1. Introduction
The representation of moist convection in atmospheric numerical models is an important source of uncertainty and potential error (Molinari and Dudek 1992; Holloway et al. 2014). Although the march toward finer grid spacings that are capable of resolving convective processes proceeds apace, many large-scale regional models, global NWP systems, and climate models will be forced to parameterize convection for the foreseeable future (Arakawa et al. 2016). Many of these systems employ schemes that relate the deep convective activity directly to the convective available potential energy (CAPE) of the near-storm environment (Yano et al. 2013). In contrast, the topic of representing convection in environments with limited conditional instability (low CAPE) has received relatively little attention. However, accurately depicting such events is shown here to have the potential to impact the quality of the model solution significantly.
The potential for vigorous moist convection in low-instability environments represents a predictability and detection challenge because traditional conceptual models and severe weather indices fail to identify such regions of possible convective activity (McCann 1978; Vescio and Thompson 2001; Davis and Parker 2014). Adopting the ingredients-based view of convection (Doswell 1987; Doswell et al. 1996), all developing cells require ascent, access to moisture, and a source of instability. In the low-CAPE context (including the zero-CAPE limit), the first two of these are typically associated with the warm sectors and frontal boundaries of midlatitude cyclones (Jewett and Wilhelmson 2006; Clark 2009; Evans 2010). The importance of strong synoptic and mesoscale forcing for ascent in the preconvective environment is emphasized by van Den Broeke et al. (2005) in relation to the quasi-linear mesoscale convective systems that can develop parallel to cold fronts under low-CAPE conditions. Along the leading edge of these fronts, the poleward transport of moisture in the warm conveyor belt (Carlson 1980; Eckhardt et al. 2004) contributes to satisfying the moisture requirement of the ingredients-based perspective (King et al. 2017). These associations are reinforced by recent studies of high-shear, low-CAPE (HSLC) convective storms (Sherburn and Parker 2014) and the environments in which they form (Sherburn et al. 2016).
Identifying the source of instability, the final necessary ingredient for convection, can be challenging in the low-CAPE environments considered here. However, Schultz and Schumacher (1999) provide a framework for understanding how potential and symmetric instabilities can be tapped by convection under low-CAPE conditions. Convective case studies by Carr and Millard (1985) and Clark (2009) highlight the possible importance of an elevated dry intrusion, which can reduce the equivalent potential temperature (θe) aloft to create a potentially unstable layer. Such a feature is also identified by Evans (2010) to be related primarily to warm-season low-CAPE events in eastern North America, while Sherburn and Parker (2014) conclude that most HSLC-related severe weather reports occur in environments characterized by at least moderate potential instability.
The importance of potential instability to moist convection was first recognized by Rossby (1932) in his consideration of layers in which ∂θe/∂p > 0 K Pa−1 (his definition of “convective instability” is identical to the “potential instability” terminology adopted here). Schultz et al. (2000) provide a detailed review of early studies on the subject, along with a description of the process that converts this near-instability to one that leads to the buoyant acceleration of ascending parcels (Sherwood 2000). The key to realizing potential instability is sustained lifting that leads to condensation at the base of the potentially unstable layer. Continued ascent steepens the lapse rate within the layer, a change that leads to the production of CAPE (Schultz et al. 2000). However, this layer is likely to be neither horizontally homogeneous nor lifted uniformly to saturation. As a result, condensation occurs at the convective cloud scale before forced ascent can convert potential instability into CAPE over a large area (Sherwood 2000). Kreitzberg and Perkey (1976) use a Lagrangian updraft (plume) model to describe how this “releasable instability” fuels quasi-equilibrium convection in which CAPE values remain low throughout the convective life cycle.
The dynamically forced vertical layer displacements required to convert potential instability into CAPE are typically largest in the free troposphere, leading to the development of elevated convection as the potential instability is released (Rosenow et al. 2018). Corfidi et al. (2008) define elevated convection as any convection whose inflow source lies above the boundary layer, a characteristic that distinguishes this class of event from its more common counterpart that relies on surface heating for initiation. The close relationship between low-CAPE and elevated convection in environments of potential instability was initially described by Colman (1990a,b), and more recently investigated by Sherburn and Parker (2014). Moore et al. (2003) provide a process-level description of this connection, concluding that potential instabilities are likely to be most relevant for elevated convection of the “frontal overrunning” type. This archetype bears a strong resemblance to the “escalator–elevator” concept illustrated by Neiman et al. (1993), in which a sloping warm conveyor belt ascent is punctuated by upright convection as localized pockets of potential instability are released. These conceptual models provide further evidence of the strong links between potential instability and elevated convection in low-CAPE environments.
The representation of deep convection under low-CAPE conditions presents a challenge to atmospheric models that are run at resolutions that are too coarse to depict explicitly the convective ingredients involved (Randall et al. 1997; Anderson et al. 2002). The problem is particularly acute for models that employ convection parameterization schemes that are sensitive to the conditional instability represented by CAPE (for example, Fritsch and Chappell 1980; Betts 1986; Kain and Fritsch 1990; Zhang and McFarlane 1995; Bechtold et al. 2001). In environments with little to no CAPE, such schemes either will fail to trigger or will depict exceedingly weak convection. A numerical model that fails to parameterize the effects of subgrid-scale convection will suffer from systematic errors in the form of delayed convective initiation (Weisman et al. 1997), insufficient triggering (Petch et al. 2002), and excessive vertical mass fluxes and precipitation rates generated by the gridscale condensation scheme (Kato and Saito 1995; Weisman et al. 1997; Roberts and Lean 2008).
In low-CAPE environments with sufficient potential instability and moisture, sustained lifting may lead to convective initiation. In a model with an inactive CAPE-dependent deep convection scheme, no parameterization represents this subgrid-scale process. Instead, the gridscale condensation scheme depicts latent heating at the base of the potentially unstable layer as the grid cell-averaged relative humidity nears saturation in the ascending airstream (Teixeira 2001; Quass 2012). The associated buoyancy increase fuels further ascent, leading to continued condensation as any CAPE generated by the realized potential instability is consumed via the “gridpoint storm” mechanism (Scinocca and McFarlane 2004). This unphysical process results in precipitation “bull’s-eyes” as the gridscale condensation scheme couples with the dynamical core to develop moist convective motions at the minimum length scale of the model. This problem is a direct result of the model’s inability to simulate accurately the release of low-CAPE instabilities (potential instability in this example) via subgrid-scale processes.
Models that employ a class of convective schemes whose activity depend on moisture convergence (Bougeault 1985; Tiedtke 1989; Banacos and Schultz 2005) have the potential to represent better the effects of convection in low-CAPE environments. This assertion is supported by results of Suhas and Zhang (2015), who conclude that closures based on this quantity yields the highest correlation with observed convection; however, they note that all relationships to the large-scale state weaken as model resolution increases. Schemes that are particularly well suited to represent the release of potential instability are those that can act in low-CAPE environments in response to elevated synoptic and mesoscale forcings for ascent. Such “midlevel” convection schemes are employed in operational systems run at both ECMWF (Tiedtke 1989) and UKMO (Gregory and Rowntree 1990); however, their impact on predictions of convection and overall guidance quality have not been documented extensively in the literature.
The purpose of this study is to describe the implementation of a convection scheme designed to represent the effects of convection in low-CAPE environments. The scheme’s development was motivated by concerns expressed by forecasters about the prevalence of precipitation bull’s-eyes in guidance generated by the Canadian Regional Deterministic Prediction System (Caron et al. 2015). This error mode is consistent with insufficient triggering of the CAPE-dependent Kain and Fritsch (1993)-based scheme that is used to parameterize deep convection in the model. The trigger and closure elements of the low-CAPE scheme draw heavily from existing midlevel convection parameterizations (Tiedtke 1989; Gregory and Rowntree 1990), consistent with the relationship between elevated and low-CAPE convection. However, in keeping with a process-oriented viewpoint and the ingredients-based framework, the new scheme will be referred to hereafter as a “low-CAPE” convection parameterization, with the “midlevel” terminology adopted only in specific reference to these predecessor formulations.
The investigation begins with an overview of the datasets and numerical model employed in this research in section 2, followed by a description of the parameterization itself in section 3. The impact of representing low-CAPE convection on summer precipitation events is evaluated in section 4, whereas the overall influence of the parameterization on guidance quality is assessed in section 5. The study concludes with a discussion of the broader implications of these results in section 6.
2. Data and model description
This study employs data from several observing networks for case study descriptions (section 4) and model evaluations (section 5). In situ data consist primarily of radiosonde and surface observations available over the Global Telecommunication System. Included in the surface observational dataset are precipitation accumulations measured at synoptic weather stations that have passed the quality control stage of the Canadian Precipitation Analysis (Lespinas et al. 2015) to ensure a baseline of validity.
Spatial precipitation structures are evaluated using the quantitative precipitation estimate from the Multi-Radar Multi-Sensor (MRMS) system, derived from gauge-corrected radar retrievals (Zhang et al. 2016). The atmospheric state is assessed using primarily the ERA-Interim (Dee et al. 2011), although the higher-resolution ERA5 (Hersbach et al. 2018) is employed for the analysis of mesoscale structures (section 4a).
The Global Environmental Multiscale (GEM) model is used in all operational applications at the Canadian Meteorological Centre. The implicit, semi-Lagrangian dynamical core solves the full governing equations on a latitude–longitude grid (Côté et al. 1998; Husain and Girard 2017). The terrain following vertical coordinate is of the log-hydrostatic-pressure type (Girard et al. 2014).
This study employs the Regional Deterministic Prediction System, in which the GEM model is configured to run hydrostatically with 0.09° (~10 km) grid spacing and a 300-s time step. In the vertical 84 levels are distributed between the surface and the 0.1-hPa model lid, with 12 levels below 850 hPa in a standard atmosphere and the lowest thermodynamic level at ~10 m above ground.
The physical parameterizations adopted by the Regional Deterministic Prediction System recently underwent a major upgrade (McTaggart-Cowan et al. 2019a). Of direct relevance here are the moist atmospheric processes that are handled primarily by either the gridscale condensation scheme (Sundqvist 1978), or by one of the model’s convection parameterizations. The latter include the shallow convection scheme proposed by Bechtold et al. (2001), a modified version of the Kain and Fritsch (1993) deep convection scheme (McTaggart-Cowan et al. 2019b), and the parameterization for low-CAPE convection described here. In addition to the direct impact of these schemes on state variables, each of these parameterizations interacts with the radiation scheme through the cloud-radiation interface described by McTaggart-Cowan et al. (2019a).
3. A low-CAPE convection scheme
The formulation of the low-CAPE convection scheme described here is based loosely on the ECMWF (2018) description of the midlevel variant of the Tiedtke (1989) scheme. An overview of the convective plume-based mass-flux scheme is provided in Fig. 1 for reference. The utility of such a Lagrangian updraft model in low-CAPE environments was first demonstrated by Kreitzberg and Perkey (1976), who investigated the parameterization of moist convection in the presence of potential instability. To avoid the double-counting of moist convective effects, the new scheme is only tested for possible activity where CAPE values are below 250 J kg−1. This limit that is more restrictive than the 500 J kg−1 typically used to identify HSLC events (Sherburn and Parker 2014), a reflection of the precedence given to the deep convection scheme in environments with moderate conditional instability (ECMWF 2018; McTaggart-Cowan et al. 2019a). Unlike HSLC severe storm studies; however, no wind shear condition is applied because the intent of the scheme is to represent the full range of low-CAPE convective intensities.
Schematic of the major components of the low-CAPE convection scheme. Yellow cylinders represent exchanges of information with other model components (specific quantities are itemized with orange boxes and dashed lines at the bottom of the plot), blue boxes represent major elements of the parameterization, and red parallelograms represent logical branches or conditions. Symbol definitions and values for the Regional Deterministic Prediction System are defined in Table 1.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
Definition of symbols used in Fig. 1, with values defined for the Regional Deterministic Prediction System for applicable parameters.
a. Trigger function
The trigger function for the low-CAPE scheme is relatively simple in comparison with the highly parameterized triggers used for deep convection (Suhas and Zhang 2014). Consistent with the conceptual model of “frontal overrunning” (Weckwerth et al. 2019), resolved vertical motions form the basis for convective initiation. These vertical wind speeds (w) can become large as gravitational or symmetric instabilities are released, particularly when the gridscale condensation scheme predicts latent heating in ascending airstreams.
Air at the first level at which the Eq. (1) inequality is satisfied is lifted to its lifting condensation level to seed the updraft (section 3b). Unlike the equivalent procedure in standard deep convection schemes, multiple layers are not mixed to create updraft parcel properties because there is no requirement for turbulent inflow as layers are dynamically lifted to initiate low-CAPE convection.
b. Updraft
c. Downdraft
Downdrafts resulting from elevated, low-CAPE convection typically occur in environments with both significant downdraft convective available potential energy and downdraft convective inhibition (Market et al. 2017). The latter limits the downdraft’s ability to reach the surface, such that downdraft detrainment may occur within the stable layer that lies beneath the updraft source level. This behavior distinguishes such convection from its boundary layer–based counterpart, for which downdraft detrainment typically occurs over a relatively shallow near-surface layer.
Although such differences in downdraft characteristics will have an impact on cold pool formation and potential secondary initiation (Kain and Fritsch 1998; Marion and Trapp 2019), there is no distinction from the perspective of the underlying physical processes. As such, a downdraft model that is similar to the one described by Kain and Fritsch (1993) is employed in the low-CAPE convection scheme. The top of the downdraft [the level of free sink (LFS)] coincides with the level possessing the minimum environmental saturation equivalent potential temperature in the cloud layer. Detrained moisture is evaporated into environmental air at this level to establish
The full profiles of Md, εd, and δd are rescaled based on the amount of condensate available for evaporation in the downdraft. The latter is related to (1 − Ep)P, where P represents the precipitation flux. In the Regional Deterministic Prediction System, Ep is set to 0.4 as an intermediate estimate of the efficiencies of convective clouds with bases more than 1.5 km above the ground (Fig. 12b of Fankhauser 1988). Alternative formulations for Ep that account for the subcloud environmental state either directly (Bluestein and Parks 1983) or indirectly via gridscale evaporation rates, failed to improve guidance skill beyond that which was achieved with the constant efficiency estimate.
d. Closure
The prescription of
e. Solver
Equation (8) is solved implicitly within the parameterization. This numerical decision reduces the need for time-splitting and improves the convergence properties of the scheme with respect to the small time-step limit.
4. Heavy precipitation case study
An unusual flow pattern over North America provides a useful test bed for illustrating the behavior of the low-CAPE convection scheme described in the previous section. On 6 July 2016, low-CAPE convection occurred both in the form of isolated convective cells in northern Ontario and as part of a long-lived squall line in the midwestern United States. A focus on this date therefore serves to document the performance of the parameterization in the context of different observed convective modes.
Each case study begins with an analysis of observational data related to convective activity. These comparisons with observed storm evolution represent attempts to ensure that the new scheme is acting in a physically reasonable manner, and that improvements in the model solution are not the result of error compensation within the system.
A jet streak centered over Quebec places both of the areas of interest in the confluent entrance region (Fig. 2a). The midwestern squall line develops in the equatorward jet entrance, an optimal location for quasigeostrophic forcing for midtropospheric ascent (Namias and Clapp 1949; Uccellini and Johnson 1979; Bluestein and Thomas 1984). The baroclinicity that supports the anomalous jet appears in the form of a pair of zonally oriented fronts that straddle the international border (Fig. 2b). Both convective events are initiated in close proximity to these fronts, consistent with conceptual models of convective development in low-instability environments (van Den Broeke et al. 2005; Sherburn et al. 2016).
Synoptic environment at 0000 UTC 6 Jul 2016 as depicted in the ERA-Interim. (a) The upper-tropospheric state is shown at 250 hPa with heights (black contours; 12-dam intervals), winds (wind barbs, with short, long, and pennant barbs representing 5, 10, and 25 m s−1 wind speeds, respectively; barbs are only plotted for wind speeds exceeding 10 m s−1) and wind speed (shaded; in m s−1, as indicated on the color bar). (b) The lower-tropospheric state is shown with sea level pressure (black contours; 4-hPa intervals) and fronts from the operational surface analysis produced by the Weather Prediction Center, as well as surface cyclone (“L”) and anticyclone (“H”) positions from the same source. In both panels, the location of the Pickle Lake sounding station is shown with a cyan crosshair symbol, the Aberdeen station is shown with a yellow crosshair symbol, and the domains of interest for the case studies are outlined: the northern Ontario domain in red in (a), and the midwestern domain in dark magenta in (b). Also shown in (b) is the first-echo location of the convective features highlighted in the case studies (green thunderstorm symbols), both of which appear prior to the valid time of this analysis.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The GEM simulations described in this section are based on integrations of the 0000 UTC 6 July 2016 Regional Deterministic Prediction System (section 2), run with the low-CAPE scheme either activated (LC) or turned off (CTL). The latter is considered the control configuration because the operational atmospheric physics suite did not contain a parameterization for low-CAPE convection until mid-2019 (McTaggart-Cowan et al. 2019a). Because an incremental analysis update technique based on a 6-h assimilation window is employed in this system (Buehner et al. 2015), the model is initialized at 2100 UTC 5 July for all integrations. This strategy permits a “hot start” of the model, in which physical quantities (including cloud and turbulence fields) are recycled within a continuous integration framework. The associated reduction of model spinup permits analyses of short-range predictions, a behavior that is useful in the current context because the divergence of solutions between model integrations is minimized even for the relatively small-scale features considered here (Zhang and Wu 2003).
To ensure the robustness of the results described in this section, multiple simulations were carried out on this case with different domain configurations, all of which yield qualitatively similar results. This suggests strongly that differences between the integrations are physically robust and not the result of “chaos seeding” (Ancell et al. 2018).
a. Isolated convection in northern Ontario
The origins of scattered, intense convection in northern Ontario are assessed in this section (quantitative precipitation estimates and relevant locations are shown in Fig. 3). The release of elevated potential instability leads to precipitation “bull’s-eyes” in simulations run without the low-CAPE convection scheme. This case highlights the direct influence that the scheme can have on the reduction of small-scale precipitation extremes.
Quantitative precipitation estimates (shaded; in mm h−1, as shown on the color bar) from the MRMS dataset at hourly intervals from (a) 2100 UTC 5 Jul to (h) 0400 UTC 6 Jul 2016. The domain employed for subsequent Ontario case study maps is outlined with a black box in each panel, and the location of the Pickle Lake sounding station is shown with a cyan crosshair symbol in (d) for reference. Surface fronts are plotted as in Fig. 2 when frontal analyses are available.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
1) Observed evolution
Isolated convective cells develop over northwestern Ontario at 2100 UTC 5 July (1700 local time), immediately poleward of the warm-frontal boundary in the region (Fig. 3a). The storms remain anchored to this feature at 0000 UTC (Fig. 3b), despite their rapid eastward progression under a strong westerly flow aloft (Fig. 2). By 0400 UTC (local midnight), the cells have largely dissipated, although scattered showers remain throughout the area.
The 0000 UTC 6 July Pickle Lake sounding is taken to be representative of conditions poleward of the surface front in the preconvective environment (Fig. 3d), wherein the radiosonde intersects the baroclinic zone near 850 hPa (Fig. 4). The sounding provides preliminary evidence that the three ingredients for convective initiation are present. The saturated layer above the frontal inversion contains ample moisture for convection, while the veering wind profile across this layer implies warm advection (“frontal overrunning”) and attendant quasigeostrophic forcing for ascent. The source of instability is less clear, as daytime heating has failed to warm the boundary layer sufficiently to overcome the convective inhibition of the 850-hPa inversion. The profile is nearly moist adiabatic above this level, devoid of appreciable CAPE. However, drying in the 750–550-hPa layer leads to a negative vertical gradient in equivalent potential temperature (θe) that is indicative of potential instability (Fig. 5).
Sounding from Pickle Lake for 0000 UTC 6 Jul 2016. The temperature is shown in red and the dewpoint is shown in blue. Winds are plotted with barbs as in Fig. 2. The sounding location is shown in Figs. 2 and 3d.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
(left) Profile of equivalent potential temperature θe labeled on the abscissa as “Eq. Pot. Temp.” and shown in the plot with a solid black line) in the Pickle Lake sounding for 0000 UTC 6 Jul 2016 (Fig. 4). Potentially unstable layers, highlighted with a red background, are computed as positive values of the vertical gradient of θe (∂θe/∂p > 0 K Pa−1) following the application of a digital filter to remove structures less than 40 hPa in depth. (right) The resulting gradient profile is shown with a dashed gray line at neutral potential stability for reference.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The release of potential instability requires layer lifting via forced ascent that may occur at synoptic scales or at the mesoscale. The ERA5 is therefore used to assess convective ingredients in the near-storm environment over the 850–750-hPa layer that is likely to represent the convective inflow (Fig. 6). A local maximum in relative humidity is indicative of available moisture (Fig. 6a); however, values remain generally below 80% in the region of interest and may serve as a limiting factor on the areal extent of convection. A similar maximum in frontogenesis (Fig. 6b) implies a forcing for mesoscale ascent in the secondary circulation across the baroclinic zone (Keyser et al. 1988). The final convective ingredient, instability, is assessed as ∂θe/∂p, which is positive in areas of potential instability (Fig. 6c). Combining these three ingredients with a set of thresholds determined by inspection of this case,1 it becomes clear that the bulk of convective activity occurs in the area where the local extremes of the convective ingredients overlap (Fig. 6d). This suggests that the observed convection in this low-CAPE region forms in response to frontogenetic forcing in a relatively moist, potentially unstable environment.
Ingredients for convection at 0000 UTC 6 Jul 2016 over the northern Ontario region outlined in Fig. 3. All quantities represent averages over the 850–750-hPa layer as diagnosed from ERA5. (a) Moisture availability is shown using relative humidity (plotted as a percentage, with a heavy red line at 70%), (b) forcing for mesoscale ascent is shown using quasi-horizontal frontogenesis (Petterssen 1936) (plotted as 1 × 10−10 K m−1 s−1 with a heavy green line at 0 × 10−10 K m−1 s−1), and (c) instability is shown using ∂θe/∂p (plotted as 1 × 10−4 K kg m−1 s−2 with a heavy blue line at 5.5 × 10−4 K kg m−1 s−2). (d) The thresholds for the ingredients are superposed, with light, medium, and dark gray shading representing one, two, and three threshold exceedences, respectively. Also shown in (d) is the MRMS precipitation rate estimate (mm h−1, as shown on the color bar) and a 10-km scale for reference.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
Before comparing the precipitation-rate estimates from the MRMS dataset with model predictions, the scale mismatch between the 1-km observations and the 10-km model grid must be addressed, particularly given the small-scale nature of the convective elements (Fig. 6d). Because the heavy-precipitation cores cover only a small fraction of the model grid, peak precipitation rates in the model should not match those of the observations. Arguably, any model-generated precipitation structure that is below about 7Δx is underresolved; however, for the purposes of addressing solely the representativeness issue, conservative remapping of the MRMS data to the model grid suffices (Fig. 7). The impact of this remapping on the precipitation maxima is large, with peak rainfall rates dropping to below 20 mm h−1. The strong influence of grid size in this case is physically relevant because it indicates that the scales associated with the convective motions are much smaller than those that can be explicitly represented by the model.
Precipitation rate (in mm h−1, as shown on the color bar) at 0000 UTC 6 Jul 2016 over the northern Ontario region outlined in Fig. 2, as estimated by the MRMS dataset on (a) the original 1-km grid and (b) remapped onto the 10-km grid of the Regional Deterministic Prediction System. The rate shown in (b) is computed using the conservative regridding capacity of the Earth System Modeling Framework (Hill et al. 2004). The track of the precipitation maximum on the 10-km grid is shown with heavy black line in (b), with hourly markers (time is in UTC) color coded following the color bar. Also shown in each panel is a 10-km scale for reference. The plot-domain-averaged precipitation rate is shown in the top-left corner of each panel.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
2) Simulated evolution
The CTL model integration for this event successfully simulates the development of precipitation in northern Ontario in the short-range forecast (Fig. 8a). However, bull’s-eyes in which precipitation rates exceed 30 mm h−1 are apparent in the precipitation field. Although such rainfall intensities are consistent with the localized maxima estimated in the full-resolution MRMS dataset (Fig. 7a), they are clearly excessive on a 10-km grid (Fig. 7b). This broadening of the precipitation cores leads to area-averaged CTL rainfall rates that nearly double the observational estimate (Figs. 7b and 8a).
Precipitation rate at 0000 UTC 6 Jul 2016 in the (a) CTL and (c) LC integrations, for comparison with the remapped MRMS estimate shown in Fig. 7b. (b),(d) The convective precipitation component is shownfor the CTL and LC integrations, respectively. (In the LC integration, convective precipitation includes contributions from both the deep and low-CAPE convection schemes.) All fields are plotted in mm h−1, as shown on the color bars at the bottom of the plot. The track of the precipitation maximum is shown with heavy black line in each panel, with hourly markers (time is in UTC) color-coded following the color bars. The 0000 UTC 6 Jul rainfall rate marker in (a) obscures the grid cell with a value >40 mm h−1 in the CTL integration. The average precipitation rate over the plot domain is shown the top-left corner of each panel.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
In a region of convective inhibition (CIN = −25 J kg−1) and small CAPE (90 J kg−1), the CTL model is releasing the potential instability via the gridpoint storm mechanism. Despite being clearly convective in nature (Fig. 7), precipitation in the CTL integration results primarily from the gridscale scheme, with only trace contributions from the deep convection parameterization because of limited CAPE (Fig. 8b). The underresolved updrafts tap potential instability at the finest scales possible in the 10-km model, but these dimensions remain much larger than reality in this case. The result is unrealistically broad updrafts that generate excessive precipitation rates.
When the low-CAPE convection scheme is activated (the LC integration), the isolated precipitation maxima of the CTL integration are replaced by an extended area over which rainfall rates approach 20 mm h−1, in line with the MRMS estimate (cf. Figs. 7b and 8c). Although the regionally averaged convective rainfall rate only increases by 0.1 mm h−1, the ratio of convective to total precipitation rises from <20% to 50% in this integration (based on domain-average precipitation rates annotated in Fig. 8). The rainfall reduction and change in convective ratio are persistent differences between the CTL and LC integrations (Fig. 9) during both the primary convective period (2100 UTC 5 July–0200 UTC 6 July) and a secondary event that is overpredicted by the model (after 0200 UTC 6 July). The dramatic reduction in precipitation rates predicted by the gridscale condensation scheme is an indication that the potential instability is processed through parameterized moist turbulence in the low-CAPE convection scheme, rather than being extracted through an underresolved interaction between gridscale condensation and model dynamics.
Time series of maximum total (solid) and convective (dashed) precipitation rates following the convective event in northern Ontario from the model initialization time (2100 UTC 5 Jul 2016) to 0600 UTC 6 Jul (tracks are shown in Fig. 8). Rainfall estimates from MRMS on the 10-km regional grid are show in black, while those from the CTL and LC integrations are shown in blue and red, respectively, as indicated in the legend. The 0000 UTC 6 Jul valid time considered in the discussion is identified with a vertical dashed line for reference.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
b. Squall line in the midwestern United States
The evolution of an intense squall line over the midwestern United States is outlined in this section (quantitative precipitation estimates and relevant locations are shown in Fig. 10). The cold pool generated by initially elevated cells promotes the development of surface-based deep convection and plays an important role in establishing squall-line structure in simulations with the low-CAPE scheme activated. This case highlights the indirect impact that the scheme can have on convective organization.
Rain-rate estimates (in mm h−1, as shown on the color bars) from MRMS at 3-hourly intervals from (a) 2100 UTC 5 Jul to (h) 1800 UTC 6 Jul 2016. Also shown in each panel are the locations of the surface stations referred to in the text: target markers for Morris, Minnesota (KMOX); Minneapolis, Minnesota (KMSP); La Crosse, Wisconsin (KLSE); and Rockford, Illinois (KRFD). The location of the Aberdeen sounding (Fig. 11) is shown in (a).
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
1) Observed evolution
The convective cells that represent the beginnings of the midwestern squall line form over western Minnesota at 1700 UTC 5 July 2016 (local noon; not shown). The 1800 UTC Aberdeen sounding (Fig. 11; 150 km to the west of the convective initiation) is not favorable for surface-based convection despite daytime surface heating because cold northerly flow undercuts the warmer air above the 850-hPa frontal inversion to create large CIN (−300 J kg−1). Instead, the Aberdeen sounding represents an environment on the cold side of the surface front that is conducive to the development of elevated convection (Horgan et al. 2007).
Aberdeen sounding for 1800 UTC 5 Jul, plotted as in Fig. 4. Green annotations show the effects of lifting a parcel to a 700-hPa cloud base, with a dashed line for the mixing ratio, a dotted line for the potential temperature, and a solid line for undilute moist adiabatic ascent. The sounding location is shown in Figs. 2 and 10a.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
Near 1800 UTC, the Morris Municipal Airport (KMOX) reports thunderstorms with cloud bases up to 2500 m above ground (~700 hPa), consistent with parcels that have undergone forced ascent from above the frontal inversion (Fig. 11 annotations). Parcels ascending from this level still need to overcome a 100-hPa layer of strong negative buoyancy before beginning free convective ascent in a “tall and thin” low-CAPE environment (Blanchard 1998). A decrease in equivalent potential temperature of 10 K between 850 and 650 hPa (Fig. 12) suggests that mesoscale ascent associated with the frontal circulation may have initiated elevated convection in this case (Trier and Parsons 1993), supported by synoptic-scale ascent in the equatorward jet entrance region (Fig. 2a). METAR reports indicate that convection remains elevated (2000 to >3000 m above ground) as the developing line passes through Minneapolis at 0000 UTC 6 July.
Profile of equivalent potential temperature (θe) in the Aberdeen sounding for 1800 UTC 5 Jul (Fig. 11), plotted as in Fig. 5.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
Over the next 6 h, the squall-line convection transitions from elevated to surface-based. Despite the development of a conceptual model by Rockwood and Maddox (1988), the processes involved with such a transition have not been studied extensively, particularly in the context of such linear features (Gray and Frame 2019). However, Marsham et al. (2011) show that evaporatively cooled downdrafts can play an important role in secondary convective initiation (Bennett et al. 2006). As the elevated squall line passes through La Crosse, Wisconsin (ceilings are ~3000 m above ground during the 0300 UTC passage), a robust cold pool is evident at the surface (Fig. 13). Screen-level temperatures drop by 6°C as the squall line passes, as winds turn to the north and increase to 18 m s−1(gusting to 30 m s−1). This evolution closely follows the conceptual squall-line model of Johnson and Hamilton (1988), and yields a density current that is capable of lifting near-surface air along the gust front to facilitate the initiation of surface-based convection (Wakimoto 1982). Observed cloud bases in the squall line drop to below 1 km as convection moves through Rockford, Illinois, shortly after 0600 UTC (Fig. 10), indicative of a completed transition from elevated to surface-based convection.
Time series of surface METAR observations at La Crosse, Wisconsin, between 0000 and 1200 UTC 6 Jul 2016. (a) Temperature, (b) sea level pressure converted from reported altimeter setting, (c) wind speed, and (d) wind direction. The units for each plot are labeled on the ordinate of the panel. A vertical gray line in all panels identifies the passage of the squall line at 0300 UTC 6 Jul 2016, while horizontal dashed gray lines in (d) identify the cardinal points for reference.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The length of the squall line increases after transition, and a large region of trailing stratiform precipitation develops by 0900 UTC (Fig. 10e). By 1800 UTC the latter has disappeared, but the remnant bowing line extends for over 700 km across southern Illinois and Indiana (Fig. 10h).
2) Simulated evolution
At the 2100 UTC 5 July initialization time of the GEM integrations, the elevated convective cells that initiate the squall line are already active over central Minnesota (Fig. 10a). Despite the “hot start” strategy, the model’s representation of convective structure is initially relatively poor. In the CTL integration, precipitation maxima bracket the observed location of the developing squall line at 0000 UTC 6 July (cf. Figs. 10b and 14a). When the low-CAPE convection scheme is activated, a coherent precipitation maximum appears in the region, although the convective mode does not reflect the linear structure of the observed rainfall (Fig. 15a).
Precipitation rates at 6-hourly intervals from the CTL integration, split into (left) total and (right) convection-only rates (shaded; in mm h−1 following the color bars). Also shown in each panel using a heavy black contour is the position of the observed squall line as analyzed from MRMS data (Fig. 10). The left column of this figure is directly comparable to the right column of Fig. 10.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
As in Fig. 14, but for the LC integration. The subdomain used to investigate early storm evolution in Figs. 16 and 17 is outlined with dark green in (a).
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
Despite being the only difference between the CTL and LC integrations, the low-CAPE convection scheme is not directly responsible for the difference in precipitation patterns at 0000 UTC 6 July (Figs. 14a and 15a), and is active only around the periphery of the rainfall maximum (Fig. 16b). However, the parameterization plays an important role in promoting the organization of this feature, as evidenced by its widespread activation in the region just 1 h earlier (Fig. 16a). This elevated convective initiation is consistent with both the environmental sounding (Fig. 11) and the observed cloud bases at this early stage of the squall-line life cycle.
Precipitation rates (in mm h−1) from the LC integration (a) 2 and (b) 3 h after initialization (valid times as indicated in the panels). The component of precipitation coming from the low-CAPE convection scheme is shown using the magenta lines of the vertical color bar, while the remainder of precipitation from all other sources is shown using the colors of the horizontal color bar. The southern Minnesota domain for this plot is indicated by the dark green outline in Fig. 15a.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The cold pool processes involved in the transition from elevated to surface-based convection appear to be well represented in the LC simulation, although they occur at least 3 h earlier than observed. The cold pool formed by downdrafts in the low-CAPE convection scheme extends across southeastern Minnesota after 2 h of integration (Fig. 17). Enhanced upward motion is evident along the leading edge of this feature, consistent with forced ascent at the head of a density current (Wakimoto 1982). The fact that precipitation is light or absent in these areas (less than 0.2 mm of accumulation after 2 h as shown in Fig. 17) suggests that the enhanced ascent is acting to relatively moisten and destabilize the preconvective environment, rather than simply identifying regions in which condensation is fueling buoyant updrafts. Consistent with the transition process described by Marsham et al. (2011), the cold pool is thereby facilitating the initiation of surface-based convection early in the LC integration. Cloud bases drop to 1000 m above ground after just 3 h of integration (0000 UTC 6 July), indicating the completion of the transition well before the developing squall line passes La Crosse, Wisconsin. This represents a transition timing error in the LC integration; however, the lack of elevated convection in the CTL configuration means that these processes are entirely absent in that simulation.
Cold pool enhancement after 2 h of integration, valid at 2300 UTC 5 Jul 2016. Total accumulated precipitation (in mm) is shown with gray shading at the 0.2-mm threshold as indicated on the vertical color bar. Cold pool enhancement is shown as LC-minus-CTL screen-level temperatures (in K) using solid contours blue-shaded as indicated on the horizontal color bar, and vertical motion enhancement (again computed as LC minus CTL) at the 0.85 hybrid-coordinate model level (Girard et al. 2014) is red-stippled for upward motions exceeding 0.5 Pa s−1. The domain for this plot matches that of Fig. 16, as indicated by the dark green outline in Fig. 15a.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
Without a robust initiating cold pool, precipitation patterns in the CTL integration remain relatively disorganized throughout the remainder of the integration (Fig. 14). This behavior stands in stark contrast to the LC simulation, in which widespread rainfall is predicted along the path of the observed squall line (Fig. 15). The enhanced cold pool in the LC simulation, defined as the LC-minus-CTL difference in screen level temperature, evolves in a manner that aligns with the structural differences in rainfall (Fig. 18). The cold pool difference increases to 6°C in the 6-h forecast (valid at 0300 UTC), consistent with the magnitude of the storm-related cooling observed at La Crosse (Fig. 13). A precursor cold pool also appears ahead of the squall line over northeastern Missouri at this time (Fig. 18b), where the low-CAPE convection scheme accurately predicts convective activity that is absent in the CTL integration (not shown). The enhancement of the primary cold pool increases to a maximum of 8°C by the end of the squall-line life cycle, with cold air extending across Illinois and Indiana behind the well-positioned decaying squall line in the LC integration. Screen-level temperature errors are reduced by ~20% across the region at all lead times (Fig. 18), a result that is indicative of improved cold pool structure in the LC simulation.
Cold pool enhancement shown as LC-minus-CTL screen-level temperatures (shaded; in °C, as shown on the color bars) at 6-hourly intervals for valid times from (a) 0000 to (d) 1800 UTC 6 Jul 2016. Also shown in each panel using a heavy black contour is the position of the observed squall line as analyzed from MRMS data (Fig. 10). The root-mean-square error (RMSE) for both simulations is shown in the top-right corner of each panel, computed against analyses from the Regional Deterministic Prediction System run with the latest model configuration (McTaggart-Cowan et al. 2019a). These analyses are used for evaluation because they employ the same grid definition and model orography as the CTL and LC simulations, two factors for which inconsistencies complicate the estimation of near-surface errors.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
5. Impact on NWP guidance
Analysis of the behavior of the low-CAPE convection scheme in the case study context (section 4) is useful for confirming that the parameterization acts in a physically realistic manner. However, an evaluation of the impact of the scheme on guidance skill over a large number of cases representing different environments is essential for NWP purposes.
Performance of the Regional Deterministic Prediction System is assessed in this section using the same configurations as in the preceding analysis: the CTL integrations are run without a low-CAPE convection scheme, while the LC integrations employ the parameterization described in section 3. The July–August 2016 period is considered here because the introduction of the low-CAPE convection scheme has little systematic impact on winter guidance. This is consistent with the fact that although the bulk of low-CAPE convection in the southeastern United States occurs in the cool season (King et al. 2017), such events are more frequent at night and during the warm season across the remainder of the continent (Evans 2010; Main et al. 2018). Forecasts are initialized from operational analyses at 36-h intervals in order to reduce computational load while promoting serial independence. This dataset is further stratified by initial synoptic hour (0000 and 1200 UTC) for near-surface evaluations to avoid smoothing the diurnal cycle; the conclusions drawn here are valid for both subsets. Initialization with operational analyses implies that this evaluation assesses sensitivity to the activation of the scheme in a forecast sequence rather than a full assimilation cycle. However, results obtained with the full suite of changes documented by McTaggart-Cowan et al. (2019b) demonstrate that the large majority of the impact can be effectively assessed in this forecast-only framework.
The clearest direct impact of the low-CAPE convection scheme is on the precipitation metrics shown in Fig. 19. The equitable threat score is improved at most accumulation thresholds (Fig. 19a), largely as a result of a reduction in the number of false alarms for thresholds of 2 mm (24 h)−1 and above (Fig. 19b). The decrease in the false alarm ratio is not accompanied by an equivalent reduction in the probability of detection (Fig. 19c), an indication that the parameterization is acting to eliminate spurious precipitation events in a selective manner. This is particularly encouraging given the dramatic reduction in the frequency of occurrence of accumulations of 5 mm (24 h)−1 and greater (Fig. 19d). The latter is consistent with the impact of the parameterization on the convective cells analyzed in northern Ontario case study (section 4a), determined to be a consequence of the parameterized release of potential instability and the suppression of the gridpoint storm feedback.
Precipitation scores for day-2 24-h accumulations (24–48-h forecast time) over North America from 1200 UTC initializations in the summer 2016 forecast sequence (21 cases total). Forecasts from the CTL are plotted in blue, and those from LC are plotted in red for (a) the equitable threat score, (b) the false alarm ratio, (c) the probability of detection, and (d) the frequency bias. Differences between the scores that are significant at the 90% level as determined using a bootstrap test are identified with a filled line marker on the time series with the improved score. Precipitation measurements from synoptic stations that have passed the quality control stage of the Lespinas et al. (2015) precipitation analysis are used as observational data here. The number of observations at each accumulation threshold is annotated in (a).
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The impact of the low-CAPE convection scheme on predictive skill for near-surface atmospheric variables is smaller than it is for precipitation (Fig. 20). Improvements to the error standard deviation2 of 2-m temperature and moisture, and 10-m winds rise to the level of statistical significance at most lead times, but the change in guidance quality is small enough to be of little practical utility. The same is generally true for changes to mean errors, although daytime cooling leads to a 0.3-K increase in the cold bias of the LC guidance compared to the CTL (Fig. 20a). This change in 2-m temperature is consistent with the cold pool enhancement noted in the midwestern squall-line case study (Fig. 18), although the relative contributions of such features and the effects of shading by the clouds predicted by the low-CAPE convection scheme has not been systematically assessed in the forecast sequence.
North American near-surface scores from 1200 UTC initializations in the summer 2016 forecast sequence (21 cases total) for (a) temperature, (b) dewpoint, and (c) wind speed. The bias (dashed lines) and error standard deviation (solid lines) are used here to quantify forecast quality. Forecasts from CTL are plotted in blue, and those from LC are plotted in red, with units plotted as labeled on the ordinate of each panel. Differences between the time series that are significant at the 90% level as determined from a bootstrap test are identified at 6-hourly intervals with a filled line marker on the time series with the improved score. Observations come from a combination of the synoptic and METAR networks that includes only stations whose altitudes in the model are within 30 m of the recorded station elevation.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The effects of parameterized low-CAPE convection on upper-air scores are more pronounced, with improvements in error standard deviation clearly visible in height and wind predictions near the tropopause (Figs. 21a,b). However, a reduction in the midtropospheric warm bias (Fig. 21c) leads hydrostatically to a 3-m decrease in upper-tropospheric heights that is evaluated as a degradation compared to radiosonde-observed values. Uncertainty in the sign of the height bias of the CTL integration is large; however, as comparison with the ERA5 (Hersbach et al. 2018) reveals a significant high bias that renders the height reductions in the LC integration a positive result (not shown).
Profile of error standard deviation (solid) and bias (dashed) against North American radiosonde observations of (a) geopotential height, (b) zonal wind, (c) temperature, and (d) dewpoint depression after 48 h of forecast time for the summer 2016 period (42 cases total). Forecasts from CTL are plotted in blue, and those from LC are plotted in red, with units plotted as labeled on the abscissa of each panel. Differences between the time series that are significant at the 90% level based on a two-sided Student’s t test are identified with a filled line marker on the time series with the improved score. The number of observations for each variable and level is identified on the ordinate to the right of the profile.
Citation: Monthly Weather Review 148, 12; 10.1175/MWR-D-20-0020.1
The significant improvements in guidance quality described here may represent an upper bound on the impact that could be expected from the introduction of a low-CAPE convection scheme. This is because deep convection in GEM is depicted using a CAPE-dependent parameterization whose activity is suppressed under under conditions of limited conditional instability. In models that employ schemes with alternative closures, convection in such environments may already be adequately represented. This appears to be the case for the ECMWF system, in which the sensitivity to the activation of the equivalent midlevel form of the Tiedtke (1989) scheme is much smaller than that reported here (P. Bechtold, personal communication).
6. Conclusions
An important subset of convective events occur in environments that are devoid of significant CAPE. Representing such events in atmospheric models that are unable to resolve moist convective processes explicitly is the objective of the low-CAPE convection parameterization introduced in this study.
The scheme is based on a convective plume model and the mass-flux equations, employing distinct triggering and closure components that enhance its ability to represent moist convection in low-CAPE environments. The direct connection of these elements to the gridscale vertical motion ensures that the scheme is able to tap instabilities through parameterized moist convection instead of permitting the model to release them in underresolved updrafts via the gridpoint storm mechanism.
The introduction of the low-CAPE convection scheme appears to improve precipitation structure under low-CAPE conditions that are not conducive to surface-based deep convection. The direct impact of the new scheme is apparent in the simulation of a set of small, intense convective cells in northern Ontario: precipitation bull’s-eyes are eliminated in the low-CAPE region of potential instability. The indirect impact of the scheme on convective structure is evident in integrations that focus on a squall line over the midwestern United States. The enhanced cold pool generated by the low-CAPE convection scheme early in the simulation leads to the secondary initiation of surface-based convection that forms the leading edge of the system. These results combine with the positive impact of the parameterization on guidance quality to suggest that the scheme is working in a physically realistic manner to represent the effects of convection in low-CAPE environments.
Although potentially unstable profiles have been emphasized in this study, the scheme has the capacity to react to any low-CAPE instability in principle. For example, a moist symmetric instability that leads to excessive vertical motions along a slant path will lead to the scheme’s activation: the trigger does not depend on the nature of the instability. Although a dedicated slantwise convection scheme would be best suited to represent convection in such cases (Nordeng 1987; Lindstrom and Nordeng 1992; Balasubramanian and Yau 1994; Schultz and Schumacher 1999; Glinton et al. 2017), the triggering of parameterized upright convection is more physically justified than the alternative of gridscale feedbacks (Tiedtke 1989). This is particularly true given the tendency for the two forms of moist convection to coexist (Rasp et al. 2016). The scheme’s focus on the presence of lifting rather than the details of the instability is consistent with the ingredients-based view of convection (Schultz et al. 2000).
Despite the positive impact that the low-CAPE convection parameterization has on model simulations, the selection of free parameters within the scheme introduces new dimensions to the problem of determining an optimal model configuration. These parameters, which include the threshold environmental mass flux for triggering (
The low-CAPE convection scheme was implemented in Canadian operational NWP systems as part of a major update to the physical parameterization suite in July 2019 (McTaggart-Cowan et al. 2019b). Despite the significant improvements in guidance skill that accompanied this upgrade, ongoing follow-up evaluations suggest that model’s long-standing positive precipitation bias has been overreduced in convectively active regions. This is particularly true in the eastern United States, where Lepore et al. (2015) show that CAPE is an effective predictor for convective activity. Given the large impact of the new scheme on precipitation totals, opportunities for the refinement of the parameterization and its associated free parameters are being explored.
Despite the increases in computing power that have allowed most regional NWP systems to adopt convection-permitting configurations, most global NWP models, ensemble systems and climate applications will need to continue to parameterize moist convection for the foreseeable future. The positive impact of the low-CAPE convection scheme on guidance skill provides a strong incentive for further investigation of the representation of this class of convection in atmospheric models that are unable to resolve completely the moist turbulent processes that may be active in such environments.
Acknowledgments
The authors would like to thank David Schultz and Peter Bechtold for insightful discussions on the physics and parameterization of low-CAPE convection over the course of this study. The efforts of two anonymous reviewers and the MWR editor (Almut Gassmann) are also greatly appreciated.
Data availability statement
Access to all data employed in this study is unrestricted. The reanalysis products used in this study can be obtained using via the references provided in section 2, while observational data can be retrieved from archives of the Global Telecommunication System. The large volume of data generated by the integrations described in this study precludes their entry into a public archive, but these data are stored at the Canadian Meteorological Centre and will be made available upon request.
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The thresholds employed in Fig. 6 are not intended to be universally applicable. Instead, they are meant simply to highlight the region in which local extremes in the ingredients overlap to create favorable conditions for convective activity.
The “error standard deviation” is computed as the standard deviation of model error, thereby depicting the random component of the error to complement the systematic component that is illustrated by the bias (mean error).
