The transport of stratospheric air into the troposphere within deep convection was investigated using the Met Office Unified Model version 6.1. Three cases were simulated in which convective systems formed over the UK in the summer of 2005. For each of these three cases, simulations were performed on a grid having 4 km horizontal grid spacing in which the convection was parameterized and on a grid having 1 km horizontal grid spacing, which permitted explicit representation of the largest energy-containing scales of deep convection. Cross-tropopause transport was diagnosed using passive tracers that were initialized above the dynamically defined tropopause (2 potential vorticity unit surface) with a mixing ratio of 1. Although the synoptic-scale environment and triggering mechanisms varied between the cases, the total simulated transport was similar in all three cases. The total stratosphere-to-troposphere transport over the lifetime of the convective systems ranged from 25 to 100 kg/m2 across the simulated convective systems and resolutions, which corresponds to ∼5–20% of the total mass located within a stratospheric column extending 2 km above the tropopause. In all simulations, the transport into the lower troposphere (defined as below 3.5 km elevation) accounted for ∼1% of the total transport across the tropopause. In the 4 km runs most of the transport was due to parameterized convection, whereas in the 1 km runs the transport was due to explicitly resolved convection. The largest difference between the simulations with different resolutions occurred in the one case of midlevel convection considered, in which the total transport in the 1 km grid spacing simulation with explicit convection was 4 times that in the 4 km grid spacing simulation with parameterized convection. Although the total cross-tropopause transport was similar, stratospheric tracer was deposited more deeply to near-surface elevations in the convection-parameterizing simulations than in convection-permitting simulations.
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 The transport of mass across the tropopause plays a significant role in the chemistry of the upper troposphere and lower stratosphere. Contributing to the total exchange are a range of processes active across a wide range of time and space scales. On the global scale, stratosphere-troposphere exchange (STE) takes place within the Brewer-Dobson circulation, which pumps mass poleward in the middle atmosphere where it descends into the lower stratosphere in the extratropics (e.g., see Holton et al.  for a review). On the synoptic scale, STE takes place within midlatitude weather systems. The direction of transport within weather systems is primarily upward in warm conveyor belts and in both directions across tropopause folds [e.g., see Stohl et al., 2003b]. These forms of synoptic- and global-scale transport have been both well observed (e.g., see review by Stohl et al. [2003a]) and resolved by simulations using numerical weather prediction (NWP) models.
 Transport across the tropopause can take place on the mesoscale within deep convection. The possible mechanisms of transport within convection include direct mixing within tropopause-penetrating updrafts [Reid and Vaughan, 2004; Mullendore et al., 2005] and diabatic alteration of the potential vorticity-defined tropopause [Wirth, 1995; Lamarque and Hess, 1994; Gray, 2006]. Observational estimates of stratosphere-to-troposphere transport (STT) in convection have focused on the evolution of ozone and water vapor in the upper troposphere. Above a midlatitude mesoscale convective complex (MCC), Poulida et al.  observed an approximately 700 m thick layer of ozone-rich stratospheric air residing beneath a layer of tropospheric air, indicating that STE was extensive across the system. Randriambelo et al.  observed elevated ozone concentrations of 200 ppbv in the tropical troposphere above the trade wind inversion, at least some of which was attributable to deep convection (with biomass burning contributing an additional source). Using aircraft measurements and simulations on a 30 km grid, Hitchman et al.  identified a region of enhanced ozone (∼100 ppbv) on the periphery of convection at an elevation of 6.5 km in an MCC event over East Asia.
 Both the observation and simulation of convective transport suffer from several difficulties. While observations of ozone profiles provide valuable information about the history of transport in the convective environment, they do not present a comprehensive picture in time and space of the dynamical mechanisms that contribute to STT within the deep convective cells. On the other hand, numerical simulations of STT in deep convection have historically suffered from one of two shortcomings. In order to accommodate a realistic representation of the evolving larger-scale state (e.g., an upper-level potential vorticity (PV) anomaly shed from a Rossby wave breaking event) a sacrifice in resolution must be made. The consequence of this sacrifice in resolution is that the convection must be represented via a parameterization scheme that makes assumptions about how the transport takes place in a grid volume (see Randall et al.  and Plant  for review of the present deficiencies of convective parameterization schemes and possible solutions thereof). Conversely, if a model is to be run at a resolution that is fine enough to permit explicit representation of convection, then assumptions must typically be made about the evolving larger-scale state. Only recently has it become within our capability to extend both the domain size and resolution such that both a realistic representation of the evolving larger-scale dynamics can be accommodated and an explicit representation of the largest scales of turbulent motion within the cloud can be permitted.
 Numerical case studies of midlatitude convective systems performed in convection-permitting (i.e., 1 km horizontal grid spacing) and mesoalpha-accommodating (i.e., 500 × 500 km) domains have the potential to reveal much about the nature of STT by deep convection. An example of one such investigation is that performed by Chagnon and Gray  (hereafter CG07) in which a mesoscale convective system (MCS) that formed over southeast UK was simulated using an operational NWP model at both high (1 km grid spacing) and low (12 km grid spacing) resolution. CG07 demonstrated that a simulated stratospheric tracer can be transported into the middle and lower troposphere within a convective system that penetrates the tropopause, but that the finer details and the means by which this transport is accomplished depend upon the manner by which the convection is represented in the model. Transport in the convection-permitting run (1 km horizontal grid spacing) was found to be less efficient at bringing stratospheric air down to near-surface elevations than transport in the coarser runs that employed a convective parameterization.
 While an analysis of a single case study can provide valuable insight into the dynamical mechanisms responsible for transport as well as the model configuration sensitivities to which the simulations are vulnerable, there remain questions concerning the representativeness of such individual case studies that must be answered before any conclusions may be considered robust. Consequently, a range of case studies is performed here in order to establish the extent to which conclusions drawn from a single case study may be extended to other cases. This is an especially important consideration in light of the difficulties associated with observing STT in deep convection. A future challenge is to characterize the seasonal and longer-term statistical properties of transport within MCSs. For the foreseeable future, advances in computing performance will not be sufficient to make it possible to run simulations in large enough domains over long enough simulation time at convection-permitting resolution to construct a climatology of STT within convective systems. However, if we are able to relate parameterized transport to explicit transport with confidence, then such climatologies could be inferred from simulations performed at coarser resolution. A necessary preliminary step is therefore to perform such case studies in order to qualify the sensitivity of transport to the parameterization of convection.
 This investigation is an extension of CG07. We seek to elaborate upon the original analysis through examination of a range of cases in which deep convection formed over the UK in order to establish the extent that simulated transport varies from case to case. By examining a small sample of cases we may identify the features of STT by convection that are robust (in the model simulations) and those that may vary from case to case. The present investigation still suffers from a few limitations. First, our analysis is performed without observations from which to infer the magnitude of transport in deep convection. Second, we are focusing on convection in the UK and are therefore unable extrapolate our results to midlatitude convection in general.
 This paper is organized as follows: Section 2 describes the method of analysis that was employed in this study, including details of the Met Office Unified Model (MetUM) and the passive tracers that are used to diagnose cross-tropopause transport. Section 3 provides background information regarding the three cases chosen for investigation. Section 4 presents the analysis of STT in the simulations. Section 5 discusses the results and suggests avenues for future research.
2. Analysis Framework
 Three cases of convection that took place over the UK in summer 2005 form the basis for the analysis presented in this paper. The dates for these cases are 24 June, 29 June, and 28 July 2005, which are referred to as cases I, II, and III, respectively. In all three cases, deep convection was observed in the vicinity of a mesosphere-stratosphere-troposphere (MST) wind profiling Doppler radar located at Aberystwyth in Wales. The MST wind profiling radar indicated that some of this convection had extended to the elevation of the tropopause, thus suggesting a possibility for STE. This section describes the modeling strategy that was applied to analyze STE in these cases. More background information regarding each of the cases is presented in section 3.
 The MetUM is an operational-class forecasting model that solves the compressible, nonhydrostatic equations of motion using a semi-Lagrangian scheme in time and fifth order spatial differencing on an Arakawa-C grid with Charney-Phillips vertical staggering of a terrain following vertical coordinate. Specific details of the numerics are described by Davies et al. . The modeling system incorporates a full suite of state-of-the-art physics schemes, including mixed phase microphysics coupled to a shortwave radiation scheme [Wilson and Ballard, 1999], the MOSES-II boundary layer parameterization [Lock et al., 2000], and a mass-flux convective parameterization [Gregory and Rowntree, 1990]. The convection scheme is called once per time step. Aside from the mixing accomplished within the nonlocal 1-D boundary layer scheme, a subgrid-scale turbulence parameterization scheme is not used. The parameter settings and physics schemes used in this study are those which were used operationally at the Met Office.
 The cases have been simulated using version 6.1 of the MetUM. The simulations were performed using three different configurations of the limited area mesoscale model having horizontal grid spacing of 12, 4, and 1 km. These configurations will hereafter be referred to as the 12, 4, and 1 km runs, respectively. Figure 1 depicts the arrangement of the domains, and Table 1 summarizes the basic properties of the three configurations, including the total domain sizes and vertical grid spacing. Note that the vertical grid spacing increases with elevation. The 12 km runs were initialized from a mesoscale analysis at 0100 UT prepared during the UK Met Office forecast cycle on the days of the cases. This outer domain covers all of the UK and extends into the western Atlantic as well as much of western Europe. The extent of the domain ensures that synoptic-scale features may evolve within the domain itself. Boundary conditions for this outer 12 km run are supplied by an operational global model forecast of the MetUM. Embedded within the domain of the 12 km run is the domain for the 4 km run, which receives boundary conditions from the 12 run. The 4 km domain covers all of the British Isles. Embedded within the domain of the 4 km run is the domain corresponding to the 1 km run, which receives initial and boundary conditions from the 4 km run. This smallest domain covers the region surrounding the MST radar facility at Aberystwyth in Wales, including some of the Irish Sea, Wales, and southern and central England. The MetUM does not support two-way nesting; information from the inner domains is not passed back to the outer domains. Both the 12 and 4 km runs were performed for 23 h, whereas the 1 km runs were performed for an 8 h period that allows several hours for convection to spin up and captures the initiation, development, and maturation of the primary convective events. The analysis of STT focuses on a comparison between the 4 and 1 km runs since the properties of the system-wide and parameterized transport in the 12 and 4 km runs were similar. (The similarity between the 12 and 4 km runs with respect to STT in these cases should not be interpreted as a general result. See Lean et al.  for a detailed comparison of the performance of the 12, 4, and 1 km configurations in forecasts of convective events in the UK.)
Table 1. Summary of Model Configurations for the Three Simulations
12 km Run
4 km Run
1 km Run
Lateral boundary condition source
12 km run
4 km run
Number of horizontal grid points (EW × NS)
146 × 182
360 × 300
448 × 352
Number of vertical levels
Δz at z = 8 km
0100 Z, mesoscale analysis
Same as 12 km run
Output dump from 4 km run
Convective parameterization scheme status
Horizontal diffusion (order, value)
4th, 1.43 × 103 m4s−1
 The three model configurations used in this study differ in several important ways. The 12 km run is too coarse to represent convection explicitly and therefore employs a convective parameterization. The 1 km run is fine enough to begin resolving the largest energy-containing scales of 3-D turbulence in the deep convective boundary layer and does not employ a convective parameterization. While this may not necessarily produce simulations that are more accurate than or serve as a benchmark for the coarser runs [Bryan et al., 2003], it nonetheless represents convection differently and therefore, when compared to the coarser runs, offers a way of testing the sensitivity of simulated transport to the means by which convection is represented. The 4 km run lies between the 12 and 1 km runs insofar as its ability to represent convection is concerned. For this configuration, the convective parameterization is modified using the procedure of Roberts  in which the adjustment time scale for the convective available potential energy (CAPE) is specified as an increasing function of CAPE. This parameter adjustment (used in the operational 4 km grid spacing MetUM) ensures that the largest values of mass flux occur at the smallest spatial scales (where the CAPE is largest), thereby avoiding the accumulation of high values of CAPE at the grid scale and thus unphysical grid point storms. In brief, the modification of Roberts ensures that the convective parameterization operates at or near the grid scale, but that larger-scale convective circulations may develop explicitly on the resolved scales. This modification, designed specifically for this model resolution, has proved reasonably successful [Lean et al., 2008].
 The diagnosis of transport across the tropopause is aided by the use of passive tracers. The tracer computation applied here is the same as that applied in CG07. The evolution of tracers is computed online using the same monotonic semi-Lagrangian advection scheme with cubic interpolation that is used to evolve the moisture and potential temperature fields. At the start of each run (in both the 4 and 1 km runs), the initial distribution of tracer is set to have a mixing ratio of 1 above the dynamically defined tropopause and a mixing ratio of zero in the troposphere. Tracer is initialized within the lateral boundary conditions in a similar manner at every time step such that no tracer may enter into the troposphere through the lateral boundaries. We take the dynamically defined tropopause to correspond to the 2 potential vorticity unit (PVU) surface. The tropopause is found objectively using the method outlined by Gray , which is capable of diagnosing folds where the tropopause elevation is a multivalued function. In addition to being advected by the grid-scale winds and processed by the boundary-layer parameterization scheme, the tracers may also be processed through (or withheld from) the convective parameterization scheme; the former tracer is here referred to as the full physics tracer, the latter is here referred to as the no-convection tracer. The difference between the distribution of tracers that are passed through and withheld from the convective parameterization indicates the role of parameterized convection in the evolution of tracer. Because some transport by convective systems takes place on the mesoscale (e.g., compensating subsidence on the periphery of the system), the parameterized contribution does not contain the entire convective transport [Lawrence and Salzmann, 2008]. Concerning the initial step function vertical distribution of tracer, we expect that some diffusion of tracer will take place that should not be interpreted as due to real physical processes. Given that convection often takes place in the vicinity of tropopause-level PV anomalies, this problem requires careful consideration. This artificial transport is estimated by examining regions of the domain that are not dynamically active. As reported in section 4, this value is small enough to afford distinction between artificial and physical transport. The MetUM uses semi-Lagrangian advection and therefore the evolution of tracer does not suffer from a Gibbs phenomenon.
3. Overview of the Three Cases
 Before presenting an analysis of simulated STT in the three cases, this section provides some background information concerning the meteorological conditions in which the convection and transport occurred. An exhaustive analysis of the specific dynamical and physical mechanisms that led to triggering and organization of convection on each of the days is beyond the scope of the present investigation. The focus of this paper is on STT by simulated deep convection for which the factors of relevance include the larger-scale conditions (e.g., dynamical anomalies on the tropopause) and the general properties of the convective cells. Further details of each of these three cases of convection are presented in studies by Browning et al.  for case I, Marsham et al. [2007a, 2007b] for case II, and Chagnon and Gray [2008, 2009] for case III. All three cases were designated as intensive observation periods during the Convective Storm Initiation Project (CSIP). (The authors of the present study were not CSIP co-investigators, nor were any CSIP data used in the production of this paper.)
Figure 2 introduces the three cases under consideration by presenting satellite infrared channel imagery and vertical profiles of vertical velocity and vertical velocity variance from the MST wind-profiling Doppler radar at Aberystwyth in Wales. The times of the satellite images correspond to times when the convection was active near Aberystwyth and satellite imagery was available (0600, 1800, and 0600 UTC in cases I, II, and III, respectively). (In cases I and III, the deep convection observed near Aberystwyth occurred in the morning. In case II, the convection occurred in the afternoon.) The analysis of tracer transport in the following section focuses on these relevant periods of convective activity. The wind profiler estimates of vertical velocity variance (Figure 2, second column) on each of the 3 days indicate the presence of deep convection near the radar. In cases II and III, the high-variance signature of convection extended to the height of the tropopause (indicated by the thin white line). In case I, it is not clear from this evidence alone whether the convection at Aberystwyth extended to the height of the tropopause.
Figure 3 presents the Met Office surface analyses at 0000 UTC on each of the relevant days. In each case the convection formed in a warm moist southerly flow ahead of a low to the south of the UK. However, surface frontal forcing only appeared to play a primary role in the initiation of convection in case III as the surface low (Figure 3c) propagated northward. In case II, scattered convection formed along an east-west oriented zone extending from Wales eastward across central England to East Anglia ahead of a strong upper-level potential vorticity anomaly (see discussion of Figure 4 later). In case I, convection was initiated at midlevels ahead of an upper-level trough approaching from the west.
Figure 4 presents the simulated PV in the 12 km runs at a model elevation of 8.4 km, which intersects the tropopause in some locations. (In the terrain-following coordinate system, model elevation is not equivalent to elevation above mean sea level. Throughout this article, unless stated otherwise, all reported elevation values correspond to model elevation.) The upper-level PV pattern indicates the location of dynamical anomalies on the tropopause. Due to their association with large-scale ascent, as well as their tendency to generate potential instability, such anomalies are often associated with convection in western Europe. Furthermore, the existence of a lowered tropopause in the vicinity of deep convection increases the likelihood that such convection could penetrate the tropopause and accomplish STE. In all cases, bands of high PV are present in the vicinity of the British Isles. Focusing specifically on central England and Wales where our proceeding analysis of tracer is performed, only in case II is a significant tropopause depression evident directly above the region where deep convection formed. This lowered tropopause is also evident in the MST data (see thin white contour on Figure 2d). In cases I and III, large horizontal gradients of upper-level PV are evident where the convection takes place.
 Simulated precipitation rates in the 4 and 1 km runs are shown in Figure 5 valid at times when the primary convective systems formed over England and Wales. In all cases, the spatial extent and timing are similar in the 4 and 1 km runs, which compare well to the observed radar-derived precipitation rates (for radar images, see Browning et al.  for case I, Marsham et al.  for case II, and Chagnon and Gray [2008, 2009] for case III). Peak rain rates through the simulations in the 1 km runs (55, 58, 52 mm/h in cases I, II, and III, respectively) were consistently higher than those in the 4 km runs (27, 30, 24 mm/h in cases I, II, and III, respectively). Peak radar-estimated precipitation rates exceeded 32 mm/h in all cases. In case I, two regions of convection were evident at this time: one extending north to south across Wales and one across the Irish Sea, the former being more intense in the 1 km run than in the 4 km run. In case II, the convection formed primarily in isolated cells that were most intense along an east-west oriented axis stretching across Wales and central England that corresponded to the region of largest upper-level PV gradient. The convection that formed in case III was the most organized widespread and intense among the three cases; a strong east-west oriented squall line extended across Wales and central England in the warm sector to the northeast of the surface low. The fraction of total precipitation that was due to the convective parameterization scheme in the 4 km runs varied between the cases, with the scheme being least active in case I. At the times shown in Figure 5, the fraction of total precipitation occurring in the convection schemes was 34%, 59%, and 57% in cases I, II, and III, respectively. The precipitation statistics are described here to characterize the general properties of the three simulated precipitation systems; however, the precipitation statistics do not appear to be correlated to the properties of simulated STT (described in section 4). The extension of updrafts (parameterized or explicit) to the tropopause level is critical for STT, whereas precipitation can also be produced within shallower or stratiform clouds.
 The general properties of the three cases may be summarized as follows: The convection in case I formed ahead of an upper-level PV anomaly that approached from the west, but the region where the convection formed was not located directly beneath a significant tropopause depression. Rather, this convection was strongest downstream of the PV anomaly and had derived its inflow not from boundary-layer air but from a stream of warm moist air located at approximately the 850 hPa level [Browning et al., 2010]. The convection in case II formed beneath a significant tropopause depression. Although there was not any strong surface forcing, the convection extended from the boundary layer through the full depth of the troposphere. In case III, the convection formed in a region of strong surface forcing, but not beneath a significant tropopause depression. In spite of the absence of a lowered tropopause, the deep convection that formed was observed to extend to the tropopause elevation. Factors that were common to all three cases include the observation that deep convection extended up to the tropopause level, and that the convection was widespread across Wales and central England. Factors that varied between the three cases included the elevation of the tropopause level, the source elevation of storm inflow, and the significance of upper-level forcing to the initiation and organization of convection.
4. Analysis of the Simulated STT
4.1. Transport in the Convection-Parameterizing 4 km Runs
 A comparison of the tracer transport in the three cases as simulated in the 4 km runs reveals that the simulated transport shares many general properties in common. Figure 6 presents the evolution of tracer in the 4 km runs at three fixed model elevations that intersect the lower stratosphere/upper troposphere (top row), the free troposphere (middle row), and the lower troposphere (bottom row). The tracer shown in Figure 6 is the full physics tracer that includes the vertical redistribution of tracer due to the convective parameterization. The tracer distribution near the tropopause level (Figure 6, top row) is indicative of the structure of tropopause itself; i.e., regions of high tracer correspond to regions where the tropopause is depressed to an elevation beneath that of the cross section. Aside from a few finer-scale structures present in the 4 km run (particularly in case III, Figure 6c), the pattern of tracer in the top row of Figure 6 resembles the pattern of upper-level PV shown in Figure 4. The tracer present at an elevation of 6.5 km (Figure 6, middle row) indicates where shallow STT (defined as transport over a short vertical distance) has taken place from the stratosphere into the free troposphere. Note that this elevation is everywhere beneath the tropopause in each case and thus any tracer arriving at this level has crossed the tropopause. In all cases, some shallow transport is evident across Wales and central England where convection is present. However, it is not clear on this evidence alone whether the simulated convection is responsible for the shallow transport in this region. A partitioning of STT among contributions from resolved and parameterized processes is presented below. Tracer that has been transported into the lower troposphere to an elevation of 3.5 km is shown in the bottom row of Figure 6. In all three cases, deep transport is evident in the region of interest where convection has taken place. The magnitude of the tracer concentration at this elevation is two orders of magnitude less than that at the tropopause. This degree of dilution is consistent with that found in CG07 and can be accomplished by an entrainment rate of 10−2 s−1 active over a period of 30 min. Note that such an entrainment rate is typically prescribed within the mass flux convective parameterization scheme to represent the rate at which the subgrid-scale cloud ensemble entrains cloud-free environmental air.
 In order to examine the vertical extent of STT in the 4 km runs, Figure 7 presents latitude-height cross sections of tracer through the respective regions of convection in each of the three cases. The locations of the sections were selected such that they intersect the regions of primary STT as indicated in Figure 6. In all cases, the full physics tracer (Figure 7, top row) indicates that a significant amount of stratospheric tracer has been transported across the tropopause, most of which is deposited in the free troposphere within just a few kilometers of the tropopause (note that the tropopause elevation is indicated by the 2 PVU contours plotted in Figure 7). In all cases, the lower-tropospheric tracer is attached to the region of free tropospheric tracer through contiguous vertically aligned streaks, which are suggestive of deep convective transport. To determine what role has been played by the convective parameterization in this transport, we examine the difference between the distributions of the full physics and no-convection tracers. The positive difference between these tracers is defined as the convective deposit region (Figure 7, middle row) where the convective parameterization has transported stratospheric tracer downward into the troposphere. The negative difference between these tracers is defined as the convective source region (Figure 7, bottom row) where the convective parameterization has removed tracer from the lower stratosphere. The parameterized convective deposit accounts for most of the total transport into the troposphere, a notable exception being within the tropopause fold near the northern edge of the section in case III. The source region in the lower stratosphere is approximately 2 km deep and has a horizontal extent of several hundred kilometers. A small portion of the source region is also located below the tropopause (e.g., see Figure 7h), indicating that the parameterization has accessed some tracer that had been previously transported by the advection scheme (some of which may be due to resolved convection). As noted previously, only a small proportion of this stratospheric tracer is deposited in the lowermost portion of the troposphere. Although the convective cells are of smaller scale and more scattered in case II than in cases I and III (see Figure 5c), the apparent extent and magnitude of the tracer transport is largest in case II. It should be noted that these differences in transport characteristics between the cases are not very well correlated to the precipitation statistics presented in section 3. Precipitation is generated in both shallow and deep updrafts and in both convective and stratiform regions. Deep transport of stratospheric air into the troposphere requires that either the convective scheme or explicit updrafts be active near the tropopause level. The precipitation rates alone are therefore of limited utility for diagnosing STT.
4.2. Transport in the Convection-Permitting 1 km Runs
 The properties of transport in the higher resolution 1 km runs in which convection is simulated explicitly also exhibit many similarities between the three cases. The domains of the 1 km runs focus specifically on the regions of convective activity in Wales and central England. Figure 8 presents the evolution of tracer in the 1 km runs at three fixed model elevations that intersect the lower stratosphere/upper troposphere (top row), the free troposphere (middle row), and the lower troposphere (bottom row; i.e., same as Figure 6 but for the 1 km runs). As in the 4 km runs, the general pattern of tracer near the tropopause level (Figure 8, top row) indicates the structure of the tropopause itself. A lowered tropopause approached from the west in case I, a lowered tropopause existed directly above the region where the convective system formed in case II, and the convection formed between upper-level PV streamers located to the south and north but not directly above the region where convection formed in case III. Unlike in the 4 km runs, the regions above the tropopause also contain localized regions of tracer-free tropospheric air (the “dark holes” seen in Figures 8a–8c). This tracer-free air is transported upward within the explicitly resolved updrafts that penetrate the tropopause level. Beneath the tropopause level in the free troposphere (Figure 8, middle row), there is evidence of shallow transport in all cases. There is also evidence of tracer-free air being transported upward through this level within small-scale updrafts. In all cases, stratospheric tracer has been deposited at this level within the active regions of convection. The transport of tracer into the lower troposphere (Figure 8, bottom row) is isolated to the most intense cells (refer to Figure 5). The tracer magnitude at lower tropospheric elevations is similar within individual convective cells among the three cases. Compared to the transport in the 4 km runs (Figure 6, bottom row), the spatial extent of tracer transported into the lower troposphere is less in the 1 km runs for cases II and III, but the peak magnitudes are similar in all cases. The simulations performed in CG07 exhibited similar resolution dependence. Among the three cases, the most significant difference between the 4 km runs and 1 km runs is evident in case I where the shallow transport to 9.7 km elevation is of larger magnitude in the 1 km run than in the 4 km run (compare Figures 6a and 8a).
Figure 9 presents latitude-height cross sections of tracer through the regions of convection in the 1 km domain. Because the tracer and PV fields contain a large degree of small-scale structure, the fields plotted in Figure 9 have been averaged in the latitudinal and longitudinal directions using a top hat-weighted averaging filter of dimension 20 × 20 km. (The 20 km averaging window was tuned to remove the noise while not altering the larger-scale structure of the tropopause in these three cases. This number may not be appropriate for additional studies of different cases.) The smoothed fields facilitate a comparison to the results in the 4 km run (Figure 7). As in the 4 km run, shallow transport to tropospheric elevations within a few kilometers of the tropopause is evident in all three cases. The vertical sections demonstrate that this shallow transport is widespread across the convective system and is not merely confined to the most intense cells. Animations of the tracer in these sections (not shown) reveal that the widespread shallow tracer is the result of a history of convective plumes, each of which accomplishes some shallow transport through direct penetration and stirring of the tropopause layer. Deep transport to the lower troposphere subsequently takes place within the resolved deep turbulent eddies associated with the strongest cells. Additional shallow transport may take place on the periphery of all the system, possibly due to entrainment in the subsiding air around the edges of the most intense convection as described by Poulida et al. , although it is difficult to distinguish between this mode of transport and the diffusion of the initial profile of tracer. While the model's boundary-layer parameterization scheme may play a role in the subsequent mixing of tracer once it has been transported to the lower troposphere, the scheme does not appear to play a primary role in transporting tracer downward from the free troposphere. Note that the tracer transported to elevations under approximately 1.5 km is less in the 1 km runs than in the 4 km runs in these cross sections. However, as is shown in section 4.3, the total tracer transported into the lower troposphere (defined as elevations below 3.5 km) is similar in the 4 km runs and 1 km runs.
4.3. Time Series of Integrated Transport
 To summarize the comparison of vertical transport between the cases and resolutions (see Figures 7 and 9), Figure 10 presents the evolution of horizontally averaged tracer in the troposphere in all of the runs as a function of height. (The narrow layer of tropospheric tracer near the tropopause must be interpreted cautiously because the tropopause elevation is not constant across the 1 km subdomain.) In the 4 km run, the full physics tracer is integrated in order to avoid ambiguities in the interpretation of convective transport identified by Lawrence and Salzmann . The most significant difference between the transport in the 4 and 1 km runs concerns the depth of transport. In the 4 km runs (and even in case I where the total transport is small in the 4 km run) a larger quantity of tracer accumulates at near-surface elevation. This is a result consistent with that reported in CG07. Although the total transport across the tropopause is similar (see Figure 11), the vertical distribution of mass accomplished by the parameterized convection occurs over a deeper portion of troposphere than that accomplished by explicit convection. Without observations against which to validate the tracer profiles, it is not possible to say whether the parameterized or explicit transport is more realistic.
 The remainder of this section presents a quantitative comparison of the tracer transport from the stratosphere into the free and lower troposphere in all three cases and in the convection-parameterizing and convection-permitting simulations. In all cases, the subdomain over which integrals are computed corresponds to the domain of the 1 km runs. Vertical integrals are computed in the following way: At each grid volume in the domain, the total tracer mass per unit area is computed as the product of the tracer concentration, air density, and grid box depth. The total tropospheric tracer integral is computed by summing the tracer mass in each column from the surface to the 2 PVU surface. As stated previously, because the 2 PVU surface is noisy in the 1 km runs (due to large gradients of diabatic heating on such small scales), the 2 PVU surface is found by analyzing a filtered PV field subject to an averaging window of width 20 km. Lower tropospheric tracer integrals are computed by integrating from the surface to a model level at an elevation of 3.5 km. While we are primarily interested in diagnosing the vertical transport by convection, in the 4 km run it is likely that some tropospheric tracer enters the subdomain through the lateral boundaries. As such, the total tracer in the 4 km runs could potentially represent a longer history of transport than that calculated in the 1 km runs. To eliminate the transport through the lateral boundaries of the subdomain from the tracer integral calculation, an additional set of 4 km runs was performed in which all of the tracer outside of the subdomain was set to zero below the tropopause at all times.
Figure 11 presents the tracer integrals in the 4 and 1 km runs from the surface to the tropopause (total integral) and from the surface to 3.5 km elevation (lower troposphere). Recall that the primary time periods of analysis begin in the morning for cases I and III and in the afternoon for case II. These time periods also correspond to the times of maximum tracer transport in all cases. In the 4 km runs, the total transport (Figure 11a) ranges from ∼30 to 80 kg/m2 with the largest transport taking place in case II and the smallest taking place in case I. (Recall that the tropopause elevation was the lowest in case II of all the three cases.) The transport into the lower troposphere (Figure 11c) is 2 orders of magnitude smaller than the total transport, ranging from ∼0.25 to 1.5 kg/m2 with the largest transport again occurring in case II. The smallest total transport into the lower troposphere took place in case I in which convection was initiated at midlevels (∼850 hPa) rather than at the surface.
 Comparing the transport in the 4 km runs to that in the 1 km runs reveals several differences and similarities. In cases II and III, there is very good agreement between the 4 and 1 km runs concerning the total and lower tropospheric transport. In these two cases, peak values of transport agree to within 10%. In contrast, for case I, there is approximately 4 times more tracer transport in the 1 km run than in the 4 km run. In cases I and II, the rate at which tracer is transported in the 1 km runs exceeds that in the 4 km runs. In case III, the rate of transport is similar but the transport occurs earlier in the 1 km run than in the 4 km run.
 The interpretation of the total tracer calculation is affected by a few caveats, which are as follows: First, in several of the cases (e.g., the lower tropospheric tracer in the 1 km run case I, Figure 11d), the peak in total tracer is followed by a decrease in total tracer. This subsequent decrease in tracer is coincident with a transport of tracer out of the 1 km subdomain through the lateral boundaries. Second, the numerical diffusion of tracer across the initial step function at the tropopause provides an artificial source of background transport. This background transport (estimated by examining several regions in which no convection or significant tropopause anomalies were present) accounts for ∼10 kg/m2 after ∼6 h of simulation time (after which time there is no apparent additional increase). While this is a large quantity of mass, it is nonetheless small enough to distinguish the total transport shown in Figure 11 as a signal of the transport by the convective systems.
 To put the aforementioned values of tracer transport in perspective, consider the following calculation: Suppose that all of the air within the first 2 km above a tropopause located at 8 km elevation was tagged as a tracer having a mixing ratio of 1 kg/kg. The total mass of tracer in this 2 km deep layer would be 533 kg/m2, assuming a density scale height of 8 km. Note that 2 km is the approximate depth of the source region of tracer mixed downward by the convective parameterization (see Figures 7h and 7i). Thus, 100 kg/m2 of total tracer transported from the stratosphere to the troposphere indicates that ∼20% of the stratospheric air residing within 2 km of the tropopause was transported with the troposphere within the subdomain encompassing these convective systems over their lifetime.
5. Summary and Discussion
 This paper has presented an analysis of STT within three midlatitude summertime convective systems simulated in the Met Office Unified Model. The investigation was designed to establish the extent to which simulated transport varies between individual cases and between convection-parameterizing and convection-permitting model configurations (i.e., the 4 and 1 km runs, respectively). The examination of transport in three cases and using two model configurations allows one to evaluate the robustness of conclusions drawn from the single case presented by CG07. Such clarification of CG07 was particularly prudent in light of two facts: First, the case examined in CG07 consisted of convection forming beneath an unusually low tropopause fold that might have been accompanied by more deep transport than a typical storm. Second, the lack of observations within evolving deep convective storms necessitates the use of numerical simulation for identifying the cloud-scale processes that lead to transport. Reliance on numerical simulation necessitates the identification of sensitivities of simulated transport to model configuration (as well as the variations thereof between cases).
 The three cases presented for analysis in this paper were selected based on the simple criterion that deep convection reaching the tropopause level was observed over a broad portion of Wales and central England. The synoptic-scale conditions and the characteristics of convection varied between the cases. For example, the convection in case I occurred ahead of a strong upper-level PV anomaly and was initiated at midlevels. The convection in case II was triggered from the boundary layer and took place directly beneath an upper-level PV anomaly and a lowered tropopause. The convection in case III was triggered by surface forcing within a relatively strong surface low, but did not take place beneath a lowered tropopause. In spite of these differences, many properties of the simulated STT were similar in each of the cases. For example, the total transport was in the range of 30–80 kg/m2 over a 6–8 h period in the 4 km runs. The transport within the convective parameterization sourced most of this mass from within the lowest 2 km of the stratosphere. Most of this mass was in turn deposited within the highest 2 km of the troposphere. Only about 1% of this mass was transported to lower-tropospheric elevations (i.e., within 3 km of the surface). A similar pattern of transport and resolution dependence was observed in the 1 km runs, with one notable exception: in case I, the partially parameterized transport in the 4 km run was 4 times smaller in total than the explicit transport in the 1 km run. In a summary of events observed during the International H2O Project (IHOP), Wilson and Roberts  identified cases of elevated convection as presenting a particular challenge for NWP model forecasts. It is possible that these problems are associated with the sensitivity of these events to gust front dynamics as detailed by Browning et al. . Nonetheless, despite the differences in the synoptic-scale environments and modes of convective organization that characterize this sample of cases, neither the variation in total STT between different mesoscale convective systems nor the variation between the STT simulated in the 4 and 1 km runs exceeds an order of magnitude.
 A question that follows from this study is whether different modeling systems that employ different physical parameterization schemes would behave similarly. Estimations of total transport across MCCs simulated by Hitchman et al.  and Buker et al.  using the Regional Air Quality Modeling System (RAQMS) ranged from 0.2 to 0.8 Tg/d of ozone. If the ∼50 kg/m2 of transport that was calculated in the present study was accomplished over a 400 × 400 km wide region over a day, then ∼0.1 Tg of ozone would be transported out of the stratosphere (a slightly smaller amount compared to the previous studies). The difference may be due to the larger size and greater intensity of the convective complexes examined in these previous studies, but it is not possible to rule out systematic differences owing to the different modeling techniques. A careful analysis of common events simulated using different model configurations is required to clarify the cause of these differences. In addition to the effect of convective parameterization schemes and horizontal resolution, Arteta et al.  demonstrated that by increasing vertical resolution near the tropopause in simulations of deep tropical convection, the representation of STT was significantly improved. Additional tests were carried out in the present investigation in which the vertical resolution in the 4 km runs was doubled to match that used in the 1 km runs. The doubling did not have a significant impact on the simulation of cases presented in this paper (not shown), but this apparent insensitivity might be due to the larger role played by synoptic forcing compared to the intense episodes of deep tropical convection simulated by Arteta et al. . The present investigation considered only cases of convection over the UK. Extrapolation of the results presented in this paper to simulations of convective systems in other midlatitude or tropical regions should be made with caution.
 An appropriate context in which to evaluate the potential sensitivity of STT in convection is that of convective adjustment. The convective adjustment paradigm conceives of an initial vertical thermodynamic profile that contains some available energy that may be used to generate convective motions. The convective motions in turn redistribute mass until a new adjusted state is established in which the available energy has been removed. This basic paradigm underlies the design of convective parameterizations whose function is to represent the removal of available energy as appropriate by subgrid-scale processes before the available energy can excite convection on the grid scale inappropriately. There are two central problems that require closure if the convective adjustment paradigm is to be implemented in practice. First, one needs to identify the presence of available energy as well as the inevitability of its release, neither of which are trivial issues. Second, one must determine how to redistribute mass vertically to remove the available energy. It is this second part of the convective adjustment with which STT is primarily concerned. Suppose that the vertical redistribution of mass that must be accomplished by convection to remove the available energy is unique to the initial thermodynamic profile. If this were the case, then the STT taking place in this convection during the adjustment process would also be unique. However, there is no reason to suppose that this is the case. In fact, there may be many legitimate permutations of mass redistribution that could remove the available energy [Tailleux and Grandpeix, 2004]. Therefore, the questions to consider are: What are the possible redistribution permutations? What are the likelihoods and contingencies for each? The differences between STT in simulations of the same convective event performed with different models/configurations may be analyzed within this context. Putting triggering and initiation issues aside, the maximum difference would be given by the range of possible vertical redistribution permutations. On the basis of our results, we hypothesize that this range is not typically broad enough to allow an order of magnitude difference in the mass exchange across vertical levels where the convection is active. For this reason, the total STT within simulated deep convection is relatively insensitive to the manner by which the convection is represented in the model, provided the general characteristics of the precipitating system do not vary significantly between the different model configurations.
 This work was supported by the National Centre for Atmospheric Science (NCAS) under the Weather Directorate. The authors are grateful to three anonymous reviewers for suggesting many improvements to the original draft. The authors wish to thank the Met Office for making the MetUM available, NCAS Computational Modelling Support for supporting the use of the MetUM and for providing boundary and initialization data, and David Hooper of the Rutherford Appleton Laboratory for recommending cases for analysis.