To simulate atmospheric flow for the island–ocean system, the size of the model domain has to have appropriate values dependent on the island size. The main criterion in this case is that a marine boundary layer has to develop at least several kilometers before it interferes with the island area. Also, the downwind area should approximately be twice of the island width so that resulting structures induced by the island can be properly represented. Since Barbados is a 24 km wide (west–east) and 34 km long (south–north) island, a model domain with a spatial extent of 102.4 km × 102.4 km is chosen. The island is located at the domain center. The model top is set to 5 km altitude. Because of the required domain size and for computational reasons, the horizontal grid spacing is set to Δx=Δy=200 m. Such a resolution can be considered a “coarse” LES; however, it is sufficient to resolve some portion of inertial range scales, as will be shown later on through spectral analysis.

Due to the presence of the island area, non-cyclic lateral boundary conditions have to be used. Within the finite volumes/differences discretization strategy adopted herein, a “zero-gradient” boundary condition is applied to all scalars and velocity components at each lateral boundary (north, east, south, west). This means that the boundary-perpendicular flux for these quantities is set to zero, which leads to a simple radiation condition near the outlets with minimal wave reflection. A pressure correction for sound waves is applied to each actual normal velocity component and not to the initial wind profile, which also suppresses artificial wave reflection near the inflow boundary. This setup ensures stability for the whole simulation time and works appropriately with the turbulence generation method, as shown at the end of this section.

For the top boundary, a free-slip condition is applied, i.e., the gradient of the tangential velocity component is zero. In order to prevent gravity wave reflection, an additional relaxation term is applied on the right-hand side of the momentum equations: Φn+1=…-Δt⋅ρK(d)(Φn(d)-Φ0), with a damping function depending on the distance to the top boundary d: K(d)=dfsin⁡2π2dw-ddwd<dw,0d≥dw.

This damping layer is applied above dw=4km model height (20 vertical layers) with a damping parameter df=1×10-3.

Surface boundary conditions are represented by a momentum flux parameterization based on the Monin–Obukhov similarity theory : τzx=-ρCm|vh|u,τzy=-ρCm|vh|v.

Cm is the drag coefficient for momentum, which is defined as follows: Cm=k2ΨM2, with ΨM=ln⁡z+z0z0-ϕmzL, and ϕm representing the integrated similarity function. L stands for the Obukhov length and k is the von Kármán constant.

The topographic data are obtained from the Consortium for Spatial Information (CGIAR-CSI) Shuttle Radar Topography Mission (SRTM) data set (http://srtm.csi.cgiar.org) at 200 m resolution. A simple smoothing algorithm is applied to guarantee a proper grid pre-processing. In the smoothed data set, the maximum elevation is lowered by about 15 m compared to the raw topography data, which is an acceptable level.

Table  summarizes the model configuration for the Barbados LESs performed in Sect. 3.

The two cases examined (22 and 27 June 2013) mainly differ in their atmospheric state and geostrophic forcing. Measured nighttime radiosonde profiles of temperature and humidity are directly used for model initialization (Fig. ), which reduces the complexity of the simulations due to the absence of horizontal inhomogeneities and a time-varying background state. There are two reasons behind the choice of using single profiles instead of averaging multiple profiles. Firstly, a single initial profile is better for comparing the LES results with lidar data (cf. Sect. ), which are obtained for a few selected cases during SALTRACE. Secondly, trade-wind inversions are only poorly represented when the soundings are averaged over many cases. This becomes apparent when considering the sharply defined inversion at the 27 June case, which is shown later on. Air density and pressure profiles are obtained by vertical integration with respect to hydrostatic equilibrium. Some simplifications are assumed for the geostrophic forcing. The wind direction is purely east (i.e., d=90∘ and vg=0), which is also for simplicity and to make it easier to define upwind and downwind regimes later on. The vertical wind profiles are expressed as piecewise linear functions for both cases. For the 22 June case, the initial wind at first linearly decreases above z=1600m altitude and then increases again above z=3000m: ui,1(z)=-10.0ms-1log⁡(z/z0)log⁡(700m/z0),z≤0.7km-10.0ms-1,z≤1.6km-10.0ms-1+4.29×10-3s-1⋅(z-3000m),1.6km<z≤3.0km-4.0ms-1-2.0×10-3s-1⋅(z-5000m),3.0km<z≤5.0km, with a roughness length z0=0.01m. A change in wind direction to southwest is observed within the layer where the wind speed decreases. However, this is not captured by the LES due to the simplifications and assumptions mentioned above. Therefore, the effect of wind directional shear might be underestimated in the model for this case. The change in wind direction (±15∘) is rather small at other altitudes, so the LES input profile can be considered a good approximation. For the 27 June case, the initial wind linearly decreases above z=3000m altitude: ui,2(z)=-11.5ms-1log⁡(z/z0)log⁡(700m/z0),z≤0.7km-11.5ms-1,z≤3km-11.5ms-1+5.25×10-3s-1⋅(z-3000m),z>3km.

In this profile there is no distinct change in wind direction. Figure  visualizes the measured (green lines) and parameterized (red lines) velocity profiles for both cases. The LES background wind profiles are parameterized to closely match the soundings. Within the boundary layer, the LES profile should be near the nighttime measurements (dark-green line) because this is mainly a representation of the marine boundary layer. For the free troposphere, the LES profile should roughly be a mean of all three soundings, since no large-scale advection term is applied on the wind components during the simulation time.

Table  shows a comparison of the two simulated cases with respect to mean flow properties, trade inversion strength, moisture load (all derived from radiosonde profiles), CCN concentrations (obtained by ground-based measurements at Ragged Point station) and the location of the Saharan dust layer (estimated from BERTHA lidar measurements at CIMH). The differences in the geostrophic forcing are already discussed. Regarding the atmospheric stability, there is a much stronger trade inversion for the 27 June case with a local virtual potential temperature gradient of 14 Kkm-1. As mentioned in the introduction, the trade inversion controls the amount of precipitation and the lifetime of cloud streets. Furthermore, there is a 18 % stronger moisture load for the 27 June case, where a faster cloud development is expected. Due to the vertical and temporal variability in the CCN number concentrations, a mean value of 300 cm-3 has been chosen for both cases, which is a typical magnitude for days with a moderate dust load, where aerosol optical depths between 0.2 and 0.4 are observed.

Surface sensible and latent heat fluxes over the island and the ocean are obtained by separate 1-D simulations with full model physics. The parameterizations there include the radiation scheme as well as land-use and soil models. The soil class “loam” was chosen to represent the average island soil type. Hydraulic and thermal parameters of this soil type can be found in and . For land surface parameterization, “shrubland” appears to be a good compromise between coastal beach areas and forest in the island interior. The roughness length of this land type is zR,island=0.2m, whereas the ocean roughness length is set to zR,ocean=0.01m. The usage of direct (compared to interactive) fluxes reduces computational costs for the LES runs and makes it easier to potentially reproduce these simulations by other models, especially due to a large number of existing radiation and land-use models. Figure  shows the diurnal variation in sensible and latent heat fluxes over the island area. The maximum sensible heat flux over the island is QSHFmax,island=425 Wm-2 and the corresponding maximum latent heat flux is QLHFmax,island=105 Wm-2. Surface heat fluxes over the ocean are constant during the whole simulation time with QSHF,ocean=6 Wm-2 and QLHF,ocean=56 Wm-2. Sunrise is at 05:36 LT and sunset is at 18:29 LT, whereby the fluxes are shifted by 30 min to represent the delay due the fact that the soil has to be heated first before energy exchange with the lower atmosphere can take place.

Later on, reference simulations with periodic boundary conditions are performed to obtain information of marine boundary layer characteristics. For these simulations, large-scale forcings from the BOMEX LES study of trade-wind cumulus convection are applied. They include a piecewise linear subsidence velocity profile with an absolute peak value of -560mday-1, radiative cooling of -2Kday-1 and large-scale advection of dry air into the lower boundary layer of -1gkg-1day-1: wsub=-4.33×10-6s-1z,z≤1500m-0.0065+1.08×10-5s-1⋅(z-1500m),1500m<z≤2100m0.0,z>2100m,dθdt=-2.315×10-5Ks-1,z≤1500m-2.315×10-5Ks-1+2.315×10-8Ks-1m-1⋅(z-1500m),1500m<z≤2500m0.0,z>2500m,dqvdt=-1.2×10-8s-1,z≤300m-1.2×10-8s-1+6×10-11s-1m-1⋅(z-300m),300m<z≤500m0.0,z>500m

The LES modeling technique has the advantage of allowing explicit resolution of turbulent production and part of the inertial range scales, and is today the most accurate and computationally feasible modeling approach in the context of high Reynolds number flows. LES results are strongly dependent on boundary conditions, therefore requiring specification of realistic inflow turbulence characteristics that propagate through the domain into the area of interest. In order to ensure that the incoming boundary layer characteristics at Barbados correspond to fully developed turbulence consistent with the imposed marine boundary layer forcing, we use the cell perturbation method recently proposed by . The cell perturbation method uses a novel stochastic approach based upon finite amplitude perturbations of the potential temperature field applied within a region near the inflow boundaries of the LES domain. This method has demonstrated superior performance when compared to a state-of-the-art synthetic turbulence generator and is computationally inexpensive .

Previous studies where the cell perturbation method was developed and validated dealt with transitions from smooth mesoscale flow to nested LES . In these idealized cases, boundary conditions at the LES domain boundaries were imposed from the mesoscale model instantaneous solution (Dirichlet boundary conditions), in which moisture effects were not considered. Herein, we further extend the application of the cell perturbation method to turbulence inflow generation for cloud modeling including terrain effects. As explained in earlier sections, zero-gradient open radiative lateral boundary conditions need to be used in order to minimize wave reflections at the boundaries that do develop in fully compressible codes like the ASAM LES model when the domain includes terrain features. In order to test the best configuration for the cell perturbation method in this particular context, we perform a series of calculations where only the upstream region of the Barbados island is considered (i.e., incoming marine boundary layer). The reduced subset of the domain consists of a 51.2km× 51.2km area in the horizontal, with the same vertical extent and large-scale forcing described in Sect.  for the 22 June 2013 case study. To represent the marine boundary layer conditions that are going to be imposed through the entire simulation period, constant sensible and latent heat fluxes of QSHF,ocean=6Wm-2 and QLHF,ocean=56Wm-2 are used (see Fig. ).

We explore the sensitivity of the generated turbulence by the cell perturbation method to the optimum perturbation Eckert number, Ec=Ug2/cpθ̃pm=0.2, where θ̃pm is the maximum potential temperature perturbation, and the perturbations are random and uniformly distributed in the interval -θ̃pm,+θ̃pm. Three square cells adjacent to the east boundary are used, which were found to provide the fastest transition to a fully developed turbulent state . The cell size is set to 4×4 grid points to ensure that the cell wavelength falls within the inertial range of three-dimensional turbulence. The perturbation timescale, tp, was obtained from Γ=tpU1(4dx)-1=1 , with U1 being the horizontal wind speed in the first vertical layer, resulting in a frequency to seed instantaneous perturbations of tp=145s. Figure  shows instantaneous contours of vertical velocity at z=zi/2=375m for different perturbation Eckert numbers, Ec =0.2, 0.33 and 0.4, and for the periodic reference run. The cell perturbation method for the three Ec numbers considerably accelerates the formation of three-dimensional turbulent structures that agree with the ones obtained in the reference simulation using periodic lateral boundary conditions. As the perturbation Eckert number increases (maximum perturbation amplitude decreases), the strength of the vertical velocities induced by the temperature perturbations is progressively reduced, and the onset of forcing-consistent turbulence seems to qualitatively occur at earlier distances from the inflow boundary.

In order to have a better understanding of the turbulence initiation and development processes, the energy spectrum evolution in the streamwise direction for the three velocity components is presented in Fig. . The cell perturbation method causes a rapid development of the upper-wavenumber portion of the energy spectrum for the u and v components. The larger scales (lower wavenumbers) require longer distances to be established due to large buoyant plumes having to emerge from the surface and populate across the entire extent of the boundary layer. This flow development pattern is consistent with the findings from for convective conditions. In contrast, the energy spectrum for the vertical velocity reveals a rapid growth of turbulent energy that reaches levels 10 times greater than the periodic quasi-equilibrium solution (dashed black line) and that progressively dissipates as the flow transitions through the domain. We attribute this behavior to the cell size, 4dx, which for the resolution employed in this study may fall in the vicinity of the limit of the inertial range. Smaller cell sizes were not considered due to the energy dissipation at high wavenumbers present in finite differences/volumes discretizations. There, an interaction with fully resolved scales and triggering of an accelerated transition to a developed turbulence state would not have taken place. In addition, the use of zero-gradient lateral boundary conditions helps to maintain the signature of the perturbations more than in the case of Dirichlet boundary conditions, hence contributing to strengthen the periodically seeded perturbations. By increasing the perturbation Eckert number from 0.2 to 0.4 (first row vs. third row in Fig. ), the energy overestimation is damped, and results after a fetch of 40km for Ec=0.4 are in close agreement with the periodic simulation used as a reference and have reached quasi-equilibrium converged statistics. The Ec=0.2 case results in an energy deficit at wavenumbers close to the integral length scale, and also at the highest wavenumbers for the w component. When the cell perturbation method is not used (NOCP panels, bottom row in Fig. ), dramatic energy deficits are found, together with an unrealistic spiky energy distribution in which the expected energy production and cascade processes are not present.

Finally, we examine the vertical distribution of relevant boundary layer quantities at a downstream distance of 40km from the east boundary (i.e., x=11.2km). Vertical profiles (Fig. ) show the best agreement with the periodic simulation for the Ec=0.4 and 0.33 cases, in particular for the turbulent kinetic energy levels and boundary layer structure. Momentum flux profiles exhibit slightly larger values in the first 250m, due to the differences in the horizontal wind speed distribution near the surface. However, the boundary layer structure is similar, with the differences being related to distinct quasi-equilibrium solutions for the periodic and the open boundary condition simulations. Similar conclusions are found for the sensible and latent heat fluxes. The cell perturbation method was originally developed and tested in the context of dry boundary layers . It is worth emphasizing that we have herein demonstrated for the first time, as can be seen from the latent heat flux profile, that the cell perturbation method has the ability to develop turbulent moisture features that are in agreement with the imposed forcing. The Ec=0.2 case fails to produce a boundary layer structure that is similar to the reference periodic case, with excessive mixing attributed to an enhanced effect of the perturbations for the reasons mentioned above. Also, the NOCP case does not provide realistic turbulent boundary layer features corresponding to a strongly underdeveloped turbulent state. Therefore, we select the Ec=0.4 setup as the inflow to be used for the island simulations presented in the remainder of the paper since it produces the most rapid development and stabilization of forcing-consistent turbulence. For the island cases, we use a domain with horizontal extent of 102.4km×102.4km, which leaves sufficient fetch for the marine boundary layer to develop prior to the start of interaction with the topography of Barbados and its local stability effects.

Besides the two mentioned case studies, two additional sensitivity studies are part of the island effect analysis. Here, the 22 June 2013 case serves as a reference case (REF). For the first sensitivity case (NOCP), the cell perturbation method is disabled so that the upwind flow is strongly underdeveloped. With this setup, the effect of having a realistic turbulent boundary layer around the island rather than idealized constant winds is investigated. In the next sensitivity case (DX400), the grid resolution is halved from 200 to 400 m horizontally and from 50 to 100 m vertically to point out the deficiencies in the use of coarser resolution without appropriate resolved turbulence and gray zone modeling for particular aspects of interest in boundary layers and cloud modeling. In this simulation, the cell perturbation method is also put off since the usage of a turbulent inflow in coarse resolution studies has not been utilized before and, moreover, appears to be questionable because the inertial subrange of the turbulence spectrum is not resolved anymore. The simulation ensemble is completed by the 27 June 2013 case, mainly characterized by its strong trade-wind inversion (INV) and stronger background trade winds compared to the REF case. Table  summarizes the settings for all simulations that deviate from the standard configuration in Tables  and .

To get a qualitative impression of the local situation simulated by the LES model, Fig.  shows a three-dimensional snapshot of the temperature and humidity field as well as cumulus clouds with up- and downdrafts visualized by isosurface fields at 12:00 LT for the reference case. The daytime convection is clearly visible by multiple updraft cells distributed over the whole island area, which subsequently leads to the development of non-precipitating shallow cumulus clouds. Advection of heated air from the central and southern part of the island towards the west can be seen in the surface temperature field (which is meant as temperature of the lowest model layer in this context), whereas the cooler marine flow narrows the thermal wake toward the meridional center of the domain up to 40 km downwind. This effect is connected with an island-induced change in wind speed and direction. The change in the humidity profile can be observed in the vertical cut plane at the western model boundary. A large amount of moisture is transported vertically upwards in the central region where also occasional cumulus clouds are present. A few tens of kilometers away in the y direction, dryer air from heights of 500–1000 m is mixed downward.

For further insight into flow dynamics, especially for the downwind region, Fig.  provides the vertical wind field at z≈zi/2 for all four considered cases. Looking at the REF and INV case, several turbulent updraft bands with lengths of about 10 km in the zonal direction and vertical velocities up to 2.5ms-1 develop all over the island area. However, one main band at y≈52km remains persistent, even at higher altitudes. This updraft band is a result of the dynamic and thermal instability over the island, forming quasi two-dimensional horizontal vortex rolls with their axes aligned in the downwind direction e.g.. Toward the evening, as the surface sensible heat flux is not positive anymore and convection fades away, the band decouples from the island and vanishes (not shown). Turbulent updraft cells within the marine boundary layer with vertical velocities between 0.5 and 1 ms-1 are also visible since a turbulent inflow is generated with the cell perturbation method described in Sect. 2.5. In the INV case, these updrafts are a bit weaker, which is most likely due to the stronger mean horizontal wind speed. Wave-like structures in the upwind vertical velocity field are observed in the NOCP case. There, the flow remains laminar in this region, and since no perturbation is applied but surface fluxes are present, these artificial convergence lines are forming. Note that this effect is not seen in the REF and INV case. This underscores the importance of having an explicit inflow turbulence generation when working on LES scales. Just by visibly comparing the “coarse” simulation DX400 with the other cases, it becomes apparent that there is a lot of structure loss in the vertical wind field. All up- and downdraft bands – even the main updraft band downwind – are almost perfectly aligned in the x direction. This shows the importance of using a grid spacing that resolves the inertial subrange of the velocity spectrum cf.. Note that with coarser grid spacings the orographical structures of the island are also less represented.

Figure  shows the surface wind fields and liquid water path for all simulated cases at 14:00 LT. In all these cases, the island convection affects both the strength (up to 4 ms-1 stronger wind speeds compared to marine surface winds) and direction (±30∘) of the wind in the downwind area of Barbados, thus leading to strong surface convergence and subsequently forming the updraft band as seen in Fig.  at y=52km. Despite having this elongated band, very little cloud formation is observed in this area for the REF, NOCP and INV cases, which is also the case for other times of the day (not shown). This means that no continuous cloud street is modeled on 22 and 27 June 2013, respectively. While cloud streets occur on around 60 % of undisturbed days, there are several effects that suppress cloud street generation . In the REF (and NOCP) case, the relatively low moisture load (RH=80% near the surface, decreasing below 60% at z≈1300m) and a weak trade-wind inversion leads to a suppression of the development of a cloud trail. Both moisture and stratification are increased in the INV case but the stronger mean trade winds (almost 12ms-1) are the suppressing factor here . Due to the absence of a turbulent inflow velocity field, the cumulus clouds over the island are horizontally aligned to the mean wind direction in the NOCP case. In the REF and INV cases, more realistic scattered cumulus cloud fields over the island area and downwind are modeled. Besides the distinct cloud bands, the DX400 case shows further very notable differences in the cloud field. First of all, clouds are broader because of the coarser grid spacing. In addition to that, a continuous cloud street is modeled, which can be considered an artifact since such a cloud band is not seen in either other simulations or satellite observations. Furthermore, the downwind horizontal velocity field is slightly stronger compared to the other cases. We attribute this behavior to the lack of resolved small scales that cannot extract energy from the large eddies and therefore grow and become more coherent. This effect is also observed to a lesser extent for the NOCP case.

In the following, the diurnal development of the convective island boundary layer is investigated. Figure  shows time series of boundary layer and cloud properties for the downwind region around the west coast of Barbados. Further mean quantities of boundary layer and cloud characteristics are diagnosed and summarized in Table . The REF and the INV case have some properties in common. They both show a strong increase in cloud cover in the downwind region between 07:00 and 08:00 LT up to a maximum value of about 16 %. The boundary layer height zi displays a diurnal variation, growing up to z=1350m around 13:00 LT in the REF case. For the INV simulation, zi is approximately 100–150 m shallower. This parameter is calculated via the bulk Richardson criterion, where the boundary layer height is defined as the height where the bulk Richardson number Rib exceeds a value of 0.25, with Rib=gθv0θv-θv0u2+v2z, where θv0 is the virtual potential temperature at the surface. Being relatively similar in boundary layer characteristics and cloud cover, there is a clear distinction between REF and INV with regard to cloud microphysical properties. Due to higher cloud base height in the REF case, the cumulus clouds tend to grow deeper, which is seen in the mean liquid water path (LWP) values as well as in the cloud base and top heights (see Table ). The cloud cover, however, is fairly comparable for these two cases. Peak updraft values also show a diurnal variation, starting from approximately wmax=1ms-1 (which is equivalent to the upwind area value) up to wmax=7ms-1 around noon. The DX400 case has overall weaker peak updrafts; however, this does not mean that there is less vertical transport of energy, moisture, momentum etc. Due to the coarser grid spacing in every spatial direction there is a higher net upward transport.

To further investigate daytime-dependent vertical mixing and layering, Fig.  shows hourly averaged vertical profiles boundary layer and cloud parameters for the downwind domain compared to the daily upwind average. Comparing again the REF and INV cases, daytime-dependent differences in the density potential temperature and specific humidity profiles can be noticed (not shown). Lower levels at z<700m are warmer and dryer compared to the marine background. The vertical turbulent transport is evidenced by the profiles of sensible and latent heat fluxes. The sensible heat flux is linearly decreasing within the mixing layer up to heights between 700m<z<900m, depending on the time of day. The maximum latent heat fluxes occur between 600m<z<800m. Above that layer, the cloud water content reaches its maximum, which is connected to latent heat release and thus to an increase in the sensible heat flux and a decrease in the latent heat flux. In the INV case, the trade inversion around z≈2000m inhibits further cloud development above this height, whereas in the REF simulation there is also a notable amount of cloud water above 2000 m. The presence of wind shear above 1500 m height leads to a secondary maximum of TKE around z=2000m, which is not the case in the shearless INV simulation.

In the NOCP case, i.e., without a turbulent inflow, persistent updraft bands form over the island area, which is consistent with the modeled cloud field from Fig. . The inflow characteristics have little effect on boundary layer properties like TKE, vertical velocity variance (not shown), sensible and latent heat flux (cf. Fig. ). However, the values for the NOCP case tend to be a bit higher than in REF, especially between 500 and 700 m. One reason for this could be that the upwind marine boundary layer already vertically transported some amount of energy, which is missing in the NOCP case. More remarkable differences are noticeable with regard to cloud development. The LWC around z≈1000m during noon is nearly doubled for the NOCP case. There is also a particularly pronounced secondary maximum of LWC around z≈2100m in the same order of magnitude. With the average over the whole daytime period taken, the mean LWP is more than doubled in the NOCP case compared to the REF case, which is in agreement with higher LWC values and also higher cloud cover (≈+3%).

More undesired effects become apparent when using a coarser spatial resolution as in the DX400 case, which is most noticeable in the averaged vertical profiles. First of all, there is less variability in the potential temperature and specific humidity fields for altitudes z>1000m, which can be explained by the lack of turbulent vertical transport within the boundary layer (this effect can be seen in the vertical profile of TKE in Fig.  and in the profile of the vertical velocity variance). The LWC, however, has maximum values of 0.028gm-3 around z≈2000m, which is a factor of 2 higher compared to the REF case. This is accompanied by strong latent heat fluxes in these layers. Cloud growth is also more inhibited at finer resolutions due to explicit entrainment of dryer environmental air e.g.. Having a distinct and quite symmetric diurnal variation in boundary layer and cloud properties in the other cases, the evening transition in the DX400 case is poorly represented, where still a notable number of clouds exist and a deeper boundary layer is modeled around 20:00 LT.

After the long-range transport of Saharan dust into the Caribbean region, these dust layers arrive at Barbados with mean base heights of about 1.5–2 kma.s.l. Due to a possible interaction with the convective island boundary layer, vertical mixing of aerosols is investigated in this subsection. As already shown in Sect. 2, these aerosol layers are represented by passive tracers in the model. They are initialized with a relative concentration of 1 within the layer where the aerosol is detected and 0 otherwise. This approach has already been used for heat island effect studies in . These relative concentrations can be related to mass concentrations of Saharan dust, e.g., 180µgm-3. This mass concentration and the Saharan dust layer heights are estimated from ground-based multi-wavelength aerosol lidar measurements and provide a rough idea of the magnitude of these quantities. Especially the particle depolarization ratio indicates that the pure dust layer begins at around 1.5 km altitude. A detailed analysis of dust layers during the campaign can be found in . Figure  displays height–distance profiles of the boundary layer tracer ϕBLT and the Saharan dust tracer ϕSDT near the west coast of Barbados. In both cases, the turbulent character over the island section is visible as a vertical distribution of the passive tracer within the higher boundary layer and the corresponding decrease in tracer concentration. It is more pronounced for the southern part of the island, which is due to the broader land area width (20 km in the south compared to 10 km in the north). It also indicates the wind shear at the island boundaries (e.g., at y=43km), which causes the advection of air masses from z>700m into the boundary layer. This effect is more pronounced further west (not shown). In the REF case, the mean boundary layer height around noon was calculated to be zi≈1400m. The passive tracer analysis additionally shows some local overshoots at heights over 2 km a.s.l. The Saharan dust tracers do have a different vertical structure. For the REF simulation, the tracer is thinned out, with maximum concentrations between 1.9km<z<2.4km, whereas in the INV case it is between 1.7km<z<2.5km. There are also no overshoots visible beyond z=1.7km. The stronger turbulent mixing in the REF case can be explained by the presence of wind shear around z≈1.5km height, whereas in the INV case the strong trade-wind inversion suppresses further development of turbulence in higher altitudes. The logarithmic scale indicates the tracer diffusion, which shows that about 1 % of the maximum concentration is present at altitudes between 1.3 and 1.5 km (depending on the case) and locally down to 1.0 km altitude due to the island effect.

Although there are already some indications of downward aerosol transport, a better quantification of these effects is still needed to achieve a better understanding of the processes behind it. For that reason, mean vertical profiles are calculated in the same manner as the boundary layer and cloud analysis. Figure  shows vertical profiles of tracer-related quantities for the REF and the INV case. The tracer profile is being deformed by vertical transport processes, which can be originated by larger-scale or turbulent processes. To distinguish between those two, the total vertical tracer flux 〈wϕSDT〉 and the turbulent vertical tracer flux 〈w′ϕSDT′〉 are computed. According to the model data, there is already a persistent downward movement east of Barbados between 1.5km<z<3.0km, which corresponds to a subsidence velocity of w=-407mday-1 for the REF case and w=-345mday-1 for the INV case. There is a total relative downward flux for the downwind area in the REF case at 1.2 km height, with a maximum magnitude of 〈wϕSDT〉=-0.03ms-1. The height of this local extremum depends on the time of day, with higher altitudes in the morning and around noon and lower altitudes toward the evening. A net positive upward flux is always present above z=2km, becoming zero at z=3km. About one-third to one-half of the total downward flux is caused by turbulent mixing, having its local maxima at z=1.8km, which is the lower bound of the Saharan dust layer. The daytime turbulent downward mixing is about 5 times stronger in the INV case but is shifted approximately 400 m toward the surface compared to REF. Due to the tracer subsidence, the layer also reaches these altitudes of maximum turbulent downward mixing, which would not be the case if the dust layer remained at its initial height of 1.7 km. The downwind total tracer flux, however, is positive (upwards) for all altitudes and is almost 1 order of magnitude stronger compared to REF. Since the mean wind speed only slightly differs between the two cases and surface fluxes are the same, it can be concluded that atmospheric stability (especially inversion strength) and the presence of wind shear in the sub-inversion layer have a major impact on altitude and strength of layers with preferably upward or downward mixing properties. The model data suggest that the net effect, i.e., effects from both mean transport and turbulent mixing, is downward transport around the dust layer base for the downwind region in REF and a net upward transport in INV.

In order to qualitatively evaluate the results obtained by the LES model, a comparison with the measurements performed by an airborne Doppler wind lidar (DWL) is presented in this section. Vertical and horizontal wind speed measurements from a flight on 20 June 2013 are compared to the simulation results of the 27 June 2013 case. A simulation with initial data at 20 June 2013 could not have been performed because no nighttime radiosonde data were available on this particular day. Although the measurements and the simulation correspond to different days, the comparison of the radiosonde profiles used for the LES initialization launched on 27 June and the dropsonde measurements obtained during the measurement flight on 20 June show a good agreement in the altitude of the trade inversion, relative humidity levels and temperature profile (Fig. ). Especially the measured horizontal wind speed profile from the dropsondes matches better to the 27 June than the 22 June simulation case.

The airborne DWL used for this comparison was deployed onboard the DLR Falcon 20 research aircraft during the SALTRACE campaign. The system, based on an instrument developed by Lockheed Martin Coherent Technologies and enhanced by DLR to provide airborne measurement capabilities, can be operated in either nadir-pointing mode or scanning mode . The nadir-pointing mode allows the retrieval of vertical wind speeds with a vertical resolution of 100 m and a horizontal resolution of approximately 200 m with a random error lower than 0.15 ms-1 and a systematic error lower than 0.05 ms-1. Note that these resolutions are almost identical to the grid spacings used in the LES. The overflight took place between 10:36 and 10:44 LT at a flight altitude of 2900 m.

Figure  shows the flight track corresponding to the overflight (plane 2 in the figure) together with the LES results of the vertical wind speed for the 27 June case at 10:30 LT. For this overflight, vertical wind measurements on the lee side and over the island are available.

A comparison between the measured and the simulated vertical wind speed profiles is displayed in Fig. , where some main structures can be recognized in both profiles. Strong vertical winds associated with convective activity over Barbados can be observed in both the simulation and the measurements. In the case of the measurements, the presence of convective clouds limits the lidar coverage over the island (between 47 and 63 km on the x axis). For the measurements performed on the lee side of Barbados and for altitudes above 1 km a series of waves with a wavelength of approximately 10 km and an amplitude of 2 ms-1 can be recognized. A similar feature can be seen in the LES data, but with a slightly weaker amplitude.

To get a better idea of the horizontal distribution of these waves at a certain level, Fig.  shows the vertical wind speed at the trade-wind inversion height for different times during the day. It seems that the strength of daytime convective activity plays a minor role since the overall pattern looks very similar in all three snapshots, with the exception of minimally stronger fluctuations toward the afternoon hours. A marked wave structure in the lee of the island is visible, which is the result of trapped gravity waves due to the strong inversion. Again, a similar wavelength amplitude of about 10 km can be seen and stronger amplitudes (comparable to the DWL measurements) originating from the northern part of Barbados are also visible.

Figure  shows a comparison between the mean and the variance of the measured and simulated vertical wind speed on the lee side (between 0 and 35 km on the x axis) of Barbados. The mean vertical wind profiles of the measurements (black line) show a reasonable agreement with the LES results regarding the overall structure (e.g., cut planes 1, 2 and 5, which are located at the southern and northern edge of Barbados, covering a similar spatial area as in the flight route). The mean vertical velocity below 1 km height indicates a downdraft region on the lee side of Barbados. This can be explained by the daytime circulation pattern in the lee of Barbados since the updraft band located between the center and southern part of the island causes downdrafts at its lateral flanks. Planes 3 and 4 reflect this behavior with positive vertical velocities below 1 km height. The variance of the vertical wind field shows an overall increase with altitude both for measurement and model results. However, the strength of these fluctuations is increased in the measurement data, which could result from differences in the forcing, e.g., stronger surface fluxes than the prescribed ones in the LES model.

A stationary lidar system deployed at the CIMH during the SALTRACE campaign was the polarizing Raman lidar BERTHA Backscatter, Extinction, lidar Ratio, Temperature, Humidity profiling Apparatus;. Continuous measurements were performed on 22 June 2013 from 09:49 to 17:23 LT and after sunset (around 18:30 LT) from 19:32 to 22:30 LT.

The range-corrected signal for the 532 nm cross polarized channel is shown in the top panel of Fig. . The vertical resolution is 7.5 m and the time resolution varies from 3 to 15 s. The mean wind speed (<3 km altitude) was approximately 10 ms-1, which results in a horizontal resolution of 30 to 150 m. A first strong dust layer in a very dry environment (20–30 % RH) was detected between 1.8 and 2.8 km, topped by a second, weaker dust layer between 2.8 and 3.7 km which was more humid (40–50 % RH). Temperature inversions set the limits of the total dust layer or Saharan Air Layer. The lidar signal shows clouds all over the day around 1 km height and close to 1800 m. On average, 20 clouds per hour cross the lidar beam with an increasing number in the afternoon, leading to a cloud cover (in this context defined on a temporal scale) of roughly 50 %. At nighttime only a single cloud was detected within 3 h of measurement, which confirms the convective character of the daytime clouds at the investigated day over the west coast of Barbados. The bottom panel in Fig. shows the LES model output of the corresponding height–time profile of relative humidity for this day and the same location. The diurnal variation in convective vertical moisture transport is clearly pronounced. Clouds (white/red coloring) develop at the same altitudes as in the BERTHA lidar measurements. Even higher and deeper clouds up to the top of the trade inversion at z=2km are resolved. Higher cloud activity can be noticed in the measurements, whereas the LES model results show fewer clouds toward the late afternoon. This effect can be attributed to the relatively low ocean latent heat flux from the marine boundary layer forcing, which tends to dry out the lower troposphere over a longer period of time (i.e., toward the afternoon and evening hours). Additionally, there is a notable increase in moisture during the afternoon (see the 16:01 LT radiosonde launch compared to the other ones) within the first 800 m of the lower troposphere. Because of the fact that no additional large-scale forcing (in this case, advection of moist air) is applied during the simulation time, this effect expectedly cannot be captured by the LES.

Further comparisons regarding the cloud base height are conducted, revealing an even better agreement between the BERTHA lidar measurements and the model results. Figure  shows the temporal evolution of the cloud base height derived from the REF case LES output and the cloud base height derived from BERTHA lidar measurements during 22 June 2013. The cloud base was detected from the lidar signal with an accuracy of ±50 m. The algorithm sets the cloud base if the 52.5 m vertically smoothed 532 nm total signal increases by a factor of 2 within 50 m. To get an overview of the day, the temporal resolution was set to 30 s. This procedure reproduces the temporal cloud evolution in Fig. . The spread gives an idea about the cloud thickness due to the fact that if a cloud overpasses the lidar beam, it is very likely that cloud water near the cloud top is detected at the beginning and/or at the end of the overpass. However, in some cases, it indicates some single clouds that start at an altitude of 1600 m. At noon, the cloud base gets higher and the clouds are generally thinner, which can be seen the in range of variation in the lidar data, which is very low at this period of time. Overall, there is less variability in the LES data due to the spatial averaging over the downwind region.