In both simulations, trajectories end their ascent at pressures between 200 and 400 hPa (Fig. a), and at temperatures between -65 and -20 °C (Fig. b). The pressures at the end of the ascent are very similar (Fig. a), but at the end of the whole simulation, trajectories in the nested simulation are located on average at 319 hPa, compared to 328 hPa for the global simulation, indicating that they remain in higher regions of the atmosphere for longer. The average end-of-ascent temperature is -44.6°C in the nested and -44.0 °C in the global simulation, and at the end of the simulation this differences grows to -41.4 and -39.6 °C (Fig. b).

At the end of the simulation, trajectories in the nested simulation at one average 24 h old (age defined as hours passed since end of ascent), compared to 25 h for the global simulation, which could in part explain the difference in pressure and temperature at this time. Because of the small shifts in the temperature and pressure distributions we will often compare variables between simulations at similar temperatures and pressures to eliminate biases (besides allowing for a more physics oriented analysis). Finally, the geographical distribution of trajectories at the beginning and end of the ascent, as well as at the end of the simulation, is similar in both simulations. The only notable difference is that in the nested simulation, WCB trajectories are found slightly further north and south at the end of their ascent (Fig. ).

The logarithm of the specific humidity (log⁡10(qv)) at the end of the ascent in the nested simulation follows a Gaussian distribution, whereas in the global simulation the distribution is skewed slightly towards larger values (Fig. a). This results in a larger mean qv value for the global simulation of 0.216 g kg⁻¹ compared to 0.212 g kg⁻¹ in the nested simulation. In both cases, qv at the end of the ascent is primarily constrained by the temperature and pressure at the end of the ascent (Fig. ), meaning that the higher qv in the global simulation is primarily due to higher temperatures and lower pressures at the end of the ascent (Fig. b). However, when looking at qv values across pressure bins (Fig. b), we find that between 225 and 250 hPa, the mean, median and lower percentiles for qv are consistently higher in the global simulation. This difference is also reflected when binning qv by temperature (between -60 and -50 °C) but is harder to identify due to the much stronger dependence of qv on T (and is therefore not shown).

We therefore also investigate the relative humidity over ice (RH_i) at the end of the ascent. Here we find that, on average, RH_i is slightly larger in the global simulation, with an average of 103.9 % compared to 103.4 % in the nested simulation (Fig. c). This difference in mean values is pronounced when binned by pressure at approximately 250 hPa (Fig. d). However, differences in the shapes of the RH_i distributions are much more striking than the differences in mean values. In the nested simulation, RH_i values have a sharp peak just below 100 % which is mostly absent in the global simulation (Fig. c). In , this peak was attributed to convectively ascending trajectories that have a higher condensation ratio and thus remove supersaturation more efficiently. Since convective trajectories are largely absent in the global simulation (Fig. ), RH_i assumes a more Gaussian distribution, with only a faint hint of a second peak below 100 %. These results clearly show that, at the end of the ascent and at pressures below 300 hPa, the vertical vapor distribution between the simulations differs greatly, and hint at the fact that this difference might be due to the lack of convectively ascending trajectories in the global simulation.

In order to determine a physical mechanism why some trajectories in the global simulation are more or less humid than their counterparts at the same pressure in the nested simulation when they finish their ascent, we adopt the same approach as and examine the relaxation timescale for supersaturation over ice (τsat,ice). For an air parcel with a vertical velocity of zero it is given by: 1τsat,ice=14π⋅CAP⋅Ni⋅ri⋅Dv(with[Ni]=m-3), with Dv the water vapor diffusion coefficient (taken as a constant value of 3×10-5m2s-1) and CAP the capacitance of ice (0.5 for a spherical particle). This equation states that the time-scale for the removal of supersaturation is inversely proportional to the number concentration of ice (Ni) times the radius of ice (ri), and is only valid when vertical velocities are small (below ∼0.1ms-1. The vertical velocities at the end of the ascent are (0.006±0.080)ms-1 in the nested, and (0.010±0.032)ms-1 in the global simulation. Therefore, we can safely use Eq. () for our analysis when looking at the end of the ascent.

As in , we find that τsat,ice plays a strong role in determining RH_i at the end of the ascent and that this dependence is the same in both the global and the nested simulation (Fig. ). Because τsat,ice-values span many orders of magnitude, we look at the distribution of log⁡10(τsat,ice)-values at the end of the ascent and find that their shape is overall similar, but shifted to larger values for the global simulation (Fig. e). The mean log⁡10(τsat,ice) in the global simulation is 3.56 (∼7000 s for τsat,ice) compared to 3.44 (∼5000 s for τsat,ice) in the nested simulation. When binned by pressure, log⁡10(τsat,ice) is larger in the global simulation from 225 to 350 hPa corresponding to the pressure range where RH_i is also either larger or similar to the values in the nested simulation. Below 225 hPa, log⁡10(τsat,ice) in the global simulation is smaller, just as RH_i. Therefore, τsat,ice seems to be a suitable diagnostic to explain difference in RH_i at tend of the ascent and in particular suggest that difference in the hydrometeor population between both simulations are causing the variations in the RH_i distribution. Differences in the hydrometeor population between global and nested simulation are explored in the next paragraph.

In both simulations, almost all trajectories are fully glaciated by the end of the ascent, with the only remaining hydrometeor species being ice (not shown). However, the ice mass and number concentrations (qi and Ni) at the end of the ascent are very different between the simulations. qi is on average 0.025 g kg⁻¹ for the nested simulation, which is almost twice as high as the average of 0.015 g kg⁻¹ for the global simulation (Fig. b). The distributions for log⁡10(qi) assume a mostly Gaussian shape in both simulations, but are more narrow and shifted to smaller values for the global simulation (Fig. c). Ni is on average 4 times higher in the nested simulation (∼4×105 1 kg⁻¹) than in the global (∼105 1 kg⁻¹) (Fig. a). Both log⁡10(Ni)-distributions have a tail towards large Ni and are similarly shaped, but again the distribution from the global simulation is shifted to smaller values. The distribution for ri is shifted to larger values in the global simulation (Fig. e), and ri values are clearly larger on average at pressures below 300 hPa (Fig. f). This indicates that in the global simulation, the overall ice content at the end of the ascent is smaller in mass and number, while ice crystal radii are larger.

When binned by pressure, qi and Ni at the end of the ascent are smaller in the global simulation in the same pressure regions (250-225 hPa) where qv and RH_i are larger in the nested simulation or roughly the same both simulations (Fig. b and d). Below 225 hPa, this behaviour is inverted, with qi and Ni being larger in the global simulation. This inversion suggests that, when changing from a convection-parameterising to a convection-permitting resolution, the amount and vertical distribution of ice transported to the UTLS change. Above 300 hPa, the ice crystal radius (ri) in the global simulation is similar to the nested simulation (Fig. g), and below this pressure it is consistently larger in the global compared to the nested simulation (Fig. f). Nevertheless, when averaged over all altitudes in the outflow, ri is larger in the global simulation (∼ 0.11 mm on average) than in the nested simulation (∼ 0.10 mm on average), reflecting the higher Ni and qi in the nested simulation. The distribution shapes of ri are similar, with the slight difference that in the nested simulation, there is a hint of a secondary peak at very small radii (Fig. e).

In the introduction, we hypothesized that the differences we see between simulations for variables such as ice crystal content and size at the end of the ascent will likely be due to larger vertical velocities in the nested simulation. We have already shown that overall, the ascent timescales are much smaller in the nested simulation (Fig. ). Even for trajectories with similar τ600, the max(Δp2h)-values are much larger than in the nested simulation (Fig. a). The intense convective motion for τ600<12, where max(Δp2h) increasing exponentially for decreasing τ600, is missing entirely in the global simulation.

determined that high vertical velocities allow for more ice crystals to remain suspended in an air parcel, and that the less time spent in the ascent means that there is also less time for the growth of larger ice crystals. Therefore, the differences in ascent velocity and time between the two simulations can plausibly explain the higher Ni and qi for pressures larger than 225 hPa in the nested simulation, as well as the overall smaller ri. However, we also found that for pressures below 225 hPa, this behaviour is inverted, with Ni and qi being larger in the global simulation (differences in ri are unchanged). This inversion cannot be explained by differences in ascent velocity. Instead, we hypothesize that the convection parameterization, which can transport ice to high altitudes in a single time-step, might lead to the higher Ni and qi values for the global simulation above 225 hPa. This hypothesis is tested in the second part of this study.

The differences in vapor and hydrometeor content at the end of ascent that we discuss in this section suggest that trajectories in the two simulations undergo distinct (micro)physical processes during their ascent. This will be discussed in Sect. . These results also raise the question of whether the condensation ratio (CR) and precipitation efficiency (PE) are different in the nested and global simulations and is discussed next. 

We use the definitions of the Lagrangian precipitation efficiency PE and condensation ratio CR from to quantify the water budget of WCB air parcels, the efficiency of vertical moisture transport and the role of cloud processes in modifying the latter. CR quantifies the fraction of vapor present at the beginning the WCB ascent that is converted into hydrometeors by the end of the ascent. It is therefore a measure of how efficiently vapor is removed. PE quantifies the fraction of hydrometeors formed during the ascent that are lost by the end of the ascent. It is therefore a measure of how efficiently hydrometeors are removed.

Based on the overall lower qv for the nested simulation discussed in the previous section we expect that the CR should be larger overall than in the global simulation, since a lower qv generally indicates that more vapor has been converted and likely dominates over differences in the boundary layer water vapor field. The distribution of CR confirms this (Fig. a). However, if considering CR for trajectories arriving at different altitudes in the outflow, CR is also larger in pressure bins where qv-values are the same or similar (Fig. c), indicating an overall greater fraction of vapor to condensate conversion in the nested simulation. This difference likely derives from differences in boundary-layer moisture field and representation of boundary-layer moisture transport in the two simulations: Trajectories in the nested simulation are more humid and warmer at the beginning of τWCB (Fig. ), and CR strongly depends on the initial qv.

However, the higher overall qv at the beginning of the ascent the nested simulation is most likely not due to a higher qv in the planetary boundary layer (PBL) WCB inflow region of the nested simulation. Rather, the higher initial qv is likely a result of the algorithm that determines the beginning of τWCB: The algorithm goes backwards from the beginning of τ600 until the ascent velocity is smaller than 8 hPa h⁻¹, and since trajectories in the nested simulation generally experience higher vertical velocities, this point can be shifted further backwards than in the global simulation. This higher overall ascent velocity in the nested simulation therefore shifts the beginning of τWCB closer to the surface, where qv is higher. We conclude that this is a potential weakness and source of error when calculating CR. Perhaps a future study should explore ways to account for this induced bias.

In the nested simulation, the PE has a more broad distribution than in the global simulation and is smaller on average (Fig. b). The bias induced for CR from the τWCB algorithm does not effect PE, because it depends more strongly on the initial hydrometeor concentration and not the vapor content. When binned by pressure, PE is smaller in the nested simulation from approximately 250 to 350 hPa, and larger below 225 hPa (Fig. d), which is mostly consistent with differences in Ni and qi as expected (Fig. b and d). This consistency confirms that the differences in hydrometeor transport, rather than the differences in vapor-to-hydrometeor conversion, drive the differences in hydrometeor content at the end of the ascent between the two simulations.

The larger spread in PE values for the nested simulation results in some trajectories precipitating nearly all hydrometeors, with 5 % of trajectories in the nested simulation having PE > 99.999 %, as opposed to just 0.5 % in the global simulation. The retention of hydrometeors strongly depends on vertical velocities as well as the hydrometeor size and type. Since showed that convective activity changes which hydrometeor species are more abundant in an ascending air parcel, we are able to attribute the different spread of PE distributions to the more convective flow in the nested simulation.

In this section, we analysed the conditions of WCB trajectories at the end of their ascent. We found that trajectories in the nested simulation end their ascent at slightly lower pressures and temperatures than in the global simulation (Fig. ). The vapor content is smaller overall in the nested simulation (Fig. a), but especially so below pressures of 250 hPa (Fig. b). RH_i is also smaller in the nested simulation and the distribution peaks below 100 %, whereas in the global simulation the distribution peaks above 100 % (Fig. c and d). We are able to trace these differences to different relaxation timescales τsat,ice between the two simulations. τsat,ice is inversely proportional to Ni (Eq. ), which at the end of the ascent is much higher in the nested simulation (Fig. a and b), which explains why τsat,ice is smaller and thus also RH_i. By analysing the moisture transport through the lens of the CR and PE, we are able to trace these differences in hydrometeor content (and therefore vapor) to differences in hydrometeor transport during the ascent (quantified by PE), as opposed to differences in the vapor-to-hydrometeor conversion (quantified by CR).

Firstly, we examine integrated process rates that are accumulated by the end of the ascent. In a previous study, showed that convective WCB trajectories exhibit higher accumulated frozen precipitation flux – defined as the net loss of frozen hydrometeors along the trajectory (qx,in-qx,out), integrated over τWCB – while slow trajectories tend to produce more rain. We find that this pattern is similarly reflected in the global and nested simulations: Compared to the global simulation, the nested simulation shows a greater integrated frozen precipitation flux, a smaller integrated rain flux, and a higher total hydrometeor flux overall (Fig. a). We also find higher integrated riming and condensation rates in the nested simulation, while the global simulation shows slightly higher integrated deposition rates (Fig. b). These difference very likely arise from the missing representation of large (convection-related) vertical velocities in the global simulation and the impact of ascent timescale on the cloud microphysical pathways as identified by .

Moisture loss via the convection parametrisation is nearly zero in the nested simulation (Fig. b), since most of the ascent occurs within domains 2 and 3 (Fig. a), where the (deep) convection scheme is switched off. This lack of the convection parametrization for most of the ascent in the nested simulation can explain the large differences observed in integrated condensation (cond) and turbulence (turbs) rates between the simulations (Fig. b): Without the option to redistribute moisture through the convection parametrisation, the higher resolution model must instead condense and precipitate water vapor via the cloud microphysics parametrisation or lose moisture to the turbulence parameterization.

The greater moisture loss due to turbulence in the nested simulation also supports our interpretation that the atmospheric flow in the nested simulation has more fine-scale structure increasing also wind shear and thus the loss of moisture due to turbulence. In the global simulation, approximately 1.5 gkg-1 of moisture is lost due to the convection scheme, and moisture lost to the turbulence scheme is small. The clear signal from the convection parameterization demonstrates that the Lagrangian diagnostics are able to pick up on the contributions from the convection parameterization scheme, even though it does not influence the wind fields with which trajectories are advected. The negative sign also indicates that the contributions to the moisture budget mostly occur in the beginning of the ascent, where the scheme removes moisture from a parcel to redistribute it vertically, as opposed to at the end of the ascent, where the scheme takes moisture from the PBL and redistributes it into the parcel.

Binning the instantaneous (not integrated) microphysical process rates by pressure and temperature (Figs.  and ) indicates that they differ primarily in magnitude rather than being shifted to different pressure or temperature regions. Notable exceptions are riming (Fig. a, d) and the influx of graupel and rain (Fig. a and b): in the global simulation, riming and the influx of graupel are largely absent below approximately 500 hPa and -10 °C, whereas in the nested simulation, trajectories still undergo substantial riming and experience graupel influx at pressures around 400 hPa and temperatures as low as -20°C. This behaviour is due to the higher ascent velocities in the nested simulation, which allow for the production and retention of larger amounts of graupel and rain at lower pressures and temperatures.

Higher vertical velocities keep particles in suspension longer which allows them to grow. This means that the nested simulation favours the production of graupel over ice and snow (supported by the larger integrated riming rate shown in Fig. b). Trajectories in the global simulation consistently experience a slightly greater influx of ice and snow than those in the nested simulation (Fig. c and d). We note that these differences only slightly change the pressure and temperature of glaciation (first time step where liquid water content is zero; Fig. ). On average, air parcels in the nested simulation glaciate at 362 hPa and -32.2 °C, compared to 356 hPa and -32.8 °C in the global simulation. Even though we attribute most of the previously identified differences between the two simulations to the difference in vertical velocities, the process of reaching full glaciation is not strongly affected by this difference. This is probably because vertical velocities between the two simulations differ most strongly in the lower troposphere (p< 500 hPa; Fig. b), whereas full glaciation occurs at around 360 hPa, where vertical velocities are much more similar (Fig. ). However, vertical velocities do influence the hydrometeor content and type, meaning that some effect on the glaciation can be expected. Since the majority of trajectories in both simulations experience slow, slantwise ascent, it is possible that the differences induced by different vertical velocities at the glaciation point are minimal.

During the ascent, i.e. TF2, the total hydrometeor and frozen hydrometeor mass mixing ratio are both higher in the nested simulation across all pressure bins (Fig. a and b). The mass mixing ratio of liquid water (Fig. c) is similar at pressures of approximately 600 hPa but larger in the nested simulation above and below this pressure. When examining the number concentrations for individual hydrometeor species (Figs.  and ), we find that the largest difference in frozen hydrometeor content is seen for graupel, which has far higher mass mixing ratios and number concentrations in the nested simulation (Fig. c and f), especially below pressures of 600 hPa. The radii of ice and snow are smaller or similar in the nested simulation (Fig. g and h), and the number concentrations mostly larger (Fig. d and e). The mass mixing ratios are similar or slightly larger (Fig. a and b). Especially for snow, the largest difference between simulations is seen for the size and number concentration, not the mass mixing ratio. Cloud droplet mass mixing ratios and number concentrations are higher in the nested simulation (Fig. a and c), whereas radii are similar. For raindrops, the mass mixing ratios and radii are larger in the nested simulation (Fig. b and f) but the number concentrations are far lower (Fig. d).

These differences can mostly be explained by the different vertical velocities experienced by trajectories in the nested and global simulation. Higher vertical velocities mean that more hydrometeors can remain suspended in the ascending air parcel, which explains higher mass and number mixing ratios in the nested simulation. The larger number and mass mixing ratios of cloud droplets (Fig. a and c) could also be due to differences in CCN activation. This process is also strongly dependent on vertical velocity, with higher vertical velocities leading to higher CCN activation rates and smaller cloud droplets. Therefore, higher vertical velocities also impact the size distribution of cloud droplets, and as a consequence thereof also influences the conversion rates of cloud droplets to raindrops, and the size of the ice particles that result from the freezing of cloud droplets. Therefore, differences in vertical velocities can also explain the different hydrometeor radii. The larger raindrops seen in the nested simulation are exempt from this explanation, and could instead be caused by the higher influx of graupel from aloft (Fig. b) which is melted to form raindrops.

In summary, the trajectories in the two simulations undergo different microphysical processes during WCB ascent phase with arguably the most important difference being a shift of precipitation to the frozen phase in the nested simulation. During the ascent and for ice, snow, and cloud drops, the nested simulation tends to favour more and smaller hydrometeors, whereas for graupel and rain the opposite is the case. Differences in the vertical distribution of hydrometeors are minor for all hydrometeor species except for graupel, which is shifted substantially to lower pressures in the nested simulation. We can plausibly attribute all of these differences to the different ascent velocities experienced by trajectories in the two simulations.