Volume 120, Issue 14 p. 7174-7188
Research Article
Free Access

Numerical simulations of extratropical tropopause-penetrating convection: Sensitivities to grid resolution

Cameron R. Homeyer

Corresponding Author

Cameron R. Homeyer

School of Meteorology, University of Oklahoma, Norman, Oklahoma, USA

Correspondence to: C. R. Homeyer,

[email protected]

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First published: 04 July 2015
Citations: 16

Abstract

Deep extratropical convection that penetrates and overshoots the altitude of the tropopause has important implications both for chemistry-climate interactions through stratosphere-troposphere exchange and for hazardous weather at the Earth's surface. In this study, the sensitivity of tropopause structure and cross-tropopause transport to the choice of numerical model resolution in simulations with explicitly resolved convection (i.e., no convective parameterization) is examined. For an observed case of overshooting convection, the Advanced Research Weather Research and Forecasting (ARW-WRF) model is run for all possible combinations of three horizontal (3 km, 1 km, and 333.33 m) and vertical (600 m, 300 m, and 150 m) grid resolutions. Although ARW-WRF is successful in producing tropopause-penetrating convection in each case, the depth of overshooting and cross-tropopause transport are found to increase with refinement in the horizontal dimension and decrease with refinement in the vertical dimension. These results are related to changes in storm intensity and the sharpness of the tropopause, where the former is found to increase with refinement in the horizontal dimension and the latter is found to increase with refinement in the vertical dimension. Comparisons of simulated storm altitudes with those observed from ground-based radar reveal large positive biases in simulations where the horizontal resolution is fine and the vertical resolution is coarse.

Key Points

  • Simulated storm altitudes and transport are sensitive to resolution
  • Tropopause structure is sensitive to vertical resolution
  • Storm intensity is sensitive to horizontal resolution

1 Introduction

Stratosphere-troposphere exchange (STE) is an important process that impacts the chemistry of the upper troposphere and lower stratosphere (UTLS) including radiatively important (greenhouse) trace gases such as ozone and water vapor [e.g., Holton et al., 1995; Stohl et al., 2003]. Processes contributing to STE encompass a broad range of spatial and temporal scales. Large-scale processes are well known and represented in numerical models. However, the impact of small-scale process, such as deep convection, is not entirely understood and these processes are not resolved in current global climate models.

Observational and modeling studies have documented mechanisms for and estimates of cross-tropopause transport in deep convection. Many of these studies focus on the tropics, where the hydration of the lower stratosphere via coupling between deep convection and large-scale ascent in the Brewer-Dobson circulation and/or monsoon anticyclones is the primary motivation [e.g., Mote et al., 1996; Sherwood and Dessler, 2000, 2001; Gettelman et al., 2004; Fu et al., 2006; Randel et al., 2010; Heath and Fuelberg, 2014]. Overshooting convection in the tropics has been found to be most frequent over land and able to both hydrate and dehydrate the lower stratosphere [e.g., Liu and Zipser, 2005; Jensen et al., 2007; Corti et al., 2008; Hassim and Lane, 2010; Pan and Munchak, 2011; Frey et al., 2015]. More recently, persistent deep convection in the tropical West Pacific has been linked with extremely low upper troposphere ozone concentrations (<20 ppbv) and argued to lead to a reduction in the oxidizing capacity of the troposphere such that otherwise short-lived ozone-destroying substances can be routinely transported into the stratosphere [Rex et al., 2014]. Recent field campaigns have been conducted to study this low-ozone region and characterize the importance of this transport mechanism for atmospheric chemistry and climate.

The impacts of overshooting convection in the extratropics are less known, though it has received a considerable amount of attention in recent years. Climatological characteristics of overshooting extratropical convection are largely limited to analyses using geostationary satellites over small regions [e.g., Bedka et al., 2010]. Several studies have documented evidence of cross-tropopause transport of ozone and water vapor from deep convection using aircraft observations [e.g., Fischer et al., 2003; Hegglin et al., 2004; Ray et al., 2004; Hanisco et al., 2007; Anderson et al., 2012; Homeyer et al., 2014a; Pan et al., 2014; Schroeder et al., 2014]. Many of these studies focus on individual cases of overshooting storms. Since direct measurement of convective overshoots is not possible with current research aircraft and alternative instrumentation, studies of tropopause-penetrating convection in the extratropics with high-resolution numerical models have also been common [e.g., Stenchikov et al., 1996; Gray, 2003; Wang, 2003; Mullendore et al., 2005; Lane and Sharman, 2006; Luderer et al., 2007; Chagnon and Gray, 2007, 2010; Lane and Sharman, 2014; Homeyer et al., 2014b; Bigelbach et al., 2014]. These modeling studies have identified important mechanisms for irreversible troposphere-to-stratosphere transport including gravity wave breaking and turbulent mixing. Stratosphere-to-troposphere transport mechanisms in overshooting convection have received little attention, though recent observations suggest that wrapping of stratospheric air around the perimeter of detraining anvil clouds is an important process and can be reproduced in numerical models [Pan et al., 2014].

Important questions pertaining to cross-tropopause transport in extratropical convection that require further attention include the following: (1) How deep and how often do storms penetrate into the extratropical stratosphere? (2) What is the impact of deep convection on the concentration and distribution of ozone, water vapor, and additional trace gases in the extratropical UTLS? (3) How does transport vary depending on storm type and organization? and (4) What is the sensitivity of model simulations of convective overshooting and transport to the choice of physical parameterization and grid resolution? The last question is important for studies of overshooting convection regardless of location and is the motivation for this study. In particular, the sensitivity of convective overshooting and transport to numerical model resolution can impact studies that seek to answer the remaining questions outlined above.

The dynamics and chemistry of any atmospheric process have important scale dependencies. For modeling studies, there are common conditions that are necessary for preventing numerical error and/or noise associated with spatial and temporal grid resolution. The Courant-Friedrichs-Lewy condition requires that integration time steps be less than the time scale of the process simulated in order for convergence of finite differencing calculations [Courant et al., 1928]. Lindzen and Fox-Rabinovitz [1989] have argued that, for accurate simulation of dynamics, the aspect ratio between horizontal and vertical resolutions be consistent with dispersion relations and/or the Rossby deformation radius of the simulated waves so that noise and/or spurious gravity waves are not generated. Gravity waves are routinely generated in deep convection and, as previously outlined, critical to simulations of troposphere-to-stratosphere transport. Though the consistent horizontal and vertical scales outlined in Lindzen and Fox-Rabinovitz[1989] are untenable in simulations with explicitly resolved convection, most models include horizontal eddy diffusion-filter damping to prevent and/or mitigate generation of spurious waves.

In addition to numerical stability conditions, several studies have illustrated that small horizontal grid spacing [O(100 m)] is required for accurate representation of gravity wave spectra and the physical process of cloud turbulence, both of which are important for convective transport and mixing [e.g., Bryan et al., 2003; Lane and Knievel, 2005; Bryan and Morrison, 2012]. Some of these studies also show that predictions of precipitation, convective updraft size, transport, and additional quantities can differ significantly when compared to cloud-resolving simulations at coarser and more commonly used horizontal resolutions [O(1 km)]. Weisman et al. [1997] and Cotton et al. [2011] have shown that convective updraft speeds increase rapidly with refinement in the horizontal dimension due to changes in the nonhydrostatic pressure perturbation. Sensitivity studies of similar parameters to changes in the vertical grid resolution are less common but show important variability related to the location and extent of refinement in the vertical dimension [e.g., Aligo et al., 2009]. Such dynamical and physical sensitivities of deep and/or overshooting convection and transport to model resolution must be identified further before these processes can be represented with confidence both in case studies and longer simulation time periods.

In this study, sensitivities for the physical characteristics of tropopause-penetrating convection and STE to changes in both the horizontal and vertical grid resolutions are examined using version 3.5 of the Advanced Research Weather Research and Forecasting (ARW-WRF) model [Skamarock et al., 2008]. Ground-based radar observations are used to evaluate the fidelity of the model simulations. Suggestions for the choice of grid resolution in future convective transport studies are given based on the results of this study.

2 Model Design

ARW-WRF is a fully compressible, nonhydrostatic three-dimensional cloud-resolving model. Simulations for this study are completed at three horizontal (Δx = 3 km, 1 km, 333.33 m) and vertical (Δz = 600 m, 300 m, 150 m) grid resolutions. For each vertical grid resolution, one-way nesting toward reduced horizontal grid spacing is performed beginning on a parent domain with 9 km horizontal grid resolution. Initial and lateral boundary conditions for the parent domain are taken from 6-hourly ERA-Interim global atmospheric reanalyses produced by the European Center for Medium-Range Weather Forecasts (ECMWF) [Dee et al., 2011]. The horizontal resolution of ERA-Interim is ∼80 km and the vertical resolution is 650–1000 m in the extratropical UTLS. Figure 1 shows the parent domain and the domains for each of the three horizontal resolutions used in the nested domain simulations.

Details are in the caption following the image
The domains of the ARW-WRF simulations completed in this study. The yellow star represents the location of the radiosonde in Figure 2.

ARW-WRF provides numerous options for the parameterization of physical processes including the planetary boundary layer (PBL), cloud microphysics, and atmospheric radiation. Since the goal of this study is to examine the sensitivity of simulated convection and transport to grid resolution alone, the choice of physics parameterizations and additional model parameters outlined below are held fixed for all simulations. The sensitivity of the results presented to the choice of physical parameterizations is not known. For parameterization of PBL processes and vertical diffusion, the YSU scheme is used [Hong et al., 2006]. Smagorinsky first-order turbulence closure is used for subgrid scale mixing in the horizontal dimension. For cloud microphysics, the Morrison two-moment bulk cloud microphysics parameterization (BMP) is used, which predicts the mixing ratio and number concentration of five hydrometeors: cloud water, cloud ice, rain, snow, and graupel [Morrison et al., 2009]. For short-wave and long-wave radiation, the RRTMG parameterization is used [Iacono et al., 2008]. The momentum and scalar advection schemes used in the model are fifth order in the horizontal and third order in the vertical.

The vertical grid spacing in each simulation increases gradually from ∼150 m near the surface to the target grid spacing at 4 km and remains constant at higher altitudes in order to (1) represent well boundary layer processes including surface turbulent momentum and thermal fluxes and (2) maintain resolution higher than or equivalent to the initial and lateral boundary conditions from ERA-Interim [e.g., Aligo et al., 2009]. The duration of each model simulation is 18 h, initialized at 18 UTC on 2 April 2012. ARW-WRF output is retained for analysis at 30 min intervals. A model top of 30 hPa (∼25 km) is used with dynamical damping applied to the upper 5 km in order to prevent spurious wave generation and wave reflection.

For transport analysis, passive tracers initialized in the troposphere and stratosphere are used in the model. The stratospheric tracer is initialized as 100% of the mass in grid volumes above the tropopause, where the altitude of the tropopause is determined following the definition of the World Meteorological Organization (WMO): “the lowest altitude at which the temperature lapse rate decreases to 2 K km−1 provided that the average lapse rate from this level to any point within the next higher 2 km does not exceed 2 K km−1” [World Meteorological Organization, 1957]. The tropospheric tracer is initialized as 100% of the mass in grid volumes at or below the height of the PBL, as determined by the YSU PBL physics scheme. Only the PBL is considered for the tropospheric tracer in order to isolate transport in deep convection, since transport of PBL air into the lower stratosphere from large-scale processes does not occur during the simulation time period. The PBL tracer is reinitialized at every model time step to account for diurnal variations in the PBL height and to provide a continuous supply of boundary layer tracer for transport analysis. Both tracers are reset in the entire column (i.e., transport is removed) near the lateral boundaries of each domain and at every model time step to prevent exchange between the parent and nested domains.

Observations used for evaluation of the simulated storms are from the Next Generation Weather Radar (NEXRAD) program Weather Surveillance Radar—1988 Doppler (WSR-88D) network in the contiguous United States [Crum and Alberty, 1993]. WSR-88Ds are S-band (10 cm wavelength) radars that are operated continuously by the National Weather Service. WSR-88D data are provided by the National Climatic Data Center (NCDC) on native spherical grids. During periods of deep convection, radar volumes for a single WSR-88D system are obtained every 4–7 min. The methods outlined in Homeyer [2014] and modified in Homeyer and Kumjian [2015] are used to create three-dimensional composites of the radar data at a horizontal resolution of 0.02 longitude-latitude (∼2 km) and 1 km in the vertical. Based on comparisons with higher-resolution satellite-based radar observations, uncertainty in the altitude of a given convective system from the composite radar data is about 500 m.

For comparison of the simulated convection with the radar observations, built-in routines in the ARW-WRF model are used to compute the equivalent horizontally polarized radar reflectivity for an S-band radar. These routines are based on that outlined in Morrison et al. [2009], taking into account Rayleigh scattering only (sufficient for comparisons with S-band) and the effects of partially melted graupel and snow. The simulated cloud top is also used for comparison and is taken to be the highest altitude of cloud particle concentrations of 0.1 per liter or greater.

3 Case Description: 2–3 April 2012

Due to the large amount of computational resources required for the sensitivity simulations and the limited area enclosed by the fine-scale domains, a case with relatively slow storm motion was chosen for this study. The targeted storm was a severe convective squall line that initiated along a deep negatively tilted upper level trough and surface cold frontal boundary extending across the U.S. central Great Plains from western Ohio to southwest Texas. Magnitudes of surface-based Convective Available Potential Energy (CAPE) ahead of the cold front were moderate, mostly ranging from 2000 to 2500 J kg−1. Figure 2 shows the skew-T log-P thermodynamic diagram for the radiosonde observation at 00 UTC on 3 April 2012 from the Norman, Oklahoma National Weather Service forecast office. The path for a surface-based convective parcel and related thermodynamic variables are superimposed. The altitude of the tropopause is ∼11.5 km (217 hPa). The ARW-WRF model simulations encompass a portion of the cold front in the Texas and Oklahoma panhandles that propagated eastward into central Oklahoma between 21 UTC on 2 April 2012 and 12 UTC on 3 April 2012 (the time period of the convective line). There were additional convective systems that formed throughout the remaining portion of the day on 3 April in central and eastern Oklahoma, but those are not targeted in these simulations, which terminate at 12 UTC on 3 April.

Details are in the caption following the image
A skew-T log-P thermodynamic diagram from the 00 UTC radiosonde on 3 April 2012 in Norman, Oklahoma. Sonde observations of air and dew point temperatures are given by the light red and green profiles, respectively. Dry (dark red solid lines) and moist (dark green solid lines) adiabatic lapse rates, constant temperatures (blue solid lines), and constant water vapor mixing ratios (dark green dashed lines) are also shown. Thermodynamic quantities derived from a surface-based convective parcel (thick black line in diagram) including the lifting condensation level (LCL), level of free convection (LFC), level of neutral buoyancy (LNB), convective available potential energy (CAPE), convective inhibition (CIN), and lifted index (LI) are provided in a table below the diagram. The WMO lapse-rate tropopause is shown by the dashed gray line.

Figure 3 shows maps of observed column-maximum radar reflectivity and 15 dBZ echo top height relative to the 00 UTC radiosonde tropopause altitude for the target storm at 1 h increments. The target squall line initiated in the Texas panhandle near 23 UTC on 2 April and reached altitudes up to 2 km above the tropopause within 2 h (Figure 3a). During the following 4 h, the storm continued to penetrate the tropopause as it translated eastward through Texas, Oklahoma, and Kansas (Figures 3b–3e). By 06 UTC, the convective line was decaying and storm top altitudes were limited to several kilometers below the tropopause. A second tropopause-penetrating storm system (seen as the southernmost cells in Figure 3e) had developed by this time and translated to the south and east along the Red River and Oklahoma-Texas border during the next several hours.

Details are in the caption following the image
NEXRAD WSR-88D radar observations of (left panels) column-maximum radar reflectivity and (right panels) 15 dBZ echo top altitude relative to the tropopause level valid at (a) 01, (b) 02, (c) 03, (d) 04, and (e) 05 UTC on 3 April 2012.

4 Results

In order to achieve consistent comparisons between simulations at differing resolution, all results presented in the following subsections correspond to the area confined within the smallest nested domain, i.e., that with Δx = 333.33 m. The Δx = 333.33 m domain has an area of about 148,000 km2. Analysis of model output is limited to the 02–05 UTC time period on 3 April 2012, corresponding to the time when the tropopause-penetrating storm was mature in all simulations. This time period is comparable to that observed from the NEXRAD WSR-88D radar network in Figure 3.

4.1 Storm Organization and Intensity

The organization and intensity of convection are important characteristics that help determine the transport potential of simulated storms. Thus, analysis of these characteristics is a logical starting point for examining sensitivity to model resolution. Figure 4 shows column-maximum radar reflectivity from all ARW-WRF simulations at a single time during the study period (03 UTC on 3 April 2012, compare to observed storm in Figure 3c). Although the timing of the simulated and observed storms is similar, there are several physical differences worth noting. First, the organization of all simulated storms conforms to the classic leading-line trailing-stratiform (LLTS) mesoscale convective system [e.g., Houze et al., 1989]. The observed storm, however, is a convective line with leading and trailing nonprecipitating anvil regions (i.e., no stratiform rain region). While such a difference in storm organization could have important implications for transport, particularly related to the extent of transport and mixing within the troposphere or from stratosphere-to-troposphere associated with the anvil wrapping mechanism, it is expected that the most important discrepancies between the simulated storms and that observed are related to meteorological parameters such as precipitation. The trailing stratiform rain region in the simulations becomes more pervasive as Δz decreases, while showing little sensitivity to Δx.

Details are in the caption following the image
For ARW-WRF simulations at 03 UTC on 3 April 2012: maps of column-maximum radar reflectivity as a function of horizontal (Δx) and vertical (Δz) grid spacing.

Another important physical characteristic related to storm organization and intensity is the radar reflectivity factor. When compared to the WSR-88D observations, the simulated storms largely overestimate reflectivity in stratiform rain regions. These biases increase with refinement in the vertical dimension. Large differences between observed and simulated reflectivity are not uncommon and have often been related to the incomplete (or vastly simplified) representation of microphysical composition and processes in bulk microphysics parameterizations [e.g., Done et al., 2004; Blossey et al., 2007].

In order to better diagnose storm intensity in the ARW-WRF simulations, the commonly used proxy of maximum convective vertical velocity (or updraft speed) is given in Table 1. In addition, the maximum area occupied by convective updrafts is provided in Table 2, in order to provide linkages between intensity and transport characteristics. As outlined in section 1, previous studies have shown that simulated convective updraft speeds increase rapidly with decreasing Δx. Some studies have also shown that as Δx decreases, the size (or area) of individual convective updrafts decreases (i.e., they become stronger and narrower). Table 1 provides two important diagnostics: (a) the maximum updraft speed at any vertical model level to estimate peak intensity and (b) the maximum updraft speed near the tropopause to determine the depth of convective updrafts, which is relevant for cross-tropopause transport. Table 2 presents similar diagnostics for updraft area rather than speed in order to further examine sensitivities relevant to transport.

Table 1. Maximum Convective Updraft Speed (in m s−1) During the Analysis Time Period (02–05 UTC on 3 April 2012) For Simulations With Chosen Horizontal (Δx) and Vertical (Δz) Grid Spacinga
Δx (m)
333.33 1000 3000
600 54 (48) 41 (25) 28 (14)
Δz (m) 300 51 (50) 39 (29) 24 (15)
150 47 (47) 40 (36) 30 (23)
  • a Maxima are listed for both the entire three-dimensional grid and for a single vertical level near the tropopause (∼11.5 km; within parentheses in the table).
Table 2. As in Table 1 But for Maximum Area (in % of Study Domain) Covered by Convective Updrafts (Vertical Velocity ≥3 m s−1)
Δx (m)
333.33 1000 3000
600 6.02 (0.52) 5.95 (0.28) 3.95 (0.05)
Δz (m) 300 8.19 (1.08) 6.82 (0.27) 4.42 (0.16)
150 10.15 (1.02) 7.53 (0.41) 4.26 (0.17)

The simulations in this study provide results consistent with previous work, with updraft speeds increasing uniformly with decreasing Δx, resulting in incremental differences larger than 10 m s−1 in most cases (see Table 1). However, the sensitivity of storm intensity to Δz is more complex. While changes in overall maximum updraft speed show little sensitivity to Δz, the maximum updraft speed near the tropopause level increases with decreasing Δz in most cases, approaching magnitudes similar to the overall maximum in each simulation. This result demonstrates that vertical grid spacing impacts storm intensity through changes in the depth of convective updrafts, while horizontal grid spacing primarily affects their magnitude.

For the area of convective updrafts, which is important for transport potential, there are clear and consistent sensitivities to grid resolution. Namely, total updraft area increases as both Δx and Δz decrease (see Table 2). This result suggests that although previous studies have found individual convective updrafts to decrease in size with decreasing Δx, the number of updrafts (and areal coverage) increases. Together, the identified increases in storm intensity (updraft speed) and areal coverage imply that cross-tropopause transport will increase as model grid spacing is decreased. Note that a subjective vertical velocity threshold of 3 m s−1 is used to identify convective updrafts here, but the sensitivities outlined above do not vary with changes in this threshold.

4.2 Tropopause Modification and Structure

Previous studies have illustrated that the altitude of the tropopause increases in the vicinity of tropopause-penetrating convective systems [e.g., Poulida et al., 1996; Homeyer et al., 2014b]. Thus, in order to provide accurate measures of convective penetration depth and STE, identification of the tropopause in each grid column and at each model time step is required. As outlined in section 3 and illustrated in Figure 2, the altitude of the tropopause in the preconvective environment for the simulated case in this study is about 11.5 km. Though not shown, tropopause altitudes in the ARW-WRF simulations prior to convective development are comparable to the observations and within the uncertainty inherent to the coarser vertical grid resolution in the ERA-Interim initial conditions (∼800 m). Domain-averaged tropopause altitudes during active periods of convection are similar, with altitudes up to 12 km near the deepest elements of the simulated storms. Differences in the tropopause altitude among the simulations prior to and during active periods of convection are smaller than differences in Δz and show little to no sensitivity to Δx, implying that varying grid resolution in the ranges investigated here has no significant impact on the predicted altitude of the tropopause.

Perhaps more important for limiting both the vertical extent of convection and STE is the sharpness of the tropopause. The sharpness of the tropopause is defined in this study as the change in static stability from troposphere to stratosphere (i.e., with increasing altitude), where for a finite depth a larger change in stability represents a sharper tropopause. In the extratropics, the lower stratosphere is typically characterized by a strong temperature inversion (and “jump” in static stability) within altitudes 2–3 km above the tropopause, referred to as the tropopause inversion layer [e.g., Birner et al., 2002; Birner, 2006]. In order to characterize the sharpness of the tropopause in the ARW-WRF simulations, we compute the domain-averaged temperature and Brunt-Väisälä frequency N (static stability) at altitudes relative to the tropopause. Figure 5 shows these profiles for all simulations with Δx = 1 km at a select time during the analysis period and the initialized profiles from ERA-Interim. Results for simulations at the remaining horizontal grid spacings and model output times after the initiation of convection are comparable.

Details are in the caption following the image
For ARW-WRF simulations with horizontal grid spacing (Δx) of 1 km: (a) temperature and (b) static stability (Brunt-Väisälä frequency N) at altitudes relative to the tropopause for vertical grid spacing (Δz) of 600 m (long dashed lines), 300 m (short dashed lines) and 150 m (solid lines). The simulation time for all profiles is 05 UTC on 3 April 2012. Initialized profiles from ERA-Interim are shown in gray (prestorm environment).

Figure 5 demonstrates that the sharpness of the tropopause increases incrementally with refinement in the vertical dimension. In particular, the maximum stability above the tropopause increases with decreasing Δz and the depth of the stability transition from troposphere to stratosphere decreases, both of which lead to a sharpening of the tropopause. This sensitivity in tropopause sharpness is not the result of changes in Δz alone. Profiles in all simulations prior to the development of convection resemble that at Δz = 600 m since the initial conditions are provided at coarser vertical resolution than the chosen grid spacings in this study. As the simulations progress, the tropopause sharpens due to the combined ascent and cooling of the upper troposphere in response to deep convection. The choice of Δz limits the degree to which the tropopause can sharpen in response to convection. In particular, since the strongest cross-tropopause vertical mixing is between the tropopause level and the next highest/lowest model levels, the depth of the mixing layer and limit to tropopause sharpness scale with Δz. This is further evident in the tropopause-relative temperature profiles, where the simulation with largest Δz produces the deepest cooling of the lower stratosphere and, consequently, weakening of the tropopause inversion layer.

Sharpening of the tropopause with refinement in the vertical dimension has important implications for convective penetration depth and cross-tropopause transport. Principally, for a positively buoyant convective parcel reaching the tropopause, the negative buoyancy imposed on the parcel as it ascends into the lower stratosphere is roughly doubled as Δz is reduced from 600 to 150 m for the profiles in Figure 5, leading to more rapid deceleration of an ascending parcel.

4.3 Storm Altitudes and Transport

Because observations of cross-tropopause transport from convection are largely limited to a few case studies from aircraft, the representativeness of modeling studies examining convective transport must be determined using alternative measurements of convection that are readily available. One such data set is the three-dimensional composite radar product used in this study, which provides information on the vertical extent of convection at high spatial and temporal resolution. Measurements of the vertical extent of convection can be compared with that simulated in the model to provide confidence in transport predictions. Figure 6 shows comparisons of storm altitude from the 10 dBZ echo top observed in the radar composite and both equivalent radar reflectivity and cloud particle concentrations from ARW-WRF for the entire analysis time period. For each model variable two tables are given: one presenting mean altitudes and the other maximum altitudes as a function of Δx and Δz in the simulations. Mean storm altitudes are computed using only the grid columns where radar reflectivity or cloud particles exist. Each table is color filled by the altitude difference between simulation and observation.

Details are in the caption following the image
For ARW-WRF simulations during the 02–05 UTC 3 April 2012 study period: tables of (left) domain-averaged storm altitudes and (right) domain-maximum storm altitudes as a function of horizontal (Δx) and vertical (Δz) grid spacing. All altitudes are given in kilometers. Storm altitudes are determined by (top row) the 10 dBZ equivalent radar reflectivity surface or “echo top” and (bottom row) the 0.1 per liter cloud particle concentration or “cloud top.” Each table is color filled by the altitude bias relative to that from the NEXRAD WSR-88D radar observations listed in the titles for each column.

Figure 6 shows that the domain-averaged echo top in the model is largely biased low compared to observation. This result is comparable to that demonstrated in previous studies [e.g., Homeyer et al., 2014b] and is likely due to limited representation of ice particle shapes and densities and differential sedimentation of precipitable particles in the BMP. However, the domain-averaged cloud top is found to be 1.5–2 km higher than that observed by radar and is expected based on the limitations of the measurement, providing confidence in the representativeness of the simulated storms. In particular, since the radar observations used are S-band, detection of only large precipitable particles is possible. In addition, because the majority of the storm area consists of nonconvective rain regions, the larger particles often do not encounter vertical motions capable of lifting them to the cloud top. The cloud top and echo top are expected to be comparable in convective rain regions since the vertical motions are stronger and parcels containing precipitable hydrometeors routinely ascend to altitudes above the LNB and upper tropospheric anvil cloud. The comparisons of domain-maximum storm top between ARW-WRF simulations and radar observations in Figure 6 largely reflect these characteristics. Notably, though the domain-averaged cloud top is found to be 1.5–2 km above that observed from radar in all simulations, the domain-maximum is found to be less than 1.5 km above that observed in most cases. However, these comparisons do show that convective depths are significantly overestimated (>2 km above that observed) when Δx is small and Δz is large. This is also evidenced by the comparisons of domain-maximum echo top altitudes, which show similar sensitivity to grid spacing. The domain-maximum echo top altitude comparisons also show that radar reflectivity in the model is biased low regardless of vertical grid spacing when the horizontal grid spacing is coarse (i.e., Δx = 3 km).

The large bias in storm top altitude for simulations with small Δx and large Δz reflects well the identified sensitivities in storm intensity and tropopause sharpness outlined previously. In particular, since convective updraft speeds increase with refinement in the horizontal dimension it is expected that storm altitudes would also increase as Δx decreases. Similarly, since the tropopause sharpens (and negative buoyancy for a tropopause-crossing parcel increases) with refinement in the vertical dimension it is expected that maximum storm altitudes would decrease as Δz decreases. Figure 6 further reveals these competing sensitivities and their impact on the fidelity of simulated storm depth and associated transport. Consideration of these sensitivities is required when interpreting the transport distributions that follow.

Figure 7 shows tropopause-relative altitudes of the passive tropospheric (boundary layer) tracer from each ARW-WRF simulation for the same analysis time as that in Figure 4 for column-maximum radar reflectivity. Previously outlined structural differences and sensitivities in storm altitudes are well represented in these maps, with decreasing area of boundary layer tracer reaching altitudes >600 m above the tropopause as Δz decreases and increasing area as Δx decreases. Figure 7 also reveals that the largest depths of injection of the passive tracer into the stratosphere are similar in each simulation, which is outlined in further detail below. It should also be noted here that transport features in the far eastern portion of the domain in the Δx = 1 and 3 km simulations are not sourced by the target convective line and have a minor/negligible impact on the magnitudes and characteristics of the total cross-tropopause transport estimates presented in the remainder of this section.

Details are in the caption following the image
As in Figure 4, but for maximum altitudes of the boundary layer tracer relative to the tropopause level.

Figures 8 and 9 show STE diagnostics for water vapor (H2O) and passive tracers in the ARW-WRF simulations. In Figure 8a, domain-averaged profiles of H2O at a time of mature tropopause-penetrating convection for simulations with Δz = 300 m are given at relative altitudes to the tropopause in order to reveal the depth of the lower stratosphere that is broadly/routinely moistened by the storm. For comparison, the initial domain-averaged profile (i.e., that prior to convective development) is also given. Figures 8b–8d show the domain-averaged change in H2O relative to the prestorm environment at tropopause-relative altitudes for simulations with Δz of 600, 300, and 150 m, respectively. These profiles illustrate the sensitivity of convective injection of H2O to the competing storm intensity and tropopause structure outlined in the previous analyses. In particular, the above-tropopause depth and magnitude of H2O injection increase as Δx decreases and decrease as Δz decreases. This sensitivity to grid resolution is largest at altitudes immediately above the tropopause level, where the increase in domain-averaged H2O mixing ratios ranges from 17–27 ppmv at Δz = 600 m to 10–15 ppmv at Δz = 150 m (about a factor of 2 difference for simulations at constant Δx).

Details are in the caption following the image
For ARW-WRF simulations at 04 UTC on 3 April 2012: domain-averaged profiles at altitudes relative to the tropopause of (a) water vapor (H2O) mixing ratio for simulations with vertical grid spacing (Δz) of 300 m and the change in H2O mixing ratio relative to the prestorm environment for simulations with Δz of (b) 600 m, (c) 300 m, and (d) 150 m. Red, gray, and blue lines correspond to simulations with horizontal grid spacing (Δx) of 3 km, 1 km, and 333.33 m, respectively.

Figure 9 shows domain-averaged and extreme STE diagnostics as a function of grid resolution for the entire analysis period using the passive tropospheric and stratospheric tracers included in ARW-WRF (see section 2). In particular, Figure 9a shows maximum tropopause-relative altitudes of troposphere-to-stratosphere transport (TST) inferred from the tropospheric tracer. Maximum altitudes of convective H2O enhancements in the lower stratosphere (>5 ppmv) are also given for comparison. For constant Δz, there is a slight increase in the depth of tracer TST with decreasing Δx. The depth of TST for H2O and its sensitivity to Δx is larger than that for the passive tracer, particularly as Δx decreases from 1 km to 333.33 m. These differences between H2O and the passive tracer are expected since increases in H2O are due both to transport of tropospheric air and sublimation of lofted ice particles. In addition, it should be noted that while these characteristics further reveal the depth of penetration and advection of air into the lower stratosphere, they do not necessarily suggest that significant (or irreversible) transport has taken place at these levels since air penetrating to the highest altitudes would be negatively buoyant. Domain-averaged TST (Figure 9c) shows inconsistent sensitivity to grid resolution. Notably, TST at Δx = 1 km is nearly equivalent at all Δz, while the magnitudes of TST increase (decrease) as Δz decreases for larger (smaller) Δx. However, these domain-averaged values do not take into account the uncertainty in the altitude of the tropopause, which is typically comparable to the vertical grid spacing. If considering only TST at altitudes above the maximum tropopause uncertainty in all simulations (i.e., Δz = 600 m), important sensitivities are revealed (Figure 9e). In particular, “deep” TST is shown to increase as Δx decreases and decrease as Δz increases, again consistent with established sensitivities in storm intensity and tropopause sharpness.

Details are in the caption following the image
For ARW-WRF simulations during the 02–05 UTC 3 April 2012 study period and as a function of horizontal grid spacing (Δx): (a) maximum tropopause-relative altitudes of troposphere-to-stratosphere transport (TST), (b) minimum tropopause-relative altitudes of stratosphere-to-troposphere transport (STT), (c) domain-averaged TST, (d) domain-averaged STT, (e) domain-averaged TST at altitudes >600 m above the tropopause, and (f) domain-averaged STT at altitudes >600 m below the tropopause. Results are displayed at constant vertical grid spacing (Δz): 600 m (long dashed lines), 300 m (short dashed lines), and 150 m (solid lines). TST and STT determined from passive tracers are shown in each panel, with TST of water vapor (identified as >5 ppmv in the stratosphere) included in Figure 9a.

Figure 9b shows minimum tropopause-relative altitudes of stratosphere-to-troposphere transport (STT) inferred from the stratospheric tracer included in ARW-WRF. These extrema show little to no sensitivity to Δx in the simulation, but do show a slight decrease in the lowest tropopause-relative altitude of STT as Δz decreases. In contrast, domain-averaged STT (Figure 9d) shows greater sensitivity to Δx, with STT decreasing as Δx decreases. There is no apparent sensitivity of domain-averaged STT to Δz. However, similar to that for TST, “deep” STT (Figure 9f; that reaching altitudes more than 600 m below the tropopause) reveals clear and consistent sensitivities to grid resolution that are not identified when including layers within the uncertainty of the tropopause. In particular, deep STT is found to decrease as Δx decreases and increase as Δz decreases, which is exactly the inverse of the grid spacing sensitivity for deep TST. In addition, magnitudes of STT exceed that of TST in most cases with the largest imbalances at large Δx and small Δz.

5 Summary and Discussion

Using the ARW-WRF model, nine simulations with explicitly resolved convection were completed in order to determine the sensitivity of tropopause-penetrating convection and STE to the choice of horizontal and vertical grid resolution. Several physical and dynamical characteristics of the simulated storms were examined. In agreement with previous studies, the intensity (updraft velocity) of simulated storms was shown to increase with decreasing Δx. While storm intensity was largely insensitive to changes in Δz, the depth of convective updrafts was found to increase with refinement in the vertical dimension (see Table 1). The altitude of the tropopause, which represents the boundary between troposphere and stratosphere and thus the critical level required for identification of STE, was found to vary little with changes in Δx or Δz. However, the sharpness of the tropopause was found to increase significantly with decreasing Δz.

Sensitivities in storm altitudes to grid resolution were shown to be representative of the competing influence of sensitivity in storm intensity and tropopause sharpness. Comparisons of the simulated storm altitudes with ground-based radar observations revealed that simulations with small Δx and large Δz significantly overestimate the altitude of the storm, implying that transport is biased in those cases. Using water vapor (H2O) and passive tracers in the model, troposphere-to-stratosphere transport (TST) and stratosphere-to-troposphere transport (STT) were estimated in each case. The transport analyses revealed that the depth and magnitude of hydration in the lower stratosphere are most sensitive to changes in Δz, with the injection of water vapor decreasing as Δz decreases and increasing as Δx decreases. Transport of passive tracers revealed consistent resolution sensitivity in deep TST and deep STT (that reaching altitudes beyond the uncertainty in the tropopause definition). In particular, TST was found to increase with decreasing Δx and decrease with decreasing Δz and STT was found to have the inverse sensitivity.

All model simulations in this study produced a leading-line trailing-stratiform mesoscale convective system, while the observed storm was a convective line with nonprecipitating leading and trailing anvil regions. It is worth noting that the Morrison BMP used in this study was designed to improve the representation of trailing stratiform precipitation in LLTS convective systems. While improving the representation of precipitation is an important problem, in the author's experience the Morrison BMP generates trailing stratiform rain regions in most convective systems regardless of the observed organization. Morrison et al. [2009] show that much of their success in stratiform rain production can be attributed to the prediction of two moments of the hydrometeor size distributions rather than less expensive single-moment predictions. Thus, more complex microphysical parameterizations that better represent differential sedimentation of hydrometeors and consequently their vertical distribution may lead to further improvements in the representation of simulated storms and observed variability in their organization. Using more complex microphysics could also lead to a reduction in the biases between observed and simulated radar reflectivity (e.g., compare Figures 3 and 4).

An important topic that was not addressed in this study is the sensitivity of convectively generated gravity wave spectra and gravity wave breaking to grid resolution, which have been shown in previous studies to be sensitive to changes in Δx [e.g., Lane and Knievel, 2005]. Though breaking gravity waves can be a critical component of troposphere-to-stratosphere transport, examination of the simulations in this study did not reveal any wave behavior that would significantly impact analysis of STE (not shown). In particular, visual inspection of constant-altitude maps and vertical cross sections of potential temperature, passive tracers, and additional relevant variables suggested that there were no significant critical layers (altitudes of preferred wave breaking) in the vicinity of the simulated storms.

Based on the results presented in this study, it is recommended that future model simulations with explicitly resolved tropopause-penetrating convection use Δx = O(1 km) and Δz≤300 m. These recommendations are largely based on the accuracy of simulated storm altitudes which, as outlined throughout, are related to sensitivities in the storm intensity and sharpness of the tropopause. While such horizontal grid spacing is common practice in current forecasting and research efforts, the common vertical grid spacing used is similar to the maximum in this study (600 m). The results here suggest that coarse Δz can lead to an overestimation in the altitude of a simulated storm and a likely biased view of STE. Moreover, it should be noted that these recommendations and identified sensitivities do not necessarily apply to large eddy simulation since turbulence and mixing is resolved in such cases and the requisite grid resolution is equivalent to or finer than the minima used in this study.

An important limitation of this study is that only one case is analyzed due to the large computational expense and required storage space for the model output. Despite this limitation, some of the identified sensitivities are expected to be common regardless of varying storm organization and environmental characteristics. First, the established sensitivity in storm intensity has been observed in several previous studies and can be related to resolution-induced changes in nonhydrostatic pressure perturbation [e.g., Cotton et al., 2011]. Second, the sharpness of the tropopause is expected to be sensitive to the choice of vertical grid spacing in all cases since the tropopause mixing layer scales with Δz. Third, the competing effects of storm intensity and tropopause sharpness are expected to produce transport sensitivities consistent with that in this study, while the magnitude of transport (and updraft velocity) will ultimately depend on the precise characteristics of a storm and its environment. Additional sensitivity tests of simulated tropopause-penetrating convection will help to further reveal the impacts of grid resolution on the characteristics of these storms and the degree to which they transport air between troposphere and stratosphere. Examining sensitivities to physical parameterizations (e.g., microphysics and PBL) in the models is also an important topic for future work.

Acknowledgments

The author acknowledges NCDC for access to the NEXRAD WSR-88D radar observations used in this study and ECMWF for providing the ERA-Interim reanalysis output, which were obtained from the Research Data Archive (RDA) maintained by the Computational and Informational Systems Laboratory (CISL) at the National Center for Atmospheric Research (NCAR); the original data are available at http://has.ncdc.noaa.gov/ and http://rda.ucar.edu/, respectively. The author also thanks three anonymous reviewers for their excellent comments and suggestions for improving the manuscript.