The simulations were carried out with the COSMO model, developed and maintained by the COSMO consortium. The COSMO model (version 4.14) is a state-of-the-art, non-hydrostatic model used at 2 km horizontal resolution with a time step of 20 s. A vertical resolution of at most (resp. at least) 150 m (20 m) in the PBL was used. The fully compressible flow equations are solved using a third-order Runge–Kutta discretisation in time . Vertical advection is computed using an implicit second-order centred scheme and horizontal advection is solved using a fifth-order upstream discretisation. Tracers, such as the hydrometeors and aerosol species, are advected horizontally using a second-order Bott scheme . The turbulent fluxes are represented using a 1-D turbulent diffusion scheme with a prognostic description for the turbulent kinetic energy. The minimum threshold for the eddy diffusivity intrinsic to the turbulence parameterisation is set to 0.01 m2s-1 . Shallow convection is described using the  mass flux scheme without precipitation production with an entrainment rate of 3×10-4 m-1. The radiative transfer is based on a δ-two-stream approach  using a relative humidity criterion for subgrid-scale cloud cover.

In previous work the model was extended with a two-moment bulk cloud microphysics scheme and the M7 aerosol microphysics scheme . The aerosol microphysics scheme describes the evolution of black carbon (BC), organic carbon (OC), sulfate (SO4), sea salt and dust. These species are binned into four internally mixed soluble and three insoluble modes determined by fixed size ranges (nucleation, Aitken, accumulation and coarse). The processes relevant to this study captured by the model include condensation of sulfuric acid vapour, hydration, coagulation, sedimentation as well as dry and wet deposition of aerosol particles. The soluble aerosol particles are activated according to . All soluble aerosol particles in the accumulation (50nm≤R≤0.5 µm) and coarse (R>0.5 µm) mode, as well as Aitken mode (5nm≤R≤50 nm) aerosol particles larger than 35 nm radius are considered as activated. Although there exist more physical activation parameterisations (e.g. ), using this simpler form of activation is still in good agreement with observations, which found the CCN concentration to scale linearly with the soluble accumulation mode number concentration ( and references therein). The number of newly activated cloud droplets is then further restricted by the available moisture content and the updraft velocity .

The cloud microphysical processes for cloud droplets and rain described by the  parameterisation contain the growth by condensation, self-collection of cloud droplets and rain drops, autoconversion, accretion, droplet breakup, sedimentation of rain and evaporation (saturation adjustment is applied). The grid-scale cloud optical properties are parameterised as a function of wavelength using the effective droplet radius .

The dynamical settings and nesting approach used in these simulations are based on the setup of . We use a one-way nesting approach, where the 2 km simulation (Δt=20 s) is nested in a 12 km simulation (Δt=90 s) run over a larger domain stretching from the northeast Atlantic to the eastern borders of Switzerland and Germany (see Fig. 1 of ). The initial and lateral boundary conditions for the dynamical fields are provided by the ECMWF Interim Reanalysis . For the aerosol tracers, the climatological means for January (1999–2009) obtained in ECHAM-HAM simulations  are prescribed as initial and lateral boundary conditions. The global simulations were performed with a two-moment bulk scheme for aerosol  and cloud  microphysics with prescribed aerosol and precursor emissions from the Japanese National Institute for Environmental Studies (NIES, ).

In the present simulations, anthropogenic aerosol emissions, excluding ship emissions, are given by the AeroCom data set . Natural emissions such as dimethylsulfide (DMS) emissions  and sea salt  emissions are computed interactively.

In order to quantify the changes in microphysical entities, a distinction between plume and non-plume grid points has to be made in the post-processing. As the only perturbation in total aerosol number concentration Na is caused by ship emissions, we defined a relative threshold concentration of Na at each grid point to determine the plume points. Only points where Nasimulation≥ 3Naclean are considered part of the ship exhaust plume. This threshold provides the required balance of being small enough to include a maximum number of plume points and being large enough to separate the core track structures from surrounding increases of Na due to aerosol being mixed away from the track region.

Another sampling was performed to determine not only the plume points, but the subset of plume points where a significant cloud response was detected. Here, the additional criterion in terms of cloud droplet number concentration Nc of Ncsimulation≥ 5Ncclean was applied.

The ability to distinguish plume from non-plume points and ship track from non-ship-track points of these criteria is shown in Sect. .

A simple metric to compare simulated cloud optical thickness to the MODIS observation was designed, as the COSP simulator , including grid-scale and subgrid-scale cloud water contributions, is not yet available within COSMO.

Cloud optical thickness τ within COSMO is diagnosed for each of the eight spectral intervals (three shortwave and five longwave) in the radiation scheme. For warm-phase clouds τ is given as τ(x,y,λi)=∫0TOAξλiqctot(x,y,z)clctot(x,y,z)dz, where ξλi denotes the extinction coefficient of each spectral band λi, qctot the total (grid-scale and subgrid-scale) liquid water content at each grid point at coordinates x (longitude), y (latitude) and z (level), and clctot the cloud cover fraction (predominantly 0 or 1 in these simulations).

As MODIS cloud optical thickness during day-time and over the ocean is predominantly defined by radiances measured within the visible , the contribution of the visible channel in COSMO (0.25≤λ≤0.7µm) to the total τ was isolated and used for the MODIS comparison.

The simulated background of this case study is very clean due to the presence of unpolluted marine air into the ship track domain and the removal of aerosol by precipitation. Aerosol concentrations as low as 285 cm-3 and CCN concentrations of 10–20 cm-3 are simulated.

The background aerosol particles are a composite of sea salt emitted within the region and sulfate particles within the Aitken mode, which are transported into the domain from the lateral boundaries. The sulfate particles formed in the mid-troposphere and were mixed downward in the driving GCM simulations. Although the aerosol and CCN concentrations are low, they are not unrealistic for this region  or for stratocumulus in general  and are consistent with the MODIS observation of optically thin stratus.

The impact of the ship exhaust in all simulations, containing either a varied emission mass flux (ship10) or emission size (ship10A), on the aerosol size distribution is illustrated in Fig. . This figure shows the averaged aerosol size distributions determined over a plume volume close to the source at 06:00 UTC and at a distance at 12:00 UTC. The selection method of the included plume grid points of each track is illustrated in Fig. . At each of these points the size distribution is determined and then bin-wise averaged over all selected plume points. As in situ size distribution measurements shown in Fig.  are obtained within a 10 km radius of the ship's position, plume points within the same radius of each ship are selected at 06:00 UTC. Furthermore, to ensure a comparison of the same volume of air between different simulations, the plume points considered for this analysis were determined in ship10 and used in all other simulations. In order to visualise size distribution changes along the plume due to dilution and microphysical processing, the distributions were determined again at 12:00 UTC over plume points selected from a volume of air centred at the same latitude as 06:00 UTC (see Fig. ) which now contains atmospherically aged aerosol particles. To highlight the variability between individual plume points, the span between the 10th and 90th percentiles (P10 and P90 respectively) is shown in addition to the averaged distribution in grey at 06:00 UTC.

In general a good agreement of the peak width is found between all simulations and observations obtained by (Fig.  blue markers) and (Fig.  orange markers), while peak amplitudes are underestimated with respect to the observations in ship and ship10A. Observed peak concentrations in aerosol number per size bin, which vary between 5000 cm-3 and 100 000 cm-3 (i.e. over two orders of magnitude), are only captured by the ship10 simulation.

However, it has to be considered that the observations shown in Fig.  were obtained within different marine boundary layers of varying background aerosol concentrations, ship emissions (in terms of mass flux and size) and PBL state, and were obtained for considerably smaller samples of air (compared to a 2 km by 2 km by 100 m volume) at different plume ages. As all of these factors influence the plume evolution, complete conformity between the simulated plumes of this case study and the observations is not to be expected. However, a qualitative comparison in terms of order of magnitude can still be made and provides valuable insights.

In addition to size distribution measurements, observations of the total perturbation in aerosol number concentration are also considered. The simulated perturbations in Na (ΔNa shown in Fig. b–d) are compared to measurements obtained by (Fig. 1 of their paper) for a bulk carrier running on marine fuel oil (Star Livorno), which was one of the five ships considered for the ship exhaust estimate of this study. The observations of ΔNa range between 3000 and 30 000 cm-3. However, only 7 % of the measurements were smaller than 5000 cm-3, while over 50 % were obtained at ΔNa>20 000 cm-3. Therefore, peak concentrations of at least 20 000 cm-3 in the vicinity of the ship can be inferred.

In the simulations ΔNa was determined at each point by taking the difference between any simulation containing ship exhaust and clean over plume points within a 10 km radius from the source at 06:00 UTC. A comparison between the simulated range of ΔNa with the observations shows that almost 75 % of the simulated perturbations are below the observed range. This indicates that the aerosol perturbation due to the literature-scale emission flux might be insufficient to generate comparable peak concentrations within the plume. On the other hand, the simulated range of perturbations as compared to the observations agrees well up to the 75th percentile (P75) with the observations of ship10. However, this agreement is obtained at the expense of a considerable overestimation of the peak perturbations in this simulation.

In addition to differences in peak amplitude, a shift of the aerosol peak towards smaller radii is detectable between the ship and ship10 simulations and observations. The difference in peak radius is strongly tied to the emission size of the ship exhaust. Whilst an emission size of 0.015 µm was specified for fresh plumes (Table ), ship exhaust radii of at least 0.03 µm were measured by . While this discrepancy in emission radius was noted, the results of this study were not found to be affected.

The aerosol size distribution in ship10A displays a distinct double-peak structure due to the bimodal emission size distribution applied (Table ). While all observations shown in Fig.  display a single peak, measurements of double-peak structures have been obtained in test bed studies . In terms of ΔNa, smaller peak perturbations are simulated in ship10A than observed, as the aged emission size distribution was developed to represent older plume segments, which consequentially are more diluted.

As time evolves and the growing plumes are increasingly diluted, the in-plume size distributions are increasingly influenced by clean air. Indeed the size distribution peak is found to shift towards the clean aerosol peak position in all simulations (Fig. b–d) by 12:00 UTC. In addition the formation of a secondary peak can be observed for ship, which is not simulated to the same extent in ship10. This is caused by the increase of background aerosol concentrations within this size range (Fig. a) and their increased impact in ship as compared to ship10.

In terms of microphysical processing, the most relevant processes include the condensation of sulfate and water vapour onto mixed aerosol particles. The presence of the ship pollutants leads to a suppression of sulfate nucleation due to the abundance of condensation nuclei within the plumes. In combination with efficient scavenging by in-plume aerosol particles, the nucleation mode aerosol concentrations are reduced.

Finally the number of activated particles was found to be strongly tied to the prescribed emission flux and to a lesser extent to emission size. As can be seen in Fig. , particle concentrations larger than 35 nm are similar between ship10 and ship10A, which are five times as high as the activated aerosol concentrations in ship. However, the percentage of activated particles lies between 3 and 6 % in most of the plume areas, which agrees well with plume measurements obtained at 0.2 % supersaturation .

After emission at ∼160 ma.s.l., the ship plume aerosols are subject to turbulent and convective boundary layer transport. Figure  provides an insight into the vertical distribution of mixed aerosols in clean and ship10. Under clean conditions, the background aerosols (Fig. a) are not homogeneously distributed in the mean boundary layer profile. Instead, the aerosol concentration is found to increase from at least 300 cm-3 near the surface to 500 cm-3 near the PBL top in stratified layers. The PBL top, as defined by the inversion, and boundary layer stability, can be inferred from Fig. c, which displays the potential temperature (θ) profile at the centre point of the ship track domain at 03:00, 06:00 and 09:00 UTC. Throughout the first 9 h of simulation, the PBL remains slightly stable in this region, which allows for persistent vertical gradients in the mixed aerosol concentrations. Higher concentrations of mixed aerosol particles up to 600 cm-3 are reached due to the increased concentration of Aitken mode sulfate above the inversion.

For the formation of ship tracks, the timescale of the ship plume reaching cloud base is of particular interest. The mean cloud base height within the ship track domain between 00:00 and 09:00 UTC was determined at ∼360 m, as shown by the white line in Fig. a and b. Figure b shows the evolution of the mixed aerosol concentration including ship exhaust averaged every 15 min at each level. As time progresses, the total number concentration increases within the PBL, due to cumulative emissions within this region. From the clearly distinguishable emission height at ∼160 m, the aerosol are mixed both downwards towards the surface and upwards towards the PBL top, as expected within a turbulent boundary layer (e.g. ). At cloud base the mixed aerosol number concentration is first raised from the background concentration of 350 to 420 cm-3 within 1 h 15 min after emission begin at 03:00 UTC. This timescale is consistent with the timescale estimate obtained for the turbulent mixing of a passive tracer assuming a gradient approach, i.e. w′c′‾=-Kc∂c/∂z, where c is the passive tracer concentration, w′ the turbulent vertical velocity and Kc is the eddy diffusivity of the tracer. Taking Kc∼Kh, the eddy diffusivity for heat, one can estimate Kc as 12.3 m2s-1 based on the mean Kh profile for the ship track domain (not shown). Neglecting variations of Kc with height, the overturning time scale within a slab of the atmosphere of extent Δz can be approximated as τturb∼Δz2/Kh. Therefore taking Δz=200 m, which is the difference in height between the cloud base and emission height, τturb is approximated as 54 min, which agrees well with the timescale obtained from the mean profiles shown in Fig. b.

In addition to turbulent transport, a fraction of the ship emissions are transported by convective fluxes into the cloud layer, just below the inversion base. At the level between 500 m and inversion base height, the mixed aerosol concentrations are raised by 10–15 cm-3 already 30 min after emission onset. However, turbulent mixing is the predominant form of vertical PBL transport at this time.

Finally, Fig. b clearly highlights the confinement of the ship plume to the boundary layer due to the strong inversion. The mixed aerosol concentrations above the PBL remain unaffected by the ship emissions.

The simulated cloud microphysical response to the plumes of increased aerosol concentration was found to be in agreement with findings of previous studies. Within plume regions, the increased number of activated aerosol led to an increase in cloud droplet number concentration and a decrease in effective radius. As a result, the cloud optical thickness increased. The strength of the response is sensitive to the plume's age and intensity (in terms of aerosol number concentration) as well as the environmental conditions, as discussed in Sect. .

Figure  displays the cloud droplet number burden summed over the PBL (columns 1 and 2) and τ (columns 3 and 4) at 09:00 and 12:00 UTC. For this purpose, the inversion top, which lies at around 800 m, was diagnosed for each column based on the temperature gradient . Although all simulations display an increase in the cloud droplet burden along the tracks, its extent varies significantly among the different simulations. At 09:00 UTC, the cloud droplet burden is increased up to 120×104 cm-2 within the plume regions in all simulations apart from ship, where maximum burdens of 15×104 cm-2 are simulated. Considering the significantly smaller number of activated aerosol within the plume in ship (Fig. b), this is to be expected. After an additional 3 h of simulation, the tracks have grown in size, but similar values of cloud droplet burden are reached at 12:00 UTC.

In ship10_V20 however, a significant decrease in the cloud droplet burden was simulated down to 20×104 cm-2 until 12:00 UTC. Whilst the ship tracks shown in rows 1–5 in Fig.  form ∼25 km from the source, or even just ∼7 km in ship10_V5, the emission sources are already separated by 313 km from the track sections displayed within the ship track domain in row 6 at 12:00 UTC, and are therefore significantly more diluted.

Additionally, little difference in cloud droplet burden is found between plumes where a fresh (ship10) or an aged (ship10A) size distribution was assumed at the point of emission. In accordance, marginal differences in cloud droplet number concentration (Nc) were simulated, as shown in Fig. . Although P75 is slightly higher in ship10, the median of Nc lies at 32 cm-3 in both simulations. This is consistent with the equivalent increase of aerosol number concentration within the size range of activation in these simulations. This result is contradictory to global studies , where a high sensitivity of the aerosol–cloud interactions to the aging of the prescribed emissions was found. The cause for these different sensitivities remains to be addressed. It could be due to different treatments of the cloud or aerosol microphysics within the different models, or it may be attributable to the different microphysical aging of the plume allowed by the higher resolution.

Comparing the simulated changes in effective radius Reff (Fig. b) as well as Nc to in situ and surface remote sensing observations of ship tracks one finds, in general, a good agreement of the simulated and observed cloud response. The observed increase in cloud droplet number concentration ranges between 40 cm-3  and 800 cm-3 , though most observed cloud droplet number concentrations lie within a narrower range of 40 to 200 cm-3 .

Similarly the in situ observations of cloud effective radii measured in ship tracks ranged between 6 and 15 µm. This is almost identical to the range spanned by P25 and P75 in all simulations. Although these values were obtained for a range of environmental conditions which are not necessarily similar to the environmental conditions of this case study, these measurements provide a basis to demonstrate the realism of our simulated cloud response.

In line with the increase in Nc, and the decrease of Reff (Fig. ), τ increases within the plume regions. In the ship10, ship10A and ship10_V5 simulations the response in τ varies between 6 to 10 at the track edges and 12 to 24 within the track centres. Within the ship simulation the response in τ is considerably weaker, following the considerably smaller perturbations to Nc and Reff, at both 09:00 and 12:00 UTC. An increase in optical thickness of 8 to 10 was simulated within the considerably smaller plume areas. A slightly stronger response was simulated at 12:00 UTC in ship10_V20, where the increase in τ ranges between 8 to 14 within the plume regions.

Due to the significant increase of cloud optical thickness within the ship track regions, the top of the atmosphere (TOA) shortwave (SW) cloud radiative effect (CRE), defined as the difference between all-sky outgoing SW and clear-sky outgoing SW radiation at TOA, was changed. Averaged over the entire ship track domain, the TOA SW CRE (Fig. c) increased in magnitude by 19 % in ship10, ship10A and ship10_V5. The stronger cooling of the clouds at the TOA is solely due to changes within the ship tracks themselves, which cover at most 6 % of the domain area, while the background TOA SW CRE variations were no larger than 5 Wm-2 (∼3 %) at any given time.

In confined regions of the simulated ship tracks, the changes in microphysical properties were found to produce localised changes of macrophysical entities, such as cloud extent and in-cloud liquid water content qc. As is shown in Fig. , regions of increased Nc due to the ship exhaust aerosol were found to coincide with regions of increased qc. The localised increase of qc is caused by the suppression of rain formation, since the influx of activated aerosol led to a significant decrease of cloud droplet size. Within the ship track domain, the stratocumulus deck is lightly precipitating with almost all precipitation evaporating before reaching the surface, thereby moistening the subcloud layer. Starting at 04:00 UTC, the rain water content within the ship track is reduced. At 09:00 UTC, the mean rain water content in ship10 within the ship track is reduced in the mean by 45 % and by 38 % at 12:00 UTC.

The resulting increase of liquid water path LWP is not only seen for the particular cross-section shown, but in several confined regions of the ship tracks (Fig. ). The background LWP ranges between 0.02 and 0.08 kgm-2 and is found to remain constant throughout the day. Within the ship10 simulation, the LWP is increased to 0.12 or even 0.16 kgm-2 in ship track regions (Fig. ), which corresponds to almost a doubling of the LWP as compared to the background.

Changes in cloud liquid water content and cloud depth due to increased aerosol concentrations have been shown to affect cloud life time . Whether the cloud life time is increased or decreased depends fundamentally on the effect of drizzle suppression on the entrainment rate and the humidity in the free troposphere . In general, precipitation acts to stabilise the boundary layer. In the case of a collapsed boundary layer such as the one analysed in this study, where cloud droplet number concentrations and accumulation size aerosol concentrations are extremely low, entrainment rates are believed to be small due to the weak radiative cloud top cooling generated by the optically thin clouds. Therefore, decreases in precipitation combined with a re-establishment of CCN have been shown to increase entrainment and lead to a re-growth of the previously collapsed boundary layer. However, entrainment rate parameterisations in most global and regional climate models are inadequate to capture such effects. During this case study we are not able to study possible effects of the ship exhaust on the PBL top as this process was found to occur on a typical timescale of the order of days (e.g. ). Due to advection of the air masses into regions of changed environmental conditions the impact of the ship exhaust on the stratiform cloud deck could only be studied for about 12 h.

Nonetheless, increases of liquid water content within these regions were found to affect the simulated cloud depth, by lowering the cloud base. This is shown explicitly in Fig. d, where the cloud base is lowered significantly within the track regions. The occurrence of an increase in LWP with a combined decrease in cloud base height over the simulated period within the ship track domain is summarised in Fig. . As can be seen in Fig. a, a 50 % LWP increase is simulated in at least 25 % of the ship track regions in all simulations but ship. Figure b displays the simultaneous occurrence of cloud base lowering, given a 50 % LWP increase. Between 09:00 and 15:00 UTC 50 to 80 % of regions with increased LWP display an additional lowering of the cloud base, while a cloud base lifting was not simulated.

This phenomenon has previously been observed using balloon soundings during the Monterey Area Ship Track campaign () campaign by , where similar environmental conditions were encountered. A lowering of the cloud base by ∼50 m was measured. Based on their data alone, no clear explanation for this phenomenon could be found. However, hypothesised that the cloud base lowering was related to dynamical effects, such as adiabatic cooling in convective plumes originating from the ship. Microphysical effects related to increases in drizzle, on the other hand were perceived as unlikely. Our simulations suggest the cloud base lowering to be a consequence of drizzle suppression and the resulting localised increase of qc within the PBL. As is shown in Table , the elevated increase in Nc (45 % above ship track mean) in regions where a cloud base lowering is detected induces a larger decrease in the rain water content (30 % below ship track mean) and hence a particularly pronounced LWP (22 % above ship track mean) and τ increase (24 % above ship track mean). As can be seen in Fig. , the cloud base is situated within the slightly stable PBL. Whilst the PBL stability and vertical mixing coefficients (not shown) are not affected by the emissions, the larger gradient in cloud water content itself, leads to an increased cloud water mixing below cloud base. There the cloud water evaporates, leading to a moistening of the subcloud layer. If a sufficient amount of cloud water is mixed downward, such that saturation is reached, the vertical cloud extent is increased. Additional cloud water condensation due to increased radiative cooling in the cloud layer within the enhanced LWP region was not simulated.

The simulated cloud optical thickness, diagnosed in the visible spectrum, is compared to the MODIS observation for τ obtained at 12:00 UTC on 26 January 2003. Within the observation shown in Fig. , three characteristic features can be determined. Firstly, considerably higher values of optical thickness (with τ>20) are detected over land than over the ocean. Secondly, a pre-frontal band structure passing through the domain, which stretches across the Bay of Biscay from 4∘ W, 47∘ N to 10∘ W, 44∘ N at 12:00 UTC, is characterised by τ values of similar magnitude. Finally, a region of ship tracks embedded within an optically thin stratified cloud layer (τ<2) located to the west of the pre-frontal band of convection was observed.

The optical thickness is shown in Fig.  for two simulations (clean and ship10) in comparison to the MODIS observation. Only one of the simulations including ship emissions is shown here, as the two features outside the small ship track region are identical (qualitatively) in all simulations. The cloud response within the ship tracks for all other simulations is shown in Fig.  for the ship track domain.

The cloud optical thickness over land as well as within the convective band is strongly underestimated in all simulations. Causes for this low bias in τ can be manifold and can not be disentangled with confidence based on this observation alone. It might be caused by an underestimation in pollution, or vertical velocity in the simulations, which would lead to a low bias in either activated cloud droplet number concentration, cloud water or both. Although the issue has to be acknowledged, it is outside the scope of this work.

We now focus our analysis on the region west of the convective cloud band. The observed background optical thickness in this region ranges from less than 2 up to a value of 4, which represents an optically very thin cloud sheet. The range of τ simulated within the background cloud compares well to observations. However, significantly more small-scale structures with higher values of optical thickness (3–4 instead of τ<2) occur within the simulations than the observations. These structures are due to subgrid-scale cloud water produced by the shallow convection scheme. Therefore, with respect to the mean state, a slightly optically thicker background cloud sheet is simulated than observed.

The perturbation in τ along the observed ship tracks varies between 5–10 in one group of tracks and 10–24 in more pronounced ship tracks. Although the simulated and observed ship tracks cannot be compared one-to-one since the prescribed ship routes vary in space from the observations, a comparison in terms of the perturbation in τ as well as the track structure can be made.

The simulated cloud response in terms of optical thickness in all simulations containing ship emissions agrees well with observations. As was done for the observed ship tracks, the simulated cloud response along the ship tracks can be grouped into the same two classes. While simulations with a smaller prescribed ship emission flux (ship), or older ship tracks (ship10_V20) lead to a smaller perturbation in τ (i.e. 5–10), the remaining simulations produced ship tracks with a larger cloud response where τ ranges between 10 and 24 as in the observations.

Furthermore, the simulations and the observations are nearly identical in terms of horizontal track extent and length. The only exception might be ship, as the ship track segments where the aerosol perturbation is sufficient to create a detectable increase in τ with respect to the background seem to be underestimated in length compared to the observations.