Biggar [21]. As to the view angle difference between the hyperspectrometer and SuperView-1, the hyperspectral data was collected by the hyperspectrometer at its nadir, as it is very difficult to maintain the same viewing geometry as the SuperView-1 on-board sensors. Simulation with MODTRAN 5 radiative transfer code suggests that the maximum error in radiance is less than 0.35%, owing to a 6.34 degree viewing angle difference between the hyperspectrometer and SV0102. The maximum error in radiance is less than 0.65%, owing to the 9.55 degree viewing angle difference between the hyperspectrometer and SV0104. Based on a root sum of squares approach, the total errors of airborne hyperspectral data measurement owing to the data logger, radiometer stability, and view angle difference are estimated to be less than 1.17% and 1.29% for SV0102 and SV0104, respectively. The measurement error for uncertainty in the TOA radiance of SV0102 and SV0104 was estimated to be generally less than 2%, as listed in Table 7.
Table 7. Errors sources and uncertainties in simulated TOA radiance of radiance-based method.
The final source of uncertainty in the radiance-based method is the atmospheric effects from the altitude of the airplane to the TOA. The atmospheric effects mainly influence the simulated total atmospheric transmittance from the altitude of the airplane to the TOA with the MODTRAN 5 radiative transfer code. Therefore, three error sources in atmospheric effects associated with aerosol type, AOT at 550 nm, and CWV were considered and analyzed. We first used a MODTRAN 5 code to simulate the total atmospheric transmittance of the path from the airplane altitude to the SuperView-1 satellite altitude, with and without atmospheric effects. Then, the TOA radiance were calculated with and without atmospheric effects. Finally, the relative differences owing to the atmospheric effects were estimated, and are listed in Table 7. The uncertainty in TOA radiance owing to the uncertainty of aerosol type and CWV is very small, i.e., less than 0.1% for SV0102 and SV0104, respectively. Moreover, the maximum uncertainty in radiance caused by the AOT at 550 nm uncertainty is less than 1% for both SV0102 and SV0104. Two reasons could explain the low uncertainty in radiance owing to atmospheric effects. First, only the atmospheric effects of the path from the airplane to satellite altitude should be corrected, which may, to some extent, reduce the uncertainty in the estimation of atmospheric properties. Second, the spectral response range of the SuperView-1 satellites’ on-board sensors is designed at the atmospheric windows, which can reduce the atmospheric effects, especially insofar as water vapor absorption.
The overall uncertainty of the predicted TOA radiance with the radiance-based method is calculated with the root sum square of the considered uncertainty sources, and the results are listed in Table 7. It can be seen from Table 7 that the maximum overall uncertainty is less than 4% for both SV0102 and SV0104. It interesting to find that the total uncertainty in the TOA radiance of the radiance-based method for SV0102 is slightly larger than that from the reflectance-based method, mainly owing to error in the hyperspectrometer radiometric calibration. In contrast, the total uncertainty in the TOA radiance of the radiance-based method for SV0104 is less than that from the reflectance-based method, which could be explained from the BRDF effects of the permanent artificial targets’ surface reflectance for the nearly 10 degree viewing angle of the SV0104.
5.3 Uncertainty analysis of the cross-calibration method
The accuracy of the cross-calibration method may be influenced by several uncertainty sources associated with spatial mismatch, the calibration accuracy of the reference sensor, SBAFs’ uncertainty, and so on [13,14,20,29]. The uncertainty error from spatial mismatch is not considered in our study, as the regions of interest (ROIs) for the permanent artificial targets can be selected accurately from the S2 and SuperView-1 images, based on the apparent ground features of the permanent artificial targets. Moreover, the calibration accuracy of the S2 reference sensor is reported to be better than 5% [7,17]. Therefore, we primarily focus on the uncertainty in TOA radiance owing to the SBAF uncertainty, which is usually caused by the ground measured reflectance, BRDF effect, and atmospheric parameters [30].
In this study, we used the ground-measured reflectance spectrum of the permanent artificial calibration targets to calculate the SBAFs. The uncertainty of the ground-measured reflectance is estimated to be approximately 1.45% as discussed in Section 5.1, which brings an uncertainty in the TOA radiance of less than 0.1% for both SV0101 and SV0103. The BRDF effect on the permanent artificial calibration targets is not considered in the SBAFs calculation. The averaged relative difference of the surface reflectance between the view zenith and nadir angle is less than 1.5% when the view zenith angle of the SuperView-1 satellites is within 10 degrees, as discussed in Section 5.1. Therefore, considering the error of the permanent artificial calibration targets’ BRDF effect, the averaged uncertainty on the TOA radiance is less than 1% over all of the VNIR channels for SV0101 and SV0103, as listed in Table 8. Atmospheric parameters are a primary error source in the SBAFs calculation, and may lead to further error in the TOA radiance prediction. Therefore, the uncertainty in TOA radiance caused by the aerosol type, AOT at 550 nm, and CWV errors are discussed here. The relative difference of the TOA radiance is calculated between the cases of rural and desert aerosol types. As listed in Table 8, the relative difference in the TOA radiance for SV0101 is approximately zero, whereas the relative difference in the TOA radiance for SV0103 is approximately 1%. It may be concluded that an inappropriate aerosol type selection can lead an evident uncertainty in the TOA radiance of the cross-calibration method when the AOT at 550 nm value is 0.2 or higher. The uncertainty in the TOA radiance in the cross-calibration method owing to the AOT at 550 nm and CWV retrieval errors, as reported by AERONET, are also calculated to be approximately zero, meaning that the influence of these two atmospheric properties on the TOA radiance prediction of cross-calibration method are very small and can be neglected.
Table 8. Errors sources and uncertainties in simulated TOA radiance of cross-calibration method.
Considering the above-discussed uncertainty sources associated with the calibration accuracy of the reference S2 and the uncertainty in the SBAFs, the overall uncertainty in the TOA radiance for the cross-calibration method for SV0101 and SV0103 was estimated using the root sum of squares of the uncertainties from each individual source, and the results are listed in Table 8. It can be seen that the maximum overall uncertainty is less than 5.15% for both SV0101 and SV0103, over all of the channels. Moreover, the uncertainty of the reference S2 is the main contribution to the overall uncertainty in the TOA radiance of the cross-calibration method.
6. Validation analysis
To further validate the reliability of the radiometric calibration results, the DN values of two land types (green vegetation and dry grass) were extracted from SuperView-1 images, and were radiometrically calibrated to radiance values using the radiometric calibration coefficients. It should be pointed out that the radiometric calibration coefficients that determined with independent methods were averaged as the final radiometric calibration coefficients of the SuperView-1 satellite sensors. Then, the surface reflectance values of the two land types were retrieved from the radiance with a radiative transfer equation, and were compared with a ground-measured surface reflectance with a SVC HR1024 spectrometer. Figure 11 shows a comparison between the measured and retrieved surface reflectance of the green vegetation and dry grass based on radiometrically calibrated radiance in the blue, green, red, and NIR channels of the SuperView-1 satellites, respectively. The relative differences between the measured and retrieved surface reflectance of the green vegetation and dry grass in the blue, green, red, and NIR channels of the SuperView-1 satellite sensors were also calculated, and are listed in Table 9.
Fig. 11. Comparison between measured and retrieved surface reflectance of the green vegetation and dry grass based on radiometrically calibrated radiance in the blue, green, red, and NIR channels of the (a) SV0101, (b) SV0102, (c) SV0103, and (d) SV0104, respectively.
Table 9. Relative differences between measured and retrieved surface reflectance of the green vegetation and dry grass based on radiometrically calibrated radiance in the blue, green, red, and NIR channels of the SuperView-1 satellites.
It can be seen from Fig. 11 that the retrieved surface reflectance of the green vegetation has a good consistency with the measured results for all of the SuperView-1 satellite sensors. Larger relative differences occur in the blue and red channels for the results due to the extremely low reflectance in these two channels, which results in a large calculated relative difference even though little absolute bias occurs between the retrieved and measured results. With regard to the comparison between the measured and retrieved surface reflectance of dry grass, the retrieved reflectance based on the radiometrically calibrated radiance show a similar trend to the measured results. Larger relative differences can be found in all four channels of SV0103. The main reason is that there was a failure to measure surface reflectance of the dry grass during our field campaign when the SV0103 overpassed the Baotou calibration site on 20 September 2018, and the surface reflectance measured on 23 September was used to validate the retrieved results instead. Other reasons (e.g. BRDF effect) when retrieval the surface reflectance of the green vegetation and dry grass may also cause the error. The validation analysis results suggest that the radiometrically calibrated coefficients calculated with independent methods in this study can used for further quantitative application.
7. Conclusions
In this study, on-orbit vicarious radiometric calibration of the high spatial resolution satellite optical sensor based on multiple ground permanent artificial calibration targets using three independent methods was introduced and applied to determine the on-orbit radiometric calibration coefficients of Chinese civilian remote sensing satellite SuperView-1 based on the collected datasets during the field campaigned on September 2018 at Baotou calibration site in China. With determined radiometric calibration coefficients using independent methods, the SuperView-1 on-board optical sensors collected images were radiometric calibrated. And then, the radiometric calibrated desert TOA radiance with different methods were compared. Comparison results show that the minimum and maximum relative differences of the radiometrically-calibrated desert TOA radiance between the reflectance-based and radiance-based methods are 1.26% and 4.23% for SV0102 and SV0104, respectively. The minimum and maximum relative differences of the radiometrically-calibrated desert TOA radiance between the reflectance-based and radiance-based methods are 0.82% and 6.83% for SV0101 and SV0103, respectively. The reasonably good agreement of the radiometrically-calibrated coefficients of the SuperView-1 on-board sensors between these independent methods is encouraging. An uncertainty analysis of the three independent methods was also provided in this study. The results suggest that the overall uncertainties of the predicted TOA radiance are less than 4.5%, 4.0%, and 5.15% for the reflectance-based, radiance-based, and cross-calibration methods, respectively. The results further indicate that reflectance-based, radiance-based, and cross-calibration methods inevitably bring inherent uncertainties. By using different and independent vicarious calibration methods for a given sensor, we may identify, remove, or account for such errors in the calibration results. The validation analysis results also suggest that the radiometrically calibrated coefficients calculated with independent methods in this study can used for further quantitative application.
Future work should be directed to the long-term ground observation of the permanent artificial calibration targets’ reflectance, the directional reflectance, and the atmospheric conditions at the Baotou calibration site. The BRDF model of the multiple permanent artificial calibration targets and aerosol type of the Baotou calibration site can then be determined more accurately. In addition, long-term monitoring of the radiometric performance of the high spatial resolution satellite on-board sensors based on these datasets should be conducted continuously, and is especially important for detecting changes in the long-term high spatial resolution remote sensing images.
Funding
National Natural Science Foundation of China (41601398); National Key Research and Development Program of China (2016YFB0500400, 2018YFB0504804); Bureau of International Cooperation, Chinese Academy of Sciences (181811KYSB20160040).
Acknowledgments
The authors would like to appreciate the editor and anonymous reviewers for their constructive comments and suggestions on this study.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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