While larger-scale aspects of cyclones are generally forecast with reasonable skill, the occurrence, location, and severity of the local regions of major wind damage are not. A broad region of moderately strong winds occurs during most of the cyclone's life cycle. This is generally found on the warm side of the cyclone (usually to the southeast) and is associated with the ‘warm conveyor belt’. Several recent papers (Browning, 2004; Clark et al., 2005; Parton et al., 2009) have focused on a particular second localised region of strong winds, and especially strong gusts, which may be short-lived (a few hours) but especially damaging. This region is close to the ‘tail’ of the characteristic ‘hook’ of the cloud head as it wraps around the cyclone, and has been dubbed the ‘sting at the end of the tail’, or ‘sting jet’ by Browning (2004), terminology similar to that used by Grønås (1995) who referred to a similar feature which he called the ‘poisonous tail of the bent-back occlusion’. The primary aim of this paper is to determine the relationship between conditional symmetric instability (CSI) and sting jets.
A cloud head and dry slot are characteristic features of explosively deepening cyclones (central pressure falls exceeding 24 hPa in 24 hours at 60°N as defined by Sanders and Gyakum, 1980) associated with exceptionally strong surface winds. These systems are often associated with a highly mobile, flat, slightly confluent upper-level trough (McCallum and Norris, 1990). Schultz et al. (1998) found that cyclones moving into confluent flow had evolutions that resembled the Shapiro–Keyser conceptual model (Shapiro and Keyser, 1990). Latent-heat release has an important role in these explosively deepening cyclones. Grønås (1995), in his analysis of the New Year's Day storm of 1992, found potential vorticity anomalies associated with the latent-heat release along the bent-back front played an important role in forming the seclusion of warm air at the centre of the cyclone; the intensification of the seclusion was linked to the onset of strong winds. Shutts (1990a), in his analysis of the great October 1987 storm in southeast England (hereafter ‘the Great Storm’), found that two thirds of the central pressure drop could be attributed to latent-heat release. Explosive development has also been linked to the presence of CSI, the release of which leads to slantwise convection. CSI is a type of moist symmetric instability that arises from the combination of inertial and convective instabilities and is released by slantwise motions in an atmosphere that is convectively stable to vertical parcel displacements and inertially stable to horizontal parcel displacements, as first defined by Bennetts and Hoskins (1979) and Emanuel (1983a, 1983b), and reviewed by Schultz and Schumacher (1999). Shutts (1990b) found that three out of five cases of explosive development were associated with warm sectors containing large SCAPE (Slantwise Convective Available Potential Energy, a measure of the degree of CSI), whereas none of the five cases of non-explosive development examined were associated with significant SCAPE. This indicates that explosive storms are more likely to have significant SCAPE.
Only a few case-studies exist that have specifically attributed a region of strong winds in an extratropical cyclone to a sting jet. To date, published results relate to the Great Storm (Browning, 2004; Browning and Field, 2004; Clark et al., 2005), windstorm Jeanette (27 October 2002; Parton et al., 2009), windstorm Gudrun (also known as Erwin, 7 January 2005; Baker, 2009), and windstorm Anna 26 February 2002; Martínez-Alvaredo et al., 2010). From these, the following conceptual model of a sting jet has emerged. The sting jet is a transient (time-scale of a few hours) mesoscale jet of air that descends from the tip of the cloud head (sometimes referred to as the cloud hook) near the tail of the bent-back front in an extratropical cyclone developing according to the Shapiro–Keyser conceptual model. This bent-back front is the consequence of the fracturing of the surface cold front which occurs during stages II and III of the four-stage Shapiro–Keyser conceptual model; the stages are (I) incipient frontal cyclone, (II) frontal fracture, (III) bent-back front and frontal T-bone, and (IV) warm core frontal seclusion. The sting jet is distinct from the well-known broad belt of strong low-level winds that accompanies the warm conveyor belt along the primary cold front and from the low-level jet associated with the cold conveyor belt. The cold-conveyor-belt jet flows rearward relative to the motion of the cyclone and so is only associated with strong Earth-relative winds in the latter stages of development when it can curve around the cyclone towards the end of the bent-back front. The sting jet descends from the cloud head to the top of the boundary layer within the frontal fracture region. Strong winds (and strong wind gusts) can be observed at the surface if mass and momentum are vertically transported through the boundary layer; the proportion of sting jets leading to strong surface winds is not yet known. In the conceptual sting-jet model (Figure 17 of Clark et al., 2005), the sting jet is first observed at the surface in stage II of the Shapiro–Keyser evolution in the dry slot just ahead of the cold-conveyor-belt jet and behind the surface cold front. It consists of air with wet-bulb potential temperature, θw, between that of the warm and cold conveyor belts. During stage III, the sting jet expands as the frontal fracture region widens. At the end of the cyclone evolution (stage IV), the cold-conveyor-belt jet wraps around the cyclone centre and replaces the sting jet at the surface. Note that sting jets are not the only possible cause of strong winds near the cloud hook; e.g. McCallum and Norris (1990) and Bader et al. (1995) attribute the strong winds here to a surge of pressure following in the wake of the centre of the storm due to marked subsidence occurring behind the confluent upper-level trough.
This conceptual model of a sting-jet cyclone is based on observational analysis that has shown localised transient strong winds in the dry slot ahead of the cloud hook (from mesoanalysis derived from anemograph traces from the Great Storm (Browning, 2004) and Mesosphere–Stratosphere–Troposphere wind profile data for windstorm Jeanette (Parton et al., 2009) and analysis of numerical weather prediction model hindcasts from which the three-dimensional structure of the sting jet has been derived (Clark et al., 2005; Martínez-Alvaredo et al., 2010; Parton et al., 2009). Parcel trajectories (derived using model-resolved winds) have demonstrated that the sting jet can be defined as a coherent ensemble of descending, drying trajectories that approximately conserve θw. Two possible dynamical causes of the sting jet were proposed by Browning (2004), motivated by observations. First, fast-moving clouds often emerge from the cloud hook and evaporate. This, together with evidence from other explosively developing storms of the importance of latent-heat release (discussed above), suggests evaporation associated with slantwise convection may enhance the strength of the surface winds. Browning (2004) proposed that this could occur by evaporative cooling acting either to intensify the slantwise circulations (which in turn amplifies the mesoscale latent-heat sources and sinks) or to reduce the static stability (leading to convective momentum transport in the potentially unstable dry slot or low-Richardson-number turbulence nearer the cloud-head tip, so enhancing the surface winds). Second, multiple bands of cloud and precipitation have been observed in the cloud heads of several sting-jet storms, implying the existence of multiple slantwise circulations (as shown schematically in Figure 14 of Browning, 2004). This, together with evidence of CSI presence or release in cloud heads (as discussed above and also in Dixon et al., 2002), suggests that these slantwise circulations could result from CSI release. In this paradigm, the sting jet is the descending branch of a slantwise circulation which, due to the cyclonic circulation upon which it is superimposed, exits the tip of the cloud head as it descends; hence a given storm could have multiple sting jets. This leads to multiple ‘fingers’ (or ‘tails’) of cloud in the cloud hook which are visible in satellite imagery.
Some support for these dynamical causes of the sting jet has come from model diagnostics. In the Great Storm, Clark et al. (2005) found that the total descent of sting-jet trajectories was positively correlated with lowering in potential temperature; i.e. θw is conserved along a trajectory through compensating decreases in potential temperature and increases in specific humidity. Parton et al. (2009) and Martínez-Alvaredo et al. (2010) also inferred evaporation along the upper half (for windstorm Jeanette) and entire ensemble (for windstorm Anna) of sting-jet trajectories respectively. In windstorm Jeanette, Parton et al. (2009) diagnosed regions of CSI release using the vertically integrated extent of realizable symmetric instability diagnostic proposed by Dixon et al. (2002) (i.e. the number of levels in a model grid column that have CSI, moisture and lift but are not potentially or inertially unstable). They found CSI release parallel to the frontal regions and in narrow bands following the curvature of the cloud head, consistent with the observed cloud banding in the cloud head having been generated through CSI release. CSI release terminated at the cloud hook from where the sting jet emanated according to back trajectories. However, as noted by Parton et al. (2009), this evidence is circumstantial and does not prove CSI release was the dynamical cause of the sting jet. Martínez-Alvaredo et al. (2010) inferred CSI release as contributing to the sting-jet generation in windstorm Anna from the presence of negative moist potential vorticity (MPV), and positive moist static stability and absolute vorticity, along a substantial proportion of the trajectories comprising the sting jet during their initial descent.
The aim of this article is to determine the spatial distribution and temporal evolution of CSI diagnostics in severe storms and hence consider whether fields of a diagnostic for CSI could be used to infer the presence of a sting jet. In doing this, we also determine which of these diagnostics is the most discriminating for the presence of a sting jet. We consider two paradigms for the relationship between CSI release and sting jets: a sting jet could be the descending branch of a slantwise circulation induced by the release of near-surface CSI by ascending air, or it could be a slantwise flow induced by the release of mid-tropospheric CSI by descending air. Only the first of these two paradigms has explicitly been considered in the literature to date, although trajectory analysis of the sting jet has consistently shown descent from a region of negative MPV, implying instability to CSI at midlevels. If CSI is released a few hours before or during the descent of a sting jet, then this instability can be inferred to have had a significant role in its generation. Several different diagnostics for CSI are calculated from the output of model simulations of four intense extratropical cyclones. A sting jet has been diagnosed in three of these cyclones (as described in published papers); for comparison, a non-sting-jet storm is also analysed. The model used and diagnostics applied are described in section 2. The results are given in section 3, followed by conclusions and discussion in section 4.
The model hindcasts were performed using the Met Office Unified Model (MetUM). This is the same model (with some variation in version number) used by Clark et al. (2005), Parton et al. (2009) and Baker (2009), and one of the two models used by Martínez-Alvaredo et al. (2010), for their simulations of sting-jet storms. The MetUM is an operational finite-difference model that solves the non-hydrostatic deep-atmosphere dynamical equations with a semi-implicit, semi-Lagrangian integration scheme (Davies et al., 2005). The model uses Arakawa C staggering in the horizontal. The vertical coordinate system is terrain following with a hybrid-height vertical coordinate and Charney–Phillips staggering. The model can be configured either as a global model or as a limited-area model (LAM) with one-way nesting. In the LAM configuration, the horizontal grid is rotated in latitude/longitude. The model parametrization of physical processes includes long- and short-wave radiation (Edwards and Slingo, 1996), boundary-layer mixing (Lock et al., 2000), cloud microphysics and large-scale precipitation (Wilson and Ballard, 1999), and convection (Gregory and Rowntree, 1990). Results are shown here for the model run on the operationally used North Atlantic–European domain. This domain covers nearly all of the North Atlantic and Europe, extending from eastern Canada, and including most of Greenland and the northern part of North Africa; the results shown in this paper are on subsections of this domain. Operationally this configuration is run with gridboxes of 0.11° (∼12 km) in the horizontal and 38 model levels on a stretched grid (lid around 39 km). Here the simulations analysed are from model runs with this horizontal resolution but with double the number of vertical levels within the same vertical domain. This results in a model level spacing of 200–300 m in the mid-troposphere. This model resolution was found to resolve the sting jet in the previous model simulations of sting-jet storms. The enhanced vertical resolution was motivated by Clark et al. (2005) (based on work by Persson and Warner, 1993) as yielding a ratio of horizontal to vertical grid spacing that could resolve CSI release.
The trajectory-based method of diagnosis of a sting jet and diagnostics for conditional instability (CI) and CSI are described in the following subsections. Variants of three diagnostics for CI and CSI are considered: CAPE (convective available potential energy), SCAPE (slantwise CAPE) and MPV* (saturated MPV). There is some debate over whether diagnostics for CSI are more appropriately calculated using geostrophic or full winds. This debate is summarised in the final subsection and the choices made here stated. The spatial distributions of these diagnostics are plotted using a system-centric format with the origin chosen so that it coincides with the system's centre defined by streamlines at a reference level above the boundary layer (chosen to be 800 hPa). For calculation of system-relative winds, the velocity of each system was defined as its velocity at this reference level, as in Martínez-Alvaredo et al. (2010).
2.2.1. Sting jets
Sting jets were identified in the model simulations by calculating back trajectories from localised regions of strong winds (defined as exceeding 40 m s−1 for windstorm Gudrun and 25 m s−1 for the other storms) in the frontal fracture region of the cyclone using the trajectory code of Wernli and Davies (1997). The model data used were output at least hourly and interpolated from model levels onto pressure levels with an interval of 25 hPa prior to calculating the trajectories (and all other diagnostics) with a timestep of 30 min. Consistent with other studies, a sting jet was identified as a coherent ensemble of approximately θw-conserving trajectories that descended from the cloud head towards the top of the boundary layer (i.e. relative humidity reduced during descent) in the frontal fracture region. The vertical transport of mass and momentum through the boundary layer to the surface (leading to strong surface wind gusts) is likely to occur predominantly via parametrized processes at this model resolution and hence the trajectories (diagnosed using resolved winds) were not required to descend to the surface. The values of various parameters were then calculated along the trajectories by interpolating the model (Eulerian) fields to the trajectory positions. We note that more than one sting jet may exist in each storm (although other sting jets are likely to be weaker than that identified) and hence do not restrict our analysis of instability diagnostics to the precise location of the identified sting jets.
Updraught CAPE is a commonly used measure of the energy obtained by the release of CI. It is the maximum kinetic energy available to an air parcel ascending vertically in a statically unstable environment, neglecting the effects of condensed water on the buoyancy and assuming that the parcel ascends with no mixing (no entrainment or detrainment with the environment) and adjusts instantaneously with the local environmental pressure. The environment is assumed to be in steady state during the parcel ascent. Both updraught and downdraught CAPE were considered. Following Emanuel (1994), updraught CAPE is defined by
where pLNB and p0 are the pressures of the level of neutral buoyancy and origin level of a pseudo-adiabatic parcel ascent, g is the acceleration due to gravity, p is pressure, Rd is the gas constant for dry air and Tv, parcel and Tv, env are the virtual temperatures of the parcel and environment, where
r is the mixing ratio and is the ratio of the gas constants of dry air and water vapour*. A range of parcel origin levels are normally considered, in which case the CAPE value given for a grid column is the maximum value. Convective Inhibition (CIN) is defined by the magnitude of the above integral between the limits of p0 and the pressure of the level of free convection. It is the energy required to lift an air parcel vertically to the level of free convection beyond which the parcel will spontaneously gain kinetic energy as it rises (until it reaches the level of neutral buoyancy). Downdraught CAPE (DCAPE) is the maximum kinetic energy available to an air parcel descending due to latent cooling from the evaporation of precipitation in sub-saturated air (or melting at the freezing level). The release of DCAPE thus leads to downdraughts and is achieved through isobaric cooling to saturation (to its wet-bulb temperature) followed by pseudo-adiabatic descent assuming just enough evaporation to keep the parcel saturated. It is defined as
where pn is either the pressure of the level of neutral buoyancy or the surface (whichever is closer to the origin level) and p0 is the origin level of a pseudo-adiabatic parcel descent.
SCAPE is a measure of the energy obtained by the release of CSI. It has been used far less in the literature than its CI counterpart CAPE, which Schultz and Schumacher (1999) attribute to be partly due to difficulties in the interpretation of the values obtained, especially where there is also CAPE present or active slantwise convection occurring. However, we consider it here as a diagnostic for CSI used in case-studies including that of the Great Storm. Shutts (1990a) found SCAPE values exceeding 1000 J kg−1 when lifting from the boundary layer in the warm sector of this storm; trajectory analysis showed that parcels ascending from this region were located in the cloud head above 500 hPa 12 hours later. Previously, to our knowledge, only updraught SCAPE (SCAPE calculated for ascending air parcels) has been used as a diagnostic for CSI in case-studies. Here we also consider downdraught SCAPE (DSCAPE). Both two- and three-dimensional (2D and 3D respectively) calculations of SCAPE and of DSCAPE have been performed (here termed SCAPE/DSCAPE and 3D-SCAPE/3D-DSCAPE).
Two-dimensional SCAPE (SCAPE calculated using a 2D thermally wind balanced (axi-symmetric or linear) and steady basic state) is a slantwise counterpart to CAPE and hence is a measure of the maximum kinetic energy available to an air parcel ascending in a conditionally symmetrically unstable environment (with the same assumptions as for CAPE). It is calculated as the CAPE along an absolute momentum, M, surface where, for a 2D environment independent of the Cartesian horizontal coordinate y, M = fx + v (f is the Coriolis parameter, x is the orthogonal Cartesian coordinate and v is the wind speed in direction y; note that here we have used the full wind to calculate M as discussed further in section 2.2.5). Here, in a 3D environment, we follow the approach of Shutts (1990c) and define the absolute momentum surface as the surface of intersection of the two components of horizontal absolute momentum that passes through the parcel's initial position. These momentum components are calculated for each model gridpoint (i.e. the reference values of longitude and latitude in the equations for the momentum components in section 3 of Shutts (1990c) are those of the gridpoint under consideration). Analogously, Slantwise Convective Inhibition (SCIN, the energy required to lift a parcel along a slantwise path to its level of free convection) is calculated as CIN along an absolute momentum surface, and downdraught SCAPE (DSCAPE) is calculated as the DCAPE along an absolute momentum surface.
The calculation of both CAPE and SCAPE assume that the time-scale for the parcel ascent (via the release of CI or CSI respectively) is very much less than the time-scale for the development of the system in which the diagnostics are calculated. Typical time-scales for the release of CI and CSI are about 0.5 and 4 h respectively, which can be compared to the time-scale for baroclinic growth of about 1 day (Emanuel, 1983b). Hence, while the assumption of steady state is a very good approximation for the release of CI, it is less good for the release of CSI. Gray and Thorpe (2001) derived a form of SCAPE applicable to 3D evolving flows and applied it to a sample case-study demonstrating significant qualitative differences between 2D- and 3D-SCAPE. 3D-SCAPE was derived by calculating CAPE along parcel trajectories calculated using the evolving model winds (specifically the component of the horizontal winds along a local tangent to the isobars and the local vertical velocity) but constrained to follow surfaces of constant absolute momentum (by searching for the intersection of the surface of the conserved component of parcel absolute momentum, which by definition is parallel to the isobars, with a line normal to the isobars and at the pressure level of the parcel after advection). Here we calculate 3D-SCAPE using the same method but assuming a constant vertical velocity rather than using the model-resolved value as in Gray and Thorpe (2001); the horizontal velocity components used are from the evolving model wind field and absolute momentum surfaces are followed as in Gray and Thorpe (2001). The model resolution has been chosen to be capable of resolving the release of CSI. However the vertical velocity field is contaminated by substantial motion due to other processes such as frontal circulations, the release of CI (where this is resolved explicitly) and gravity waves, both from orography and from the adjustment process. Sampling this at time intervals longer than the gravity wave period makes it impossible for trajectories to follow the gravity wave component of the vertical velocity accurately, which led to trajectories that did not ascend smoothly and indeed sometimes did not ascend at all. (Note that the model used here uses a slightly smaller grid spacing than that used by Gray and Thorpe (2001), and has a significantly higher effective resolution because it has little additional diffusion and uses the more compact Arakawa C-grid rather than the B-grid used by the model version used by Gray and Thorpe.) A constant vertical velocity (omega) of −2 Pa s−1 was assumed in all storms. This implies an ascent of 300 hPa in about 4 h, consistent with typical assumed time-scales for slantwise ascent. For sample cases the values of 3D-SCAPE calculated were found to be self-consistent with this value of omega from calculation of the conversion of SCAPE to kinetic energy. This omega value is also consistent with the estimated value of −1 Pa s−1 for a specific set of ascending trajectories starting along the warm front in one of the windstorms analysed in this paper (Anna). It was found that the results were not critically sensitive to the choice of omega (e.g. values of DSCAPE for a sample storm were very similar calculated using values of −2 and −4 Pa s−1; not shown). Analogously, 3D-DSCAPE was calculated as the DCAPE along trajectories calculated using the evolving horizontal winds, descending with a constant velocity of 2 Pa s−1, and constrained to follow surfaces of constant absolute momentum. Note that 3D-SCAPE and 3D-DSCAPE fields are always plotted at the initiation gridpoint of the parcel ascent or descent respectively.
Diagnostics based on MPV are also commonly used for diagnosis of moist symmetric instability, where
where ρ is density, ζ is absolute vorticity, and θe is equivalent potential temperature. PSI (potential symmetric instability) exists where MPV is negative and the atmosphere is inertially and potentially stable. CSI exists where MPV* (saturated MPV, calculated using saturated θe instead of θe) is negative and the atmosphere is inertially and conditionally stable. Here we consider three MPV-based diagnostics: (i) the evolution of MPV* along the ensemble of sting-jet trajectories, (ii) snapshots of the spatial distributions of MPV* averaged over pressure layers within which the sting jet has been identified, and (iii) the evolution of gridpoints in the cloud head that are here termed CSI points. CSI points are gridpoints in the cloud head satisfying the criteria of negative MPV*, positive static stability (calculated using a formula based on Durran and Klemp (1982) for the static stability of a saturated atmosphere) and positive inertial stability (fζ > 0). Note that the mass per grid point is approximately constant because we have transformed to equal pressure layers and the horizontal grid boxes are approximately square. These criteria are closely related to those used by Dixon et al. (2002) to identify points comprising their vertically integrated extent of realizable symmetric instability diagnostic; this diagnostic was applied to a sting-jet storm by Parton et al. (2009). However, here we do not directly apply criteria to the vertical motion or relative humidity. The reason for this is that we want to include regions that are releasing CSI through both upward and downward slantwise motions (i.e. analogous to the SCAPE and DSCAPE diagnostics). We consider the time dependence of both the fraction of CSI points and the average MPV* of those gridpoints in the semi-objectively defined cloud heads of the systems (calculated on individual pressure levels and averaged over pressure layers). The cloud heads are defined as between 600 and 700 hPa (the approximate pressure levels that sting jets descend from) and are bounded by a case-specific θw value to the east and a relative humidity value of 90% elsewhere.
2.2.5. Comments on the use of geostrophic or full winds for diagnosis of CSI
CSI is normally calculated relative to a thermally wind balanced and non-evolving basic state. Hence the geostrophic absolute momentum (Mg, the absolute momentum calculated using the geostrophic wind) should be used to calculate SCAPE and MPV* (and ζg for determining inertial instability). However, fields of Mg are in general noisier than fields of M, especially for LAM output (since the geostrophic velocity field is calculated from gradients in the pressure field). Hence, many researchers have found it preferable to use the full (non-geostrophic) wind; Schultz and Schumacher (1999) and Clark et al. (2002) and references therein contain discussion on this issue. Other authors have instead argued for the use of the full winds based on theoretical grounds (Gray and Thorpe, 2001) or because the full winds are likely to be more representative than the geostrophic winds in curved-flow environments (Novak et al., 2004; Novak et al., 2006). Here we use the full winds to calculate CSI diagnostics from the LAM output, but briefly compare the results for MPV* with those calculated from global model output using both full and geostrophic winds.
2.3. Case-study simulations: Motivation and model set-up
Case-studies of four intense windstorms that affected northwest Europe are presented. Previous studies of three of these storms have demonstrated the existence of a sting jet: Browning (2004) and Clark et al. (2005) for the Great Storm, Martínez-Alvaredo et al. (2010) for windstorm Anna, and Baker (2009) for Gudrun. The fourth storm, Tilo (7–8 November 2007), was chosen as it appeared to be a good candidate for a sting-jet storm based on satellite imagery, operational model surface analyses, and the existence of strong wind gusts. However, a clear sting jet could not be identified using the criteria given in section 2.2.1. Hence, CSI diagnostics from this storm are included for comparison with the other storms to determine the degree to which they can act as discriminators of sting-jet storms.
The MetUM simulations analysed here for the Great Storm, windstorms Gudrun and Anna are those described in Clark et al. (2005), Baker (2009) and Martínez-Alvaredo et al. (2010) respectively. The simulations of the Great Storm were performed using version 5.2 of the MetUM (with modifications equivalent to version 5.3) and the simulations of Anna and Gudrun were performed using version 6.1 of the MetUM. The trajectories for the Great Storm had to be recalculated from the model output but agree well with the results given in Clark et al. (2005). The simulation of Tilo was performed for this study and hence details are given here. The simulation was initialised from operational MetUM global analyses at 0600 UTC 7 November 2007. To produce the required lateral boundary conditions for the North Atlantic–European domain, the MetUM was run in its global configuration. Consistent with the operational analyses, the global model was run with a horizontal grid of 640 × 481 gridpoints (a grid spacing of 0.56° in longitude and 0.37° in latitude, approximately equivalent to a grid spacing of 45 km in the extratropics) and 50 vertical model levels (lid around 60 km).
3.1. Synoptic overviews
Figure 1(a–c) shows the system-relative wind speed for the three sting-jet storms at the approximate times when and pressures where the identified sting jets reached their maximum pressure. A distinct region of strong winds exists in the frontal fracture region for the three sting-jet storms. For windstorm Tilo, the system-relative wind speed is shown at the time when and pressure where it is a maximum in the frontal fracture zone (Figure 1(d)), but a distinct strong wind region does not exist. Note also that the warm conveyor belt in Tilo is very much weaker than in the sting-jet storms; the warm conveyor belt in Gudrun is relatively weak at the 850 hPa level plotted, but is much stronger at 900 hPa (not shown) whereas for Tilo it is weak at all levels. Clark et al. (2005) showed that in the Great Storm the surface wind distribution emphasised the sting jet more than the warm conveyor belt because the latter was stably stratified and so the winds did not reach the ground so effectively and hence there is not a direct relationship between winds at the surface and at the top of the boundary layer. A synoptic analysis is also shown for each storm. Frontal fracture has occurred in all four storms in the region between the cold front and the bent-back front.
The Great Storm caused a trail of destruction as it crossed southeast England on the morning of 16 October 1987, with peak observed surface gusts of up to 50 m s−1 (Burt and Mansfield, 1988). The central pressure fall was 26 hPa in 12 hours reaching a lowest central pressure of 952 hPa at 0000 UTC 16 October (Woodroffe, 1988); this satisfies the criterion for explosive development according to Sanders and Gyakum (1980). At this time it had just about developed a warm seclusion and the cloud head was beginning to hook around, suggesting it had reached stage IV of the Shapiro–Keyser evolution. Clark et al. (2005) identified a sting jet using trajectory analysis. One ensemble of trajectories satisfying the criteria for a sting jet descended from the cloud head at a mean pressure of 740 hPa (but minimum pressure of 640 hPa) at 0000 UTC 16 October reaching a maximum mean pressure of 870 hPa at around 0400 UTC 16 October.
Windstorm Anna led to observed surface wind gusts exceeding 35 ms−1 as it crossed the UK on 26 February 2002. Martínez-Alvaredo et al. (2010) identified the four stages of the Shapiro–Keyser conceptual model as occurring at around 1200 UTC 25 February, 0000 UTC 26 February, 0300 UTC 26 February and 1100 UTC 26 February respectively using satellite imagery, Met Office distributed charts (Dominy, 2006) and ECMWF operational analyses. This explosive cyclone had a central pressure drop of 31 hPa from 1200 UTC 25 February to 1200 UTC 26 February. The sting jet was identified as a coherent ensemble of parcel trajectories that occurred in simulations performed with both the MetUM and German COSMO (Consortium for Small-scale Modelling) model. In the MetUM, the jet defined by the ensemble mean began its descent from the cloud head at around 560 hPa at 0100 UTC 26 February and reached a maximum pressure of about 710 hPa at 0700 UTC 26 February.
Windstorm Gudrun caused significant damage as it passed over the UK and then Scandinavia during 7–9 January 2005, with observed surface wind gusts exceeding 40 m s−1. Analysis of satellite imagery (as shown in Baker, 2009) and Met Office distributed charts shows that this cyclone followed the Shapiro–Keyser conceptual model with the four stages starting at around 1800 UTC 7 January, 2200 UTC 7 January, 0300 UTC 8 January and 0800 UTC 8 January respectively. The central pressure drop was around 42 hPa in 24 hours (between 1200 UTC 7 January and 1200 UTC 8 January), satisfying the criterion for an explosively deepening cyclone. Baker (2009) identified a sting jet in this storm as a coherent ensemble of parcel trajectories that began its descent from the cloud head at about 650 hPa (ensemble mean) at 1800 UTC 7 January and reached a maximum pressure of about 825 hPa at about 0400 UTC 8 January. The sting jet in all three windstorms dried as it descended while conserving θw and terminated its descent (as analysed using trajectories) near the top of the boundary layer in the frontal fracture zone.
Windstorm Tilo passed to the north of Scotland on 7–8 November 2007, producing peak observed surface winds of more than 30 m s−1 over Scotland and extreme waves in the North Sea. The four stages of the Shapiro–Keyser conceptual model occurred at about 0000 UTC 7 November, 1800 UTC 7 November, 0000 UTC 8 November and 0600 UTC 8 November respectively based on satellite imagery and Met Office distributed charts for the first two stages and these data with additionally the Met Office North Atlantic–European domain analyses and short-range operational forecasts for the last two stages. A warm core seclusion had developed by the last of these times. This was also an explosive development with a central pressure fall of around 30 hPa from 0600 UTC 7 November to 0600 UTC 8 November 2007. A region of descending, relatively dry (RH< 80%), strong winds (speed > 35 m s−1) was located at around 700 hPa in the frontal fracture zone from 2100 UTC 7 to 0600 UTC 8 November. However, backward trajectory analysis (trajectories calculated backwards from 0100 UTC 8 November) showed that the descending jet was weak in that the ensemble descended more slowly than in the other three cases (0.3 Pa s−1 for Tilo compared to 0.5, 0.8 and 1.3 Pa s−1 for Gudrun, Anna and the Great Storm respectively), and was composed of far fewer trajectories (only about 20 trajectories compared to more than 100 trajectories for the other three cases). The damaging near-surface winds (between 800 and 900 hPa) were instead due to a strong undercutting cold conveyor belt. Hence, although a jet satisfying the characteristics of a sting jet (as defined in section 2.2.1) was identified in this system, this jet was very much weaker than that in the other storms and hence we refer to this system as a non-sting-jet system.
3.2. SCAPE and CAPE
In this section the paradigm that the sting jet is the descending branch of a slantwise circulation induced by the release of the CSI of ascending air parcels is considered. SCAPE and CAPE have been calculated lifting from the near-surface (1000–825 hPa) and from midlevels (800–750 hPa) (hereafter termed near-surface and midlevel SCAPE and CAPE) for times approximately corresponding to stages I to III of the Shapiro–Keyser conceptual model; the final time chosen is approximately two or three hours prior to that when the sting jet (if it existed) reached its lowest level as diagnosed from the trajectory analysis. Figure 2 shows the times at which SCAPE and CAPE are plotted relative to the periods over which the sting jets (or weakly descending jet for windstorm Tilo) descend. Figures 3–6 show near-surface CAPE and near-surface and midlevel SCAPE at three times for the sting-jet storms but at just one time for Tilo because they show comparatively little evolution in this case. None of the storms have significant midlevel CAPE (values are < 50 J kg−1 except for a small region on the inner edge of the bent-back front in the Great Storm) and hence this field is not shown. The midlevel SCAPE is also negligible in Tilo and is not shown. The values of SCAPE or CAPE plotted at a grid point are the maximum values lifting from all pressure levels (25 hPa increment) within the near-surface and midlevel pressure layers. Note that the grey-scale shading used for plotting SCAPE and CAPE for the sting-jet storms is the same but uses greater values than those used for Tilo; this reflects the much weaker instabilities present in Tilo than in the sting-jet storms. The location of the sting jet identified by trajectories is shown by a circle on all plots showing the horizontal distribution of a field. The sting jets are initially located above the pressure level at which θw contours are plotted and hence they appear to move towards the frontal fracture region as they descend; θw is actually approximately conserved as the sting jets descend, by definition. An analysis of CAPE and SCAPE in these storms is now presented beginning with an overview and followed by a comparative analysis of the storms in the following regions: the cold air behind the cold front, frontal zones, the cloud head, and the cloud-head tip/sting jet.
For the sting-jet storms (i.e. excluding Tilo) there is some collocation of regions of strong near-surface SCAPE and strong near-surface CAPE (with values of both diagnostics exceeding 500 J kg−1, top and middle rows in Figures 3–5). However, the regions of strong near-surface SCAPE are more extensive, implying that there exist some regions where CSI could be released. (Note that, when both instabilities are present, the release of CI, if initiated, is likely to dominate due to its larger growth rate.) In contrast, the distribution of midlevel SCAPE shows localised regions (bottom rows in Figures 3–5).
3.2.2. Cold air behind the cold front
The sting-jet storms all have regions of relatively strong near-surface CAPE and more extensive near-surface SCAPE (values exceeding 300 and 500 J kg−1 respectively) in the cold air mass to the west of the systems, as would be expected (top and middle rows of Figures 3–5); however, extensive regions of non-negligible CIN also exist here (up to 50 J kg−1, not shown) implying that not all of the CAPE can be released through upright convection. In contrast, there is negligible near-surface CAPE and SCAPE in Tilo in this cold air mass (Figure 6).
3.2.3. Frontal zones
All four storms have bands of near-surface CAPE along the cold front or in the neighbouring warm conveyor belt (top rows in Figures 3–5 and 6(b)). In windstorms Anna and Gudrun, this region of near-surface CAPE extends from the tip of the cloud head towards the cold front. A region of near-surface and midlevel CAPE is also found along the inner edge of the bent-back front in the Great Storm (the only storm with CAPE along the bent-back front). In Tilo, a localised region of strong near-surface CAPE occurs in the warm seclusion when this develops. The near-surface CAPE in these frontal regions is nearly always associated with near-surface SCAPE (middle rows, Figures 3–6) and negligible collocated CIN and SCIN (not shown), although the SCAPE is much more extensive and greater in magnitude. Along the cold front of the Great Storm (and also in Gudrun to a lesser extent) there is also midlevel SCAPE (bottom rows, Figures 3 and 5). SCAPE along the cold fronts in the sting-jet storms decays with time. This implies that either upright convection or a mixture of upright and slantwise convection are occurring in these regions. In contrast, CAPE and SCAPE along the cold front, bent-back front and in the warm seclusion in Tilo increase with time (not shown).
3.2.4. Cloud head
Only windstorms Gudrun and Anna have near-surface and midlevel SCAPE in the cloud head on the warm side of the bent-back front; CAPE is negligible here (Figures 4 and 5). This SCAPE decays with time (the area and magnitude of SCAPE diminishes) suggesting that it is being released by slantwise ascent. There are no collocated regions of significant inhibition to slantwise convection (SCIN) lifting from near-surface or midlevels in this region for Gudrun; in Anna, near-surface and midlevel SCIN develops in this region when midlevel SCAPE decreases after 0100 UTC on 26 February 2002 (SCIN not shown).
3.2.5. Cloud-head tip/sting jet
The three sting-jet storms have near-surface SCAPE but no near-surface CAPE at the tip of the cloud head at the first time shown (Figures 3–5(a), (d), (g)). However, CAPE does exist in the vicinity of the cloud-head tip in windstorms Anna and Gudrun at all times shown (and also actually in the cloud head tip at 2200 UTC 7 January 2005 in Gudrun, Figure 5(b)) but not in the Great Storm. The near-surface SCAPE decays with time (the area and magnitude of SCAPE diminishes) suggesting that it is being released through slantwise ascent; SCIN is negligible here (not shown). In Gudrun and Anna the sting jet is in a region of near-surface SCAPE at the first time shown, but not in such a region by the last time shown, suggesting the SCAPE is released as the sting jet descends; the sting jet exists in a region that has neither SCAPE or CAPE in the Great Storm. In Anna and Gudrun, the release of CAPE near the tip of the cloud head, generating upright convection, may have enabled downward momentum transport of strong winds from the top of the boundary layer, generating the observed strong surface wind gusts.
In windstorm Tilo there is weak (50–100 J kg−1) CAPE at the tip of the cloud head extending from within the cloud head, through the dry slot region and into the frontal fracture zone but negligible collocated SCAPE (compare left and right panels in Figure 6). Peak values of CAPE increase with time from 2000 UTC to 2200 UTC 7 November 2007 as the frontal fracture zone develops and then diminish slightly (Figure 6(b) shows these fields at 0000 UTC 8 November), suggesting the CAPE is being released through upright ascent. (There is no CIN in this region throughout this period; values are < 10 J kg−1, not shown.) This implies that upright convection is occurring in the cloud-head tip, dry slot and frontal fracture zone in preference to slantwise convection, and is a plausible explanation for the lack of a diagnosed sting jet in this windstorm.
3.3. DSCAPE and DCAPE
In this section the paradigm that the sting jet is a descending slantwise circulation induced by the release of the CSI of descending air parcels is considered. For the sting-jet storms, DSCAPE and DCAPE have been calculated for parcels descending from a layer that includes the approximate mean pressure level of the ensemble of sting-jet trajectories at the given time and for time ranges approximately corresponding to the descent of the trajectories; for windstorm Tilo, these diagnostics have been calculated for parcels descending from a fixed layer. These layers are specified in the figure captions. As for SCAPE and CAPE, fields of DSCAPE and DCAPE are shown at three times for the sting-jet storms (Figures 7–9) but just one time for Tilo (Figure 10) because the fields show comparatively little evolution for Tilo. The values of DSCAPE and DCAPE plotted at a grid point are the maximum values descending from all pressure levels within these pressure layers. The times shown in Figures 7–10 are offset later relative to those shown in Figures 3–6 because the paradigms considered (as described in the last paragraph of section 1) suggest that the relationship (if it exists) between these downdraught instabilities and the sting jet should occur during the descent of the sting jet, whereas the relationship between the corresponding upright instabilities and the sting jet could occur a few hours prior to the start of the descent of the sting jet. Figure 2 shows times at which DSCAPE and DCAPE are plotted relative to the periods over which the sting jets –or weakly descending jet for Tilo –descend.
The spatial distribution and magnitudes of DSCAPE and DCAPE are very similar. Recall that the DSCAPE and DCAPE in the dry slot are unlikely to be released because this requires the saturation of air parcels; however, these instabilities may be realizable in other regions that are unsaturated at the pressure level at which relative humidity is contoured since near-saturated air may exist at the level from which air parcels descend. DSCAPE and DCAPE exist in collocated bands along the cold front extending into the dry slot and (with lesser magnitude) in the cold air behind the cold front in all four storms. In Tilo, this extends into the developing warm seclusion (Figure 10) and in the Great Storm this extends along the inner edge of the bent-back front at early times (until 0100 UTC, Figures 7(b) and (e)). Both DSCAPE and DCAPE decay in magnitude along the cold front and in the dry slot as the storms develop (most strongly in the Great Storm and Gudrun). Regions of instability extend into the outer convex edge of the cloud head in the three sting-jet storms and into the tip of the cloud head in Tilo. Only in the Great Storm at 2300 UTC 15 October is the region of DSCAPE substantially larger than that of DCAPE, implying slantwise circulations may exist driven by descent from the cloud-head level. DSCAPE and DCAPE in the cloud head decrease in extent after 0100 UTC 16 October, suggesting they are being released.
Windstorms Gudrun and Anna have a distinct localised region of DSCAPE approximately collocated with the sting jet (horizontally collocated and a maximum calculated for air parcels descending from the mean level of the ensemble of sting-jet trajectories). This region of localised DSCAPE is present from about the time the sting jet begins to descend (as determined by the trajectories) until the time when it reaches its lowest level (from 1900 UTC 7 January (not shown) to 0400 UTC 8 January (Figure 9(f)) for Gudrun and from 0100 UTC (Figure 8(d)) to 0600 UTC 26 February (Figure 8(f) shows 0500 UTC) for Anna). In the Great Storm, the sting jet moves into a region of DSCAPE (and later also DCAPE) at 0100 UTC 16 October (Figure 7(d)) around the time the sting jet starts to descend. In contrast to the sting-jet storms, there are no regions of DSCAPE without DCAPE in Tilo. For Gudrun and Anna, a region of DCAPE (calculated for air parcels descending from the same level as that used to calculate the DSCAPE) also becomes collocated with the sting jet as the sting jet descends, from 2200 UTC 7 January for Gudrun (Figure 9(a)) and from 0500 UTC 26 February for Anna (Figure 8(c)). It is possible that downdraught convective instability is being created in these storms because the downdraught CSI cannot be released fast enough. However, it is not possible to determine from these simulations whether this is an artifact of the model configuration (e.g. insufficient model resolution) or it happened in reality.
3.4. Three-dimensional SCAPE and DSCAPE
SCAPE and DSCAPE fields calculated using a method applicable for 3D evolving flows are analysed in this section and compared to the equivalent fields calculated assuming 2D steady-state flows (and analysed in the previous two subsections). As for SCAPE, 3D-SCAPE has been calculated lifting from both the near-surface (1000–825 hPa) and from midlevels (800–750 hPa). It has been calculated for ascents starting at only two or three times for each storm (these times being near the start of the period over which SCAPE was calculated; results from only one time are shown here) since the ascent takes place over several hours. 3D-DSCAPE has been calculated in an analogous way to DSCAPE (i.e. calculated for parcels descending from approximately the mean level of the ensemble of sting-jet trajectories). Figure 11 shows 3D-SCAPE and 3D-DSCAPE for all four storms. For the sting-jet storms, 3D-SCAPE is shown for ascents initiated at the times corresponding to the first time shown in Figures 3–5 and 3D-DSCAPE is shown for descents initiated at the times corresponding to the first time shown in Figures 7–9. For Tilo, 3D-SCAPE and 3D-DSCAPE are shown for ascents and descents (respectively) initiated earlier than the single time shown in Figures 6 and 10, so that these fields are calculated over the same stages of the evolution of all four storms. 3D-SCAPE and 3D-DSCAPE have been calculated over smaller regions than SCAPE and DSCAPE due to the high computational cost of calculating the 3D ascents and descents.
When comparing the 3D- and 2D-diagnostics, the 2D-diagnostics at all times shown should be considered because the ascents and descents used for the 3D-diagnostics take place over several hours. In general the 3D-diagnostics (in particular 3D-SCAPE) are noisier than the comparable 2D-diagnostics. This is likely to be a consequence of the complexity of the calculation of these 3D versions which require a momentum surface to be followed over several hours of storm evolution. However coherent regions of 3D-SCAPE and 3D-DSCAPE exist that are generally strongly correlated with those of SCAPE and DSCAPE respectively for each storm. The magnitudes of the diagnostics are also roughly comparable when the evolution of the 2D-diagnostics over the entire ascent and descent periods are considered. (Recall that for the sting-jet storms SCAPE and DSCAPE generally decrease with time whereas for Tilo they generally increase with time.)
For windstorms Anna, Gudrun and Tilo, the 3D-SCAPE diagnostic does not identify any regions susceptible to the release of CSI that were not identified from the SCAPE diagnostic. In contrast, for the Great Storm there is substantially greater near-surface 3D-SCAPE than SCAPE in the cloud-head tip (compare Figures 3(d), (e) and (f) with Figure 11(a)). There is very little midlevel 3D-SCAPE in any of the storms. The region of SCAPE shown in the warm seclusion of Tilo in Figure 6(b) is not seen in 3D-SCAPE; this is probably because it does not appear in SCAPE until the warm seclusion develops at 2300 UTC 7 November 2007 (not shown). The patterns of 2D- and 3D-DSCAPE are closely related. However, the distinct localised regions of DSCAPE approximately collocated with the sting jets in Anna and Gudrun are not distinct in 3D-DSCAPE (although there are localised maxima close to the sting-jet position in Gudrun). We hypothesize that this is because the parcel trajectories are approaching the trajectories resulting from CSI release, and hence values of 3D-DSCAPE are less than those of DSCAPE where DSCAPE is actually being released.
3.5. Moist potential vorticity
One advantage of MPV* in comparison to SCAPE and DSCAPE as a diagnostic for CSI is that it can be calculated at a specific point without the need to follow momentum surfaces and hence can be tracked along sting-jet trajectories. In windstorm Gudrun, MPV* is negative following sting-jet trajectories prior to the sting jet descent (back to about 1300 UTC) and throughout much of its descent as shown in Figure 12. This shows that the presence of instability is not a sufficient criteria for the descent of a sting jet. The increase in MPV* after about 0000 UTC may be due to the release of CSI or CI. This is consistent with the reduction in SCAPE lifting from both near-surface and midlevels and both DSCAPE and DCAPE descending from the level of the sting jet at the location of the sting-jet trajectories during their descent. Note that there is some evidence that the trajectories are entering a region of boundary-layer mixing after 0200 UTC (Baker, 2009). MPV is similarly initially negative (in the MetUM) or close to zero (in the COSMO model) along the sting-jet trajectories at the start of their descent from the cloud head in Anna (note that MPV has similar values to MPV* at this time since the air is near-saturated; Martínez-Alvaredo et al., 2010); in the Great Storm, MPV* is negative throughout the descent of the sting jet in the upper part of the jet, whereas it starts negative but becomes positive in the lower part prior to the descent of the sting jet (not shown). By contrast, the weakly descending jet identified in Tilo is at all times associated with positive MPV* (not shown), supporting the conclusion that this jet is of different character to the sting jets identified in the other three storms.
The spatial distribution of MPV* has been determined by calculating MPV* averaged over pressure levels forming a layer of between 75 and 100 hPa in pressure-depth about the level of the descending sting jet at that time (as determined by the trajectories). For Tilo the averaging layers were chosen to follow the identified weakly descending jet that did not satisfy the criteria for a sting jet (the jet described in section 3.1). Figure 13 shows the evolution of MPV* for Gudrun. MPV* is positive in the warm conveyor belt extending into the inner edge of the cloud head. There is a general collocation between regions of negative MPV* and the combined distributions of positive SCAPE (lifting from midlevels) and positive DSCAPE (descending from the level of the diagnosed sting jet). This is consistent with the criteria for the inference of the presence of updraught and downdraught CSI using both diagnostics. For example, for Gudrun at 1900 UTC, the regions of negative MPV* map to similar (although slightly displaced) regions of midlevel SCAPE at this time (compare Figures 13(a) and 5(g)). At 2200 UTC the region of negative MPV* in the cloud head (along the bent-back front) maps to a similar region of midlevel SCAPE at this time, the region of negative MPV* at the tip of the cloud head maps to the region of positive DSCAPE and DCAPE collocated with the position of the sting jet and the negative MPV* in the dry slot maps to regions of positive SCAPE, DSCAPE and DCAPE (compare Figure 13(b) with Figures 5(h) and 9(a) and (d)). As the regions of SCAPE decay with time, the distribution of negative MPV* becomes more closely mapped to that of positive DSCAPE and DCAPE alone (compare Figures 13(c) and 9(b) and (e)). This relationship between regions of negative MPV* and positive SCAPE and DSCAPE is mirrored in Anna and the Great Storm (not shown). Of the four storms, Tilo is unique in that MPV* in the majority of the cloud head is strongly positive (values exceeding 0.2 PVU, not shown); the exception is a small and decaying negative region on the inner edge of the cloud head where the warm seclusion forms. This is consistent with the lack of midlevel SCAPE and DSCAPE in this windstorm.
Reductions in updraught CSI with time in the sting-jet generation and bent-back front regions in the cloud head of Gudrun and Anna were inferred from the decay of the SCAPE diagnostic; a reduction in downdraught CSI with time in the bent-back front region in the cloud head of the Great Storm was inferred from the decay of the DSCAPE diagnostic. An equivalent inference from the MPV* diagnostic would result from an observed reduction of negative MPV* in these regions. A reduction in CSI is evident from the calculation of the fraction of CSI points, and the average MPV* over those points, within the semi-objectively defined cloud heads (as defined in section 2.2.4, Figure 14). The fraction of CSI points decreases with time in all the sting-jet storms during the time of the descent of the sting jet. Note that these fractions correspond to large numbers of CSI points; for example the total number of gridpoints (over five levels) in the cloud head of Gudrun is in the range 6000–7000 during the period considered; hence the number of CSI points at the end of the time period (0400 UTC) is about 1500. The average negative MPV* over the CSI points initially reduces towards zero as the number of CSI points decreases in the Great Storm and Gudrun, but then plateaus while the fraction of CSI points continues decreasing; in Anna the average MPV* is relatively constant throughout the period shown.
For windstorm Gudrun, the magnitudes and locations of the maximum 850 hPa wind speed and minimum surface pressure in the global model and LAM output show close agreement until 0400 UTC 7 January 2005 (the time when the sting jet descends to its lowest level in the limited-area simulation). At this time, in the LAM only, the location of the maximum wind speed moves from the warm conveyor belt to the frontal fracture zone and its magnitude increases strongly. Calculations of the fraction of CSI points in the cloud head and average MPV* over those points for the global model simulation (Figure 14(c) and (f)) reveal three key findings: first, similar values of both diagnostics comparing the LAM and global simulations (both using the full rather than geostrophic winds); second, similar fractions of CSI points but less reduction of negative MPV* with time comparing plots with MPV* and ζ calculated using geostrophic winds to those using the full winds; finally, a substantial delay in the onset of the reduction of the fraction of CSI points in the global model (the value is approximately constant until 2200 UTC on 7 January 2005), although the average MPV* and MPVg starts becoming less negative from the start of the period. The delay in the reduction of the fraction of CSI points suggests that the global version of the model is less able than the limited-area version to release CSI (as would be expected for coarser resolution).
4. Conclusions and discussion
The temporal and spatial evolution of diagnostics for CSI have been analysed in four severe extratropical cyclones to examine the relationship between the release of CSI and the generation of sting jets; a sting jet was identified in three of these storms (the Great Storm and windstorms Anna and Gudrun) but not in the other storm (Tilo) despite it having many of the apparent features of sting-jet storms.
Both 2D and 3D calculations of SCAPE and DSCAPE have been analysed where the 2D calculation assumes a 2D thermally wind balanced steady basic state and the 3D calculation allows for a 3D evolving basic state. The 3D diagnostics are generally noisier than the comparable 2D ones, but have similar spatial distributions and comparable magnitudes. In particular, the 3D diagnostics do not identify any new regions where slantwise convection may be occurring other than a region in the cloud-head tip of the Great Storm (which is not near the sting-jet location). We conclude that 2D calculations are likely to be sufficient to identify regions of susceptibility to slantwise convection in these storms.
The values of all forms (updraught, downdraught, 2D and 3D) of SCAPE and CAPE are substantially greater and the regions much larger for the sting-jet storms than for Tilo, such that there is much more vertical and slantwise convective instability in the sting-jet storms. The distribution of these instabilities has been analysed across the entire storm: cold air behind the cold front, frontal zones, cloud head and cloud-head tip/sting jet. Here we summarise the results from the cloud head and cloud-head tip/sting jet regions as most relevant to the development of the sting jet.
In the cloud head of the sting-jet storms, there exist some regions of significant SCAPE and negligible CAPE implying CSI (to ascending air parcels) exists and can be released in preference to CI leading to slantwise circulations. This SCAPE decays with time in Anna and Gudrun, consistent with its release (in the Great Storm the SCAPE is only evident in the 3D-SCAPE). Only CAPE exists in the cloud head of Tilo, implying that just upright convection can occur. Regions of both DSCAPE and DCAPE exist in the cloud head of all four storms. The Great Storm is unique in having substantially larger regions of DSCAPE than DCAPE prior to the descent of the sting jet, implying that CSI (to descending air parcels) exists and can be released in preference to CI, again leading to slantwise circulations but driven from midlevels. In the other storms, either both instabilities may be released or CI may be released in preference to CSI.
The three sting-jet storms have SCAPE in the vicinity of the cloud-head tip (from where the sting jet initiates); two of them (Anna and Gudrun) also have CAPE here. This SCAPE decays with time suggesting that it is being released. In Anna and Gudrun the sting jet (as identified by trajectories) is in a region of SCAPE (but no CAPE) at the first time shown (around the time the sting jet starts to descend), but not in such a region by the last time shown, suggesting that SCAPE is being released as the sting jet descends and that this may contribute to its development. In the Great Storm, the sting jet is not in a region of SCAPE or CAPE. In Tilo, there is no SCAPE (instead only weak CAPE) in the cloud-head tip, which is a plausible explanation for the lack of a sting jet. There are distinct local maxima of DSCAPE approximately collocated with the sting jets in Anna and Gudrun; this maximum decays with time in Gudrun. DCAPE develops in this region in both windstorms as the sting jet descends; we hypothesize that this DCAPE could be generated because the model is failing to release DSCAPE fast enough, although further simulations would be required to test this. The sting jet in the Great Storm does not start off in a region with DSCAPE or DCAPE but moves into a region of DSCAPE (and lesser DCAPE) at the time that it starts to descend.
CSI has also been assessed through MPV*. The spatial distribution of negative MPV* maps to the combination of the distributions of (positive) DSCAPE and SCAPE, as would be expected for this alternative diagnostic for CSI. The average numbers of so-called CSI points (gridpoints with negative MPV* but which are inertially and statically stable) in the semi-objectively defined cloud heads of the sting-jet storms decrease with time as the sting jets descend; the average MPV* values at these points increase towards zero before plateauing or are relatively constant, while the numbers of CSI points continue decreasing. These results are consistent with the concurrent observed decay of SCAPE.
We conclude that the sting-jet storms are distinct from windstorm Tilo in terms of the distributions and magnitudes of CI and CSI, with these being much larger in magnitude and more extensive in the sting-jet storms. In particular we note that there is no SCAPE and only a small amount of DSCAPE in the cloud-head tip in Tilo. This contrasts with the sting-jet storms. In Anna and Gudrun, SCAPE in the cloud head decays with time, implying that slantwise circulations (driven from near-surface and/or midlevels) occur and that the sting jets could occur as the descending branch of such circulations. There is also a distinct localised region of DSCAPE collocated with the identified sting jet (as defined by back trajectories) in these sting-jet storms, implying that slantwise circulations can also be driven from midlevels through descent and that this mechanism can drive sting jets. In the Great Storm there is very little SCAPE in the cloud head but a large region of DSCAPE and no DCAPE, suggesting that slantwise circulations in the cloud head may be driven from midlevels through descent. The identified sting jet moves into a region of DSCAPE as it starts to descend.
The presence of a distinct localised region of DSCAPE in windstorms Anna and Gudrun (but not in Tilo) suggests that this can potentially be used to identify storms that have a sting jet. Possible sting-jet storms would be identified as storms in which significant DSCAPE exists in the region of the storm where sting jets occur, namely in the frontal fracture region at or near the tip of the cloud head. Precise specification of this sting-jet diagnostic, including threshold values for DSCAPE and other parameters, and investigation of its utility is the subject of current research.
The presence of CSI release in the sting-jet storms and sting jets, and its absence in the non-sting-jet storm, strongly suggests that this mechanism is important in the generation of the sting jet in these cases. However, it does not exclude the possibility that evaporative cooling of the descending air (the other proposed sting-jet mechanism discussed in section 1) had a role in generating these sting jets or that sting jets can be generated purely through evaporative cooling. Indeed, the example of windstorm Tilo shows that CSI release is not a necessary criterion for the presence of weakly descending jets that satisfy the definition of sting jet used here. The descent of the sting jet from the cloud head into the dry frontal fracture zone means that evaporative cooling will occur but, as noted by Clark et al. (2005), this may simply offset the adiabatic warming associated with ascent and possible potential warming due to mixing. When considering sting jets generated by the release of downdraught CSI, evaporation into the descending air is necessary to allow the instability to be accessed; hence the relative importance of two mechanisms cannot be determined.
We thank the Met Office for making the MetUM available and the National Centre for Atmospheric Science Computational Modelling Services for providing computing and technical support and diagnostic facilities for use of the model. We also thank Prof. Heini Wernli and an anonymous reviewer for comments that have improved this paper. The project was funded by the Natural Environment Research Council (grant reference NE/E004415/1).