The In-service Aircraft for a Global Observing System (IAGOS) operates measuring equipment on commercial aircraft to provide in situ atmospheric measurements on a global scale. The IAGOS dataset, which starts in 1994, consists of the former research project MOZAIC, CARIBIC (now IAGOS-CARIBIC), and the currently active CORE program. In this study, we only considered the aircraft that are part of the CORE program, as shown in Table , as these were predominantly active throughout the operational periods of Sentinel-2 and Landsat 8 and 9.

We use the air temperature (T) and the relative humidity w.r.t. liquid (RHl) from the IAGOS-CORE dataset, both of which are measured by the IAGOS capacitive hygrometer (ICH). The ICH uses a capacitive humidity sensor (a modified Vaisala HUMICAP^® sensor) and a platinum resistance temperature sensor (PT100) . The IAGOS aircraft trajectory data and ICH measurements are provided every 4 s. During this study we observed a time shift in the IAGOS data in the order of 0–15 s when compared to ADS-B data or satellite imagery. To resolve this, we linearly interpolate the IAGOS measurement and position data to a 0.1 s resolution and select the time at which the aircraft position is closest to the annotated aircraft position, when corrected for parallax (see Appendix ).

IAGOS data undergo quality control, the outcome of which is communicated by means of a validity flag. These flags are either good (0), limited (2), erroneous (3), not validated (4), or missing value (7) . For this study, only measurements flagged as good (0), for both T and RHl, were used. This entails that the measurements passed all required quality control tests. In addition to these validity flags, we utilise the estimates of measurement uncertainty that come with IAGOS data for both T and RHl to construct 95 % confidence intervals. The uncertainty of T and RHl measurements are estimated to be 0.5 K and 5 %–6 % respectively, with the latter determined by comparing the ICH measurements with the FISH and SEALDH-II instruments during the AIRTOSS-ICE field campaign . However, instead of taking this constant T and RHl uncertainty, we rely on the uncertainty estimates provided directly by the IAGOS data processing. In general, these uncertainties are comparable to the 0.5 K for air temperature and 5 %–6 % for RHl, but they offer a more accurate representation of the uncertainty associated with individual measurements.

Humidity measurements by the ICH in the upper troposphere and lower stratosphere (i.e. the aircraft cruise altitude region) may also be affected by reduced sensor sensitivity and long sensor response times. Firstly, relative humidity measurements by the ICH have been reported to suffer from reduced sensitivity to water vapour concentrations in dry stratospheric air masses , with a lower detection limit between 10 ppmv and 30 ppmv . This loss of sensitivity is primarily caused by adiabatic heating of the air flow, as it is brought to rest within the ICH housing. Because of this temperature increase, the measured RHl is lower than the ambient RHl. The effect of this lower detection limit on the analysis conducted in this study will be further discussed in Sect. . Secondly, the humidity sensor has a temperature-dependent response time, which varies from 1 s at 300 K to 120 s at 210 K. Several studies have attempted to correct this time delay or mitigate its effects on downstream analysis. For example, aggregates measurements to a coarser 1 min resolution, whereas tries to reconstruct the measured signal by use of a temperature-dependent exponential moving average. We find that reconstructing RHl for the IAGOS flights at 4 s timestamps results in a noisy signal (on average increasing the first-difference (i.e., the difference between successive samples) standard deviation by 43.3 %), resulting in more outlier measurements. Resampling to 1 min timestamps mitigates this noise, but does so at the expense of temporal resolution. Therefore, we chose not to apply any of the aforementioned correction methods.

We use numerical weather prediction (NWP) data from the ECMWF ERA5 reanalysis dataset . Air temperature (T), specific humidity (q) and pressure (p) are used to compute RHl and RHi with the expressions for the saturation pressure w.r.t. liquid from and ice from . Other variables required to use the CoCiP contrail model also come from the ERA5 dataset. The reanalysis data are downloaded from the Analysis-Ready, Cloud Optimized (ARCO) ERA5 Dataset hosted on Google Cloud, which has a regular grid of 0.25°×0.25° horizontal resolution and includes 137 vertical model levels extending from the surface to approximately 80 km. The air temperature and relative humidity are linearly interpolated in the horizontal and vertical dimensions to match the aircraft's position and time.

We use two aircraft performance models (APMs) to estimate the engine fuel mass flow and the overall propulsion efficiency which are required as inputs for modelling contrail formation and evolution: the Base of Aircraft Data (BADA) Family 4 Release 4.2 and the Poll–Schumann (PS) model. The aircraft type and engine combinations for the IAGOS fleet are given in Table . All computations were performed using the open-source pycontrails library . Flight trajectories provided by IAGOS at 4 s resolution were resampled to 1 min, in order to reduce the influence of small positional uncertainties and obtain smoother overall propulsion efficiency outputs. Both APMs require data on air temperature and horizontal winds as input, which can either come from ERA5 or the IAGOS measurements. We have quantified the changes in overall propulsion efficiency estimated by both APMs when using these different meteorological data sources: the resulting root-mean square “error” was found to be close to 0.005 for the PS model, and 0.009 for the BADA 4.2 model, which is almost 2 orders of magnitude smaller than typical propulsion efficiency values of 0.3–0.4. Due to the relatively small magnitude of these meteorology-dependent efficiency differences, we have chosen to perform aircraft performance calculations with the data source that is used for the prediction of contrail formation, which we discuss in more detail in Sect. .

Comparison of the two APMs shows that BADA 4.2 propulsion efficiencies show larger intra-flight variability than those obtained from the PS model. As a result, the efficiency values calculated for the satellite observation times also show increased variability, typically ranging between 0.2 and 0.4 during cruise, as opposed to 0.25 to 0.35 with the PS model. Moreover, during descent, BADA 4.2 calculates an overall propulsion efficiency of zero, whereas the PS model calculates values between 0.1 and 0.3. For the subsequent analyses, we therefore only use the PS propulsion efficiency estimates. Additional details and a comparison of the two performance models are provided in Appendix .

In the PS model, the overall propulsion efficiency at the optimum condition is expected to have an uncertainty of no more than ±10 % . Since this uncertainty is related to the optimum condition, an extra 2.5 % buffer is added to account for suboptimal conditions. In the updated version , an extra uncertainty of ±2.5 % is added due to the effect of in-service engine deterioration, based on the reasoning that an airline only allows for an increase of 5 % in fuel consumption before a maintenance intervention is planned. Thus, we take an uncertainty related to the overall propulsion efficiency of 15 % into consideration for the subsequent analyses. For example, for an efficiency of 0.3, we take the confidence interval as [0.255, 0.345]. We note that this constant 15 % uncertainty does not take into account local flight conditions and can mask local thrust variations.

We use aircraft position data (either from IAGOS data or by use of ADS-B data) in combination with satellite ephemeris and imaging sensor specifications to estimate if and where a given aircraft should be located in a particular satellite image: this process is referred to as “collocation”. We find that interpolation of aircraft position data to the image capture time and converting this to the local UTM coordinate system used within the image, leads to differences between the predicted and observed aircraft position on the order of several kilometers. Given that two or more aircraft are occasionally found within a distance of a few kilometers in these images, we apply several corrections to the collocation process in order to resolve such ambiguities. Specifically, we improve the accuracy of the collocation process by accounting for parallax displacement of the aircraft and by using a more precise image capture or “scan” time corresponding to the specific area of the image where the aircraft is expected to be located.

The images are orthorectified to the Earth's surface during Landsat and Sentinel-2 processing, meaning that pixels are geometrically corrected assuming they lie at ground level. While this correction ensures accurate positions for surface features, it introduces a parallax displacement for objects located above the surface of the Earth when they are captured by the instrument at an off-nadir angle. Given the viewing geometry (represented by zenith and azimuth angles) of the satellite instrument and the altitude of the object, this parallax displacement, typically on the order of 1 to 2 km, can be estimated. These viewing angles are provided for each image pixel in the Landsat image metadata, whereas the Sentinel-2 imagery only provides a coarse resolution (25 × 25 km) estimate. We have created an algorithm to correctly upsample the Sentinel-2 viewing angle data which takes into account the staggered architecture of the sensors in the Sentinel-2 MSI (see Fig. ). This algorithm is described in Appendix . The geometric (GNSS) altitude of the aircraft, with respect to sea-level (WGS-84), is obtained from the aircraft position data.

The second correction involves the estimation of the time at which individual image pixels were scanned. Although each satellite image is given a single “sensing time”, this corresponds to the pixel scan time averaged over the entire scene. In practice, scanning such a scene (110 km by 110 km for Sentinel-2 and 170 km by 185 km for Landsat) takes approximately 16.8 s for the Sentinel-2 instrument and 32 s for the Landsat instrument, during which an aircraft cruising at 250 m s⁻¹ can move 4.2 and 7.6 km, respectively. For this reason, it is important to obtain a pixel-by-pixel estimate of the scan time. Both the Landsat and Sentinel-2 imagers are push-broom scanners, but their staggered sensor architecture implies that the pixel scan time is not only a function of the along-track position (as one would expect for a push-broom scanner) but also a function of the cross-track position (determining whether the pixel is scanned by an odd or an even detector). To account for this, we first find the satellite ephemeris position (and the corresponding time) closest to a given pixel, and then apply a constant time offset that depends on the detector used to capture the pixel. Further details on this process can be found in Appendix .

The results of these corrections to the collocation process are evaluated by quantifying the distance between the predicted aircraft position and the manually annotated position of the aircraft in the satellite image, and are shown in Fig.  for the Sentinel-2. The collocation errors for Landsat are shown in Appendix . We decompose the error into components normal and tangential to the flight path. As shown in Fig. b, the residual error after applying the corrections is predominantly tangential to the flight path. To help interpret the magnitude of the error statistics shown in Fig. a–b, we show an example of an aircraft found in a Sentinel-2 image in Fig. c along with the predicted aircraft positions with and without corrections. The corrected collocation process estimates the position of 95 % of the aircraft to within a distance of 487 m, whereas the process without the discussed corrections can only narrow down the aircraft position to 3.06 km (for 95 % of the data). This constitutes an order of magnitude improvement in the accuracy of the collocation process.

We hypothesise that the residual errors in the collocated positions are due to: ADS-B timestamp and positional uncertainties (typically in the order of several tens of meters according to ), the omission of digital elevation models (which are used in Sentinel-2 and Landsat processing) in the collocation algorithm, and optical distortions due to the lens composition .

The collocation process described in Sect.  is used to find the location of IAGOS aircraft within both Sentinel-2 and Landsat imagery, after which we manually identify whether the aircraft in question is forming a contrail. If a contrail is found, it is annotated either by use of a (multi)polygon (for Sentinel-2 imagery) or a linestring along the longitudinal axis of the contrail (for Landsat imagery). As this step is done manually, there might be non-reproducible biases in the placement of the contrail edges, and thus the derived contrail widths. This is particularly relevant for older, more diffuse contrails, where the contrail edges become less distinct from the background.

The first step in this annotation process is to determine the exact location of the aircraft, which is typically found close to but not exactly at the collocated position. In 12 % of cases, out of the total number of cases where an intersection is found between the IAGOS trajectory and the satellite tiles, the aircraft was found to be obscured by clouds or the trajectory data was incomplete. These cases are excluded from the analysis. The second step is to determine whether the aircraft – in case it is visible in the imagery – is forming a contrail. If this is indeed the case, we also annotate the outline (centerline) of the contrail within Sentinel-2 (Landsat) imagery using a polygon (linestring).

For annotating the Sentinel-2 imagery we use the Copernicus Browser , an ESA platform for visualising satellite data. This tool automatically mosaics adjacent images, enabling contrails to be annotated continuously across the full Sentinel-2 swath width of approximately 290 km. The contrails were manually outlined by the authors as polygon features following their visible extent in the green band, which offers 10 m spatial resolution and generally the highest contrast against the background; the blue band appears less bright over clouds or ocean background, while the red band is less bright over land. Additional bands, including the red, blue, and cirrus bands, were used as aid during the annotation process. The cirrus band was especially useful for long-lived contrails or contrails present above white or “noisy” surfaces (e.g. snowy mountains, salt plains, or cities). In Appendix , we show four example contrails over clouds, an ocean, a forest, and an urban area (see Fig. ). In addition, we include two cases in which the contrail is visible either only in the true-colour image or only in the cirrus band (see Fig. ).

For annotating the contrails found within Landsat imagery: we download the relevant scenes (a scene covers an area of 170 by 185 km) and process these to obtain zoomed images centered on the collocated aircraft position (covering an area of 8 by 8 km). In each case, we computed three images: a true colour image, a monochromatic image from the cirrus band, and a false colour image from the thermal bands (B10 and B11), following the colour scheme from . The cirrus band was used for annotating the contrail, with the help of other true colour and false colour images where necessary. Figure  shows an example of a contrail as seen in the true colour image, cirrus band, and false colour image.

Because we annotate on zoomed images in Landsat, and we thus have no information on the full lifetime of these contrails, we will not use these cases for determining metrics such as contrail age and width evolution. In Sentinel-2 imagery, a fraction of annotated contrails extends beyond the swath: implying that we cannot see the full extent of the contrail. Such annotations are flagged accordingly to avoid potential misinterpretation.

The Sentinel-2 contrail annotations are further processed to obtain estimates of the contrail width as a function of its age. To estimate the centerline of a polygon, we first compute its minimum rotated rectangle (MRR). When multiple polygons are present, as is the case when the contrail crosses the detector borders, each polygon is processed individually. Then, we compute the longest edge of the MRR and its centroid to construct a centerline along the longest axis. We place points along the polygon centerline spaced by 100 m and estimate the contrail width at these points by computing the width of the polygon orthogonal to the centerline. The age of a contrail at each point (along the centerline) is determined by first calculating the distance from that point to the location of the aircraft. This distance is then divided by the aircraft's groundspeed to estimate the contrail age. The main limitation of this method is that it does not account for horizontal advection of the contrail by the wind. For instance, if the horizontal wind vector is aligned with the direction of flight, a point located 1000 m from the aircraft may have been advected further downstream or upstream. Assuming a wind speed of 50 m s⁻¹ and an aircraft groundspeed of 250 m s⁻¹, this can lead to an error in contrail age of approximately 20 %. Alternative methods, such as generating centerline points by advecting the flight path according to wind, are limited by the accumulation of wind speed errors: over time, these errors can cause the advected path to diverge from the actual contrail. As a result, measurements of contrail width may be taken at an angle that is not perpendicular to the contrail, leading to an overestimation of its width. Thus, the choice of method is a trade-off between uncertainties in contrail age or in contrail width. It is important to note that this uncertainty in the estimated contrail age introduces noise into the correlation between contrail width and age, and thus into the later comparisons against model predictions of the early evolution.

An example of a Sentinel-2 annotation and the corresponding estimated contrail width is given in Fig. . As mentioned before, while the green visible band is used for the annotation, we visualise the cirrus band in Fig. d for clarity. The estimated contrail width (see Fig. f) is not found to be a smooth function of contrail age: several “jumps” are noticeable for contrail ages larger than 100 s. These jumps are in part due to the contrail crossing detector boundaries: which introduces discontinuities in the contrail annotation (see Fig. b). However, the remainder of the variability in Fig.  corresponds to the breakdown of the wake vortex pair. In other annotations such as Fig. , we can directly see the inception of the Crow instability which ultimately leads to the breakdown of the vortex pair.

We assess the agreement between SAC predictions and satellite observations using a contingency table, given in Table , which classifies each prediction as a true positive (TP), false positive (FP), false negative (FN), or true negative (TN).

The entries of the contingency table are combined into metrics that are used to assess the performance of the SAC. Specifically, we make use of the precision Pr and recall Re which are defined by 7Pr=TPTP+FP,Re=TPTP+FN. The precision corresponds to the fraction of predicted contrails that are observed, and the recall corresponds to the fraction of observed contrails that were also predicted to form. They have been used previously to quantify the performance of contrail forecasts by and .

In addition to using the dataset created in this work, we also use two existing observational datasets of contrails for quantifying the performance of the SAC. These are the dataset presented by and the dataset described by , both of which consist of contrails found in ground-based camera images. We also compare the differences in SAC performance found when switching meteorological data sources to the results by .

Both and directly provide entries of the contingency table, which we use to compute precision and recall according to the definitions above. In contrast, do not provide these numbers and we therefore process their dataset to obtain the entries of the contingency table. Their dataset consists of ground-based camera images with contrail annotations that are matched to flights passing through the camera field of view (FOV) based on ADS-B data, not limited to IAGOS aircraft. In order to be included in the contingency table, we require that (1) the camera zenith angle is limited to a maximum of 60° to avoid geometric distortion near the image borders; (2) only flights above an altitude of 7 km are considered, as lower-altitude aircraft are not expected to form contrails; 3) flights without a valid flight_id are discarded to avoid erroneous matches caused by unreliable ADS-B data. For each remaining flight we determine whether it formed a contrail by checking for annotations with the relevant flight_id in the images where the flight is within the FOV and images after the flight exited the FOV. The SAC has been computed for each flight with an overall propulsion efficiency of 0.30 (0.35 and 0.40 were also tested but resulted in lower precision values) using temperature, humidity and pressure from the ECMWF ERA5 reanalysis dataset .

The application of the collocation process to IAGOS data for the years 2013 to 2022 has resulted in a total of 543 annotated collocations (366 in Sentinel-2 imagery and 177 in Landsat 8/9 imagery). For 195 of these Sentinel-2 collocations, we have annotated the contrail that is being formed by the IAGOS aircraft. The spatial and temporal distribution of the collocations are shown in Fig. . Most collocations are found over (or close to) land masses, since the Sentinel-2 and Landsat satellites are primarily used for land observations. IAGOS aircraft have been collocated in climb (54 times), cruise (455 times) and descent (34 times) phases. The mean geometric (GNSS) altitude of the collocations is 10.5 km, with 90 % of the collocations being above 9.0 km. Further details on the vertical distribution of the collocations are discussed in Sect. . Figure b shows that almost all collocations occur from 2017 onward, with a single exception in 2013. The limited availability of data between 2013 and 2018 can be attributed to an error in the IAGOS data acquisition until 2018. The affected measurements have since been corrected, but all repaired data carry a validity flag of 2 and are therefore excluded from the analysis. Additionally, the decrease in 2020–2021 can be attributed to a reduced number of flights during the COVID-19 pandemic. In the period 2017 to 2021, the Sentinel-2 program had two satellites operational, compared to only one Landsat satellite (Landsat 9 was only commissioned at the end of 2021), resulting in more Sentinel-2 collocations.

The number of collocations found for each aircraft in the IAGOS fleet as well as the total number of flights during the years 2013 to 2022 are given in Table , along with details on the aircraft type and engine. The IAGOS fleet covers bypass ratios between 5.0 and 6.4. These subsequent results may therefore not apply to modern lean-burn or high-bypass engines. Since both Sentinel-2 and Landsat satellites operate in sun-synchronous orbits, each location on Earth is observed consistently at the same local time. Consequently, the number of collocations associated with each aircraft is strongly influenced by typical flight routes and departure schedules. For example, F-GZCO recorded 474 flights in 2022, yet only 10 collocations were identified. During this period, the aircraft predominantly operated routes across Europe and North-Africa, with 86 % of departures occurring after the local satellite revisit time. In contrast, aircraft operating inter-continental routes, such as transatlantic flights, have a higher probability of being collocated, as their trajectories can be captured by multiple satellite overpasses.

For each collocation within the dataset, we evaluate the Schmidt–Appleman criterion (SAC) using both IAGOS and ERA5 data and compare this to the corresponding annotation. One such comparison is given in Fig. , for a case where no contrail formation is observed. The overall propulsion efficiency used within the evaluation of the SAC is derived from the PS model using IAGOS data as input: this is used to construct the threshold mixing line in Fig. . The shaded area represents the envelope of threshold mixing lines resulting from varying the efficiency by ±15 %. The ambient conditions obtained from ERA5 and IAGOS data are both shown in Fig. . In this particular case, the SAC evaluated using ERA5 data incorrectly predicts that contrail formation should occur. When using the IAGOS data however, the SAC is not satisfied in agreement with the observation. We give three more of these examples in Appendix , using both Sentinel-2 and Landsat imagery. The example provided in Fig.  shows a difference in ERA5 and IAGOS-based air temperatures of 1.9 K, which is on the higher end of the examples in the dataset. Over the whole dataset, we found a mean difference of -0.583 K (TERA5-TIAGOS), with a standard deviation of 0.757 K.

The results from the evaluation of the SAC predictions using the entire dataset are given in Table  as a function of the satellite platform and meteorological data used. For the “IAGOS (within uncertainty)” meteorological data source, we consider the SAC prediction to be correct if any combination of temperature and relative humidity values within the 95 % confidence intervals leads to a correct prediction (see the examples in Figs.  and ). We now discuss the results in Table  by focusing on the effect of observation quality, the effect of the meteorological data source and by comparing the results to the literature. Firstly, for identical weather data, observations based on Landsat exhibit a consistently lower precision than those based on Sentinel-2, with differences ranging from 0.048 to 0.084, while recall remains comparable between the two (differences < 0.034). The lower SAC precision for Landsat observations is driven by a relative increase in false positives, where the SAC is satisfied but no contrail is observed. This reduction in precision when using Landsat instead of Sentinel-2 observations is found to be statistically significant (p-value of 5 %), and we hypothesise that the reduced resolution of the Landsat RGB imagery compared to the Sentinel-2 RGB imagery (30 m instead of 10 m) leads to a larger number of contrails that are unobservable. During the early part of the jet phase (below 10 s), the widths of the vortices are in the order of 10's of meters. As a consequence, an instrument with a coarser spatial resolution of 30 m might struggle to detect these features since more background radiation is coming into a pixel, reducing the contrast with the background. Examples of how a reduced image resolution complicates the contrail observation process can be found in Appendices  and . To assess the possibility that the observed differences in precision and recall between the Landsat and the Sentinel-2 observations are due to sampling effects, we have performed Monte Carlo simulations (further explained in Appendix ). The results indicate that under the null hypothesis that the precision and recall have the same value for the two satellites, the probabilities of finding the observed differences in precision and recall are 0.005 and 0.06 respectively. In other words, the observed differences in precision and recall for the two different satellites are unlikely to be explainable by random sampling effects alone.

Secondly, we see that the use of IAGOS instead of ERA5 data leads to better agreement between the SAC predictions and observations for both satellite instruments. The precision increases by 0.067 for the Sentinel-2 observations and by 0.034 for those from Landsat. In the analysis of , the SAC was calculated using ERA5 and compared against SAC calculated using IAGOS, which was considered the ground truth. Their results indicate a precision of 0.923 and a recall of 0.992. When we consider the SAC computed using IAGOS data as the ground truth – rather than the satellite observations – we find a precision of 0.932 which is within 1 % of the value found by .

Table  shows that the use of ERA5 data results in a larger number of false positives than when using IAGOS data as input for the SAC. One possible explanation for this is the reported mean cold bias of approximately 0.5 K in ERA5 temperatures , which lowers ΔTLC and can increase the number of false positive predictions by the SAC. The increase in false positives leads to a decrease in precision, without affecting recall.

In addition, we evaluated the effect of using the relative humidity of the clear-sky portion of the ERA5 grid point, calculated from specific humidity and cloud cover fraction . In 76 % of the collocations in Table  the cloud cover fraction was 0.0. In the remaining 24 % cases with partial cloud cover, the clear-sky RHi did not have an effect on the predictions of the SAC.

Lastly, we discuss the evaluation results where the SAC prediction is considered to be correct if any combination of overall propulsion efficiency, air temperature or relative humidity values within the 95 % confidence intervals of IAGOS data leads to a correct prediction. This increases the precision to 0.990 (0.942) and the recall to 0.995 (0.988) for the Sentinel-2 (Landsat) observations. Thus, the SAC correctly predicts 99.2 % of Sentinel-2 observations and 96.6 % of Landsat observations when IAGOS measurement uncertainty is taken into account.

In other observational datasets, the level of agreement between observations and SAC predictions is found to be lower than that obtained using the dataset introduced here. Using the data from , we obtain a precision of 0.717 and an average recall of 0.982 across all waypoints. Similarly, using the dataset from , we obtain a precision of 0.444 and a recall of 0.973 when comparing annotated contrails with corresponding flight trajectories. In both ground-based studies, the reported precision is lower than that observed in the Landsat and Sentinel-2 results presented here. One contributing factor may be the spatial resolution of ground-based methodologies. At an altitude of 10 km, the all-sky camera used in , has an effective pixel resolution of approximately 50–100 m, which likely contributes to an increased number of false positives. However, the wide-angle camera used in , has a resolution at 10 km of approximately 5–10 m, higher than both satellites. We thus further attribute the remaining discrepancy to reduced observation quality inherent to ground-based camera methods, including the presence of low-level clouds, or sun glare effects. Overall, the higher precision reported by compared to is consistent with the hypothesis that spatial resolution is the dominant factor in contrail formation detection, which would also explain the higher precision found for Sentinel-2 observations relative to Landsat.