Cross-calibration method based on an automated observation site

Dong Huang; Dong Huang; Dong Huang; Xin Li; Xin Li; Xiaobing Zheng; Xiaobing Zheng; Wei Wei; Wei Wei; Fuxiang Guo; Fuxiang Guo; Fuxiang Guo; Quan Zhang; Quan Zhang

doi:10.1364/OE.481861

1. Introduction

After a satellite sensor is launched, changes in its characteristics and in the surrounding environment cause the sensor to age, reduce its sensitivity, and seriously affect its radiometric performance. To meet the quantitative requirements of satellite data and the sensor observation consistency requirements during monitoring, continuous and precise remote-sensor calibrations are required [1–4].

For different optical remote sensors, different on-orbit satellite radiometric calibration methods have been developed successively to meet the needs of different applications. These methods mainly include prelaunch calibration, onboard calibration, and vicarious calibration methods [5–12].

Vicarious calibration methods independently evaluate the accuracy of satellite remote sensing data and have been widely used in recent decades. At the same time, the instruments and equipment used in these methods can be traced back to SI, thus providing a bridge for measurement standards and remote sensor observations [12]. The traditional vicarious calibration method requires the simultaneous manual measurement of surface reflectance and atmospheric data during the satellite transit time, and personnel and cost requirements of these measurements limit the frequency of in situ tests. In addition, different personnel operations and instrument measurements may introduce some uncertainties [13]. To overcome these difficulties, the Committee on Earth Observation Satellites (CEOS) Working Group on Calibration & Validation (WGCV) launched an Automated Radiative Calibration Network (RadCalNet) [14]. Creating standard automated observation sites and network of unified processing technologies have become trends; RadCalNet deployed automated observation sites located in the United States, France, Namibia, and Baotou, China [14–16], and the National Satellite Meteorological Center of China, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences and other institutes have carried out automated calibration research and verification work since 2014 [17]. In 2017, an automated vicarious calibration system (AVCS) was established at the Dunhuang radiometric calibration test site; this system includes an automated test-site radiometer (ATR) and an automated precision solar radiometer (PSR) for automated remote-sensor calibration and in-orbit performance monitoring [18]. These networks can continuously provide data such as surface reflectance data, atmospheric parameters. The establishment of these networks has improved the evaluation frequency of the radiation measurement accuracies of remote sensors. At the same time, automatic measurements of the same instrument and the processing of the same standards can prevent uncertainties arising due to different factors [14,19], but some shortcomings remain. The long-term deployment of various field-observation instruments cannot be maintained in a timely manner, and the calibration of these instruments also leads to deviations in the accuracy of the observed data. In addition, fixed empirical models, such as aerosol models and atmospheric models, are generally used when a station's unified processing technology necessitates radiative transfer models for calculation, and this further affects the calibration accuracy, especially in the water-vapor-absorption band. Jing et al. evaluated the reliability of RadCalNet top-of-atmosphere (TOA) reflectance data at specific sites using TOA reflectance data from different satellite sensors. The average relative differences between the RadCalNet-predicted and sensor-measured TOA reflectances were basically within 5%. However, the TOA reflectance differences between RadCalNet data and sensor data in the water band were large, and the relative difference in the individual results could even exceed 40% [20].

Cross-calibration is a more indirect vicarious calibration method [21]. Cross-calibration is a calibration process in which a calibrated and high-precision reference remote sensor is used to calibrate the target remote sensor [21]. Cross-calibration has the advantages of easy implementation and low cost. At the same time, the two considered sensors can be bound on the same radiation scale to achieve a consistent radiation evaluation of the two satellite sensors and to ensure interoperability between the sensor data [21–23]. The basic idea of classical cross-calibration is to select the target remote sensor and the reference remote sensor to observe images under the same or similar conditions, establish the matching relationship between bands according to the band spectral response, and compare the observation values of the reference sensor and target sensor [24]. The same or similar observation conditions of the reference sensor and the target sensor are generally obtained by synchronous or near-synchronous observation of ground targets such as pseudo-invariant calibration sites (PICS) and extraterrestrial reference targets such as the Moon [25,26]. Pseudo-invariant calibration sites are places where the Earth’s surface has relatively stable temporal, spatial and spectral radiation performances; PICS, such as Libya 4 and Algeria 3, are often used as cross-calibration observation targets [21,26]. There are strict restrictions on the observation time, spatial extent, observation geometry, spectrum, etc., of the two satellite sensors during cross-calibration, thus greatly reducing the cross-calibration opportunities [21,23]. For example, Farhad used Libya 4 as the observation target to perform cross-calibration (30-min separation) on the Landsat 8 Operational Land Imager (OLI) and Sentinel 2A MultiSpectral Instrument (MSI). From 2015 to 2018, eight pairs of fine weather data were matched [27]. Twin satellite sensors are mutually complementary in observing the Earth, such as Aqua/Terra Moderate Resolution Imaging Spectroradiometer (MODIS) [28] and Sentinel-2A/Sentinel-2B MSI [29]; Terra and Aqua are morning and afternoon satellites, respectively, and Sentinel-2A and Sentinel-2B are high-resolution polar-orbiting satellites in the same orbit with a phase of 180° to each other. Because of the orbit and phase difference, synchronous observations of such satellite sensors are very limited, and cross-calibrations are thus more difficult [30,31]. In addition, due to the lack of real-time surface and atmospheric data, there is little research on the cross-calibration of water-vapor-observation bands, which are sensitive to atmospheric changes. Recently, Angal et al. combined RadCalNet observation data and Aqua/Terra MODIS near-nadir overpass observation data collected on the same day to achieve cross-calibration and an observation consistency evaluation of the first seven bands of Terra MODIS and Aqua MODIS using double-difference technology and achieved good results; however, the authors did not cross-calibrate the water-vapor-observation bands. In addition, the cross-matching angle was limited to the near-nadir observations taken on the same day, and the crossing frequency was low [32].

In this paper, by combining the advantages of AVCS and cross-calibration, an AVCS-based cross-calibration method is proposed. Through AVCS real-time continuous observation data and bidirectional reflectance distribution function (BRDF) model angle correction processes, the observation-condition differences between two satellite remote sensors are matched in a relatively wide time range, thus improving the cross-calibration frequency and realizing cross-calibrations of different sensors as well as observation consistency evaluations. By combining the continuous observation data of AVCS from 2018 to 2022, the proposed method is used to conduct cross-calibrations between Aqua/Terra MODIS and Sentinel-2A/Sentinel-2B MSI and to analyze the impacts of parameters such as the surface reflectance, water vapor content, and aerosol optical depth observed by AVCS on the cross-calibration results.

2. Calibration site and datasets

2.1 Dunhuang test site

The Dunhuang test site (40.14°N, 94.32°E) is an important member of the China Radiometric Calibration Sites (CRCS) and is located approximately 35 km west of Dunhuang city, Gansu Province, China. The Dunhuang test site is approximately 60 km long from east to west and approximately 40 km long from north to south. The average elevation is approximately 1250 m. The landform types at the Dunhuang test site include the Danghe alluvial fan Gobi. As shown in Fig. 1, the land surface is flat and uniform, with no vegetation coverage on the site surface, and the region belongs to a dry continental climate and is surrounded by the Gobi desert, with stable spectral characteristics, a dry atmosphere, many sunny days, and low aerosol influence [33,34]. The Dunhuang test site has been successfully used for the absolute radiation calibration of many Chinese satellites, such as HJ-series satellites, FY-series satellites, and GF-series satellites, since the 1990s [35–37].

2.2 Datasets

2.2.1 Automated vicarious calibration system (AVCS)

The AVCS of the Dunhuang test site includes a channel-type ground radiometer (Automated Test-site Radiometer, ATR), an automatic solar photometer (Automated Precision Solar Radiometer, PSR) and a hyperspectral irradiance (Automated Hyperspectral Irradiance Meter, HIM), as shown in Fig. 2. All three instruments are deployed at the Dunhuang test site for long-term observation and record continuous and stable data. These observation data are sent to the data-processing center through the Beidou and 4 G remote communication modules.

Fig. 1. Location and characteristics of the Dunhuang test site from the (a) 2019-10-6 operational land imager (OLI) image of the Dunhuang test site and (b) a site view of the Dunhuang test site.

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Fig. 2. Structure diagram of the AVCS.

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The ATR instrument covers 8 channels from visible light to shortwave infrared (SWIR), with band settings of 400 nm, 450 nm, 500 nm, 600 nm, 675 nm, 810 nm, 1000 nm, and 1550 nm. This instrument uses silicon and indium gallium arsenide detectors. The ATR optical head collects radiance data every 3 minutes with a 10° field of view on a fixed frame for measuring band surface reflectance. Based on the measured band surface reflectance, the reference reflectance in the surface reflectance library of Dunhuang test site was scaled and adjusted to obtain the hyperspectral surface reflectance within the wavelength range of 350 nm-2500 nm [16–18,38,39]. The PSR instrument covers 9 channels from the visible light to the near-infrared (NIR) spectrum, and each channel is observed independently. The PSR automatically tracks solar observations and simultaneously measures the surface temperature, humidity, pressure and other environmental parameters, which are then used to calculate the aerosol optical depth (AOD), atmospheric water vapor content and other atmospheric parameters [40,41]. The observation period is 3 min. The HIM instrument is arranged on the roof of the observation base of the Dunhuang test site. By driving the small ball on the four-bar linkage to block the direct sunlight from entering the integrating sphere glass cover, this instrument can automatically obtain real-time downlink total irradiance, direct irradiance, diffuse-to-total ratio and other atmospheric parameters, measuring these data once every 6 min [18,42,43]. The PSR, ATR, and HIM instruments all carry out precise temperature control.

2.2.2 Sensor data

Aqua/Terra MODIS images are MODIS LAADS public data, labeled as grade-1 MYD021KM and MOD021KM, respectively, and stored in HDF format with a spatial resolution of 1 km. A total of 9 pixels (3 km × 3 km) around the central point of the Dunhuang test site (40.14° N, 94.32° E) were taken to extract the DN value. The images of Aqua/Terra MODIS from August 2018 to May 2022 were selected. For the obtained DN value, excessive outliers such as saturation values are removed, and the average value is taken as the DN value of the target area. Sentinel-2A/Sentinel-2B MSI images are ESA public data, labeled as L1C JPEG2000 files, and the spatial resolution of these images varies from 10 m or 20 m to 60 m according to the different wavebands. The images of Sentinel-2A/Sentinel-2B MSI from August 2018 to October 2021 were selected. Similarly, the DN value of the 3km × 3 km area around the central point of the Dunhuang test site is taken, and the abnormal points with excessive values are removed and averaged. The spectral band setting specifications of the satellite sensors used in this paper are shown in Table 1; B17-19 of the Aqua/Terra MODIS constitute the water-vapor-observation band, and B9 of Sentinel-2A/Sentinel-2B MSI is the water-vapor-observation band; thus, water vapor absorption is relatively strong in these bands.

Table 1. Spectral band characteristics of the sensors^a

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3. Methodology

3.1 Cross-calibration method based on the AVCS

The top-of-atmosphere (TOA) reflectance observed synchronously by the satellite sensor and AVCS can be expressed as follows:

(1)$$TO{A_{\rho \textrm{sat}}} = c \cdot TO{A_{\rho AVCS}}$$

where $TO{A_{\rho \textrm{sat}}}$ is the TOA reflectance measured by the satellite sensors, $TO{A_{\rho AVCS}}$ is the band-predicted TOA reflectance for the AVCS, and c is a correction factor, ideally equal to 1. Furthermore, we can obtain the following expressions:

(2)$$TO{A_{\rho \textrm{sat1}}} = {c_1} \cdot TO{A_{\rho AVCS1}}$$

(3)$$TO{A_{\rho \textrm{sat2}}} = {c_2} \cdot TO{A_{\rho AVCS2}}$$

(4)$$TO{A_{\rho \textrm{sat1}}} = TO{A_{\rho \textrm{sat2}}} \cdot \frac{{TO{A_{\rho AVCS1}}}}{{TO{A_{\rho AVCS2}}}} \cdot \frac{{{c_1}}}{{{c_2}}}$$

where $TO{A_{\rho AVCS1}}$ and $TO{A_{\rho AVCS2}}$ are the band TOA reflectance of the target satellite sensors predicted by the AVCS and the band TOA reflectance of the reference satellite sensors predicted by the AVCS, respectively, $TO{A_{\rho sat2}}$ is the band TOA reflectance measured by the reference satellite sensors, $TO{A_{\rho sat1}}$ is the band TOA reflectance of the target satellite sensors predicted by cross-calibration, and $TO{A_{\rho AVCS1}}$ and $TO{A_{\rho AVCS2}}$ are obtained from the same system observation; the observation relationship between these two terms is stable under similar conditions. The ratio of ${c_1}$ and ${c_2}$ is approximately equal to 1:

(5)$$TO{A_{\rho \textrm{sat1}}} = TO{A_{\rho \textrm{sat2}}} \cdot k$$

where k is the cross factor and $k = TO{A_{\rho AVCS1}}/TO{A_{\rho AVCS2}}$.

A flow chart of the cross-calibration method designed based on the AVCS is shown in Fig. 3. The transit-image data of the two satellite sensors are extracted. In fine weather, the BRDF model, the second simulation of a satellite signal in the solar spectrum – vector (6SV) model [44] and AVCS observation data such as surface reflectance, 550-nm AOD, atmospheric water vapor content and other parameters, are used to calculate the predicted TOA reflectance of reference satellite sensor and target satellite sensor during transit using the automated vicarious calibration method [7,17,18,40–42]. Since the surface reflectance measured by AVCS is a vertical observation, the surface bidirectional reflectance distribution function (BRDF) should be used to correct the surface reflectance to the satellite sensor observation direction:

(6)$${R_M}({{\theta_v},{\theta_s},\varphi } )= {f_{iso}} + {f_{geo}}{k_{geo}}({{\theta_v},{\theta_s},\varphi } )+ {f_{vol}}{k_{vol}}({{\theta_v},{\theta_s},\varphi } )$$

(7)$${\rho _v}({{\theta_v},{\theta_s},\varphi } )= \frac{{{R_M}({{\theta_v},{\theta_s},\varphi } )}}{{{R_M}({0,{\theta_s},0} )}} \cdot {\rho _{AVCS}}$$

where $\varphi = {\varphi _v} - {\varphi _s}$, ${\theta _v}$, ${\varphi _v}$, ${\theta _s}$, and ${\varphi _s}$ are the viewing zenith angle, viewing azimuth angle, solar zenith angle and solar azimuth angle, respectively, ${f_{iso}}$, ${f_{geo}}$, and ${f_{vol}}$ are the weights occupied by the three kernels, ${k_{geo}}$ is the geometric optics kernel, ${k_{vol}}$ is the volume scattering kernel, ${\rho _{AVCS}}$ is the vertical surface reflectance measured by AVCS, and ${\rho _v}({{\theta_v},{\theta_s},\varphi } )$ is the surface reflectance in the satellite sensor observation direction after BRDF correction. The BRDF model parameters were calculated by the AVCS team in the previous site survey [45,46]. $TO{A_{\rho AVCS}}$ is calculated as follows:

(8)$$TO{A_{\rho AVCS}} = \frac{{\smallint TO{A_{{\rho _v}}}(\lambda )T(\lambda )d\lambda }}{{\smallint T(\lambda )d\lambda }}$$

where $TO{A_{\rho AVCS}}$ is the band TOA reflectance of the satellite sensors predicted by the AVCS, $TO{A_{{\rho _v}}}(\lambda )$ is the hyperspectral TOA reflectance predicted by the AVCS during satellite transit within the wavelength range of 350 nm-2500 nm, and $T(\lambda )$ is the satellite sensor band relative spectral response (RSR).

Fig. 3. Flow chart of the cross-calibration method based on the AVCS.

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3.2 Data and quality control

The observation data of the AVCS were selected to conduct the cross-calibrations between the Aqua/Terra MODIS and Sentinel-2A/Sentinel-2B MSI.

There are few instances in which the target satellite sensor and reference satellite sensor transit synchronously or nearly synchronously and collect data that meet the cross-calibration conditions. Since AVCS has continuous observation data, cross-calibration is not limited to synchronous or near-synchronous observation, and can match effective data in a wider time range. To reduce the impact of the different observation conditions of the reference and target satellite sensors and increase the opportunities for cross-calibration, the observation data must be quality-controlled as follows:

1. To prevent the impact of large changes in the water vapor content on the cross-calibration results on different observation days, the difference in the water vapor content between the target satellite and the reference satellite during transit is limited to no more than 20% (0.2 g/cm²@PW <1 g/cm²);
2. In order to reduce the impact of the AOD difference, the AOD at 550 nm is limited to less than 0.3;
3. To increase the crossing chance and reduce the error in the BRDF model correction results, the satellite observation zenith angle is limited to <40°;
4. To ensure the consistency and data stability of the satellite observations of the reference satellite, target satellite and AVCS, clear weather screening is carried out. The linear correlation between the logarithm of the ATR observation signal (ln (DN)) and the airmass is greater than 0.99 45 minutes before and after the satellite transit is restricted. As shown in Fig. 4, on August 7, 2018, the linear correlation between the ATR observation ln (DN) and airmass m before and after the Aqua MODIS transit occurred exceeded 0.997. At the same time, the selected satellite image data STD/MEAN was less than 2.5%.

Fig. 4. The linear correlation between the DN logarithm observed by ATR and the airmass.

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Based on the above conditions, we screen effective observation data of reference satellites with the closest time interval before and after the transit of target satellites.

4. Results and discussion

To compare the visual observations of the cross-calibration effect, we use the ratio of the predicted TOA reflectance and the target satellite-measured TOA reflectance to characterize the deviation between the two:

(9)$$rati{o_{bias}} = \frac{{TO{A_{\rho - predicted}}}}{{TO{A_{\rho - measured}}}}$$

where $TO{A_{\rho - predicted}}$ is the TOA reflectance predicted by the AVCS or cross-calibration and $TO{A_{\rho - measured}}$ is the sensor-measured TOA reflectance.

4.1 Aqua MODIS and Terra MODIS

With Aqua MODIS as the reference satellite, the Terra MODIS target satellite is cross-calibrated. From August 2018 to May 2022, there were approximately 560 matching pairs between the observation data of each MODIS instrument and the corresponding AVCS. According to the above method, the observation data of the target satellite Terra MODIS and the reference satellite Aqua MODIS were screened in consideration of weather factors, the satellite observation zenith angle and other data-control conditions during satellite transit. Finally, 112 data pairs met the cross-calibration conditions.

Figure 5 shows the Terra MODIS B1 TOA reflectance, as well as the TOA reflectance predicted by the AVCS and cross-calibration. Due to the low atmospheric water vapor in winter, the surface and atmosphere are drier, and the TOA reflectance reaches its highest point in winter. The variation trends of these three values are basically consistent, and the TOA reflectance obtained from the cross-calibration is close to that measured on Terra MODIS. The data losses during part of the transit time mainly include the following instances. First, automatic equipment can have observation problems, such as ATR signal and temperature control anomalies and HIM sun tracking anomalies. The second issue is the equipment calibration process; some instruments must be returned to the laboratory for radiometric calibration. The third is environmental issues, including instances in which the weather at the Dunhuang test site changes or is seriously affected by sand or dust, making the weather stability, aerosol content, etc., fail to meet the calibration conditions; in addition, snow cover in winter and spring can cause abnormally large surface reflectance values. Other satellite sensor observation data are missing for similar reasons.

Fig. 5. TOA reflectance, AVCS-predicted TOA reflectance and cross-calibration-predicted TOA reflectance for Terra MODIS B1 over the Dunhuang test site.

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Figure 6 shows similar results for Terra MODIS ocean observation band B12. The number of cross-calibration results is relatively small in this case because the reference satellite Aqua MODIS B11-B12 bands were saturated most of the time when transiting over Dunhuang, and the amount of available data was thus small and was concentrated in winter, thus further revealing the advantages of the AVCS, as the traditional low-frequency calibration is difficult to complete in a timely manner.

Fig. 6. TOA reflectance, AVCS-predicted TOA reflectance and corss-calibration-predicted TOA reflectance for Terra MODIS band 12 over the Dunhuang test site.

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Aqua/Terra MODIS B17-19 is a water-vapor-observation band that is greatly affected by water vapor, and B18 is more sensitive to water vapor interference. Figure 7 shows the B18-measured TOA reflectance, the AVCS-predicted TOA reflectance and the cross-calibration-predicted TOA reflectance when Terra MODIS passed over the Dunhuang test site. The TOA reflectance predicted by the AVCS was obviously different from the TOA reflectance measured by Terra MODIS, which was larger overall. The B18 TOA reflectance predicted by the cross-calibration was close to that measured by Terra MODIS. Other water-vapor-observation bands B17 and B19 also showed similar phenomena.

Fig. 7. TOA reflectance, AVCS-predicted TOA reflectance and corss-calibration -predicted TOA reflectance for Terra MODIS band 18 over the Dunhuang test site.

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To analyze the specific deviation in the calibration results, we use Eq. (9) to calculate the deviation of the AVCS-predicted TOA reflectance and the cross-calibration-predicted TOA reflectance from the measured TOA reflectance on Terra MODIS. Figure 8 shows that both average deviations are less than 1%, and the maximum deviations are not more than 8%. As shown in Fig. 9, due to the influence of water vapor absorption, the Terra MODIS B18 TOA reflectance deviation between the AVCS-predicted value and the measured value on Terra MODIS is large, with the maximum deviation even reaching 70%. The deviation of Terra MODIS B18 TOA reflectance between the cross-calibration-predicted and sensor-measured values is relatively small, with an average deviation of only 2.7%.

Fig. 8. The deviation of the AVCS-predicted TOA reflectance and cross-calibration-predicted TOA reflectance from the TOA reflectance measured by Terra MODIS B1.

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Fig. 9. The deviation of the AVCS-predicted TOA reflectance and cross-calibration-predicted TOA reflectance from the Terra TOA reflectance measured by Terra MODIS B18.

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Table 2 summarizes the results obtained for all MODIS bands. The µ symbol represents the average value of the predicted/measured ratio over the time series, and the σ/µ symbol represents the uncertainty of the predicted value. Terra MODIS B13-B16 is saturated when it passes through the Dunhuang test site, and its measurement results cannot be obtained. The deviations of SWIR bands B5-B7 are larger than those of other bands, and this finding is consistent with the results of other scholars [32,47]. This result may be due to B5-B7 being far from the ATR observation band, causing the surface reflectance uncertainty to increase due to scaling and adjustment issues, or may be related to the onboard calibration consistency between the Terra MODIS and Aqua MODIS instruments. Further research is needed. The deviations in the water-vapor-absorption bands between the AVCS-predicted and sensor-measured TOA reflectance are significant, especially for B18, with a difference of 25.2% and an uncertainty of 12.99%. However, the deviation between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance is relatively small. Except for the B5-B7 bands, all bands show agreement within 3% between the cross-calibration predicted and sensor measured, and in most bands, this agreement is better than 2%.

Table 2. Summary of the ratios of predicted TOA reflectance to Terra MODIS-measured TOA reflectance

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4.2 Sentinel-2A and Sentinel-2B

Similar to the results described above, Sentinel-2A was used as the reference satellite for the cross-calibration of the target satellite Sentinel-2B. Approximately 60 pairs of matching pairs were obtained between the observation data of each MSI instrument and the corresponding AVCS. According to the weather factors during satellite transit and other data control conditions, the final number of data pairs meeting the cross-calibration conditions was 20.

To analyze the impacts of the specific deviation and spectral difference of the calibration results on the cross-calibration results, we use Eq. (9) to calculate the deviation of the AVCS-predicted and cross-calibration-predicted TOA reflectance from the Sentinel-2B MSI-measured TOA reflectance. As shown in Fig. 10(a), for Sentinel-2B B3, the AVCS-predicted and cross-calibration-predicted TOA reflectance were consistent with the sensor-measured TOA reflectance, and the consistency between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance was better than 1%. As shown in Fig. 10(b), for Sentinel-2B B9, due to the influence of water vapor absorption, the difference between the AVCS-predicted TOA reflectance and measured TOA reflectance was significant, with the maximum difference exceeding 33%. The deviation between the cross-calibration-predicted TOA reflectance and measured TOA reflectance was relatively small, and the average relative deviation was only 2.2%.

Fig. 10. The deviation of the AVCS-predicted TOA reflectance and cross-calibration-predicted TOA reflectance from the Sentinel-2B MSI-measured TOA reflectance: (a) Sentinel-2B MSI B3 and (b) Sentinel-2B MSI B9.

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We further calculated and summarized the deviations between the predicted and measured values of each channel of Sentinel-2B MSI, as shown in Table 3. For the Sentinel-2B MSI nonwater vapor observation band, the consistency between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance was within 1%, and for water vapor observation band B9, the consistency between the cross-calibration-predicted TOA reflectance and sensor-measured TOA reflectance was within 2.2%. The uncertainty of the cross-calibration-predicted value was further reduced compared to the AVCS-predicted value.

Table 3. Summary of the ratios of predicted TOA reflectance to Sentinel-2B MSI-measured TOA reflectance

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4.3 Aqua and Sentinel-2A/2B

Similar to the results described above, Aqua was used as the reference satellite for the cross-calibration of the target satellite Sentinel-2A and Sentinel-2B. Combined with the band information in Table 1, bands with similar spectra are selected for cross-calibration. Figure 11 shows similar relative spectral response(RSR) for the spectrally overlapping bands of Aqua MODIS and the two MSI. According to the weather factors during satellite transit and other data control conditions, the final number of data pairs meeting the cross-calibration conditions were 24 and 20 respectively.

Fig. 11. RSR for the spectrally overlapping bands of AQUA MODIS and MSI (Sentinel-2A and Sentinel-2B).

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To analyze the impacts of the specific deviation and spectral difference of the calibration results on the cross-calibration results, Eq. (9) was used to calculate the deviation between the cross-calibration-predicted TOA reflectance and the two MSI-measured TOA reflectance. As shown in Fig. 12, for Sentinel-2A MSI B3 and Sentinel-2B MSI B3, with Aqua MODIS as the reference satellite, the average relative deviations between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance is 1.9% and 2%, respectively.

Fig. 12. The deviation of cross-calibration-predicted TOA reflectance from the two MSI-measured TOA reflectance: (a) Sentinel-2A MSI and (b) Sentinel-2B MSI.

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We summarize the cross-calibration results of the two MSI bands described above, as shown in Table 4. With Aqua MODIS as the reference satellite, the consistency between cross-calibration-predicted TOA reflectance and the Sentinel-2A MSI-measured TOA reflectance is less than 3.7%, and the consistency between cross-calibration-predicted TOA reflectance and the Sentinel-2A MSI-measured TOA reflectance is less than 3.8%. In general, for Sentinel-2B MSI, with Aqua MODIS as the reference satellite, the deviation between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance is greater than the results in Table 3. This may be related to the difference in radiation performance between Aqua MODIS and the two MSI. For comparable bands, the deviation between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance for Sentinel-2A MSI is in good agreement with that for Sentinel-2B MSI. The difference between the two is very close to the results of cross-calibration of Sentinel-2B MSI with Sentinel-2A MSI as the reference satellite above.

Table 4. Summary of the ratios of predicted TOA reflectance to two MSI-measured TOA reflectance

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4.4 Analysis of the correction factor effect

According to Formula (4) and Formula (5), the cross-calibration effect of two bands based on the AVCS depends on the degree to which the ratio of correction factors ${c_1}/{c_2}$ of two observations is close to 1. In the process of method description and case calculation above, the main differences in observation conditions are the surface reflectance, aerosol optical depth and atmospheric water vapor content observed by AVCS. There are some uncertainties in the observation data, and their impact on cross-calibration needs to be analyzed. The Aqua MODIS and Terra MODIS spectra have similar relative spectral response. Here, it is assumed that these two spectra are the same; in the following section, MODIS is taken as an example to analyze its impact on the correction factor.

4.4.1 Effect of the water vapor content

Terra MODIS B17-19 has relatively strong water vapor absorption compared to other wave bands, and the water vapor content affects the predicted TOA reflectance. Figure 13(a) shows, for Terra MODIS B18, the deviation between the AVCS-predicted TOA reflectance and the sensor-measured TOA reflectance changes obviously with an increasing water vapor content. The deviation between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance changes slightly with an increasing water vapor content. As shown in Fig. 13(b), the results obtained for Terra MODIS B19 are similar. As shown in Fig. 14, for Terra MODIS B17, B18, and B19, the deviation of the AVCS-predicted TOA reflectance and sensor-measured TOA reflectance showed significant positive correlations with the water vapor content, and the deviation of the AVCS-predicted TOA reflectance for bands B1 and B7 changed little with the water vapor content.

Fig. 13. The variation in deviation between the AVCS-predicted TOA reflectance or cross-calibration-predicted TOA reflectance and Terra MODIS-measured TOA reflectance with water vapor changes: (a) Terra MODIS band 18 and (b) Terra MODIS band 19.

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Fig. 14. The variation in the TOA reflectance ratio-bias of the AVCS-predicted/sensor-measured values with water vapor changes.

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The main reason for the large deviation of the predicted TOA reflectance and sensor-measured TOA reflectance is that the water-vapor-absorption transmissivity calculation is restricted by the satellite transit real-time atmospheric water vapor profile data and atmospheric water vapor content, thus making the forward modeling of the TOA reflectance of each band difficult. On the one hand, due to long-term field observation, large temperature difference and Gobi dust pollution optical lens will affect the observation accuracy of water vapor content of solar photometer. On the other hand, the precision of the atmospheric water vapor profile data used to calculate the water vapor absorption transmissivity can affect the results. In this paper, real-time atmospheric water vapor profile data were obtained by scaling the 62 US atmospheric model profile data of the 6SV radiative transfer model by the atmospheric water vapor content observed by the solar photometer, which has a certain error when compared to the actual profile data collected at the Dunhuang test site.

As shown in Fig. 14, the variation range of atmospheric water vapor content that can be used for calibration at the Dunhuang test site was approximately 0-1.8 g/cm2, and most values were within 0.5 g/cm². To further analyze the specific impact of the water vapor content, we assume that the atmospheric conditions at the Dunhuang test site conformed to the midlatitude summer atmospheric model. The 62 US atmospheric model was used in this paper. According to the results in Fig. 14, the AVCS-predicted TOA reflectance was generally high. We assumed that the retrieval of water vapor content was 20%(0.2 g/ cm2@PW <1) lower than true value. Figure 15 shows the surface reflectance used in simulation calculation, which is from the surface reflectance library of Dunhuang test site. The assumed surface reflectance, atmospheric parameters and geometric parameters were input into 6SV to simulate TOA reflectance.

Fig. 15. Surface reflectance used in the simulation calculation of TOA reflectance.

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As shown in Fig. 16(a) below, the TOA reflectance of bands B1 and B2 changed little with a change in the water vapor content, while the TOA reflectance of bands B17, 18 and 19 changed significantly with changes in the water vapor content. These differences were greater under different atmospheric models. Considering the influence of the difference in atmospheric models and a low water vapor content of 20%, the maximum difference in band B18 reached 47.5%. According to the following formula (10), as shown in Fig. 16(b), the change range of the B1 band correction factor with a change in the water vapor content was 0.996-1.002, and the difference in the Aqua/Terra MODIS spectrum was very small. Assuming that the Aqua/Terra MODIS B1 band was cross-calibrated and that the change in ${c_1}/{c_2}$ with the water vapor content was 0.994-1.006, other nonwater vapor absorption bands were basically similar. For the water vapor absorption band, taking B18 as an example, the variation range of the correction factor with a water vapor content range of 0.1-1.9 g/cm² was 0.678-0.757, and the change in ${c_1}/{c_2}$ with the water vapor content was 0.896-1.117. To prevent excessive water vapor changes from affecting the cross-calibration results, the difference in the water vapor content between the two satellites during transit was limited to no more than 20% (0.2 g/cm²@PW <1). Within the limited range of water vapor content changes, the cross factor ratio ${c_1}/{c_2}$ of the cross-calibration varied between 0.975-1.025 with changes in water vapor content. The cross-calibration results in the water vapor absorption bands B17, B18, and B19 reflected the significantly improved accuracy of the AVCS calibration. The cross-calibration-predicted TOA reflectance of water vapor observation bands B17, B18, and B19 were significantly closer to the sensor-measured TOA reflectance than the AVCS-predicted TOA reflectance.

(10)$${c_{water}} = \frac{{TO{A_{\rho sat - ({\textrm{MLS} + water} )}}}}{{TO{A_{\rho AVCS - ({\textrm{62US} + wate{r_{ \downarrow 20\%}}} )}}}}$$

where $TO{A_{\rho sat - ({\textrm{MLS} + water} )}}$ is the true TOA reflectance and $TO{A_{\rho AVCS - ({\textrm{62US} + wate{r_{ \downarrow 20\%}}} )}}$ is the AVCS-predicted TOA reflectance when the 62 US atmospheric model is used and the observed water vapor content is 20% lower than the true value.

Fig. 16. Variations in the TOA reflectance and correction factor with water vapor changes: (a) TOA reflectance and (b) correction factor.

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4.4.2 Effect of surface reflectance

As the most important parameter in the vicarious calibration process, the surface reflectance directly affects the radiometric calibration results. Assuming that the other parameters are accurate, the systematic surface reflectance error caused by the ATR sand dust pollution lens and calibration coefficient change is 10% lower than the true value. The TOA reflectance corresponding to the surface reflectance of different bands is calculated by changing the surface reflectance at 10% intervals. As shown in Fig. 17(a), the TOA reflectance changes significantly with the change in surface reflectance. The difference in the TOA reflectance of each channel caused by a change in the surface reflectance of 10% is approximately 10% and increases with increasing surface reflectance.

Fig. 17. The variations in the TOA reflectance and correction factor with surface reflectance: (a) TOA reflectance and (b) correction factor.

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According to formula (11), as shown in Fig. 17(b), the change in correction factors c of each band with surface reflectance is very small. For example, the change range of correction factor c of B1 is 1.074-1.1; for the two observations of the reference satellite and target satellite, the change range in ${c_1}/{c_2}$ with surface reflectance is 0.976-1.024. The spectral shape of the Dunhuang test site is very stable, the surface reflectance relative change of each band is less than 33%, and the band surface reflectance amplitude change is far less than 0.1-0.505. In actuality, ${c_1}/{c_2}$ is very close to 1.

(11)$${c_{ref}} = \frac{{TO{A_{\rho sat - ({BRF} )}}}}{{TO{A_{\rho AVCS - ({BR{F_{ \downarrow 10\%}}} )}}}}$$

where $TO{A_{\rho sat - ({BRF} )}}$ is the true TOA reflectance and $TO{A_{\rho AVCS - ({BR{F_{ \downarrow 10\%}}} )}}$ is the AVCS-predicted TOA reflectance when the surface reflectance is 10% lower than the true value.

4.4.3 Effect of aerosols

As important atmospheric parameters, the aerosol model and 550-nm AOD are input into the radiative transfer model 6SV. Dunhuang represents a typical desert aerosol model year round [7,48]. The desert aerosol model used in this paper is very close to the real aerosol model. Therefore, it is only necessary to analyze the influence of AOD measurement error on cross calibration. To analyze the influence of aerosol changes, suppose that the AOD observed by AVCS is 0.05 higher than the true value due to issues such as the decay of the PSR calibration coefficient, sand dust attachment optical lens, etc. The TOA reflectance corresponding to different bands in different aerosols were simulated and calculated by changing the 550-nm AOD at an interval of 0.05. The surface reflectance is shown in Fig. 15. As shown in Fig. 18(a), the TOA reflectance did not change significantly when the AOD increased by 0.05, and the TOA reflectance change of each band was less than 0.5%. According to formula (12), within the AOD range of 0.1-0.3, as shown in Fig. 18(b), the change in each band correction factor c with the AOD change is very small. The change in ${c_1}/{c_2}$ with surface reflectance ranges from 0.999-1.001, and ${c_1}/{c_2}$ is very close to 1.

(12)$${c_{AOD}} = \frac{{TO{A_{\rho sat - ({\textrm{Desert} + AOD} )}}}}{{TO{A_{\rho AVCS - ({\textrm{Desert} + AO{D_{ \uparrow 0.05}}} )}}}}$$

where $TO{A_{\rho sat - ({\textrm{Desert} + AOD} )}}$ is the true TOA reflectance and $TO{A_{\rho AVCS - ({\textrm{Desert} + AO{D_{ \uparrow 0.05}}} )}}$ is the AVCS-predicted TOA reflectance when the 550 nm AOD is 0.05 higher than the true value.

Fig. 18. The variations in the TOA reflectance and correction factor with AOD: (a) TOA reflectance and (b) correction factor.

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In summary, by limiting the difference between the transit observation conditions of similar bands of the two sensors, the AVCS measurement can be used to conduct cross-calibration between two sensors, and this method can mitigate the contribution of the AVCS measurement uncertainty, especially in the water-vapor-observation bands. Of course, similar to traditional cross-calibration methods, the method proposed in this paper also has the limitation of spectral matching, and significant spectral differences will also affect the effect of cross-calibration [49,50]. For the method proposed in this paper, the measurement uncertainty of AVCS has different effects on different spectral bands, resulting in the cross-factor ${c_1}/{c_2}$ deviating from 1. For example, assuming that the Aqua MODIS B17 band is used as a reference satellite for cross-calibration with Terra MODIS B18. Based on the simulation results in in Section 4.3.1, for Aqua MODIS B17, the variation range of the correction factor with a water vapor content range of 0.1-1.9 g /cm² was 0.893-0.939, for Terra MODIS B18, the variation range of the correction factor with a water vapor content range of 0.1-1.9 g/cm² was 0.678-0.757. To prevent excessive water vapor changes from affecting the cross-calibration results, the difference in the water vapor content between the two satellites during transit was limited to no more than 20% (0.2 g/cm²@PW <1). Within the limited range of water vapor content changes, the cross factor ${c_1}/{c_2}$ of the cross-calibration varied between 0.753-0.823 with changes in water vapor content. According to the above results, the correction factors of each band are within a certain range, and the relationship is relatively stable, thus provides a basis for reducing the effect of cross-calibration of different bands. In this paper, the zenith angle of the selected satellite observation was within 40°, and the cross-calibration did not limit the geometric difference between the observations of the two satellites; however, the BRDF was used to correct the observation geometry in the AVCS observation process, which has limited influence. In future work, we will further limit the differences in observation conditions such as the water vapor content, aerosol optical thickness, and observation geometry angle between the matching reference satellite and the target satellite during transit in a widened time range to reduce uncertainty in the results and explore the impacts of spectral differences on the cross-calibration results.

5. Conclusion

In this study, we propose a cross-calibration method that uses AVCS observation data from the Dunhuang test site as a bridge to realize cross-calibration of two remote sensors. Compared to the traditional cross-calibration method, the proposed approach breaks the limits of synchronous and near-synchronous observations and can match the approximate observation conditions in a widened time range, thus improving the calibration frequency. Using this method, we successfully realized the cross-calibration of Aqua/ Terra MODIS and Sentinel-2A/ Sentinel-2B MSI. The research results show that the AVCS has a good effect on the cross-calibration of the studied sensor types. The consistency between the two MODIS cross-calibration predicted TOA reflectance and the sensor-measured TOA reflectance was within 3% (5% in SWIR bands), the consistency between the two MSI cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance was within 1%, the consistency of the TOA reflectance between the cross-calibration results of the water-vapor-observation bands and the sensor-measured values was within 2.2%, and for Aqua MODIS and the two MSI, the consistency between the cross-calibration-predicted TOA reflectance and the sensor-measured TOA reflectance was within 3.8%. Compared to the AVCS-predicted TOA reflectance, the calibration accuracy of the water-vapor-observation band was significantly improved following calibration by the proposed method, and the contribution of absolute uncertainty related to the AVCS measurements was also reduced. This method thus provides a new idea and means for on-orbit stability monitoring and cross-calibration of remote sensors, and the proposed approach can be applied to cross-calibrate other remote sensors. The influence of spectral differences on the cross-calibration results will be further studied in the future.

Funding

Hefei Institutes of Physical Science, Chinese Academy of Sciences (YZJJ202208-CX); the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA28050401); National Natural Science Foundation of China (No.42105139).

Acknowledgments

We thank the AVCS team for their contributions to the project and the manuscript.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Band	AVCS predicted/measured		Cross-calibration predicted/measured
Band	µ	σ/µ	µ	σ/µ
1	1.005	0.0211	0.996	0.0235
2	0.983	0.0284	0.986	0.0262
3	0.997	0.0242	0.971	0.0213
4	0.998	0.0181	0.989	0.0198
5	0.992	0.0337	0.954	0.0328
6	0.991	0.0251	0.969	0.0258
7	1.032	0.0415	0.961	0.0365
8	1.009	0.0243	0.992	0.0248
9	0.990	0.0257	0.979	0.0240
10	1.001	0.0210	0.991	0.0179
11	1.029	0.0176	1.017	0.0170
12	1.014	0.0188	1.009	0.0223
17	1.034	0.0415	0.970	0.0282
18	1.252	0.1299	0.973	0.0476
19	1.138	0.0867	0.998	0.0389

Band	AVCS predicted/measured		Cross-calibration predicted/measured
Band	µ	σ/µ	µ	σ/µ
1	1.008	0.0142	1.010	0.0101
2	1.001	0.0193	1.003	0.0165
3	0.990	0.0236	0.997	0.0197
4	0.973	0.0223	1.000	0.0211
5	0.984	0.0197	1.005	0.0227
6	0.983	0.0201	1.005	0.0233
7	0.979	0.0225	1.006	0.0237
8	1.005	0.0223	0.999	0.0278
8A	0.983	0.0236	1.004	0.0253
9	1.171	0.0782	1.022	0.0540

Band	Cross-calibration for Sentinel-2A predicted/measured		Cross-calibration for Sentinel-2B predicted/measured
Band	µ	σ/µ	µ	σ/µ
MSI B1	0.986	0.0239	0.995	0.0162
MSI B2	0.986	0.0294	0.987	0.0211
MSI B3	0.981	0.0363	0.980	0.0250
MSI B4	0.963	0.0357	0.962	0.0290
MSI B8A	0.973	0.0458	0.982	0.0376
MSI B9	0.981	0.0404	1.004	0.0439

Band	AVCS predicted/measured		Cross-calibration predicted/measured
Band	µ	σ/µ	µ	σ/µ
1	1.005	0.0211	0.996	0.0235
2	0.983	0.0284	0.986	0.0262
3	0.997	0.0242	0.971	0.0213
4	0.998	0.0181	0.989	0.0198
5	0.992	0.0337	0.954	0.0328
6	0.991	0.0251	0.969	0.0258
7	1.032	0.0415	0.961	0.0365
8	1.009	0.0243	0.992	0.0248
9	0.990	0.0257	0.979	0.0240
10	1.001	0.0210	0.991	0.0179
11	1.029	0.0176	1.017	0.0170
12	1.014	0.0188	1.009	0.0223
17	1.034	0.0415	0.970	0.0282
18	1.252	0.1299	0.973	0.0476
19	1.138	0.0867	0.998	0.0389

Band	AVCS predicted/measured		Cross-calibration predicted/measured
Band	µ	σ/µ	µ	σ/µ
1	1.008	0.0142	1.010	0.0101
2	1.001	0.0193	1.003	0.0165
3	0.990	0.0236	0.997	0.0197
4	0.973	0.0223	1.000	0.0211
5	0.984	0.0197	1.005	0.0227
6	0.983	0.0201	1.005	0.0233
7	0.979	0.0225	1.006	0.0237
8	1.005	0.0223	0.999	0.0278
8A	0.983	0.0236	1.004	0.0253
9	1.171	0.0782	1.022	0.0540

Cross-calibration method based on an automated observation site

Abstract

1. Introduction

2. Calibration site and datasets

2.1 Dunhuang test site

2.2 Datasets

2.2.1 Automated vicarious calibration system (AVCS)

2.2.2 Sensor data

3. Methodology

3.1 Cross-calibration method based on the AVCS

3.2 Data and quality control

4. Results and discussion

4.1 Aqua MODIS and Terra MODIS

4.2 Sentinel-2A and Sentinel-2B

4.3 Aqua and Sentinel-2A/2B

4.4 Analysis of the correction factor effect

4.4.1 Effect of the water vapor content

4.4.2 Effect of surface reflectance

4.4.3 Effect of aerosols

5. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (18)

Tables (4)

Equations (12)

Optics Express

Aqua/Terra MODIS			Sentinel-2A/Sentinel-2B MSI
Band	Wavelength range/nm	Res/m	Band	Central Wavelength/nm	Bandwidth/nm	Res/m
1	620-670	250	1	443	20	60
2	841-876	250	2	490	65	10
3	459-479	500	3	560	35	10
4	545-565	500	4	665	30	10
5	1230-1250	500	5	705	15	20
6	1628-1652	500	6	740	15	20
7	2105-2135	500	7	783	20	20
8	405-420	1000	8	842	115	10
9	438-448	1000	8A	865	20	20
10	483-493	1000	9	945	20	60
11	526-536	1000
12	546-556	1000
17	890-920	1000
18	931-941	1000
19	915-965	1000