1. Introduction
Diabatic processes in the atmosphere, especially the release of latent heat through condensation and freezing, have been shown to have a large impact on atmospheric dynamics by modifying the upper-tropospheric potential vorticity (PV) distribution. Warm conveyor belts (WCB) are the predominant diabatically influenced phenomena in the midlatitudes. They are defined as broad airstreams that originate from the boundary layer of the cyclone’s warm sector and subsequently rise along the cold front (Harrold 1973). WCBs transport large quantities of heat and moisture poleward and upward and are associated with bands of clouds and precipitation in extratropical cyclones (Browning 1990). Climatological analyses of WCBs have shown a preferred occurrence in the winter and over the oceans (Madonna et al. 2014; Eckhardt et al. 2004). Furthermore, they are of particular importance for extratropical precipitation extremes (Pfahl et al. 2014), especially when they interact with bands of increased humidity at low levels (e.g., atmospheric rivers; Sodemann and Stohl 2013). WCBs are usually described as slowly and slantwise ascending airstreams; however, they may also contain embedded convective activity to various degrees. This has been discussed by Neiman et al. (1993) who proposed an elevator–escalator conceptual model to describe this phenomenon. Furthermore, in a conditionally unstable environment it is also possible that the ascent along the cold front consists entirely of deep convection. Away from the frontal regions additional deep convection, often in the form of mesoscale convective systems (MCS), can occur, especially during the warm season. Although such convective systems are usually not associated with a WCB, they also contribute to upper-level PV modification.
Many numerical studies of WCBs use Lagrangian trajectory calculations (Wernli and Davies 1997), in which air parcel locations are tracked as they are advected by the model-resolved flow. With the aid of such trajectory calculations WCBs are identified by requiring parcels to fulfill certain criteria, such as an ascent of 600 hPa within 48 h. The evolution of physical properties of the ascending particles (e.g., moisture or hydrometeor concentrations) can be used to evaluate the importance of certain processes in modifying the dynamics of a cyclone (Joos and Wernli 2012). A lower limit to the ascent time criterion is not generally applied in WCB studies, meaning that fast convective motions are not excluded in principle. They are, however, indirectly excluded by the coarse resolutions and the long output time intervals that previous studies on WCBs have used. In addition, the convection parameterization scheme required at these resolutions directly introduces latent heat into the sounding based on closure assumptions to represent the effects of nonresolved vertical motions and thus hides them from the resolved flow. Not surprisingly a high sensitivity of the relative diabatic contributions to the choice of the convection scheme was found by Martínez-Alvarado et al. (2014). Although the total contribution of the convection scheme was small in their cold-season study, this is unlikely to be true for continental warm-season cases. In addition, Martínez-Alvarado and Plant (2014) found differences in trajectory ascent times and WCB outflow height when using a damped version of the convection scheme.
As an alternative to trajectory calculations tracer variables can be used to investigate vertical motions in simulations. For example, Donnell et al. (2001) and Agustí-Panareda et al. (2005) found that, even in simulations with parameterized convection, upright convection and turbulent mixing are responsible for transporting boundary layer tracers into the WCB region of a cyclone. In a follow-up study, Agustí-Panareda et al. (2009) investigated boundary layer ventilation in two types of WCB associated with kata and ana cold fronts, respectively. They found the role of convection to be similar in both types of WCB. Purvis (2003) used observations of chemical tracers to analyze ventilation processes in the real atmosphere. In their study, embedded convective transport, rather than slantwise ascent, is responsible for transporting tracers from the boundary layer to the free atmosphere. These studies imply that the details of air parcel ascent are of major importance for the distribution of tracers in the atmosphere.
Misrepresentation of diabatically driven upward motions in models can lead to inaccurate forecasts of the upper-level PV structure and can strongly impact downstream development. For WCBs this has, for example, been shown by Grams et al. (2011) and Madonna et al. (2015). Since the PV anomaly in the outflow usually acts to strengthen the already existing upper-level ridge, a systematic underestimation of low-PV transport by WCBs could contribute to the decrease in Rossby wave amplitude with increasing forecast time found by Gray et al. (2014). In the continental warm season, only a small fraction of precipitation is related to WCBs (Pfahl et al. 2014), indicating that convective processes can also represent an important source of upper-level PV modification. Rodwell et al. (2013) suggest that MCSs can significantly degrade medium-range forecasts. In their study, the presence of high values of convective available potential energy (CAPE) over the North American continent was correlated with “forecast busts,” a pronounced decrease in forecast skill downstream over Europe about 6 days later.
Making use of advances in computing resources and numerical modeling, the goal of the present study is to revisit the problem of ascending motions in midlatitude cyclones and associated upper-level PV modification in a case study approach by using a convection-permitting resolution together with an accurate online trajectory calculation. This setting removes a primary limitation of previous studies on convective-scale motions, since deep convective transport occurs through resolved motions rather than being inferred from a parameterization scheme. Therefore, we will focus on vertical motions related to extratropical cyclones in general, which in addition to slantwise WCB ascent will also include embedded convective motions and purely convective ascent in fronts and MCSs. Three different cases are selected in which varying amounts of convective activity can be expected, ranging from a classic wintertime WCB to a highly convective summertime squall line.
The paper is organized as follows. The model and trajectory calculation method will be described in section 2. The three chosen cases are described in some detail in section 3. In section 4 cross-tropospheric ascent time distributions of the three cases will be presented and discussed. Subsequently, in section 5, we investigate mesoscale convective structures embedded in the ascending airstreams. Finally, we explore PV modification by diabatic processes during the ascent and compare the inflow and outflow PV values (section 6). We conclude with a summary and discussion of our results in section 7.
2. Methods
To investigate the mesoscale structure of parcel ascent, numerical simulations were conducted with the nonhydrostatic, limited-area weather forecasting model,Consortium for Small-Scale Modeling (COSMO; Baldauf et al. 2011), which, following the COSMO-DE operational setup, has a horizontal grid spacing of 2.8 km and 50 terrain-following levels in the vertical. The vertical grid spacing decreases from around 100 m near the surface to 500 m at a height of 10 km. The model uses a Runge–Kutta scheme to solve the model equations (Doms and Baldauf 2015). Deep convection is considered to be resolved so that only shallow convection is parameterized with a modified Tiedtke (1989) scheme. Further parameterizations are detailed in Doms et al. (2011) and are used here with no modifications to the operational configurations. The COSMO model utilizes a rotated, spherical grid. The location of the domain origin and the horizontal extent of the domain are listed in Table 1 for each simulation case. Initial and boundary conditions were taken from the analysis and the deterministic forecast of the European Centre for Medium-Range Weather Forecasts (ECMWF) using a COSMO simulation with coarser horizontal grid spacing of 7 km and parameterized convection as an intermediate step.
Details of model simulations.
An online trajectory calculation tool by Miltenberger et al. (2013), developed for the COSMO model, was used to calculate air parcel trajectories during the model run. This tool employs a Petterssen scheme (Petterssen 1940) to advect the parcels every model time step (25 s) according to the model-resolved wind field. Despite interpolation errors in the Petterssen scheme the trajectory positions are as accurate as the simulated flow and are not limited by the longer intervals of data output. The main disadvantage of this method, however, is that the number and position of the trajectories have to be fixed before starting the model. We, therefore, either determined the region and time interval of the WCB inflow from previous studies on coarser grids or covered the simulation domain almost completely. Thus, the number of trajectories started in each simulation varies and the absolute number of ascending trajectories is not related to the strength and extent of the updrafts. Since, in this study, we were interested only in cross-tropospheric ascent, trajectories were started near the ground only (i.e., at heights between 500 and 3000 m above sea level in intervals of 500 m). Starting intervals and horizontal spacing between the trajectories are also listed in Table 1.
From all parcel trajectories we selected those that ascend more than 600 hPa in less than 48 h. This criterion has been widely used to identify WCBs (Wernli and Davies 1997; Madonna et al. 2014) and, in our setup, will also include trajectories rising in deep convection. An ascent of 600 hPa, while dependent on season and latitude, generally implies an ascent from the boundary layer to the tropopause region.
3. Case studies
Three case studies of midlatitude cyclones were selected: one in which convective ascent is expected to dominate (JUL), one in which the ascent is mainly slantwise (JAN), and one in which both convective and slantwise ascent are important (OCT). A brief, synoptic description for each of the cases, together with the most important characteristics of the simulated trajectories, is given below. Animations depicting the synoptic evolution and the trajectories are available online as supplemental material.
a. Convective case (JUL)
On 20 July 2007 a cold front approached highly unstable air over central Europe, thereby triggering an intense squall line. The majority of ascent in this case is associated with deep convection. This event was part of the Convective and Orographically induced Precipitation Study (COPS; Wulfmeyer et al. 2011) and was also analyzed in recent studies on WCB inflow moisture (Schäfler et al. 2011) and error growth (Hanley et al. 2013; Selz and Craig 2015b,a).
This event was characterized by a persistent, upper-level trough located southwest of the British Isles. Warm, moist air was advected to central Europe from the southeast, destabilizing the atmosphere and, together with latent and sensible heat fluxes, producing high convective instability. On 20 July, a narrow squall line formed ahead of the associated cold front, which, in Fig. 1a, can be seen stretching from Belgium to southern Germany. This squall line removed the CAPE and caused heavy precipitation over France and Germany before decaying over the North Sea early on 21 July.
(a) Surface precipitation (mm h−1, blue shading), CAPE (J kg−1, yellow shading), and surface pressure (gray contours, in 5-hPa intervals); (b) 2-PVU contour on the 325-K surface (thick black line, area with larger values is shaded with blue) and 500-hPa geopotential height (gray lines, in 25-m intervals). Both are valid at 1400 UTC 20 Jul 2007. Additionally, every 100th ascending trajectory color is shown in (b) coded by pressure (hPa). For details on the selection criterion see section 2.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
The majority of ascending parcels originate in the continental boundary layer, converge at the squall line, and then ascend rapidly to the upper troposphere (Fig. 1b). There, the parcels fan out broadly, some turning anticyclonically, others wrapping around the cyclone core.
b. Slantwise case (JAN)
A strong cyclone dominated weather over the eastern Atlantic from 28 January to 2 February 2009. This case and the associated WCB have been studied previously by Joos and Wernli (2012) and serves as an example of synoptically forced, slantwise ascent.
Early on 29 January a surface cyclone formed ahead of a large upper-level trough. Over the course of the day, the cyclone deepened explosively with a maximum rate of 44 hPa in 24 h and, in our simulation, reached a minimum surface pressure of 953 hPa. A long cold front extending more than 1000 km was associated with this system. In the early stages, precipitation at the front was narrow and had a cellular structure. On 30 January, as the cyclone moved north, the cold frontal rainband became detached from the cyclone core and was more stratiform (Fig. 2a). CAPE was low valued in the warm sector (<200 J kg−1) for the entire simulation period. On 31 January the cyclone dissipated over Iceland.
As in Fig. 1, but valid at 0600 UTC 30 Jan 2009. The 2-PVU contour is shown on the 305-K surface. Every 50th parcel trajectory is shown.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
Most WCB trajectories start their ascent in the boundary layer of the warm sector and then rise to midlevels at the surface cold front. They subsequently ascend in a slantwise fashion as they travel poleward past the cyclone center (Fig. 2b). The WCB outflow is coincident with an extended upper-level ridge. In this ridge, all parcels turn anticyclonically and some can be seen moving back southward. The ascent is stretched out over 30° latitudinally, which indicates a major heat and momentum displacement. Additionally, some parcels ascend at the warm front in the T-bone region of the cyclone. These trajectories originate farther north and approach the warm front from the south, where they ascend quickly to upper levels. These trajectories do not fit the classic WCB picture. However, the transition between the parcels associated with warm frontal and cold frontal ascent is continuous and no significant difference in temperature or moisture could be found. Therefore, no distinction is made for further analysis. Additionally, the outflow location of the parcels ascending at the warm front is very similar to that of the classic WCB parcels, so that all ascending parcels contribute to the transport of energy and the modification of the upper-level ridge.
c. Mixed case (OCT)
The autumn period from 12 to 18 October 2012 was characterized by a cold front moving across the Mediterranean Sea. Two phenomena were associated with this system: a WCB extending from the Mediterranean Sea to Scandinavia and intense, deep convection over the Adriatic Sea. Therefore, a combination of convective and slantwise ascent processes can be expected. This case was already investigated as part of the THORPEX North Atlantic Waveguide and Downstream Impact Experiment (T-NAWDEX-Falcon) observation campaign (Schäfler et al. 2014).
On 14 October a cyclone formed ahead of an upper-level trough, located over the North Sea. As the cyclone intensified to a minimum surface pressure of 990 hPa, a cold front developed, extending from northern Germany to southern Spain. On 15 October the cold front and the associated narrow band of precipitation moved eastward across the western part of the Mediterranean Sea (Fig. 3a). Here, CAPE values were moderate with 500–1000 J kg−1. Once the front reached the Alps, a lee cyclone developed, triggering intense convection over the Adriatic Sea where large values of CAPE could be found (>2000 J kg−1). This development was associated with a PV streamer reaching as far south as Sardinia.
As in Fig. 1, but valid at 0300 UTC 15 Oct 2012. The 2-PVU contour is shown on the 320-K surface. Every 50th parcel trajectory is shown.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
The ascending trajectories originate, to a large extent, in the maritime boundary layer. From here two sets of parcels can be identified. In the earlier stages, when the cold front is located in the western part of the Mediterranean Sea, the trajectories ascend along the cold front to the midtroposphere, and are then advected northward to the Baltic region and Scandinavia (Fig. 3b). This airstream exhibits classic WCB behavior, in which the ascent extends over several thousands of kilometers. In the later stages, when the lee cyclone and the associated surface cold front have split from its parent cyclone, the majority of parcels ascend quickly in deep convection associated with a region of large convective instability south of Italy.
4. Ascent statistics
To analyze the average ascent velocity we define, for each trajectory, the cross-tropospheric ascent time as the shortest time interval in which the parcel ascends 600 hPa. Figure 4 shows the distribution of this cross-tropospheric ascent time for the three cases. The OCT histogram is stacked with the different shadings representing two categories of trajectories as defined below. First, we will focus on the overall distribution.
Histograms of 600-hPa ascent times for (left) JUL, (middle) JAN, and (right) OCT. The bin width is 30 min. The OCT (right) histogram is a stacked histogram, where the light (dark) shading indicates convective (nonconvective) parcels as defined in the text.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
The JUL distribution peaks at very short ascent times, indicating rapid ascent. A detailed analysis (not shown) reveals that the peak is located at around 20 min, which corresponds to a vertical velocity of 2 hPa s−1 or 1800 hPa h−1 averaged over 600 hPa. There is a tail toward longer ascent times, with a roughly exponential decay. The ascent time distribution for JAN, on the other hand, is positively skewed around a maximum at approximately 10 h, which equates to an average vertical velocity of 60 hPa h−1. This is faster than the climatological WCB average (Madonna et al. 2014), but is similar to the ascent rates observed for the WCB1 branch in Martínez-Alvarado et al. (2014).
There is little overlap between the JUL and JAN distributions. For example, only 2.1% of JAN parcels ascend in less than 4 h, compared to 50% of JUL parcels. Similarly, half of the JAN parcels need more than 20 h to rise 600 hPa, compared to 8.6% of the JUL parcels. This implies a clear separation of cross-tropospheric ascent times of more than one order of magnitude between the cases. In the JUL case, where large values of CAPE are present ahead of the cold front, the majority of ascent is rapid and practically vertical. In contrast, almost no very rapidly ascending parcels are observed in the wintertime JAN case, which lacks large instabilities in the prefrontal atmosphere.
Since the cold front in the OCT case crosses areas with low and high CAPE, one would expect to observe a mixture of the two parcel ascent types. Indeed, the ascent time distribution for the OCT case has two peaks: one at 25 min and one at 24 h. To quantitatively distinguish between convective and slantwise ascent we define a second criterion, which requires a lifting of 400 hPa in less than 150 min. Trajectories that meet this criterion will be classified as convective (light gray shading in Fig. 4), trajectories that do not will be classified as nonconvective (dark gray shading). The parameters (400 hPa and 150 min) were chosen to provide the clearest separation between the key examples JUL and JAN.
Applying this separation criterion to OCT trajectories results in 55.5% convective trajectories (OCTc) and 44.5% nonconvective trajectories (OCTnc). The OCTc distribution is qualitatively very similar to the JUL distribution, while the OCTnc distribution resembles the JAN distribution. Most convective trajectories ascend within a few hours or less, while the nonconvective ascent time distribution has a maximum at around 1 day. This is about twice the maximum of the JAN distribution, but the distribution is less skewed than JAN resulting in similar mean ascent times.
The separation of the OCT case into convective and nonconvective trajectories also results in some spatial and temporal separation of the trajectories. The majority of convective parcels rise over southern Italy, while most OCTnc parcels rise farther west over the northwestern Mediterranean Sea (Fig. 5). The convective trajectories immediately reach the upper troposphere, where they are advected eastward. For OCTnc parcels, a slantwise ascent behavior is clearly visible as they rise more slowly over central Europe. This spatial separation is in agreement with the distinct peaks in the temporal distribution of ascent starting times (Fig. 6). OCTnc trajectories typically ascend 1 day before most OCTc parcels. The convective OCTc peak is associated with convective systems developing at the cold front of the lee cyclone (see animation in online supplemental material).
Trajectories for (left) OCTc parcels and (right) OCTnc parcels color coded by their pressure. Additionally, black dots demarcate the point at which the rising trajectories cross 750 hPa. Only every 20th trajectory is drawn.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
Histogram showing time at which parcels cross the 750-hPa level for OCTc (red) and OCTnc (green). The bin width is 30 min.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
There is, however, a considerable amount of overlap, both spatially and temporally, between the two trajectory categories. This indicates the continuous transition from one regime to the other, and highlights the limitations of our simple separation criterion. For the most part, however, the essential characteristics of slantwise, “nonconvective” ascent and abrupt, “convective” ascent are well represented and will be used for the following analysis. Note that the trajectory density is not constant throughout the domain and integration period. Especially during the later stages, the supply of trajectories decreases significantly. Heavy, presumably convective, precipitation over the Adriatic Sea early on 16 October is not captured by any of the trajectories (see animation in online supplemental material). This might cause the decrease in ascending trajectories observed at around 70-h forecast lead time.
5. Embedded convection in slantwise WCB ascent
In this section the extent of convection embedded in the slantwise ascending cases (JAN and OCTnc) is investigated. To start with, Fig. 7 shows an example of 10 randomly selected trajectories from all 3 cases, treating OCTc and OCTnc seperately. The convective parcels (JUL and OCTc) generally ascend abruptly from the boundary layer to the upper troposphere. However, the example parcels from the nonconvective cases (JAN and OCTnc) also show an ascent behavior, which is far from smooth and gradual, as one would have expected from the classic WCB conceptual picture. Rather, distinct phases of rapid ascent are clearly visible. This indicates that, even for nonconvective parcels in our case studies, there is significant convective-scale variability during WCB ascent.
Evolution of pressure with time for 10 randomly selected ascending trajectories for (top left) JUL, (top right) JAN, (bottom left) OCTc, and (bottom right) OCTnc.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
To systematically detect phases of embedded convection we define a convective ascent phase (CAP) of a trajectory as an ascent interval where the vertical velocity is continuously greater than 0.1 hPa s−1. This threshold lies in between the typical vertical velocities of slantwise and convective ascent. We, however, chose a somewhat higher value compared to the threshold in section 4 to exclude turbulent fluctuations near the grid scale (see below at the end of this section). Each CAP can be characterized by its extent (pressure difference between start and end), its vertical location (mean pressure), and its horizontal location. Two-dimensional histograms show the vertical extent of the CAPs against height (Fig. 8). Note that one trajectory can have several CAPs. The number of CAPs exceeds the number of CAP-containing trajectories by 14%–30%.
2D-histogram showing the midpoint (in hPa) of the CAPs on the x axis and the vertical extent (in hPa) on the y axis. The relative frequency is defined as the number of CAPs per bin divided by the number of trajectories with a CAP. Since one trajectory can have more than one CAP, the sum of all relative frequencies can be more than 100%. The total percentage of trajectories experiencing at least one CAP is also given in the top right of each figure. The bin width in both directions is 20 hPa.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
As expected, a large majority of parcels in the convective cases (95.0% for JUL and 98.9% for OCTc) have at least one CAP during their 600-hPa ascent. For most JUL parcels the CAPs span a large fraction of the 600-hPa ascent. The requirement of the CAPs to be within the 600-hPa ascent puts an upper limit on the vertical extent of the CAPs. The CAP midpoint is centered around 550 hPa, indicating that the rapid ascent typically starts at around 800 hPa, just above the boundary layer, and extends to around 300 hPa. The beginning of the rapid ascent at 800 hPa coincides with the level of free convection for this case. Note that the CAP start level marks the onset of a faster vertical movement and not the ascent itself, which does originate from the boundary layer (the average pressure of parcels before ascent is 900 hPa).
With 63.9% of all ascending trajectories having at least one CAP, the JAN case also contains significant convective activity located mostly at the cold front (Fig. 9). From the CAP histogram one can identify that parcels start their rapid ascent in the boundary layer, where they quickly rise around 150 to around 800 hPa. This layer is also characterized by strong turbulence, which is not present at upper levels. A cross section through the frontal zone of the cyclone reveals an almost vertical cold front from the surface to around 2 km, which corresponds to the extent of the CAPs up to about 800 hPa (Fig. 10). This frontal structure is typical for a “rearward-sloping” WCB, associated with an ana cold front, as described by Browning (1990, see his Fig. 8.8). The rapid lifting at the surface front, also called line convection, is forced by strong low-level convergence even though small values of CAPE might also contribute. Above 2 km the ascent is mostly gradual and phases of rapid convective ascent are rare.
Positions of parcels currently experiencing a CAP valid at (a) 1200 UTC 29 Jan 2009 (JAN) and (b) 2200 UTC 14 Oct 2012 (OCT). The parcels are color coded by their pressure. Precipitation and CAPE are also plotted as in Fig. 1. Only a part of the simulation domain is shown. The red line in (a) indicates the location of the vertical cross section in Fig. 10. The red cross in (b) indicates the position of the thermodynamic diagram in Fig. 11.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
Vertical cross section from west to east at the position indicated by the red line in Fig. 9a. Colors show the equivalent potential temperature 
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
For the OCT case we first apply the separation into convective and nonconvective parcels described in section 4. With this, the OCTc parcels show similar ascent characteristics as the JUL parcels, but with a more distributed CAP maximum. This implies that not all parcels ascend quickly throughout the troposphere. Such a broader distribution is not unexpected since a perfect separation is not possible due to spatial and temporal overlap of the two regimes (see Figs. 5 and 6).
From the OCT parcels that have been classified as nonconvective, 49.5% undergo one or more CAP, which is less than for the JAN case. In addition the histogram in Fig. 8 reveals that the embedded convective motions are much shallower. Small displacements at around 750 hPa make up most of the CAPs, but longer CAPs with a vertical extent of 100 hPa are also present at this level. Despite some boundary layer turbulence, most of the convective ascent is centered above the boundary layer between 800 and 600 hPa. Figure 9 shows a snapshot of the weather situation, taken when most OCTnc have started their ascent (at the time of the maximum in Fig. 6). A thermodynamic sounding just east to the rainband (Fig. 11) reveals a small amount of CAPE and a level of free convection just below 800 hPa. This corresponds with the layer where most of the CAPs were detected. Entrainment probably limits the vertical extent of convective ascents to about 600 hPa.
Skew T–logp diagram corresponding to the location marked by the red cross in Fig. 9 at 2000 UTC 14 Oct 2012 (2 h prior). The temperature is drawn in blue, the dewpoint temperature is drawn in green, and the ascent of a mixed layer parcel is plotted in gray.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
In all four cases, even smaller vertical fluctuations can be identified in most of the example trajectories in Fig. 7, which indicate some turbulence near the grid scale. This turbulence also appears as a local frequency maximum at the bottom end of the CAP histograms (Fig. 8). The amplitude of these frequency maxima is sensitive to the choice of the CAP threshold in the sense that more particles are included when the threshold is lowered. This turbulence also correlates with vertical instabilities, but is present at all heights, especially when a lower threshold is used. Since these motions are close to the grid scale and do usually not persist for more than one output time step (5 min) they are probably not well resolved in our model or may even be artificial. We, therefore, decided to basically exclude them by raising the threshold in comparison to section 4 and focus on the better resolved, larger convective motions.
6. Diabatic modification of θ and PV
To compare the cases in terms of cross-isentropic ascent, the mean evolution of potential temperature over time is given in Fig. 12 together with the θ distributions just before and just after the ascent. Comparing the convective cases (JUL and OCTc) and the nonconvective cases (JAN and OCTnc) among each other, the potential temperature increase [Δθ = θ (outflow) − θ (inflow)] is similar, but 
(a) Temporal evolution of potential temperature (K) for all three cases, where OCT is divided into convective and nonconvective trajectories (see text). Before averaging all trajectories were centered around the time where they first cross the 600-hPa level (t = 0). (b) Histograms of potential temperature (K). The blue (red) histogram shows the mean value of each trajectory averaged 3 h before (after) the start (end) of the 600-hPa ascent. Additionally vertical lines represent the respective average. The bin width is 1 K.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
A clear separation between the inflow and outflow potential temperature distributions can be seen for all four cases (Fig. 12b). There is little overlap between the distributions, and generally the 5th–95th interpercentile range (hereafter simply called range) is smaller than the means of the pre- and postascent θ distributions. However, the width of the outflow distribution is, in general, larger than the inflow distribution and this effect seems more pronounced in the convective cases.
Similar to potential temperature the evolution of potential vorticity and its inflow and outflow distributions are given in Fig. 13. In all four cases the PV increases in the first phase of the ascent and decreases afterward as suggested by (1) and consistent with previous studies (e.g., Joos and Wernli 2012; Madonna et al. 2014). Thus the resulting PV maximum is located somewhere in the middle of the ascent, at around 600 hPa for the convective cases and a bit below for the nonconvective cases. Maxima for the convective cases, particularly JUL, are much higher, which, through (1), can be linked to the large difference in diabatic heating rates.
(a),(b) As in Fig. 12, but for potential vorticity (PVU). The bin width in (b) is 0.1 PVU.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
It can be seen that in all four cases the mean inflow PV and the mean outflow PV almost exactly match, with the mean outflow PV being slightly larger. Especially compared to the width of the PV distribution the change in mean is negligibly small (Fig. 13b). This equality of inflow and outflow PV holds only on average, however, and is not seen when following individual particles. In fact, the correlation coefficient between individual inflow PV values and outflow PV values is very close to zero and varies between −0.008 (JUL) and 0.09 (OCTc). This implies that while the coherent ensemble of trajectories retains their PV, individual parcels do not. Large small-scale fluctuations of the heating rate and the vorticity modify the PV tendency locally in a random way but cancel over larger areas or, equivalently, over a large number of particles.
As with potential temperature the PV distribution of the outflow is broader than that of the inflow, and this broadening is again much stronger in the convective cases. For the nonconvective cases the increase of the width is relatively small and the distributions almost overlap, despite some outliers in the tails of the JAN case outflow. In contrast, for the convective cases the distribution gets significantly broader with the width increasing by a factor of 2.5–4. This increase in spread can qualitatively be understood from (1), which states that variability in the individual outflow PV values comes from the product of variability in the z derivative of the heating rate and variability in the absolute vorticity. The first factor can be approximated with the increase in potential temperature spread (Fig. 12b). However, this increase in θ spread is much smaller than the increase in PV spread for the convective cases. The missing spread could be due to the increased variability in absolute vorticity in the convective ascents, as indicated by Fig. 14b, which shows the range of absolute vorticity values in the ascending air masses. In the center of the ascent, where the diabatic heating rates also peak, the vorticity range is 2–3 times larger in the convective cases, which together with the 
Temporal evolution of (a) diabatic heating rate (K h−1) and (b) the absolute vorticity of the 5th–95th interpercentile range (s−1). Other details are as in Fig. 12a.
Citation: Monthly Weather Review 144, 10; 10.1175/MWR-D-16-0112.1
7. Summary and discussion
The aim of this paper is to investigate cross-isentropic airmass ascent in midlatitude cyclones with the inclusion of fast convective motions. To this end, a limited-area model (COSMO) in convection-permitting resolution together with online calculations of trajectory positions were used to simulate three cases: a summertime case (JUL) with high CAPE and mostly convective driven ascent, a wintertime case (JAN) dominated by slantwise ascent, and an autumn case (OCT) where both ascent types are present.
First, we compared statistics of cross-tropospheric (
Next, the prevalence of embedded convective motions in the slantwise-ascending cases (JAN and OCTnc) was investigated (section 5). Embedded convection defined as periods of rapid ascent were present in roughly half of the ascending parcels in these cases (Fig. 8). In JAN, these rapid ascent phases typically occur at low levels associated with synoptically forced line convection from the boundary layer to a height of approximately 2 km. In OCTnc the rapid ascent phases are located above the boundary layer at approximately 700 hPa, which could be linked to a layer of conditional instability. These results are in good agreement with the numerical and observational boundary layer ventilation studies mentioned in the introduction (e.g., Agustí-Panareda et al. 2009), which also suggest that, regardless of frontal type, convection plays an important role in tracer transport.
In section 6 we investigated the impact of diabatic heating on potential temperature and PV during the ascent. A larger increase in potential temperature was found in the convective cases (about 28 K), compared to the nonconvective cases (about 20 K), which correlates with the water vapor content in the inflow air mass. In all cases average PV increases below the maximum of latent heating and decreases above, resulting in a PV maximum at midlevels. This maximum is more pronounced in the convective cases due to higher rates of latent heat release. However, the inflow–outflow PV difference, averaged over all ascending particles, is close to zero for all cases (0.07–0.12 PVU; 1 PVU = 106 K kg−1 m2 s−1) and appears negligible in comparison to the large spread of the individual PV values in the inflow and outflow airstream (Fig. 13b). The spread of PV values in the outflow is increased compared to the inflow spread and this increase is more pronounced in the convective cases, which appears to be related to higher variability of the vorticity field.
Our study significantly reduces the model error compared to similar work conducted so far by using a resolution that is high enough to avoid a parameterization scheme for deep convection. Nevertheless, this resolution is still insufficient to simulate small-scale details of convective updrafts, shallow convection, or turbulence properly. Hence, parameterization schemes for shallow convection and turbulence are still required. However, the clear separation of typical simulated vertical velocities in convective and slantwise ascent shown in section 4 indicates that the resolution we used is already high enough to distinguish these processes. Future large-eddy simulations of midlatitude cyclones are likely to modify the distribution of the convective updraft by including even faster ascents. The basic separation, however, should be largely unaffected by an increasing resolution.
In the mainly slantwise ascending cases fast convective motions could be detected as well, although they were shallow and restricted to a certain layer of higher instability (section 5). The estimates of embedded convection may be more sensitive to further improvements in resolution, since these shallow motions are probably not fully resolved with a 2.8-km grid spacing. In addition, unresolved turbulent eddies may also contribute to offsetting trajectories from a steady ascent. To the extent that the planetary boundary layer is well mixed, the effect of these eddies would be mainly to add some variability to the trajectories, with little change to the properties of air parcels until they leave the boundary layer. Above the boundary layer, the absence of unresolved small-scale motions can be more significant, as indicated by the tracer transport study of Chagnon and Gray (2010). Fast vertical motions with displacement amplitudes close to the vertical grid spacing were indeed present in our simulations at all heights. Such grid-scale turbulence might, however, not be realistic and we have not considered it in detail in our study.
Distributions of potential temperature show very little overlap between inflow and outflow and indicate that in isentropic coordinates the inflow and outflow layers are shallow compared to their distance. Similar results were found by Madonna et al. (2014) and this argument was also used by Methven (2015) for the construction of his thought experiment. However, it should be kept in mind that the large 
Our results suggest that PV modification by diabatic processes between inflow and outflow air mass is insensitive to the ascent characteristics, which were vastly different among our cases. In fact, Methven (2015) argued that details of the ascent are basically unimportant and the cross-isentropic mass flux is the dominant quantity that defines the properties of the ascending airstream. However, in his thought experiment the PV of the inflow and outflow volumes is determined by isentropic advection from upstream, which does not constraint the inflow–outflow PV change across different cases. Furthermore, it is questionable if the concept of material volumes that cross the troposphere without mixing can still be applied to convection-permitting simulations and convective systems. The cross-isentropic mass flux on the other hand has been shown to be sensitive to convective parameterization (Martínez-Alvarado et al. 2014) and is, therefore, most likely also sensitive to resolution. Especially in convective cases large differences can be expected, but also shallow layers of embedded convection missing in coarser simulations might alter the estimated cross-isentropic mass flux significantly. A direct comparison of high-resolution convection-permitting simulations with online trajectory calculation to results from coarse simulations or reanalyses in future work could provide a more meaningful evaluation of the role and accuracy of convection schemes in terms of upper-level PV modification by WCBs or convective systems.
Finally, the extent and type of convective activity in airmass ascent could imply different levels of predictability, since the time scale of intrinsic predictability between convective-scale motions and synoptic motions differ by about a factor of 10 (Hohenegger and Schär 2007b). Previous studies have shown errors to grow faster in regions of high convective activity (Hohenegger and Schär 2007a), which subsequently perturb forecasts on larger scales (Selz and Craig 2015b). Misrepresentation of WCBs as well as MCSs in models have the potential to lead to large forecast errors within a few forecast days (Gray et al. 2014) or even to forecast “busts” (Rodwell et al. 2013). It would be of interest in future studies to directly compare the growth of errors in different types of airmass ascents and investigate their importance for longer lead-time predictability.
Acknowledgments
The authors thank two anonymous reviewers for their comments that helped to improve the quality and clarity of this article. The research leading to these results has been partly done within the Transregional Collaborative Research Center SFB/TRR 165 “Waves to Weather” funded by the German Science Foundation (DFG). We appreciate the use of ECMWF’s computing and archive facilities. We are grateful to DWD for providing the COSMO model. The authors would also like to thank John Methven for insightful discussions during the preparation of the manuscript.
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