Detection of NO2 pollution plumes from individual ships with the TROPOMI/S5P satellite sensor

This paper presents an analysis of tropospheric NO2 column measurements from the TROPOspheric Monitoring Instrument onboard the Copernicus Sentinel 5 Precursor satellite (TROPOMI/S5P) for an oceanic area in the central Mediterranean on 2 July 2018. The day and area were selected because of the stable and cloud-free weather conditions with low wind speeds throughout most of the area, while covering one of the busiest worldwide international shipping corridors. In addition, the area was affected by sunglint, i.e. sunlight that is directly reflected by the ocean surface waves to the satellite which greatly enhances the signal-to-noise ratio of the satellite observations. The satellite measurements reveal plume-like emission structures in tropospheric NO2 columns while automated identification signal (AIS) data of ship locations reveal a total of 185 ships in the area. Combined with information about wind speed and wind direction within 3 h prior to the TROPOMI/S5P overpass, the ship tracks can almost perfectly be aligned with the plume-like tropospheric NO2 structures. In addition, information about ship length and ship speed, combined with an analysis of ship tracks and ship position, reveal that nearly all emission plume-like tropospheric NO2 structures can be attributed to the largest ships, mostly container ships and crude oil tankers. Overall, our results show for the first time ever that NO2 emission plumes from ships can be detected and attributed to individual ships using satellite measurements, while also providing strong support for using satellite sunglint measurements.


Introduction
Ships at sea are strong emitters of nitrogen oxide (NO x = NO + NO 2 ) and sulphur oxide (mostly SO 2 ) air pollution. Recent estimates by Johansson et al (2017) indicate that the global shipping fleet emitted a total of 6.4 Tg N to the atmosphere in the year 2015, which amounts to 13% of the global nitrogen (N) emissions (e.g. Miyazaki et al 2017). The emissions of ships lead to enhanced concentrations of regulated pollutants such as NO 2 , SO 2 , and particulate matter (Viana et al 2014, Jonson et al 2020. This air quality degradation is damaging to human health (e.g. Liu et al 2016) and contributes to excessive nitrogen deposition over ecosystems (e.g. Jägerbrand et al 2019).
To reduce the negative impact of ship emissions, the International Maritime Organization (IMO) has implemented progressive regulations to decrease the emissions from ships in the open ocean, as well as even stricter measures in four special emission control areas close to densely populated coastal regions. The IMO regulations within the so-called NECA and SECA (nitrogen and sulphur emission control areas) require that ships constructed after 1999 use engines that are compliant with NO x emission limits (IMO MARPOL ANNEX VI-regulation 13 2020), and that all ships burn fuel with a sulphur content smaller than 0.5% (by mass) and smaller than 0.1% since 1 January 2020 (IMO MARPOL ANNEX VI-regulation 14 2020). This effectively prohibits the burning of lowgrade quality ship fuels that were traditionally used in international shipping (Lack and Corbett 2012). However, fuel that is high in sulphur content is considerably cheaper than low sulphur fuels (Cullinane and Bergqvist 2014), inciting ship owners to circumvent the IMO regulations. How to globally monitor emissions and enforce regulation, especially over the vast open oceans, remains an outstanding question (SCIPPER 2020).
Current compliance monitoring includes port state authorities conducting checks of engine room logs and bunker delivery notes as well as taking fuel samples for a limited number of ships. On-board measurements at the ships exhaust pipes (Agrawal et al 2008), land-or ship-based downwind measurements of emission plumes using sniffer techniques (Lack et al 2009, Pirjola et al 2014 and the DOAS (differential optical absorption spectroscopy) approach (e.g. Mclaren et al 2012, Schreier et al 2015 are some of the methods currently used. Other methods comprise ship plume measurements from airborne platforms such as helicopters, small aircrafts, and drones (Van Roy and Scheldeman 2016). Mobile platforms typically measure pollutant (e.g. NO x and SO 2 ) to CO 2 ratios during plume transects (Beecken et al 2014) or measure reflected skylight for remote optical sensing with the DOAS technique (Berg et al 2012). These methods require proximity to the ships monitored, are deployed infrequently, and are thus impractical or prohibitively expensive for checking the large number of ships sailing the world's oceans.
Earth observation satellites have the potential to play a key role here. So far, the spatial resolution and data quality of satellite sensors allowed for monitoring tropospheric NO 2 enhancements over the busiest shipping routes only after averaging months or years of data (e.g. Beirle et al 2004, Richter et al 2004, Vinken et al 2014, Georgoulias et al 2019. The temporal evolution of these enhancements has been observed and linked to temporal patterns of economic activity (de Ruyter de Wildt et al 2012, Boersma et al 2015). However, the capacity of satellite measurements to attribute observations to individual ships has not been demonstrated yet.
Since October 2017, the TROPOspheric Monitoring Instrument onboard the Copernicus Sentinel 5 Precursor satellite (TROPOMI/S5P) (Veefkind et al 2012) observes global pollution at a much higher spatial resolution (originally 7 km × 3.5 km at nadir and 5.5 km × 3.5 km since August 2019) than its spaceborne precursors (resolution ranging from 40 km × 320 km for the Global Ozone Monitoring Experiment onboard ERS-2 to 13 km × 24 km for the Ozone Monitoring Instrument onboard EOS AURA). The unique resolution and superior data quality have proven TROPOMI/S5P capable of pinpointing small local NO 2 sources such as individual power plants , gas compressor stations (van der A et al 2020) and daily city-scale emissions (Lorente et al 2019).
Here we show for the first time that satellite-based tropospheric NO 2 measurements from TROPOM-I/S5P provide sufficient detail on NO 2 pollution to be traced back to the emissions from individual ships. By combining ship location data in the hours before and up to the satellite's overpass with wind direction and wind speed in the marine boundary layer along with an emission proxy based on ship length and speed we show that we can identify the individual ships or groups of ships that cause the observed NO 2 plumes.

Satellite observations
TROPOMI/S5P (Veefkind et al 2012) was launched on 13 October 2017 and the operational phase started in April 2018. The instrument measures the topof-the-atmosphere solar radiation reflected by and radiated from the Earth between 270-500 nm and 675-775 nm, and in the shortwave infrared. The two dimensions of the detector allow to simultaneously measure 450 spectra over the entire 2600 km strip, corresponding to a spatial resolution for individual pixels of 7 km (along) × 3.5 km (across) at nadir (5.5 km × 3.5 km since 6 August 2019). The equator crossing time is near 13:30 local solar time. For the scopes of this research, we use level-2 tropospheric NO 2 column data (version 1.2.2 and 1.3 data publicly available via https://s5phub.copernicus.eu/).
The NO 2 columns are retrieved with a threestep procedure described in the Algorithm Theoretical Baseline Document (van Geffen et al 2019). In the first step, NO 2 slant column densities, defined as the integrated amount of NO 2 along the average photon path from the Sun through the atmosphere back to the sensor, are obtained from the radiance and irradiance spectra using the DOAS technique in the 405-465 nm window (Boersma et al 2018 where NO 2 has prominent spectral features. Then, the slant column is separated into a stratospheric and tropospheric part based on information from a data assimilation system (Dirksen et al 2011). Finally, the tropospheric slant columns are converted into tropospheric vertical column densities by application of a tropospheric air mass factor (AMF) based on a look-up table of altitude-dependent AMFs and actual information on surface and cloud characteristics, and on the vertical distribution of NO 2 predicted by the TM5-MP model on a 1 • × 1 • grid (Lorente et al 2017). TROPOM-I/S5P tropospheric NO 2 columns show excellent correlation with independent aircraft and ground-based instruments but are biased low by about 30% (e.g. Lorente et al 2019, Verhoelst et al 2020).

Ship data
In 2000, IMO adopted the requirement for all ships to carry automatic identification systems (AIS) (IMO 1998(IMO , 2004(IMO , 2015. The regulations, in summary, prescribe that all vessels involved in commercial operations at sea are required to broadcast an AIS signal, including the ship's identity, type, position, course and speed among others. These data are frequently updated and broadcasted, typically every few seconds. The broadcasted VHF signal can be received by land-based stations and satellites. Due to limited range of ground-based stations and the focus of this study on ship operations in the open sea, the most important data source is AIS signals received by satellites. In areas with high vessel density, an interference of messages may occur, constraining the reception of all broadcasted signals by a single satellite (Hoye 2004). However, part of this issue is resolved by over 60 satellites receiving AIS signals globally and the continuous technological improvement of receivers (Eriksen et al 2010).
Despite the relevance of these data for a wide range of public applications in the field of security, safety and the marine environment (Fournier et al 2018) there is no open access to satellite AIS data at the moment. AIS data are available from several commercial providers. Within the scope of this research, the Human Environment and Transport Inspectorate (ILT) was granted access to such sources.
While data in the AIS signal for identification, location, speed and heading are generally of good quality, additional information on for example ship dimensions are known to suffer from data and entry errors. To reduce errors in this study ship details regarding type and dimensions are retrieved from official ship registries.

Wind speed and direction
We use 10 m wind data from the European Center for Medium range Weather Forecasts (ECMWF). More specifically, wind fields (direction and speed) were taken from the ECMWF operational model analyses at a 0.25 • resolution at 6-hourly timesteps. Assessment of this ECMWF wind speed product using observational data from spaceborne scatterometers has indicated a global low bias of −0.4 m s −1 (Chelton and Freilich 2005), while locally, the ECMWF wind products can be biased up to ± 2 m s −1 (Belmonte and Stoffelen 2019, Trindade et al 2020).

Matching ships to observed NO 2 plumes
Here we use AIS ship location data in conjunction with quality assured tropospheric NO 2 data (qa_value > 0.5, cloud fraction < 0.5) from TRO-POMI/S5P to attribute observed NO 2 enhancements on 2 July 2018 over a region in the central Mediterranean (dashed box area in figure 1(b)) to specific ships. This scene is selected from a large number of TROPOMI/S5P tropospheric NO 2 and ECMWF near surface wind field images for the 1-year period July 2018-June 2019. The observed features which are located in an area of busy shipping routes (figure 1(a)) and point directly to ship plumes along with an absence of clouds (clear-sky scenes identified via the retrieved effective cloud pressure; see section 1 of the electronic supplement for details and van der A et al 2020), calm wind conditions (limited dispersion of the ship plumes) and the fact that the TROPOMI/S5P measurements in the area were taken under sunglint viewing conditions (area defined as 'sunglint possible' by the TROPOMI algorithm; geolocation_flags = 2) make this day a perfect candidate for the scopes of this study (see figure 1 Sunglint is observed in satellite data when the satellite viewing zenith angle and solar zenith angle is such that the sunlight is directly reflected towards the sensor, and the sea surface is sufficiently calm, so the ocean 'acts' like a mirror. Indeed, the TRO-POMI/S5P scene albedo values in figure 1(e) and the RGB image (figure 1(f)) at nearly the same time taken from the Visible Infrared Imaging Radiometer Suite onboard the Suomi National Polar-Orbiting Partnership (VIIRS/Suomi NPP) show that TRO-POMI/S5P clearly observed sunglint. Satellite measurements taken in sunglint geometries have a significantly increased sensitivity to NO 2 close to the apparently bright surface as compared to non-glint geometries taken over a low albedo sea surface. This is illustrated in figure 1(c) showing higher normalized tropospheric slant columns (NO 2 slant column density/geometric AMF) and more distinct plumes in the sunglint scene southwest of Greece. TROPOMI's good sensitivity to NO 2 is further corroborated by the high scene albedo (figure 1(e) and section 1 of the electronic supplement) and associated tropospheric AMFs within the sunglint region (figure 1(d)). The dark spot appearing in the middle of the sunglint scene (figures 1(d)-(f)) is due to the very low wind conditions (see section 1 of the electronic supplement for details).
The spatial correspondence between NO 2 satellite-based measurements and ship locations is not trivial. The plume emitted by each ship will be advected by the prevailing winds and hence the NO 2 plume observed by TROPOMI/S5P will not necessarily coincide with the ship's track over the past hours. To attribute a plume to a particular ship, a simple 'morphing' technique is applied on the ship position data in order to calculate the position of the pollution plume at the time of S5P overpass (see figure S2 (available online at https://stacks. iop.org/ERL/15/124037/mmedia)). Assuming a NO x lifetime of a few hours we use AIS ship coordinate data for the past 3 h prior to the S5P overpass (around 11:43 UTC) and wind speed and direction data at 10 m above sea level (asl) from the ECMWF for 12:00 UTC. The ship coordinates are collocated with the corresponding wind data. We assume that the plume emitted at each ship position has travelled a distance s = u ·|∆t| in the direction of the wind (the earth's curvature is taken into account) with a speed u equal to the wind speed at the ship location for a time period ∆t (difference between the AIS time at the ship position and the S5P overpass time).
It has to be noted that the wind speed and direction is assumed fixed for each ship position during ∆t; however, this is not very important here as wind speeds are generally low (mostly below 5 m s −1 ) and wind speed and direction will not change significantly within the distances traveled by the ship plume on 2 July 2018. Plume dispersion and chemistry have not been accounted for and wind is assumed not to change with time and height. Despite these simplifications, our simple ship emission plume projections align well with the tropospheric NO 2 patterns observed by TROPOMI/S5P (see Results section and figure 2).
Finally, we match up the projected ship plumes with the TROPOMI/S5P tropospheric NO 2 column fields. This allows us to quantify the overall NO 2 pollution burden associated with each individual ship. overpass time. A total of 185 ships were found to sail in the greater area. The sailing direction of the ships can be identified, as dark magenta colors are used for the ship positions close to TROPOMI's overpass time and brighter magenta colors for earlier ship positions. Most of the ships follow two shipping routes (from and towards the Suez channel and the Black Sea), that do not exactly coincide with the observed TROPOM-I/S5P NO 2 enhancements. This is to be expected as the plume originating from each ship is advected by the prevailing winds. The projected plumes, based on the AIS ship positions in the last 3 h and the ECMWF wind data, coincide much better with the observed NO 2 enhancements than the original AIS positions (figures 2(a) and S3). A striking example is shown in figure 2(b) where the original AIS locations and the corresponding projected plume for one specific ship are shown. This is a large (ship length; L s = ∼334 m) fast traveling (ship speed; u s = 19.7 knots or else 36.5 km h −1 ) container ship .

Results
Despite the generally good colocation of the calculated plume locations of all the ships and the TRO-POMI/S5P NO 2 enhancements, there are still a large number of ships that do not coincide with high NO 2 values; these are mostly small vessels (e.g. fishing boats). In order to identify which ships are indeed responsible for the observed NO 2 plumes we filtered the ships according to their length. Only ships with L s >200 m were taken into account as smaller ships are expected to emit significantly less (see equation (1)). A total of 40 ships were identified in our study domain, mostly container ships and crude oil tankers (see figure 2(c)). Details about those 40 ships are provided in table S1 of the electronic supplement (length, vessel type, year built, gross tonnage, deadweight, and width usually referred as breadth).
Each calculated ship plume location was matched to the corresponding tropospheric NO 2 values seen in figure 2. The spatial average of the tropospheric NO 2 values coinciding with the plume of each ship was calculated and subsequently the ships were ranked according to their NO 2 levels. The individual ship number along with the average sailing speed and the corresponding NO 2 value are given in table S1. The effect of the ECMWF wind field uncertainty on the matching of ship plume locations and NO 2 is not significant as shown in section 2 of the electronic supplement. Figure 2(c) shows that many of the observed NO 2 enhancements can be attributed to the pollution emitted by these large ships in the hours before the TROPOMI/S5P overpass. The use of ECMWF wind field data at 1000 hPa (∼125 m asl) in the morphing returned similar results to the 10 m wind data, while the 950 hPa (∼545 m asl) data performed much worse, (see figure 2(c) and figures S4 and S5) showing that at least for the very specific scene studied here the 10 m data are representative of the wind fields within the lower boundary layer. The AIS locations and the calculated plumes of each individual ship separately are given in figures S6-S45. Figure 2(c) also shows that TROPOMI detects relatively high NO 2 concentrations over areas where the plumes of more than one ship coincide (e.g. Ships 2, 11 and 15) or cross (e.g. Ships 22 and 6) and in mixed cases of clusters of ships, mostly over areas with higher wind speeds (around 5 m s −1 ) (e.g. Ships 3, 7 and 14). In these cases, it is difficult to disentangle the relative contribution of the individual ships to the observed NO 2 levels. However, apart from those cases there are ships (e.g. Ships 9 and 18) which are totally isolated, and their projected plumes coincide well with the observed NO 2 plumes. These ships mostly sail in calm waters (wind speeds smaller than ∼3 m s −1 ) where dispersion by the wind is limited and the NO 2 plumes appear as long and narrow enhancements relative to the background. Taking this into account, the 40 largest ships were separated into three classes: (1) isolated ship plumes, (2) plumes in close proximity to other ships' plumes (clusters) and (3) plumes crossing other ships' plumes (see also table S1) based on a visual assessment including wind speed and direction.
To gain more insight into the sensitivity of TRO-POMI/S5P for detecting ship emissions we use a NO x emission proxy E s (see appendix A for details) which is given by: The advantage of E s over other ship emission proxies (e.g. Fan et al 2016) is that it can be derived solely based on AIS data, while other reported emission proxies require additional information not contained in the AIS data. As u s may change with time, E s is calculated for each AIS ship location and then an average value is calculated per ship taking into account only locations which were previously matched to a TROPOMI/S5P pixel. The average E s values for the 40 major ships in the area are given in table S1. Obviously, there are other factors affecting emissions which are not incorporated in equation (1), such as engine age, propulsion efficiency, fuel type and the loading level (ships emit more when fully loaded and maintaining the same speed). Here, E s is used as a proxy for ship emission intensity bearing in mind the aforementioned uncertainties.
In figure S46 we show the tropospheric NO 2 levels (thick black line and dots) averaged over the calculated plume of each major ship in the area along with the ships' emission proxy E s values (bars). We see that high NO 2 levels tend to coincide with higher E s values (Pearson correlation coefficient R of 0.62); however, this is not very clear due to mixing individual ships with clusters of ships or ships crossing other ship's plume. For example, a ship with lower emission intensity sailing in parallel or close to one or more ships with high emissions will exhibit high NO 2 values but low E s values. To avoid such a confusion, the NO 2 -E s relations are studied for each ship class separately. Figure 3(a) shows the NO 2 levels that coincide with the projected plumes of the perfectly isolated ships (thick black line and dots) and the average E s values (bars). It should be noted that Ships 1 and 26 were filtered out as only a part of their projected plume is within the study domain (corresponding only to AIS locations 2 to 3 h prior to the TROPOMI/S5P overpass). We see that there is a good correlation between the observed tropospheric NO 2 and E s (R = 0.88).
In figure 3(b) the average NO 2 levels over clusters of ships in the area with the corresponding average E s values are presented. More specifically, five clusters were identified (Cluster 1: Ships 4 and 8, Cluster 2: Ships 3, 7 and 14, Cluster 3: Ships 2, 11 and 15, Cluster 4: Ships 16 and 31 and Cluster 5: Ships 38 and 39). A good correlation between the tropospheric NO 2 and the E s values is seen, similarly to the isolated ships. Figure 3(c) shows the tropospheric NO 2 levels at locations where pairs of ship plumes are crossing. A total of ten crossings were first identified in figure 2(c). The crossing coordinates for each ship are calculated by minimizing the distance between the projected plumes of a pair of ships. However, due to the spatiotemporal resolution of the AIS data used here, only in six cases the crossing coordinates of ships were falling within the same TROPOMI/S5P pixel. Hence, six crossing cases are finally reported (Crossing 1: Ships 22 and 6, Crossing 2: Ships 10 and 8, Crossing 3: Ships 10 and 23, Crossing 4: Ships 30 and 18, Crossing 5: Ships 19 and 27 and Crossing 6: Ships 10 and 29). For each pair of ships, the NO 2 values appearing in figure 3(c) are the measurements corresponding to the central pixel where the two ship plumes cross. Assuming that the NO 2 in this pixel is a consequence of the emissions of both ships, the corresponding E s values in figure 3(c) are the sum of the E s values of the two ships at the crossing coordinates (cumulative E s ). Again, we see that tropospheric NO 2 values follow the variability of E s well.
The overall good correlation between TROPOM-I/S5P NO 2 and E s for all the three cases together (R = 0.85) suggests that the enhanced NO 2 columns observed here are indeed due to emissions from the largest and fast-sailing ships in the area. It should be noted that the younger ships examined here (constructed after 1 January 2011; Tier II emission standards) are on average larger and sail faster exhibiting higher NO 2 levels (see table S1 and discussion in section 3 of the electronic supplement).
Finally, we also applied a longitude-dependent background correction to the NO 2 data to distinguish the tropospheric NO 2 column enhancement due to shipping emissions from the free tropospheric background or residual boundary-layer NO 2 (see section 3 of the electronic supplement for details). Our results did not change significantly (ships, clusters of ships or crossing ships with higher E s values generally coincide with higher NO 2 levels as shown in figure S47 with an overall R value of 0.85). This suggests that for the scene we study here a background correction is not vital; however, we acknowledge that for other scenes or areas with higher background NO 2 a correction could be necessary.

Discussion
The results presented here show that: (1) ship emission plume-like structures can be observed in daily TROPOMI/S5P NO 2 columns over the central Mediterranean under sunglint conditions, (2) these structures remain after division of the NO 2 slant column densities by the geometrical AMFs, and thus are not an artifact of the retrieval algorithm, (3) these structures can be aligned with ship plumes when morphing the 3 h ship tracks before the TROPOM-I/S5P overpass time with the prevailing near surface winds, and (4) these plume structures appear to be best detectable for the largest ships. In addition, results are robust with regard to uncertainties in wind speeds used for projecting the ship plumes.
Our results indicate that ships frequently travel along the same shipping lane but occasionally ship tracks also cross each other. As a result, emissions mix and attribution of tropospheric NO 2 column values to emissions of a single ship becomes complicated. In our analysis we identified isolated ship plumes by visual inspection, but the need for a more objective method in future studies is acknowledged.
Our results also show that TROPOMI/S5P can track emission plumes from the largest ships, or aggregates of smaller ships whose emissions merge, resulting in detectable NO 2 enhancements. More research using more TROPOMI/S5P scenes and thus exploring more ship types should provide better statistics on the detection limits of ships from TROPOM-I/S5P data. This information is also relevant for future satellite missions like the Copernicus Anthropogenic Carbon Dioxide Monitoring CO 2 M (Sierk et al 2019) that plan to measure tropospheric NO 2 columns at higher spatial resolutions.
In addition, an outstanding question remains under what atmospheric conditions ship plumes can be best detected. The effect of viewing geometries and wind speed, which affects both surface reflectance under sunglint as well as plume dispersion and humidity, should be investigated in more detail. Also, the detectability of NO 2 pollution plumes from individual ships over different areas around the globe (e.g. open seas, ports and shorelines) should be studied.
Undoubtedly, the detection of ship plumes under favorable conditions only is a limitation of satellite remote sensing. A 1-year (July 2018-June 2019) analysis we did for the Mediterranean Sea (see section 4 of the electronic supplement for details) showed that the possibility of having conditions like the ones in the scene studied here (i.e. quality assured cloudfree NO 2 retrieval under sunglint viewing geometry and near surface wind speeds less than 5 m s −1 ) is ∼5%-10% on an annual basis ( figure. S48(b)). The majority of sunglint viewing scenes over the area appear in summer, less appear in spring and much lesser in autumn. For sunglint conditions only (regardless of the wind speed) the possibility increases to ∼10%-15% ( figure S48(a)). For low wind speed conditions only (under all viewing geometries) the possibility is much higher, exceeding 50% in some coastal areas ( figure S48(d)).
In our study we rely on a simple ship emission proxy based on ship length and speed. However, there are many factors that determine ship emission such as hull shape, engine type, fuel type, and weight which is not captured by the emission proxy formula. Modelling ship engine performance and emissions is an active field of engineering research (e.g. Jalkanen et al 2012, Johansson et al 2017 and such models could be used to better estimate ship emissions based on ship characteristics. In turn, the possibility of TROPOMI/S5P and future satellite missions to start monitoring emissions from individual ships should be of great value for verification of ship engine performance and emission modelling. This is very important as the shipping sector is expected to grow making emission control and monitoring more challenging (Rogelj et al 2018). In addition, the use of updated ship emissions in climate modeling studies would allow for more accurate projections of climate's current state and future.
Finally, although not shown and discussed here, we have consistently observed similar patterns in daily TROPOMI/S5P data under sunglint conditions throughout the Mediterranean. Performing a global assessment will drastically increase the number of events available for analysis. Many more cases will allow for a much more detailed systematic analysis of various findings of our paper and issues discussed here.

Concluding remarks
We have shown for the first time that NO 2 pollution plumes can be observed in single overpass TROPOM-I/S5P tropospheric NO 2 column data under favorable conditions (cloud-free skies, low winds and sunglint) and can be attributed to emissions from large individual ships as well as groups of ships sailing in close proximity. Our findings open up a new avenue for analysis and development of applications, including ship emission monitoring for regulation compliancy. This is particularly important, as there are global efforts underway to define regulations to reduce air pollution emissions from shipping.

Appendix A
Ship emissions to first order depend on the ship's speed (resistance) and its water displacement or volume. In fluid dynamics, resistance depends on the square of the speed (u s 2 ). The water resistance of a ship traveling through water is proportional to A s × u s 2 where A s is the area of the ship and u s its speed. The impulse of a moving ship through water then equals u s multiplied by the resistance, so the impulse is proportional to A s × u s 3 (Fan et al 2016). For large international ships the length-widthheight dimensions and ratios are not expected to vary that much, if only because ship design focuses on efficiency as fuel is a dominant cost in international shipping. Logically, ship designs are expected to be rather similar. Hence, the ship area A s is then to first order expected to be proportional to the square of the ship length (A s ∼ L s 2 ), which also has an area dimension. Combined, we come up with an emission proxy E s of L s 2 × u s 3 . A speed-to-the-power-three relation is also consistent with findings from a computation study on ship engine performance and emission parameters mapping (Theokatos and Tzelepis 2015). data analysis and interpretation and co-authored the paper. JvV provided the AIS data, contributed to the data analysis and interpretation and co-authored the paper. RvdA and XZ provided the ship emission proxy formula derived from an ongoing research project and commented on the paper. PZ provided research budget (PANACEA) and commented on the paper. JdL provided research budget (AOMD), contributed to the data analysis and interpretation and co-authored the paper.