Sting jets in intense winter North-Atlantic windstorms

Extratropical cyclones dominate autumn and winter weather over western Europe. The strongest cyclones, often termed windstorms, have a large socio-economic impact due to the strong surface winds and associated storm surges in coastal areas. Here we show that sting jets are a common feature of windstorms; up to a third of the 100 most intense North-Atlantic winter windstorms over the last two decades satisfy conditions for sting jets. The sting jet is a mesoscale descending airstream that can cause strong near-surface winds in the dry slot of the cyclone, a region not usually associated with strong winds. Despite their localized transient nature, these sting jets can cause significant damage, a prominent example being the storm that devastated southeast England on 16 October 1987. We present the first regional climatology of windstorms with sting jets. Previously analysed sting-jet cases appear to have been exceptional in their track over northwest Europe rather than in their strength.

Recent work with the original cyclone track dataset used in this article has revealed that some of these tracks correspond to storms that are not in the set of 100 most intense cyclones between the winters of 1989/90 and 2008/09. Hence, the phrase 'the 100 most intense cyclones' in the article should read as 'a set of 100 cyclones'. Although these findings change the character of the cyclones considered, almost all the findings would be correct given this change. The only exception is Figure 3a, since that figure shows the distribution of cyclones according to cyclone intensity (as measured by relative vorticity) for the 100 most intense cyclones rather than the set of 100 cyclones actually considered. To reflect the distribution for the set of 100 cyclones actually considered, this figure should be substituted for figure 1 here; although details differ, the structure of the distribution has the same features as the published figure. The already significant main conclusion of the article, that sting jets are a common feature of windstorms, is strengthened when the actual set of 100 most intense cyclones is considered: the percentage of sting-jet cyclones increases from the previously reported range of 23%-32% to a revised range of 39%-49% (for same thresholds in the size of a precursor region as those given in the original article).
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Maximum relative vorticity distribution of whole sample of intense cyclones (grey) and those cyclones with sting-jet precursors (black). Bin width is 0.5 × 10 −5 s −1 ; bin centres start at 11.5 × 10 −5 s −1 and finish at 16.5 × 10 −5 s −1 .

Introduction
Worldwide, European windstorms are second only to United States hurricanes as a traded catastrophe risk (Browning 2004). While larger-scale aspects of extratropical cyclones are generally forecast with reasonable skill, the occurrence, location, and severity of the local regions of major wind damage are not. Two regions of strong low-level winds commonly occur during the passage of a cyclone. The warm conveyor belt is a broad region of moderately strong surface winds that exists throughout most of the cyclone's life cycle in the warm sector of the cyclone (to the south of the storm centre in the northern hemisphere). When the cyclone is mature the cold conveyor belt may also produce strong surface winds if it hooks around the cloud head that can be seen curving to the northwest around the storm centre. Additionally, a third localized region of strong winds, and especially strong gusts, which may be short lived (a few hours) can exist close to the 'tail' of the cloud head hook as it wraps around the cyclone centre. This 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 that he called the 'poisonous tail' of the bent-back occlusion.
Sting jets are defined as accelerating, drying airflows that descend from the cloud head in the mid-troposphere (beneath the dry intrusion) towards the top of the boundary layer while conserving wet-bulb potential temperature. The descent occurs in the frontal fracture region of cyclones that follow the Shapiro-Keyser (Shapiro and Keyser 1990) conceptual model (Browning 2004, Clark et al 2005. This region is usually relatively clear of cloud and is hence known as the 'dry slot'. Sting-jet momentum can then be transferred from the top of the boundary layer to the surface via boundary-layer processes, such as turbulent mixing, generating strong surface winds and gusts; this momentum transfer may be promoted by the weak moist static stability in the frontal fracture region. Despite their damage potential the frequency and global distribution of sting-jet cyclones are unknown. The limited published research on sting jets to date almost exclusively consists of analyses of case studies (Browning 2004, Browning and Field 2004, Clark et al 2005, Martínez-Alvarado et al 2010, Parton et al 2009, Baker 2009). The one exception is a climatology of strong mid-tropospheric mesoscale winds observed by the vertically pointing mesosphere-stratosphere-troposphere (MST) radar (Vaughan 2002) located near Aberystwyth, Wales (Parton et al 2010). Nine potential sting-jet cases were identified in seven years, but this number only represents possible sting-jet events passing over Aberystwyth. Their mesoscale nature (∼150 km across) means that sting jets are not resolved by operational weather forecast models with domains large-enough to cover storm tracks. Nor are they represented in the even coarser resolution multi-year reanalysis datasets; hence wind climatologies based on these may miss the most damaging parts of windstorms. Furthermore, observational datasets do not provide sufficient temporal resolution over the oceans to allow exhaustive identification of these transient features.
To determine the climatological characteristics of stingjet cyclones we have developed a method to diagnose the precursors of sting jets (rather than the unresolved sting jets themselves) from reanalysis datasets (Martínez-Alvarado et al 2011). We search for conditional symmetric instability (CSI) in the moist frontal fracture zones of cyclones. The method is applied to the 100 most intense North-Atlantic cyclones during 20 winter seasons (December-January-February, DJF) of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis, ERA-Interim (Dee et al 2011). The predicted presence or absence of a sting jet is then verified by performing high-resolution, sting-jet resolving, simulations with the Met Office weather forecast model (Davies et al 2005) for 15 randomly sampled cases.

Reanalysis data and cyclone tracks
ERA-Interim is a 6-hourly, global, gridded dataset of the state of the atmosphere consistent with both a numerical model derived from the operational ECMWF forecasting system (IFS Cy31r1/2) and observations via a 12 h 4D-Var data assimilation cycle. In the horizontal direction the data used has been interpolated from the original T255 spectral resolution onto a regular latitude-longitude grid at the equivalent grid spacing of 0.7 • × 0.7 • . In the vertical direction it was interpolated from the original 60 model levels to pressure levels between 1000 and 300 hPa, with a 25 hPa level separation between 1000 and 750 hPa and a 50 hPa level separation elsewhere. Following the work by Catto et al (2010), an objective feature tracking algorithm (Hodges 1994, 1999, Hoskins and Hodges 2002 has been applied to ERA-Interim. The tracks of the 100 most intense cyclones (with respect to 850 hPa relative vorticity truncated to T42 resolution to emphasize the synoptic scales) over the North Atlantic ocean during the winter seasons (DJF) from 1989/1990 to 2008/2009 have been identified.

Diagnostic for sting-jet precursor conditions
We applied a diagnostic designed to detect sting-jet precursor conditions in low-resolution datasets (Martínez-Alvarado et al 2011) to each cyclone from 0000 UTC on the day before to 1800 UTC on the day after the day on which the maximum relative vorticity occurred. The diagnostic for sting-jet precursor conditions (Martínez-Alvarado et al 2011) detects downdraught CSI as measured by downdraught slantwise convective available potential energy (DSCAPE) in the moist frontal fracture zone. The release of this CSI is a cause of sting jets and DSCAPE is present in cyclones with sting jets but not present in other, equally intense, cyclones that do not have sting jets . Insufficient model resolution does not prohibit the accumulation of CSI, only its realistic release to generate a sting jet (Martínez-Alvarado et al 2011).

Definition of DSCAPE.
DSCAPE is defined as the potential energy available to a hypothetical air parcel for descent, while conserving absolute momentum, from a pressure level p top to a pressure level p bottom , assuming that it becomes saturated through the evaporation of rain or snow falling into it from upper levels (Emanuel 1994). The pressure levels p top and p bottom are prescribed: p top is varied from 800 to 450 hPa and p bottom is kept constant, and equal to 950 hPa. Thus, DSCAPE is computed as where R d is the dry air gas constant, p is pressure, T v,p is the parcel virtual temperature, and T v,e is the environmental virtual temperature. The integral in (1) is evaluated along a surface of constant vector absolute momentum in a similar way to that used for the calculation of SCAPE (Shutts 1990). The maximum value of DSCAPE (DSCAPE * ) and associated value of p top (p * top ) for a vertical column is used as a representative DSCAPE value for the underlying grid point.

Thresholds for diagnostic.
A minimum threshold for DSCAPE * is imposed but this is not sufficient to discriminate CSI regions that could generate sting jets. For example, there are often large amounts of DSCAPE in dry regions such as the cyclone dry slot; DSCAPE in these regions cannot be released due to the lack of moisture required to saturate air parcels and trigger their descent. Additional conditions are imposed to restrict the regions with CSI identified to only those that are cloudy and near a cold front (and so potentially near a frontal fracture zone). The following recommended thresholds (Martínez-Alvarado et al 2011) are imposed on relative humidity, RH, the magnitude of the gradient of wet-bulb potential temperature, |∇θ w |, and cross-front θ w -advection, V · ∇θ w , where V is the horizontal wind vector: (2) Mean values were used of θ w and V over layers of 100 hPa depth centred around p * top (vertically delimited by pressure levels above and below p * top ). Maximum values of RH were used from within those same layers.
Further constraints, not included in Martínez-Alvarado et al (2011), were imposed on the position, relative to cyclone centres, of precursor regions. Previous studies have shown that regions from which sting jets originate are typically located within a 300 km radius from a cyclone's pressure centre (e.g. Gray et al 2011). In this study, the centre of a precursor region was required to lie within a radius of 700 km from the pressure-based cyclone position (in the full-resolution data and associated with the truncated T42 relative vorticity position) in order to be considered as a potential sting-jet precursor; this encompassed the whole cloud head. Precursor regions entirely in the sector between 300 • and 100 • relative to the direction of cyclone motion and beyond 250 km from the cyclone centre were discarded as these lay along the warm conveyor belt of the cyclone (CSI release may occur here but it will not lead to sting jets). Figure 1 shows a graphic description of these elements. The cloudy area (cloud head and warm conveyor belt) in that figure was defined by a 550 hPa relative humidity (RH > 80%) composite over every cyclone with CSI and every time instability was exhibited.
The size of the precursor region was defined by the number of connected grid columns in which a parcel descending from p * top satisfies the precursor conditions. To describe the shape and location of the average precursor region the central position of this region for each cyclone was computed in polar coordinates, taking radial and azimuthal position separately, relative to its direction of travel. The maximum upper and maximum lower deviations from the central position were then calculated in both the radial and azimuthal direction. These deviations were averaged over the precursor regions for all cyclones to obtain a representative shape considering possible asymmetries in the shape of the regions. In practice these asymmetries turned out to be small.

Verification of the presence of sting jets
In the absence of a suitable observational dataset, verification of the cyclones as having had or not having had a sting jet has been achieved by performing high-resolution, sting-jet resolving, simulations with the Met Office Unified Model (MetUM) (Davies et al 2005). Fifteen cyclones drawn randomly from the 100 intense cyclones were simulated; the number was limited by computational cost but it is shown to be sufficient to demonstrate skill.

Numerical model.
The MetUM version 7.1 was used to perform the sting-jet resolving cyclone simulations. This 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). It uses Arakawa C staggering in the horizontal (Arakawa and Lamb 1977) and is terrain following with a hybrid-height vertical coordinate and Charney-Phillips staggering (Charney and Phillips 1953) in the vertical. Parameterization of physical processes includes long-wave 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).
The limited-area domain comprised 720×432 grid points (with a spacing of 0.11 • ∼ 12 km), covering nearly all of the North Atlantic, Europe and North Africa, and 76 vertical levels (lid around 39 km, mid-tropospheric vertical spacing around 280 m). This vertical spacing yields a vertical to horizontal scale ratio of around 1:40, consistent with the ratio used by Clark et al (2005) and resolution recommendations to resolve CSI release Warner 1991, 1993). Lateral boundary conditions were produced by running the MetUM in its global configuration. The global model was initialized using global ECMWF operational analyses (ECMWF 2010) obtained at a grid spacing of 0.25 • and 60 vertical levels. These were interpolated to the global model resolution with 640 × 481 grid points (spacing 0.4 • ∼ 40 km meridionally) and 50 vertical levels (lid around 60 km). The limited-area model was initialized by interpolating the initial conditions produced for the global model.

Detection of sting jets.
Sting jets were identified using a three-step method (Martínez-Alvarado et al 2010): (a) localization and clustering of near-surface sting-jet points, (b) backward-trajectory analysis (Wernli and Davies 1997) and (c) analysis of the evolution of atmospheric variables along trajectories. At the end of their descent sting jets are here defined as low-level strong, descending winds in a relatively dry region within the frontal fracture zone hence meeting the criteria |V| > 35 m s −1 , w < −0.05 m s −1 , RH < 80%, and θ w,min < θ w < θ w,max where w is vertical velocity. The θ w values delimiting the frontal region, θ w,min and θ w,max , have been set on a case-by-case basis. Clusters of points satisfying these criteria were identified and backward trajectories from these clusters computed. Relative humidity, pressure and θ w were computed along trajectories to determine if they descended from a cloudy region (i.e. the cloud head) while conserving θ w . Specific humidity and θ were computed along trajectories to determine if evaporative cooling contributed to their descent. Saturated moist potential vorticity (MPV * ), absolute vorticity (as a measure of inertial instability, and defined as ζ a = f + ξ , where f is the Coriolis parameter and ξ is relative vorticity) and moist static stability (N 2 m ) (Durran and Klemp 1982) as a measure of gravitational instability of a saturated atmosphere were computed along trajectories to assess CSI.

Sting-jet cyclone characteristics
The number of cyclones with a sting-jet precursor is dependent on a threshold used for the minimum size of the precursor region (defined by the number of connected grid columns in which the diagnostic is satisfied where the area of one grid box is ∼4000 km 2 ). This was optimized using the cases verified by high-resolution modelling and the skill of the precursor diagnostic is inferred from a 2 × 2 contingency table (table 1) relating the presence or absence of a precursor to the presence or absence of a sting jet. Six of the fifteen cases simulated at high resolution developed trajectories consistent with the definition of a sting jet. If the minimum size threshold was set to between five and eight grid columns inclusive then five of the six sting-jet cases had precursor regions and seven of the nine cases without sting jets did not have precursor regions. The precursor diagnostic has skill for these size thresholds as this yields a p-value of 0.035 using Fisher's exact test; other size thresholds yield p-values above 0.05 (i.e. the 95% significance level). For minimum size thresholds yielding significant verification results, between 23 and 32 of the 100 cyclones had sting-jet precursor regions. Analysis is now presented of the maximum possible number of sting-jet cyclones, i.e. using a minimum precursor region size of five grid columns.
The analysed portions of the cyclone tracks are mapped every 6 h for the cyclones with and without sting-jet precursors in figures 2(a) and (b) respectively. Sting-jet precursors occurred only once for most of the tracks (69%) though there were tracks with two (16%), three (12%) and five (3%) precursor occurrences possibly suggesting multiple sting jets. The precursor regions occurred throughout the North Atlantic. The analysed tracks follow the classical North-Atlantic storm track (Hoskins and Hodges 2002). However, a difference between the start locations of the analysed tracks with and without sting-jet precursors exists: those with sting-jet precursors all originated south of 50 • N whereas those without originated as far north as 65 • N. This may be indicative of a requirement for a warm moist airmass where these cyclones form, consistent with the known importance of diabatic processes in the generation of sting jets. There is a strong tendency for the sting-jet precursors to occur in the 30 h prior to the occurrence of the cyclone's maximum intensity ( figure 2(c)). This is consistent with the sting-jet conceptual model in which sting jets occur during frontal fracture in stages II and III of the evolution of cyclones following the Shapiro-Keyser (Shapiro and Keyser 1990) conceptual model (Clark et al 2005).
The frequency distribution of the maximum relative vorticity of all of the 100 most intense North-Atlantic cyclones, and just those with sting-jet precursors, shows that there are fewer cyclones with increasing vorticity as expected ( figure 3(a), note that the first vorticity bin contains relatively few cyclones because other cyclones with vorticity in this range are not among the 100 most intense). Sting-jet precursors occur in cyclones throughout the vorticity range. The 100 most intense cyclones are relatively evenly distributed over the 20 winter seasons (figure 3(b)) with between 2 and 10 of these cyclones occurring in each season; between 0 and 3 of these cyclones have sting-jet precursors each year. Recent studies have found contradictory results regarding long-term trends in the frequency and intensity of extreme cyclones in the second half of the 20th century (e.g. Ulbrich et al 2009). Statistically significant trends cannot be inferred from the limited data presented here; however, we note that the three winter seasons in which there were no sting-jet cyclones all occurred during the last six seasons analysed.
The locations of sting-jet precursors are shown in a system-relative reference frame in figure 4(a). Each precursor region has been rotated such that the direction of motion of the cyclone is orientated to the right. The dots represent the locations of the grid points within every precursor region relative to the corresponding cyclone centre. There are grid points in areas apparently restricted (warm conveyor belt area in figure 1). However, these grid points belong to precursor regions lying at least partly within the permitted area (cloud head area in figure 1). The grid points span the space to the west of the cyclone centre where the cloud head lies The maximum energy available to the descending sting jet through the release of CSI, measured by maximum downdraught slantwise convective available potential energy in an atmospheric column (DSCAPE * ), ranges from the minimum threshold considered (200 J kg −1 ) to 900 J kg −1 with a mode of 300-350 J kg −1 (figure 4(b)). The pressure level from which the descending jet has this maximum energy (p * top ) is typically above 650 hPa (90% of cases) with many cases at 450 hPa, which constitutes the lowest pressure considered ( figure 4(b)). These results imply that the identification of sting-jet precursor regions is sensitive to these thresholds for energy and pressure and that a definitive sting-jet precursor cannot be defined.

Sting-jet characteristics
The characteristics of sting jets found by applying trajectory analysis to the high-resolution model output are now described. The evolution of pressure, relative humidity and saturated moist potential vorticity (MPV * ) along one ensemble of sting-jet trajectories from each cyclone are shown in figure 5. More than one ensemble of trajectories satisfying the criteria for a sting jet was found in some cyclones, those illustrated are chosen because they descend for similar periods and have comparable ensemble sizes. The trajectories are plotted over the 10 h prior to the time at which they reach their lowest level in the atmosphere; the vertical lines mark the onset of the sting-jet descent from the mid-troposphere towards the top of the boundary layer (the transport of momentum from here to the surface by parameterized processes in the model cannot be diagnosed from trajectories calculated using the model-resolved winds). The one false-negative case (for which a sting-jet precursor was not identified) was the cyclone of 12 December 1994 (bottom row in figure 5). The ensemble-mean trajectory descent rate ranges from ω = 0.4 to 0.9 Pa s −1 which compares well to previous studies (0.5, 0.8, and 1.3 Pa s −1 for windstorms Gudrun and Anna and the Great October storm respectively ). However, the true-positive cases achieve this descent rate for a minimum of 5 h compared to just 2 h for the false-negative case. The false-negative case is also distinct in that it remains at low levels throughout its development (below the 700 hPa level). The transition from cloudy air to dry air after the onset of descent is shown in the decrease in relative humidity for all cases. The existence of negative MPV * , but static and inertial stability, along a moist descending trajectory implies that CSI is being released. Each sting jet has at least some trajectories satisfying these criteria and, in all but the case of 26 December 1998, the mean MPV * is close to zero throughout almost all of the period shown (figure 5(c)); almost all ensemble members were statically and inertially stable (not shown). Further analysis of the case of 26 December 1998 revealed that the low-level strong winds in the frontal fracture region were the result of two different airstreams merging together at upper levels. The first stream approached the cyclone centre from the southwest at upper levels and had negative MPV * ; this was the sting jet. The second stream was a frontal circulation rising cyclonically around the cyclone centre and had partially negative MPV * at lower levels that became positive as it ascended; this stream could be releasing CSI as it ascends in the frontal circulation. As the streams met, MPV * became negative in some of the upper-level trajectory parcels, while lower-level ones experienced an increase in the value of MPV * . This merging of different airstreams has been observed previously in a sting-jet storm (windstorm Anna (Martínez-Alvarado et al 2010)) suggesting it could be a common occurrence. In windstorm Anna the sting jet was of similar size (defined by the number of trajectories) to the frontal circulation, whereas in the 26 December 1998 case the sting jet was much smaller than the frontal circulation.

Discussion and conclusions
The first regional climatology of sting-jet cyclones has been produced by applying a recently developed method for diagnosing sting-jet precursor regions in models incapable of resolving the sting jets themselves. The method has been applied to the 100 most intense extratropical cyclones that occurred in winter in the North-Atlantic region between 1989 and 2009. The method is demonstrated to have skill by performing high-resolution sting-jet resolving weather forecasts of a sample of the cyclones. Between 23 and 32% of the cyclones examined satisfied the diagnostic for the sting-jet precursor (dependent on the minimum area threshold chosen for the precursor region). The diagnostic depends on thresholds chosen to define the moist frontal fracture region (in which sting jets occur), the minimum energy available to be released from a type of atmospheric instability associated with sting jets and the highest pressure level from which the sting jet can descend. Consistent with previous work, these results imply that these thresholds are somewhat arbitrary; features consistent with the definition of sting jets exist for a spectrum of available energies and descent levels. It is left to future work to determine the relationship between these variables and the strength of the resultant sting jet (measured by metrics such as surface winds, top of boundary-layer winds, sting-jet extent etc).
The sting-jet precursor regions cover most of the area corresponding to the southern edge of the cloud head of the storm that curves around the storm centre to the northwest; it is from the cloud head tip that the sting-jet emanates. The precursor regions occur along the entire North-Atlantic storm track. However, the first points in the analysed track sections (which occur the day before the time of maximum intensity of the cyclones) are skewed to the south for cyclones with sting-jet precursors, relative to the entire set of cyclones. This is indicative of the requirement for warm moist air to fuel the diabatic processes that generate sting jets. Consistent with previous case studies the precursors preferentially occur prior to the time when the cyclone reaches its maximum intensity.
Trajectories calculated along the sting jets in the high-resolution simulations demonstrate the expected characteristics of sting jets. In particular, CSI is released in the descending sting jet. The sting-jet descent rates and peak horizontal wind speeds at the top of the boundary layer compare well with previously analysed case studies. These results suggest that sting jets are a relatively generic feature of North-Atlantic cyclones and that previously analysed sting-jet cyclones are more exceptional in their path over populated areas (which led to their identification as sting-jet storms) than in the strength of their sting jets. We also note that the Great October storm was exceptional in both its path and its strength (not matched by any of the high-resolution simulated cyclones discussed here).
These results have potential impact for end-users including the insurance/reinsurance industry, policy makers and engineers responsible for the design of infra-structure subject to wind load (Baker 2007). More research is needed to determine the relationship between metrics for the existence of sting jets (such as the instability-based diagnostic applied here) and the strength of the associated observed surface winds and gusts.