rus
Issue #4/2025
P. A. Zashchepka, V. A. Zaitsava, R. V. Fiodartsau
Absolute Error Estimation of the RACE Atmospheric Correction Module Based on Space Images From the Sentinel‑2 Satellites
Absolute Error Estimation of the RACE Atmospheric Correction Module Based on Space Images From the Sentinel‑2 Satellites
DOI: 10.22184/1993-7296.FRos.2025.19.4.312.323
The article discusses two atmospheric correction modules: RACE (A Robust Atmospheric Correction Procedure) and Sen2Cor of the Earth observation satellites “Sentinel‑2” (ESA) (image processing level: L2A) and their quantitative comparison. The RACE module processed 22 Sentinel‑2 scenes with the L1C processing level, various shooting conditions and a wide variety of objects. The average absolute error for all scenes in the derived albedo ranges was estimated for each of the 22 scenes for the B2, B3, B4 and B8 Sentinel‑2 spectral channels. As a result of the RACE absolute error estimation for the spectral channels considered, it was shown that the RACE module was comparable in the albedo determination accuracy at the Earth’s level to the Sen2Cor module.
The article discusses two atmospheric correction modules: RACE (A Robust Atmospheric Correction Procedure) and Sen2Cor of the Earth observation satellites “Sentinel‑2” (ESA) (image processing level: L2A) and their quantitative comparison. The RACE module processed 22 Sentinel‑2 scenes with the L1C processing level, various shooting conditions and a wide variety of objects. The average absolute error for all scenes in the derived albedo ranges was estimated for each of the 22 scenes for the B2, B3, B4 and B8 Sentinel‑2 spectral channels. As a result of the RACE absolute error estimation for the spectral channels considered, it was shown that the RACE module was comparable in the albedo determination accuracy at the Earth’s level to the Sen2Cor module.
Absolute Error Estimation of the RACE Atmospheric Correction Module Based on Space Images From the Sentinel‑2 Satellites
P. A. Zashchepka 1, 2,V. A. Zaitsava 1, R. V. Fiodartsau 2
Peleng JSC, Minsk, Republic of Belarus
Belarusian National Technical University, Minsk, Republic of Belarus
The article discusses two atmospheric correction modules: RACE (A Robust Atmospheric Correction Procedure) and Sen2Cor of the Earth observation satellites “Sentinel‑2” (ESA) (image processing level: L2A) and their quantitative comparison. The RACE module processed 22 Sentinel‑2 scenes with the L1C processing level, various shooting conditions and a wide variety of objects. The average absolute error for all scenes in the derived albedo ranges was estimated for each of the 22 scenes for the B2, B3, B4 and B8 Sentinel‑2 spectral channels. As a result of the RACE absolute error estimation for the spectral channels considered, it was shown that the RACE module was comparable in the albedo determination accuracy at the Earth’s level to the Sen2Cor module.
Keywords: Earth’s remote sensing, albedo, scenes, atmospheric correction, absolute error, spectral luminance factors
Article received:17.04.2025
Article accepted:16.05.2025
INTRODUCTION
At the upper atmosphere boundary, radiation is generated both due to reflection from the earth’s surface and due to the atmospheric scattering and absorption [1]. The radiation absorption and scattering in the atmosphere are caused by the interaction of light with gas molecules, water vapor, aerosols, and other particles available in the atmosphere. In order to convert the albedo values at the upper atmosphere boundary to the albedo values at the Earth’s surface, it is necessary to perform atmospheric correction (AC) of the target information (TI) [2].
The AC algorithms used to process the Earth’s remote sensing data from space can be divided into two groups: empirical and based on a physical model [3]. The algorithms based on a physical model reconstruct the albedo of natural objects at the Earth level with due regard to the radiation absorption and scattering by atmospheric gases, aerosols and clouds, depending on the latitude and seasonal model of the atmosphere. In such AC algorithms, some variables are relatively stable, while others are more changeable. The most stable variables shall include the Rayleigh scattering [4], as well as temperature, pressure and gas content in the atmosphere [5]. The most variable parameters are the aerosol optical thickness (AOT) and the water vapor concentration.
COMPARABLE METHODS
OF ATMOSPHERIC CORRECTION
The aim of the study was the absolute error estimation of the albedo recovery by the RACE AC module (A Robust Atmospheric Correction Procedure), developed Institute of Physics of the Belarus National Academy of Sciences [6]. The RACE module uses the measurement results obtained in space to determine any atmospheric parameters and recover albedo at the Earth’s level for the spectral range of 0.4–1.0 μm.
In this paper, the RACE module was tested using the L1C processing level data from the Sentinel‑2 satellites. The obtained albedo values at the Earth’s level were compared with the L2A processing level data provided after using the specialized Sen2Cor AC module [7].
The Sen2Cor module applies algorithms based on the radiation transfer model that allows for the factors such as air humidity and aerosol content, cloudiness and other atmospheric conditions to be considered. One of the features of this module is its strict compliance with the ESA (The European Space Agency) standards and recommendations for satellite data processing that contributes to the higher quality processing and the reduced absolute error in determining the Earth’s albedo that does not exceed 0.04 [8].
RACE ATMOSPHERIC CORRECTION MODULE
To test the RACE module, the images from the B3, B7, B8a and B11 channels with an original resolution of 10 and 20 m were scaled to a resolution of 60 m (Table 1). The images with a resolution of 60 m were used to determine the atmospheric parameters, snow and cloud masks, and the images with a resolution of 10 m were used to obtain the albedo at the Earth’s level.
The input parameters of the RACE algorithm were adjusted based on the spectral response characteristics of the Sentinel‑2 satellite channels.
The RACE module uses a latitude-seasonal model of the atmosphere that consists of several layers: the troposphere layer (about 2–3 km) and the stratosphere layer with the upper and middle part of the troposphere (above 3 km). In addition to the atmosphere, a vertical aerosol model is applied, where the lower and middle troposphere layers are determined by the Continental model, and the upper troposphere with the stratosphere uses the H2SO4 aerosol model [6]. During the calculation process of radiative properties, the efficient RAY code is used [9].
When testing the RACE module using the Sentinel‑2 satellite images, some individual latitude-seasonal atmospheric models, solar angles and shooting angles were applied for each scene.
After generation of the atmosphere and aerosol models, a pixel-by-pixel mask of the clouds and snow is formed. The criterion [6] was used to detect any clouds and snow:
RTOA(B1) − Rmol(B1) > 0.2,
where RTOA is the albedo at the top of the atmosphere (TOA), Rmol is the contribution of the molecular gas atmosphere to the TOA.
To separate snow from clouds, the NDSI index [10] was used:
NDSI = ≥ 0.8. (10)
The criterion RTOA(B10) > 0,2 was used to identify the cirrus clouds.
To determine any water vapor in the atmosphere, an iterative water determination scheme at a wavelength of 945 nm with a reference signal of 865 nm was applied [6].
After determining the water vapor concentration, the AOT value was calculated. The AOT determination algorithm uses a single-wave calculation method with due regard to the measurement results in only one shortest-wave channel. After determining the AOT value using a fixed aerosol model, the AOT was calculated at a wavelength of 550 nm [6].
The final program result was a set of parameters for recalculation from the albedo units at the upper atmosphere boundary to the albedo of the Earth’s surface for the B2, B3, B4 and B8 channels [6].
ABSOLUTE error ESTIMATION
FOR ONE SCENE
The verification steps are demonstrated below using the example of a La Crau scene (shooting date: September 11, 2022). It contains a lot of various objects: greenery, city, water, and sand. Fig. 1 shows color images of the scene obtained based on the data at the upper atmosphere boundary L1C (a), based on the data after processing by Sen2Cor L2A (b) and after processing by the RACE module (c).
The albedo distribution histograms for the B2, B3, B4 and B8 channels at the upper atmosphere boundary (processing level L1C) and at the Earth’s level (L2A and RACE) are shown in Fig. 2.
It is shown on the color images in Fig. 1 and the histogram for channel B2 in Fig. 2 that there is a shift in the scene gamma without any atmospheric correction towards a higher albedo and regular coordination between the adjusted albedo distribution using two AC methods.
To obtain the quantitative estimates for the comparison of AC methods, the calculation of the RACE absolute error relative to Sen2Cor was used as the delta frame value [11]:
∆ρi,j = ρrace i, j − ρsent i, j,
where ρrace i, j – an albedo obtained after processing by the RACE AC module; ρsent i, j – an albedo obtained after processing by the Sen2Cor AC module (the albedo values are taken as a standard); i and j are the row and column numbers of the image, respectively.
After the ∆ρ determination process, the error matrix was converted into the value vector and a pixel-by-pixel dependence of the RACE albedo accuracy on the Sen2Cor albedo value was prepared (Fig.3).
To simplify further analysis, the entire albedo range from 0 to 1.0 was divided into 10 equal subranges with an increment of 0.10. For each of them, the following values were calculated [12]
average value: ∆ρmean = Σ ∆ρi,
where n is the number of points within the range;
standard deviation:
∆ρσ = ;
weight of average error: w = ,
where N is the number of all analyzed points in the frame.
The calculation results for the La Crau scene for the analyzed channels in the established ranges are given in Table 2.
According to Table 2, the scatter charts of absolute accuracies were prepared for the B2, B3, B4 and B8 channels for the La Crau scene (Fig. 4). In the case of analyzing one scene, the weights w are not used in the calculation and are indicated on the chart as a histogram (for information purposes).
For this scene, there is a nearly linear dependence of the absolute error for each channel. It can be seen that with an increase in the reference albedo value, there is a decrease in the RACE convergence relative to Sen2Cor.
EVALUATION
OF TOTAL ABSOLUTE error
According to the comparison sequence presented above, 22 scenes obtained from satellites of the family were processed. Sentinel –2 with different shooting conditions and a wide variety of objects. Table 3 shows the names of the analyzed places, their geographic coordinates and the date of shooting.
As an illustrative example of the diversity of the objects analyzed, Fig. 5 shows a scene of Antarctica with a combination of water, snow and ice.
After calculating the average values, root-mean-square deviations and absolute error weights in the derived ranges for all 22 scenes, the weighted averaging of all parameters in these same ranges was performed. For each subrange, the following values were calculated [13]
averaged mean value for all scenes:
∆ρ =,
where M is the number of scenes analyzed;
average root-mean-square deviation for all scenes:
∆ρ = ;
average weight across all scenes: wall = .
The calculation results for the average values of absolute RACE accuracies for all scenes are given in Table 4.
For each channel, a relevant scatter chart is made indicating the relevant weighting coefficients in the form of a histogram (Figure 6).
According to the source data [8], the absolute error of retrieving ground reflectivity by the Sen2Cor method relative to the ground measurements within the albedo range from 0.0 to 0.5 does not exceed the average value ∆ρsent / ground = 0.02–0.04. When comparing the analyzed methods, the absolute error of the RACE AC method relative to Sen2Cor in the same albedo range (Table 4) does not exceed the average absolute value of the error ∆ρrace / sent = 0.015. Therefore, it is possible to confirm comparability of the Sen2Cor and RACE methods.
CONCLUSION
When comparing the RACE and Sen2Cor AC methods, 22 scenes obtained by the Sentinel‑2 satellites with the L1C processing level using the RACE method were processed, including a wide variety of objects, and their convergence was verified in four spectral channels B2, B3, B4 and B8 with a resolution of 10 meters. As a result of this analysis, the following data was obtained:
for the channel B2, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.005 and root-mean-square deviation ±0.011;
for the channel B3, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.001 and root-mean-square deviation ±0.011;
for the channel B4, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.003 and root-mean-square deviation ±0.011;
for the channel B8, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.005 and root-mean-square deviation ±0.011,
The completed analysis showed that the RACE AC module under consideration is comparable in the albedo determination accuracy at the Earth’s level to the Sen2Cor AC method, that is, it is comparable to the Sen2Cor module.
AUTHORS
Zashchepka Petr Aleksandrovich, e-mail: 1zashchepko@mail.ru, 2nd category research engineer, Peleng JSC, master’s student, Belarusian National Technical University, Minsk, Republic of Belarus.
ORCID ID: 0009-0004-1901-2818
Zaitsava Valiantsina Afanasievna, e-mail: zaitseva53@inbox.ru, leading research engineer, PhD in Physics and Mathematics, Peleng JSC, Minsk, Republic of Belarus.
Fiodartsau Rostsislau Valerievich, e-mail: feodrw@gmail.com, PhD in Technical Sciences, head of the Department of Process Equipment, Associate Professor, Belarusian National Technical University, Minsk, Republic of Belarus.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
P. A. Zashchepka 1, 2,V. A. Zaitsava 1, R. V. Fiodartsau 2
Peleng JSC, Minsk, Republic of Belarus
Belarusian National Technical University, Minsk, Republic of Belarus
The article discusses two atmospheric correction modules: RACE (A Robust Atmospheric Correction Procedure) and Sen2Cor of the Earth observation satellites “Sentinel‑2” (ESA) (image processing level: L2A) and their quantitative comparison. The RACE module processed 22 Sentinel‑2 scenes with the L1C processing level, various shooting conditions and a wide variety of objects. The average absolute error for all scenes in the derived albedo ranges was estimated for each of the 22 scenes for the B2, B3, B4 and B8 Sentinel‑2 spectral channels. As a result of the RACE absolute error estimation for the spectral channels considered, it was shown that the RACE module was comparable in the albedo determination accuracy at the Earth’s level to the Sen2Cor module.
Keywords: Earth’s remote sensing, albedo, scenes, atmospheric correction, absolute error, spectral luminance factors
Article received:17.04.2025
Article accepted:16.05.2025
INTRODUCTION
At the upper atmosphere boundary, radiation is generated both due to reflection from the earth’s surface and due to the atmospheric scattering and absorption [1]. The radiation absorption and scattering in the atmosphere are caused by the interaction of light with gas molecules, water vapor, aerosols, and other particles available in the atmosphere. In order to convert the albedo values at the upper atmosphere boundary to the albedo values at the Earth’s surface, it is necessary to perform atmospheric correction (AC) of the target information (TI) [2].
The AC algorithms used to process the Earth’s remote sensing data from space can be divided into two groups: empirical and based on a physical model [3]. The algorithms based on a physical model reconstruct the albedo of natural objects at the Earth level with due regard to the radiation absorption and scattering by atmospheric gases, aerosols and clouds, depending on the latitude and seasonal model of the atmosphere. In such AC algorithms, some variables are relatively stable, while others are more changeable. The most stable variables shall include the Rayleigh scattering [4], as well as temperature, pressure and gas content in the atmosphere [5]. The most variable parameters are the aerosol optical thickness (AOT) and the water vapor concentration.
COMPARABLE METHODS
OF ATMOSPHERIC CORRECTION
The aim of the study was the absolute error estimation of the albedo recovery by the RACE AC module (A Robust Atmospheric Correction Procedure), developed Institute of Physics of the Belarus National Academy of Sciences [6]. The RACE module uses the measurement results obtained in space to determine any atmospheric parameters and recover albedo at the Earth’s level for the spectral range of 0.4–1.0 μm.
In this paper, the RACE module was tested using the L1C processing level data from the Sentinel‑2 satellites. The obtained albedo values at the Earth’s level were compared with the L2A processing level data provided after using the specialized Sen2Cor AC module [7].
The Sen2Cor module applies algorithms based on the radiation transfer model that allows for the factors such as air humidity and aerosol content, cloudiness and other atmospheric conditions to be considered. One of the features of this module is its strict compliance with the ESA (The European Space Agency) standards and recommendations for satellite data processing that contributes to the higher quality processing and the reduced absolute error in determining the Earth’s albedo that does not exceed 0.04 [8].
RACE ATMOSPHERIC CORRECTION MODULE
To test the RACE module, the images from the B3, B7, B8a and B11 channels with an original resolution of 10 and 20 m were scaled to a resolution of 60 m (Table 1). The images with a resolution of 60 m were used to determine the atmospheric parameters, snow and cloud masks, and the images with a resolution of 10 m were used to obtain the albedo at the Earth’s level.
The input parameters of the RACE algorithm were adjusted based on the spectral response characteristics of the Sentinel‑2 satellite channels.
The RACE module uses a latitude-seasonal model of the atmosphere that consists of several layers: the troposphere layer (about 2–3 km) and the stratosphere layer with the upper and middle part of the troposphere (above 3 km). In addition to the atmosphere, a vertical aerosol model is applied, where the lower and middle troposphere layers are determined by the Continental model, and the upper troposphere with the stratosphere uses the H2SO4 aerosol model [6]. During the calculation process of radiative properties, the efficient RAY code is used [9].
When testing the RACE module using the Sentinel‑2 satellite images, some individual latitude-seasonal atmospheric models, solar angles and shooting angles were applied for each scene.
After generation of the atmosphere and aerosol models, a pixel-by-pixel mask of the clouds and snow is formed. The criterion [6] was used to detect any clouds and snow:
RTOA(B1) − Rmol(B1) > 0.2,
where RTOA is the albedo at the top of the atmosphere (TOA), Rmol is the contribution of the molecular gas atmosphere to the TOA.
To separate snow from clouds, the NDSI index [10] was used:
NDSI = ≥ 0.8. (10)
The criterion RTOA(B10) > 0,2 was used to identify the cirrus clouds.
To determine any water vapor in the atmosphere, an iterative water determination scheme at a wavelength of 945 nm with a reference signal of 865 nm was applied [6].
After determining the water vapor concentration, the AOT value was calculated. The AOT determination algorithm uses a single-wave calculation method with due regard to the measurement results in only one shortest-wave channel. After determining the AOT value using a fixed aerosol model, the AOT was calculated at a wavelength of 550 nm [6].
The final program result was a set of parameters for recalculation from the albedo units at the upper atmosphere boundary to the albedo of the Earth’s surface for the B2, B3, B4 and B8 channels [6].
ABSOLUTE error ESTIMATION
FOR ONE SCENE
The verification steps are demonstrated below using the example of a La Crau scene (shooting date: September 11, 2022). It contains a lot of various objects: greenery, city, water, and sand. Fig. 1 shows color images of the scene obtained based on the data at the upper atmosphere boundary L1C (a), based on the data after processing by Sen2Cor L2A (b) and after processing by the RACE module (c).
The albedo distribution histograms for the B2, B3, B4 and B8 channels at the upper atmosphere boundary (processing level L1C) and at the Earth’s level (L2A and RACE) are shown in Fig. 2.
It is shown on the color images in Fig. 1 and the histogram for channel B2 in Fig. 2 that there is a shift in the scene gamma without any atmospheric correction towards a higher albedo and regular coordination between the adjusted albedo distribution using two AC methods.
To obtain the quantitative estimates for the comparison of AC methods, the calculation of the RACE absolute error relative to Sen2Cor was used as the delta frame value [11]:
∆ρi,j = ρrace i, j − ρsent i, j,
where ρrace i, j – an albedo obtained after processing by the RACE AC module; ρsent i, j – an albedo obtained after processing by the Sen2Cor AC module (the albedo values are taken as a standard); i and j are the row and column numbers of the image, respectively.
After the ∆ρ determination process, the error matrix was converted into the value vector and a pixel-by-pixel dependence of the RACE albedo accuracy on the Sen2Cor albedo value was prepared (Fig.3).
To simplify further analysis, the entire albedo range from 0 to 1.0 was divided into 10 equal subranges with an increment of 0.10. For each of them, the following values were calculated [12]
average value: ∆ρmean = Σ ∆ρi,
where n is the number of points within the range;
standard deviation:
∆ρσ = ;
weight of average error: w = ,
where N is the number of all analyzed points in the frame.
The calculation results for the La Crau scene for the analyzed channels in the established ranges are given in Table 2.
According to Table 2, the scatter charts of absolute accuracies were prepared for the B2, B3, B4 and B8 channels for the La Crau scene (Fig. 4). In the case of analyzing one scene, the weights w are not used in the calculation and are indicated on the chart as a histogram (for information purposes).
For this scene, there is a nearly linear dependence of the absolute error for each channel. It can be seen that with an increase in the reference albedo value, there is a decrease in the RACE convergence relative to Sen2Cor.
EVALUATION
OF TOTAL ABSOLUTE error
According to the comparison sequence presented above, 22 scenes obtained from satellites of the family were processed. Sentinel –2 with different shooting conditions and a wide variety of objects. Table 3 shows the names of the analyzed places, their geographic coordinates and the date of shooting.
As an illustrative example of the diversity of the objects analyzed, Fig. 5 shows a scene of Antarctica with a combination of water, snow and ice.
After calculating the average values, root-mean-square deviations and absolute error weights in the derived ranges for all 22 scenes, the weighted averaging of all parameters in these same ranges was performed. For each subrange, the following values were calculated [13]
averaged mean value for all scenes:
∆ρ =,
where M is the number of scenes analyzed;
average root-mean-square deviation for all scenes:
∆ρ = ;
average weight across all scenes: wall = .
The calculation results for the average values of absolute RACE accuracies for all scenes are given in Table 4.
For each channel, a relevant scatter chart is made indicating the relevant weighting coefficients in the form of a histogram (Figure 6).
According to the source data [8], the absolute error of retrieving ground reflectivity by the Sen2Cor method relative to the ground measurements within the albedo range from 0.0 to 0.5 does not exceed the average value ∆ρsent / ground = 0.02–0.04. When comparing the analyzed methods, the absolute error of the RACE AC method relative to Sen2Cor in the same albedo range (Table 4) does not exceed the average absolute value of the error ∆ρrace / sent = 0.015. Therefore, it is possible to confirm comparability of the Sen2Cor and RACE methods.
CONCLUSION
When comparing the RACE and Sen2Cor AC methods, 22 scenes obtained by the Sentinel‑2 satellites with the L1C processing level using the RACE method were processed, including a wide variety of objects, and their convergence was verified in four spectral channels B2, B3, B4 and B8 with a resolution of 10 meters. As a result of this analysis, the following data was obtained:
for the channel B2, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.005 and root-mean-square deviation ±0.011;
for the channel B3, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.001 and root-mean-square deviation ±0.011;
for the channel B4, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.003 and root-mean-square deviation ±0.011;
for the channel B8, the averaged results in the efficient albedo range from 0.0 to 1.0: absolute mean error −0.005 and root-mean-square deviation ±0.011,
The completed analysis showed that the RACE AC module under consideration is comparable in the albedo determination accuracy at the Earth’s level to the Sen2Cor AC method, that is, it is comparable to the Sen2Cor module.
AUTHORS
Zashchepka Petr Aleksandrovich, e-mail: 1zashchepko@mail.ru, 2nd category research engineer, Peleng JSC, master’s student, Belarusian National Technical University, Minsk, Republic of Belarus.
ORCID ID: 0009-0004-1901-2818
Zaitsava Valiantsina Afanasievna, e-mail: zaitseva53@inbox.ru, leading research engineer, PhD in Physics and Mathematics, Peleng JSC, Minsk, Republic of Belarus.
Fiodartsau Rostsislau Valerievich, e-mail: feodrw@gmail.com, PhD in Technical Sciences, head of the Department of Process Equipment, Associate Professor, Belarusian National Technical University, Minsk, Republic of Belarus.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
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