Estimating the impact of ship emissions on local air quality is a topic of high relevance, especially in large harbor cities. For chemistry-transport modeling studies, the initial plume rise and dispersion play a crucial role for the distribution of pollutants into vertical model layers. This study aims at parameterizing the vertical downward dispersion in the near field of a prototype cruise ship, depending on several meteorological and technical input parameters. By using the microscale chemistry, transport and stream model (MITRAS), a parameterization scheme was developed to calculate the downward dispersion, i.e., the fraction of emissions, which will be dispersed below stack height. This represents the local concentration in the vicinity of the ship. Cases with and without considering the obstacle effect of the ship have been compared. Wind speed and ship size were found to be the strongest factors influencing the downward dispersion, which can reach values up to 55 % at high wind speed and lateral wind. This compares to 31 % in the case where the obstacle effect was not considered and shows the importance of obstacle effects when assessing the ground-level pollution situation in ports.

Ship emissions are among the harmful anthropogenic influences on air quality
and human health, especially in big harbor cities. Regarding air quality,
this covers various gaseous pollutants like sulfur dioxide (SO

The urge to quantify ship emissions gained even more attention due to the fast growth in shipping activity during the last decades (Brandt et al., 2013; United Nations Conference on Trade and Development, 2019). Many ship plume modeling studies focus on global- or regional-scale plume dispersion, chemistry and their parametrization (e.g., Aksoyoglu et al., 2016; Huszar et al., 2010; Vinken et al., 2011). For emission calculation, they can make use of global (Corbett et al., 2007; Wang et al., 2008) or regional (Aulinger et al., 2016; Jalkanen et al., 2009, 2012) shipping emission inventories. Increasing trends in ship emissions in northern Europe have been modeled for the North Sea (Matthias et al., 2016) and Baltic Sea (Karl et al., 2019), and the efficiency of emission reduction measures has been evaluated.

Matthias et al. (2018) pointed out the importance of correct spatial and temporal distribution of emissions in chemistry-transport models, which are connected with uncertainties. The distribution depends strongly on data availability, interpolation procedures and initial assumptions. For example, an emission overestimation for single ships can occur if ship emissions are diluted instantaneously and equally into a large grid (von Glasow et al., 2003; Vinken et al., 2011). This problem can be overcome by using smaller-scale models and a bottom-up approach for emission inventories (Aulinger et al., 2016; Eyring et al., 2010; Jalkanen et al., 2009, 2012; Johansson et al., 2017).

However, new problems arise when modeling is performed on a single-ship level. On the technical side, this includes the correct localization of ships, which can nowadays be done by using automatic identification systems (AISs). The emission factors are calculated as a function of several technical parameters like fuel type, engine load, engine power, engine type and ship size, ship class, as well as the performed activity (e.g., cruising, maneuvering, or berthing), the latter to be derived from AIS data (Aulinger et al., 2016).

But also new methods for spatially allocating the emissions from big ships
need to be developed, since the emission height often lies significantly
above ground level. The exhaust gas leaves the stack with a certain exit
velocity and a temperature of several hundred

Many analytical single-plume models are based on Gaussian dispersion formulas (Briggs, 1982; Janicke and Janicke, 2001; Schatzmann, 1979). This means that the pollutant distribution corresponds to a normal probability distribution. An example is the offshore and coastal dispersion (OCD) algorithm of Hanna et al. (1985). An accurate representation of plume rise and downward dispersion processes in the near field under different meteorological conditions is important, since it changes the effective emission height and may cause the vertical concentration profile to deviate from a Gaussian shape (Bieser et al., 2011; Brunner et al., 2019). Based on a large eddy simulation study, Chosson et al. (2008) pointed out that Gaussian plume dispersion models might not be well suited for the early plume development.

Despite not running at full engine power inside of the harbor,
ocean-going ships still consume large amounts of fuel for heat and
electricity production and therefore emit atmospheric pollutants while at
berth (Hulskotte and Denier van der Gon, 2010). These have been found to be
up to 5 times higher compared to other activities like maneuvering or
cruising during the course of a year, as ships spend more time at berth and
also have a high auxiliary engine power demand for hotel services
(Tzannatos, 2010). This can lead to severe air quality problems in harbor
areas. Murena et al. (2018) applied a computational fluid dynamics model to
assess the impact of cruise ship emissions on the facades of waterfront
buildings in Naples, Italy. The highest SO

More research is needed to better understand the effect of technical and meteorological parameters on the downward dispersion process that causes these strong pollution scenarios inside of a harbor. Although the OCD model of Hanna et al. (1985) includes effects of pollutant downward dispersion behind the obstacle, i.e., the vessel, by lowering the effective plume height and adjusting dilution parameters in the model, this effect has yet to be applied to large ships.

The aim of this study is to quantify the main factors that have an impact on the downward dispersion process for a large cruise ship. For this purpose, an Eulerian microscale model is used to calculate the downward dispersion in close proximity to the ship. Furthermore, a parameterization is developed for the downward dispersion depending on the crucial meteorological influences and the technical specifications of the ship. Finally, it will be shown under which conditions the obstacle effect on the downward dispersion needs to be considered.

The dispersion of an exhaust plume is affected by several meteorological and technical parameters (Fig. 1). The upward movement, i.e., the plume rise, is mainly determined by the initial temperature of the exhaust and its exit velocity, which can be calculated by dividing the gas volume flow by the stack diameter. The stack angle describes whether the exhaust flow is directed vertically, horizontally or at an angle. The stack height only has an indirect effect on the plume rise, as higher emitted gases experience a stronger wind speed inside the boundary layer.

Conceptual model of parameters affecting the shape and movement of a ship plume (bold text indicates technical parameters; italic indicates ambient parameters).

Turbulence enhances the plume dispersion, leading to dilution of the embedded gases by entrainment of ambient air into the plume. The dispersion increases with the wind speed. It depends also on the ship geometry and the flow direction of the wind towards the vessel. Furthermore, a stronger turbulence occurs in the case of higher surface roughness.

The ambient vertical temperature profile determines the atmospheric stability. The presence of an inversion can strongly decrease the strength of the plume dispersion, as it thermodynamically hinders the vertical movement of air masses. Depending on the altitude of the inversion and the exhaust temperature, the plume may or may not break through the inversion.

The microscale chemistry, transport and stream model (MITRAS) is a non-hydrostatic, three-dimensional Eulerian model, based on the Navier–Stokes equations, the continuity equation and the conservation equations for scalar properties like temperature, humidity and trace gas concentrations (Grawe et al., 2013; Salim et al., 2018; Schlünzen et al., 2003, 2018). It accounts for obstacle-induced turbulence on the wind field as well as effects of thermal stratification.

In this study, a non-equidistant grid is used with the highest resolution of
2 m

The emission occurs continuously in one model cell right above the ship
stack, which is an impenetrable obstacle cell (Fig. 2). The emitted gas is
as a passive trace gas (e.g., CO

Visualization of the stack emission for wind direction from left to right. Passive trace gas emission occurs in the cell above the stack, which has a constant exhaust temperature and a vertically directed exhaust velocity. The arrows indicate the change of the ambient wind field due to the obstacle and the plume temperature.

Idealized meteorological conditions are used to investigate effects of single variations of input parameters on the dispersion process. The range of input values is listed in Table 1. One input parameter per model run was varied while the other meteorological and technical parameters were fixed at predefined default values.

Input parameters for this study. While varying a single input parameter in the investigation range, all others remain at default setting.

The ambient temperature is set to 15

The atmospheric stability is varied in a range of different lapse rates,
covering one unstable condition (

The wind speed is investigated in the range of 2–15 m s

The effect of wind direction is relevant in correspondence to the
orientation of the ship. Frontal wind is herein defined at an angle of
0

This study represents a cruise ship prototype. From an online database (Port of Hamburg, 2020), the average length and width of cruise ships that were visiting Hamburg harbor during the years 2018 to 2019 has been calculated. The stack height was approximated from freely available photos (e.g., Vesseltracker, 2020). The ship prototype has a length of 246 m, a width of 30 m and a stack height of 52 m (see Table 1 and Fig. 3). This corresponds to a typical cruise ship that can carry between 1000 and 2500 passengers. A non-moving source is assumed, i.e., a hoteling ship at berth.

Side view of the prototype cruise ship in the MITRAS domain with
the

The study goes beyond a case study. A loaded container ship of similar size, and exhaust characteristics would deliver similar results because its shape is comparable. On top of that, for all investigated input characteristics, the results of stack-only cases are presented as well. Therefore, one can assume that results for smaller ships lie between these two cases.

The exhaust gas temperature depends on technical parameters of the ship's
engine and can be found in engine data sheets provided by manufacturers like
Caterpillar (CAT, 2020), Wärtsilä (Wärtsilä, 2020) and MAN
(MAN, 2020) on their websites. For large cruise vessels, it ranges between
approximately 300 and 400

When investigating plume dispersion, one needs to separate two regimes: the momentum-driven regime and the buoyancy-driven regime. In the momentum-driven regime, the movement of the plume is affected by (a) the initial plume rise due to both the exit velocity and the high-temperature convective upward transport and (b) the dispersion due to turbulence generated by the obstacle (i.e., the ship) inside the wind field. In the buoyancy-driven regime, the movement of the plume is determined by the wind field and turbulence generated by the ambient conditions (e.g., orography effects and surface roughness). Here, the plume temperature is equal to the ambient temperature. The microscale model (MITRAS) can investigate plume behavior in both regimes on a high resolution.

MITRAS is used to capture the initial plume rise and turbulence effects in
the momentum-driven regime. The vertical concentration profiles are
calculated at a distance outside of the momentum-driven regime, i.e., when
the buoyancy-driven regime is reached. Then, the concentration profiles are
calculated on a 100 m

Schematic sketches of the investigation area. Vertical
concentration profiles are evaluated at a distance of 100 m downwind of the
ship for layers of 100 m

Since the plume needs to have cooled down to ambient temperatures to be
considered outside the momentum-driven regime, test simulations have been
performed to find a distance at which this condition is met (see Appendix B). This was the case at a distance of 100 m downwind of the ship.
Therefore, all concentration profiles are calculated as 100 m

In the following, the term “downward dispersion” (

For single regression analyses, downward dispersion values are investigated
depending on the variation of a single input parameter at a time while the
others remain at default settings (Table 1). To assess the sensitivity of
the downward dispersion to each input parameter, an effective range

Figure 5 presents an exemplary output of the MITRAS model for the default
conditions, i.e., frontal wind at 5 m s

MITRAS model results for default conditions (frontal wind at 5 m s

The following subsections describe the results of single- and multi-parameter regressions that were performed in order to describe the relationship between the downward dispersion and the input parameters. From the multi-parameter regression, a parameterization is derived that covers all input parameters in the investigation range. A bootstrapping procedure is presented to test how well the parameterization results match with the MITRAS model results. The obstacle effect is evaluated, and finally some limitations of the modeling approach are discussed.

Single-parameter regressions are performed after basic statistic formulae (see Appendix C) to investigate the impact of individual input parameters, i.e., wind speed, exit velocity, wind direction, plume temperature and atmospheric stability on the downward dispersion.

The dependence of the downward dispersion from wind speed was modeled in
the range of
2–15 m s

Figure 6 presents results of a single linear regression for the dependence
of downward dispersion on varying wind speeds with and without the obstacle
effect. Other input parameters remained constant at default values (Table 1). A linear relationship with correlation coefficients

Dependence of the downward dispersion

Effective ranges of investigated input parameters on the downward dispersion under default settings.

A similarly strong linear relationship has been found between the exit
velocity of the exhaust gas and the downward dispersion (Fig. 7 and Table 2)
with regression

Dependence of the downward dispersion

The strength of the downward dispersion was investigated depending on
different wind directions in relation to the orientation of the ship.
Frontal wind (angle of 0

The downward dispersion correlates linearly with the cosine of the flow
angle

Dependence of the downward dispersion

The exhaust plume temperature depends on technical parameters like the
engine power and the use of a heat exchanger, and therefore a range of
possible temperatures (200–400

Dependence of the downward dispersion

Once again, a strong linear relationship with correlation coefficients

The effect of atmospheric stability

Dependence of the downward dispersion

Since the square of a negative vertical temperature gradient would result in
a positive value, a sign function was applied. The mathematical expression
is

Multiple regression is performed according to the equations in Appendix C2.
The downward dispersion ratio depends linearly on all investigated input
parameters, their cosine (in the case of the angle of wind direction) or their
squares (in the case of atmospheric stability). With that in mind, a training
dataset for the multiple regression was created. Here, all independent
input parameters are varied at the same time (but in the given range), and
the downward dispersion ratio is calculated with MITRAS. For a set of 39
different combinations (Table C1) of input parameters with the obstacle effect
and 27 without, the estimation coefficients

Here,

A bootstrapping procedure is applied to estimate how well the parameterization can represent the model data. For this purpose, downward dispersion ratios were calculated with the parameterization formulae (Eqs. 4 and 5) and compared to the original MITRAS results for all investigated cases and ranges. The individual parameterization results are listed in Table C1. Table 3 gives the overall results of the bootstrapping procedure.

Results of the bootstrapping procedure for cases with and without considering the ship-induced obstacle effect.

With a mean absolute error of 1.9

Another aim was to investigate under which conditions the strongest downward dispersion occurs and which effect the consideration of the obstacle has on the downward dispersion.

From the single-parameter regressions, it is assumed that the strongest
downward dispersion occurs at high wind speed (15 m s

Visualization of the obstacle effect in MITRAS. Examples for
lateral wind with

The calculated downward dispersion ratio for this condition is 54.9 % and 31.1 % with and without the obstacle effect, respectively. This means that a significant proportion of nearly 25 % of the emission can be dispersed downwards only by taking into account the turbulence caused by the ship.

Despite efforts to represent real conditions as best as possible, the results are subject to a few limitations or uncertainties that will be discussed in the following section. For a general comparison of our MITRAS results with a common dispersion model, see Appendix D.

One factor that is not considered in this study is relative humidity. Here,
a distinction must be made between the relative humidity of the ambient air
and the relative humidity of the exhaust. By using the Lagrangian concept
based on the so-called projected area entrainment (Lee and Cheung, 1990),
Affad et al. (2006) stated that the relative humidity of the ambient air has
only a slight impact on the plume rise, diameter and temperature for values
between 20 % and 90 %. It can have an impact on particle growth, but as
this study focuses on a passive gaseous tracer, this effect is neglected.
On the other hand, the humidity of the exhaust gas might have a larger
impact on the plume rise. Since water vapor has a lower density than air, an
exhaust gas mixture of high humidity will show a stronger plume rise.
Furthermore, as the gas will quickly condense, it will release latent heat
and rise further. However, the database on humidity of ship exhaust is
sparse. It could play a role in the case of vessels using a scrubber to wash out
SO

Second, the emission is assumed to occur in the grid cell above the stack,
which has a size of 2 m

Another assumption was that the ship has been considered as a non-moving source, i.e., a hoteling ship. However, the results can be applied to a moving ship by calculating the vector sum of the wind and the vessel speed. It is difficult to account for complex maneuvers, though, as the resulting wind vector may change quickly and the technical conditions like exhaust temperature and exit velocity may also vary with the speed of the ship.

The shape of the vessel and the location of the stack are additional parameters that can influence the exact value of downward dispersion. Parameterizing them is beyond the scope of this study as the shape was chosen to investigate the average effect of a cruise-ship-sized vessel on pollutant concentrations close to ground. However, to get an impression, an exemplary comparison of MITRAS results for a cruise ship and container vessel can be found in Table S2 in the Supplement.

The chosen model surface is water but assuming a hoteling ship, the land surface effects may play a role for the dispersion. This effect has not been part of this study, as this is a highly variable parameter that depends on the structure of the harbor, the city and the orography. These effects need to be covered by a larger-scale model.

A ship plume modeling study was performed with the microscale numerical model (MITRAS) to investigate the downward dispersion of the exhaust in close proximity to a modeled cruise ship (i.e., in the momentum-driven regime). A set of 39 different scenarios with varying meteorological and technical input parameters was analyzed. A multiple regression algorithm was used to estimate a parameterization function for the downward dispersion. This parameterization has been tested against the MITRAS model results through a bootstrapping procedure.

From single-parameter regressions, a positive linear relationship of the
downward dispersion from wind speed and negative linear relationships from
exit velocity, plume temperature and the cosine of the angle of wind
direction were found. The downward dispersion ratio was larger in the case of
lateral wind than in the case of frontal wind. In the case of atmospheric stability,
the downward dispersion showed a squared dependence from the vertical
temperature gradient multiplied by the sign function. From all these input
parameters, the wind speed shows the largest effect on the downward
dispersion in the investigated range (2–15 m s

A comparison of the model results and the parameterization from multiple
regression shows a good agreement with a mean absolute error of 1.9

The parameterization functions can also be used for container ships of a similar size. It may also be applied to different emission situations like industrial stacks.

In a future study, other plume parameters will be derived from the vertical concentration profiles in a similar way to the downward dispersion. This includes the height of the plume axis and the shape of the vertical plume profile, which may deviate from the often-assumed Gaussian distribution. These results can further be used in a city-scale model, which only calculates the plume dispersion inside the buoyancy-driven regime.

Input data for wind speed data were used from the Hamburg weather mast, provided
by the Integrated Climate Data Center (ICDC) (ICDC, 2020). The weather mast
is positioned at a meteorological measurement station in Billwerder, Hamburg
(

Boxplots of hourly wind speed data for the year 2018 from the Hamburg weather mast. Red lines indicate median values; lower and upper whiskers end at 5th and 95th percentile, respectively.

Statistical data on hourly wind speed values [m s

Figure B1 presents results for maximum temperatures in the MITRAS domain for
one case with the highest temperature (400

Results for calculated maximum temperatures in the MITRAS domain
in distance downwind from the stack for a case of a 400

This section describes the general application of linear and multiple regression on the model results.

A simple approach to estimate a target variable

The variable

Data table for regression analyses.

To get an impression of similarities and differences of MITRAS results with a common dispersion model, the results are compared under similar conditions with results from the integral plume model IBJpluris (Janicke and Janicke, 2001), which can be used to describe the plume dispersion in the momentum-driven regime. IBJpluris calculates average plume properties like concentration and temperature along the plume centerline and applies a circular Gaussian dispersion around this central axis. IBJpluris does not account for obstacle-induced turbulence effects and is therefore only compared to stack-only conditions in MITRAS.

Since the primary output of IBJpluris is the plume centerline and not the
downward dispersion, a similar centerline height for MITRAS was calculated
to compare the plume behavior. Therefore, the centerline in MITRAS

By calculating effective ranges,

The higher plume rise in MITRAS is consistent with the interaction of the hot plume with the ambient air. MITRAS accounts for the change in the thermodynamic field, and the heat balance equation creates an additional buoyancy which is not considered in simpler approaches. This explains the high effective range for temperature and stability changes.

This shows that the results for stack-only conditions are reasonable and that MITRAS provides a more complex improvement over simple Gaussian approaches in the near field.

All regression results can be obtained by applying the functions in Appendix C on the data of Table C1. A data table (“regression_data.csv”) and a Python script (“multiple_regression.py”) have been added as a Supplement.

The supplement related to this article is available online at:

All authors were responsible for conceptualization; RB and DG formulated the methodology; RB calculated the results; all authors contributed to the discussion and conclusion; RB was responsible for the writing. All authors have read and agreed to the published version of the manuscript.

The authors declare no conflict of interest. The funders had no role in the design of the study, in the collection, analyses or interpretation of data, in the writing of the manuscript or in the decision to publish the results.

The authors would kindly like to thank Heinke Schlünzen, Bernd Leitl and Kay-Christian Emeis for the fruitful discussions during the preparation of the manuscript. We would further like to thank the Meteorological Institute of University Hamburg for providing wind data of the Hamburg weather mast.

This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. 645514). The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.

This paper was edited by Susannah Burrows and reviewed by two anonymous referees.