Accurate radiometric calibration of space-borne instruments measuring the solar radiation reflected by the Earth-atmosphere system is essential for quantitative remote sensing of land, ocean, and atmosphere properties. Radiometric calibration is performed in the laboratory before launch, but accuracy is not perfect and sometimes insufficient. In fact, this engineering calibration refers to standards (Datla et al., 2011) while science applications require a calibration with respect to solar irradiance which shows different spectral distribution. Since instruments degrade after launch due to out-gassing when the instrument leaves the atmosphere, aging of the optics, contamination of optical parts in orbit, and exposure of optical parts, detectors, and electronics to space radiation, satellite platforms are often equipped with onboard calibration devices (Kang et al., 2010; Delwart and Bourg, 2011; Okuyama et al., 2018; Xiong et al., 2020). Indirect, so-called “vicarious” methods are also used, either alternatively (in the absence of onboard calibrators) or to check the onboard device (Fougnie et al., 1999, 2007; Martiny et al., 2005; Hlaing et al., 2014; Chen et al., 2021).

Satellite ocean-color instruments have provided observations on spatial and temporal variability of the world’s oceans unattainable by conventional means, which requires very high accuracy in absolute calibration because the signal to extract is relatively small compared with the measured signal, dominated by atmospheric scattering (Gordon, 1997; Frouin et al., 2019). Atmospheric correction subtracts the atmospheric scattering signal but amplifies the relative errors on the retrieved ocean parameters due to imperfect radiometric calibration. Long-term and consistent ocean color datasets, i.e., with minimized errors/biases between different sensors, is particularly important in the context of climate studies (Sathyendranath et al., 2019). Although the “system” vicarious calibration (SVC) has traditionally been carried out for most heritage and current ocean color sensors by applying gain factors to Top-Of-Atmosphere (TOA) signals so that the remotely derived geophysical parameters fit the corresponding in situ measured parameters after atmospheric correction (Murakami et al., 2005; 2022; Franz et al., 2007; Ahn et al., 2015), biases/errors may still exist in the ocean-color products from different instruments (Djavidnia et al., 2010; Mélin, 2010; Zibordi et al., 2012; Mélin et al., 2016; Bisson et al., 2021), making it difficult to merge the data correctly and generate consistent time series.

Radiometric cross-calibration of ocean-color instruments, therefore, is an important activity to ensure product consistency and generate climate data records, all the more as many such instruments, US and foreign, have been or will be launched, on both polar orbiters, e.g., the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard Aqua and Terra (hereafter referred to as MODIS-A and -T), the Medium-Resolution Imaging Spectrometer (MERIS) on the Envisat, the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (SNPP) and the Joint Polar Satellite System (JPSS) series, the Second-Generation Global Imager (SGLI) on the Global Change Observation Mission-Climate (GCOM-C) satellite, the Ocean and Land Colour Instrument (OLCI) on the Sentinel-3 series, the Ocean Color Imager (OCI) on the Phytoplankton, Aerosols, Clouds, and Ecosystems (PACE) platform, and geostationary satellites, e.g., the Geostationary Ocean Color Imager (GOCI), GOCI-II, the and the Geosynchronous Littoral Imaging and Monitoring Radiometer (GLIMR). A better merging of the geophysical ocean-color products would obviously require processing all the Level-1 data with the same algorithm applied to different sensors that have been cross-calibrated, meaning with a common reference to the same absolute radiometric calibration.

Radiometric cross-calibration can be easily defined as viewing the same radiance at the same time, but it is much more difficult to achieve during in flight operations of different sensors on different orbits. Apart from viewing the Moon, one must rely on measuring the solar radiation reflected by the Earth-atmosphere system at the same time and location because of its time variability. Moreover, the Earth-atmosphere system may have some bidirectional reflectance function that requires observing under the same solar and viewing geometry. At last, if the spectral bands of the channels to be compared do not have the same or close definition, some empirical transformations must be applied to make the comparison thus the cross-calibration.

Bright surfaces, mostly arid deserts like White Sands and the Sahara Desert have been used to calibrate, thus possibly cross-calibrate satellite sensors for land surface remote sensing with some success (Lacherade et al., 2013). The methodology assumes that the variations of the bidirectional reflectance of the surface with the viewing and solar geometry is accurately known and that the atmosphere has a minimum influence. Moon calibration is about the same technique with the advantage of no atmosphere interference but requires some maneuvers of the polar orbiting platform to view the Moon (Eplee et al., 2011). Cao et al. (2004) suggested cross calibrating the sensors over the polar regions by taking advantages of the multiple passes of a polar orbiting platform at high latitude. This allows one to better solve the requirements on geometry and simultaneity.

Ocean (and aerosols over the ocean) remote sensing, however, deals with a lower dynamic of the radiometry than over the land surface. Therefore, one cannot use the highly reflecting “stable” targets of the desert and polar caps because of possible linearity and saturation problems of ocean-color sensors. Ocean targets used with some successes are waters at instrumented buoys like MOBY and BOUSSOLE (Clark et al., 1997; Antoine et al., 2006; Antoine et al., 2008) and the “stable” waters in the center of the subtropical gyres (Hagolle et al., 1999). But most of the TOA radiance is dominated by atmospheric scattering. More generally the measured signal, mostly atmospheric, changes strongly with geometry through atmospheric scattering and with time through aerosol/sub-cloud variability. The SVC method does not explicitly solve the problem and is only performed in the visible. The near-infrared bands remain un-calibrated and may lead to overall systematic biases. For example, about 3%–3.5% differences have been identified between MODIS-A and VIIRS/SNPP in the long near infrared bands (Sayer et al., 2017; Barnes et al., 2021) and such differences at this wavelength partly contribute to the cross-sensor biases of downstream geophysical products (Barnes et al., 2021).

Viewing the same location by two polar-orbiting sensors at the same time and with the same geometry is not an easy task. In-flight comparison between polar-orbiting sensors is limited by the requirements for simultaneously viewing a location with the same geometry. The probability of such event for sensors onboard platforms having different equatorial crossing times increases with latitude. It is nevertheless not very frequent over the polar region, see Cao et al. (2004). An alternative way is to consider the viewing and illumination geometries and then simulate the expected TOA radiances using the water-leaving radiances from other sensors so that more match-up data are available for cross-calibration, as is done for MODIS-T (Kwiatkowska et al., 2008; Meister and Franz, 2011). Inter-calibrating two different geostationary sensors is even more difficult or unfeasible when their sub-satellite points are far away on the Equator.

This study utilizes a geostationary sensor, i.e., the Advanced Himawari Imager (AHI) on board Himawari-8, to cross-calibrate satellite ocean color sensors in polar orbits, i.e., MODIS-A, MODIS-T, and SGLI onboard GCOM-C. The geostationary sensor can be viewed as a robin between polar-orbiting sensors. This is facilitated by the frequent time and geometry coincidences, about daily, when the polar-orbiting sensor crosses the field-of-view of the geostationary sensor around the Equator. In previous studies, AHI onboard Himawari has been utilized to cross-calibrate the solar reflective bands of VIIRS and MODIS (Yu and Wu, 2016; Qin et al., 2018) and the thermal emissive bands of MODIS-A and MODIS-T (Chang et al., 2019), although the calibrations are not ocean specific. Murakami et al. (2019) did some preliminary work on cross-calibrating SGLI, MODIS-A, and VIIRS with AHI over global oceans using modeled bidirectional reflectance distribution function (BRDF) and aerosol signals. However, none of these studies attempted to use AHI to cross-calibrate polar-orbiting sensors. In Section 2, a brief description of the different satellite sensors is provided, including both the spectral and spatial characteristics as well as data access. In Section 3, the generic methodology and algorithm for the cross-calibration of polar-orbiting sensors is presented. The procedure consists of cross-calibrating separately the polar-orbiting sensors against the geostationary sensor of reference. This requires spectral matching the bands of the polar-orbiting sensors to equivalent reference bands and finding coincidences between observations by the polar-orbiting sensors and the geostationary sensor of reference. In Section 4 and Section 5, the results of spectral band matching, coincident pixels selection, and cross-calibration (first for individual polar-orbiting sensor separately with respect to the geostationary sensor, then between polar-orbiting sensor pairs) are shown. The uncertainties on the cross-calibration coefficients at various bands are also estimated. In Section 6, finally, the cross-calibrating method and results obtained for SGLI, MODIS-A, and MODIS-T are summarized. Advantages and limitations are discussed, as well as the potential of using new and future geostationary sensors.

Cross-calibration of satellite instruments is a process or operation that relates the detector output of a sensor in a spectral band to the detector output of another sensor in a similar spectral band. The procedure requires that the observations by the two instruments are collocated in space and time and that the respective viewing zenith and azimuth angles are close. This is not easy to achieve when the two instruments are on different polar orbits, as indicated in Section 1, which is the case for global ocean-color sensors. To increase the number of coincidences, this study utilizes a sensor in geostationary altitude as an intermediary or robin, against which the sensors to cross-calibrate are matched.

Consider the cross-calibration of two polar-orbiting sensors. Denote by ρ 1 i t and ρ 2 j t ′ the reflectance measured at time t by the first sensor and t ′ by the second sensor in spectral bands i and j , respectively, and by ρ r e f t and ρ r e f t ′ the reflectance measured at t and t ′ by the geostationary sensor in a spectral band of reference. It is assumed here, for simplicity, that the polar-orbiting and geostationary sensors observe at the same time. Differences in observation time, generally small, will be accounted for in application. The cross-calibration coefficients between each polar-orbiting sensor and the geostationary sensor, A 1 i and A 2 j , can be written as: A 1 i = ρ r e f t /   f 1 i ρ 1 i t (1) A 2 j = ρ r e f t ′ / f 2 j ρ 2 j t ′ (2) where f 1 i and f 2 j are empirical functions that relate ρ 1 i and ρ 2 j to ρ r e f . These functions are determined theoretically, from simulations for realistic environment and geometry conditions. If the two sensors are perfectly inter-calibrated, A 1 i is equal to A 2 j . Differences between A 1 i and A 2 j , on the other hand, will indicate that the calibration of the two sensors is not consistent and, therefore, needs to be adjusted accordingly. It is assumed, indeed, that the three sensors involved do not exhibit degradation or other changes between t and t ′ . The difference between these times, however, is expected to be small, i.e., a few hours.

Note that depending on the spectral band, the ρ r e f measurements may not be well correlated to ρ 1 and ρ 2 measurements in a single spectral band, but to measurements in several spectral bands. For example, the blue band of AHI is relatively large (with bandwidth of 50 nm) and can only be accurately represented using two spectral bands of SGLI (see Section 4). The formalism remains the same, but Eqs 1, 2 become: A 1 M = ρ r e f t /   f 1 M ρ 1 i t ,   i = 1 ,   2 ,   … , M (3) A 2 N = ρ r e f t ′ /   f 2 N ρ 2 j t ′ ,   j = 1 ,   2 ,   … , N (4) where the empirical functions f 1 M and f 2 N now relate ρ r e f to a combination of measurements ρ 1 i in M spectral bands and ρ 2 j in N spectral bands. Consequently, differences between A 1 M and A 2 N will only be indicative of calibration inconsistencies in combination of spectral bands, not single bands. If not complete, this information is useful, and A 1 M should be equal to A 2 N in any calibration normalization.

Since the spectral bands of the sensors to cross-calibrate and the geostationary sensor, i.e., AHI/SGLI, AHI/MODIS-A, and AHI/MODIS-T, do not match exactly, it is essential to perform spectral matching before any further analyses. The accuracy of cross-calibration depends on how well SGLI, MODIS-A and -T data can be transformed into equivalent AHI data. Figure 1 displays the normalized spectral response of AHI, MODIS-A, MODIS-T, and SGLI bands. Only the bands that have overlap with other sensors are shown. It is clear that there are differences between the sensors except that MODIS-A and MODIS-T have almost identical relative spectral responses. The SGLI and MODIS bands are available in the proximity of, if not within, almost each of the AHI bands. Both SGLI and MODIS are spectrally similar at 443, 490, 530, and 867 nm. Unfortunately, there is no such well-matched SGLI or MODIS spectral response for AHI bands except for MODIS at 859 nm. The AHI bands generally have relatively large bandwidth and/or are not centered on the same (or similar) wavelength as SGLI and MODIS. Due to these differences, it would be difficult to directly pair one SGLI or MODIS band with one AHI band for some cases. Instead, multiple SGLI or MODIS bands may be combined.

Matching the AHI reflectance was achieved as follows. If the spectral band of the polar-orbiting sensor is either centered on about the same wavelength or has similar bandwidths as the band of the geostationary sensor, their reflectance, ρ G E O and ρ L E O (subscripts G E O and L E O representing the geostationary and polar-orbiting, or Low Earth Orbiting sensors, respectively), are related by a simple linear fit, i.e., ρ G E O = C 0 + C ρ L E O . If the spectral band of the geostationary sensor is large, one needs to compute its reflectance by combining reflectance in several spectral bands i of the polar-orbiting sensor, i.e., ρ G E O = C 0 + ∑ i C i ρ L E O i .

Radiative transfer simulations using the Second Simulation of a Satellite Signal in the Solar Spectrum Vector (6SV) code (Kotchenova et al., 2006; Kotchenova and Vermote, 2007) were used to simulate ρ G E O and ρ L E O for a wide range of aerosols and marine reflectance conditions. The TOA reflectance was computed at SGLI and MODIS (Aqua and Terra separately) wavelengths, for total aerosol optical thickness values ranging from 0.1 to 0.3 at 550 nm. Maritime, continental, and urban aerosol models were considered. Simulations were carried out for Sun zenith angles (SZA) ranging from 0° to 60°, view zenith angles (VZA) from 0° to 45°, and relative azimuth angles from 0° to 180°. Only conditions with minimum glint, i.e., with glint reflectance less than 0.05, were selected. Gaseous absorption was considered and varied in the simulations, i.e., water vapor ranging from 0 to 5 g/cm² and ozone from 0.1 to 0.35 cm-atm. Wind speed was assumed constant, i.e., 5 m/s, as the impact of wind speed is negligible when Sun glint is minimal, and chlorophyll concentrations were set to vary from 0.1 to 10.0 mg/m³ to specify different marine reflectance (Figure 8 of Morel and Maritorena, 2001). Only Case 1 waters were considered to avoid the high variability of coastal turbid waters, i.e., the matching corresponds to situations encountered in open waters, where the coincidences will be selected. Considering that correcting for gaseous absorption using ancillary ozone and water vapor data may be necessary in some cases to achieve sufficient accuracy in the spectral matching, the coefficients of the linear and multi-linear regressions were obtained with and without gaseous absorption.

Table 1 lists the combinations of SGLI, MODIS-A, and MODIS-T bands used to generate each of the equivalent AHI bands. The goal is to make sure the spectral band conversion from the polar-orbiting sensors to AHI is sufficiently accurate with the smallest number of polar-orbiting bands as possible. In the spectral matching, two sets of geometries, i.e., (VZA ≤30°, SZA ≤30°), and (VZA ≤45°, SZA ≤60°), with and without gaseous absorption, were tested. The accuracy of spectrum matching is generally higher when using reduced geometry (results not shown), i.e., VZA ≤30° and SZA ≤30°, which is expected since small differences in the optical properties of the aerosols and gas absorbers in different spectral bands are amplified when VZA and SZA are large (i.e., large air mass). The effect of gaseous absorption does not significantly degrade the quality of the spectral matching for AHI at 471 nm, 510 nm, and 639 nm, but this is the not the case when matching other pairs of bands, for example, AHI at 2,257 nm with SGLI at 2,209 nm. This is due to water vapor absorption that mainly occurs in the near- and short-wave infrared and varies significantly for different spectral bands. In matching those bands, correcting first the TOA reflectance for gaseous absorption may reduce the RMS difference by a factor of 2–8. Considering that the reduced geometry may not be applicable to satellite imagery, spectral matching using (VZA ≤45°, SZA ≤60°) and without gaseous absorption was adopted.

The TOA reflectance in each AHI band can be accurately reconstructed using a single band or two bands of the polar-orbiting sensors via linear regression (Table 2). Since MODIS-A and MODIS-T have almost the same spectral response functions, it is no surprising that the relations of converting MODIS bands to AHI bands as well as the achieved root mean square difference (RMSD) are similar. As shown in Table 2, the largest RMSD is found for AHI 639 nm, which can be up to 0.00252 (3.7%) and 0.00255 (3.7%) when reconstructed using the MODIS-A and -T reflectance at 678 nm. This is probably due to AHI at 639 nm having a much larger bandwidth and MODIS at 678 nm being located near the edge of this AHI band (Figure 1). The RMSD is slightly smaller when using SGLI at 672 nm, and MODIS-A and -T at 667 nm, i.e., 0.00221 (3.2%), 0.00190 (2.8%), and 0.00194 (2.8%), respectively, and even smaller when using MODIS-A and -T at 645 nm (RMSD of 0.9% and 0.7%, respectively), as these wavelengths are closer to the center of the referenced AHI band. Similarly, the transformation from MODIS-A and -T at 2,130 nm to equivalent AHI at 2,257 nm shows a relatively large RMSD, i.e., 0.00058 (2.5%), but the spectral matching using SGLI at 2,209 nm is more accurate, i.e., 0.00017 (0.7%). In general, except for the wavelengths mentioned above, the RMSD of spectral matching are quite small, i.e., less than 0.7%. Note that accurate estimation of the reflectance at AHI wavelengths of 471 and 510 nm requires combinations of two bands and multi-linear regression in some cases. Take AHI(471) and SGLI(443) for example, the TOA reflectance is well correlated via linear regression, to a RMSD of 0.00227 (1.7%) (results not shown). A much better spectral matching is obtained, however, when the TOA reflectance in AHI(471) is regressed against the two SGLI bands at 443 and 490 nm, which gives a RMSD of 0.00052 (0.4%). The linear relations between bands of polar-orbiting sensors and AHI bands were then applied to the satellite measurements, from which the effect of gaseous absorption was beforehand removed (see Section 5).

This study provides a generic methodology to cross-calibrate satellite ocean-color sensors in polar orbit. The methodology utilizes a geostationary sensor of reference, i.e., in our case AHI on board Himawari-8, which acts as the intermediary between the ocean-color sensors considered, namely SGLI, MODIS-A, and MODIS-T. This allows one to find numerous coincident measurements in space, time, and geometry over oceanic regions, an advantage over other cross-calibration techniques. The procedure consists of cross-calibrating each of the polar orbiting ocean-color sensors against the referenced geostationary sensor separately and then ratioing the cross-calibration coefficients.

Spectral matching of AHI spectral bands was first performed using a single band or two band combinations of SGLI, MODIS-A, and MODIS-T, based on radiative transfer simulations for various of geometry and geophysical conditions. Results show that the TOA reflectance at AHI blue and green wavelengths can be accurately reconstructed with RMS differences less than 1%. The spectral matching accuracy is degraded for AHI 639 nm, with RMS differences above 3% when using SGLI at 672 nm and MODIS-A and -T at 678 nm. This is because the SGLI and MODIS red bands are quite different from the AHI band at 639 nm, i.e., with narrower bandwidths and different band centers. Although the AHI reflectance at wavelengths longer than 639 nm, i.e., 857 and 1,610 nm, can be precisely reconstructed, large radiometric noise from the AHI imagery makes it more difficult to cross-calibrate polar-orbiting ocean sensors with sufficient accuracy at those wavelengths. Such large noise is expected since AHI is not designed for ocean targets but for meteorological research. Therefore, and also because of the small number of days to determine the unknown population variance of the polar-orbiting sensors’ calibration coefficients in the NIR and SWIR, only AHI data at 471, 530, and 639 nm was used to estimate cross-calibration coefficients, and these bands were the bands of reference.

Application of the methodology to MODIS-A, MODIS-T, and SGLI using AHI quantified the magnitude of inter-calibration coefficients in comparable spectral bands or combination of spectral bands. Only 3 days with mostly clear sky ocean pixels were selected, i.e., 11 May 2018, 22 January 2019, and 25 January 2020. Numerous coincident pixels were obtained from images acquired on the three different dates and used to determine the cross-calibration coefficients and associated uncertainties. It was found that MODIS-A and MODIS-T after SVC are well cross-calibrated in the bands of reference, with differences of about 1% from unity, generally within the uncertainties, for all band combinations. Using diverse band combinations further suggested that the MODIS-A and MODIS-T individual bands at 443, 469, 488, 531, 547, and 555 nm are also well cross-calibrated. In comparison, larger differences, i.e., 1.4%, 3.4%, and 1.1%, between SGLI and MODIS-A were found for the equivalent AHI bands at 471, 510, and 639 nm. Similar results were obtained between SGLI and MODIS-T, with differences of 1.5%, 4.6%, and 1.5%, respectively. The uncertainty of the cross-calibration coefficients between SGLI and MODIS was ±0.8%–1.0% at 471 and 510 nm, and larger, i.e., ±1.9%–2.3% at 639 nm. This larger uncertainty at 639 nm can be attributed to the relatively large uncertainty in SGLI TOA signals at 672 nm as well as the spectral matching error and AHI radiometric noise which result in larger measurement errors at this wavelength. The results also suggest that the uncertainties of cross-calibration coefficients can be reduced when adding more days of observations. These cross-calibration differences are above the estimated uncertainties at 510 nm, affirming that significant differences exist between SGLI and MODIS-A and -T TOA signals, especially in the blue-green spectral range. The differences of about 4% in the blue and green between SGLI and MODIS signals far exceed the absolute radiometric calibration uncertainty required for ocean color remote sensing (i.e., a fraction of 1%) and may introduce discrepancies between ocean-color products generated from SGLI and MODIS-A and -T imagery if the same atmospheric correction scheme were applied. However, the different atmospheric correction and SVC procedures applied to SGLI and MODIS may alleviate the impact of TOA signal discrepancies between SGLI and MODIS-A and MODIS-T on downstream ocean color products.

The findings provide the basis for a normalized calibration of SGLI, MODIS-A, and MODIS-T, which is important to generating consistent long-term ocean-color products from multiple satellites. Basically, we expect the radiance measured at a certain wavelength by all the sensors in given geophysical and geometric conditions to be the same. However, as mentioned above, this might not be the case when using level 1b data after SVC adjustment if the atmospheric correction scheme and SVC procedure are not the same for all sensors, i.e., caution must be exercised in the interpretation of deviations from unity of the cross-calibration coefficients. The method proposed in this study can be applied operationally, and to other optical sensors operating in polar orbit. It can also be performed prior to SVC, as this calibration may be considered as part of the atmospheric correction process. Due to the limitation of the AHI spectral bands, the cross-calibration using this intermediary sensor was mostly accomplished using multiple bands instead of a single band. The relatively high AHI radiometric noise, the limited number of days, and the large uncertainty of the polar-orbiting sensors’ calibration coefficients (or the lack of information about their uncertainty) in the NIR and SWIR prevented cross-calibrating in this spectral range. Yet the methodology is generally applicable to those longer wavelengths, provided that the number of coincidences during a day and the number of days are sufficiently numerous, the spectral matching is accurate, and the population variance of the calibration coefficients is not too large; otherwise, the resulting cross-calibration coefficients might be too inaccurate for meaningful conclusions. The methodology, however, has great potential with geostationary sensors that have ocean color capabilities. The Geostationary Ocean Color Imager (GOCI) follow-on, GOCI-II (Ahn and Park, 2020), in particular, collects data in 12 narrow ultraviolet, visible, and near-infrared bands at 0.25 km resolution, allowing direct band-to-band mapping with polar-orbiting ocean color sensors. This was not possible with GOCI, which only observed in local area mode around South Korea (Choi et al., 2012; Ryu et al., 2012). But such geostationary sensors, which have low radiometric noise and narrow spectral bands, require more time to acquire a scene than sensors onboard weather geostationary satellites, yielding less frequent coincident observations. In fact, GOCI-II observes 10 times during daytime in regional mode, but only once a day in full disk mode, making it difficult to obtain proper coincidences in low-latitude regions for cross-calibrating polar-orbiting sensors. Nevertheless, other geostationary sensors such as the Spinning Enhanced Visible InfraRed Imager on board Meteosat Second Generation, the Advanced Baseline Imager carried by the Geostationary Operational Environmental Studies R series, and the Flexible Combined Imager onboard Meteosat Third Generation, though with restricted number of spectral bands and not primarily intended for ocean research, can still serve as useful references in the cross-calibration of ocean-color sensors in polar orbit.