The instrument in Athens is located at the National Observatory of Athens in Penteli, Greece. The Athens metropolitan area, with approximately 3 million inhabitants in the Attica region , is strongly influenced by anthropogenic activity. Under certain meteorological conditions, local topography causes pollutants to accumulate within the urban area . Additionally, due to its hot and dry climate, Athens occasionally experiences wildfires, as observed, for example, in 2018 and 2024 . Mountains with Mediterranean vegetation are located to the north. To the east, the landscape features mountainous vegetation interspersed with smaller residential areas, while to the south lie the airport and lower-density residential and industrial zones. The city centre of Athens and the port of Piraeus are situated to the southwest.

The MAX-DOAS instrument is installed on a building roof on a hill (500 m above sea level; a.s.l.) to the east of the city (see Fig. ). Measurements are routinely conducted in multiple directions. For this analysis, we use data collected between January 2021 and December 2023 from the viewing direction oriented toward the city centre (indicated by the purple line in Fig. ). Additional details regarding the instrument hardware and setup are given by . Meteorologically, the region experiences low precipitation, pronounced diurnal and seasonal cycles in short-wave radiation, and relatively high temperatures exhibiting clear seasonal and daily variations during our measurements (Fig. ). The prevailing winds during the measurement period come from northern directions, frequently reaching speeds above 9 m s⁻¹ (Fig. S2).

The second station is located near Orléans, France, on the premises of a radio station in Traînou, which is regularly used for scientific measurements, including the ICOS project . Traînou (approx. 3500 inhabitants; ) is situated about 100 km south of Paris and 17 km northeast of Orléans (116 000 inhabitants; ).

Crucially for this study, the site is adjacent to a large forested region (Fig. ). The Orléans State Forest covers roughly 350 km2, and comprises a mixture of broadleaf and evergreen tree species . Thus, this measurement site is strongly influenced by biogenic activity, with minimal local anthropogenic emissions, although pollutant plumes from Paris can occasionally be detected under northerly winds.

The MAX-DOAS instrument is mounted on an elevated position (approx. 10 m above ground level; a.g.l.), enabling low-elevation scans directly above the forest canopy. Data analysed in this study cover the period from July 2023 to July 2025, focusing on measurements taken towards the forest (Fig. ). Orléans experiences strong seasonal and diurnal variations in short-wave radiation, though its maximum values are comparatively low due to its higher latitude (Fig. ). Precipitation is moderate without a clear seasonality. Temperatures are among the lowest of the investigated sites, with a less pronounced seasonal cycle than at Incheon and Athens. The prevailing wind direction is from the southwest, frequently exhibiting high wind speeds exceeding 9 m s⁻¹ (Fig. S2).

The third instrument was installed on the roof of the Environmental Satellite Center in Incheon, part of the Seoul Metropolitan Area (SMA) in South Korea. With approximately 3 million inhabitants, Incheon is South Korea's third-largest city. The SMA is the most densely populated region in the country . It is situated in an anthropogenically dominated environment, with Seoul city centre approximately 32 km to the east, Incheon city centre to the south, and the harbour area to the west (Fig. ). The northern edge of the metropolitan area borders North Korea (about 20 km north), where some forested mountains are located.

As part of the GEMS Map of Air Pollution (GMAP) 2021 campaign and the Satellite Integrated Joint Monitoring of Air Quality (SIJAQ) 2022 campaign, MAX-DOAS measurements were conducted for about one year. For this study, we analyse data from October 2021 to November 2022, focusing on the urban azimuth viewing direction.

Meteorologically, heavy rainfall occurs between June and September, while the rest of the year is comparatively dry. This signal indicated the influence of the East Asian monsoon and tropical cyclones. No pronounced diurnal precipitation cycle is observed. The seasonal precipitation pattern affects short-wave radiation, which declines during the wet months but otherwise shows strong seasonal and diurnal cycles with high peak values. Temperatures also exhibit strong seasonal and diurnal variability, with the lowest temperatures across all sites recorded in December and January. The prevailing wind direction is from the northwest (especially during Winter) or west (Fig. S2).

The fourth instrument is located on the tall ATTO Tower in Brazil, deep within the Amazon rainforest. Situated approximately 150 km northeast of Manaus (population 2 million, ), the ATTO site serves as a remote research site in the heart of the rainforest (Fig. ). The surrounding area is sparsely populated, resulting in the site being predominantly influenced by biogenic activity. During the dry season wildfires are more frequent and affect local atmospheric conditions .

The instrument was installed at a height of 80 m in October 2017 and measurements are still ongoing at the time of writing. However, not all data are yet analysed in scientific quality, so the used dataset ends in August 2022. Some data gaps occurred due to the challenging hot and humid climate affecting hardware and electronics. The dataset analysed in this study was originally obtained by , who also provides a detailed description of the site and instrumentation. Some figures from that publication are reproduced here using our own processing methodology based on their dataset. In such cases, the figure captions indicate which panels are affected.

Meteorologically, the ATTO Tower is characterised by a tropical climate, see Fig. . Precipitation is largely confined to the wet season (December–May), with much drier conditions prevailing during the rest of the year. Within this season, rainfall typically occurs between 10:00 and 16:00 LT. Temperatures are consistently high, showing daily but minimal annual variation. Short-wave radiation exhibits a strong diurnal pattern but remains relatively stable on seasonal timescales, with only a slight reduction during the wet season. Prevailing winds are from the northeast, but compared to the other sites, wind speeds are predominantly low, typically below 3 m s⁻¹ (Fig. S2).

The four stations cover a broad range of environmental conditions; however, they cannot represent the full diversity of atmospheric regimes. In particular, both urban sites, Incheon and Athens, are located near the coastline, implying potential influences from marine air masses and sea-salt aerosols that may not be representative of inland urban environments. The datasets were collected during non-overlapping periods, as the station locations originate from long-term measurement activities. While this limits strict temporal comparability, the analysis focuses on characteristic relationships rather than direct year-to-year contrasts.

The horizontal orientation of the light paths introduces an additional spatial averaging that is inherent to MAX-DOAS measurements and is illustrated in Fig. . The retrieved dSCDs represent the concentration along the effective light path, whose length within the boundary layer depends on atmospheric visibility. Under clear conditions, photons scattered at distances of up to approximately 15 km from the instrument can contribute to the signal .

Beyond viewing geometry, the origin and transport history of observed air masses determine the spatial representativeness of each site. Annual and seasonal horizontal footprints derived from backward simulations (details in Sect. ) show, as expected, the highest sensitivity in the vicinity of each instrument (Fig. ). The ATTO footprint shifts seasonally with the movement of the ITCZ. At Orléans, persistent sensitivity to both the city and the surrounding forest reflects mixed anthropogenic and biogenic influences, with enhanced sensitivity towards Paris (100 km to the northeast) during MAM. Athens exhibits strong sensitivity to the urban area and more remote northern regions, with reduced sensitivity to the city centre and harbour in JJA. Incheon shows pronounced sensitivity to northwestern source regions during DJF, with a less directional footprint in the remaining seasons. Overall, the footprint analysis is consistent with the site descriptions and classifications, but reveals minor seasonal sampling biases that should be considered when comparing sites.

Uncertainties from MAX-DOAS data can be grouped in (1) random effects and (2) systematic effects. Following the error budget discussion from for the HCHO retrieval from MAX-DOAS data, random uncertainties are connected to photon shot noise for silicon based detectors and are generally well captured, if not even overestimated, in the dSCD uncertainties from the DOAS fit. For scientific grade instruments, the systematic uncertainties outweigh the random uncertainties. Pointing misalignments, uncertainties of the wavelength calibration, and the uncertainties in the retrieval are common sources for systematic uncertainties . These amount to around 20 % for HCHO and are typically not included in dSCD uncertainties.

Systematic differences in data collection and processing between sites are unavoidable. The instruments do not share identical hardware, and ATTO, the only instrument operated by the Max Planck Institute for Chemistry, uses slightly different fit settings compared to the other instruments. In addition, the O4 vis dSCDs at ATTO are scaled as described above. At Incheon, viewing elevations below 3° are blocked, thereby reducing sensitivity close to the surface compared to measurements at 1° or 2° elevation. At Athens, the instrument is located at 500 m a.s.l., while the city centre lies near sea level. Under shallow boundary layer conditions, such as in winter, the effective light path may therefore only partially sample the polluted boundary layer, resulting in lower measured columns. However, since CHOCHO and HCHO concentrations peak in summer, when the boundary layer is typically well developed, this effect is expected to be small.

To quantify the uncertainty of RGF, we modify the uncertainty propagation from to include the O4 ratio: 6RGF*=ab⋅cd7sRGF*=cbd⋅sa2+-acb2d⋅sb2+abd⋅sc2+-acbd2⋅sd212 with a, b, c, d, sx representing dSCDvisCHOCHO, dSCDUVHCHO, dSCDUVO4, dSCDvisO4, and the respective standard error. We use the uncertainties obtained from the DOAS fit to account for random uncertainties. The annual and seasonal median uncertainties of RGF* per station are listed in Table S9 in the supplement. The random uncertainties are higher during winter (Orléans, Athens, Incheon) and wet season (ATTO). The relative uncertainties of RGF* on an annual scale range from 10 % to 20 % for all stations.

A diurnal cycle describes the variation over a day. It allows to compare with other variables that change regularly over the day, e.g. incoming solar radiation or car traffic. For the case of RGF, multiple diurnal cycles were reported. At two sites, one in India (semi-urban) and one in Thailand (rural), and observed a diurnal cycle with a noon maximum for RGF based on VCDs retrieved from MAX-DOAS measurements. The values ranged from 2 %–4 %. also found the diurnal cycle of RGF to be less pronounced in the dry season compared to the wet season, which we will revisit for ATTO in Sect. .

investigated the diurnal cycle at two predominantly biogenic sites at higher altitudes (Sierra Nevada Mountains, 1315 m; Rocky Mountains 2286 m) with field campaigns in July 2009 and August 2010 utilizing in-situ instruments. The average RGF values for both campaigns were about 2 % and 1.7 %. At the Sierra Nevada site, RGF increased to about 3 % around midday to afternoon. Whereas the Rocky Mountains campaign showed only minor diurnal variability. attributed the observed enhancements primarily to anthropogenic VOCs and biomass burning plumes encountered during the campaigns.

The diurnal cycles of RGF* in local solar time (LST) differ strongly across the four stations (Fig. ). Anthropogenic sites show pronounced diurnal variability, while the biogenic sites show relatively little variation over the day. At ATTO and Orléans, the diurnal cycles are relatively flat. In contrast, Athens and Incheon exhibit higher average values and strong diurnal patterns, with peaks around 10:00 LST in Athens and noon in Incheon. In Athens, the cycle follows morning rush hour, whereas Incheon has a noon maximum, indicating different drivers of RGF* over the day for both cities.

The diurnal pattern of RGF* is broadly consistent across seasons, although seasonal offsets in the absolute values are present. The largest offset occurs between the wet and dry seasons at ATTO, which is discussed in detail in Sect. . Notably, although the diurnal cycles of HCHO and CHOCHO individually change between seasons, their ratio RGF* retains a similar diurnal shape throughout the year (Fig. ).

Except at ATTO, data availability decreases in the early morning and late afternoon due to the applied SZA filter, which excludes measurements at large SZA. Throughout this study, marker size is scaled to the number of observations per bin; smaller markers therefore indicate reduced bin size. The detailed mapping of bin sizes is provided in the Supplement (Fig. S4). Data from these times of day are mainly collected during summer months, introducing a seasonal bias in the early and late portion of the diurnal cycle. Furthermore, the number of valid data points decreases substantially during the winter months at Orléans, Incheon, and Athens, primarily because we filter by relative error of CHOCHO dSCDs, which increases for low atmospheric concentrations. Filtering by relative error is needed to limit the scatter of RGF*, but it means that RGF* is more representative for high CHOCHO and HCHO columns.

The effect of scaling the vis O4 dSCDs for ATTO is highlighted again by showing the original data with the blue lines in Fig. . The overall high O4 dSCDs in the visible lead to a really low O4 ratio (Fig. m), which is mirrored in the overall low level of RGF* (Fig. a). The O4 ratio, after scaling ATTO, is of similar magnitude across sites and does not contribute to a pronounced diurnal cycle.

Examining the components of RGF* in Fig.  reveals that CHOCHO behaves differently across the four stations. HCHO dSCDs follow a U-shaped diurnal cycle at all stations, with a maximum in the morning and evening and a minimum around noon. This pattern has previously been attributed to enhanced sinks (photolysis and OH oxidation) dominating around midday . However, the underlying processes are more complex as they can also promote secondary formation of CHOCHO and HCHO by breaking down VOC precursors.

The diurnal cycle of the CHOCHO dSCDs varies in magnitude and shape across stations. ATTO also shows a pronounced U-shape. Orléans exhibits a relatively flat diurnal cycle. Contrasting to that, the anthropogenic stations show a different behaviour. Here, we find higher daily averages plus a maximum in Athens around 10:00 LST and in Incheon over noon. The shapes of the diurnal cycles at the anthropogenic stations suggest a stronger link to anthropogenic activity for CHOCHO than HCHO. Since direct CHOCHO emissions are suspected to be low , anthropogenically emitted precursors with a high CHOCHO yield might be a possible explanation, like aromatics or acetylene/ethylene . Furthermore, other effects independent from emissions could have an influence, like differences in photolysis, OH loss, heterogeneous uptake, and wet removal, but our dataset does not allow to separate such effects. Resulting different photochemical lifetimes of CHOCHO and HCHO might also contribute to the shape of the diurnal cycle of RGF*. Under simplified conditions, a longer lifetime of CHOCHO compared to HCHO, results in an increase of RGF* and a decrease otherwise (see Fig. S7).

Considering these curves, the diurnal cycle of RGF* appears to be driven by CHOCHO. The enhanced daily mean RGF* in Athens and Incheon can be explained by the overall higher CHOCHO levels. The shape of RGF* diurnal cycle can be attributed to the behaviour of CHOCHO dSCDs. Similar shapes between CHOCHO dSCDs and HCHO dSCDs lead to flat cycles at ATTO and Orléans, whereas the different shapes of CHOCHO dSCDs and HCHO dSCDs lead to a pronounced diurnal cycle of RGF* at the anthropogenic stations.

A direct quantitative comparison with previous studies is complicated by methodological differences: whereas report in-situ point measurements and and derive RGF from VCDs, our RGF* is based on corrected dSCDs, which integrate over a slant light path and are therefore sensitive to a different effective measurement volume (Sect. ). Despite this, the qualitative diurnal patterns are broadly consistent. The midday peak observed at Incheon is also reported for rural and semi-urban sites in Southeast Asia . However, the occurrence of similar patterns across differently classified sites highlights a broader challenge in the literature: the lack of a uniform site categorisation complicates cross-study comparisons of RGF. At our predominantly biogenic sites ATTO and Orléans, the diurnal cycle is comparatively flat, which is consistent with the weak diurnal variability reported by for high-altitude biogenic sites.

In summary, RGF* shows enhanced average values over the day for anthropogenic stations, due to enhanced CHOCHO levels. This indicates that RGF* contains information about the different environments, which supports its usage as a proxy for VOC origin. The pronounced diurnal cycles for anthropogenic stations, however, complicate the interpretation as the timing of the measurement becomes important. The implications for comparing RGF values of different studies are discussed in Sect. .

The variation over the year, the seasonal cycle, enables to investigate how a variable is connected to changes of other variables based on seasons. Multiple studies have reported seasonal cycles for RGF so far: and found a relatively flat seasonal pattern at Pantnagar (India, described as semi-urban) based on MAX-DOAS VCDs. At a second site, Phimai (Thailand, described as rural), the seasonal cycle showed an increase from January to September. Similarly, , analysing one year of MAX-DOAS VCDs from Guangzhou (China), found enhanced RGF values from November to April and lower values during the rest of the year.

The overall shape of the seasonal cycle of RGF* is similar across all four stations, with one minimum and one maximum per year (Fig. ). At Orléans, Athens, and Incheon, the lowest values occur in July and August (late summer), while the highest values are observed between October and March (winter). At ATTO, the seasonal cycle is shifted by several months, with a minimum in October (dry season) and a maximum extending into June (wet season). Notably, the minimum phase at the biogenic sites tends to be more prolonged compared to the anthropogenic sites. Fewer data points are available in winter due to filtering based on relative error (see Sect. ).

Examining the components of RGF* separately reveals that both trace gases behave differently for all four stations, whereas the O4 ratio is similar. Looking at the seasonal cycles of HCHO dSCDs we see one enhanced period during the middle of the year, a narrow peak during June and July for Athens, and an extended peak over four months spanning from June to October for the other stations. The annual means and the amplitude are comparable between the stations. The seasonal cycle of CHOCHO dSCDs is relatively flat with one peak in different months from June (Athens) to October (Incheon). One can see a shift to higher annual mean values from ATTO to Incheon. The anthropogenic stations show the highest CHOCHO dSCDs and more variability over the year.

Aggregating all data points by month and grouping them by dominant environment, i.e. Orléans and ATTO as biogenic and Athens and Incheon as anthropogenic, yields mean RGF* values of 3.2±1.1 % in the biogenic environment and 4.2 ± 0.8 % in the anthropogenic environment. Looking at mean RGF* per station leads to 3.4 ± 0.9 %, 2.7 ± 1.3 %, 3.9 ± 0.8 %, 4.6 ± 0.7 % for ATTO, Orléans, Athens, and Incheon respectively. Applying statistical tests, as described in Sect. , leads to significant differences (t = -5.8, p = 8 × 10⁻⁸) between the biogenic and anthropogenic group. A Welch-ANOVA (F = 19, p = 3 × 10⁻⁸) combined with a Games–Howell post-hoc test resulted in significant differences for all station pairs except ATTO–Orléans and Athens–Incheon. More detailed results can be found in the Supplement (Tables S6 and S7). It should be noted, that the aggregated data points maintain a significant autocorrelation due to the seasonal cycle.

Three seasonal shifts of the station footprints were identified from Fig.  for the non-tropical sites: increased sensitivity toward Paris during MAM at Orléans, reduced sensitivity to the harbour and city centre during JJA at Athens, and enhanced sensitivity to less densely populated regions northwest of Incheon during DJF. None of these shifts is clearly reflected in the seasonal cycle of RGF*, suggesting that a simple seasonal categorisation might not be enough to capture clear pathway dependencies .

For all stations except ATTO, the seasonal cycle of HCHO dSCDs closely resembles the seasonal cycle of temperature, which is shown on a second axis in Fig. . While temperature variability in ATTO is limited, a slight increase during September–October coincides with peak HCHO values. The seasonal cycle of CHOCHO does not show a clear influence by temperature. This highlights ATTOs unique tropical conditions: the near-constant temperature throughout the year means that seasonal variability in both trace gases is governed by processes other than temperature.

suggested, that the two trace gases undergo different processing in the dry and wet season and that the seasons probably have a different precursor composition. As reported by , enhanced RGF* values in the wet season and reduced values in the dry season are found, see Fig. . The daily mean is reduced by 0.7 %pt. in the dry season. The shape of the diurnal cycle is relatively flat. Since forest fires predominantly occur in the dry period, previously excluded pyrogenic activity may contribute to the observed changes. This would be supported by enhanced NO2 levels and aerosols during the dry season as shown by . Since biomass burning has been reported to lead to higher RGF levels , the observed low median values at this site are unlikely to reflect a significant pyrogenic contribution. Individual pyrogenic events may nonetheless produce enhancements in RGF* that are not captured in the median.

The discrepancy between wet and dry season is in agreement with the findings of , where they found higher RGF during the wet season and lower RGF during the dry season in Phimai (Thailand). Furthermore, both seasons share the same diurnal cycle for . However, their diurnal cycle had a pronounced noon maximum, which is not present in this dataset, and might, even though the Phimai site is described as rural, hint at a stronger anthropogenic influence than at ATTO, see Sect. .

Having these points in mind, the seasonal cycle of RGF* seems to be driven, contrary to the diurnal cycles, by the variability of HCHO. The variability of HCHO dSCDs is strongly connected to the variability of temperature for non-tropical stations and seems to be connected to the dry/wet season for ATTO. The enhanced annual mean RGF* at anthropogenic stations can be explained by overall higher CHOCHO levels.

As with the diurnal cycle, a direct quantitative comparison is complicated by the fact that previous studies derive RGF from VCDs, whereas our RGF* is based on corrected dSCDs at the lowest elevation angles, which correspond to a different effective measurement volume (Sect. ). With this caveat in mind, the seasonal pattern at our anthropogenically influenced stations resembles most closely the winter enhancement reported by for Guangzhou. Our absolute RGF* values are lower than those reported by , which may partly reflect the difference in measurement volume (dSCD vs VCD) rather than a true difference in RGF. At our more remote stations, the magnitude of RGF* is comparable to that reported by for Pantnagar, even though no progressive annual increase is observed like at Phimai.

published global RGF maps based on the TROPOMI observations for the year 2019. Although our RGF* is derived from dSCDs and therefore does not correspond to the exact same measurement volume (Sect. ), a comparison of the magnitude of annual means is still meaningful. Extracting RGF values at our measurement sites from their maps for 2019 suggests the following ranking: Incheon > ATTO > Orléans. Athens could not be identified in their maps due to its vicinity to the coastline. Furthermore, maps show enhanced RGF values during the wet season compared to the dry season at the ATTO site, which is consistent with our observations.

To conclude, we see a similar pattern for seasonal cycles as for diurnal cycles: RGF* exhibits a cycle and its average and its amplitude are more pronounced for anthropogenic stations, but this time originating from variations in HCHO. This complicates the interpretation of RGF* as a proxy for VOC origin, because many other seasonal effects can contribute to its variation, e.g. temperature, which are difficult to disentangle from changes in VOC origin over the year. Moreover, longer time series are needed for measurement campaigns to avoid sampling biases.

As anthropogenic emissions are typically lower on the weekend, the weekly cycles can be used as an indicator for the contribution of anthropogenic emissions . reported a weekly cycle in Athens for glyoxal and to a lesser extent for formaldehyde, but only for measurements dominated by urban air.

To our knowledge, no previous study has investigated weekly cycles specifically for RGF, but from the findings of , we expect a weekend effect may occur. In Fig. , ATTO and Orléans display flat weekly cycles, while the anthropogenic stations show an offset between weekday and weekend. Moreover, as seen and discussed before for diurnal and seasonal cycles, the average value throughout the week is higher for the anthropogenic stations. It should be noted, that RGF* for Incheon is reduced not only during the weekend but also on mondays.

For both stations, the mean weekday RGF* exceeds the mean weekend value by 0.5 %pt., corresponding to a reduction of approximately 10 % on weekends. Although this relative difference is comparable to our systematic uncertainties, these uncertainties are expected to affect all days uniformly and should therefore not be relevant for the weekend effect. As described in Sect. , the differences between weekday and weekend are significant for Athens (t = 4.4, p = 2 × 10⁻⁵) and Incheon (t = 2.7, p = 8 × 10⁻³).

For ATTO and Orléans the weekly cycles of both OVOCs are relatively flat and show no weekend effect (Fig. ). Comparing both OVOCs over the week for the anthropogenic stations, CHOCHO dSCDs show a strong weekend effect for Athens and Incheon. HCHO dSCDs, however, do not show a strong decrease on the weekend, therefore the weekend effect observed for RGF* is driven by the weekend effect from CHOCHO dSCDs.

To summarize, RGF* exhibits a weekend effect for anthropogenic stations, driven by the weekend effect of CHOCHO dSCDs. Showing a weekend effect supports RGF* usage as a proxy for different VOC origin, as changes in anthropogenic emissions are mirrored in RGF*.

Few studies have investigated meteorological influence on RGF until time of writing. , who analysed long-path DOAS measurements in Shanghai during summer, mentioned an increase of RGF with temperature over their campaign period. The temperature dependence of RGF* exhibits a similar pattern across all stations (Fig. ): at lower temperatures, values remain relatively stable with some fluctuations. However, starting from about 15 °C, RGF* decreases with a maximum reduction of up to 1.9 %pt. observed at Athens. The O4 ratio does not vary with temperature. Looking at HCHO dSCDs it is visible, that the HCHO levels grow exponentially with increasing temperatures across all stations. CHOCHO dSCDs also rise with temperature, most clearly visible for Orléans and way less pronounced for ATTO, Athens, and Incheon.

An exponential behaviour is expected, especially for the biogenic stations, as biogenic emissions of precursors are known to increase exponentially with temperature ; higher temperatures enhance biogenic activity, which in turn leads to greater VOC emissions. In addition, the secondary formation via OH oxidation should increase with temperature as reaction rates rise .

For the anthropogenic stations, the situation is different. Here, we expect the anthropogenic emissions to be temperature independent and attribute the exponential increase with temperature primarily to the increased secondary formation at high temperatures. Adding to that, recent studies suggest that local biogenic VOC emissions in urban environments may play a more important role in local atmospheric chemistry than previously assumed . It is noteworthy that both trace gases do not behave identically at the anthropogenic stations. All above named arguments, increased secondary formation or potential local biogenic sources, hold for HCHO and CHOCHO, therefore, an important piece of information is still missing.

To summarize, RGF* decreases with higher temperatures in our dataset, which is driven by the strong exponential increase with temperature of HCHO. Similar to the other sections, this complicates the interpretation of RGF as a proxy for VOC origin, as the RGF* values depend on temperature regardless of the environment of the sites. This has to be considered in the interpretation of RGF* when using simple thresholds.

As shown in the previous section, RGF* exhibits a strong dependence on temperature in our dataset. To isolate the variability not associated with temperature, we apply a regression-based correction to remove the temperature-correlated component. Specifically, deviations of RGF* from its arithmetic mean are fitted using an outlier-robust orthogonal linear regression. Influence from residuals exceeding two standard deviations from zero is reduced by applying linear weighting beyond this threshold. The fitted temperature-dependent component is then subtracted from the dataset.

After removal of the fitted component, the temperature-normalised RGF* (Fig. e–h) shows only weak dependence on temperature. The diurnal cycles remain largely unchanged by the temperature correction, apart from a slightly reduced amplitude. In contrast, the seasonal variability is substantially reduced at all non-tropical sites, where the seasonal cycle nearly vanishes. At ATTO, however, the seasonal cycle persists, consistent with the comparatively small seasonal temperature variability in the tropics. Revisiting the remaining meteorological variables using the temperature-normalised RGF* shows that most of the previously observed variability disappears (see Fig. ). This is consistent with the strong intercorrelations among the meteorological variables, indicating that the temperature-driven component can account for most of the variability seen for the other parameters.

Overall, removing the temperature-driven component largely eliminates both the apparent dependence of RGF* on other meteorological variables and the seasonal variability at the non-tropical sites. This suggests that temperature, or processes closely coupled to it, accounts for most of the observed seasonal variability in RGF*, while playing a lesser role in driving diurnal variability.

RGF has been computed from data gathered by various different platforms and with different measurement techniques since its first usage. Table  lists the various approaches to compute RGF: volume mixing ratios (VMRs), dSCDs with correction terms, and mean VCDs. All these quantities represent RGF in a different measurement volume. For the particular case of VMR RGF and satellite column-averaged RGF, discusses possible causes for disagreements and also briefly mentions the topic of different measurement volumes. We want to further generalize and expand on this inherent difference between the measurement techniques.

Firstly, VMRs obtained by in-situ measurements determine the RGF at the position of the instrument at the sampling time. Here RGF represents the smallest measurement volume, a point measurement. For RGF values computed via dSCDs from a low elevation angle with O4 correction (this work), the situation is similar to RGF via VMRs. However, a different volume is probed. Looking towards the horizon, the retrieved dSCDs are dominated by absorption in the lowest layer. Therefore, the resulting RGF is dominated by the volume along the average light path close to the surface until the scattering point. Lastly, there is column-averaged RGF from either ground-based instruments or satellite-based instruments. Both platforms allow to probe the whole atmospheric column, however with different vertical sensitivities, see Sect. . The column-averaged RGF represents the whole column including the vertical information about the trace gases. However, satellite columns are obtained for the whole ground pixel area, which is larger than the inherent spatial averaging for ground-based columns due to the field of view (FOV).

So even though, all ratios of CHOCHO and HCHO are called RGF, they do not necessarily represent the same measurement volume. Different measurement volumes go along with different kinds of averaging or no averaging at all in the case of in-situ RGF. Therefore, processes of different scales (spatial or temporal) contribute differently to the RGF representing different measurement volumes.

As discussed in the validation study of the TROPOMI HCHO product using ground-based MAX-DOAS observations by , satellites and ground-based MAX-DOAS instruments have opposite vertical sensitivity profiles. Satellite-based instruments have minimal sensitivity near the surface, whereas MAX-DOAS instruments are most sensitive at the surface, with sensitivity decreasing to near zero above approximately 3 km altitude. found that accounting for these sensitivity differences can reduce the bias between the two platforms by up to 20 %.

For RGF, this implies that satellite-derived values are biased toward higher atmospheric layers compared to ground-based measurements, even when vertical profiles or vertical column densities (VCDs) are used. Notably, previous studies have shown that RGF can vary with altitude. For example, demonstrated that the diurnal behaviour of RGF changes significantly within the lowest 1 km, which may help explain some discrepancies between satellite and ground-based observations.

Pronounced diurnal and seasonal cycles in RGF* are visible at anthropogenic sites in our dataset. In the presence of such cycles, the time/period of measurement becomes critical. For short duration campaigns, the seasonal cycle has to be considered to avoid a sampling bias.

The diurnal cycle plays an important role when intercomparing satellites or comparing satellites with ground-based instruments. Sun-synchronous low-Earth orbit satellites, such as the one hosting the TROPOMI instrument, pass at a fixed local solar time over the equator and thus only capture a snapshot of the diurnal variability. Given that our observed diurnal cycles are relatively symmetric around noon and the overpass times surround noon (see Fig. ), only minor differences are expected between commonly used satellite instruments such as GOME-2, SCIAMACHY, TROPOMI, and OMI. Only for Athens, the diurnal cycle is shifted to earlier hours, so a notable effect is observed: the measurements during morning overpass are higher by approximately 0.5 %pt. than the afternoon.

When comparing satellite measurements to ground-based instruments, however, systematic differences can emerge in daily averages. In the most extreme case, for Incheon, this could result in an overestimation by TROPOMI of about 0.5 %pt. relative to the daily average. Importantly, since diurnal variability is most pronounced at anthropogenic sites, the magnitude of this effect differs across environments. Consequently, a spatially variable bias is expected between studies relying solely on satellite data and those based on ground-based observations. When directly comparing both platforms, it is important to use only data close to the overpass time to eliminate this bias. It is worth noting that new and upcoming geostationary satellites (e.g., GEMS, TEMPO, Sentinel-4) provide diurnal coverage, which should help eliminate such biases when comparing RGF from different platforms.

In the literature, one can find two different methodologies to computation RGF values. Firstly, RGF as the mean of the individual ratios (in the following called instantaneous RGF) and, secondly, RGF as the ratio of the mean of the HCHO and CHOCHO columns (in the following called global RGF).

Both approaches can be applied to any aggregated dataset, but in practise the global ratio is often used for RGF based on satellite data. Satellite retrievals are more challenging than ground-based retrievals: the increased distance to surface-level trace gases and the satellite viewing geometry result in lower sensitivity near the surface and the short integration time limits the signal to noise ratio of the individual measurement. To improve the signal-to-noise ratio, satellite measurements are commonly averaged over a defined period and area before calculating RGF from the averaged VCDs. The instantaneous RGF is primarily applied for datasets from ground-based instruments, as in this work, since the ground-based instruments generally provide a higher signal-to-noise ratio due to a longer integration time.

The order of operations matters as the division and the mean do not commute in general (∑A∑B≠∑AB), so the ratio of means (global RGF, Eq. ) is not the mean of ratios (instantaneous RGF, Eq. ). Here N refers to the number of CHOCHO dSCDs and M refers to the number of HCHO dSCDs. The instantaneous RGF requires pairs of simultaneous CHOCHO and HCHO measurements (M = N), therefore ensuring direct comparability but reducing data coverage. The global RGF is more forgiving and allows filtering every trace gas individually (M ≠ N), leading to potential sampling biases. If valid CHOCHO data occur mainly in summer while valid HCHO measurements are available throughout the whole year, the resulting global RGF would mix a seasonal average with an annual average and thus misrepresent the true annual relationship of CHOCHO and HCHO. 8RGFinstant=1N∑iNdSCDiCHOCHOdSCDiHCHO9RGFglobal=1N∑iNdSCDiCHOCHO1M∑iMdSCDiHCHO

As the usage of the global RGF is required for practical reasons, we investigate how both approaches differ by applying both methodologies to our ground-based dataset. The quality filters are applied in a way, consistent with the previous sections, that only valid pairs of simultaneous CHOCHO and HCHO measurements (M = N) are considered for the analysis.

The instantaneous RGF consistently yields higher values compared to the global RGF across all analyses made during this study. A clear systematic bias is visible for the differences between the instantaneous RGF and the global RGF in Fig. , and the magnitude of this bias varies depending on the station, month, and time of day. Looking at the diurnal cycles, a large systematic difference is present at ATTO (Fig. a) throughout the day. The largest differences occur in Orléans (Fig. b), where discrepancies reach just below 1 %pt. around 10:00 LST. In contrast, the anthropogenic sites Incheon and Athens (Fig. c, d) show much closer agreement between the two approaches, with overall smaller differences. A more detailed view of the 10:00 LST bin distributions, as well as extended daily time series for Orléans, is provided in the Supplement (Figs. S5 and S6).

The magnitude of the difference between both methods depends primarily on the variability and shape of the underlying HCHO and CHOCHO distributions within each bin, as well as on their correlation. The consistently higher instantaneous RGF values are driven by small HCHO dSCDs in the denominator, which disproportionately increase individual ratios and introduce skewness. Consequently, the bias between both methods increases with growing asymmetry of the ratio distribution. For a more formal reasoning of the conditions under which the ratio of means equals the mean of ratios see .