Exhaust gas plumes originating from passing ships between 26 May 2022–14 October 2023 were examined at the remote sensing site of Utö island (59°47′ N, 021°22′ E), situated in the outermost part of the southwestern Finnish archipelago (Fig. ). The island is small, its area is 0.81 km2, and its year-round population is less than 40 people. Ships entering and exiting the ports of the cities Turku and Naantali pass in proximity (approximately 500 m) of Utö island. Moreover, in Utö there is a pilot station to supply pilotage for the archipelago fairway. Pilot boarding speed is normally around 10 kn, which means that vessels with higher operating speeds need to slow down significantly for the pilot boarding or disembarking, and ships that have service speeds close to the boarding speed do not need to alter speed. Some passing vessels are on regular routes to and from the ports supplied by the Utö fairway, and their officers carry pilot exemptions. In this case, these ships do not need to slow down at the pilot station. Based on this, a dataset was created with as many ships as possible passing the pilot station at various speeds.

A wide range of meteorological, aerosol particle, gas, and biological measurements are carried out in Utö Atmospheric and Marine Research Station owned by the Finnish Meteorological Institute (FMI) . The station belongs, for example, to the HELCOM marine monitoring network and to the Integrated Carbon Observation System (ICOS). The station has three different measurement locations: (A) sea station, (B) ICOS station, and (C) air quality station (see the map of Utö, Fig. ).

An AIS receiver and an automatic camera are installed in the sea station. When the AIS signal from the approaching ship is received, the camera starts to take pictures every 30 s automatically. Meteorological data (wind speed and direction, pressure, and temperature) are measured in the Sea station and synchronized with the AIS data in the file. The plumes were identified manually by checking the AIS information of passing ships and possible increases in the BC and CO2 when the wind was from the direction of the nearest shipping lane (180–360°). Then, the start and end times of the plumes were selected based on the BC and CO2 data. The average duration of the plume was about 5 min. Figure  shows an example of one ship passing Utö – data of the ship's location, speed, true heading, and course over the ground were acquired from the AIS data. The plume origin point (a black cross in Fig. ) was determined based on an assumption that the emission plume was transported to the station directly following the wind direction. Therefore, the closest data point from the direction of the wind was selected to represent the speed, true heading, and course over the ground of the ship.

At the air quality station, BC concentration was measured with an aethalometer (Magee Scientific model AE33) and CO2 concentration with a LI-COR infrared gas analyser (Biosciences model LI-7000). Both of these instruments were installed in the same sample line, which had an inlet on the roof of the measurement station roughly at the height of 10 m from the sea surface (5 m from the ground level). The sample line had one Nafion dryer installed. The aethalometer and LI-COR resolutions are 1 min and 5 s, respectively.

BC measurements by an aethalometer are based on filter collection and optical detection. In deriving the BC concentration, a constant mass absorption cross-section, which describes the relation between light absorption and BC mass, is assumed. Therefore, based on the recommendations by , the definition of the measured BC is the so-called equivalent black carbon (eBC). However, for clarity, we use the term BC to refer to the measurements throughout the article. The 880 nm channel with the default mass absorption cross-section of 7.77 m2 g-1 of the AE33 was used to acquire the BC concentration. Normally, the AE33 data are corrected with a dual-spot correction algorithm, which corrects for measurement artefacts caused by the filter . However, probably due to sample relative humidity being too high in the sample line (despite the Nafion dryer), the dual-spot correction did not work optimally. Therefore, instead of the dual-spot correction, a correction algorithm suggested by was applied. The correction factors derived by the algorithm were used as 30 d running medians e.g.. With this correction scheme, the aethalometer data were more stable, and changes in the filter spot did not cause disturbances in the data.

Both BC and CO2 were converted to dry-air and STP conditions (0 °C and 1013.25 hPa), and the CO2 mixing ratio was converted to the same mass unit as the BC measurement (µg m-3) using the ideal gas law and the molar mass of CO2: 1cCO2gm3=cCO2(ppm)⋅P⋅MCO2RT, where cCO2 (g m-3) is the concentration of CO2 in mass units, cCO2 (ppm) is the mixing ratio of CO2, P (Pa) is the pressure, MCO2 (44.01 g mol-1) is the molar mass of CO2, R (8.31 kg m2 s-2 K-1 mol-1) is the ideal gas constant, and T (K) is the temperature.

Before defining the BC and CO2 concentrations for each plume, the background levels were subtracted from the BC and CO2 data. We applied a method introduced by to calculate the background, which was defined as the median value of 6 min before the plume started and 6 min after the plume ended, omitting the period of the plume (example in Fig. 2). Finally, the dispersed emissions ΔBC and ΔCO2 were calculated as integrals over the duration of the plume. Also, a method, which was developed by and previously applied at Utö to study the effect of sulfur restrictions on aerosol particle number concentration by , was tested. In the method, the background is determined as the 25th percentile of 40 consecutive measurements. In our study, where the plumes originated from a relatively short distance (about 2 km) and were short in duration (about 5 min), the method by produced more well-defined plumes as it took variation in background concentrations better into account. The method by suits automatic plume detection, whereas the method by requires more manual work.

Further, the BC emission factor per fuel consumed EFBC can be defined as a dimensionless ratio of ΔBC and ΔCO2 times the amount of CO2 in the exhaust, which is derived from the fuel carbon content (FCC; in kg C per kg fuel): 2EFBCkgBCkgfuel=ΔBCΔCO2×MCO2MC×FCCkgCkgfuel, where MCO2 is the molar mass of CO2 (44.01 g mol-1), and MC is the molar mass of carbon (12.01 g mol-1). FCC is 0.85 and 0.87 for heavy fuel oil (HFO) and marine gas oil (MGO), respectively . Arithmetic mean (AM), geometric mean (GM), median (MED), and standard deviation (SD) were calculated for observed plumes and individual groups of examined vessels.

A total of 211 plumes from 47 different ships representing 10 different vessel types were selected for examination. Ships were identified by Automatic Identification System (AIS) data, and ship-specific details were extracted from the IHS Markit ship database. Vessel actual draughts were extracted from AIS data and compared to design draughts from the IHS Markit ship database. Plumes caused by ships with a ratio between actual draught per design draught < 0.9 were considered to be in a ballast condition and others in a laden condition. Examined vessels are shown in Table  and each vessel with their specific details in Table  of Appendix A.

The vessels were categorized based on whether they had an exhaust gas cleaning system (EGCS) installed or not. All vessels had medium-speed four-stroke main engines and were expected to use heavy fuel oil (HFO) if equipped with an EGCS and very low sulfur marine gas oil (MGO) if not equipped with an EGCS. Ships equipped with an EGCS could also operate using MGO and with the EGCS switched off, which could explain possible outliers in the data.

The apparent wind experienced by the vessel was computed using the true wind speed and direction combined with the heading and speed over ground of the vessel recorded from the AIS data using trigonometry . The ambient wind data were used to calculate the sea state in the Beaufort scale, and the added resistance with resulting speed loss created by sea state was calculated by the method created originally by , revised by the same authors .

Aerodynamic and hydrodynamic resistance combined with ship AIS speed data was then used to model the estimated main engine load at the time when the exhaust gas plume data were collected by calculating the resistance through the water using the method created by . Separate resistance constants were used for ships with one or two propellers and ships with and without a bulbous bow. For the calculation of the ship’s block coefficient, the method suggested by was used to estimate the wet surface of each vessel. Vessel parameters were obtained from the IHS Markit ship database. On ships that have multiple main engines and two propellers, a minimum of two engines were assumed to be online at any time, and the maximum engine load before switching on a new engine was set to 90 %. For diesel–electric vessels and ships equipped with shaft generators, the estimated auxiliary engine power was added to the main engine power needed for specific speeds. The auxiliary engine power (PAE) was estimated using the International Maritime Organization Energy Efficiency Design Index (EEDI) formulas .

For ships with total installed main engine power PME > 10 000 kW, 3PAE=0.025PME+250kW, and for ships with PME ≤ 10 000 kW, 4PAE=0.05PME.

There were 6 diesel–electric ships with multiple engines among the studied vessels (Cruise 1, 2, and 3; Ropax 1; Other 1; and Other 2), 30 with shaft generators, and 11 with neither. Each ship's main engine power was modelled to its service speed +5 kn. The additional speed was needed as the service speed is typically reached with 80 % main engine load, but many ships in the dataset were ice-classed with additional installed main engine power. If the power needed for the speed exceeded the total installed main engine power, the main engine load was set to 100 %. A sample of unadjusted modelled engine loads is presented in Fig. . It is worth noting that not all vessels use 100 % main engine load, even at a service speed of +5 kn, in the model. This is probably true in real life; for example, ships with ice class might have excess engine power as per the ice class demands. Also, vessels designed for towing cargo, such as Tug 1 in the dataset, have more main engine power installed than they would need to reach their design service speed +5 kn (Fig. ).

The AIS data contain a value for the ship's draught, which is fed to the AIS transmitter from the ship. These values were compared to the design draughts of each vessel. If the ratio of actual draught per design draught was less than 0.9, the vessel was considered to be in a ballast condition and otherwise in a laden condition, when passing the measuring site (Fig. ). Two vessels, Tug 1 and Fish 1, reported actual draughts that were significantly larger than their design draughts, which could be caused by user error or error in the ship database. Smaller exceedance of the design draught could be because of trim or water density, which is usually around 1.010 t m-3 in the Baltic Sea, and the design draught is calculated for a water density of 1.025 t m-3. Actual draughts and water density of 1.010 t m-3 were used in the modelling of resistance through the water.

Modelled main engine load and measured BC values from ship plumes were analysed for correlation and to create statistical models to estimate emissions created by changes in speed and main engine load. The obtained regression formula coefficients for BC output (gBC(kgfuel)-1) as a function of engine load were used to model the absolute BC emission (gBCh-1) as a function of speed. For this, the main engine fuel consumption (FME) of each ship was modelled using a base-specific fuel oil consumption (SFOCBase) in g kWh-1 obtained from the IHS Markit ship database for the specific ship multiplied by the unitless generic relative specific fuel oil consumption (SFOCRelative) described by : 5FME=SFOCBase×SFOCRelative, where 6SFOCRelative=(αL2+βL+γ), where L is the engine load (0–1), α=0.45, β=-0.71, and γ=1.28. BC emission (g h-1) was then calculated as 7BCsgh=FMEgfuelkWh×PME(kW)×BCLgBCgfuel, where BCs is the BC output (g h-1) for a specific speed, FME is the main engine fuel consumption for a specific speed (g fuel kWh-1), PME is the modelled main engine power need for specific speed, and BCL is the load-specific BC output (gBC(gfuel)-1).

BC output in grams per nautical mile (nmi) was calculated as 8BCdgnmi=BCs(gh)Snmih, where BCd is the BC output in grams per nautical mile, BCs is the BC output in grams per hour, and S is the speed of the vessel in nautical miles per hour.

Vessel total greenhouse gas emissions were calculated using 20- and 100-year global mean warming potential (GWP20 and GWP100) of BC, estimated as 1600 and 460 in combination with vessel CO2 emissions to determine the effect of speed change on the total greenhouse gas (GHG) as CO2 equivalent (CO2e). Emission factors used for CO2 were 3.11 for HFO and 3.21 for MGO . The code for modelling the engine load was created using the Python programming language. The data analysis was performed in R (version 4.2.1) and plotted using the Ggplot2 package .

The fuel-based emission factors (gBC(kgfuel)-1) for vessels equipped with an exhaust gas cleaning system (EGCS) were significantly lower (arithmetic mean – 0.22, geometric mean – 0.17, median – 0.15, SD – 0.21) than for vessels without an EGCS (AM – 0.99, GM – 0.82, MED – 0.83, SD – 0.68). The statistical significance in the difference of calculated emission factors between EGCS-equipped vessels and vessels without an EGCS was confirmed with the Mann–Whitney U test (p<0.01). There is no statistically significant difference (p=0.06) between BC emissions of ships in a ballast condition (AM – 0.50, GM – 0.32, MED – 0.29, SD – 0.50) and ships in a laden condition (AM – 0.44, GM – 0.24, MED – 0.18, SD – 0.63). The fuel-based emission factors for ships with service speeds > 15.0 kn were significantly lower (p<0.01) (AM – 0.25, GM – 0.18, MED – 0.15, SD – 0.24) than ships with service speeds ≤ 15.0 kn (AM – 1.06, GM – 0.88, MED – 0.86, SD – 0.71). EFBC as a function of ship service speed between different loading conditions and the EGCS is presented in Fig.  of Appendix B. Vessel-type BC emission factors are presented in Table  and Fig. .

Vessel speed over ground correlates negatively with the BC emission factor. Pearson's correlation between speed and BC emission factor on ships with an EGCS was -0.60 (95 % confidence interval -0.70 to -0.49, p>0.01), and on ships without an EGCS it was -0.32 (95 % confidence interval -0.51 to -0.09, p=0.01). The correlation between speed over ground and the BC emission factor on ships with service speeds >15.0 kn was -0.69 (95 % confidence interval -0.76 to -0.59, p<0.01) and on ships with service speeds ≤15.0 kn -0.21 (95 % confidence interval -0.44 to 0.05, p=0.12). The correlation between speed over ground and BC emission factor on ships in a ballast condition was -0.72 (95 % confidence interval -0.80 to -0.62, p<0.01), and on ships in a laden condition it was -0.63 (95 % confidence interval -0.74 to -0.49, p<0.01).

Tug 1, which only had one exhaust gas plume in the dataset and passed the measuring site at a very low speed, has an emission factor 4 times larger than the mean for vessels without an EGCS. A visual confirmation from the automatic camera at the measuring site confirmed that Tug 1 was towing a barge while passing Utö. As modelling the engine load was impossible, Tug 1 was removed from further analysis, leaving 210 plumes in the dataset. All except for one vessel passing the measuring site with a speed >15 kn over the ground were equipped with an EGCS. Most vessels without an EGCS were also ships with lower service speeds and therefore would not need to slow down for the pilot exchange. They also emit more BC than the EGCS-equipped vessels and therefore create bias in the analysis if included. Further analyses were performed only for the EGCS-equipped vessels using 142 exhaust gas plumes and three different vessel types in the dataset.

Visual examination combined with knowledge from previous literature confirmed a non-linear relationship between the modelled engine load and the BC emission factor. To define the emission factor of BC as a function of engine load, second-degree polynomial regression was fitted to the logarithm of observed and modelled values. Adjusting for meteorological parameters had a small effect when fitting the regression. In the exhaust gas plumes emitted by an EGCS-equipped vessel, the correlation between unadjusted modelled engine load and BC emission factor was -0.61 (95 % confidence interval -0.70 to -0.50, p<0.01), and the goodness of fit (adjusted r2) of the polynomial regression was 0.46. When the engine load was adjusted for weather conditions, the correlation between engine load and BC emission factor was -0.61 (95 % confidence interval -0.69 to -0.48, p>0.01), and the adjusted r2 of the polynomial regression was 0.41. The EGCS dataset was dominated by plumes measured from roro-type vessels (137 observations), and the adjusted r2 for roro-type vessels was only 0.39. Two plumes were observed from EGCS-equipped cruise vessels, each from a different vessel. For the Cruise 3 vessel, the model fits well (observed EFBC – 0.21, predicted – 0.25) but poorly for the Cruise 2 vessel (observed EFBC – 0.09, predicted – 0.29). Three plumes were observed from EGCS-equipped vessel Ropax 1 on which the model predicts well with a higher engine load (observed EFBC: 0.11 and 0.15, predicted: 0.13 and 0.14) but poorly with a lower engine load (observed – 1.07, predicted – 0.31). The obtained load-based emission factor formula for the BC output from EGCS-equipped vessels is 9log10(LEFBC)=2.10L2-2.85L-0.02, where LEFBC is the load-based BC emission factor (g kg fuel-1), and L is the engine load (0–1) (Fig. ).

As shown above, the fuel consumption-based BC emissions from ships that are equipped with an EGCS are dependent on the engine load. As the engine load varies with different power demands, which again is dependent on the speed of the vessel, BC emissions can be modelled as a function of vessel speed. Five different ships representing various vessel types were chosen as a sample from the studied vessels. Three of them have conventional propulsion systems (Roro 1, Roro 2, and Tanker), which means the main engines are connected mechanically to the propeller shaft. The other two (Ropax and Cruise) are diesel-electric, which means the main engines are connected to generators, and propellers are rotated with electric motors. An 80 % engine load was chosen as cut-off, as the data from our observations were limited to around 80 % modelled engine load. Chosen vessels also had different specific fuel oil consumption (SFOCBase) based on the ship database information varying from 180 to 220 g kWh-1.

BC emission was modelled as grams per hour and as grams per nautical mile to distinguish between service speed and reduced speed. Due to the parabolic models for fuel consumption and BC emission factor curves, BC emissions increase non-linearly from when the ship starts moving until reaching the first peak, which seems to be at around 10–12 kn speed. BC emissions then decrease until reaching similar levels than at 5 kn speed. This seems to happen at around the ship service speed, from where the BC emissions seem to increase again. Vessel service speed is reached where main engine fuel consumption is around SFOCBase, this being typically around 60 %–80 % load for most marine engines. Within the modelled vessels, this would be around 15–20 kn speed. Increasing speed further also increases the BC emissions non-linearly. CO2e emissions from black carbon represent on average 15.5 % of total greenhouse gases using GWP20 and 5.2 % using GWP100. As CO2 dominates the total greenhouse gas emissions, they are reduced non-linearly with a reduction of speed (Fig. ).