Radiometric cross-calibration of Sentinel-2B MSI with HY-1C SCS based on the near simultaneous imaging of common ground targets

Heyu Xu; Wenxin Huang; Xiaolong Si; Qingjun Song; Qingjun Song; Xin Li; Xu Weiwei; Yue Ma; Liming Zhang

doi:10.1364/OE.479445

1. Introduction

With the growing development and maturity of technologies, remote sensing has played an increasingly important role in resource surveys, ecological environment monitoring, urban and rural planning and construction, major natural disaster monitoring, and agricultural, forestry and animal husbandry research [1,2]. The effective application of remote sensing data depends not only on the design and performance of satellite sensors but also on the quantitative level of data. The basic premise of data quantification is radiometric calibration. The calibration accuracy determines the quantitative application level of the resulting data. The main research content is to establish the quantitative conversion relationship between a remote sensor's digital number and the known radiation input physical quantities expressed in SI units. Generally, radiometric calibration can be divided into prelaunch laboratory calibration and postlaunch onboard calibration according to different implementation stages [3–5]. Prelaunch calibration is used to obtain the basic instrument parameters, such as its spectral response function, radiometric response model, dark current and modulation transfer function, and these calibration results can be used as a basis for evaluation to determine whether the radiometric response of the remote sensor has deteriorated or changed during orbit. After launch, the performances of optical remote sensors change with the space environment due to factors such as the vacuum conditions, bombardment of space energy particles, spectral responses of the transparencies, and slow aging of the electronic system [6,7]. Therefore, sensors must also undergo postlaunch calibrations.

The postlaunch calibration process can be divided into the following main types: (1) On-board calibration, which depends mainly on on-board calibration equipment. For example, the Landsat 7/Enhanced Thermal Mapper Plus (ETM+) satellite is equipped with an integrating sphere and blackbody that can be used with a full-aperture solar calibrator (FASC) and partial-aperture solar calibrator (PASC) to achieve onboard radiometric calibration in the near-infrared, visible and thermal infrared bands. Although this calibration system is not affected by the surface type or atmosphere and has high calibration accuracies, the radiation performance of the calibrator itself changes with the passage of time and the degradation of the calibration equipment, making it difficult to maintain a high radiometric calibration accuracy over long-term satellite lives [8]. The Moderate-resolution Imaging Spectroradiometer (MODIS) [9] carried by the Terra and Aqua satellites uses the Sun as the illumination source, combines with the diffuser to achieve on-board radiometric calibrations, and uses the Solar Diffuser Stability Monitor (SDSM) to monitor the degradation of the optical characteristics of the diffuser surface, thus maintaining its high-precision radiometric calibration ability over long terms. Hai Yang (HY)-1C/D [10] and the Medium-resolution Imaging Spectrometer (MERIS) [11,12] are also equipped with a “Solar + Diffuser” calibration system. The results of many years of calibration show that this calibration system can perform end-to-end, full-aperture, high-frequency and high-precision calibration. Due to the high cost and technical difficulty, only a few remote sensors are equipped with onboard calibration systems. (2) The second type involves site calibration; Slater et al. [13,14] obtained the thermal mapper (TM) site calibration coefficient by using a reflectance-based method, irradiance-based method and radiance-based method. This method is relatively mature but has high requirements with regard to the calibration site and atmospheric conditions, and the human and material resource consumption costs are too large to meet the needs of high-frequency and high-precision calibration [15–17]. (3) The cross-calibration uses the remote sensor with high precision as the reference to realize the calibration of the remote sensor to be calibrated through the synchronous observation of the same ground object [18,19]. This method has higher requirements for the spectral parameter setting and the spatial resolution of the remote sensor and requires a relatively high surface uniformity in the cross-calibration area. If the reference sensor is a multispectral sensor, its band spectral setting will differ from the remote sensor to be calibrated. Therefore, it will be necessary to obtain the spectral band adjustment factor (SBAF) [20,21] to reduce the calibration uncertainty caused by the different band spectral parameter settings, limiting the improvement capacity of the calibration frequency. If a hyperspectral remote sensor is used as the reference, continuous spectral data can be obtained by interpolating and iterating the hyperspectral data to achieve cross-calibration without calculating the SBAF. This method can simplify the calibration process and improve the calibration accuracy, which is of great significance in the study of Earth observations.

The Hai Yang (HY)-1C satellite was successfully launched at the Taiyuan Satellite Launch Center on September 7, 2018. As the successor of HY-1B, its main function is to carry out the high-precision and large-scale detection of oceans and coastal waters globally. To solve the limitations associated with cross-calibration methods among multiple satellites and ensure a high onboard calibration accuracy of the satellite ocean color remote sensing instrument, for the first time, the SCS developed by the Beijing Institute of Space Mechanics and Electronics is carried onboard the HY-1C satellite platform and is used as the radiometric calibration reference source for cross-calibration of the Coastal Zone Imager (CZI), and other sensors perform cross-calibrations [22,23]. As the cross-calibration reference, the SCS needs to be capable of high-precision spectral calibration and radiometric calibration tasks. Therefore, the Anhui Institute of Optics and Mechanics, Chinese Academy of Sciences, has designed an on-board “calibration diffuser + wavelength diffuser” calibration system for the SCS [24]. The research results show that SCS based on the onboard calibration system can achieve spectral calibration with a central wavelength error of 0.08 nm and a bandwidth error of 0.20 nm [10] and can achieve absolute radiometric calibration with an uncertainty of more than 3% [23,24]. This paper first introduces the cross-calibration process and method of the Sentinel-2B/MSI using the HY-1C/SCS as the reference sensor. The continuous spectrum is obtained by the deconvolution method to remove the influence of the spectral response function, thus achieving accurate spectral response matching and effectively solving the calibration uncertainty caused by the differences in the band spectrum parameter settings. The MSI calibration coefficients are obtained by processing the Earth-observation images taken by the MSI and SCS on January 24, 2019. Then, the MSI calibration coefficients are applied to different scenes, such as oceans, farmlands and soils, and the cross-calibration accuracy is validated by comparing the consistency of the results with MODIS-derived reflectance images.

2. Materials and methods

2.1 Sensor overview

The optical path system of the SCS is equipped with a rotating telescope assembly (RTA) and half-angle mirror (HAM) [25,26]. When observing the Earth, light first enters the instrument through the RTA, then enters the fixed rear optical system through the HAM reflection, forms 101 continuous wavebands with a spectral resolution of 5 nm through the grating–splitting process, and finally reaches the load focal plane. Through the combined rotation of the RTA and HAM, the SCS can switch between the Earth and diffuser observations. Figure 1(a) provides a simplified block diagram of the functional implementation of the SCS.

Fig. 1. SCS diagram: (a) SCS simplified block diagram; (b) schematic diagram of the SCS onboard calibration system

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The research team led by Professor Zhang Liming of Hefei Institute of Physical Science, Chinese Academy of Sciences, designed the onboard calibration system, as shown in Fig. 1(b). The calibration system mainly includes the following components: (1) the calibration solar diffuser (CSD), which is mainly used for the periodic on-board calibration of the SCS. The use frequency is high, the cumulative exposure time is long, and the bidirectional reflectance distribution function (BRDF) of the CSD surface degrades with increasing cumulative exposure time. To achieve high-precision on-board radiometric calibration within the satellite lifespan, BRDF degradation needs to be monitored and corrected. (2) The reference solar diffuser (RSD) is made of the same material and process as the CSD and has a similar optical performance. The use frequency is low, and the cumulative exposure time is far less than that of the CSD. The surface optical performance can be considered to be stable without degradation during on-orbit operation, and it is used as a reference to monitor the BRDF degradation of the CSD. (3) The Earth-doped wavelength diffuser (EWD) is a diffuser containing rare-Earth erbium, which has a characteristic absorption peak. It is mainly used to monitor and correct the wavelength drift and bandwidth change issues of the SCS. (4) The solar attenuation screen (SAS) is mainly used to attenuate the solar energy incident on the diffuser so that the remote sensor's entrance pupil energy when observing the diffuser is equivalent to that when observing the earth, thus ensuring the accuracy of the onboard calibration coefficient in Earth observation applications.

Sentinel-2 is composed of Sentinel-2A and Sentinel-2B satellites and can realize high-frequency Earth observations with a revisit period of five days by means of networking and cooperative observations [27–32]. The main payload of Sentinel-2 is the MSI, a 13-band push-broom imager with 12 independent detector arrays, covering a 295-km strip width in the visible near-infrared to shortwave infrared (400∼2400 nm) spectral range, mainly including 10-m (B2, B3, B4, and B8), 20-m (B5, B6, B7, B8a, B11, and B12) and 60-m (B1, B9, and B10) spatial resolutions. Sentinel-2B and HY-1C are both morning stars, and the local overpass time of their intersection point is close to 10:30 AM. Therefore, Sentinel-2B/MSI B1∼B7 and B8a are cross-calibrated with HY-1C/SCS as the reference sensor. The relative spectral response functions of the SCS and MSI channels are shown in Fig. 2.

Fig. 2. Relative spectral response function: (a) SCS partial channels B66 – B88; (b) MSI bands B1∼B7 and B8a

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2.2 Calibration theory

The essence of cross-calibration is the transmission of radiometric standards. Its premise is that under the same geometric observation conditions, two remote sensors that transit at the same time receive the same radiance through the entrance pupil when observing the same ground object. The simultaneous nadir overpass (SNO) method is a comparison of synchronous measurements of two or more sensors at the orbital intersection under almost the same observation conditions, mainly imaging at high latitudes. In this paper, the SNO-x method is used for cross-calibration, which is a method that inherits the traditional SNO method. It extends the SNO orbit to low latitudes so that cross-calibration can be carried out in a wide dynamic range (such as sea surface, desert targets, green vegetation, etc.). Illustration of the cross-calibration between the MSI and SCS using the SNO-x method showing the field of view coverage area of the SCS as a reference (green strip) and MSI (red strip) [33–36], as shown in Fig. 3.

Fig. 3. Illustration of the cross-calibration method of MSI with SCS as the reference sensor

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The cross-calibration process is shown in Fig. 4. First, the orbital prediction model is used to determine the timing of cross-calibration. Then, the images of ROIs are obtained by spatial resampling, spatial matching and other processing steps. Finally, combining the relative spectral response functions of SCS and MSI, spectral matching is performed to reduce the uncertainty caused by spectral differences, and then cross-calibration results are obtained.

Fig. 4. Cross-calibration flow chart

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As a reference sensor, the radiometric calibration accuracy of the SCS directly determines the reliability of the cross-calibration results. The SCS uses sunlight as the light source to illuminate the CSD and form a uniform surface light source, thus providing a radiometric calibration input for the SCS. The SCS-output DN value at the calibration time can be expressed as follows:

(1)$$DN({\lambda _i}) = R({\lambda _i}) \ast \frac{{{E_{Sun}}({\lambda _i})\cos ({\theta ^{in}})}}{{{d^2}}}H({\lambda _i}){f_{lab}}({\theta ^{in}},{\phi ^{in}};{\theta ^{ov}},{\phi ^{ov}};{\lambda _i})\tau (\theta _{SAS}^{in},\phi _{SAS}^{in})$$

where ${\theta ^{in}}$ and ${\phi ^{in}}$ represent the zenith and azimuth angles of the solar incident diffuser, respectively; ${\theta ^{ov}}$ and ${\phi ^{ov}}$ represent the observation zenith angle and azimuth angle, respectively; $\theta _{SAS}^{in}$ and $\phi _{SAS}^{in}$ represent the azimuth angle and zenith angle of the solar incident SAS, respectively; $d$ represents the Sun–Earth distance factor; ${\lambda _i}$ represents the ${i^{th}}$ band center wavelength; ${E_{Sun}}({\lambda _i})$ represents the equivalent solar constant outside the atmosphere; $H({\lambda _i})$ represents the BRDF degradation factor; ${f_{lab}}({\theta ^{in}},{\phi ^{in}};{\theta ^{ov}},{\phi ^{ov}};{\lambda _i})$ is the interpolation result of the laboratory-measured BRDF value; $\tau (\theta _{SAS}^{in},\phi _{SAS}^{in})$ is the transmittance of SAS; and $R({\lambda _i})$ represents the radiation response coefficient of the SCS.

When the SCS observes the Earth, its output DN value can be expressed as follows:

(2)$$D{N_{t\arg et}}({\lambda _i}) = R({\lambda _i}) \ast \frac{{{E_{Sun}}({\lambda _i})\cos (\theta _{t\arg et}^{in})}}{{d_{t\arg et}^2}}\frac{{{\rho _{t\arg et}}({\lambda _i})}}{\pi }$$

where $\theta _{t\arg et}^{in}$ is the solar zenith angle; $d_{t\arg et}^{}$ is the Sun–Earth distance factor; and ${\rho _{t\arg et}}({\lambda _i})$ is the reflectance at the top of the atmosphere.

Combining Eq. (1) and Eq. (2), the expression of the top-of-atmosphere reflectance of the surface object can be expressed:

(3)$${\rho _{t\arg et}}({\lambda _i}) = \frac{{\cos ({\theta ^{in}})H({\lambda _i}){f_{lab}}({\theta ^{in}},{\phi ^{in}};{\theta ^{ov}},{\phi ^{ov}};{\lambda _i})\tau (\theta _{SAS}^{in},\phi _{SAS}^{in})\pi }}{{{d^2}DN({\lambda _i})}}\frac{{D{N_{t\arg et}}({\lambda _i})d_{t\arg et}^2}}{{\cos (\theta _{t\arg et}^{in})}}$$

The reflectance calibration coefficient can be expressed as follows:

(4)$${R_\rho }({\lambda _i}) = \frac{{\cos ({\theta ^{in}})H({\lambda _i}){f_{lab}}({\theta ^{in}},{\phi ^{in}};{\theta ^{ov}},{\phi ^{ov}};{\lambda _i})\tau (\theta _{SAS}^{in},\phi _{SAS}^{in})\pi }}{{{d^2}DN({\lambda _i})}}$$

Equation (3) can be rewritten as follows:

(5)$${\rho _{t\arg et}}({\lambda _i}) = {R_\rho }({\lambda _i})\frac{{D{N_{t\arg et}}({\lambda _i})d_{t\arg et}^2}}{{\cos (\theta _{t\arg et}^{in})}}$$

According to Eq. (5), the equivalent reflectance at the entrance pupil of the SCS can be obtained, which is taken as the measured reflectance, and the continuous entrance-pupil spectrum at a 1-nm interval can be obtained through cubic spline interpolation [37,38]. Then, it is convolved with the relative spectral response function to obtain the new equivalent reflectance and compared with the initial measured reflectance. If the termination conditions are met, the spectral radiance obtained by interpolation can be considered the actual spectral radiance of the entrance pupil. If the accuracy requirements are not satisfied, interpolation iterations are conducted repeatedly until the accuracy requirements are met [39,40]. First, the measured reflectance is taken as the initial value:

(6)$$\rho _0^{SCS} = \{ {\rho_{\textrm{mes}}^{SCS;b}} |(b = 1,2,\ldots ,n)\} $$

(7)$$\rho _0^{SCS}(\lambda ) = spline\_{\mathop{\rm int}} erp(\rho _0^{SCS})$$

where $\rho _0^{SCS}(\lambda )$ is the 1-nm interval spectral reflectance obtained by cubic spline interpolation of the initial reflectance.

The k-th iteration process is as follows:

(8)$$\rho _k^{SCS;b} = \frac{{\int {\rho _k^{SCS;b}(\lambda ){R^{SCS;b}}(\lambda )d\lambda } }}{{\int {{R^{SCS;b}}(\lambda )d\lambda } }}$$

(9)$$\rho _k^{SCS} = \{ {\rho_k^{SCS;b}} |(b = 1,2,\ldots ,n)\} $$

(10)$$\rho _{k + 1}^{SCS;b} = \rho _k^{SCS;b} + a \ast (\rho _{\textrm{mes}}^{\bmod ;b} - \rho _k^{SCS;b}({\lambda _b}))$$

where $\rho _{k + 1}^{SCS;b}$ and $\rho _k^{SCS;b}$ represent the equivalent reflectance during the k + 1-th and k-th iterations, respectively; $\rho _k^{SCS;b}(\lambda )$ is the spectral reflectance obtained in the k-th iteration; and a represents the scaling coefficient of each iteration, generally 1.

When the difference between the obtained reflectance and the initial measured reflectance is less than a certain threshold, the iteration is terminated. At this time, the spectral reflectance can be used as the actual entrance pupil spectral reflectance, and the threshold conditions can be expressed as follows:

(11)$${||{ {\rho_k^{SCS}\textrm{ - }\rho_0^{SCS}} ||} _2} \le c$$

where ${||{ {} ||} _2}$ represents the 2-norm and $c = {10^{ - 9}}$.

Since the imaging times of the SCS and MSI are close and their imaging geometric conditions are similar, it can be considered that the spectral radiance of the entrance pupil at the cross-imaging time of the two sensors is approximately the same. The continuous spectral radiance obtained can be convolved with the spectral response functions of MSI to obtain the predicted reflectance as follows:

(12)$$\rho _{pre}^{MSI;b} = \frac{{\int {\rho (\lambda ){R^{MSI;b}}(\lambda )d\lambda } }}{{\int {{R^{MSI;b}}(\lambda )d\lambda } }}$$

where ${R^{MSI;b}}$ and $\rho (\lambda )$ represent the spectral reflectance and spectral response function of the ${b^{th}}$ band of the MSI, respectively.

The cross-calibration coefficient and offset can be obtained by linear regression between the measured reflectance obtained by processing the region of interest (ROI) of MSI and the predicted reflectance calculated by Eq. (1)2.

2.3 Validation Method

Terra MODIS has successfully operated for more than 20 years and has high onboard calibration accuracy. Therefore, Terra MODIS is used as a reference to evaluate the reliability and accuracy of the cross-calibration. The validation process is shown in Fig. 5: (1) Obtain the images of the same ground object targets from the SCS, the MSI and MODIS through orbit simulation prediction. (2) Through the spatial resampling process, spatial matching and homogeneity screening, the ROIs satisfying the validation conditions are obtained. (3) The mean DN value in the ROIs of the SCS are obtained by statistics, and the measured reflectance of the entrance pupil can be obtained by combining its onboard calibration coefficients. Then, the continuous spectral reflectance can be obtained by interpolation iteration. According to Eq. (1)4, the SBAF can be obtained by combining the spectral response functions of the MSI and MODIS. (4) The mean DN value of the MODIS ROI image can be obtained through statistics, and the measured reflectance can be obtained by combining its onboard calibration coefficients and offsets; the calculated reflectance after spectral correction can be obtained by combining the SBAF. (5) The MSI-measured reflectance can be obtained through statistics of ROI images, and the calculated reflectance can be obtained by combining the cross-calibration coefficients and offsets. (6) Finally, the consistency between the MODIS-calculated reflectance and MSI-calculated reflectance and between the MODIS-calculated reflectance and MSI-measured reflectance are compared to complete the reliability evaluation of the cross-calibration.

Fig. 5. Cross-validation flow chart

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The MODIS-measured reflectance can be obtained by combining the mean DN value of the ROIs with its onboard calibration gains and offsets and can be expressed as:

(13)$$\rho _{mes}^{Mod,b} = \frac{{(\overline {D{N^b}} - offse{t^b})\ast Scal{e^b}}}{{\cos (\theta _{t\arg et}^{\bmod is})}}$$

Since both MSI and MODIS are multispectral remote sensors, their spectral response shapes are quite different. Therefore, the SBAF must be calculated to compensate for the energy differences caused by spectral differences and improve the reliability of the validation results.

The SBAF is calculated as follows:

(14)$$SBAF = \frac{{{{\int {\rho (\lambda ){R^{MSI;b}}(\lambda )d\lambda } } / {\int {{R^{MSI;b}}(\lambda )d\lambda } }}}}{{{{\int {\rho (\lambda ){R^{Modis;b}}(\lambda )d\lambda } } / {\int {{R^{Modis;b}}(\lambda )d\lambda } }}}}$$

where ${R^{Modis;b}}(\lambda )$ represents the MODIS relative spectral response function and $\rho (\lambda )$ is the SCS spectral reflectance obtained by interpolation and iteration. Therefore, it is necessary to select MODIS, SCS and MSI images of the same surface features during validation, and the SCS data are used to provide spectral reflectance information to calculate the SBAF.

The MODIS-calculated reflectance after spectral correction can be obtained by combining the SBAF:

(15)$$\rho _{cal}^{Mod,b} = SBAF\ast \rho _{mes}^{Mod,b}$$

To further quantitatively analyze the reliability and accuracy of the cross-calibration results, the MODIS-calculated reflectance is taken as the true value, and the MSI-measured reflectance and the MSI-calculated reflectance are taken as the predictive values [41]. Since the deviation between the predicted value and the true value differs among different scenes, we use the root-mean-square relative error (RMSRE) to evaluate the average relative error in ROIs:

(16)$$RMSRE = \sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {{{(\frac{{\rho _i^{act} - \rho _i^{est}}}{{\rho _i^{act}}})}^2}} } \ast 100$$

where n represents the total number of ROIs; i is the serial number of ROIs; and $\rho _i^{act}$ and $\rho _i^{est}$ represent true and predicted values, respectively.

3. Cross-calibration results

The cross-calibration results are obtained by processing the SCS and MSI images acquired on January 24, 2019. The SCS image and MSI images are shown in Fig. 6. In the figure, the SCS spatial resolution is 1.1 km, and the MSI spatial resolution is 10 m. A single SCS pixel corresponds to thousands of pixels in the MSI image. The MSI remote sensing image thus needs to be spatially resampled. In this paper, spatial resampling adopts the cubic convolution interpolation method, as this method has a high interpolation accuracy and can retain the original image details to the maximum extent.

Fig. 6. Cross-calibration images: (a) SCS image; (b)∼(c) MSI image

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Then, the SCS image is relatively calibrated to eliminate the image stripe noise caused by pixel response inconsistencies. Finally, with an observation zenith angle less than 15° and nonuniformity less than 5% as the threshold conditions, the cross-calibration area $I_{\textrm{ref}}^{\textrm{UNI}}$ satisfying the uniformity requirements of the SCS can be obtained by circular filtering according to the 5 × 5 pixel size window. Using the longitude and latitude information of the pixel points, the MSI image pixel positions closest to each pixel point in $I_{\textrm{ref}}^{\textrm{UNI}}$ can be obtained one by one according to the shortest distance method; the expression is as follows:

(17)$${\boldsymbol T} = \left[ {\begin{array}{ccc} {{{(M_{i,j}^{ref} - M_{1,1}^c)}^2}}& \cdots &{{{(M_{i,j}^{ref} - M_{1,n}^c)}^2}}\\ \vdots & \vdots & \vdots \\ {{{(M_{i,j}^{ref} - M_{m,1}^c)}^2}}& \cdots &{(M_{i,j}^{ref} - M_{m,n}^c)^{2}} \end{array}} \right]\textrm{ + }\left[ {\begin{array}{ccc} {{{(N_{i,j}^{ref} - N_{1,1}^c)}^2}}& \cdots &{{{(N_{i,j}^{ref} - N_{1,n}^{ref})}^2}}\\ \vdots & \vdots & \vdots \\ {{{(N_{i,j}^{ref} - N_{m,1}^c)}^2}}& \cdots &{(N_{i,j}^{ref} - N_{m,n}^{ref})^{2}} \end{array}} \right]$$

where $M_{i,j}^{ref}$ and $N_{i,j}^{ref}$ represent the longitude and latitude coordinate values of pixel points in the ${i^{th}}$ row and ${j^{th}}$ column of $I_{ref}^{\textrm{UNI}}$, respectively; $M_{m,n}^{ref}$ and $N_{m,n}^{ref}$ represent the longitude and latitude coordinates of pixel points in the ${m^{th}}$ row and ${n^{th}}$ column of the MSI image. The following steps can be followed to obtain the area used for calibration in the MSI image: 1) The row and column number (n, m) corresponding to the minimum value in the above matrix are determined; then, the corresponding pixel DN value in the MSI image to be calibrated is found according to the row and column number; 2) According to Eq. (1)3, each pixel in $I_{ref}^{\textrm{UNI}}$ can provide a T matrix, and step 1) can be repeated to obtain the uniform area for cross-calibration in the MSI image with a one-to-one correspondence to the pixel in $I_{ref}^{\textrm{UNI}}$.

After screening, 19 ROIs meeting the conditions were obtained. The observation and solar illumination angles of the two remote sensors in the ROIs are shown in Table 1. It can be seen in the table that the solar zenith angles are similar, with differences less than 0.3°, and the observation zenith angle differences are less than 12°. The difference in the atmospheric radiation transmission path is small and is thus suitable for cross-calibration.

Table 1. Cross-calibration area imaging information of the SCS and MSI

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The mean DN value of the SCS ROIs is statistically obtained; then, by combining the onboard calibration coefficients, the SCS measured reflectance can be obtained, as shown in the curve marked with a symbol in Fig. 7. The top-of-atmosphere spectral reflectance of each region can be obtained through iterative interpolation according to Equations (6–11). The results are shown in Fig. 7, and the solid line in the figure represents the spectral radiance of the continuous entrance pupil obtained by iterative interpolation.

Fig. 7. SCS-measured reflectance of ROIs and spectral reflectance

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The MSI relative spectral response function is convolved with the spectral reflectance in Fig. 7 to obtain the MSI-predicted reflectance, which is taken as the X axis; then, the MSI-measured reflectance obtained by statistics is taken as the Y axis for linear regression. The results are shown in Fig. 8. The slope of the fitting line in the figure is the cross-calibration coefficient, and the intercept is the calibration offset. Table 2 lists the coefficients and offsets of the MSI obtained by linear regression.

Fig. 8. Linear regression results between the measured equivalent reflectance and predicted equivalent reflectance

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Table 2. Cross-calibration results

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4. Validation and discussion

By analyzing and comparing the relative spectral response functions of the MODIS and MSI, bands B10, B4, B1 and B15 of MODIS are selected to validate B2∼B4 and B6 of the MSI. The relative spectral response functions of the corresponding channels are shown in Fig. 9.

Fig. 9. MODIS and MSI spectral response functions for validation

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The image used for cross-validation is shown in Fig. 10. The images in the red solid line frames are the MSI images, the image in the blue dotted line frame is the SCS image, and the wide image is the MODIS image. The spatial resolutions of the MSI, SCS and MODIS are 1 km, 1.1 km and 10 m, respectively. It can be seen that the public area image includes images of different reflectance scenes, such as ocean, cities and farmlands, and cross-calibration results can be validated in a large dynamic range.

Fig. 10. Cross-validation image

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The image is processed according to the flow chart shown in Fig. 5 to obtain 58 ROIs. Figure 11 shows the SBAF calculated according to Eq. (1)4. The X-axis in the figure is the sequence number of ROIs, and the Y-axis is the SBAF. SBAF varies with the surface characteristics.

Fig. 11. SBAF of each band

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The difference between the MSI-measured reflectance and MODIS-calculated reflectance and the difference between the MSI-calculated reflectance and MODIS-calculated reflectance are calculated. The results are shown in Fig. 12. In the figure, the X-axis represents the serial number of ROIs, and the Y-axis represents the absolute value of the difference. It can be seen from the figure that the differences between the MODIS-calculated reflectance and the MSI-calculated reflectance in most cross-verification areas are less than the differences between the MSI-measured reflectance and the MODIS-calculated reflectance, indicating that the MSI- calculated reflectance is closer to the MODIS-calculated reflectance, that is, the cross-calibration has a high reliability.

Fig. 12. Difference between reflectance values

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The RMSRE results are listed in Table 3, where RMSRE-1 represents the RMSRE between the MODIS-calculated reflectance and the MSI-calculated reflectance and RMSRE-2 represents the RMSRE between the MODIS-calculated reflectance and the MSI-measured reflectance. It can be seen in the table that RMSRE-1 is less than RMSRE-2, the mean RMSRE-1 value of each band is 2.16%, and the mean RMSRE-2 value of each band is 3.06%; that is, the MSI-calculated reflectance is closer to the MODIS-calculated reflectance, indicating that using the SCS as the reference sensor can achieve high-precision cross-calibration of the MSI.

Table 3. RMSRE results

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The cross-radiometric calibration of the MSI is thus carried out with the SCS as the reference sensor in this work. The sources of uncertainty mainly include the following:

(1) The essence of cross-calibration is the process by which radiometric standards are transmitted. Therefore, the calibration accuracy of the SCS directly affects the cross-calibration accuracy. Although the SCS can achieve high-precision radiometric calibration by using the solar diffuser calibration system, due to the influence of factors such as radiometric response model errors, stray light in the system, and the calculation accuracy of the diffuser's outgoing radiance, an uncertainty of 3% remains.
(2) Although the interval between the MSI and SCS cross-imaging times is less than 10 min, the change in solar illumination angle, the difference in the remote sensor observation angle and atmospheric stability, and the spatial distribution of the bidirectional reflectance distribution function (BRDF) on the surface all lead to changes in the amount of radiation scattered and absorbed by the atmosphere and the resulting direct and diffuse irradiance. Since the atmospheric parameters at the cross-imaging time cannot be known, the calibration uncertainty caused by these factors cannot be analyzed quantitatively. It can be seen in Table 1 that the observation zenith angles of the two sensors are close, and the solar zenith angles are almost the same, so the calibration uncertainty caused by surface BRDF characteristics and atmospheric instability will not be too large, which can be reasonably considered as 2.0% [37].
(3) Moreover, due to the different illumination and observation angles at the imaging times, the atmospheric radiation transmission path of “Solar → Earth → remote sensor” also differs, so an error arises between the spectral reflectance at the SCS entrance pupil obtained by iterative interpolation and the actual spectral reflectance at the MSI entrance pupil, and this error directly affects the cross-calibration accuracy. The simulation results of these errors identified using the 6S model show that under the data conditions used in this paper, the uncertainty caused by different atmospheric paths shall not exceed 1.5% [42].
(4) Some uncertainty is caused by spatial resampling errors, and the spatial resolution difference between the MSI and SCS is large. Therefore, SCS images must be spatially resampled when spatially matching and selecting ROIs to achieve the goal of unifying the spatial resolution. The cubic spline interpolation method is selected for spatial resampling in this paper, and its accuracy directly determines the difference between the resampled-image DN-value distribution and the actual surface reflectance distribution. The smaller this difference is, the smaller the calibration uncertainty is. Since the cross-calibration method is selected for imaging a large area of uniform ground objects, the spatial resolution difference and the uncertainty introduced by spatial registration are not the main factors affecting the cross-calibration comprehensive uncertainty. The analysis shows that this uncertainty is 1% [43].

Assuming that the error sources are mutually independent, according to the error propagation law, we can concur that the cross-calibration comprehensive uncertainty is the root mean square of the squared sum of all errors. The cross-calibration uncertainty values are listed in Table 4 below.

Table 4. Cross-calibration uncertainty quantification results

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5. Conclusions

In this paper, the hyperspectral remote sensor SCS is used as the reference to perform radiometric cross-calibration of MSI. It is not required that a ground correction field be established, the onboard calibration system be used, or the SBAF be calculated. The proposed cross-calibration method has the characteristics of low calibration cost and high frequency. This method has strict requirements with regard to the spectral parameter settings, relative spectral response function, spatial resolution, imaging time, and spectral matching accuracy. The cross-calibration accuracy greatly depends on the absolute radiometric calibration accuracy of the SCS. First, the cross-calibration method and process are introduced, and the cross-calibration coefficients and offsets of the MSI are obtained by processing the images acquired by two sensors on January 24, 2019. Then, the cross-calibration results are applied to other scene images with different reflectance, and the MSI-calculated reflectance can be obtained. Finally, with MODIS as the reference sensor, the SBAFs between the MODIS and MSI are obtained by processing the ROIs of MODIS, the MSI and the SCS; the RMSRE is calculated between the MODIS and MSI reflectance values to analyze and evaluate the cross-calibration precision. It can be seen from an analysis of the results that the mean RMSRE between the MODIS-calculated reflectance and the MSI-calculated reflectance is 2.16%, while the mean RMSRE between the MODIS-calculated reflectance and the MSI-measured reflectance is 3.05%. The MSI-calculated reflectance is closer to the MODIS-calibrated reflectance. The sources of uncertainty in cross-calibration are analyzed, and the results show that the comprehensive cross-calibration uncertainty is 4.03%, indicating that the cross-calibration results using SCS as the reference sensor have high accuracy and reliability, and SCS can be used as the reference sensor for the cross-calibration of other sensors.

According to this analysis, the uncertainty of the SCS radiometric calibration, radiation transmission path differences, spatial matching, surface BRDF and atmospheric stability are found to be the main factors affecting the cross-calibration accuracy. Therefore, in future work, it will be necessary to optimize the cross-calibration process, quantitative correction of atmospheric radiation transfer and surface BRDF characteristics to improve the cross-calibration accuracy. At the same time, each uncertainty in the calibration process needs to be quantitatively analyzed in combination with different scene images of different dates.

Funding

Hefei Institutes of Physical Science, Chinese Academy of Sciences (E23Y0G46).

Acknowledgments

The authors would like to thank the Editor and anonymous reviewers for their constructive comments and suggestions on this manuscript and the National Satellite Ocean Application Service for providing data support. Finally, we thank the Beijing Institute of Space Mechanics & Electricity for providing the SCS prelaunch test data.

Disclosures

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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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No.	Sensor	Solar angle		View angle
No.	Sensor	Zenith/°	Azimuth/°	Zenith/°	Azimuth/°
1	SCS	62.148	159.477	0.217	291.951
1	MSI	62.329	159.000	10.096	103.217
2	SCS	62.065	159.434	0.217	291.888
2	MSI	62.258	158.932	10.287	110.517
3	SCS	63.920	160.390	0.217	293.312
3	MSI	64.090	159.910	9.808	103.519
4	SCS	63.570	160.211	0.217	293.042
4	MSI	63.739	159.722	9.908	100.885
5	SCS	62.123	159.464	0.217	291.932
5	MSI	62.308	158.998	10.048	103.229
6	SCS	61.253	159.008	0.217	291.270
6	MSI	61.431	158.539	10.175	110.561
7	SCS	61.129	158.943	0.217	291.175
7	MSI	61.317	158.466	10.266	110.451
8	SCS	60.658	158.693	0.217	290.818
8	MSI	60.854	158.202	10.436	110.226
9	SCS	60.535	158.626	0.217	290.725
9	MSI	60.712	158.155	10.289	110.360
10	SCS	60.452	158.582	0.217	290.662
10	MSI	60.641	158.087	10.474	110.161
11	SCS	60.180	158.436	0.217	290.457
11	MSI	60.371	157.935	10.556	110.057
12	SCS	60.122	158.405	0.217	290.413
12	MSI	60.307	157.926	10.412	110.199
13	SCS	58.357	157.436	0.217	289.087
13	MSI	58.437	156.950	10.723	109.747
14	SCS	58.210	157.353	0.217	288.977
14	MSI	58.397	156.869	10.711	109.747
15	SCS	58.152	157.321	0.217	288.934
15	MSI	58.340	156.831	10.754	109.695
16	SCS	57.989	157.229	0.217	288.812
16	MSI	58.193	156.721	10.929	109.518
17	SCS	57.850	157.150	0.217	288.708
17	MSI	58.052	156.671	10.776	109.643
18	SCS	57.556	156.983	0.217	288.489
18	MSI	57.763	156.508	10.798	109.594
19	SCS	55.004	155.472	0.217	286.596
19	MSI	55.209	154.983	11.185	109.049

Band	Slope	Offset	R-square
B1	1.1504	-0.0379	0.9901
B2	1.0811	-0.0161	0.9926
B3	1.0489	-0.0063	0.9938
B4	0.9901	-0.0015	0.9982
B5	0.9776	-0.0002	0.9980
B6	0.9782	0.0004	0.9991
B7	0.9861	-0.0005	0.9994
B8a	0.9760	0.0012	0.9996

MSI band	RMSRE-1/%	RMSRE-2/%
B2	1.75	3.53
B3	2.08	2.43
B4	2.23	3.11
B6	2.58	3.17
Mean	2.16	3.06

Source of uncertainty	Uncertainty (K = 2)
Uncertainty of the SCS radiometric calibration	3.00%
Surface BRDF and atmospheric stability	2.00%
Radiation transmission path differences	1.50%
Spatial matching	1.00%
Comprehensive uncertainty	4.03%

No.	Sensor	Solar angle		View angle
No.	Sensor	Zenith/°	Azimuth/°	Zenith/°	Azimuth/°
1	SCS	62.148	159.477	0.217	291.951
1	MSI	62.329	159.000	10.096	103.217
2	SCS	62.065	159.434	0.217	291.888
2	MSI	62.258	158.932	10.287	110.517
3	SCS	63.920	160.390	0.217	293.312
3	MSI	64.090	159.910	9.808	103.519
4	SCS	63.570	160.211	0.217	293.042
4	MSI	63.739	159.722	9.908	100.885
5	SCS	62.123	159.464	0.217	291.932
5	MSI	62.308	158.998	10.048	103.229
6	SCS	61.253	159.008	0.217	291.270
6	MSI	61.431	158.539	10.175	110.561
7	SCS	61.129	158.943	0.217	291.175
7	MSI	61.317	158.466	10.266	110.451
8	SCS	60.658	158.693	0.217	290.818
8	MSI	60.854	158.202	10.436	110.226
9	SCS	60.535	158.626	0.217	290.725
9	MSI	60.712	158.155	10.289	110.360
10	SCS	60.452	158.582	0.217	290.662
10	MSI	60.641	158.087	10.474	110.161
11	SCS	60.180	158.436	0.217	290.457
11	MSI	60.371	157.935	10.556	110.057
12	SCS	60.122	158.405	0.217	290.413
12	MSI	60.307	157.926	10.412	110.199
13	SCS	58.357	157.436	0.217	289.087
13	MSI	58.437	156.950	10.723	109.747
14	SCS	58.210	157.353	0.217	288.977
14	MSI	58.397	156.869	10.711	109.747
15	SCS	58.152	157.321	0.217	288.934
15	MSI	58.340	156.831	10.754	109.695
16	SCS	57.989	157.229	0.217	288.812
16	MSI	58.193	156.721	10.929	109.518
17	SCS	57.850	157.150	0.217	288.708
17	MSI	58.052	156.671	10.776	109.643
18	SCS	57.556	156.983	0.217	288.489
18	MSI	57.763	156.508	10.798	109.594
19	SCS	55.004	155.472	0.217	286.596
19	MSI	55.209	154.983	11.185	109.049

Radiometric cross-calibration of Sentinel-2B MSI with HY-1C SCS based on the near simultaneous imaging of common ground targets

Abstract

1. Introduction

2. Materials and methods

2.1 Sensor overview

2.2 Calibration theory

2.3 Validation Method

3. Cross-calibration results

4. Validation and discussion

5. Conclusions

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (12)

Tables (4)

Equations (17)

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