Monitoring the TROPOMI-SWIR module instrument stability using desert sites

Since its launch in 2017, the TROPOMI instrument on S-5P has provided very high quality data using daily global coverage for a number of key atmospheric trace gasses. Over its first 1,000 days in operations, the SWIR module has been very stable and the continuously monitored calibration has remained of high quality. This calibration relies on a combination of extensive pre-launch and post-launch measurements, complemented by regular monitoring of internal light sources and background measurements. In this paper we present a method and results for independent validation of the SWIR module 5 calibration and instrument stability by examining the signal stability of a sample of 23 pseudo-invariant calibration desert sites. The data covers over two years of operational data. With a Lambertian surface assumption, the results show that the SWIR module has little to no instrument degradation down to an accuracy of about 0.3% per year, validating results obtained from the internal calibration suite. The method presented here will be used as ongoing validation of the SWIR calibration.

The BRDF of desert sand, in particular its accuracy and effect at off-nadir viewing angles, has been described and characterized by Bruegge et al. (2019a). They find that desert sand has a characteristic hot-spot in the backwards direction of the incoming solar radiation. They also show that these BRDFs are not well characterized at large off-nadir viewing angles, with 55 differences of 5% in a normalized solution w.r.t. the zenith shown as typical. The MODIS product (Schaaf et al., 2011) is the most complete, but also suffers from inaccuracies. These are relevant for TROPOMI, due to its very wide swath opening.
In this paper we present an analysis of the site stability of a sample of 23 PICS in the Saharan, Arabian and Namibian deserts 3 . The sample was adopted from the analysis of Bacour et al. (2019), which itself revisited the original Saharan PICS sample from Cosnefroy et al. (1996) and Lacherade et al. (2013). Most analyses of PICS sites are done at visible wavelengths 60 and/or at high resolutions of imagers. In this analysis, we will use continuum channels of the TROPOMI SWIR channel.
Section 2 provides the final sample, while the data usage of TROPOMI is presented in Section 3. This includes data filters and restrictions as well as a few assumptions in our analysis. Section 4 gives the results while the impact is discussed in Section 5.

Saharan sites
Saharan PICS have been used for monitoring for a large number of sensors (e.g. Cosnefroy et al., 1996;Lacherade et al., 2013;Bacour et al., 2019). These studies have shown the Sahara to be reasonably stable across large spatial scales and relatively invariant in time. The most recent in-depth review of the spatial and temporal variability of Saharan PICS can be found in Bacour et al. (2019) where the original lists of Cosnefroy et al. (1996); Lacherade et al. (2013) were inspected. An update of coordinates was given as compared to the original locations of Cosnefroy et al. (1996), as well as a quantified ordering on spatial homogeneity across 20 and 100 kilometers as well as temporal stability. In this study we have adopted the final sample 70 of Bacour et al. (2019) in their Tables 2 and 3. We will be using their coordinates to track the temporal variability of the SWIR and NIR channel continuum signal. As a typical TROPOMI pixel is at least 7x5 km 2 but can be as large as 20x7 km 2 (especially during the early parts of operations), the sites are inspected on their temporal stability and spatial homogeneity at 20 km (TVar (20km) and SHom(20km), as reported in Table 2 of Bacour et al. (2019).

75
S5-P has daily overpasses over all sites shown in Table 1. For most sites, multiple overpasses only exist every ∼5 days due to the proximity to the equator. An overpass is valid if a pixel is located less than 0.2 degrees from the reference location given in Table 1. At the equator this equals 22 km. At typical Saharan latitudes, the separation is less then 20 km. Note that if multiple pixels qualify, only the pixel with the smallest separation to the reference position is used. TROPOMI data was processed using the operational version of the L1b version 01.00.00. Several filters are applied to improve the overall data quality. These 80 are listed in Table 2. Apart from the separation restriction, the viewing zenith angle must be smaller than 50 degrees, the cloud fraction of the pixel must be below 0.02, a successful and valid irradiance measurement should have been taken within  a day of the overpass and the solar zenith angle must be below 60 degrees 4 . Cloud fraction is defined as a number between 0 and 1 representing the area of a pixel covered by clouds. A number of 0 is completely cloud-free, while 1 represents a pixel completely covered by clouds. The cloud fraction information was extracted from the support data included in the operational 85 data product of the CH 4 offline processor, version 1.2.0. Given the straylight correction as defined in Tol et al. (2018) and applied in the processor, no filtering was used for cloud presence beyond the sounding pixel. With the constraints described above, the largest variable parameter is the size of the TROPOMI overpass pixel. The size of a TROPOMI pixel is dependent on its location in the swath. At nadir, a typical TROPOMI pixel at SWIR wavelength is 7×7 km 2 , while at the edge pixels can dramatically increase in size in the across-track direction, growing to sizes of up to 7×26 km 2 . Note that after August 2019, 90 this was reduced to 5.5×7 km 2 due to shorter integration times. As seen from Bacour et al. (2019), spatial homogeneity at larger scales (i.e. 100 km) can be significantly worse than its counterpart at 20 km scales. As such, it is imperative to avoid contamination from large scales and focus only on the central regions. TROPOMI-SWIR soundings are thus restricted to viewing zenith angles of 50 degrees or less. Effectively this constrains soundings to positions away from the edges of the swath. This also automatically limits the pixel to a maximum pixel size in the across-track direction, while in the along-track 95 dimension the resolution is set by the sampling time. The pixel size is thus dependent on the location through the viewing angle and on the date due to the change in integration time. In general, pixels are always smaller than 7 km in the along-track and 8.5 km in the across-track For our analysis, the surface is assumed to be Lambertian in nature. It is well documented that off-nadir soundings are affected by non-Lambertian effects (e.g. Bruegge et al., 2019a). Although correction routines can be applied, these often rely 100 on ground measurements to derive the correction factors within a modified Rahman-Pinty-Verstraete model (Rahman et al., 1993b, a). Even in such a well-characterized site such as railroad Valley, differences of 5% are seen in normalization factor (Bruegge et al., 2019b, a). These differences appear to be dependent on measurements used to derive the free parameters in a mRPV model. Ground measurements are not available for any of the sites listed above. Measurements from space, such as MODIS or MISR, are of insufficient quality to reliably improve the data. This is particularly apparent at larger viewing zenith 105 angles. A choice was made to accept a higher amount of scatter introduced by the lambertian assumption, but include relatively large viewing angles (up to 50 degrees) while excluding more extreme angles (TROPOMI can observe at almost 65 degrees).
The alternative, limiting us to very small viewing zenith angles and only include overpasses near or at nadir angles, severely constrained the available data. To compare data over the full time-span, data is corrected by dividing by the cosine of the solar zenith angle. An additional constraint by limiting the maximum solar zenith angle was implemented to filter a few problematic 110 cases. Last but not least, soundings are required to have a valid irradiance measurement using TROPOMI-SWIR within a day. This filter is aimed at possible problematic soundings taken after an orbit maneuver or anomaly. This affect less than 0.1% of all TROPOMI measurements.
If an overpass is considered valid, the radiance is derived by taking the median signal for all pixels with center calibrated wavelength between 2312.7 to 2312.9 nanometers. Deep absorption features of CH 4 as well as H 2 O are avoided. Uncertainty 115 of the radiance measurements is propagated at each correction using standard mathematical rules. Note that the uncertainty on the radiance of a sounding is small and includes only the shot noise of the detector, photon noise and uncertainties of the calibration data included during L1b processing. Table 3 shows the median radiance and its standard deviation (both in absolute and relative scales) of accepted soundings for 120 all sites from a period starting April 28th 2018 to 1st October 2020. In addition to these statistical properties, the slope of a

Results
Arabia2 2 0 2 4 6 8 Slope [10 9 mol m 2 sr 1 nm 1 s 1 ] / 1000 days the DLED has its own degradation. Figure 2 shows the complete time series of four sites of our sample. These four sites were chosen at random to represent the sample. The results of all other sites are presented in given in supplemental material.  2019) show that instrumental variation in measurement to measurement due to detector noise is much smaller, and that the uncertainty from instrumental effects is dominated by photon noise only, which is estimated to be on the order of 0.1%).
The higher measurement to measurement variation reported in Ludewig et al. (2020) seen in the irradiance were attributed to electronic noise. However, due to more in-depth analysis carried out, it is now attributed to surface roughness of the diffusers 135 (van Kempen & Ludewig, priv. comm). The distribution of viewing angles from TROPOMI SWIR over a full year is large, due to the large swath of TROPOMI that allows for daily global coverage.
The linear fits found are very shallow, with typical number between 0 and 5×10 −9 mol m −2 sr −1 nm −1 s −1 per 1,000 days. This equates to a maximum increase in transmission of 0.7% per year. The average of the slope is equal to 0.3 % per year. Note that many sites are found at lower values, and a few even showing a negative slope. Given the typical standard deviation, we 140 attribute the slopes to statistical variations. The impact on SWIR instrument degradation is discussed below.

Nadir view
Given the influence of non-lambertian reflection on the standard deviation, the stability of the four sites with various quality (Egypt1, Algeria3, Libya3 and NamibiaPICSAND1, see Fig. 4) is shown using only viewing angles less than 7.5 degrees from nadir. The results are given in Table 4 with the full results given for completeness. Differences are marginal, with the largest 145 differences seen in the linear fit. For some, the standard deviation improved. The main difference was found in the reliability of the removal of the yearly variation through the 365-period sine wave. Interestingly, the fit parameters were nearly identical as that derived above, with only the reliability of this fit found to be significantly worse. This is easily explained due to the significantly lower amount of data used as input for the fit.

Origin of yearly variation 150
The sine wave used to correct an observed yearly variation has no clear origin. It is not instrumental in nature given the results of van  and ongoing monitoring (see www.sron.nl/tropomi-swir-monitoring/) and should thus be attributed to a feature present in the surface. The amplitudes and period offsets with respect to January 1st 2018 are given in Table 5.
It appears that the yearly variation is slightly regionally distributed. Sites in the south-western variation (Mauritania, Mali, Niger and Algeria1 and Algeria2, have a larger amplitude (6 to 11) period offset with some negative days, while eastern Sahara 155 sites (Libya, Egypt, Sudan) tend to have smaller amplitudes (4-5) and show a slight positive offset. The Namibian desert site is clearly offset due to its location on a southern hemisphere. The sites in the Arabian desert are grouped south (Arabia1 and  Arabia2) and north (Arabia3 and ArabiaPICSAND1) in amplitude, but show no correlation in period. Arabia1 has a relatively large offset.
As to the origin, three possibilities are entertained. The first is shadowing of dune formation. Minima would be expected 160 around mid-December, which is not clearly seen. However, due to the site location, regional dependency would not be expected. The second is a dependency to rock or sand composition for reflectance and BRDF. Our data is insufficient to make any conclusions on this. However, it would be related to location and size of hotspot and would be incompatible with the observation that the yearly variation is detected with similar amplitudes with nadir overpasses. and H 2 O is considered beyond the scope of this paper. Last but not least, varying moisture content within the sand may have yearly contributions, changing the reflectance even in a Lambertian assumption. Whatever the origin, it can be concluded that using a correction on a yearly variation improved the data quality. The results above show that the sample of Saharan PICS are well-suited as a validation of the instrument stability, both using viewing angles up to 50 degrees and to only 7.5 degrees. The standard deviations seen are similar from site to site. This was achieved by a strict filter on clouds (cloud coverage of <0.02) and correcting for the solar zenith angle during any overpass.
In addition, observed yearly variations were removed by fitting a sine wave with a period of a single year. The results clearly show no evidence for TROPOMI-SWIR instrument degradation or increased transmission. The results validate the conclusions 175  The lack of difference using filters with both 50 and 7.5 degrees is somewhat surprising given the attributed influence of non-lambertian reflectances (which peak at angles of 20-30 degrees from zenith) and the inclusion of larger TROPOMI pixels 180 (due to the swath size of TROPOMI). Note however that following Bacour et al. (2019) most sites were assumed to be spatially homogeneous. This likely explains the lack of influence of larger pixels at larger viewing angles. Subsequently, we can conclude that the spatial homogeneity conclusions indeed apply to SWIR wavelengths following this study.
The variation from site to site is also relatively small, but do appear to be correlated by region. The Namibian desert has a significantly lower radiance, while the sites in the Arabian desert only show a lower radiance by about 3-5% as compared 185 to the Saharan Desert. Differences within the Sahara (i.e. east-west or per country) appear to be marginal and warrant further investigation.
The most obvious improvements that can be made are in the field of non-lambertian effects. TROPOMI covers a very large range of angles. Given the recent conclusions of the BRDF studies in e.g. RailRoad Valley (Bruegge et al., 2019a), measurements at larger viewing angles must be corrected to make comparisons.

190
Code and data availability. All L1b-data is freely available through the Copernicus Open Access hub (https://scihub.copernicus.eu). The pys5p code that is the basis of the analysis code can be found on Zenodo ( Competing interests. There are no known competing interests.
Author contributions. The work was started by FO under supervision of TvK as part of an internship. TvK expanded conclusions and 195 additional work, including writing the paper. The base software packages were written and provided by RvH.