Large-Eddy Simulation of Ship Tracks in the Collapsed Marine Boundary Layer : A Case Study from the Monterey Area Ship Track Experiment

Abstract. For the first time, a large eddy simulation (LES) coupled to a bulk aerosol scheme is used to simulate an aircraft-sampled ship track. The track was formed by the M/V Sanko Peace on 13 June 1994 in a shallow drizzling boundary layer with high winds but very low background aerosol concentrations (10 cm −3 ). A Lagrangian framework is used to simulate the evolution of a short segment of track as it is advected away from the ship for 8 h (a downwind distance exceeding 570 km). Using aircraft observations for initialization, good agreement is obtained between the simulated and observed features of the ambient boundary layer outside the track, including the organization of the cloud into mesoscale rolls. After 8 h, a line of aerosol is injected to start the ship track. The simulation successfully reproduces the significant albedo enhancement and suppression of drizzle observed within the track. The aerosol concentration within the track dilutes as it broadens due to turbulent mixing. A sensitivity study shows the broadening rate strongly depends on the alignment between the track and the wind-aligned boundary layer rolls, as satellite images of ship tracks suggest. Entrainment is enhanced within the simulated track, but the observed 100 m elevation of the ship track above the surrounding layer is not simulated, possibly because the LES quickly sharpens the rather weak observed inversion. Liquid water path within the simulated track increases with time even as the ambient liquid water path is decreasing. The albedo increase in the track from liquid water and cloud fraction enhancement (second indirect effect) eventually exceeds that from cloud droplet number increases (first indirect or Twomey effect). In a sensitivity study with a higher initial ambient aerosol concentration, stronger ship track aerosol source, and much weaker drizzle, there is less liquid water inside the track than outside for several hours downwind, consistent with satellite estimates for such situations. In that case, the Twomey effect dominates throughout, although, as seen in satellite images, the albedo enhancement of the track is much smaller.


Introduction
Ship tracks are one of the most striking examples of anthropogenic impact on the atmosphere.Conover (1966) first identified "anomalous cloud lines" over the ocean in early visiblewavelength satellite imagery.He correctly hypothesized that cloud condensation nuclei (CCN) forming in plumes of ship emissions could perturb marine boundary layer (MBL) clouds and increase their reflectance.Twenty years later, Coakley et al. (1987) found that many ship tracks without an obvious visible-wavelength albedo signature could still be detected using near infrared (IR) satellite imagery, because of the sensitivity of near-IR radiative transfer to the cloud droplet size spectrum.Later work (Coakley and Walsh, 2002;Chen et al., 2012;Christensen and Stephens, 2012) deduced liquid water path (LWP) changes between ship tracks and the surrounding environment, showing that tracks could also exhibit LWP decreases, not just LWP increases.
The effects of aerosols on cloud radiative properties are often partitioned into the first (Twomey, 1977) and second (Albrecht, 1989;Liou and Ou, 1989;Stevens and Feingold, 2009) aerosol indirect effects.The first indirect effect is the change in net top-of-atmosphere (TOA) shortwave radiation (positive downward) resulting from a change in cloud droplet number when holding other properties constant, while the Published by Copernicus Publications on behalf of the European Geosciences Union.
second aerosol indirect effect is the additional net TOA shortwave change due to impacts on macrophysical cloud properties like water content, precipitation, turbulence and cloud lifetime that result from microphysical feedbacks.Ship tracks owe their existence to aerosol-cloud interactions, and thus provide an excellent means to study them.
The first in situ measurements of ship tracks were made with an aircraft by Radke et al. (1989) in a solid stratocumulus deck, and from a ship by Hindman et al. (1994) under cleaner conditions with a lower background cloud fraction.Ackerman et al. (1995) used these observations as the basis for a modeling study.They classified ship tracks as "Type 1", with an obvious albedo enhancement in visible satellite imagery, or "Type 2", evident only in near-IR (3.7 µm) images.They employed a one-dimensional column model with a turbulence closure, which is a computationally efficient way to focus on aerosol-cloud interaction but has limited scope, since it cannot simulate horizontal dispersion, the circulation structure of a ship track, or horizontal covariations between turbulent eddies and cloud throughout the boundary layer.In their simulations of the Type 1 track (based on the observations of Hindman et al., 1994), LWP and cloud droplet number concentration N d were elevated above the control run for the entirety of the simulation (a positive first and second aerosol indirect effect), yielding a substantial increase in albedo (greater than 50 %).They also simulated a Type 2 ship track (based on the observations of Radke et al., 1989) and found a daytime LWP reduction (negative second aerosol indirect effect), due to enhanced subcloud drizzle evaporation giving a less well-mixed boundary layer.These results compared reasonably well to the limited available observations.
Community interest in aerosol cloud interactions as exemplified by ship tracks led to the Monterey Area Ship Track experiment (MAST; Durkee et al., 2000a) in 1994.Aircraft surveys by multiple platforms provided in situ measurements of many ship tracks and their contrast with the ambient boundary-layer conditions.During research flight A338 on 13 June 1994, the United Kingdom Meteorological Office (UKMO) Meteorological Research Flight (MRF) C-130 sampled a Type 1 ship track generated in a collapsed boundary layer by the M/V Sanko Peace.Arguably, this is one of the best-sampled Type 1 ship tracks documented in the scientific literature.An interesting and unusual feature of the case was the observation that the ship track appeared elevated as much as 100 m above surrounding cloud tops.Taylor and Ackerman (1999) summarized the extensive set of aircraft measurements and performed comparison simulations using their 1-D column model.They obtained good agreement with the relative albedo enhancement seen in the observations, with comparable LWP, effective radius r e , and N d in both the track and background environment, but again their modeling framework was not designed to simulate the horizontal structure of the track and its downstream evolution.
An obvious step up in modeling sophistication would be to use a large eddy simulation (LES) coupled to an aerosol physics model.Surprisingly few LES of real ship tracks have been attempted.The studies of Wang and Feingold (2009) and Wang et al. (2011) examined idealized ship tracks in an 800 m deep boundary layer, at the upper limit of the 300-800 m MBL depth range typical of the MAST cases (Durkee et al., 2000b).Their simulated tracks showed regions of albedo reduction around the ship track that in the area mean largely canceled out the enhanced in-track albedo, yielding a very weak total aerosol indirect effect.However, they had no observational constraint, a limitation that the present study aims to address.
We revisit the Sanko Peace case using an LES model with a coupled bulk aerosol model developed by Berner et al. (2013).The case provides an opportunity to test the skill of this model, which combines a sophisticated representation of turbulence with an intermediate-complexity description of the aerosol and its interaction with cloud processes, against observations, and more generally test whether this modeling framework can significantly add to one-dimensional turbulence closure methods.Our work is organized as follows: further detail on the observations and previous modeling work is given in Sect. 2. Model formulation is described in Sect. 3 and forcing and initialization detailed in Sect. 4. The simulations are discussed in Sect.5, including sensitivity studies on track orientation and background aerosol concentration, and a simplified model for cloud albedo (Platnick and Twomey, 1994;Brenguier et al., 2000) is used to partition the simulated albedo enhancement into contributions from the first and second indirect effects.In Sect.6, we briefly discuss the interpretation of the simulations in the context of cloudaerosol regimes (Rosenfeld et al., 2006;Berner et al., 2013), followed by conclusions in Sect.7.

The Sanko Peace case study
Our case study description draws from the work of Taylor and Ackerman (1999), additional analysis of the flight data (kindly provided by Simon Osborne of the UKMO), and satellite imagery for the case.For details of the aircraft instrumentation and sampling strategy, the interested reader is referred to the Taylor and Ackerman (1999) study.The boundary layer was quite shallow, with cloud tops at 300 m and very clean background aerosol concentrations of 10 cm −3 .CCN and condensation nuclei (CN) concentrations were negligible above the inversion up to a kilometer in depth.MBL wind was moderately strong, with aircraft observed speeds of ∼ 14 m s −1 (150 m altitude) from the north-northwest, driving coherent roll structures within the boundary layer (for a review of boundary layer roll vortices, see Etling and Brown, 1993).We obtained Geostationary Operational Environmental Satellite (GOES) visible imagery at the time of aircraft sampling, which is shown in Fig. 1.The roll organization within the boundary layer is readily apparent; unfortunately, high cirrus cloud obscured the boundary-layer clouds near Figure 2 shows an aircraft profile of the environmental wind, liquid water content q l , total water q t , cloud droplet concentration N d (in cloud) and unactivated aerosol concentration N ad (above cloud; for instrumentation details, see Taylor and Ackerman, 1999), and absolute temperature T abs (black curves), with overlaid geostrophic wind forcing and idealized initial profiles (blue curves, discussed below in Sect.4).The inversion structure is quite distinctive, with three nearly isothermal layers, each ∼ 100 m in depth, separated by 2-3 K inversions.These layers are all quite moist, with q t values of 9.25-10 g kg −1 , nearly identical to the wellmixed layer below.While N d in the cloud varies between 25-30 cm −3 , the air in the 100 m layer above is essentially pristine, with negligible N ad , and only small concentrations above up to 1 km (10-30 cm −3 , of which a large portion is likely at the smaller end of the size spectrum).This structure could reflect differential advection in layers above the inversion base.It is also suggestive of the result of an aerosolcloud-precipitation feedback-induced collapse of a deeper boundary layer (Ackerman et al., 1993), in which the secondary inversions mark the subsided locations of previous stratocumulus layers which became too optically thin to drive sufficient turbulence to sustain themselves.Taylor and Ackerman (1999) reported that the ship track rapidly deepened by 100 m above the surrounding back-ground cloud in less than an hour of downstream development.This rapid deepening may have been partially enabled by the weak cloud-top inversion, but their simulation, which idealized the observed profile, did not produce nearly as much deepening as was observed.Recent remote sensing studies have shown deepening of Type 1 ship tracks to be relatively common (Christensen and Stephens, 2011), but almost no other in situ profiles of the environments that support such deepening are available.

Model formulation
In the present work, simulations are performed using the System for Atmospheric Modeling (SAM) version 6.9 (Khairoutdinov and Randall, 2003).SAM uses a dynamical core formulated on the anelastic approximation to the Navier Stokes equations to represent fluid motion resolved on the grid.The effects of subgrid turbulence are handled using the 1.5 order turbulent closure model of Deardorff (1980).Scalar advection is performed using the piecewise parabolic method of Blossey and Durran (2008).Coriolis force is included using an f plane approximation, with the Coriolis parameter specified appropriately for the latitude of the case considered.Liquid static energy, s l = c p T + gz − Lq l , is the conserved thermodynamic variable, as the ice phase is not present in the warm rain cases under consideration.Here c p is the isobaric heat capacity of air, g is gravity, z is height, L is the latent heat of vaporization, and the liquid water mass mixing ratio q l is the sum of cloud water (drops smaller than 25 micron radius) q c and rain water (drops larger than 25 micron radius) q r .Water vapor q v is advected separately, and condensation is calculated by saturation adjustment.Surface fluxes are calculated in each grid from Monin-Obukhov theory.Background profiles of the wind components u and v, liquid water mixing ratio q l , total water mixing ratio q t , absolute temperature T abs , and total aerosol number concentration N a (the sum of cloud droplet number concentration N d , rain droplet number concentration N r , and interstitial aerosol number concentration N ad ) observed by the MRF C-130 prior to sampling the Sanko Peace ship track (black curves).Overlaid are profiles of the forced geostrophic wind components U g and V g , as well as the initial profiles of q t and T (blue curves).
Microphysical tendencies are calculated using the twomoment Morrison scheme (Morrison and Grabowski, 2008;Morrison et al., 2005) with the precipitation parameterization of Khairoutdinov and Kogan (2000).A number of modifications have been made, including the use a lookup table for cloud droplet sedimentation and raindrop fall speeds, rain evaporation, and the shape parameter for the gamma rain distribution.
A simple bulk aerosol scheme (described in Berner et al., 2013) has been coupled to the microphysics.It predicts mass and number for a single accumulation mode with a log-normal size distribution of aerosol number that has an assumed geometrical standard deviation σ g = 1.6.This approach requires a minimal number of additional advected scalars while allowing for the inclusion of realistic aerosolcloud-precipitation feedbacks; a limitation of this method is that it does not represent the growth of a separate Aitken mode of smaller particles to CCN-active sizes.Processes affecting aerosol in the scheme include activation, autoconversion, accretion, evaporation, scavenging of interstitial unactivated aerosol by cloud and rain, and fallout to the surface.A surface source based on the sea-salt parameterization of Clarke et al. (2006) is included.Radiation calculations are performed using the Rapid Radiative Transfer Model (RRTM; Mlawer et al., 1997), which in our implementation utilizes a combined cloud-drizzle r e diagnosed from the 3-D microphysical fields.Unactivated aerosol is not included in the radiation calculation.

Model domain, resolution, and boundary conditions
Simulations in this paper are run on a 51.2 km × 12.8 km domain with 50 m horizontal resolution.Vertical spacing is 15 m near the surface, shrinking to 5 m in a layer from 70 to 500 m in depth, and then stretching continuously to the do-main top at 29 km (necessary to avoid reengineering the implementation of the radiative transfer scheme in the model).The time step is 0.5 s.Boundaries are doubly periodic in the horizontal, with a sponge layer in the upper portion of the domain to absorb gravity waves and prevent spurious reflections from the rigid lid.

Initialization and forcing
The goal of our model initialization and forcing is to produce a boundary layer qualitatively and quantitatively similar to the background environment described by Taylor and Ackerman (1999).As the evolution of the boundary layer prior to sampling and large scale meteorological forcings remain uncertain, the final initial values and forcings were empirically chosen using pilot simulations to improve the quantitative match between observations and the hour-8 boundary layer statistics.

Temperature, moisture, and wind
The horizontal coordinates x and y are aligned such that the boundary-layer mean wind, which is from 30 • west of north, lies along the −y direction.u and v denote the wind components in the x and y directions.The blue curves in Fig. 2 show the geostrophic wind profiles U g and V g used to force the model, which were chosen to approximately produce the observed wind profiles, as well as the smoothed q t , total aerosol concentration N a , and T profiles used for model initialization.The initial q l profile is diagnosed from saturation adjustment; N a is the sum of interstitial aerosol N ad , cloud droplets N d , and rain N r .
In Fig. 3, red and blue curves show y-averaged profiles of u and v, liquid water mass mixing ratio q l , q t , absolute temperature T abs and cloud droplet concentration N d for up-Figure 3. Profiles of y-averaged u and v winds, liquid water mass mixing ratio q l , total water mass mixing ratio q t , absolute temperature T abs , and cloud droplet concentration N d after 8 h, immediately before the ship track perturbation is introduced.Profiles are sampled at the locations of mesoscale updrafts (red curves) and downdrafts (blue curves), identified by maxima or minima in the y-averaged liquid water path.
drafts and downdrafts from the control run at hour 8, overplotted with the aircraft observations (black curves).The coherent roll organization of the boundary layer results in considerable differences in wind shear, q l , and N d between the roll-scale updrafts and downdrafts.For instance, wind speeds are 2-3 m s −1 faster in the downdrafts, since surface drag decelerates the flow before it ascends in the updrafts.Total water content in the updrafts is substantially larger than the downdrafts, reflecting the strong precipitation within the updrafts and broader downdraft regions.The initial stair-step temperature structure above the inversion has been mixed/diffused out after 8 h.If the observed structure results from the boundary layer collapse process discussed in Ackerman et al. (1993), this suggests that the model is too diffusive in the region above the inversion or perhaps allows mixing not present in the real case.Alternatively, the observed structure may result from layered advection.
Since the observed wind shear at cloud top is large and N d is at the upper end of the observational range, it is likely that the aircraft profiled through the center of a roll-scale updraft.The forcing parameters and initial conditions have therefore been tuned to match the mean updraft structure after the 8 h, when the roll vortices are fully developed and the ship track is inserted.
Because of the low cloud base, the C-130 could not radiometrically observe the SST.Taylor and Ackerman (1999) used a sea surface temperature (SST) of 287 K; in our pilot simulations, the T abs and q l profiles matched observations better with an SST of 288 K, so that is used here.With our choice of geostrophic wind profile and SST, the final updraft profile matches the observations reasonably well, though the inversion jumps are smeared somewhat by averaging due to variations in cloud top along the y axis.

Radiation
Since the observations are inadequate to resolve temporal evolution of the other meteorological forcings in this case, radiative forcing is diurnally averaged.The model uses an insolation-weighted solar zenith angle appropriate to the date and latitude (13 June, 34 • N).

Subsidence
A constant divergence assumption is applied from 3000 m to the surface, implying a linear subsidence profile which acts as a large-scale forcing on the thermodynamic and microphysical fields.Accurate divergence measurements are quite difficult to obtain from observations; ERA-interim reanalysis (Dee et al., 2011) values for subsidence are quite variable in space and time along the coast of Southern California for the Sanko Peace case.We used an empirically determined divergence of 6.4 × 10 −6 s −1 , which maintains a realistic and fairly constant MBL height through the majority of the simulation.

Microphysics
The initial MBL aerosol concentration is set to 10 per mg dry air for the baseline case.Aerosol concentrations given in these units are conserved for adiabatic parcel motions, and thus preferred.This is comparable to the mean N d reported by Taylor and Ackerman (1999) (their values are reported in units of cm −3 , which are roughly 30 % larger than values in units of mg −1 within the shallow boundary layer; this comparison also assumes that in the model, most aerosol will be activated in updrafts, which holds for the simulated conditions).The initial geometric mean radius of the aerosol is chosen as 0.1 µm.Free tropospheric aerosol is set to zero, as After 8 h of simulation, we branch off a ship track run.To represent the track, the aerosol concentration between z = 0 − 100 m in a single line of grid columns down the center of the domain along the y axis is instantaneously set to s = 15 000 mg −1 , with a geometric mean radius of 0.1 µm.This approach is an approximation to the emissions from a ship steaming into the low-level wind.It would be more realistic to insert the aerosol at a location that follows the ship motion, but given the ship relative wind speed V rel = 20 m s −1 , the track would take only 10 min to advect across the 12.8 km length of the domain in the y direction.Our initialization procedure makes the track evolve similarly at all y, allowing us to conveniently use y averaging to robustly characterize the overall track evolution.The track simulation is continued for another 8 h.For comparison, we also continue the control run with no added ship emissions.
We justify our choice of s as follows.First, we link the grid perturbation s and the implied aerosol source strength S. Given the perturbed depth h = 100 m, horizontal grid spacing x of 50 m, air density ρ a of 1.2 kg m −3 , and fraction of viable CCN f CCN set to 0.15, = 15 000 mg −1 → S = 1.2 × 10 16 s −1 .
Taylor and Ackerman (1999) performed their 1-D simulation of the Sanko Peace with an implied S of 3.0 × 10 16 s −1 .They based their choice on the aerosol measurements of the Cosco Tai He, described in Hobbs et al. (2000).Their implied source was twice the strength of the upper bound derived in Hobbs et al. (2000), done in order to counteract the underprediction of supersaturation (and thus activation) in their model.Since the aerosol scheme used in our study only includes the accumulation mode, we further need to assume a value of f CCN .Ferek et al. (1998) found that 10-30 % of particles emitted are initially activated, while increasing supersaturation over time could contribute to increased activation downstream, along with the possibility of further CCN production via gas deposition growth of Aitken mode particles to CCN active size.Aircraft measurements reported by Hobbs et al. (2000) estimated the initially activated fraction in a range from 4-25 % with significant variation between the different ships sampled, with an estimate of 8 % for the Cosco Tai He.
While the activation scheme in our model (Abdul-Razzak and Ghan, 2000) has some capability to capture changes in activation due to variations in updraft strength, the growth of smaller particles to CCN active sizes is neglected.Assuming a larger value for f CCN of 0.15 to roughly approximate the growth of CN to CCN downstream, our value of S is 1.2 × 10 16 s −1 , in line with the Hobbs et al. (2000) measure-ments for the Cosco Tai He.The Sanko Peace is a smaller ship, so the analog is not perfect, but the above calculations suggest our source strength is reasonable.We also perform a high-aerosol sensitivity study with an initial background boundary-layer aerosol concentration of 300 mg −1 .In an initial pilot simulation with the same source strength as in the control simulation, the plume rapidly diluted with minimal microphysical or macrophysical impact.In order to observe a clear signal, we increase the amplitude of the source by a factor of 10 for the high-aerosol case.

Simulations
Four simulations will be discussed.Run BaseSpinup is the starting point for our study, in which an initial sounding adapted from the ambient C-130 vertical profile preceding sampling of the Sanko Peace track is spun up for 8 h, at which time the model evolution agrees reasonably well in a quantitative sense with observations of the key thermodynamic and microphysical variables.At this point, the simulation is branched into runs BaseTrack, in which an aerosol perturbation representing the ship track is inserted, and BaseCtrl, which is left unperturbed; both branches are evolved for a further 8 h.Two sensitivity studies are also performed.In run SensPerp, wind forcing is rotated 90 • clockwise to orient the rolls parallel with the longer x dimension of the domain; the aerosol perturbation is now perpendicular to the roll structure, resulting in more rapid turbulent diffusion through the boundary layer.Lastly, run SensHiAer enhances the background aerosol concentration and that of the ship track perturbation as described in Sect.4.4 above.Both sensitivity runs spin up for 8 h, at which point the tracks are inserted and evolved for an additional 6 h.Thermodynamic, dynamical, and microphysical statistics of the BaseCtrl run are nearly identical to those sampled from the background regions of the BaseTrack and SensPerp runs, suggesting that BaseCtrl is an adequate control for run SensPerp.A comparison between the general statistics of BaseCtrl and the out-of-track background environment in BaseTrack suggests that sampling of the background for SensHiAer provides an adequate control for that case, so separate control branches for the sensitivity runs are not performed.

Background environment
We begin by examining the evolution of the unperturbed background environment in BaseSpinup.Roll structures develop almost immediately, with a cross-axis length scale of a few hundred meters, growing to approximately 1.7 km at hour 4 and 2.5 km at hour 8. Figure 4 shows x-y plots of albedo, MBL depth averaged aerosol number, LWP, and surface precipitation intensity.The albedo plot strongly resembles the GOES imagery in the enlarged panel of Fig. 1 and other similar roll-organized boundary layers.The modeled roll wavelength is smaller than the approximately 5 km scale in the satellite imagery, which we attribute to the continued upscale evolution of the real boundary layer vs. an 8 h spinup from rest in the model.
LWP and albedo maxima (minima) mark the updrafts (downdrafts).Despite the very shallow boundary layer, LWP averages ∼ 100 g m −2 in the updrafts, with maxima exceeding 150 g m −2 .Cloud base beneath the updrafts is mostly at the surface.While there are large variations in albedo in the cross-roll direction, domain cloud cover is quite high (∼ 87.5 % at hour 8, based on a 10 g m −2 minimum cloud water path (CWP) threshold).Aerosol number concentrations are 25-30 mg −1 in the updrafts, where air recently in contact with the surface source is converged, while downdraft air is aerosol-depleted (∼ 10 mg −1 ) due to collisioncoalescence losses in the clouds and mixing with the pristine air entrained from above.Domain average surface precipitation is 0.5 mm day −1 , but locally, precipitation is up to 6 mm day −1 in narrow regions beneath the updrafts with highest LWP, and such rain bands contribute a significant fraction of the mean precipitation.
Figure 5 shows an x-z snapshot at hour 8 of the yaveraged vertical velocity and a slice of total aerosol number concentration N a taken across the domain at y = 6.4 km.For reference, the cloud contour q c = 0.01 g kg −1 is also shown.In the simulation, a small amount of aerosol detrains in the layer immediately above the rolls as a result of evaporation and mixing.The observations had essentially no aerosol above cloud top (with one exception discussed below in Sect.5.3), suggesting the model may again be slightly too diffusive with the very sharp vertical gradient in the aerosol field.Typical peak vertical velocities in the updrafts are 0.5-0.8m s −1 in very narrow bands of ∼ 200 m wide (variations in the updraft position along the roll diminish this when averaging in y).The w slice also shows that the downdrafts are considerably broader than the updrafts.

Ship track injection and evolution
In this section, we analyze branch BaseTrack and compare it to the unperturbed BaseCtrl.The albedo A is computed in each column from the TOA downwelling and upwelling shortwave radiative fluxes, Figure 6 shows the albedo A at 0.5, 1.5, 3.0, and 8.0 h after the aerosol injection, which is initially below a roll-scale updraft, producing a sharp, bright albedo signature which diffuses with time.For most of the following discussion, we consider Hovmöller plots of the salient fields, interpreting downstream distance as the time after injection multiplied by the 20 m s −1 ship-relative wind speed.Plots of albedo and surface precipitation use data output once a minute from the model, and are formed by combining transects at y = 6.4 km from all times.Calculation of the N a and LWP fields required data available in the 3-D outputs once every 10 min.
In order to better represent the variability of these fields, we substitute spatial resolution for time resolution of these variables by sequentially cycling through transects at each of the 10 y locations nearest y = 6.4 km for each 3-D output, yielding the same number of transects for all fields.Note that these plots present a highly compressed view of the along-track direction, in that the 8 simulated hours correspond to a downstream distance of 576 km, given the 20 m s −1 ship-relative surface wind speed, while the cross-track domain width is 48 km.The right-hand axis of panel d in Fig. 7 and Fig. 16 shows equivalent downstream distance.
The albedo of unbroken stratocumulus clouds can be related to their cloud droplet concentration (which is in turn related to N a ) and LWP; the relative importance of N d and LWP contributions to the track albedo response is explored in Sect.5.6.Figure 7 shows a Hovmöller plot of the time evolution of albedo, N a , LWP, and surface precipitation.
At 30 min after injection, the ship track aerosol has been laterally mixed across slightly more than 1 km, diluting the initial concentration from an MBL depth-averaged value of 5000 mg −1 to values between 100-325 mg −1 .Assuming nearly complete activation (as is simulated in this case) and a vertically well-mixed profile, this gives a peak N d of 420 cm −3 at 300 m altitude, a value nearly 4 times larger than observed in an observational transect sampled 30 min downstream of the ship (Taylor and Ackerman, 1999).Imperfect alignment of the ship's course and the roll axis may have led in reality to more rapid turbulent diffusion of the aerosol than in the simulation.Consistent with this hypothesis, the observed track width of 4 km is 4 times as large as the simulated width.Section 5.3 further discusses of how track orientation affects track width.Other possibilities are that the effective aerosol injection strength S may be overestimated, or that the plume takes more than 30 min to develop a quasisteady aerosol size distribution with a fully developed accumulation mode.
In contrast with the obvious aerosol perturbation and albedo increase, there is a negligible change in LWP between the track and the surrounding environment after 30 min (Fig. 7c).The lack of a strong cloud macrophysical response indicates that the radiative response of the cloud at this time results entirely from the Twomey effect.Despite the shift towards smaller cloud droplets, substantial surface precipitation remains inside the simulated track at this time.Figure 7d shows no real difference in precipitation rate between the track and background.The time lag between the aerosol injection and the visible manifestation of the track in the pseudo-albedo field gives a sense of the timescale for the perturbation of the microphysics via activation.There is an additional delay before changes in cloud properties alter surface precipitation characteristics, as existing rainwater in the column takes some time to sediment out.The narrow band of peak rain rates exceeding 4 mm day −1 disappears 20 min after visible cloud brightening (50 min after injection), and virtually all surface precipitation ceases by hour 9.5.
The aerosol perturbation diffuses slowly over the next hour, broadening the track from 1 to 3 km by laterally mixing into two additional roll updrafts and diluting MBL depthaveraged aerosol number concentrations within the track to 60-100 mg −1 .Peak updraft LWP values diminish within the track 90 min after injection but increase in the regions adjacent to the central updraft.This lateral redistribution of cloud water out of the updrafts is likely due to drizzle inhibition.Figure 7d shows essentially no area beneath the central updraft of the track where surface precipitation exceeds 0.25 mm day −1 after 90 min, as compared to peak rates of ∼ 4-6 mm day −1 under the background updraft cores.
After 3 h, the track has spread to 5 km width, and MBL depth-averaged N a has diluted to 30-60 mg −1 .The rough inverse scaling of N a with lateral dispersion (boundary layer depth is not changing much within this period) suggests that local source and sink terms are of secondary importance compared to the advective redistribution of the original aerosol perturbation within the track; we will examine the aerosol budget of the track more precisely below.LWP and optically thick cloud increase throughout the track, with peak LWPs exceeding 100 g m −2 .While surface precipitation begins to recover under the track 150 min after injection, the average rain rate in the track remains suppressed, as the maximum rain rate in the track is less than half that of the background despite increasing LWP.
At the end of the simulation, 8 h after the aerosol injection, the track is ∼ 15 km wide, spanning six distinct updrafts, with LWPs as high as 100-140 g m −2 .These large values of LWP coupled with slow declines in N a (and hence N d ) result in the redevelopment of drizzle and surface precipitation beneath the updrafts in the track.
In contrast with prior LES modeling work of idealized ship tracks in a deeper, open-cell boundary layer (Wang and  Feingold, 2009; Wang et al., 2011), Fig. 7a does not show a suppression of background cloud albedo on the flanks of the track due to an induced secondary circulation.Thus, in this shallow, collapsed boundary layer, the simulated track induces a more significant area-integrated albedo perturbation than those seen in previous studies.
Figure 8 compares the y-averaged stream function and aerosol fields averaged over hour 15 (the seventh hour after the BaseTrack aerosol injection) in simulations BaseTrack and BaseCtrl.Over hour 15, aerosol-cloud-precipitation feedbacks within the track act to reinforce the roll circulation, while the rolls outside the track (and throughout Ba-seCtrl) become shallower and weaker as the boundary layer collapses.While this would also tend to strengthen the downdrafts and induce cloud thinning on the edges of the track, this does not seem to reduce albedo there.A possible explanation is that the shift in droplet sizes that has inhibited drizzle and reduced moisture desiccation in the updrafts overcomes any tendency for cloud thinning in downdrafts.

Continued evolution of the background state
During the 8 h after aerosol injection, the background environment also evolves significantly, with declines in mean LWP (38 %), N a (34 %) and albedo (30 %), relative to their hour-8 peak.The decline in LWP is due to a loss of cloud water, as the rain water path (RWP) for the background remains approximately 10 g m −2 throughout.
To better understand this evolution, we analyze domainmean statistics for hours 8-16 of the unperturbed control branch, for which there is no track that needs to be removed.Figure 9 shows profiles of liquid-water potential temperature θ l , cloud water q c , N d , radiative heating rate Q RAD , and resolved buoyancy flux B at hours 8, 12, and 16.As mean N d rapidly diminishes, the cloud becomes optically thinner.This causes the radiative cooling peak, which initially resides just below cloud top, to broaden and shift deeper into the cloud layer, acting to stabilize the upper MBL, as seen in the progressively shallower region of positive buoyancy flux and less well-mixed θ l profiles at hours 12 and 16.The combination of weakening updrafts and larger cloud droplet sizes resulting from decreased N d makes it increasingly difficult to support cloud, which leads to a collapse of the boundary layer, as earlier found in a one-dimensional closure model by Ackerman et al. (1993).Much of the MBL turbulent kinetic energy is shear-driven, but this does not prevent the collapse.The increasingly negative buoyancy flux in the updrafts causes the roll structure to become less coherent and wavelengths to shrink, in agreement with the results of sensitivity studies in Chlond (1992) and Müller and Chlond (1996).For further detail regarding boundary layer roll dynamics and the relative importance of shear and buoyancy, the interested reader is referred to the LES study of Glendening (1996).

Aerosol number budget inside and outside the track
In order to further understand the evolution of the track, we examine the MBL depth-averaged aerosol number budget.The only source is the wind speed dependent surface flux, while autoconversion, accretion, interstitial scavenging, and entrainment dilution (since there is no aerosol above the boundary layer) all act as sinks.All these terms are a function of the local column properties, while advection redistributes aerosol between columns.In Fig. 10, we examine time series of the area averaged N a budget and source terms inside the background environment (left panel) and ship track (right panel).Grid columns are classified as part of the track if their N a exceeds twice the domain median N a of the unperturbed control branch at the same point in time.The local entrainment rate w e is calculated using a flux-jump approach (see e.g., Faloona et al., 2005) on 8 × 8 tiles of grid columns.The entrainment tendency is then calculated as N a | w e = w e (N a FT − N a ) /z i , where w e is the entrainment rate, N a FT is the free tropospheric aerosol concentration (zero in this case), and z i is the inversion height, using coarsened spatial maps of z i and N a .
Accretion is initially the largest component of the loss term in both the background environment and track, with a large contribution from scavenging of interstitial aerosol.For the track, the large initial spike in accretion is due to the activation of many new cloud droplets at the base of updrafts with significant precipitation, initially allowing for large loss of aerosol number.However, the simultaneous increase in N d drives the cloud droplet distribution towards a smaller mean radius, reduces autoconversion efficiency, and inhibits new drizzle formation.After this brief period of reduced accretion, increased LWP resulting from earlier drizzle suppression begins to enhance precipitation again, with efficient collection of N d in large-scale updrafts.In the background, both accretion and autoconversion diminish, as the continual reduction in background N d leaves a smaller available population of droplets to be scavenged by precipitation or to autoconvert into drizzle.
The second largest term is the interstitial scavenging of aerosol by cloud, which increases throughout the simulation in the background environment, but is sharply reduced within the track.This is somewhat counter-intuitive, as the collision efficiency for interstitial scavenging increases with decreasing droplet diameter (e.g., see the appendix of Berner et al., 2013, and references therein).While detailed examination of this effect is beyond the current scope, a possible interpretation is that while the collision efficiency may increase in the track, the reduced sedimentation rate of the smaller cloud droplets decreases the gravitational collection factor in the interstitial scavenging term, causing this term to be smaller in the track compared to the background.
Entrainment is the third largest number sink term within the track.Entrainment dilution rate is initially larger in the track due to an enhanced entrainment rate and the larger aerosol concentration in the boundary layer, since dilution is proportional to the difference between the boundary layer and FT concentrations.As the track broadens with lateral mixing and the aerosol concentration in the track approaches that of the background, dilution weakens and becomes the weakest sink term at the end of the simulation.Outside the track, entrainment (and therefore entrainment dilution) is much weaker, and autoconversion is the third strongest term.
The final sink is due to loss of aerosol number to the sea surface in sedimenting cloud droplets and secondarily in falling raindrops.This term is small but non-negligible and improves budget closure, since the simulated cloud frequently extends to the sea surface (Fig. 5).Within the track, it is small during the first 5 h due to the small (and hence slowly falling) cloud droplets.By the end of the simulation, though, the cloud droplets are more numerous in the track and have become large enough to sediment more efficiently, leading to a larger sedimentation loss than in the background at that time.

Comparison with observations
The MRF C-130 flew a series of in-cloud and above-cloud transects perpendicular to the track 40 km from the Sanko Peace.This distance was estimated by Taylor and Ackerman to be approximately 35 min downwind, assuming ship relative winds of 20 m s −1 .Taylor and Ackerman (1999) provided detailed analysis of these aircraft observations.
We compare these observations with the simulated ship track.As discussed above, due to uncertainties in the actual aerosol source strength and alignment between the track and background roll structure, it is unrealistic to expect a perfect match in aerosol concentration or track width.For comparison, we examine transects from model output at 40 min after the aerosol perturbation is injected, as 3-D fields were saved every 10 min.Note that for this comparison, N d has units of cm −3 .
Figure 11  Cloud cover at this level is lower than in the observations, resulting in a low bias to the background N d , but the peaks of 20 cm −3 are consistent with observations (the average is not cloud-conditional, as spatial variability and N d gradients create noise).The track itself is narrower than in the observations at this time, spanning barely 2 km as opposed to 4 km in the transect presented by Taylor and Ackerman.The narrower track width in the model helps explain larger peak concentrations relative to the observations, with the maximum of 178 cm −3 significantly in excess of the observed peak of 130 cm −3 .However, the average simulated value across a 2 km window including the track is only 67 cm −3 , similar to the observed mean of 60 cm −3 across the ∼ 4 km wide track.
Taylor and Ackerman (1999) found that drizzle size droplets contributed significantly to the effective radius, as values of r e determined from in situ distributions of cloud droplet sized particles were several µm smaller than those retrieved radiometrically, a discrepancy fixed by including drizzle-size droplets in the calculation.A modified effective radius is used within the model to include this effect: r e = (q c + q r ) q r r er + q c r ec .
The observations averaged two-second blocks of data for computing r e , which is equivalent to a four grid-point average in the model framework.In the second panel on the left, the model r e transect shows a mean of 18 µm within the background and a drop to 10 µm within the track, in excellent agreement with the observations.The representative simulated r e transect is noisier than the observations, likely in part due to the more broken cloud compared with the observed case, as well as the relatively coarse sampling of the spatial variability of the droplet distribution resulting from the 50 m horizontal grid spacing.Aircraft albedo observations are not directly comparable with the model output, as they were measured just above cloud top, whereas the model values are for TOA and affected by the overlying atmosphere; thus here our comparison is mainly qualitative.The albedo transect clearly demonstrates the lower overall albedo and more broken nature of the modeled MBL structure.The observed albedo never falls below 0.27, while in several spots the model albedo falls below 0.1.The background peak albedos are broadly consistent at ∼ 0.3 with the observations, suggesting that either evaporation of thin cloud flanking the large scale updrafts is excessive or precipitation is too intense within the model, removing liquid water that would otherwise be available for cloud flanking the updrafts.However, the albedo peak within the model transect of 0.47 yields a comparable increase relative to the background mean as does the observed value of 0.52.
Figure 12 shows profiles of cloud and rain water conditionally sampled from the track and background at 40, 90 and 420 min after track injection, averaged over both updrafts and downdrafts.The rain mixing ratio is scaled by a factor of 4 for clarity.The background profile of q l (which includes both cloud and rain water), constructed by Taylor and Ackerman is overplotted in black.The peak in liquid water for the background is located near 210 m, with cloud tops at or slightly above 300 m.Significant rainwater remains in the column at 40 min, but decreases are apparent near the top of the profile, as the autoconversion source of new drizzle is diminished with the shift to smaller cloud droplets.This profile is qualitatively consistent with the in situ measurements, which showed slight increases within the track of liquid water content (LWC) for the instruments most sensitive to cloud size droplets, and slight decreases of LWC for instruments with higher sensitivity to drizzle; this is qualitatively consistent with decreasing q r and increasing CWP, depending on the cut-off diameters for the respective instruments.After 90 min, the peak in cloud water within the track has lifted to 250 m and liquid water content (LWC) has increased by 50 % to 0.3 g kg −1 , while rainwater in the track has become negligible.After 6 h, the peak in track LWC has increased slightly while shifting back downwards to 225 m.Drizzle in the track is recovering towards the background profile, though the background cloud water peak has decreased 20 % while shifting downwards to 150 m.
In Fig. 8, a plume of aerosol in the inversion layer is evidently emanating from the ship track, due to broadening of the inversion layer above the cloud top due to sheardriven mixing.One transect flown by the C-130 did show an increase in Aitken mode particles above cloud top.The above-cloud aerosol plume was sufficiently surprising in an otherwise pristine environment to be explicitly noted in the flight summary.However, the observed concentrations (∼ 15 cm −3 ) were small compared both to those simulated and to the observed cloud droplet concentrations within the track.This is not definitive, as the available data are inadequate to tell how close to cloud top the data were taken, but it appears that more aerosol is detrained in the model than is supported by the observations.While the simulated track maintains higher cloud tops than the background at 40 min after injection, it does not deepen as rapidly or as much as the observationally reported 100 m (Taylor and Ackerman, 1999).One hour after the aerosol perturbation, the difference between cloud tops inside vs. outside the track ranges between 20-30 m.The maximum separation in run BaseTrack between cloud tops in the track and background is 60 m, but this only develops by the end of the simulation and is driven more by the collapse of the background than the continual deepening of the ship track.Figure 13 shows a Hovmöller plot of the y-averaged entrainment derived using the local flux jump calculations; while averaging in y blurs maxima in the surrounding environment, it is clear that the central circulation in the ship track is entraining air at least twice as rapidly as the background average.If aerosol concentrations were higher just above the entrainment zone than in the boundary layer, then this could act as a positive feedback that would accentuate the track.Given the highly elevated aerosol concentrations typical of a ship track, however, it is likely that entrainment is usually a negative feedback that enhances the dilution of track aerosol concentrations, since FT aerosol concentrations larger than the track values are likely rare in the remote MBL.Etling and Brown (1993) noted that the presence of roll structures can have a profound influence on turbulent fluxes within the boundary layer, and that the effective turbulent diffusion can be highly anisotropic.This affects the dispersion of aerosol within shear driven boundary layers.The shear between updrafts and downdrafts of individual rolls tends to diffuse perturbations along them much more rapidly than mixing can transport a scalar between adjacent rolls.In the case of ship tracks, we expect ship tracks with a larger crossing angle relative to the roll axis to spread more rapidly than a track that parallels the roll axis.We tested this using run SensPerp by rotating the geostrophic wind 90 • clockwise, such that the ship track is now inserted perpendicular to the rolls rather than parallel to them.This run is spun up for the same initial 8 h period as in BaseSpinup, after which the track is inserted and the run continued for a further 6 h. Figure 14 shows the albedo field for run SensPerp at hours 9, 11, and 13; rapid broadening of the track is readily apparent.

Sensitivity of track to relative wind direction
In Fig. 15, the background (blue), track (red), and domain averaged (black) statistics of albedo, N a , LWP, and precipitation are shown for SensPerp, BaseTrack, and SensHiAer (to be discussed below).The BaseTrack simulation is shown in the middle panel to facilitate comparison with both sensitivity studies.The fraction of the domain within the track at each time in each run can be inferred from the ratio of vertical distances of the black curve from the blue vs. from the red curve.The initial aerosol pulse is spread much more rapidly in SensPerp than in BaseTrack, indicated by the more rapid decrease of in track N a in Fig. 15, as the aerosol quickly enters all roll cells across the domain and rapidly disperses along the rolls.This suppresses precipitation across a broader area in SensPerp, increasing domain-mean LWP, N a , and albedo.However, because the injected aerosol in SensPerp is distributed more broadly than in BaseTrack, the in-track perturbation is smaller, so precipitation more quickly recovers to environmental values.
The larger domain-mean albedo in SensPerp than in Base-Track can be related to results of Wang et al. (2011).For their case, they found that for a precipitating boundary layer with a low background aerosol concentration, a larger domainmean albedo increase could be achieved with a uniform aerosol source across the whole domain (loosely analogous to SensPerp, regarding the enhanced lateral mixing as analogous to spreading the original source) than for a single point source (analogous to BaseTrack).In their non-precipitating cases, for a given domain-mean aerosol source, the domainmean albedo increase was independent of the injection configuration, indicating a more "linear" regime.

Simulated track in a polluted environment
In a second sensitivity study SensHiAer, the initial background aerosol concentration is set to 300 mg −1 .We also increase the injection aerosol source strength by a factor of 10 compared to the baseline case to make the track stand out clearly against the polluted background.The higher bound-ary layer aerosol concentration shifts the cloud droplet distribution to smaller sizes, limiting drizzle formation and reducing surface rain rates relative to the BaseTrack case.Reduced precipitation allows for a more turbulent cloud and greater entrainment, leading to boundary layer deepening, a thicker cloud, and larger LWP.During the 8 h spin-up before the aerosol injection, stronger entrainment dilution and cloud processing lead to a decline of N a to 100-120 mg −1 , while the boundary layer deepens to ∼ 400 m.
The right column of Fig. 16 shows Hovmöller plots of albedo, N a , LWP, and surface precipitation, assembled similarly to Fig. 7.The Twomey effect renders the track visible in the first hour despite the bright surrounding cloud.Comparison of the right two columns of Fig. 15 shows that the track mean albedo gain is less than in clean cases, despite the much stronger aerosol injection, as the background cloud is significantly brighter.
Within the first hour, the LWP in the ship track decreases a few percent below the background, as is commonly observed in Type 2 ship tracks (Coakley and Walsh, 2002;Chen et al., 2012).Entrainment is nearly 40 % greater in the ship track vs the background.While the air above the inversion is quite moist (9.2 vs. 10 g kg −1 in the MBL), it is also potentially warmer, so cloud water evaporation due to entrainment warming may promote the in-cloud LWP decrease, consis- tent with results of Ackerman et al. (2004), Bretherton et al. (2007), and Wood (2007).Alternatively, it is possible that this LWP difference reflects changing in-track contributions from high-LWP updrafts and low-LWP downdrafts of the circulation as the track spreads.The smooth time evolution of the in-track and environmental LWP suggest that their difference is real, rather than an averaging artifact.Once the difference is established, the track and background LWPs reconverge over the next 4 h (seen in Fig. 15).While the LWP in both the track and background initially increase at a similar rate during hour 9 due to continued cloud deepening, cloudaerosol feedbacks in the background allow for an increasing precipitation rate, arresting the LWP increase and leading to net loss from the background cloud by hour 12.By contrast, the elevated aerosol concentration in the track largely inhibits precipitation and allows for continued LWP gains, such that the track LWP exceeds that of the background after hour 12.5.Despite significant differences in boundary layer organization and background thermodynamic profile, SensHiAer evolves quite similarly to the high-aerosol case of Wang and Feingold (2009), which is also in a nearly overcast and nonprecipitating cloud regime.

Attribution of albedo response
In this section, we estimate the contributions of the first and second aerosol indirect effects to the increase of TOA albedo A in the ship track.To do this, we first estimate the "bulk" albedo A bulk of the cloud-containing layer, including both the fraction f cld of the columns within of that layer that contain cloud, and the clear columns in between.Since the cloudcontaining layer is thin, we neglect any clear-sky absorption or scattering within it, so its bulk albedo is due only to its cloudy columns: where A cld is the horizontal-average cloud albedo.
We use a simplified model for cloud albedo (e.g., Platnick and Twomey, 1994;Brenguier et al., 2000) as a function of cloud-mean N d and in-cloud liquid water path W cld : x-t Hovmöller plot for run SensHiAer; panels as in Fig. 7. where In Eqs.
(3) and (4), g = 0.85 is the asymmetry factor for light scattering from a small spherical water droplet, k = 0.8 is a breadth parameter for the droplet size distribution, f ad is an assumed ratio of the liquid water content profile to its adiabatic value, set to 0.65 in the drizzly low-aerosol runs and 0.9 in the high-aerosol sensitivity case, and ad = 2 × 10 −6 is a representative rate of adiabatic increase for liquid water content with height, in units of kg kg −1 m −1 .Using Eqs. ( 2), (3) and (4), we can separately estimate A bulk for the track and environment at each time based on their respective mean values of cloud fraction, LWP and N d .Horizontal cloud heterogeneity and inaccuracies in the assumed vertical structure of the in-cloud liquid water profile in the cloud will lead to errors in these estimates of A bulk .
We use an empirical fit to go from A bulk to TOA albedo A. While we did not store the radiative fluxes for each column of the LES at each time, we did store their domain-mean values, which we use for this fit.Let SW ↓ and SW ↑ denote the domain-mean downwelling and upwelling shortwave fluxes, and let superscripts − and + denote fluxes at the cloud base and cloud top.To estimate the bulk albedo from the cloud base and cloud top fluxes, we must consider shortwave radiation impinging on the cloud from below as well as above.We neglect cloud-layer absorption, so a fraction 1 − A bulk of the upwelling shortwave radiation at cloud base exits through the cloud top, while by definition a fraction A bulk of the downwelling shortwave radiation at the top of the cloud layer is also reflected upward.After minor algebra, this implies that The cloud layer base and top are defined as the bottom and top model levels where domain-mean cloud fraction exceeds 0.05.A scatterplot of domain-mean A bulk vs.A including all output times from both the control and high-aerosol simulations yielded an accurate linear fit, which we also use separately for the track and environmental regions.Together with Eqs.(2), ( 3) and ( 4), (6) allows the LES TOA albedo to be predicted from the cloud fraction, LWP and N d , both inside and outside the track.The empirically determined intercept, 0.07, which should be the clear-sky albedo, is reassuringly similar to the ocean surface albedo of 0.08.The top panels of Fig. 17 show the track and background values for A derived from the LES-predicted radiative fluxes and the simplified model in each simulation.The simplified model predicts the evolution of the track and background albedos, and their difference, reasonably accurately, so is useful for decomposing their albedo difference into component contributions.
An approximate linearized decomposition of the response of A bulk into changes due to N d , f cld and W cld can be used to interpret the albedo response of the boundary layer to the ship track.It is derived from Eqs. (2), (3), and (4): This is mapped via the linear fit (Eq.6) to changes in A.
We use the in-track conditions to define the reference state, which makes the linearization more accurate than using the background conditions.The bottom panels of Fig. 17 apply this decomposition to our three ship track simulations.It captures the magnitude and evolution of the albedo difference predicted by the full idealized model and by the LES radiation code, validating the meaningfulness of this decomposition.
In run BaseTrack, Fig. 17 indicates the initial brightening of the track over the first hour is due primarily to increased N d (first aerosol indirect effect).Over the next several hours, however, the aerosol perturbation is laterally mixed and subject to various microphysical sinks, diminishing the N d per-turbation.Simultaneously, precipitation suppression in the track induces a steady increase in W cld .By the time the simulation ends at hour 16, the albedo contributions of enhanced N d and LWP are comparable and when the cloud fraction enhancement in the track is also considered, second indirect effects are more significant to the track albedo perturbation than the first indirect effect.This pattern is repeated in run SensPerp, but here the LWP contribution becomes more rapidly significant.
In contrast, the albedo response of Run SensHiAer is dominated over the entire simulation by the first indirect effect, and the slight decrease of LWP within the track leads to a weakly negative second indirect effect during part of the simulation.In cases with a drier free-troposphere in which enhanced entrainment in the track may lead to a more pronounced decrease of LWP, the albedo in the track can actually be reduced compared to the environment (Chen et al., 2012).Cloud cover is not an important contributor to the second indirect effect in this case, since it remains nearly 100 % both inside and outside the track.
The importance of the second aerosol indirect effect in later stages of the SensPerp and BaseTrack runs indicates the need to simulate cloud macrophysical responses to aerosol.Similarly, run SensHiAer show that even in a very shallow cloud-topped boundary layer topped by a humid free troposphere, the second indirect effect need not be positive.Suppression of cloud surrounding the track in the simulations of Wang and Feingold (2009) is another form of negative second indirect effect which does not occur in our simulations due to the different environment.The range of possible effects poses a challenge for parameterization of cloud-aerosol interactions.
6 Ship tracks and aerosol-cloud regimes Rosenfeld et al. (2006) suggested that closed cell, open cell, and collapsed boundary layer organizations exemplified aerosol-cloud regimes, where the availability of CCN would control boundary layer dynamics via precipitation and feedbacks on turbulence and cloud macrophysical structure, which in turn would modulate the CCN.They proposed that the boundary layer could naturally evolve via cloud-aerosolprecipitation interactions from closed cells to open cells, followed by transition to a collapsed state, but that strong injections of aerosol, such as from ship exhaust, could then reverse the process.Berner et al. (2013) explored the theme of aerosol-cloud regimes using LES, supporting the idea that closed cells, open cells, and collapsed boundary layers are "regimes" in the sense that under steady large-scale forcing, they evolve slowly with little qualitative change in structure over periods of days, with comparatively rapid transitions occasionally occurring between regimes.Do the Type 1 ship tracks simulated in the present work constitute a regime shift from a collapsing state back towards closed cell organization?
A framing of this question appropriate for our simulations is to ask whether, despite horizontal turbulent dilution, the mean microphysical and macrophysical properties within the track keep diverging from the background for an extended period, promoting a long track lifetime.Figure 15 shows that this is not the case; in BaseTrack, the track-mean cloud and aerosol properties are tending toward the background properties; since runs SensPerp and SensHiAer end at hour 14, the cloud properties have not evolved as much as in BaseTrack, but the approach of aerosol concentration toward the background suggests that cloud properties will eventually follow suit.With free-tropospheric aerosol, it is conceivable that a strong positive aerosol-entrainment feedback could amplify the in-track aerosol and cloud perturbations and foster a much more prominent and long-lived track.Indeed, the west part of Fig. 1 shows several prominent ship tracks in which the in-track cloud albedo remains high well downwind of the track head, despite substantial broadening of the track.

Conclusions
In this study, we have for the first time compared an LES with a coupled bulk aerosol scheme to a well-observed ship track.We simulated the Sanko Peace ship track from the 1994 MAST field campaign.The track formed in a shallow, low-aerosol boundary layer under high winds.We used a Lagrangian approach, simulating at high resolution a region around the track which evolves with time, corresponding to increasing downstream distance from the ship.Overall, the baseline simulation is quite successful.It compares well to important observed features, including prominent roll organization and microphysical characteristics of the ambient boundary layer, the magnitude of the cloud droplet number enhancement and albedo increase within the track, and the suppression of drizzle.
There are some discrepancies between simulation and observations, including the simulated ambient cloud being more broken than observed, the track being too narrow for its downstream distance from the source, less deepening of the simulated cloud tops in the track, a stronger and more single-layered temperature inversion compared to the observations, and apparently excessive aerosol in the shear-driven mixing layer just above the cloud top.These discrepancies are likely due to some combination of biases in the forcings used to drive the LES and in the aerosol source strength, better alignment of the simulated track along the wind than observed, and possible deficiencies in model physics.
The aerosol concentration in the simulated tracks evolves mainly by lateral dilution (at a rate sensitive to the orientation of the ship to the wind) as the tracks broaden.The winddriven surface aerosol source is countered by losses mainly due to accretion (which increases with time in the track as the in-track LWP increases) and cloud scavenging of interstitial aerosol (reduced within the track).
Liquid water path is enhanced in the Type 1 tracks, even though they also enhance entrainment of warmer air from aloft.For the simulated Type 2 ship track in a high-aerosol environment, entrainment is again enhanced, and depresses LWP below the background mean for 3.5 h until the surrounding cloud layer thickens and begins to drizzle, perhaps eventually leading to a transition to a Type 1 behavior.
In our simulated Type 1 tracks, albedo response is initially dominated by the first indirect effect.The second indirect effect becomes increasingly important over time and is responsible for the majority of the albedo perturbation by the end of the simulation.Our sensitivity study of a Type 2 track is dominated by the first indirect effect for the entirety of the 6 h run, with a negative second indirect effect for half of that time.Comprehensive ship track observations in a wider range of environments could be used to further test how well the quantitative details of aerosol-cloud interaction are represented by current aerosol models coupled to LES, or other types of process models.

Figure 1 .
Figure 1.GOES satellite imagery of the eastern Pacific near California at 20:13 UTC on 13 July 1994.A number of ship tracks are clearly visible well off shore.The right panel gives an enlarged view of clouds to the southwest of Monterey; despite cirrus obscuring the view, several tracks are apparent, indicated with arrows.The solid arrow marks the estimated location of the Sanko Peace at the time of the image.

Figure 2 .
Figure 2. Background profiles of the wind components u and v, liquid water mixing ratio q l , total water mixing ratio q t , absolute temperature T abs , and total aerosol number concentration N a (the sum of cloud droplet number concentration N d , rain droplet number concentration N r , and interstitial aerosol number concentration N ad ) observed by the MRF C-130 prior to sampling the Sanko Peace ship track (black curves).Overlaid are profiles of the forced geostrophic wind components U g and V g , as well as the initial profiles of q t and T (blue curves).

A
. H. Berner et al.: Large eddy simulation of ship tracks in the collapsed marine boundary layer aircraft observations showed negligible CN/CCN above the inversion.Thus the only supply of aerosol to the cloud layer is from the parameterized surface salt flux, which is large due to the high wind.

Figure 4 .
Figure 4. x-y snapshots of domain (a) albedo A, (b) liquid water path (LWP), (c) total aerosol number concentration N a , where brackets denote an average through the boundary layer depth, and (d) surface precipitation rate (0.05 mm day −1 threshold) for run BaseTrack at hour 8.

Figure 5 .
Figure 5. x-z snapshots of (a) y-averaged vertical velocity w and (b) vertical slice of total aerosol number concentration N a at y = 6.4 km for run BaseTrack at hour 8. White contours mark the 0.01 g kg −1 cloud water mixing ratio boundary.Differences in contour appearance result from y-average applied to the fields in (a).

Figure 7 .
Figure 7. x-t Hovmöller plots for run BaseTrack of (a) A, (b) N a , where brackets denote a column average through the depth of the MBL, (c) LWP, and (d) surface precipitation rate.The axis on the right-hand side of the albedo plot shows the equivalent downstream distance from the ship.

Figure 8 .
Figure 8. x-z slice of y-averaged aerosol concentration N a and y-averaged stream function ψ for runs (a) BaseCtrl and (b) BaseTrack in a mean over hour 14 to 15, the seventh hour after track injection.Positive stream function (solid white contours) indicates counterclockwise circulation, while negative stream function (dashed contours) indicates a clockwise circulation.Contours shown have magnitudes of ±5, 20, 35, 50, 65 kg m 2 s −1 .

Figure 9 .
Figure 9. Domain average profiles from run BaseCtrl for (a) liquid-water potential temperature θ l , (b) cloud water q c , (c) cloud droplet number concentration N d , (d) radiative heating rate Q RAD , and (e) resolved buoyancy flux B. Times shown are for hours 8 (red), 12 (green), and 16 (blue).

Figure 10 .
Figure 10.Regional aerosol budgets for run BaseTrack.(a) Time series of budget term magnitude in the background (solid) and (b) within the ship track (dashed).
compares y-averaged transects of droplet number concentration N d , effective radius r e , and albedo A with comparable plots reproduced from Figs. 2, 4 and 5 of Taylor and Ackerman (1999).The x axis of the original Taylor and Ackerman figures is given in time.Assuming constant heading and 100 m s −1 flight speed, each minute covers 6 km, so their transects are 24-30 km in length.The in-cloud leg analyzed by Taylor and Ackerman was flown at 285 m altitude, so the model transects of N d and r e are taken from the closest model level (283.75 m).For the N d transect, the qualitative agreement with the aircraft observation is quite good.

Figure 11 .
Figure 11.Model transects at hour 8.7 of (a) N d , (b) r e , and (c) albedo.We compare the modeled top of atmosphere albedo (A TOA ) with the observed cloud albedo (A Cld , as the 3d fields for radiative fluxes were not saved and thus computing a modeled cloud albedo is not possible.In each panel, the heavy black curve is the domain y-average, and the grey-filled region is bounded by ±2σ about the mean, where σ is calculated at each x as the square root of the variance of all values in y.Observations from Taylor and Ackerman (1999) Figs. 2, 4, and 5 are reproduced in the right hand column.The model transects are shown for the time that most nearly corresponds with the observed transects in terms of downstream evolution after aerosol perturbation (about 40 min).

Figure 12 .
Figure 12.Profiles of cloud (red lines) and rain (multiplied by factor of 4 for clarity; blue lines) water mass mixing ratios, regionally averaged in the ship track (dashed lines) and background (solid lines) in run BaseTrack.Plots are shown for hours (a) 8.7, (b) 9.5, and (c) 15.Black overlay in (a) is the composited observational profile for q l from Taylor and Ackerman (1999).

Figure 13 .
Figure 13.Hovmöller plot of y-averaged entrainment rate w e for run BaseTrack.

Figure
Figure 16.x-t Hovmöller plot for run SensHiAer; panels as in Fig. 7.

Figure 17 .
Figure 17.Top row: simple model (solid lines) and rapid radiative transfer model (RRTM; dashed lines) predicted A for the track (red lines) and background (blue lines) in runs SensPerp (first column), BaseTrack (second column), and SensHiAer (third column).Bottom row: Albedo change due to changes of N d (red lines), W cld (blue lines), and f c (green lines), as well as total predicted change A by the sum of terms (solid black lines) and derived from RRTM (dashed black lines).Runs are as in top row.