Satellite remote sensing data has been increasingly used in various operational applications, such as atmospheric applications . The increased number of satellite missions has led to the rapid growth of remote sensing archives from diverse satellite missions. These archives help to track and monitor atmospheric conditions and phenomena. In addition to high spatial and radiometric resolution, they offer global coverage. One of these applications, which received considerable attention in the last decades, is the retrieval of trace gases . Accurate emission monitoring over timelines spanning decades is essential for assessing measures to improve, for example, air quality and for understanding atmospheric processes.

Major trend analyses regarding the atmospheric environment require long-term datasets to provide a continuous and comprehensive view of gases. The time series analysis should have more than a decade of data, which could be greater than the individual satellite lifetime . To avoid discontinuity in time series data, it is necessary to fully use the ever-increasing number of satellite systems from the historical and current missions. To generate consistent time series data from multi-mission sensors, several factors should be considered, including the differences in the sensors' characteristics, such as overpassing time, data quantity, viewing geometry, solar geometry, instrument-related effects, and atmospheric conditions .

Cross-calibration is a method of ensuring the consistency, accuracy, and comparability of measurements from different instruments, platforms, and missions. Cross-calibration consists of comparing the monitored measurements to reference instruments . For trace gas applications, monitored parameters include reflectance or radiance and solar irradiance. The optimal situation to perform the cross-calibration is to acquire the measurements from both sensors simultaneously in the same geometrical and solar conditions. However, the spatiotemporal coincidence measurements are usually not very frequent, which complicates the cross-calibration.

Vicarious calibration is a well-known method of absolute calibration based on precise measurements of spectral reflectance from ground instruments over a target , or measurements acquired over sites with invariant surface properties such as deserts or oceans . Man-made features, such as concrete structures, preserve the ground reflectance values and do not change significantly over time. These features, known as pseudo-invariant targets, can also serve as reference measurements for calibration . This type of cross-calibration is independent of the satellites’ onboard calibration systems.

Pseudo-Invariant Calibration Sites (PICS) are one of the most widely used sites in the vicarious calibration methods . proposed desert sites in Africa and the Arabian Peninsula with 100×100km2. demonstrated the methods and criteria used for identifying PICS based on observations taken from Meteosat-4 from July 1989 to January 1990. The selection criteria ranged from spatial and temporal variability of the surface reflectance, cloud cover, precipitation, geomorphology, and bidirectional effects. It has been assumed that these sites had spatial uniformity better than 3 % in a multi-temporal series of cloud-free images . The primary characteristics of these sites are limited precipitation, a lack of vegetation cover, and minimal human-induced changes. Many studies assumed that the PICS remain temporally invariant , and the radiance upwelling from the Earth can be assumed to be constant . Therefore, the main part of the changes observed in the temporal stability of sites will be directly related to the changes that occurred to the sensors.

The Global Ozone Monitoring Experiment (GOME) and Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) were used primarily for the retrieval of trace gases. compared the life mission top-of-atmosphere (TOA) reflectance – hereafter referred to as reflectance, unless stated otherwise – data of GOME and SCIAMACHY over the PICS under near-clear-sky conditions. They found that the reflectance time series of SCIAMACHY observations were more uniform and stationary compared with the GOME reflectance time series. The same study showed that GOME reflectance suffered from severe degradation in 2001 and toward the end of its life mission, in agreement with . Therefore, it was recommended to use SCIAMACHY as the reference sensor in the cross-calibration. The SCIAMACHY data from 2003 were selected as a reference to perform the harmonization between GOME and SCIAMACHY. This choice was due to (i) SCIAMACHY being at the beginning of the mission and exhibiting no or negligible instrument degradation. The reference point for the SCIAMACHY degradation was taken as 27 February 2003. Choosing the same year minimized degradation-related uncertainties. (ii) SCIAMACHY has better capabilities for in-flight calibration, and Level 1b data have better degradation correction .

The reflectance and solar irradiance from Level 1 of GOME and SCIAMACHY have been cross-calibrated in the Fundamental Data Records in the Domain of Satellite Atmospheric Composition (FDR4ATMOS) project . The FDR4ATMOS focused on three spectral windows in the ultraviolet, visible, and near-infrared (UV/VIS/NIR), as these regions contain well-characterized absorption features of many key atmospheric trace gases (see Table 4).

This cross-calibration between the satellite spectrometers GOME and SCIAMACHY implies several unique challenges. Despite the significant temporal overlap of the two missions, there were no simultaneous observations at the same locations. Additionally, a difference in spatial resolution further complicates the cross-calibration process. These challenges highlight fundamental differences between spectrometer cross-calibration and that of imaging satellite instruments, which typically do not face such constraints. Cross-calibration of imaging sensors does not require the stringent point-to-point accuracy needed for spectroscopic trace-gas retrievals, as imaging applications are less sensitive to small radiometric inconsistencies than Differential Optical Absorption Spectroscopy (DOAS)-based retrievals, which typically demand relative accuracy on the order of 10-4. In contrast, trace gas retrievals using data from GOME require specialized approaches that maintain the integrity of spectral data throughout the calibration process.

This paper focuses on addressing these issues, proposing a methodology tailored specifically for cross-calibrating satellite spectrometers, rather than conventional imaging instruments. The paper is structured as follows: Sections 2 and 3 describe the sensors and study areas. The cross-calibration method is presented in Sect. 4. Sections 5 and 6 present the results and the discussions, respectively. Finally, the conclusion and final remarks are given in Sect. 7.

GOME (1995–2011) was a passive nadir-viewing, grating spectrometer, covering the UV, VIS, and NIR spectral ranges. It was mounted on the second European Remote Sensing (ERS-2) satellite . GOME could provide global coverage every 3 d. The primary objective of the mission was to collect observations to measure the total column of ozone, nitrogen dioxide, clouds, aerosols, pollutants, and other atmospheric compositions . The mission measured the upwelling solar radiation reflected or scattered by the Earth's atmosphere and surface in the wavelength range of 240–790 nm.

GOME operated using both forward and backward scanning modes, producing four ground pixels per scan cycle (3 forward and 1 backward), each with an integration time of 1.5 s. In the forward scan, three pixels were recorded in the east, nadir, and west directions, each covering a minimum spatial resolution of 40×320km2. The backward scan produced one pixel with a coarser spatial resolution of 40×960km2. The instrument was equipped with three Polarization Monitoring Devices (PMDs) and four detector channels. The spectral resolution was approximately 0.2 nm in the UV range and 0.4 nm in the VIS and NIR. The PMDs are broadband detectors specifically designed to capture polarization information with high spatial resolution.

SCIAMACHY (2002–2012) was a passive imaging spectrometer aboard the ENVISAT satellite . It operated across the UV, VIS, NIR, and shortwave infrared (SWIR) spectral regions, covering wavelengths from 240 to 2400 nm. The instrument featured three distinct observation modes: nadir, limb, and solar/lunar occultation.

The primary mission objective was to monitor various processes that affect the chemical composition of the troposphere and stratosphere . In nadir mode, SCIAMACHY provided measurements at a spatial resolution between 26×30 and 32×233km2, depending on the wavelength and orbit phase. The swath width was 960 km. The instrument was equipped with eight detector channels and seven PMDs. Various atmospheric gases, aerosol characteristics, radiation budgets, and cloud properties were retrieved.

The differences between GOME and SCIAMACHY are illustrated in Table 1.

The fully calibrated Level 1 products from GOME (Level 1b) and SCIAMACHY (Level 1c) were used as input for the cross-calibration method. Both products contained solar irradiance and radiance measurements used to compute reflectance, as explained later in Sect. 4.1.1. For SCIAMACHY, cloud information from Level 2 was added to the standard Level 1c products, whereas GOME Level 1b products already contained cloud information. The PMD measurements in both GOME and SCIAMACHY products were sun-normalized.

The following are the main parameters from both sensors used in this research study:

Reflectances: This denotes the proportion of incident solar radiation that is reflected toward the sensor. It includes contributions from both the Earth's surface and the atmosphere through scattering. Reflectance is used because instrumental effects common to both Earth and Sun observation light paths, such as etalon interference, are largely canceled through the ratioing process. Furthermore, the retrieval of most atmospheric parameters is based on the reflectance. Reflectance served as a key parameter for the derivation of the transfer functions (TFs), which were used to update the GOME observations based on SCIAMACHY observations, as defined in Sect. 4.1.4. The reflectance measurements were denoted as Rg and Rs, for GOME and SCIAMACHY, respectively.

The FDR4ATMOS cross-calibration workflow is illustrated in Fig. 2. The diagram illustrates the steps used to perform the cross-calibration between Rs and Rg: (i) spatial collocation of SCIAMACHY and GOME scenes over the selected sites, (ii) averaging the spatially higher resolved SCIAMACHY over the GOME ground pixel for the overlapped scenes, yielding Rscia2gome, (iii) re-gridding the data and computing the ratio of Rscia2gome/Rg for the investigated spectral ranges and the selected sites, (iv) removing outliers and applying PMDs-based filters, and (v) fitting the filtered ratio.

The ratios from Eq. (4) were computed for overlapping GOME and SCIAMACHY pixels using two datasets in Table 3: (i) considering only pixels that directly intersect the PICS, and (ii) including all ground pixels in a scan that had an overlap with the PICS. The comparison revealed minimal differences in the ratios used to derive TFs, regardless of which dataset was employed. Figure 5 presents the median values and corresponding standard deviations for Bands 2B (Fig. 5a) and 3 (Fig. 5b). The largest discrepancy was observed for Band 2B in the east viewing geometry, with a maximum difference of approximately 1.5 %. Overall, the magnitude of uncertainties was found to be consistent across the different bands.

We chose to use ratios from all collocated pixels to increase the statistics. The resulting ratios are illustrated in Fig. 6. In general, although the ratio patterns varied across the bands, each band exhibited a consistent pattern across the PICS. For Band 2B (Fig. 6a–c), the ratios–particularly at the shorter wavelengths–were dependent on the VZA. For Band 3 (Fig. 6d–f), the ratios increased with wavelength across the PICS. In contrast, for Band 4 (Fig. 6g–i), the ratios on the left and right sides of the O2 A-band remained constant and are independent of wavelength.

The derived TFs for each spectral band, along with their median and standard deviation values, are shown in Fig. 7. For Bands 2B and 3, the TFs were modeled using third-degree polynomial fits. The TF of eastward VZA was closer to 1 than those for nadir and westward VZA (Fig. 5b), indicating that the reflectance values for East VZA were, on average, similar between the two sensors. However, the standard deviation for East VZA was relatively higher than for Nadir and West VZA, indicating a wider spread of reflectance values in the East direction compared with the other viewing angles.

For Band 4, the TF was obtained by averaging the ratios on the left and right sides of the O2 A-band, yielding a constant value of 0.93, which represented the TF for Band 4, including the O2 A-band (blue dashed line in Fig. 7c). The uncertainty in the TFs was indicated by error bars corresponding to 1 sigma.

Among the VZA classes in Band 2B, the nadir view exhibited the lowest uncertainty. In contrast, the uncertainties for the west and east VZA classes were, on average, approximately 3 and 2 times higher than that of the nadir VZA, respectively. For Bands 3 and 4, larger uncertainties were observed. On average, the uncertainties in Bands 3 and 4 were about 4 times greater than the uncertainties in the Band 2B nadir TFs.

The PMD analysis of the GOME and SCIAMACHY pixels used in the derivation of TFs, based on PMD channels 1, 2, and 3 – representing Bands 2B, 3, and 4, respectively – is shown in Fig. 8. The analysis included the statistical indicators μ, σ, and CV.

For Band 2B (Fig. 8a), based on μ measurements from PMD channel 1, the PMD values from GOME and SCIAMACHY showed different correlations, with R2 values of 0.99, 0.89, and 0.70 for west, nadir, and east VZA pixels, respectively. The PMD measurements exhibited a clear dependence on the VZA. SCIAMACHY tended to underestimate the PMD values compared to GOME for the nadir and east VZA pixels, while a slight overestimation was observed for the west VZA pixels.

For Bands 3 and 4 (Fig. 8b and c), the correlation of PMD measurements between GOME and SCIAMACHY was lower, with R2 values of 0.36 and 0.63, respectively, indicating weaker agreement compared to Band 2B. In both cases, SCIAMACHY generally underestimated the PMD values relative to GOME.

The σ values of PMD measurements for Band 2B from both GOME and SCIAMACHY (Fig. 8d) were relatively low, indicating more spatially uniform and homogeneous pixels with R2 values of 0.55. In contrast, for Bands 3 (Fig. 8e) and 4 (Fig. 8f), the σ values of GOME PMDs were higher than those of SCIAMACHY, suggesting that less homogeneous pixels were involved in the cross-calibration for these bands. A similar trend was observed in CV: lower variability was seen in Band 2B (Fig. 8g) compared to Bands 3 (Fig. 8h) and 4 (Fig. 8i). By looking at the shaded areas in Fig. 8g–i, the PMD measurements of GOME pixels exhibited higher variability than those of SCIAMACHY.

The PMD-based filter was applied to the GOME pixels used in the derivation of the TFs of Fig. 7. This filter was applied separately for each site and each PMD channel, as illustrated in Fig. 9. The red scatter points represent the GOME pixels for which the absolute value of relative difference in the PMD standard deviation compared with SCIAMACHY pixels was less than 25 %. The filter resulted in a significant reduction in the sample size. After applying this filter, 39 out of 151 GOME pixels were retained for the next iteration of cross-calibration, yielding the TFs denoted as TFs with PMD.

The fitted TFs for the bands without applying the PMD filter (black dashed curves) were consistent with the TFs derived when the PMD-based filter was used (colored curves), as shown in Fig. 10a–c. The differences in the median values of both TFs are highlighted in Fig. 10d–f. The maximum absolute difference was 1.75 % for Band 2B west VZA (Fig. 10d). Overall, the TF values (with and without the PMD-based filter) changed only slightly and not significantly. However, the uncertainties of the TFs were markedly reduced when the PMD-based filter was applied (Fig. 10g–i). For Band 2B west, the uncertainty was decreased by up to 70 % (Fig. 10g). In contrast, there was no uncertainty reduction for Band 2B nadir and east VZA. For Bands 3 and 4, the uncertainty reduction reached up to 5.5 % (Fig. 10h) and 19 % (Fig. 10i), respectively.

The main challenges mentioned in the introduction about the GOME and SCIAMACHY cross-calibration were tackled in the methods by applying the following strategies:

The cross-calibration was performed using observations acquired over PICS, which are community-accepted calibration sites. For these sites, the probability of rapid changes in atmospheric and meteorological conditions within the 30 min acquisition time difference between the sensors is relatively low.

Including all measurements from the complete scanline, rather than limiting the analysis to only those directly intersecting with the PICS, did not significantly impact the cross-calibration results. This was likely due to the similar scene characteristics and surface reflectance signals typical of desert environments. The advantage of PICS was not significantly lost for the spectrometer ground pixel that extends beyond the defined boundary of PICS. Additionally, the small time difference in the collocation assisted in mitigating significant differences in the content of the cross-calibrated pixels.

The ratios of reflectance values of both sensors were in the range between 0.8 and 1.1 for the GOME bands before applying the PMD-based filter. GOME radiance and irradiance data were corrected for degradation, but the correction was solely based on irradiance measurements. A possible differential degradation that affected the reflectance was not corrected. It is found that the TFs for the East VZA exhibit larger uncertainties compared with those for the West and Nadir VZA. The PMD measurements of GOME and SCIAMACHY in Band 2B show a dependence on the VZA, which was consistent with the derived TFs for the same band (see Fig. 8a). As shown in the figure, the PMDs for the East VZA were less correlated than those for the West and Nadir VZAs, indicating less homogeneous pixels in the East viewing direction. Consequently, the uncertainties associated with the East VZA were higher than those for the Nadir and West VZAs.

The derived TFs of Band 2B exhibited a stronger dependence on VZA compared to those for Bands 3 and 4. This behavior was attributed to the significant UV degradation of the GOME instrument since 2001, which was scan mirror-dependent and varied with the viewing angles , particularly at shorter wavelengths. In contrast, the degradation was less pronounced at longer wavelengths, resulting in reduced VZA dependency for Bands 3 and 4. Consequently, the impact of degradation on TFs was expected to be more substantial over time.

A notable observation was that the uncertainty appeared to be wavelength-dependent. In the UV, the measured signal was dominated by atmospheric scattering, whereas the contribution from surface reflection increased with wavelength. Consequently, scene inhomogeneity due to surface variability became more pronounced at longer wavelengths. Since GOME and SCIAMACHY did not sample identical ground pixels, surface inhomogeneity could lead to differences in the derived TFs for individual overpasses, resulting in increased scatter around the true TFs.

GOME and SCIAMACHY were both equipped with PMDs, which provided sub-pixel-scale measurements. The PMD measurements from GOME pixels involved in the cross-calibration were consistently higher than those from the corresponding SCIAMACHY pixels due to: (i) GOME PMDs had roughly double the spectral bandwidth compared to SCIAMACHY (see Table 2), and the optics were different, (ii) the GOME measurements were at the equatorial crossing time of 10:30 against SCIAMACHY at 10:00, hence, the GOME PMDs would receive larger signals, (iii) PMD data on Level 1b were not corrected with the cos (phi) factor (as the reflectance was), (iv) the larger values in PMDs GOME could explain that we have more sampling and less averaging than for a SCIAMACHY pixel. Nevertheless, different levels of correlation were observed between the two instruments, with the strongest correlation for Band 2B.

The PMD analysis revealed that the degree of spatial uniformity was wavelength-dependent. A broader range of σ and CV values was found for Bands 3 and 4 compared to Band 2B (see Fig. 8g–i), suggesting reduced pixel homogeneity at longer wavelengths. This reduction in homogeneity contributed to higher uncertainties in the TFs derived for Bands 3 and 4.

The PMD analysis highlighted the crucial role of PMD measurements in assessing pixel homogeneity for cross-calibration. It provided a basis for developing robust filtering criteria using PMD-derived indicators, which enabled the exclusion of spatially non-uniform pixels. Overall, most cross-calibrated pixels from both sensors were spatially homogeneous, with absolute differences in σPMDsensor,j below 0.01. Applying the PMD-based filter lead to the exclusion of a considerable number of GOME pixels from the TF derivation. Nevertheless, the absolute TF values with and without the filter showed no significant differences, while the uncertainties of many TFs were substantially reduced. This selective adjustment demonstrated that the PMD-based filter effectively improved TF estimates in the presence of non-homogeneous pixels. Ultimately, this approach broadens the applicability of TF derivation by enabling the inclusion of a more diverse range of surface types and reflectance conditions, rather than relying solely on desert scenes.

The derived TFs still exhibit some limitations and constraints that should be addressed to improve their accuracy and representativeness further:

i.

Temporal dependency: The derived TFs depended on data from the year 2003. It was reported by that degradation became severe toward the end of the GOME mission lifetime. Since the TFs are expected to be influenced by degradation, particularly in the UV, it is recommended to apply reflectance degradation corrections to the GOME data prior to TF derivation in order to ensure long-term consistency. This is envisaged for the next version of the TFs within the FDR4ATMOS project.