CLAAS-3 provides detailed information on various cloud properties, offering high spatial and temporal resolution (3 km × 3 km at nadir, every 15 min) and covering the period 2004–present. As mentioned before, CLAAS-3 retrievals are based on observations from SEVIRI, which flies on board geostationary Meteosat Second Generation (MSG) satellites Meteosat-8, Meteosat-9, Meteosat-10 and Meteosat-11, covering the period 2004–present. For the CLAAS-3 processing, SEVIRI solar channel observations were calibrated based on the latest (collection 6.1) Aqua MODIS reflectances, following the approach described in Meirink et al. (2013). Extended to include all four MSG satellites, this methodology ensures a temporal stability of CLAAS-3 that is suitable for long-term analyses (see, e.g., the CLAAS-3 validation report, available in Meirink et al., 2022). The instantaneous (level 2) retrievals, which are based on the calibrated (level 1) reflectances, are aggregated into (level 3) daily and monthly averages at 0.05° × 0.05° and monthly diurnal averages at 0.25° × 0.25°. The areas covered include Africa, Europe, the Atlantic Ocean, parts of South America, the Indian Ocean and the Middle East. CLAAS-3 includes cloud fractional coverage (fc), cloud phase (liquid and ice), cloud top height, pressure and temperature, cloud optical thickness (τ), effective radius and water path (W), and Nd. Details on the retrieval algorithms and the validation of CLAAS-3 are given in Benas et al. (2023) and in dedicated technical documentation available in Meirink et al. (2022).

Regarding the cloud properties examined in this study, Nd is retrieved from re and τ, assuming an idealized stratiform boundary layer cloud, as described in Bennartz and Rausch (2017), while re and τ are retrieved based on a look-up table (LUT) of pre-calculated reflectances (Roebeling et al., 2006; Nakajima and King, 1990). W is also calculated from re and τ, assuming vertically homogeneous water content (e.g., Stephens, 1978). Since the 0.6 µm and the 3.9 µm channels are used for the retrieval of re and τ, it follows that re, τ, W and Nd are only available during daytime, which is defined as solar zenith angle values lower than 75°. For consistency, fc is also provided in daytime time slots (fc,day) in addition to the all-day retrievals fc.

All data used in this study come from level 3 monthly averages, either of all time slots or diurnally resolved, and refer to liquid clouds only, as aggregated from level 2. Thus, the successful exclusion of ice clouds from this analysis depends on the performance of the CLAAS-3 cloud phase retrieval algorithm. Evaluation results of CLAAS-3 cloud phase, available in Meirink et al. (2022), show good performance and very good agreement with reference data sets over the wider SE Atlantic region.

Occurrences of cloud edges and broken clouds, which are associated with retrieval biases in re and τ (and consequently W and Nd), can also affect level 3 averages. In CLAAS-3 level 3 aggregation algorithms, level 2 results of re and τ falling outside the LUT, which are usually associated with such cases, are excluded from level 3 averages. While this process does not ensure complete removal of the mentioned retrieval biases, it is expected that their impact on level 3 values will be minor. Additionally, different biases in and outside the shipping corridor are not expected.

For the identification of the shipping corridor we use shipping traffic density data available from a collaboration of the World Bank with the IMO. This data set is based on all hourly ship positions received by the Automatic Identification System (AIS) between January 2015 and February 2021 (Cerdeiro et al., 2020). The data represent the total number of AIS positions reported by ships in grid cells of dimensions 0.005° × 0.005° (approximately 500 × 500 m at the Equator).

For the present study, the original ship density values are aggregated to a coarser resolution of 0.25° using 50 × 50 grid cell blocks. The threshold for ship density classification is determined by calculating the mean plus 1 standard deviation of the ship density values within the wider SE Atlantic region shown in Fig. 1. Using this threshold, the ship density values are converted to a binary flag, with a flag value of 1 for cells with ship density values greater than the threshold and 0 for cells with values below the threshold. Finally, the flag is downscaled to the original CLAAS-3 level 3 resolution of 0.05°, in order to determine the corridor center in CLAAS-3 coordinates. This is done by selecting, in each latitudinal row, the central grid cell from the ones marked as “corridor”, i.e., having a flag value of 1.

While the threshold used is arbitrary, it is efficient in distinguishing the major shipping corridors from lower “background” ship density values, as Fig. 1 shows. Two corridors are identified in the study area (20–10° S, 10° W–10° E), which is shown in red. We focus on the denser one, which produces notable differences in the Nd and re values (Fig. 2a and b). This corridor is also further away from the coast, hence least subject to the influence of terrestrial emission sources.

The methodology used for the quantification of the shipping corridor effect on cloud properties takes advantage of the good alignment of prevailing winds in the region with the corridor orientation. This alignment constrains the emissions and renders their effects on clouds more pronounced (Diamond et al., 2020).

To assess how shipping corridor emissions impact cloud properties, we first calculate the angle between the shipping corridor and the south-to-north direction. Then, for each point positioned at the corridor's center, we determine the line perpendicular to the corridor, based on this angle. We then identify the grid cells along this line and calculate their distances from the corridor center (measured in kilometers). This process yields cloud property data variations with distance from the corridor's center on both sides. By averaging these values along the corridor line, we create a distribution centered on the midpoint of the corridor. This distribution provides insights into how cloud properties change relative to their distance from the corridor center on both sides.

The underlying assumption in this approach is that the corridor effect will manifest as a deviation from an underlying smooth distribution. Motivated by the analysis of Diamond et al. (2020), in which the shipping-affected area spans 5.0° in the east–west direction, we define a distance of 250 km on both sides of the corridor center as a reasonable estimate of the affected area. To quantify the corridor effect, we apply a cubic fit to the 500 km affected range, based on data from the ranges 250–400 km away from the corridor on both sides. These ranges, and the fitted values within the affected area, represent a scenario without the shipping corridor, and they are subtracted from the actual values in order to estimate the corridor effect. When reporting an average corridor effect based on these differences, we focus on the corridor core, defined as a 150 km wide area (±75 km) around its center.

To assess the statistical significance of the corridor effect on a cloud variable, we examine the distribution of the corridor effect values within the corridor core region, defined above. If the 95 % confidence level (2σSD range, assuming a normal distribution) does not contain zero, we conclude that the corridor effect is statistically significant at the 0.05 level.

All CLAAS-3 variables come with a pixel-based estimated uncertainty at instantaneous (level 2) retrievals. This uncertainty is propagated to level 3 daily and monthly averages. The implementation of the error propagation follows Stengel et al. (2017). For the daily averages, two cases are provided in CLAAS-3, with uncertainty correlations c equal to 0.1 and 1.0. For the monthly averages, which are computed based on the daily averages, the same two scenarios are available in CLAAS-3, using the daily mean uncertainty correlation c=0.1. For consistency, here we use the scenario where c=0.1 also for the monthly mean uncertainty. When averaging monthly mean data, we calculate the uncertainty of the averaged data (σ〈x〉) based on 1σ〈x〉2=1NσSD2+c〈σi〉2, where N is the number of grid cells, σSD the standard deviation of the monthly mean values and 〈σi〉 the average uncertainty of these values (based on the c=0.1 scenario for monthly means).

For the quantification of the uncertainty of the no-ship scenarios, we repeat the cubic fit approach described above five times, varying the distance of the data ranges used in the fit from 150–300 to 350–500 km. The uncertainty of the no-ship scenario is then given by the standard deviation of these five runs. As mentioned before, the range 250–400 km is used for the quantification of the corridor effect. The corresponding uncertainty of the corridor effect is finally calculated as the combined uncertainty of the actual profile and the no-ship scenario.

Figure 2a and b show maps of Nd and liquid re averages over the study region, calculated from the entire CLAAS-3 monthly time series (2004–2023). The shipping corridor appears as a straight line in a NW–SE direction in both Nd and re. Consistently with the Twomey effect, Nd in the corridor is higher than in the surroundings, and re is lower. This is shown even more clearly in the across-corridor average distributions of Nd (Fig. 2c) and re (Fig. 2d) and the ensuing differences from the no-ship scenarios (Fig. 2e and f, respectively). Estimation of the average corridor effect, as described in the previous section, yields an increase in Nd by 6.1 ± 1.5 cm⁻³ on average over the affected core region and a decrease in re by 0.21 ± 0.04 µm. The 2σSD values of the distribution of the corridor effect in the corridor core are 2.3 cm⁻³ and 0.08 µm, for Nd and re, respectively, showing that the effect on both is statistically significant at the 95 % confidence level. The average effect values agree well with those given by Diamond et al. (2020) for approximately the same region, even though they use a different approach and a wider region to determine their “NoShip” scenario. For Nd, they found a corridor effect of ∼ 5 cm⁻³ (based only on Aqua MODIS), while the effect found for re was -0.29 µm for Aqua MODIS and -0.28 µm for Terra MODIS.

Corresponding results for W and fc,day, the two cloud variables associated with possible adjustment mechanisms, are shown in Fig. 3. In the W case, the corridor perturbation is still apparent (Fig. 3c and e), with an effect of -1.6 ± 0.5 g m⁻² in the core region. The 2σSD variation of the effects in the core is 0.5 g m⁻², implying that the corridor effect on W is statistically significant. The mean effect on W (-1.6 g m⁻²) is closer to the Aqua MODIS-based estimate of -1.3 g m⁻² from Diamond et al. (2020) than to the estimate from Terra MODIS (-0.5 g m⁻²). The response of W to Nd changes is complicated and depends strongly on the local meteorological and cloud conditions (see, e.g., Gryspeerdt et al., 2019, and references therein). The negative response found here is consistent with studies of similar cloud regimes (Manshausen et al., 2022; Gryspeerdt et al., 2019). The higher Nd values resulting from the ship emissions lead to an increase in the entrainment rate of dry air at the cloud top, thus decreasing W (Bretherton et al., 2007). Globally, however, results are not conclusive. A positive W adjustment is reported in Manshausen et al. (2022), while Wall et al. (2022, 2023) find decreases in W over global oceans when sulfate concentrations increase. However, these two studies are not limited to ship tracks, so their findings may not be directly comparable to the previous one. More recently, Tippett et al. (2024) showed that the W response to aerosol perturbations from ship emissions is weak on average, after correcting for biases in prior research based on tracking ship-affected air masses (Manshausen et al., 2022, 2023), related to correlations between wind and cloud properties. Several studies analyzing visible ship tracks also indicate weak W response to emitted aerosol (e.g., Toll et al., 2019).

In the case of fc,day there is a weak feature that appears centered along the corridor, with slightly higher values on the sides (between 100 and 200 km) compared to the center (Fig. 3d). Estimation of the corridor effect shows a weak increase of 0.03 ± 0.02 %, which is statistically insignificant at the 95 % confidence level (2σSD=0.08). Diamond et al. (2020) also report weak, non-significant increases in daytime cloud fraction from MODIS on both Terra (0.05 %) and Aqua (0.15 %) over roughly the same region. However, based on the shape of the across-corridor fc,day distribution (Fig. 3d) and the corresponding effect (Fig. 3f), it is possible that the corridor emissions induce a decrease in fc,day in a narrower range; in fact, the estimated uncertainty of the no-ship scenario (grey band in Fig. 3d) includes both possibilities on the sign of the corridor effect: an increase or a decrease in fc,day. This is also shown in Fig. S2d, where the no-ship scenarios based on data from different distance ranges from the corridor center are shown: results for Nd, re and W show that this method is robust for calculating the corridor effect on these variables. In the fc,day case, however, if we assume that unaffected areas start closer to the corridor center, and we apply the no-ship scenario fit accordingly, the corridor effect switches from positive to negative and leads to a decrease in fc,day by -0.22 ± 0.23 % on average. While the reason that the corridor would affect fc,day in a narrower range compared to other cloud properties is not obvious, a decrease in fc,day would be more in line with the decrease in W. Apart from the expected error in the method, another possible explanation of Fig. 3d and f is that the effect is more complicated, with a decrease closer to the corridor center and an increase on its sides. Investigation of such a scenario, however, requires modeling underlying processes beyond the scope of this study.

The same analysis was also conducted for τ, the cloud optical thickness. Based on the relationship of τ with Nd and W (see, e.g., Eq. (2) in Bennartz and Rausch, 2017), and the changes over the corridor of the two latter, a small decrease should be expected in τ. However, there is no apparent corridor effect in the across-corridor τ distributions, unlike the cloud properties examined before (see Fig. S3). This result may be due to τ variability across the corridor dominating the signal and highlights a limitation in our methodology: if the corridor does not manifest as a deviation from an otherwise smooth background, no conclusive remarks on its effect can be made. Two opposing mechanisms, namely an increase in τ due to the Twomey effect and a decrease due to the decreasing W, may also be acting here. Finally, this across-corridor τ distribution, which is a time series average, does not exclude the possibility of discernible corridor effects appearing in the seasonal and diurnal results. Thus, τ is still examined in the analyses that follow.

Apart from differences in the methodology for the shipping corridor identification and the estimation of its effects, the different spatial resolutions of MODIS and SEVIRI are also a factor that may play an important role when comparing our results with those from Diamond et al. (2020), who focused on almost the same region. A coarser resolution will lead to decreased τ and increased re values; this is the result of an increased probability of pixels containing a mixture of cloudy and clear scenes, which will lead to lower reflectances in both the visible and the shortwave infrared channel used in the retrievals. Thus, the coarser resolution of SEVIRI (∼ 3 km) can lead to biases with corresponding MODIS results (∼ 1 km resolution). However, it is beyond the setup of this study to disentangle such biases from differences originating in the methodology of the two studies and in the two sensors themselves. Additionally, the different resolution is not expected to affect the corridor effect significantly: the effect is estimated based on retrievals from the corridor and surrounding areas, which will be similarly affected by the coarser resolution of SEVIRI compared to MODIS.

Figure 4 shows the seasonal variability in Nd, liquid re (Fig. 4a), W and fc,day (Fig. 4b) spatial averages over the study domain and the corresponding corridor effects. Average monthly values of the effect, along with their statistical significance at the 95 % confidence level, are shown in Table 1. The corridor effect on Nd, re (Fig. 4c) and W (Fig. 4d) is consistent in sign and detected throughout the year, albeit with varying strength (see Fig. S4b, d and f for respective monthly profiles).

The highest Nd values appear in May, June and July and secondarily in March and April (Fig. 4a). Lower values occur in local spring and summer, with the lowest occurring in September. Liquid re is anti-correlated with Nd, with the highest values occurring in August and September and the lowest in April–June. The seasonal cycle of Nd is very similar to corresponding results from previous studies based on MODIS (Bennartz and Rausch, 2017; Grosvenor et al., 2018), with CLAAS-3 exhibiting higher values. The peak in July and the rapid drop in August and September are prominent in all data sets. A similar Nd seasonal cycle peaking in summer is also found in Li et al. (2018) over a larger region and using both MODIS and CALIPSO data. Zeng et al. (2014) also find Nd peaks west of Namibia in April and July, based on MODIS and CALIOP data. Previous studies report that the seasonal cycle of Nd in this region is affected mainly by aerosol emissions from southern Africa (Grosvenor et al., 2018; Li et al., 2018; Bennartz and Rausch, 2017). The presence of absorbing aerosols from biomass burning activities above the cloud layer, which is typical in this region for certain months, could also have an artificial effect on the retrieved τ and re: by darkening the scene, especially in the 0.6 µm channel, smoke aerosols over clouds can lead to the retrieval of lower τ as well as lower re. However, when using the 3.9 µm channel reflectance, the effect on re is – in comparison to shorter wavelengths – relatively small (Haywood et al., 2004). Since the Nd retrieval depends weakly on τ and much more strongly on re (see, e.g., Eq. (2) in Bennartz and Rausch, 2017), the absorbing aerosol effect on Nd is also expected to be modest compared to retrievals based on smaller wavelengths (e.g., 1.6 µm). Furthermore, smoke aerosols in the region are expected to have a similar effect in both corridor-affected and unaffected parts, thus influencing the corridor effect calculations even less than area-wide average values.

The strong seasonal cycle of the (in-cloud) W follows that of fc,day (Fig. 4b), which peaks between August and November. In turn, the seasonal peak in fc,day coincides with the season of maximum static stability, which follows the seasonal cycle of sea surface temperature (SST; Klein and Hartmann, 1993) inversely. Thus, thicker clouds in September–November can explain the peak in W but also the higher re values, which are expected to grow with height. This season is also reported by Diamond et al. (2020) as giving the strongest corridor signal. In our case, the corridor effect on Nd is consistently positive and statistically significant throughout the year (meaning more cloud droplets in observations compared to a scenario without ships) and appears stronger from July to December (Fig. 4c and Table 1). Similarly, for re, there was a consistently significant negative corridor effect, meaning smaller cloud particles in reality compared to a no-ship scenario. The presence of the corridor also causes a decrease in W throughout the year (Fig. 4d and Table 1). In the case of fc,day, the corridor signal is ambiguous and appears to change sign during the year (Fig. 4d and Table 1). However, a closer examination of monthly across-corridor profiles of effects on fc,day (Fig. S4h) shows that only in austral summer months (mainly October, December, February and March) do the profiles appear as deviations roughly symmetrical across the corridor center, indicating a distinguishable corridor effect. In these cases, actual values are lower than in the no-ship scenario. Thus, while the time series average corridor effect on fc,day is ambiguous (Fig. 3f), a clearer signal of fc,day decreasing over the corridor appears in austral summer. In other months, it is difficult to draw any conclusion on the shipping corridor effect on fc,day. Therefore, a statistically significant effect in these months (i.e., May–September values in Table 1), which is not accompanied by an across-corridor profile of changes as described before, should not be interpreted as a meaningful corridor effect.

Results of across-corridor τ profiles per month are shown in Fig. S4i and corresponding profiles of corridor effect in Fig. S4j. The latter, however, are only provided for completeness: the corridor does not manifest convincingly in any month examined, so the calculated effects in Fig. S4j cannot be used to draw any conclusion.

Figure 5 shows the diurnal variability of the Nd and re averages over the study area (Fig. 5a, c) and the corresponding average corridor effects (Fig. 5b, d). Corresponding across-corridor profiles of effects for every time slot when data are available are shown in the Fig. S5. Since Nd and re can only be retrieved during the day, it was required that for each time slot, the study region is completely covered with data from all months in the time series. In this way, time slots at the beginning and end of the day, when high solar zenith angles may lead to problematic retrievals, were omitted. For the same reason, the two extremes of the remaining available time slots (08:00 and 15:00 UTC) were also removed from the analysis. A statistical significance analysis of the diurnal cycles was not performed due to the coarser resolution of these data, which leads to very few points inside the corridor core.

Nd is nearly constant during the available time slots of the day (Fig. 5a). The effect of the corridor on Nd also appears stable during the day, ranging between 5 and 6 cm⁻³, with somewhat higher values in the afternoon (Fig. 5b). Liquid re decreases slightly during the day (Fig. 5c), in consistency with previous findings (Seethala et al., 2018). The corridor effect on re also gets weaker as the day progresses, stabilizing early in the afternoon (Fig. 5d).

Diamond et al. (2020) report larger corridor effects on Nd during the Terra overpass (∼ 10:30 local time), compared to Aqua (∼ 13:30 local time), contrary to this study. Their estimation of the relative change in Terra Nd is based on respective changes in W and re because of the absence of a published Terra Nd product. For re they report similar effects during the Terra and Aqua overpasses, as also found here (Fig. 5d).

Corresponding results for W show a strong decrease during the day, accompanied by a weakening of the corridor effect (Fig. 6a and b). In the afternoon, the corridor effect on W is about half compared to the morning value. The decrease in W during the day is in good agreement with results of Seethala et al. (2018): they also report peak values of W early in the morning and a decrease until the afternoon. A small decrease is also reported for re during the day. The decrease in W is associated with the cloud thinning, which is apparent in the fc diurnal plot (Fig. 6c).

The estimated corridor effect on W by Diamond et al. (2020) is lower in the morning (Terra overpass) than in the afternoon (Aqua overpass). This contrasts with our findings, which show similar decreases in the two relevant time slots (10:30 and 13:30 UTC in Fig. 6b), with a somewhat weaker effect during the Aqua overpass. Other studies of ship tracks in the northeastern Pacific, where the cloud conditions are similar, show even larger W decreases for Terra MODIS than for Aqua MODIS, with the former being almost double the latter (Christensen et al., 2009; Segrin et al., 2007). These results hinder concrete conclusions regarding the differences in the corridor effect between morning and afternoon from being drawn and highlight the value of using observations in more frequent time intervals, such as CLAAS-3, for similar analyses. However, diurnal observations should also be treated with caution, since they may suffer from diurnally varying biases related to scattering geometry (Smalley and Lebsock, 2023).

Since fc can also be retrieved at nighttime, the full 24 h cycle variation is available, showing the cloud thinning during day and the thickening during the night (Fig. 6c). It is interesting to note that the corridor effect on fc changes sign between day and night (Fig. 6d). It is negative during the night and becomes positive at day, contrary to what would be expected from the diurnal cycles of precipitation and evaporation, which maximize at night and day, respectively (e.g., Sandu et al., 2008). A closer examination of the fc difference profiles per time slot, however, shows that the positive day time differences have a local minimum at the corridor center (Fig. S5d). This is reminiscent of the pattern found also in the seasonal analysis of fc,day, suggesting that selection of a narrower range for the corridor-affected area during the day would lead to lower (or even negative) effects on fc. However, since this indication of a narrower affected area does not appear in other variables, no concrete conclusion can be drawn regarding the effect of ship emissions on fc during the day. It can be safely concluded, however, that during the night the shipping corridor exerts a negative effect on fc, as can be shown by examining shipping corridor and no-ship scenario profiles of fc on an individual time slot basis (Fig. S6).

Results on the diurnal variation of τ over the region, across-corridor profiles and corresponding estimates of corridor effect are shown in Fig. S7. Average values of τ decrease during the day, as expected (Fig. S7a). The diurnal variation of the corridor effect shows practically no effect in the morning, with slightly positive values in the afternoon (Fig. S7b). However, these results should be interpreted with caution, since corresponding across-corridor profiles have high uncertainty and show little or no appearance of corridor-centered perturbations (Fig. S7c and d–i).

In order to examine the strength of the corridor effect before and after 2020, when the stricter IMO regulations on sulfur-containing emissions were implemented, we repeated the analysis described in Sect. 3.1 for two time periods: 2004–2019 and 2020–2023. While the two time periods are not equal, the longer period before 2020 is more representative of the entire CLAAS-3 time range and reduces the risk of being affected by large year-to-year variability. The across-corridor distributions of the effect on Nd, re, W and fc,day are shown in Fig. 7. The effect of the shipping corridor on Nd, re and W has weakened notably from 2020 onward, acquiring almost half the values of the 2004–2019 period. On average, before 2020 the ship emissions caused an increase in Nd by 7.00 ± 1.49 cm⁻³, which weakened to 2.73 ± 1.50 cm⁻³ from 2020 onward. Similarly for re, the average decrease by 0.25 ± 0.04 µm due to ship emissions before 2020 weakened to 0.09 ± 0.04 µm from 2020 onward. Corresponding average effects on W are -1.80 ± 0.47 g m⁻² and -0.99 ± 0.52 g m⁻². In the fc,day case, results are less clear. The across-corridor distribution before 2020 shows some resemblance to the full period distribution (Fig. 3f), although with weaker characteristics. From 2020 onward, no corridor effect is apparent based on the shape of the distribution.

The corridor effects on Nd, re and W appear statistically significant at the 95 % confidence level in both time periods. Similar results were obtained when the differences between the corridor effect profiles before and after 2020 were examined: significant differences were found for Nd, re and W but not for fc,day. These results are summarized in Table 2.

In the case of τ, since the cubic fit approach does not produce useful results in either of the two periods examined, we analyzed the across-corridor profiles of absolute values. As shown in Fig. S8a and b, a significant decrease in τ is apparent in the period after 2020. This is analyzed further below.

To further examine how the recent changes in ship emissions affected the cloud properties along the corridor compared to less affected areas, we calculated, for each cloud property and grid cell in the study area, the difference between the averages from the periods from 2020 onward and before 2020. Results are shown in Fig. 8.

The shipping corridor is clearly visible in the Nd and re maps. In the case of Nd it manifests as stronger decreases, compared to an overall background decrease which is stronger closer to the coast. In the case of re, it appears as larger increases in the southern part of the corridor and smaller increases in the northern part, compared to background decreases. In the maps of W and fc,day differences, the corridor is not apparent. Instead, for both variables large decreases appear over the entire area. The same is true for τ (Fig. S8c). As discussed in Sect. 3.2, SST is the main driver for the seasonal variability of fc,day, and this is also the case for a longer term. Thus, a possible explanation for this apparent absence of a corridor effect change during the examined period is that changes due to ship emissions are hidden by a wider and stronger effect of SST changes on fc,day. This scenario is examined in more detail below.

The statistical significance of the differences shown in Fig. 8 was also assessed by comparing the average differences with their combined uncertainties. In the cases of Nd and re, differences are only significant in the southeastern part of the region (Fig. S9a and b), while they cover larger parts in the W, fc,day (Fig. S9c, d), and τ (Fig. S8d) cases. In no case is the shipping corridor highlighted from adjacent areas in terms of significance of differences. Similar findings over the region are also reported in Diamond (2023). The corridor, however, is clearly visible in the Nd and re differences maps in Fig. 8, which is a strong indication that these differences originate in ship emission changes.

As a further step in the assessment of the long-term changes in corridor averages and effects, the time series of monthly average Nd, re, W and fc,day over the corridor and the corresponding corridor effects were also analyzed. Figure 9 shows the resulting time series of averages (left column) and evolution of the corridor effects (right column). All time series were deseasonalized and smoothed using a 12-month running average.

Results show a considerable variability in Nd and re during the study period (Fig. 9a and c). In more recent years there has been a tendency of Nd to decrease and re to increase, which may be due to natural variability, anthropogenic causes or a combination thereof. The corridor effect on these two variables has notably weakened in recent years, with values that are not found before 2020 (Fig. 9b and d). Features before 2020 may also be linked to fluctuations in shipping activity. Examining a region in the NE Pacific, Yuan et al. (2022) report dips in the ship track density in 2009–2010 (after-effect of the 2008 financial crisis) and 2014–2016, likely caused by a strong slowdown in the Chinese economy. Abrupt decreases in the corridor effect on Nd in 2010 and 2014 (Fig. 9b) may be associated with these circumstances.

It is also worth noting that fc,day decreases considerably from 2020 onward compared to the period before, with values returning closer to long-term averages in 2023 (Fig. 9g). Similar features also appear in the W time series (Fig. 9e). The corresponding corridor effects on fc,day and W, however, are less notably different from 2020 onward compared to the years before (Fig. 9h and f). As in the overall changes over the region examined in Fig. 8, the time series of τ shows very similar characteristics to the series of fc,day and W (Fig. S8b).

As mentioned before, SST is one of the main drivers of cloud variability in marine low-cloud regimes (Andersen et al., 2023), and this can largely explain these findings. Diamond (2023) also reports low cloud albedo values in 2020–2022 (which are consistent with the lower fc,day values found here) and suggests that these may be related to unusually warm SST during these years. Interestingly, Gettelman et al. (2024) suggest that a large part of the unusually high SSTs in 2023, especially in the Northern Hemisphere, can be attributed to the IMO regulations and their effect on clouds, claiming that in 2021–2023 cloud anomalies were more likely to drive SST anomalies than the other way around. While an analysis of these causation mechanisms is beyond the scope of this study, an examination of SST data from Aqua MODIS (Fig. S10) yields a correlation coefficient R=-0.67 between SST and fc,day, confirming their correlation over the study region.