Objective detection of sting jets in low-resolution datasets

Transcription

1 METEOROLOGICAL APPLICATIONS Meteorol. Appl. 20: (2013) Published online 4 October 2011 in Wiley Online Library (wileyonlinelibrary.com) DOI: /met.297 Objective detection of sting jets in low-resolution datasets Oscar Martínez-Alvarado,* Suzanne L. Gray, Peter A. Clark, and Laura H. Baker Department of Meteorology, Joint Centre for Mesoscale Meteorology, University of Reading, Reading RG6 6BB, UK ABSTRACT: Sting jets are transient coherent mesoscale strong wind features that can cause damaging surface wind gusts in extratropical cyclones. Currently, we have only limited knowledge of their climatological characteristics. Numerical weather prediction models require enough resolution to represent slantwise motions with horizontal scales of tens of kilometres and vertical scales of just a few hundred metres to represent sting jets. Hence, the climatological characteristics of sting jets and the associated extratropical cyclones cannot be determined by searching for sting jets in low-resolution datasets such as reanalyses. A diagnostic is presented and evaluated for the detection in low-resolution datasets of atmospheric regions from which sting jets may originate. Previous studies have shown that conditional symmetric instability (CSI) is present in all storms studied with sting jets, while other rapidly developing storms of a similar character but no CSI do not develop sting jets. Therefore, it is assumed that the release of CSI is needed for sting jets to develop. While this instability will not be released in a physically realistic way in low-resolution models (and hence sting jets are unlikely to occur), it is hypothesized that the signature of this instability (combined with other criteria that restrict analysis to moist mid-tropospheric regions in the neighbourhood of a secondary cold front) can be used to identify cyclones in which sting jets occurred in reality. The diagnostic is evaluated, and appropriate parameter thresholds defined, by applying it to three case studies simulated using two resolutions (with CSI-release resolved in only the higher-resolution simulation). Copyright 2011 Royal Meteorological Society and British Crown Copyright, the Met Office KEY WORDS conditional symmetric instability; SCAPE; Shapiro Keyser cyclone; windstorm Received 10 March 2011; Revised 5 August 2011; Accepted 15 August Introduction Sting jets are transient coherent mesoscale strong wind features that descend from the mid-tropospheric cloud head towards the top of the boundary layer in the frontal fracture region of some Shapiro Keyser type extratropical cyclones (Browning, 2004; Clark et al., 2005). Their importance stems from their potential to generate intense winds at the surface (if boundary-layer momentum transport occurs) and subsequent property damage and loss of life. Several studies have analysed the development of sting-jet storms from observational (Browning, 2004; Parton et al., 2009) and numerical (Clark et al., 2005; Baker, 2009; Parton et al., 2009; Martínez-Alvarado et al., 2010) viewpoints. The release of conditional symmetric instability (CSI) has been proposed as one of the main mechanisms for the development of sting jets (Browning, 2004; Clark et al., 2005). CSI is a moist instability that occurs when an atmosphere that is stable to vertical displacements (convectively stable) and stable to horizontal displacements (inertially stable) is unstable to slantwise displacements due to the combination of inertial and convective instability (as defined by Bennetts and Hoskins (1979), Correspondence to: O. Martínez-Alvarado, Department of Meteorology, University of Reading, Earley Gate, PO Box 243, Reading RG6 6BB, UK. O.MartinezAlvarado@reading.ac.uk Now at Departments of Mathematics and Civil, Chemical and Environmental Engineering, University of Surrey, Guildford, UK. The contribution of this author was written in the course of his employment at the Met Office, UK, and is published with the permission of the Controller of HMSO and the Queen s Printer for Scotland. Emanuel (1983a, 1983b), and reviewed by Schultz and Schumacher (1999)). Increasing evidence has shown that CSI release contributes to the development of sting jets (Parton et al., 2009; Martínez-Alvarado et al., 2010; Gray et al., 2011). Evaporative cooling of rain and snow falling from upper levels into the sting jet is necessary for the release of CSI by descending air parcels and has also been proposed as a mechanism that enhances the development of sting jets (Clark et al., 2005; Parton et al., 2009; Martínez-Alvarado et al., 2010). This study develops a diagnostic that will solve one of the several unanswered questions regarding sting jets: what are the climatological characteristics of sting jets in extratropical cyclones? To the authors knowledge, the study by Parton et al. (2010) is the only one to date that provides information on the climatological frequency of sting jets. Their analysis of midtropospheric mesoscale strong wind events, as observed by the MST (Mesosphere-Stratosphere-Troposphere) radar based in Aberystwyth (Wales, United Kingdom), found 9 possible sting jet cases from 117 strong wind events over 7 years. However, it is very difficult to extrapolate from this point analysis of strong winds to a climatology of these events over a region such as that covered by the North Atlantic storm track. In contrast to the UK, Mass and Dotson (2010) in their study of major extratropical cyclones of the Northwest United States state there is little evidence of the sting jet mechanism in radar and satellite observations and high-resolution model simulations of case studies; however, a systematic search for sting jets has yet to be performed. The most definitive observational signature of a sting jet is a transient (a few hours) localized region (perhaps 100 km across) of strong surface winds in the frontal fracture zone. Copyright 2011 Royal Meteorological Society and British Crown Copyright, the Met Office

2 42 O. Martínez-Alvarado et al. Such regions could perhaps be identified over land from station observations or even insurance claims (for exceptional cases) but there is no suitable observational dataset over the oceans (note that the 12-hourly QuikSCAT dataset does not provide data at a given point at frequent enough intervals to enable confident identification of sting jets, although it may be possible to develop a methodology to use this dataset). The other two observational signatures of a sting jet are from satellite imagery. First, cloud bands and associated fingers of cloud are seen at the tip of the cloud head as it wraps around the cyclone centre. These cloud bands can be associated with slantwise circulations and evaporation. The strong surface gusts due to a sting jet in the October 1987 storm over the United Kingdom were found close to the leading edge of the cloud-head bands (Browning, 2004): this proximity led to the hypothesized mechanisms which were later supported by modelling studies as described above. However, although such cloud bands and fingers are seen in the cloud heads of cyclones that possess sting jets, these features are frequently observed in intense cyclones and the proportion of these cyclones that possess sting jets is not known. Second, shallow low-level cloud features are seen in the dry-slot region of cyclones. Browning and Field (2004) attributed shallow arc-shaped and smaller chevron shaped cloud features observed here in the Great Storm of October 1987 to boundary-layer convergence lines generated by sting jets. The other sting jet studies to date (referenced above) are individual case studies using either observations or model hindcasts. Model simulations require resolutions achieved by grid spacing of about 10 km in the horizontal and about m in the vertical in the mid-troposphere to resolve the release of CSI (Persson and Warner, 1993) and this resolution has also been found necessary to resolve sting jets consistent with CSI release being a driving mechanism for sting jets (Clark et al., 2005; Martínez-Alvarado et al., 2010). This vertical resolution is higher than that used in current large-domain operational numerical weather prediction models, e.g. the Met Office Unified Model (MetUM) currently runs over a North Atlantic European domain with a horizontal grid spacing of 0.11 and midtropospheric vertical grid spacing of about m. Hence, such current operational forecasts are unlikely to represent sting jets realistically and additionally there is no long-term dataset of high-resolution simulations. It is concluded that development of a regional sting jet climatology from observations or operational numerical weather prediction forecasts of actual sting jets would be challenging. Hence, it has been chosen instead to develop a method of identifying atmospheric regions that could lead to the development of sting jets. The objective of this study is to develop a method of identifying extratropical cyclones in which sting jets develop through CSI release from gridded, low-resolution atmospheric datasets, such as global reanalyses. Reanalyses such as those produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Uppala et al., 2005) and the National Center for Environmental Prediction (NCEP) (Kalnay et al., 1996) are the longest and most complete atmospheric datasets available. However, the horizontal resolution of these datasets is about 100 km and so, while CSI is generated in the models used to generate these reanalyses, CSI release is not resolved (nor is it parameterized). Instead, unstable regions tend to accumulate instability until it is released in an unrealistic way, possibly due to the action of the models convection schemes. Hence, while sting jets are not represented in reanalysis datasets, the CSI precursors to sting jets should be present and it is hypothesized that these can be used to infer cyclones in which sting jets develop in reality. To this aim different relevant atmospheric fields in three case-study model simulations at two resolutions (only one of which is high enough to resolve CSI release) are compared and discussed. Specifically, the limited area and global versions of the MetUM are used. The rest of the article is organized as follows. The details of the proposed diagnostic are presented in Section 2. This diagnostic requires the determination of thresholds for parameters and the approach for this is described in Section 3. This approach is based on the analysis of three case studies, which are reviewed in Section 4, and the analysis of four derived atmospheric fields, which is described in Section 5. Finally, the recommended thresholds of the proposed diagnostic s parameters are summarized in Section 6, where final conclusions are also given. 2. Definition of the objective diagnostic The objective diagnostic for identifying sting jet cyclones from gridded, low-resolution datasets follows directly from the conclusion of Gray et al. (2011) that downdraught slantwise convective available potential energy (DSCAPE) could be used as a discriminating diagnostic for the sting jet. The spatial distribution and temporal evolution of CSI in four severe storms was analysed by Gray et al. (2011): a sting jet was identified in three of these storms but the fourth storm did not have a sting jet, even though it had many of the apparent features of sting jet storms. DSCAPE was found to be collocated with the sting jets in the three sting jet storms and had a localized maximum in two of these storms. The storm without a sting jet had smaller DSCAPE values in the frontal fracture region of the storm with no localized maxima. Three of the four storms analysed by Gray et al. (2011) are also analysed in the present paper using the simulations performed by Gray et al. (2011). The fourth storm, the Great Storm of October 1987, was not analysed here because a global model simulation of this storm was not available (Gray et al. (2011) used the limited area model simulation of Clark et al. (2005)) Definition of DSCAPE DSCAPE is the available potential energy of an air parcel restricted to move along a surface of constant absolute momentum, assuming that it becomes saturated at constant pressure through the evaporation of rain or snow falling into it from upper levels. This definition is based on those of downdraught convective available potential energy (DCAPE) (see, for example, Emanuel, 1994) and slantwise convective available potential energy (SCAPE) (Emanuel, 1983a, 1983b). Thus, it can be computed as: DSCAPE = pbottom p top R d ( Tv,e T v,p ) d ln p (1) where R d is the dry air gas constant, p is pressure, and T v,p and T v,e are the parcel and environmental virtual temperatures, respectively (the code used was written by Kerry Emanuel and is available from emanuel/home.html). The integral in Equation (1) is evaluated along a curve of constant vector absolute momentum, defined by its components M = f x + v and N = f y u (where f is the Coriolis parameter, (x, y) are the orthogonal Cartesian co-ordinates and (u, v) the corresponding velocity components), analogous to

3 Objective detection of sting jets in low-resolution datasets 43 the method for the calculation of SCAPE described by Shutts (1990). The momentum components are calculated for each model gridpoint (i.e., the reference values for longitude and latitude in the equations for the momentum components in Section 3 of Shutts (1990) are those of the gridpoint under consideration). The frontal-fracture region can be regarded as an evolving, curved environment, where the full wind is more representative than the geostrophic wind. Hence, in this study the full, rather than geostrophic, wind is used for the computation of absolute momentum (Gray and Thorpe, 2001; Novak et al., 2004, 2006, 2008). However, the long-standing debate on the most appropriate wind definition to be used in the assessment of moist symmetric instability is acknowledged (Schultz and Schumacher, 1999; Schultz and Knox, 2007, and references therein). p top and p bottom are prescribed pressurelevels at the top and bottom of the hypothetical downdraught. For the calculation of DSCAPE here, p bottom is prescribed as 950 hpa whereas p top varies within a given interval (P low, P high ), where P low is prescribed as 450 hpa and an appropriate value for P high is to be determined under the assumption that there is a maximum pressure from which air must descend to be called a sting jet. Each horizontal location x is characterized by the maximum DSCAPE value (denoted by DSCAPE ) for the vertical column. Furthermore, the pressure at the top of the downdraught, p top, is defined as the pressure level where DSCAPE is found. p top is interpreted as the most likely level from which a sting jet would descend. Thus, the horizontal distributions of DSCAPE and p top are given by: DSCAPE (x) = max DSCAPE(x,p top ), (2) P low p top P high DSCAPE(x,p top) = DSCAPE (x). (3) It is assumed that there is a minimum threshold value of DSCAPE beyond which the release of this energy would lead to a strong descending stream that can develop into a sting jet 2.2. Further conditions for the identification of sting jet cyclones The conditions on DSCAPE and p top, must be complemented by further conditions regarding the location of the unstable zone, which must occur in cloudy regions in the vicinity of the secondary cold front (specifically in the frontal fracture region), where a sting jet could be expected. Here the terminology used by Browning (2004) is used and the bent-back front is considered to be composed of a warm front and a secondary cold front (see Browning s Figure 2 for a conceptual model of an extratropical cyclone undergoing transition from stages III to IV which illustrates these fronts). Three additional conditions are used to differentiate regions that could give rise to sting jets. These conditions can be classified as position or moisture conditions. The objective of the position conditions is to identify the frontal zones including both the primary and secondary cold fronts. There are sophisticated techniques available to objectively locate fronts (e.g. Hewson, 1998). However, for this application the interest is in the frontal zones rather than the actual position of the fronts themselves. Therefore, position conditions are imposed on the magnitude of the horizontal gradient of wet-bulb potential temperature, θ w, and the horizontal advection of θ w, A(θ w ) = v θ w where v is horizontal velocity. The position conditions are imposed on the mean values of θ w and A(θ w ) over a layer of thickness p centred on p top. θ w is used to place the unstable regions in the neighbourhood of a front. Thus, the condition imposed on θ w is that it must exceed a minimum threshold ( θ w min ). To decide whether a front is cold or warm the horizontal advection θ w was used. The condition imposed on this variable is also that it must exceed a minimum threshold (A min ), where A min is a positive constant, so that cold air flows toward warm air. Given that A(θ w ) = θ w v cos α, where α is the angle between θ w and v, the conditions on θ w and A(θ w ) can be combined to yield v cos α A min / θ w min, which imposes a lower bound on the cross-front horizontal velocity component. The objective of the moisture condition is to distinguish between the cloud head and the dry intrusion: CSI is found in the dry intrusion but no moisture is available for its release. Relative humidity with respect to ice (RH) is used as a measure of the moisture availability to saturate the parcels by evaporation of precipitation. It is assumed that there is a minimum threshold value of RH required, here set to 80%. The moisture condition is imposed on the maximum value of RH within the same layer of thickness p centred on p top. 3. Method and model configuration The objective diagnostic described in Section 2 requires the calibration of four parameters. These are the minimum DSCAPE, the maximum descent pressure, P high, the minimum θ w,and the minimum θ w advection, A min. In this section the method to calibrate these parameters and the numerical weather prediction model that will be used for this purpose are described. Since the objective diagnostic introduced in Section 2 is designed to be applied to low-resolution atmospheric datasets, the limited area model (LAM) simulations of three extratropical cyclones will be compared with global model simulations of these same storms. The first storm is Anna, a cyclone that passed over the UK during the early hours of 26 February This cyclone featured a sting jet which has already been subject of detailed examination (Martínez-Alvarado et al., 2010; Gray et al., 2011). The second cyclone is Gudrun, which passed over the north of the UK from around 1800 UTC 7 January 2005 to 1300 UTC 8 January A sting jet occurrence during the passage of Gudrun has also been subject of in-depth examination (Baker, 2009; Gray et al., 2011). The third cyclone is Tilo, which passed to the north of the British Isles during 7/8 November Analysis of a numerical simulation of this storm failed to find a sting jet despite this case having strong surface winds and a fractured cold front (Gray et al., 2011). Therefore, this case will be used to compare and contrast the results with the two sting-jet cases. The three cyclones developed closely following the Shapiro Keyser model of cyclogenesis (Shapiro and Keyser, 1990), although storm Gudrun showed an interesting variation with the development of two parallel warm fronts (and corresponding cold conveyor belts (Baker, 2009)). Cyclones Anna and Tilo were named by the adopt-a-vortex scheme run by the Institute of Meteorology of the Free University of Berlin. Storm Gudrun was named by the Norwegian Meteorological Institute (although it has also been named Erwin by the adopt-a-vortex scheme). The LAM and global model simulations analysed are those described by Martínez-Alvarado et al. (2010) for storm Anna, Baker (2009) for storm Gudrun, and Gray et al. (2011) for storm Tilo. The simulations were all performed using version 6.1 of the MetUM, an operational non-hydrostatic finite-difference model that solves the non-hydrostatic deepatmosphere dynamical equations with a semi-implicit, semi- Lagrangian integration scheme (Davies et al., 2005). Details of

4 44 O. Martínez-Alvarado et al. the LAM and global model simulations can be found in the above referenced papers and only the resolutions are repeated here. In the global configuration, the MetUM was run at two different resolutions. For storms Anna and Gudrun, the model was run with a horizontal grid of gridpoints (0.83 longitude and 0.55 latitude, approximately equivalent to gridboxes of 65 km in the extratropics) and 38 vertical model levels (lid around 39 km). For storm Tilo, the model was run with a horizontal grid of gridpoints (0.56 longitude and 0.37 latitude, approximately equivalent to gridboxes of 45 km in the extratropics) and 50 vertical model levels (lid around 60 km). The two different resolutions were used due to purely practical reasons since initial conditions for each storm were available at the indicated resolutions. In the LAM configuration the horizontal grid is rotated in latitude/longitude. The Met Office s North Atlantic European domain and associated model configuration (with this MetUM version) was used for the simulations presented here. Operationally this used gridpoints with gridboxes of 0.11 ( 12 km) in the horizontal and 38 vertical levels, with lid around 39 km. The same horizontal grid spacing was used in this study but, due to the critical influence of the vertical resolution on the simulation of sting jets (Clark et al., 2005; Parton et al., 2009), 76 vertical levels were used. The additional levels were inserted between the existing 38 levels yielding a level separation of between 200 and 370 m (as in Martínez-Alvarado et al., 2010), enabling the model to represent slantwise motion due to the release of CSI (Persson and Warner, 1991, 1993; Clark et al., 2005). Note that the current version of the MetUM is run with gridpoints with the same gridbox size in the horizontal but 70 model levels (with the lid around 80 km yielding a similar vertical resolution in the midtroposphere to the 38 level configuration). 4. Review of the case studies 4.1. Storm Anna The cyclone began its development around 1200 UTC 25 February According to six-hourly Met Office operational synoptic analyses (ASXX charts, Dominy, 2006), the pressure dropped 31 hpa in 24 h from 996 hpa at 1200 UTC 25 February 2002, satisfying the criterion for explosively deepening extratropical cyclones (Sanders and Gyakum, 1980). The cyclone reached stage II (frontal fracture) as defined by the Shapiro Keyser life-cycle model by 0000 UTC 26 February 2002, whereas stage III (bent-back front and frontal T-bone) was reached around 0300 UTC. The warm-core frontal seclusion, marking the onset of stage IV, appeared at approximately 1100 UTC. For the simulation of storm Anna, the MetUM was initialized with the global operational analysis from the ECMWF at 1200 UTC 25 February The analysis fields (originally at a grid spacing of 0.5 and 60 vertical model levels) were interpolated onto the resolutions of the global and the verticallyenhanced LAM domains, as required. A sting jet has been identified in this storm as a region of relatively dry, strong descending winds, in two simulations (using two different mesoscale models, the MetUM and the Consortium for Small Scale Modelling (COSMO) model) at pressure levels between 800 and 650 hpa at 0700 UTC 26 February 2002 (Martínez- Alvarado et al., 2010). Backward-trajectory analysis revealed that this sting jet started descending from levels between 675 and 500 hpa, considering maximum and minimum trajectory ensemble pressures, (between 575 and 500 hpa, considering ensemble mean pressure ± one standard deviation) around 0100 UTC 26 February This sting jet descended from a region characterized by moderately high values of DSCAPE (Gray et al., 2011) in the presence of sufficient moisture to allow the release of CSI. More details on the development of this sting jet can be found in Martínez-Alvarado et al. (2010) Storm Gudrun According to ASXX charts, the cyclone started developing around 1800 UTC 6 January 2005 over the North Atlantic. According to Baker (2009), stage II of the Shapiro Keyser lifecycle model was reached around 2200 UTC 7 January 2005, whereas stage III was reached around 0300 UTC 8 January Stage IV was reached around 5 h later. This also corresponds with the frontal configuration in the corresponding ASXX charts (interpreted under the Shapiro Keyser life-cycle model). With a minimum mean sea level pressure drop of around 42 hpa in 24 h (between 1200 UTC 7 January 2005 and 1200 UTC 8 January 2005, according to ASXX charts), storm Gudrun also satisfies the criterion to be classified as an explosively deepening cyclone (Sanders and Gyakum, 1980). The simulation of storm Gudrun was initialized with the Met Office s operational analysis from the global MetUM at 0900 UTC 7 January The analysis fields were interpolated onto the resolution of the vertically-enhanced LAM domain. A sting jet was identified in this storm at 0400 UTC 8 January 2005 between 875 and 800 hpa (maximum and minimum trajectory ensemble pressures) or 850 and 800 hpa (ensemble mean pressure ± one standard deviation). Using backward-trajectory analysis, it was determined that this sting jet descended from a region of high relative humidity by more than 150 hpa (mean) during 10 h from pressure levels between 750 and 600 hpa (maximum and minimum trajectory ensemble pressures) or 700 and 600 hpa (ensemble mean pressure ± one standard deviation) at 1800 UTC 7 January 2005 (Baker, 2009) Storm Tilo Based on ASXX charts corresponding to the interval between 0000 UTC 7 November 2007 and 0000 UTC 9 November 2007, storm Tilo started developing around 0000 UTC 7 November 2007 approximately 280 km from the south coast of Greenland. The storm reached stage II of the Shapiro Keyser life-cycle model around 1800 UTC 7 November 2007 when it was located south of Iceland. Stage III was reached around 0000 UTC 8 November 2007, and the warm-core frontal seclusion appeared around 0600 UTC on the same day. With a minimum mean sea level pressure drop of around 30 hpa in 24 h, from 1006 hpa at 0600 UTC 7 November 2007 to 976 hpa at 0600 UTC 8 November 2007, storm Tilo also satisfies the criterion to be classified as an explosively deepening cyclone (Sanders and Gyakum, 1980). The simulation of storm Tilo was initialized with the Met Office s operational global analysis at 0600 UTC 7 November The method to locate low-level regions of potential sting jets in the LAM simulation shows strong ( V > 35 m s 1 ), descending (w <0ms 1 ) and relatively dry (RH <80%) winds between 650 and 850 hpa located in the frontal fracture zone (279 K < θ w < 280 K) from 2100 UTC 7 November 2007 up to 0600 UTC 8 November Backward trajectory analysis with trajectories ending at 0100 UTC

5 Objective detection of sting jets in low-resolution datasets 45 Figure 1. Hourly minimum mean sea level pressure tracks (filled markers) and corresponding 850-hPa strongest wind speed locations (open markers) for cyclones (a) Anna (starting at 2000 UTC 25 February 2002), (b) Gudrun (starting at 1600 UTC 7 January 2005), and (c) Tilo (starting at 1400 UTC 7 November 2007) in the global model (circles/solid lines) and LAM (triangles/dashed lines) simulations. 8 November 2007 shows that there was a weak slowly descending stream composed of only about 20 trajectories that descended at a rate of about 0.3 Pa s 1. In contrast, the other two cases had streams composed of more than 100 trajectories that descended at rates of 0.5 and 0.8 Pa s 1 for storms Gudrun and Anna respectively. Beneath this weak stream there was a powerful cold conveyor belt which was responsible for the strong winds at 850 hpa of more than 40 m s Comparison of the global model and LAM simulations Figure 1 shows minimum mean sea level pressure tracks for the three cyclones as simulated by both global and LAM simulations, covering from part of stage I to the onset of stage IV of the Shapiro Keyser model of cyclogenesis. Although at times the cyclone tracks depart from each other by a few hundred kilometres, especially at the early stages of the cyclones life cycles, the correspondence between both simulations is remarkable. The track difference for a given time ranges between 13 and 250 km for storm Anna, 21 and 290 km for storm Gudrun, and 5 and 80 km for storm Tilo. These results show that there is a good agreement across simulations in the development of the large-scale circulation of the three cyclones. Figure 1 also shows the location of the 850 hpa strongest winds for the three cyclones according to both simulations. The simulations of storm Anna show agreement during the first 12 h that are shown here, in which minimum mean sea level pressure tracks and strongest wind tracks move almost parallel to each other (Figure 1(a)). After this period, at 0800 UTC and 3 h before the end of stage III, the LAM simulation shows a different strongest-wind pattern, with the strongest winds closer to the position of the minimum mean sea level pressure than in the global model simulation, and a difference between simulations of 470 km. The strongest winds are due to a developing cold conveyor belt and possibly to the transfer of momentum due to mixing from the sting jet that reached its lowest level around 0700 UTC. A very similar behaviour is exhibited by storm Gudrun (Figure 1(b)), in which the disagreement between the global model and LAM simulations takes place starting at 0400 UTC (4 h before the end of stage III), with a difference between simulations of 500 km. The strongest winds near the cyclone s centre are initially due to the sting jet in this system, which reached its lowest level at 0400 UTC, and later due to the cold conveyor belt and possibly to the transfer of momentum from the sting jet through the boundary layer due to mixing. In contrast, storm Tilo s strongest-wind tracks agree in the global model and LAM simulations throughout the interval shown here (Figure 1(c)). Figure 2 shows the minimum mean sea level pressures and strongest wind speeds for both simulations for the three storms. In all three cases, the LAM simulations yield deeper systems (lower pressures), with a difference at the end of the period shown here of 7 hpa in Anna, 3 hpa in Gudrun, and 4 hpa in Tilo. There is also a systematic underestimation of strongest wind speeds by the global model simulations in the three cases, especially towards the end of stage III. The systematically stronger wind speed in the LAM simulations compared to the global model simulations contributes to the enhancement of the frontal fracture in the LAM simulations (see, for example, Figures 9 and 11), although effect of resolution differences on thermodynamic evolution are likely to contribute as well. For cyclones Anna and Gudrun, the differences increase during the periods when the strongest-wind locations in the global model and LAM simulations diverge and persist even when the locations converge again. The differences are 10 m s 1 in Anna and 23 m s 1 in Gudrun at the end of the time period considered. The difference in strongest-wind speed locations and magnitudes are at least partly due to mesoscale features that are not well resolved with the resolution of global models and that can be important for the analysis of risk posed by extratropical cyclones. 5. Diagnostic fields The diagnostics from the global model and LAM simulations of the three case studies are compared here and parameter thresholds determined by first analysing the DSCAPE and p top distributions (Section 5.1), second by analysing the θ w and A(θ w ) distributions (Section 5.2), and finally by analysing the distribution of DSCAPE in regions that satisfy the combined conditions for the objective identification of sting jets with appropriate thresholds (Section 5.3). Henceforth, figures will be presented using reference frames following each system assuming constant system velocity along a great circle. This assumption is only valid for short periods which, nevertheless, include the relevant period in the evolution of each system. The constant eastward and northward velocity components (with respect to the LAM grid) for each system are (20.0, 6.0) m s 1 for Anna, (24.7, 13.7) m s 1 for Gudrun, and (17.8, 6.7) m s 1 for Tilo. These velocities were used to define the system centre at each time in the LAM simulations and these positions were then used for the central positions of the cyclones simulated by both the LAM and global model when plotting.

6 46 O. Martínez-Alvarado et al. Figure 2. (a) Hourly minimum mean sea level pressure and (b) corresponding 850-hPa strongest winds for cyclones Anna (starting at 2000 UTC 25 February 2002, black lines), Gudrun (starting at 1600 UTC 7 January 2005, light grey lines) and Tilo (starting at 1400 UTC 7 November 2007, dark grey lines with plus symbols) in the global model (solid lines) and LAM (dashed lines) simulations Distributions of DSCAPE and p top The distributions of DSCAPE and p top are given in the following section. It is important to realize that the diagnostic DSCAPE analysed here is slightly different to the diagnostic DSCAPE analysed in Gray et al. (2011) due to the different objectives of the two studies. Here DSCAPE is calculated for air parcels descending from a wide range of pressures (from 800 to 450 hpa) to determine if DSCAPE can be used as a diagnostic for realizable CSI that could be associated with sting jets. In Gray et al. (2011) DSCAPE was calculated for air parcels descending from a pressure layer corresponding to the diagnosed sting jet to determine the relationship between DSCAPE and the sting jet in extratropical cyclones Storm Anna Figure 3(a) and (b) show the distribution of DSCAPE and p top in the LAM simulation of storm Anna at 0100 UTC 26 February 2002 (corresponding to the time when the sting jet started descending). The black circles in those frames represent the position of the sting jet at this time according to backwardtrajectory analysis. Figure 3(a) clearly shows the correspondence between the sting jet and a DSCAPE local maximum, with 400 J kg 1 < DSCAPE < 500 J kg 1. Furthermore, this local maximum is located vertically at the pressure-layer ( hpa) from where the sting jet originally descends (Table 1, Figure 3(b)). The local maximum of DSCAPE at the level from where the sting jet starts its descent and the presence of negative MPV at the start of the sting jet trajectories (found by Martínez-Alvarado et al. (2010)) are indicative of the presence of CSI at the origin of the sting jet. A more comprehensive discussion can be found in Gray et al. (2011). The DSCAPE distribution is similar in the LAM and global model simulations (compare Figure 3(a) and (c)). However, unlike the LAM simulation, the global model simulation does not show a local maximum near the position where the sting jet occurs in the LAM simulation (cf. Figure 3(a) and (c)). However, DSCAPE > 200 J kg 1 can still be found in the same region, indicating the presence of CSI here. The p top distribution is also similar in the LAM and global model simulations Storm Gudrun Figure 4 shows the distribution of DSCAPE and p top in the LAM and global model simulations of storm Gudrun at 2200 UTC 7 January By this time the sting jet had already descended an average of 100 hpa in 4 h: it continues descending for a further 6 h. The values of DSCAPE at the tip of the cloud head (as defined by the marked rectangle), at the position where a sting jet was located in this storm, are between 300 and 500 J kg 1 (Figure 4(a)). These values are similar to those found in storm Anna. However, unlike that case, there is no clear maximum associated with the sting jet. Instead, the area of enhanced DSCAPE (larger than 300 J kg 1 )isa broad region that extends beyond the tip of the cloud head. Embedded in that same location, there is also an area with larger DSCAPE values (DSCAPE > 500 J kg 1 ). However, this area is not related to strong descending air streams (as assessed by forward-trajectory analysis starting from such areas, not shown). From the distribution of p top in the LAM simulation (Figure 4(b)), DSCAPE occurs for p top between 800 and 600 hpa at the tip of the cloud head. These values are in very good agreement with the results from backward-trajectory analysis which shows that, at this time, the sting jet in the LAM simulation was located between 775 and 700 hpa (considering the ensemble mean pressure ± one standard deviation). These pressure values appear in a small region that coincides with the position of the sting jet and is surrounded by lower values of p top (p top < 600 hpa), forming a high-pressure isolated region. This could result from DSCAPE being released by the sting jet but not in the surrounding regions. It is hypothesized that the distribution of p top was more uniform prior to the descent of the sting jet and consequent increase in p top in the sting jet region. It is also noted that the lack of a clear maximum in DSCAPE associated with the sting jet is a consequence of the variability in p top in the cloud head tip. A localized maximum in DSCAPE is found for air parcels descending from the pressure of the diagnosed sting jet (see Figure 8d of Gray et al., 2011). The structure of the distribution of DSCAPE in the global model simulation resembles that in the LAM simulation. There is also a region at the tip of the cloud head with DSCAPE > 300 J kg 1, indicating the presence of CSI in the correct

7 Objective detection of sting jets in low-resolution datasets 47 Figure 3. (a,c) DSCAPE,inJkg 1,and(b,d)p top, in hpa, for storm Anna at 0100 UTC 26 February 2002 in the LAM (upper row) and global model (lower row) simulations. Also shown are 825-hPa θ w isolines (thin lines), model-derived edge of cloud (bold lines) and model-derived cloud-covered area (stippled) determined as the 80% RH-contour and the area where RH >80%, respectively, at 550 hpa (LAM) and 575 hpa (global model). Black circles in (a) and (b) represent the position of the sting jet according to backward trajectories taken from the LAM simulation. This figure is available in colour online at wileyonlinelibrary.com/journal/met location (Figure 4(c)). In the global model simulation (in this region) DSCAPE does not reach values beyond 500 J kg 1, apart from in the dry slot. The distribution of p top in the global model simulation shows good agreement with the LAM simulation. In both simulations p top is in the range 500 hpa < p top < 800 hpa, although the distribution in the global model simulation is much more uniform (Figure 4(d)). For example, there is no clear high-pressure isolated region corresponding to the sting jet as in the LAM simulation Storm Tilo Figure 5 shows the distribution of DSCAPE and p top in the LAM and global model simulations of storm Tilo at 2200 UTC 7 November The smoother structure of the distribution of DSCAPE in the LAM simulation compared to the two previous cases is immediately apparent (Figure 5(a), cf. Figures 3(a) and 4(a)). In particular large DSCAPE values (DSCAPE > 300 J kg 1 ) only exist in the dry slot sector; the tip of the cloud head is characterized by lower values. The p top values and distribution (Figure 5(b)) are consistent with those computed for storms Anna and Gudrun for the dry slot. The distributions of both DSCAPE (Figure 5(c)) and p top (Figure 5(d)) in the global model simulation are in excellent agreement with those in the LAM simulation (Figure 5(a) and (b)) Remarks There is consistency between storms Anna and Gudrun with respect to the assumption that sting jets require a minimum amount of DSCAPE to develop. Table 1 shows the lower-bound DSCAPE values associated with the presence of sting jets in these case studies and in the Great Storm of October 1987 (Browning, 2004; Clark et al.,2005) accordingtotherespective LAM simulations. In these cases the minimum value is around 300 J kg 1. However, the global model simulations tend to show lower values of DSCAPE than the LAM simulations. For instance, the sting jet within storm Anna would be located in a region where DSCAPE is around 200 J kg 1 in the global model simulation (Figure 3(c)). Table 1 also shows that sting jets can descend from a range of minimum pressure levels from 500 to 800 hpa. These values were taken from backward-trajectory analyses performed on LAM simulations. These values are in good agreement with

8 48 O. Martínez-Alvarado et al. Table 1. Minimum DSCAPE associated with the start of the descent of the sting jet (Gray et al., 2011) and pressures from which the sting jet starts to descend (Clark et al., 2005; Baker, 2009; Parton et al., 2009; Martínez-Alvarado et al., 2010). Storm Date Min. DSCAPE (J kg 1 ) Pressure at start of descent (hpa) Great Storm 15/16 October Jeanette 27 October 2002 N/A (5 km) 500 (4 km) 550 Anna 25/26 February Gudrun 7/8 January Min. Max. Figure 4. (a,c) DSCAPE,inJkg 1,and(b,d)p top, in hpa, for storm Gudrun at 2200 UTC 7 January 2005 in the LAM (upper row) and global model (lower row) simulations. Also shown are 825 hpa (LAM) and 850-hPa (global model) θ w isolines (thin lines), model-derived edge of cloud (bold lines) and model-derived cloud-covered area (stippled) determined as the 80% RH-contour and the area where RH >80% at 500 hpa. Black circles in (a) and (b) represent the position of the sting jet according to backward trajectories taken from the LAM simulation. For an explanation of white dashed square see text. This figure is available in colour online at wileyonlinelibrary.com/journal/met the results from the computation of DSCAPE and p top in both the LAM and global model simulations. In the case of Gudrun, the apparent mismatch is due to the fact that the sting jet started descending 4 h before the time presented here. Even so, the vertical location of DSCAPE agrees very well with that of the sting jet for the time presented here. Therefore, to identify extratropical cyclones in which sting jets develop from CSI release in low-resolution datasets it is considered that reasonable threshold values for the minimum DSCAPE and maximum p top (P high ) are 200 J kg 1 and 800 hpa respectively. These threshold values would include as many sting-jet cyclones as possible, and certainly the two cases discussed here. The definition of a sting jet as descending from the mid-troposphere is not inconsistent with a P high value of 800 hpa because it is considered that any trajectories descending from this level are likely to be on the lower limits of the sting jet, outside the core where the highest density of trajectories exists Distributions of θ w and positive A(θ w ) Storm Anna Figure 6 shows distributions of θ w and positive A(θ w ) (i.e. where dry-cold air masses flow towards relatively moisterwarmer regions) in both the LAM and global model simulations

9 Objective detection of sting jets in low-resolution datasets 49 Figure 5. (a,c) DSCAPE,inJkg 1,and(b,d)p top, in hpa, for storm Tilo at 2200 UTC 7 November 2007 in the LAM (upper row) and global model (lower row) simulations. Also shown are 825 hpa θ w isolines (thin lines), model-derived edge of cloud (bold lines) and model-derived cloud-covered area (stippled) determined as the 80% RH-contour and the area where RH >80% at 700 hpa. This figure is available in colour online at wileyonlinelibrary.com/journal/met of storm Anna at 0100 UTC 26 February Recall that the variables are not on a single pressure level: instead, they are representative of a layer that tracks p top. The primary cold front (CF1) is located in the lower right quadrant and appears as the elongated region with θ w > Km 1 (Figure 6(a)). The warm front (WF), also with θ w > Km 1, appears in the upper right quadrant with an east west orientation. Behind this front, between the two quadrants on the left-hand side, a third local maximum appears. This local maximum can be considered as a trace of the secondary cold front (CF2). This interpretation is supported by Figure 6(b), which shows positive A(θ w ) in the LAM simulation at p top. Inthis figure, the primary cold front is characterized by large values of A(θ w ) (A(θ w )> Ks 1 ). The sting jet (black circle) occurs just behind the secondary cold front in a weaker frontal region, where θ w > 10 5 Km 1. In the global model simulation there are only two regions where θ w Km 1, which correspond to the primary cold front and the warm front (Figure 6(c)). At the storm-relative location of the sting jet in the LAM simulation, θ w 10 5 Km 1 in the global simulation. The positive A(θ w ) distribution in the global model simulation (Figure 6(d)) resembles that in the LAM simulation (Figure 6(b)). However, primary and secondary cold fronts appear within the same range of A(θ w ) values, showing the whole frontal fracture zone as a single region with A(θ w )> Ks 1, in which the sting jet would be located Storm Gudrun Figure 7 shows distributions of θ w and positive A(θ w ) in both the LAM and global model simulations of storm Gudrun at 2200 UTC 7 January Storm Gudrun exhibits more fine-scale structure than storm Anna (Figure 7(a), cf. Figure 6(a)). The frontal structure in storm Gudrun ( θ w > Km 1 ) is also more complex than in storm Anna. Two warm fronts appear in the upper right quadrant, one to the south of the 825 hpa 281 K isotherm (WF1), the other to the north of the 825 hpa 279 K isotherm (WF2), as diagnosed by Baker (2009). A third warm front appears in the eastern edge of the cloud band that forms the warm conveyor belt (WF3). The primary cold front (CF1) appears towards the bottom of the lower right quadrant. The secondary cold front (CF2) appears in the two quadrants on the left-hand side, in a characteristic S-shape along the 825 hpa 279 K isotherm. The secondary cold front in windstorm Gudrun is more distinctly identified by

10 50 O. Martínez-Alvarado et al. Figure 6. (a,c) θ w at p top, ink(10 5 m) 1,and(b,d)θ w advection at p top, ink(10 5 s) 1, in (a,b) the LAM and (c,d) global model simulations for storm Anna at 0100 UTC 26 February Additional labels in (a) and (c) mark the position of the warm front (WF), the primary cold front (CF1), and the secondary cold front (CF2). The rest of symbols are as described in Figure 3. This figure is available in colour online at wileyonlinelibrary.com/journal/met this diagnostic than in windstorm Anna. Like the sting jet in storm Anna, the sting jet in storm Gudrun is located on the cold side of the secondary cold front (black circle). A comparison of the distributions of positive A(θ w ) in storms Anna and Gudrun lead to similar conclusions to those reached from comparing the distributions of θ w i.e., the fine-scale structure in the LAM simulation of Gudrun is richer than in that of Anna (Figure 7(b), cf. Figure 6(b)). The signature of possible gravity waves, with wavelengths between 50 and 60 km and wave-fronts nearly parallel to the secondary cold front, is visible to the south of the sting jet. The position of the fronts is also more apparent in the global model simulation of Gudrun than in that of Anna. Each front in the LAM simulation of Gudrun, apart from WF2 to the north of the 825 hpa 279 K isotherm, has a counterpart in the global model simulation. These fronts are characterized by θ w > Km 1 (Figure 7(c)). However, the rich fine-scale structure in A(θ w ) in the LAM simulation is not captured by the global model simulation in which primary and secondary cold fronts appear as part of a single block characterized by A(θ w )> Ks 1, although a local maximum (A(θ w )> Ks 1 ) appears collocated with part of the secondary cold front (Figure 7(d)). The storm-relative location of the sting jet in the LAM simulation is over the secondary cold-frontal region in the global model simulation, partially collocated with the local maximum in A(θ w ) Storm Tilo Figure 8 shows distributions of θ w in both the LAM and global model simulations of storm Tilo at 2200 UTC 7 November The structure of this field in the LAM simulation of this storm is simpler than that in the previous two examples (Figure 8(a)). The warm front (WF) and primary cold front (CF1) are characterized by larger values of θ w than in storms Anna and Gudrun. The warm frontal zone appears as a broad region of enhanced θ w in the upper right quadrant. This broad region seems to split in two parallel warm fronts, like those observed in storm Gudrun (Baker, 2009). The primary cold front is clearly delineated by a line of large θ w starting to the south in the lower left quadrant and approaching the cyclone centre through the lower right quadrant. By contrast, the secondary cold front is not easily discernible. There is one region with θ w > Km 1 that might correspond to the secondary cold front (CF2). This region is located around 130 km to the west of the cyclone centre. Although slightly broader, every front appears very similar in the global model simulation implying a lack of mesoscale structure in

11 Objective detection of sting jets in low-resolution datasets 51 Figure 7. (a,c) θ w at p top, ink(10 5 m) 1,and(b,d)θ w -advection at p top, ink(10 5 s) 1, in (a,b) the LAM and (c,d) global model simulations for storm Gudrun at 2200 UTC 7 January Additional labels in (a) and (c) mark the position of warm fronts (WF1, WF2, WF3), the primary cold front (CF1), and the secondary cold front (CF2). The rest of symbols are as described in Figure 4. This figure is available in colour online at wileyonlinelibrary.com/journal/met this storm (Figure 8(b)). The contours of large positive A(θ w ) for this storm (not shown) are largely coincident with those of θ w (Figure 8) in cold-frontal regions in both simulations Remarks The distributions of θ w and A(θ w ) can be used to locate cold frontal zones, including frontal fracture regions where sting jets are expected. Reasonable threshold values for the minimum θ w and A(θ w ) are 10 5 Km 1 and Ks 1 respectively to identify the secondary cold front region using low-resolution datasets. These threshold values would include as many frontal fracture regions as possible, and certainly those in the two cases discussed here Distributions of DSCAPE in regions identified by the combined conditions The conditions for the presence of releasable CSI in a moist mid-tropospheric region in the vicinity of a secondary cold front (with the thresholds derived in the previous two subsections) are now combined to implement the diagnostic to find CSI regions potentially associated with the development of sting jets, as described in Section 2. Figure 9 shows DSCAPE in regions that satisfy these conditions in storm Anna at 0100, 0300 and 0500 UTC 26 February 2002 in the LAM and global model simulations. In the LAM simulation, the unstable area that remains is collocated with the mean position of the sting jet (both horizontally and vertically) at 0100 UTC (Figure 9(a)). At 0300 UTC the unstable area in the cloud head tip has depleted, especially around the region where the sting jet is located (Figure 9(c)). This process continues further so that at 0500 UTC this unstable area is almost completely depleted (Figure 9(e)). A similar behaviour is found in the global model simulation. At 0100 UTC, when the sting jet is about to start descending, there is an unstable area collocated with the approximate position of the sting jet, just as in the LAM simulation (Figure 9(b)). The collocation between an unstable area in the global model simulation and the approximate position of the sting jet (from the LAM simulation) remains at 0300 UTC (Figure 9(d)). The extent of the unstable area has decreased, but the DSCAPE values have slightly increased to exceed 300 J kg 1. At 0500 UTC there is still a small unstable area

12 52 O. Martínez-Alvarado et al. Figure 8. θ w at p top, ink(10 5 m) 1, in (a) the LAM and (b) global model simulations for storm Tilo at 2200 UTC 7 November Additional labels mark the position of the warm front (WF), the primary cold front (CF1), and the secondary cold front (CF2). The rest of symbols are as described in Figure 5. This figure is available in colour online at wileyonlinelibrary.com/journal/met close to the location where the sting jet is in the LAM simulation. Although both simulations show unstable area depletion, the behaviour of the depletion rate is different in both. Figure 10 shows the time evolution of the average DSCAPE in a circle of 100 km radius centred at the location of the sting jet diagnosed in the LAM simulation: the depletion rate (the difference between the average DSCAPE at successive times) is also plotted. The LAM simulation exhibits a relatively constant depletion rate throughout the period of analysis ( UTC). By contrast, the depletion rate in the global model simulation is more variable with time, especially near the start of the analysis period. This different behaviour may be due to the inability of the global model simulation to release CSI in a realistic way. The differences between the LAM and global model simulations are even more evident in storm Gudrun. Figure 11 shows DSCAPE in regions that satisfy the combined conditions for realizable CSI in a moist mid-tropospheric region in the vicinity of a secondary cold front in the LAM and global model simulations of this storm at four different times: 1900 and 2200 UTC 7 January 2005, and 0100 and 0400 UTC 8 January In the LAM simulation it is clear that DSCAPE is being consumed as CSI is released during the descent of one or more sting jets, whereas in the global model simulation a noticeable amount of DSCAPE is always present. The amount and distribution of DSCAPE at 1900 UTC 7 January 2005 in the LAM simulation (Figure 11(a)) resembles that in the global model simulation (Figure 11(b)). Three hours later DSCAPE has experienced some depletion in the LAM simulation (Figure 11(c)); in contrast, the global model simulation only shows a DSCAPE redistribution at that same time (Figure 11(d)). By 0100 UTC, the LAM simulation shows a nearly complete depletion of DSCAPE (Figure 11(e)), whereas the global model simulation shows a decrease in but still considerable amount of DSCAPE in the region where the sting jet would be expected (Figure 11(f)). Similar DSCAPE distributions are still present at 0400 UTC when the sting jet has reached its lowest level (Figure 11(g) and (h)). Storm Tilo did not show any unstable regions satisfying the combined conditions for realizable CSI in a moist frontal fracture zone during its evolution in either the LAM or global simulation (not shown). 6. Summary and conclusions There is currently very limited knowledge of the climatological characteristics of sting jets and the associated extratropical cyclones. A diagnostic has been developed and evaluated for the identification of extratropical cyclones in which sting jets occur from low-resolution gridded data (such as reanalysis data). This diagnostic is currently being applied by the authors to the latest ECMWF reanalysis (ERA-Interim, Uppala et al., 2008) to develop a climatology of sting jets over the North Atlantic. It is assumed that CSI release is necessary for sting jets to develop and that the most discriminating diagnostic for CSI in sting jets is DSCAPE. The choice of DSCAPE follows directly from earlier work by the authors (Gray et al., 2011). It is hypothesized that, while sting jets themselves will not be resolved by low-resolution models because CSI release is not resolved, the signature of CSI in low-resolution data can be used to infer the presence of a sting jet in the actual cyclone. This assumption, and the diagnostic method, have been evaluated by comparing model simulations using two resolutions (only one of which is high enough to resolve CSI release) for three case studies which comprise three of the four cases analysed by Gray et al. (2011). Sting jets, identified by trajectory analysis using the higher-resolution model output, occurred in two of these cases; a sting jet was not identified in the third case despite general structural similarities with the other two cases. The diagnostic for the identification of sting jet cyclones is designed to detect regions of substantial DSCAPE at the mid-levels in moist air in the vicinity of a secondary cold front. Based on the analyses of the case studies, threshold values have been proposed for the four associated parameters: a minimum DSCAPE value of 200 J kg 1 determined for air descending from a range of pressure levels with a maximum pressure of 800 hpa to identify regions with sufficient CSI in the mid-troposphere and minimum values for θ w and A(θ w )

13 Objective detection of sting jets in low-resolution datasets 53 Figure 9. DSCAPE,inJkg 1, in the remaining regions after the conditions for sting jet generation susceptibility have been applied to (a,c,e) the LAM and (b,d,f) global model simulations for storm Anna at 0100 UTC (upper row), 0300 UTC (middle row), and 0500 UTC (lower row) 26 February The rest of symbols are as described in Figure 3. This figure is available in colour online at wileyonlinelibrary.com/journal/met of 10 5 Km 1 and Ks 1 respectively to identify the secondary cold front. A minimum relative humidity of 80% and a minimum pressure for the descending air parcels of 450 hpa was also assumed. Regions satisfying the diagnostic were found to exist in both the high- and low-resolution simulations of both the sting jet cyclones: no regions satisfying the diagnostic were found in either simulation of the cyclone that did not have a sting jet. The evolution of the regions satisfying the diagnostic was different in the high- and low-resolution simulations with the area of the region diminishing with time (indicating the

14 54 O. Martínez-Alvarado et al. Figure 10. DSCAPE (solid lines) and DSCAPE production rate (dashed lines) averaged over a 100 km radius circle centred on the position of the sting jet identified in the LAM simulation in the global model (circles) and the LAM (crosses) simulations for storm Anna. release of CSI) at a more constant rate in high-resolution simulations. This difference in behaviour is consistent with the expectation that CSI is not released in a physically realistic way in the low-resolution simulations and that CSI release leads to the development of sting jets (at least in these two storms). One obvious limitation of this study is that it is based on the detailed analysis of only two sting jet storms (with some additional information from two further sting jet storms). These four sting jet storms are the only storms in the published literature (at this time) in which a sting jet has been identified through detailed analysis including trajectory analysis that demonstrates descending air from the cloud head in the frontal fracture zone. Further evaluation and possible refinement of this diagnostic for sting jet cyclones is currently being performed by the authors using case studies identified by applying it to the ERA-Interim dataset. One disadvantage of this method is that the computation of DSCAPE is computationally expensive mainly because it requires the computation of a hypothetical slantwise trajectory for each grid point in the analysed sub-domain. Acknowledgements We thank the Met Office for making the MetUM available, and NCAS (National Centre for Atmospheric Sciences) CMS (Computational Modelling Support) for providing computing and technical support. This work has been funded by the United Figure 11. DSCAPE,inJkg 1 in the remaining regions after the conditions for sting jet generation susceptibility have been applied to (a,c,e,g) the LAM and (b,d,f,h) global model simulations for storm Gudrun at 1900 UTC 7 January 2005 (a,b), 2200 UTC 7 January 2005 (c,d), 0100 UTC 8 January 2005 (e,f), and 0400 UTC 8 January 2005 (g,h). The rest of symbols are as described in Figure 4. This figure is available in colour online at wileyonlinelibrary.com/journal/met