The Assessment of Cross Calibration/Validation Accuracy for KOMPSAT-3 Using Landsat 8 and 6S

Abstract

In this study, we performed cross calibration of KOMPSAT-3 AEISS imaging sensor with reference to normalized pixels in the Landsat 8 OLI scenes of homogenous ROI recorded by both sensors between January 2014 and December 2019 at the Libya 4 PICS. Cross calibration is using images from a stable and well-calibrated satellite sensor as references to harmonize measurements from other sensors and/or characterize other sensors. But cross calibration has two problems; RSR and temporal difference. The RSR of KOMPSAT-3 and Landsat 8 are similar at the blue and green bands. But the red and NIR bands have a large difference. So we calculate SBAF of each sensor. We compared the SBAF estimated from the TOA Radiance simulation with KOMPSAT-3 and Landsat 8, the results displayed a difference of about 2.07~2.92% and 0.96~1.21% in the VIS and NIR bands. Before SBAF, Reflectance and Radiance difference was 0.42~23.23%. Case of difference temporal, we simulated by 6S and Landsat 8 for alignment the same acquisition time. The SBAF-corrected cross calibration coefficients using KOMPSAT-3, 6S and simulated Landsat 8 compared to the initial cross calibration without correction demonstrated a percentage difference in the spectral bands of about 0.866~1.192%. KOMPSAT-3 maximum uncertainty was estimated at 3.26~3.89%; errors due to atmospheric condition minimized to less than 1% (via 6S); Maximum deviation of KOMPSAT-3 DN was less than 1%. As the result, the results affirm that SBAF and 6s simulation enhanced cross-calibration accuracy.

1. Introduction

In general, the vicarious calibration is difficult next reason; cost, labor, spatial coverage and other factors. To overcome these limitations, approached cross calibration method and this has been successfully used for other satellite instruments (Teillet et al., 2001, Dinguirard et al., 1999). Cross calibration is important for a common radiometric scale from different sensors. One of method use a well calibrated sensor as a radiometer to achieve characterization of other sensors (Chander et al., 2013). And it can be improved accuracy through an additional calibration known as vicarious calibration needs to be applied (Concha et al., 2019).

However, their bands may have different Relative Spectral Response (RSR) (Chander et al., 2010). Not all satellites have the same color filter transmittance and sensor reactivity, even though their purpose is to observe visible bands. Therefore, the differences in RSR should be corrected. For the exactly cross calibration between two sensors, needs to be resolved the uncertainty arising from their RSR differences. If a change in RSR of the sensor is suspected, the best that can be done is to compare the changes in response to the various onboard calibrators (Barsi et al., 2014). But KOMPSAT-3 has not onboard calibrators.

Thus, there is need for the Spectral Band Adjustment Factor (SBAF) as an important tool to reduce the cross calibration uncertainties that the spectral differences between bands of the multispectral sensors. The purpose of this paper is to produce consistent band calibration coefficients that allow calibration of KOMPSAT-3 DN (Digital Number) to values with physical units. Conversion to a sensor spectral radiance and top of atmosphere (TOA) reflectance are fundamental steps in comparing products from different sensors. The main contributions of this study are as follows:

KOMPSAT-3 and Landsat 8 has the differences of RSR and day & time between each other, we applied the SBAF using KOMPSAT-3 and Simulated Landsat 8. Cross Calibration was performed using the KOMPSAT-3, Second Simulation of the Satellite Signal in the Solar Spectrum (6S) and Landsat 8 images obtained in Libya 4 Pseudo Invariant Calibration Site (PICS). And we validate SBAF and each calibration coefficients between Initial Calibration Coefficient, Simulated Landsat 8 and calculated by 6S.

2. Study area and data used

1) Sensor overview

The sensors used for the current calibration studies include KOMPSAT-3 Advanced Earth Imaging Sensor System (AEISS) and Landsat 8 Operational Land Imager(OLI). Landsat 8 integrity is well known in the remote sensing user community and continues to be very stable since launch (Markham et al., 2004). Table 1 lists the specifications of the KOMPSAT-3 AEISS and Landsat 8 OLI. For clarity the bands considered in this paper are named Blue, Green, Red, and Near Infra Red (NIR).

Table 1. Schematic of Sensors used in this study

KOMPSAT-3 is an optical high resolution Korean observation mission of the Korea Aerospace Research Institute (KARI). The mission is funded by Korea Ministry of Education, Science and Technology (KMEST) and launched on May 18 2012. It has pan and visible and near infrared (VNIR) multispectral such as a 15 km swath width, a 2.8 m (Multi), 0.7 m (Pan) Ground Instantaneous Field Of View (GIFOV) for the multispectral and the panchromatic band.

Landsat 8 is the latest platform in the 40 year Landsat series of satellites from February 11 2013. The VNIR bands retain many of the characteristics of previous Landsat sensors, such as a 185 km swath width, a 30 m and 15 m GIFOV for the multispectral and panchromatic band. The sensor changed from a whiskbroom (ETM+) to a pushbroom(Irons et al., 2012).

2) Relative spectral response at the KOMPSAT-3 and Landsat 8

The RSR is important step for the data calibration. Despite numerous efforts, the results often vary among different investigators by RSR (Masonis et al., 2001). Accurate calibration requires continuous monitoring of the gain and offset due to degradation of sensor sensitivity with time (Tahnk et al., 2001). It is commonly agreed that for satellite sensors lacking onboard calibration in solar spectrum, the total relative uncertainties of calibration are within 5% (Rossow et al., 1999). An essential part of this uncertainty is related to the effect of RSR function, when it is not accounted for properly during vicarious calibration or sensor inter calibration (Teillet et al., 2001).

Fig. 1 shows the band average RSR of KOMPSAT-3 AEISS and Landsat 8 OLI. In general, Landsat 8 OLI bands are narrower than the KOMPSAT-3 bands because the Landsat 8 OLI band edges have been refined to avoid atmospheric absorption features. The Landsat 8 OLI NIR band is substantially narrower, and so avoids the water vapor absorption feature at approximately 825, 940 nm. These NIR RSR differences mean that even when both sensors are observing the similar band of the electromagnetic spectrum at the same time, they may detect different radiance values depending on the RSR of the target.

Fig. 1. Relative spectral response of Sensors.

3) Image selection

All cloud free images over the Libya 4 PICS were selected since the launch of the KOMPSAT-3, (http:// arirang.kari.re.kr/ISIS/map/map.jsp). Moreover, all of the available Landsat 8 OLI (path 181 row 40) data were downloaded via EarthExplorer (http://earthexplorer. usgs.gov) as a reference for the cross calibration of KOMPSAT-3. The two sensors have different overpass times, only clear scenes observed by each sensor were employed. All images from both sensors, beginning January 2014 until the end of December 2019, were searched and 121 (KOMPSAT-3) and 154 (Landsat 8) were selected.

PICS based calibration methods have been used over and over again by numerous researchers (Cosnefroy et al., 1996; Helder et al., 2010; Angal et al., 2013; Cao et al., 2008; Smith et al., 2002). A host of PICS have been recommended by Committee on Earth Observation Satellites (CEOS) and these stable sites have been used extensively to monitor the post launch temporal stability of optical satellite sensors, and for cross calibration and inter comparison purposes (Lacherade et al., 2013; Govaerts et al., 2012; Mishra et al., 2014; Helder et al., 2013).

Libya 4 PICS is a high reflectance site located in the Desert in Africa at coordinates +28.55°N and +23.39°E and at an elevation of 118 m above sea level. It is referenced in the worldwide reference system 2 with path 181 and row 40. Libya 4 PICS is named as opposed to Libya because of the presence of other PICS in Libya. The PICS was referenced in and considered by the Centre National d’Études Spatiales to be one of the best sites, based on long term trending of North African and Arabian sites.

In this study, cross calibration was conducted using the KOMPSAT-3 AEISS with reference to the Landsat 8, which performs radiometric CAL/VAL by an onboard calibrator. Each Region of interest (ROI) for cross calibration was selected to be homogenous, with a size of about 9 × 9 km; and to match in the spatial resolution of 30 m between KOMPSAT-3 and Landsat 8 images (Fig. 2).

Fig. 2. KOMPSAT-3 and Landsat 8 at Libya 4 PICS.

3. Method overview

In this study, we performed a sensor radiometric calibration based on earth scenes imaged inflight, which is a useful method when an onboard calibrator is not available and lunar calibration is not feasible. The radiometric CAL/VAL consisted of four stages: (a) 6S simulated by K3 and L8 in day and time (b) SBAF calculated by KOMPSAT-3 and Simulated Landsat 8 (c) SBAF with Landsat 8 and simulated K3 (d) Cross calibration with KOMPSAT-3 and Simulated Landsat 8 with SBAF

1) Conversion top of atmosphere radiance and reflectance image

Results of both radiance and reflectance based cross calibration will be presented in this paper. Standard Landsat 8 OLI products are rescaled to TOA spectral reflectance and TOA spectral radiance using the radiometric rescaling coefficients provided in the product metadata (MTL) file.

There was a change to TOA Radiance referring to the result of vicarious calibration conducted (Kim et al., 2015) and since there is no on board calibration for KOMPSAT-3, the usual formula expected to be a linear correlation between a sensor’s DN and radiance is as follows:

L_λ= gain × DN + offset

L_λis Band average spectral radiance predicted at the sensor, gainis Change in radiance as a function of DN, offsetis DNvalue where zero radiance is detected

Landsat 8 OLI image data can be converted to TOA radiance using a conversion equation given as:

L_λ= M_L· Q_cal+ A_L

L_λ= Spectral Radiance, M_L= Radiance multiplicative scaling factor for the band, A_L= Radiance additive scaling factor for the band, Q_cal= L1 pixel value in DN

A point of note here is that, a similar equation for radiance conversion is also applicable to KOMPSAT-3.

At the sensor or TOA reflectance is used to reduce illumination differences among images and to normalize for solar irradiance; because atmospheric effects and surface topographic effects are not corrected, such as the Earth’s surface and atmospheric reflectance. When comparing the radiometric quality obtained from the other sensors, the effect of SZA due to the differences in time in obtaining materials could be removed if TOA reflectance was used instead of the TOA radiance. The equation to calculate the TOA Reflectance (p_λ) of KOMPSAT-3 is as follows:

\(p_{\lambda}=\frac{\pi \cdot L_{\lambda} \cdot d^{2}}{E S U N_{\lambda} \cdot \cos \theta_{s}}\)

p_λ= Planetary reflectance, L_λ= Spectral radiance at the sensor aperture, ESUN_λ= Band dependent mean solar exoatmospheric irradiance, θ_s= SZA (radians), d²= Earth sun distance (astronomical units)

Landsat 8 OLI image data can be converted to TOA reflectance using equation given as:

\(p_{\lambda}^{\prime}=M_{p} \cdot Q_{c a l} \cdot A_{p}, \quad p_{\lambda}=\frac{p_{\lambda}^{\prime}}{\cos \theta_{s}}\)

p_λ′= TOA Planetary Spectral Reflectance, without correction for solar angle, M_p= Reflectance multiplicative scaling factor for the band, A_p= Reflectance additive scaling factor for the band L1 pixel value in DN, p_λ= TOA Planetary Reflectance, θ_s= Solar Elevation Angle(Radians)

2) Spectral band adjustment factor: SBAF

Every satellite because of different applications and technological developments has a different RSR. Thus, even for the spectral bands designed to look at the same region of the electromagnetic (EM) spectrum, sensor response can be substantially different because their analogous bands may have different RSR. The state of the art electro optical sensors being used for today’s cross calibration applications require more complete characterization of the spectral band differences to permit increasingly smaller cross calibration possibilities; particularly in the cross calibration of sensors whose RSR are not directly comparable. The differences in spectral responses between two sensors can cause a systematic band offset during cross calibration because the sensors respond differently to the same EM source.

Thus, for accurate cross calibration between these two sensors, the uncertainty arising from their RSR differences needs to be resolved.

A compensation for differences in spectral response functions can be made after having some prior knowledge of the spectral signature of the ground during the overpass time. This compensation factor used to compensate for the spectral band differences is known as SBAF. The intrinsic offsets between two sensors caused by RSR mismatches can be compensated by using a target specific SBAF, which takes into account the spectral profile of the target and the RSR of each sensor.

Although the sensor measures the spectral radiance reaching the sensor, a reduction in image to image variability can be achieved by converting the at sensor spectral radiance to exoatmospheric TOA reflectance.

In this study, we used the KOMPSAT-3, 6S and Landsat 8 for SBAF at the Libya 4 PICS. Although the SBAF is discussed in this section, readers are directed elsewhere for detailed mathematical expressions. The SBAF can be calculated using the following formula by utilizing the integral values of the RSR (Kaewmanee et al. 2012):

\(S B A F=\frac{\bar{L}_{\lambda}(A)}{\bar{L}_{\lambda}(B)} \quad \bar{L}_{\lambda}\left(A^{*}\right)=\frac{\bar{L}_{\lambda}(A)}{S B A F}\)

\(\overline{L}_{\lambda }^{}(A)\) = the simulated TOA radiance or reflectance for sensor A, \(\overline{L}_{\lambda }^{}(B)\) = the simulated TOA radiance or reflectance for sensor B, \(\overline{L}_{\lambda }^{}(A^{*})\) = compensated TOA radiance or reflectance for sensor A when using the SBAF to match sensor B

3) Cross calibration

Geometrically, a feature observed by these sensors will be represented by slightly different numbers of image pixels because of the differences in viewing geometry and sensor scanning times. This makes it very difficult to establish sufficient geometric control to facilitate radiometric comparisons on a point by point and/or detector by detector basis. Therefore, the analysis approach made use of image statistics based on large areas in common between the image pairs

These large area, hereafter ROI were carefully selected using distinct features common to both of the images. Both bright and dark regions were selected to obtain maximum coverage over each sensor’s dynamic range. KOMPSAT-3 and Landsat 8 image pairs can be geometrically registered, but that involves resampling. For this particular study, any kind of resampling was avoided to obtain the highest radiometric accuracy without corrupting the pixels due to resampling. The use of ROI common to both the KOMPSAT-3 and Landsat 8 image data successfully avoids radiometric effects due to residual image miss-registration.

The mean target statistics obtained from the ROI were converted to radiance and reflectance. Cross calibration results were tested for a slope value of 1.0 (corresponding to exact agreement in radiances between the two sensors) at a 1% significance level after fitting a regression line to data from the common ROI. The regression lines were determined for data within each band, as was an overall regression combining all data points from all bands.

4. Results

1) Radiance accuracy assessment for a calibration coefficient using 6S and simulated Landsat 8

KOMPSAT-3 and Landsat 8 has a difference of 2~3 hours in overpass time because of local time pass time and difference in orbit of satellite. These facts lead to lots of problems in Cross Calibration. Changes of geometric characteristics of the Sun can be assumed by changing Sun Zenith angle in day hours. This problem can be solved by 6S every day. 6S (Second Simulation of a Satellite Signal in the Solar Spectrum version 1) is an advanced radiative transfer code designed to simulate the reflection of solar radiation.

So, we simulated 108, 702 times radiance and reflectance at Libya 4 PICS (28.961°N, 23.796°E) by 183days (2 day interval), 11:31:07 UT (KOMPSAT3 average pass time), 11:55:06 UT (Landsat 8 average pass time), 11 tilt angle (-30, -24, -18, -12, -6, 0, 6, 12, 18, 24, 30 deg), 3 water vapor (2.1, 2.8, 3.5 g/cm²), 3 ozone (0.28, 0.31, 0.34 g/m³), visibility(20, 30, 40 km).

Simulation by 6S and KOMPSAT-3 of TOA Radiance in Libya 4 PICS for 6 years was conducted to presume DN of KOMPSAT-3 using the geometric characteristics of the SZA based on the result of Fig. 3.

Fig. 3. The TOA Radiance trend in Libya 4 PICS by 6S (a) and KOMPSAT-3 (b), (X: day, Y: Radiance (B, G, R, N (W · sr^-1· m^-2· μm^-1), Sun Zenith Angle (deg)).

Usually, for differences caused by SZA and SAA, as demonstrated by Table 3. However, as a result of normalization for data measured in clear days, there was a difference in the period of high solar altitude and low altitude. The SZA and the measured radiance were analyzed by linear regression equation to overcome the difference. As a result, there was a high correlation (R² 0.99), and based on this, the Simulated TOA Radiance by AIR MASS was estimated referring to shooting location, SZA depending on time.

Table 3. The accuracy statistics of TOA Radiance at Libya 4 PICS for Simulated and measured Landsat 8

Between measured TOA Radiance of Landsat 8 & KOMPSAT-3 corrected by SZA. The first half of 2 years data was used to predict equation for estimation, and the last half images were used to verify Radiance. Every band of Landsat 8 showed a high degree of correlation over 0.99 and TOA Radiance difference was lower than 1%. On the basis of such results, Landsat 8 Simulated Radiance was verified on the same date KOMPSAT-3. And we was Simulated Radiance from the same date where Landsat 8 was solved the Cross Calibration problem of images depending on the discordance between time and dates.

2) Reflectance without SBAF

The TOA reflectance trends from the KOMPSAT-3 and Landsat 8 images were compared as a function of time to monitor the slope and offset to evaluate the cross calibration between the two sensors.

We evaluated the reflectance of KOMPSAT-3 and Landsat 8 without SBAF, which indicated a stable response. Then, the slope from the long term trends was tested for a slope of 0.0, and the t-test results from the Libya 4 PICS suggested that the current radiometric calibration is good for all bands.

The Landsat 8 (1.02~1.58%) reflectance stability are lower than KOMPSAT-3 (1.93~2.41%) as shown in Table 4.

Table 4. TOA reflectance Without SBAF (L8: Landsat 8, K3: KOMPSAT-3)

Without SBAF, according to the estimated TOA reflectance, the percentage difference in Offset between KOMPSAT-3 and Landsat 8 is 0.42% in the blue band, 1.59% in the green band, 5.80% in the red band and 23.23% in the NIR band. Negative values were observed in all bands except the blue band, indicating that KOMPSAT-3 was observed lower than the TOA reflectance of Landsat 8.

In addition to sensor calibration, the differences between the KOMPSAT-3 and Landsat 8 TOA reflectance are likely caused by a combination of the RSR characteristics of the two sensors, spectral signature of the target, and the atmospheric composition during overpass. The succeeding sections describe how these differences can be reduced by accounting for the spectral differences in the analogous bands.

The reason is that as shown in Table 5 and Fig. 1, the RSR of each band differs in KOMPSAT-3 and Landsat 8. For the Nominal spectral band width overlap ratio, blue, green band are same more than 90%. However, Reds are calculated as 83%, NIR are overlapped as 28.6%, the precise overlap ratio based on RSR is calculated as the order of blue, Green which overlap ratio is high. Conclusively, Blue and Green bands showed relatively small difference but Red and NIR band showed big difference. Therefore, the effect of Red, NIR band’s SBAF is higher than Blue and Green bands.

Table 5. Spectral Band overlap ratio on KOMPSAT-3 and Landsat 8 by RSR (unit : %)

3) Calculate SBAF for a cross calibration

To perform an accurate cross calibration between these two sensors, the differences due to spectral responses need to be understood and quantified. To compute SBAF, the spectral signature of the target was derived using other satellite’s radiance measurement. Generally, SBAF adjustment requires satellite images acquired on the same day. However, in this case, same day and time images were not available, so we utilized simulated data from similar RSR satellites. For SBAF Validation, TOA Radiance based on KOMPSAT-3 and Landsat 8 should be simulated. In order to Simulate TOA Radiance, Landsat 8 Radiance at the shooting time of KOMPSAT-3 was estimated and the results were compared.

The range of RSR in NIR band was bigger than SBAF in Blue, Green, Red bands and it is thought that extensive NIR band range of KOMPSAT-3 that includes vapor absorption band affected it. SBAF estimation result is in the Table 6. Blue, Green, Red, and NIR band’s SBAF difference had -0.4, -0.81, 0.56 and 1.17% respectively. However, larger variance is observed in NIR band, due to the presence of the water vapor absorption features in this band. Table 7 shows the reflectance with SBAF result calculated by Simulated TOA Radiance.

Table 6. The Comparison of SBAF between KOMPSAT-3 and Landsat 8

Table 7. Measured and Simulated Reflectance with SBAF result at Libya 4 PICS (unit :%)

As a result of comparison of SBAF estimated TOA simulated-reflectance or radiance and measured-reflectance or radiance for day and time correction, the difference revealed a less than 1% in the Blue, Green, Red and NIR bands (SBAF correction). Thence, KOMPSAT-3 is thought to be less stable than Landsat 8, in NIR band in Table 7.

For Blue band, the difference between KOMPSAT-3 and Landsat 8 TOA reflectance was 0.42%. After SBAF correction, this difference was -0.21~-0.32%. For Green band, the percentage difference between the TOA reflectance measured by KOMPSAT-3 and Landsat 8 was reduced from -1.59 to 0.06~0.14% after SBAF. For Red band, the disagreement between KOMPSAT-3 and Landsat 8 TOA reflectance increased from 5.8 to -0.12~-0.19% with SBAF. For NIR band, before SBAF compensation, the percentage difference between the TOA reflectance measured by KOMPSAT-3 and Landsat 8 was -23.23%, whereas after SBAF correction, the value was -0.27~0.31%, which indicates a significant improvement in Table 4 and Table 7. After SBAF correction for the RSR Difference at each band, it improved Accuracy and quality among sensors.

Before SBAF correction Landsat 8 OLI images provided higher TOA reflectance than KOMPSAT-3. The differences were greater in NIR bands than visible bands.

The Largest difference without SBAF was In NIR (22.1%) for the KOMPSAT-3 and Landsat OLI, whereas, in the visible bands, a difference of -2.2~2.1% can be expected in each band when imaging a bright desert. The uncertainties were higher in the NIR bands, but were all about ±1%. This is a systematic error in the cross calibration (Pagnutti et al., 2003; Paynter et al., 2012; Thome et al., 2001). The average percentage difference between ETM+ and MODIS TOA reflectance before (-16.24~5.63) and after SBAF (-5.53~4.28) were similar. There was a similar pattern in the % DIFF after SBAF values, with little differences between the bands. The spectral bandwidth and overlap ratio for KOMPSAT-3 and Landsat 8 OLI was only 17% in NIR. The NIR difference was consistent between different bands, with the TOA reflectance reported by OLI being generally higher (Thome et al., 2003) The NIR band was abnormal by RSR in two sensors.

4) Radiance accuracy assessment for a cross calibration

As shown as Fig. 4, Table 8 and Table 9, the radiance similarity amongst KOMPSAT-3, 6S and Simulated Landsat 8 with SBAF had 97.37~100.54% in each band. And Correlation (0.967~0.990) had high relationship with each other. The Radiance of KOMPSAT-3 was 1.21~2.44% lower than 6S. Radiance difference standard deviation was 1.76~2.09%. The Radiance KOMPSAT-3 was -0.45~1.39% lower than that of Simulated Landsat 8 with SBAF.

Table 8. TOA Radiance and Stdev between K3, 6S and Simulated Landsat 8 (W · sr^-1·m-2 · μm^-1)

Table 9. TOA Radiance between K3, 6S and Landsat 8 Using Initial Calibration value (2014.2.21.)

Fig. 4. Measured by KOMPSAT-3 (K3), Simulated by 6S (6S) and simulated by Landsat 8 (S.L8) with SBAF (over the Libya 4 PICS TOA Radiance (X: front, Y: Rear).

Radiance difference standard deviation was 1.85~ 2.63%. The Radiance of 6S was 1.77~3.06% lower than between Simulated Landsat 8 with SBAF. Radiance difference standard deviation was 2.04~2.42%.

Radiance difference comes from satellite pass time and tilt angle. By Table 1, Landsat 8 was Nadir and pass time difference was just 10sec while at the KOMPSAT- 3, tilt angle and pass time difference was about 9.66 deg and 359 sec. So, Radiance difference Stdev. is bigger than Landsat 8.

5) The result of the cross calibration coefficient using KOPMSAT-3, 6S and Landsat 8

The result of estimating with average SBAF to the KOMPSAT-3 radiance is as shown in Fig. 4. In every band, the result was similar to KOMPSAT-3 in TOA Reflectance with SBAF than Without SBAF. Table 10 summarizes the Calibration Coefficient of KOMPSAT-3, 6S and simulated Landsat 8 with SBAF, and the difference % for all spectral bands was compared 0.866~1.192% and the Simulated Landsat 8 and 6S calibration Coefficient difference % for all spectral bands was compared 1.709~2.965% with Initial and new(Simulated L8 with SBAF and 6S) Calibration Coefficient.

Table 10. Measured and Simulated Reflectance with SBAF result at Libya 4 PICS (unit : %)

The difference of Simulated L8 with SBAF & 6S Coefficient was influenced by difference of ESUN value which are used in TOA Reflectance. The Channce & Kurutz(CHKUR) (Chance et al., 2010) solar spectrum was used for Landsat, but Fontenla Solar spectrum (Fontenla et al., 2009) was chosen for KOMPSAT-3. 6S solar spectrum used Fontenla for matching KOMPSAT-3 RSR. The difference between various solar models can be greater than 3% depending on the spectral bands.

And, the other reason was tilt angle and pass time variation. Landsat 8 was Nadir (tilt) and 20 sec (Time Table 11. The uncertainty of Cross calibration Coefficient (%) variation). But, KOMPSAT-3 was 9.66 deg and 350 sec in Table 1. so, KOMPSAT-3 had some BRDF by tilt angle and direction and Radiance difference by SZA.

 Table 11. The uncertainty of Cross calibration Coefficient (%)

6) Uncertainty evaluation

Even though the SBAF improved the cross calibration accuracy in this study, many factors still affected the process, and it was difficult to quantify all of these factors rigorously.

In the present work, BRDF (Bi directional Reflectance Distribution Function) effects have not been corrected; it is therefore not unlikely that some of the high absolute errors are a consequence of the anisotropic behavior of reflectance or radiance. As atmospheric path radiance, diffuse radiance and related adjacency effects have not been removed during the cross calibration process, some influence on the results can also be expected.

In this study, however, images with KOMPSAT-3 tilt angle below 10 degrees and images that show clear clouds were selected among the images to minimize the difference of shooting time, BRDF, Path Radiance, Diffuse Radiance. Additionally, Uncertainty was estimated for Aerosol and Water Vapor which can partly affect path Radiance.

It is considered most ideal to estimate uncertainty with the subjects of 2 satellites in the same shooting time and date. In this study, the estimation of uncertainty of TOA Reflectance and radiance depending on Water Vapor and Aerosol, in the same date and to the difference in orbit.

Consequently, in Blue band which is influenced the most by Rayleigh scattering, the degree of uncertainty by Aerosol was relatively high, while NIR band which is highly affected by water vapor showed the highest degree of uncertainty by water vapor. The KOMPSAT-3 overall maximum uncertainty was around 3.26~3.89% in Table 11, and the reliability was similar to that of the other satellites like Landsat 8.

(1) The uncertainty of the Landsat 8 calibration, which is about 3%

(2) The uncertainty caused by BRDF effect, which is one of the critical steps in the cross calibration process. However, in this study we neglected the BRDF correction. In general, this error is approximately 2% when the viewing zenith angle is less than 30° (Gao et al., 2013) by EO-1 Hyperion over Libya 4 PICS suggest that a sensor can be calibrated to better than 1% accuracy with the BRDF model in a clear atmosphere

(3) To determine the uncertainty in atmospheric conditions we used a desert model, in which the spectral correction was derived via 6S model. The calculations of two-way transmittance for downward and upward radiances using the same input parameters are subjected to very small errors because of the error correction in 6S model. Based on both their simulations and ours, the final error caused by atmospheric parameters was less than 1% (Teillet et al., 1990).

(4) Image co registration error: any inaccurate registration between the images acquired by the two sensors introduces errors to the calibration. Given the exceptional uniformity of the surface at the center of the Libya 4 PICS, the maximum deviation of DN from KOMPSAT-3 was less than 1%.

(5) At the Libya 4 PICS: this site exhibits reasonable spatial, spectral, and temporal uniformity and has minimal cloud cover, thus, average deviations are less than 1.9% reflectance level based on reference spectrum (Bacour et al., 2019)

While these estimates of individual errors may not be rigorous due to a lack of information to quantify them more precisely, we estimated that the total uncertainty of the cross calibration method was within 4%, which also incorporates the uncertainty in the Landsat 8 calibration.

5. Conclusions

This paper presents the results of the assessment of the accuracy of cross-calibration coefficient for KOMPSAT-3 AEISS using Landsat 8 and 6S via 6 year-images acquired in the Libya 4 PICS site. The analysis considered image statistics based on large areas ROI common to the image pairs as opposed to the detector-by-detector basis that is vulnerable to geometric uncertainties.

The standard Landsat 8 OLI images were rescaled to TOA spectral radiance or reflectance using the parameter provided by the product metadata file. These were subsequently simulated together with KOMPSAT-3 data to generate a spectral signature of ground during overpass necessary to estimate the compensation factor for any resultant spectral band differences.

Some of the significant sensors Radiance disparities originated from the Satellites pass time and tilt angles such as; 20 sec & nadir and 350 sec & 9.43 deg for Landsat 8 and KOMPSAT-3 respectively. Thus, for any accurate cross calibration between these two sensors, the uncertainties arising from their RSR and geometric differences need be resolved. After effecting the SBAF estimation, the two sensors displayed the SBAF differences in Blue, Green, Red and NIR bands as -0.4, -0.81, 0.56 and 1.17% respectively.

The results of the radiance similarity for the cross calibration coefficients among KOMPSAT-3, 6S and simulated Landsat 8 with SBAF correction equals 97.37~100.54% in each band, demonstrating a suitable correlation (0.967~0.990) between sensors. However, a Radiance standard deviation difference of about 1.85~2.63% was assumed to have emanated from the ESUN values used in the resolution of the TOA reflectance.

The cross calibration of KOMPSAT-3 was 0.01786~ 0.01834 (Blue), 0.02552~0.02596 (Green), 0.02160~ 0.0225 (Red) and 0.01301~0.01332 (NIR). The Cross Calibration Coefficient was lower than 2%.

In this study, the BDRF effect was not considered and since individual errors could not be efficiently quantified due to limited precise information, we estimated the total uncertainty of the cross calibration method to be 4% integrating Landsat 8 calibration inaccuracy.

Nevertheless, the results of this study testify that SBAF immensely enhanced cross-calibration accuracy, and subsequent studies should consider meticulous quantification of identified and unforeseen errors as regular radiometric calibration remains imperative to sensors integrity.

It was found that the influence of Aerosol in Blue band and influence of water vapor in NIR band were significant as a result of estimation of uncertainty of water vapor and aerosol using data. It is deemed that sensor monitoring and continuous Radiometric Cross Calibration for damaged sensor are needed, and for improvement of accuracy.