Assessing the predictability of Medicanes in ECMWF ensemble forecasts using an object-based approach
Enrico Di Muzio, Michael Riemer, Andreas H. Fink, Michael Maier-Gerber
OO R I G I N A L A R T I C L E
Assessing the predictability of Medicanes inECMWF ensemble forecasts using an object-basedapproach
Enrico Di Muzio | Michael Riemer | Andreas H.Fink | Michael Maier-Gerber Institute of Meteorology and ClimateResearch, Karlsruhe Institute of Technology,Karlsruhe, 76131, Germany Institute of Atmospheric Physics,Johannes Gutenberg University Mainz,Mainz, 55128, Germany
Correspondence
Enrico Di Muzio, Institute of Meteorologyand Climate Research, Karlsruhe Instituteof Technology, Karlsruhe, 76131, GermanyEmail: [email protected]
The predictability of eight southern European tropical-likecyclones, seven of which Medicanes, is studied evaluatingECMWF operational ensemble forecasts against operationalanalysis data. Forecast cyclone trajectories are comparedto the cyclone trajectory in the analysis by means of a dy-namic time warping technique, which allows to find a matchin terms of their overall spatio-temporal similarity. Eachstorm is treated as an object and its forecasts are analysedusing metrics that describe intensity, symmetry, compact-ness, and upper-level thermal structure. This object-basedapproach allows to focus on specific storm features, whiletolerating their shifts in time and space to some extent.The compactness and symmetry of the storms are gener-ally underpredicted, especially at long lead times. However,forecast accuracy tends to strongly improve at short leadtimes, indicating that the ECMWF ensemble forecast modelcan adequately reproduce Medicanes, albeit only few daysin advance. In particular, late forecasts which have beeninitialised when the cyclone has already developed are dis-tinctly more accurate than earlier forecasts in predictingits kinematic and thermal structure, confirming previousfindings of high sensitivity of Medicane simulations to initial a r X i v : . [ phy s i c s . a o - ph ] D ec D I M UZIO ET AL . conditions.Findings reveal a markedly non-gradual evolution of en-semble forecasts with lead time, which is often far from aprogressive convergence towards the analysis value. Specif-ically, a rapid increase in the probability of cyclone occur-rence (“forecast jump”) is seen in most cases, generally be-tween 5 and 7 days lead time. Jumps are also found forensemble median and/or spread for storm thermal structureforecasts. This behaviour is compatible with the existenceof predictability barriers. On the other hand, storm positionforecasts often exhibit a consistent spatial distribution ofstorm position uncertainty and bias between consecutiveforecasts. K E Y W O R D S predictability, Medicanes, forecast jumps, ensemble forecasts,dynamic time warping, object-based approach | INTRODUCTION
The Mediterranean region has long been known as a hotspot for cyclogenesis (Peterssen 1956) due to itsgeography (Buzzi and Tibaldi 1978). Despite its relatively high latitude, a small but significant fraction ofMediterranean cyclones displays some similarity to tropical cyclones both in their appearance in satelliteimages and in their kinematic and thermal structure. Such Mediterranean tropical-like cyclones, alsoknown as
Medicanes (short for Mediterranean hurricanes), have been documented since the beginningof the satellite era (Ernst and Matson 1983; Mayengon 1984; Rasmussen and Zick 1987). Medicanesconstitute a major threat due to intense winds, torrential rainfall and associated floods. These stormsare usually shorter-lived than North Atlantic hurricanes but may exhibit several tropical-like traits in themature phase of their life cycle, such as high axial symmetry, a warm core, a strong tendency to weakenafter making landfall and a cloud-free, weak-wind region at their centre resembling the eye of a hurricane(Emanuel 2005; Cavicchia et al. 2014a).Medicanes are distinguished among Mediterranean cyclones by the complex pathway leading to theirformation and maintenance. While hurricanes develop in regions of near-zero baroclinicity and drawtheir energy from very warm tropical oceans, Medicanes arise from pressure lows that are born undermoderate to strong baroclinicity. The interaction between the warm sea and cold air associated to a deepupper-level trough provides the necessary thermodynamic disequilibrium for these storms to developa warm core (Emanuel 2005; Cavicchia et al. 2014a). It can thus be maintained that Medicanes are theresult of a synergy between synoptic-scale processes, which provide the necessary environment for theirdevelopment, and mesoscale processes such as deep convection and latent heat fluxes from the sea, which I M UZIO ET AL . 3 are crucial for their maintenance (Homar et al. 2003; Emanuel 2005; Tous et al. 2013). For this reasonand because of their small size (Miglietta et al. 2013; Picornell et al. 2014), scarce data availability and thecomplex orography of the Mediterranean region, predictability of Medicanes is generally limited (Claudet al. 2010; Pantillon et al. 2013).Despite the increased research interest in the last two decades, Medicanes are by nature elusive, dueto their low frequency of occurrence (less than two per year, according to Cavicchia et al. 2014a) and thefact that they normally occur over the sea, where observations are sparse. For this reason, many studies sofar have focused on modeling aspects (Homar et al. 2003; Fita et al. 2007; Davolio et al. 2009; Migliettaet al. 2011; Chaboureau et al. 2012a; Miglietta et al. 2013; Cioni et al. 2016; Mazza et al. 2017; Pytharouliset al. 2017; Cioni et al. 2018) and fewer on observational aspects (Pytharoulis et al. 2000; Reale and Atlas2001; Moscatello et al. 2008; Chaboureau et al. 2012b; Miglietta et al. 2013). Further studies examinedMedicanes in relation to climate change (Romero and Emanuel 2013; Cavicchia et al. 2014b; Walsh et al.2014; Romero and Emanuel 2017), a critical aspect given the vulnerability of the Mediterranean regionto future climate change (Giorgi and Lionello 2008). Research efforts so far focused on deterministicsimulations of Medicanes using high-resolution, convection-permitting models (Fita et al. 2007; Davolioet al. 2009; Cioni et al. 2016; Mazza et al. 2017; Pytharoulis et al. 2017; Cioni et al. 2018) as they aredeemed to best reproduce small-scale processes playing a crucial role in storm maintenance during thetropical-like phase. Few studies analysed Medicanes using ensemble forecasts (Cavicchia and von Storch2012; Chaboureau et al. 2012a; Pantillon et al. 2013; Mazza et al. 2017) of which only Pantillon et al. (2013)used operational ensemble forecasts.Ensemble forecasts have been shown to be a valuable tool to predict extreme weather events severaldays in advance (e.g. Buizza and Hollingsworth 2002; Palmer 2002; Lalaurette 2003; Magnusson et al.2015), analyse tropical cyclones (Torn and Cook 2013; Rios-Berrios et al. 2016) and their predictability(Munsell et al. 2013; Zhang and Tao 2013). Among operational ensemble forecast systems, the EuropeanCentre for Medium-Range Weather Forecasts (ECMWF) model has shown high predictive skills for ex-treme weather events (Lalaurette 2003) including tropical cyclones (Yamaguchi and Majumdar 2010;Hamill et al. 2011) and it has been successfully used to study their predictability (Magnusson et al. 2014;González-Alemán et al. 2018). Specifically, Pantillon et al. (2013) used ECMWF operational ensemble fore-casts to study the predictability of the 2006 Medicane and found that they were able to more consistentlycapture early signals of its occurrence with respect to ECMWF deterministic forecasts.The present study fills a gap in the existing literature in that it systematically investigates the pre-dictability of eight recent (2011-2017) southern European tropical-like cyclones (seven of which areMedicanes), evaluating ECMWF operational ensemble forecasts against operational analysis. Our goalis to assess whether and how long in advance these forecasts can adequately reproduce Medicanes. Wealso analyse the temporal evolution of the predictability of these storms by identifying particularly rapidchanges of the ensemble statistics with lead time (hereafter referred to as forecast jumps for brevity) thatstand out compared to the gradual convergence towards the analysis value that might be expected. Wefinally investigate whether there is any consistent bias in the ensemble forecasts, as it could be expectedgiven the model’s relatively low horizontal resolution and parameterized convection. This is not a straight-forward task, as Medicanes are by their very nature low-probability events and as such are found near the D I M UZIO ET AL . tail of the forecast distribution, as observed by Majumdar and Torn (2014).In this study, we evaluate ensemble forecasts against analysis data using an object-based approach.Object-based methods gained popularity in recent decades for the verification of precipitation forecasts(Ebert and McBride 2000; Wernli et al. 2008) and have since been applied to the analysis of other atmo-spheric features, such as the jet stream (Limbach et al. 2012) and Rossby waves (Wiegand and Knippertz2014). These methods allow to avoid the “double penalty problem” (Ebert and McBride 2000; Wernli et al.2008) that arises in case of a mere displacement of an otherwise well predicted atmospheric feature if anEulerian error metric is used. An object-based method, in contrast, can identify that the ensemble spreadis due to a displacement of the feature and that only this aspect exhibits reduced predictability. In additionto spatial displacements, we allow (small) temporal shifts of the forecast features. This approach helpsidentify matching features in the forecast, which is beneficial to study low-probability weather events, inparticular at longer lead times.The paper is structured as follows. In Section 2, the data and methods used are described: in particular,a dynamic time warping technique that allows to consider temporal shifts in the forecasts is illustrated indetail. A brief overview of the eight storms analysed is given in Section 3, highlighting their salient features.Results are presented in Section 4, with a focus on the evolution of ensemble forecasts with lead time;this section is organized in subsections, addressing in sequence forecasts of storm occurrence, position,thermal and kinematic structure and intensity. The results are finally discussed in Section 5, alongsideconcluding remarks. | DATA AND METHODS
In this section, an illustration is provided of the methods and techniques that are used to analyse theECMWF operational analysis and ensemble forecast data in order to apply the object-based approachintroduced in Section 1. Mean sea level pressure (MSLP) lows are first identified and tracked in bothanalysis and ensemble data. Forecast cyclones are then matched to the reference cyclone in the analysis,using a DTW technique to maximize the similarity of the trajectories. Forecasts are evaluated over atime interval as opposed to a fixed forecast time: the choice of the time interval depends on the cyclone’sintensity as well as dynamical and thermal structure measured by suitable metrics. A short description isfinally provided of the graphics used in evaluating the ensemble forecast statistics. | Data
ECMWF operational analysis data is used as reference data to verify ensemble forecasts, which areinitialized twice daily (at 0000 and 1200 UTC) and consist of 50 perturbed forecasts or members and acontrol forecast. Time resolution is 6 hours for both analysis and ensemble data.Both the high-resolution, deterministic model (HRES), which is used to generate analysis data, andthe ensemble prediction system (ENS) have undergone some changes during the time period consideredin this study (2011-2017). Between 2011 and early 2016, horizontal grid spacing is 16 km for the HRESand 32 km for the ENS; afterwards, grid spacing decreases to 9 km for the HRES and 18 km for the I M UZIO ET AL . 5
ENS. Five and three events respectively occurred during these two time periods (see also Table 1 inSection 3). Vertical resolution also changed for both HRES and ENS during the analysed time period. Thereader is referred to the ECMWF webpage for a detailed documentation of model changes and updates: . | Cyclone detection and tracking
Many available cyclone detection methods (Neu et al. 2013) are not suitable for Medicanes, which have amuch smaller radius compared to most types of cyclones (see e.g. Miglietta et al. 2011; Picornell et al. 2014).This issue is especially apparent when the input data has a relatively low horizontal resolution (Walsh et al.2014) which is the case for ECMWF ensemble forecast data. For this reason, we have developed a newdetection method to identify pressure lows in both analysis and forecast data. This method has proveneffective in detecting very small cyclones, while still being capable of detecting larger cyclones as well asfiltering out spurious ones produced by noise or orographic effects.The cyclone detection method used in this study is based on MSLP contours, spaced at 1 hPa intervals,and low-level vorticity, defined as relative vorticity averaged over the 1000, 925 and 850 hPa levels. Givenour focus on the mature phase of cyclones, only closed contours are considered, thereby neglecting opensystems (e.g. diminutive waves, see Hewson 2009). Pressure lows are identified as objects falling into atleast one of two categories: (1) a set of four or more concentric contours; and (2) a set of two or moreconcentric contours with a radial MSLP gradient of 5 hPa/400 km or larger, calculated within a 400 kmdistance from the centre of the innermost contour, over at least 4 consecutive 30 ◦ -spaced azimuthaldirections. The second category is necessary to include also earlier stages of a cyclone in which its closedcirculation is still developing but a small pressure low is already present at the boundary of a larger regionof low pressure, with a large MSLP gradient in its vicinity.Detected lows are discarded when at least one of the three following conditions is met: (1) the areaof all MSLP contours exceeds 500000 square km (low is too large); (2) the area of the second innermostcontour is 50 times or more larger than the area of the innermost contour and MSLP gradient is smallerthan 5 hPa/400 km in all directions (low is considered noise); and (3) contours are too thin and irregularlyshaped (low is considered noise – this typically occurs in the vicinity of high orography). The centre of eachpressure low is finally placed where low-level vorticity reaches a local maximum within a 100 km distancefrom the MSLP minimum. The values of thresholds and parameters have been chosen conservatively, so asto minimise the number of discarded lows. The outcome of cyclone detection shows little sensitivity tosmall variations of these thresholds and parameters.After being detected, pressure lows are tracked in time using a method adapted from Hewson andTitley (2010), which uses 1000-500 hPa geopotential height difference (thickness) and 500 hPa windspeed: while a short description is given here, the reader is referred to the article above for a detailedexplanation. In this tracking scheme, a likelihood score (expressed in km) is computed for each possiblepairing of a pressure low at the previous output time and one at the current output time (hereafter referredto as “past low” and “present low”, respectively). The score estimates the likeliness of the pairing beingcorrect: that is, how likely the present low is the result of the past low advancing to a new position. D I M UZIO ET AL . In the present study, the likelihood score is built on two parameters: half-time separation and thicknesschange. Half-time separation is the distance between the past and the present low, after they are movedforward and backward in time, respectively, for 60% of the time interval, considering 500 hPa wind asthe steering flow. Thickness change is the difference in 1000-500 hPa thickness between the positions ofthe past and the present low. A third parameter which was originally used in the likelihood score formula,namely feature type transition (Hewson and Titley 2010), is kept fixed to 60% (Hewson 2009, Table 2)when calculating the likelihood score, as the only type of feature considered in the present study is theclosed low.The smaller the likelihood score is, the more likely the pairing is correct – a low score results from asmall half-time separation and a small thickness change. Pairings are discarded if the past and the presentlow are more than 600 km apart or if their likelihood score is higher than 700 km. After computing thelikelihood score for all possible pairings, they get ranked from the lowest (most likely) to the highest (leastlikely). The ranking is finally read from top to bottom and each pairing is either accepted, if neither low wasalready previously paired, or rejected otherwise. When a pairing is accepted, the present low becomesthe last element of the track that contains the past low. At the end, the remaining present lows form newtracks. | Evaluation metrics
In order to evaluate ensemble forecasts four metrics are used that are deemed to provide an adequatepicture of each cyclone’s intensity, kinematics and thermal structure: these are MSLP, symmetry, com-pactness and the upper-level thermal wind. The statistics of ensemble forecasts of these metrics will beexamined in Section 4, together with those of storm position forecasts (see also explanation in Subsection2.6).Storm intensity is represented by the cyclone’s lowest MSLP. The intensity of Medicanes may beslightly underestimated by ECMWF operational analysis data due to insufficient horizontal resolution, aneffect that is estimated to be around 2 hPa (see e.g. Cioni et al. 2016; Pytharoulis 2018). An even largerunderestimation can be expected for ensemble forecasts, given their resolution (Picornell et al. 2014;Walsh et al. 2014) which is half of that of the analysis data.In order to quantify the symmetry of the cyclone’s low-level circulation, a symmetry parameter S isdefined for any MSLP contour as follows: S = 1 + arctan ( π ( πA / P − )) where A is the area and P theperimeter of the contour. This seemingly complex formula is based on a straightforward expression ofsymmetry ( A / P ); this function is then scaled so that maximum symmetry – a perfectly round contour –equals 1 ( πA / P ) and finally stretched by applying the arctangent, so that values of high symmetry aremore widely spaced (they would otherwise tend to bunch towards 1). The last step allows to better identifythe highly symmetric, mature phase of the cyclone and interpret the ensemble statistics more clearly.The S parameter attains values of approximately 0.5, 0.2, 0 for ellipse-shaped contours having a minoraxis of length 1 and a major axis of length 2, 3, 5 respectively. The symmetry parameter of any pressurelow (hereafter referred to as just “symmetry”, for the sake of brevity) is obtained by averaging S over thefour innermost MSLP contours, spaced at 1 hPa intervals. The S parameter constitutes a representative I M UZIO ET AL . 7 metric for the high symmetry attained by Medicanes during their mature, tropical-like phase, with S valuesexceeding 0.8, as opposed to their early stages as well as the majority of extratropical cyclones which havemuch lower S values.Medicanes also tend to be much smaller than extratropical cyclones, as already pointed out, withstrong pressure gradients in the vicinity of their centres. In order to give a measure of such gradient,a “compactness” parameter (hereafter referred to as just “compactness”) is defined as the azimuthallyaveraged radial MSLP gradient within a 150 km radius around the cyclone centre, expressed in hPa/100km.Finally, the − V UT metric is chosen to quantify the cyclone’s upper-level thermal structure, namely itscold or warm core. The − V UT parameter represents upper-level thermal wind, being one of three quantitiesdefining the cyclone phase space (CPS) introduced by Hart (2003). A positive (negative) sign of − V UT indicates an upper-level warm (cold) core, while the absolute value is proportional to its magnitude. Giventhe lower height of the tropopause in the midlatitudes with respect to the tropics (Picornell et al. 2014) andthe smaller size of Medicanes compared to tropical cyclones (Miglietta et al. 2013), − V UT is calculated in aslightly different way from Hart (2003), using a smaller radius of 100 km and lower levels of 925, 700 and400 hPa similarly to (Picornell et al. 2014). A 12-hour running mean is used in the present study to smooththe CPS trajectories, differently from Hart (2003) who uses a 24-hour mean: this choice is motivated bythe short life of most Medicanes and of their tropical-like phase in particular. | Choice of the evaluation time interval
Ensemble forecasts are evaluated against analysis data over a time interval rather than at a single forecasttime. This approach has the benefit of enhancing signals, in that it can spot desired features – e.g. a stormintensity maximum – over a larger set of forecast times, thereby overlooking small timing errors (e.g. themaximum occurring a few hours earlier or later than forecast). The rationale for our approach is to focus onspecific storm features and consider a forecast to be sufficiently accurate if the features are successfullypredicted, albeit at a slightly incorrect time. This strategy is valuable especially in extracting informationfrom early forecasts.The evaluation time interval (hereafter referred to as ETI) is 24 hour long, corresponding to 5 points(i.e. 5 output times) of the cyclone track extracted from analysis data (hereafter “reference track”). Slightlyshorter or longer ETIs were tested before settling on 24 hours, showing little sensitivity. The ETI issubjectively selected to best represent the mature, tropical-like phase of the cyclone, on the basis ofthe symmetry, compactness and − V UT parameters introduced in Subsection 2.3 (MSLP is not used as themature phase of Medicanes often does not correspond to their most intense one).An example of ETI selection is shown in Figure 1. As a first step, the 5 consecutive reference trackpoints having the highest average − V UT value are selected, given that − V UT is considered the most relevantparameter in distinguishing tropical-like cyclones from fully baroclinic cyclones (see e.g. Mazza et al. 2017).As a second step, the initial 5-point selection is shifted by at most 2 points, corresponding to maximum12 hours earlier or later. This adjustment is only applied when necessary, to select output times withas high symmetry and compactness as possible: for storm Qendresa (Figure 1), for instance, the initial D I M UZIO ET AL . selection is shifted 1 point to the left (6 hours earlier) thereby increasing the average value of symmetryand compactness. F I G U R E 1
Features of storm Qendresa (November 2014) as retrieved from analysis data. Upper panel: MSLP (hPa)and upper-level thermal wind − V UT ; lower panel: symmetry and compactness. The ETI is highlighted in gray: in this casethe selected period is from 0600 UTC on 7 November 2014 to 0600 UTC on 8 November 2014. | Track matching
The tracking procedure outlined in Subsection 2.2 is used for each storm to retrieve the reference trackas well as tracks of MSLP lows in individual forecasts. The next step is then to compare all tracks froma single member of the ensemble with the reference track in order to find the best match. In order toavoid penalizing (small) discrepancies in the timing of storm motion and take into account the overallspatio-temporal similarity between tracks, we use a dynamic time warping (DTW) technique (Berndtand Clifford 1994) which has been successfully applied to a recent case study of North Atlantic tropicaltransition (Maier-Gerber et al. 2018). Originally developed for speech recognition (Sakoe and Chiba 1978),DTW is able to match two time series nonlinearly, thereby taking into account differences in signal speedand providing a more intuitive matching (Keogh and Ratanamahatana 2005). Using the DTW techniqueto match cyclone tracks allows to focus on the spatial accuracy of forecasts, ignoring small (local) timingerrors as long as the forecast track bears a high spatial similarity to the reference one. The average timedifference between DTW-paired track points may be later used to assess whether there is an early orlate bias. In the following, we briefly describe the structure of the DTW technique to illustrate how it isapplied to matching cyclone tracks. The reader is referred to Berndt and Clifford (1994) and Keogh and I M UZIO ET AL . 9
Ratanamahatana (2005) for more detailed explanations of the algorithm.DTW requires first a suitable metric to express the spatial distance between each pair of track points.We choose great circle distance but note that any distance metric could be used in principle. The aim isthen to minimize the overall distance between the two input tracks R = r , r , . . . r m and S = s , s , . . . s n by finding the best possible way of matching them. In order to do so, a m × n distance matrix D is firstcomputed: D ( i , j ) = d ( r i , s j ) for each i = 1 , . . . m and j = 1 , . . . n , where d ( r i , s j ) is the spatial distancebetween the r i and s j track points. A cumulative distance matrix M is then defined recursively as follows: M ( i , j ) = D ( i , j ) + min [ D ( i − , j ) , D ( i − , j − ) , D ( i , j − )] . The best match is finally obtained as the warpingpath , defined as the succession of M elements minimizing the cumulative distance at every point. Eachelement of the warping path represents a pair of matched track points, as shown in the fictitious examplein Figure 2. We note that the two tracks have here different lengths and that multiple points of one trackare matched to a single point of the other.
00 06 12 18 0012 18 00 06 12 18 00 06 12
12 18 00 06 12 18 00 06 120006121800 (a) (b)
F I G U R E 2
Example of DTW matching of the reference track (blue) and a forecast track (red). Numbers denote UTCtimes. a) Spatial match; matched track points are highlighted by a black dashed line. b) Cumulative distance matrix M and warping path, represented as black filled circles, for the track match in a). The warping window is highlighted in redwhile the equal-time match is highlighted in green. A DTW technique is usually applied with some constraints, which introduce physically meaningfulrequirements (Berndt and Clifford 1994). Monotonicity and continuity constraints are first imposedto assure that all track points are matched at least once and with increasing time. A warping window(highlighted in red in Figure 2) only allows the warping path to exist in the vicinity of the diagonal of the M matrix (i.e. the succession of equal-time elements), thereby restricting the time difference between anypair of matched track points to a maximum absolute value of 12 hours. Using a warping window ensures aphysically meaningful track match, preventing the match of two points that are spatially close but verydistant in time. Finally, boundary conditions require the warping path to start from (end at) the forecasttrack point that is closest to the first (last) analysis track point, to prevent the algorithm from matching toomany far away forecast track points to the first or last analysis point, which it would be forced to do if theforecast cyclone moves fast (an example is seen in Figure 2, where the first two forecast track points arenot matched to the first analysis track point). These conditions ensure that similarity is maximised in the I M UZIO ET AL . matching process.DTW is applied to match the reference track’s 24-hour ETI to each track in an ensemble member. Onlyforecast tracks that are at least 24 hours long (5 output times) are considered. Furthermore, a 48-hourinterval is selected from each track, spanning the ETI plus further 12 hours (2 output times) at both ends, tomeet the warping window constraint. If the forecast track only exists for a fraction of these 48 hours, onlythe existing part is considered (the example in Figure 2 shows the longest possible forecast track, at 48hours or 9 output times). The spatio-temporal distance between (the selected interval of) the forecast andreference tracks is finally computed in two steps: the average distance between a single reference trackpoint and all associated forecast track points is first computed; the final track distance is then obtained byaveraging the result of the above calculation over all reference track points.For a given ensemble member, forecast tracks having a 600 km or larger spatio-temporal distancefrom the reference track are discarded. This threshold has been chosen after testing the sensitivity of theresults to its value, similarly to Maier-Gerber et al. (2018). If no forecast tracks are left, the member isconsidered to have no cyclone (such members will be named “no-storm members” hereafter). Otherwise,the track with the shortest spatio-temporal distance is considered to be the best match, i.e. the mostsimilar to the reference track. Members having a best match will be named “storm members” hereafter. | Evaluation of ensemble forecasts
Ensemble forecasts of the eight storms are evaluated in Section 4. Given that forecasts are evaluated overa time interval rather than at a fixed forecast time, lead times refer to the central time of the ETI. For eachstorm, the latest forecast considered is the one initialized either at the beginning of the ETI, if this beginsat 0000 or 1200 UTC, or 6 hours earlier, if the ETI begins at 0600 or 1800 UTC. For the sake of simplicity,in Section 4 plots displaying the evolution of forecast statistics with lead time, the latest forecast is alwayslabeled as “0.5 day” (the small 6-hour difference introduced by varying beginning time of the ETIs does notaffect the results).Section 4 plots show the statistics of 16 consecutive ensemble forecasts of one of the metrics intro-duced in Subsection 2.3, for a maximum lead time of 8 days. Box-percentile plots (Esty and Banfield 2003)are preferred to standard box-and-whisker plots in that they display the whole distribution of input data:the width of each irregular “box” is proportional to the percentile p of the ordinate if p ≤ , or to − p if p > ; the maximum width is thus reached at the median, while outliers are revealed by thin spikes ateach tail. These forecasts are relative to the extreme value of each metric (the lowest value for MSLP, thehighest value for the others) computed for each storm member within the DTW-matched interval of thebest track; the reference value shown in the plots is also the extreme value computed in the referencetrack’s ETI.Storm position forecast statistics (Figure 6) are investigated by means of EOF analysis. For each stormmember, a 2D storm position error is expressed as the average longitude and latitude difference betweenthe reference track and the forecast track, computed using the DTW-matched points in an analogousmanner as the spatio-temporal distance. EOF analysis (Wilks 2011) is then performed on all 2D error valuesfor each forecast (one value for each storm member). The eigenvectors of their covariance matrix define a I M UZIO ET AL . 11 rotated coordinate system where variability is maximized along the x-axis. The spread of storm positionforecast errors is proportional to their variance in this coordinate system and it is represented in Figure 6as an ellipse whose axes are aligned to the ones of the rotated system and have lengths proportional tothe variance along each eigenvector. This compact representation of storm position errors provides animmediate visual grasp of their extent and spatial distribution. | OVERVIEW OF THE STORMS
The eight storms analysed in this study are briefly illustrated here. A summary of their main features asretrieved from analysis data is given in Table 1, where storm duration, period and region of occurrence areprovided along with extreme intensity, symmetry, compactness, 10 m wind speed and upper-level thermalwind. Storm names were chosen by the Institute of Meteorology at the Free University of Berlin. Thestorm trajectories, intensity and upper-level thermal wind values are displayed in Figure 3.
TA B L E 1
Period and region of occurrence, duration, MSLP [hPa], symmetry, compactness [hPa/100 km], 10 metrewind [ms − ], upper-level thermal wind − V UT for the eight storms, as inferred from operational analysis data. Values arethe lowest (for MSLP) or highest (for other quantities) reached in the life cycle of the cyclone. 10 metre wind iscomputed in a 300 km around the centre of the storm. Storm Period Region Duration MSLP Symmetry Compactness 10 m wind − V UT Rolf Nov. 2011 WM 96 h 997 0.95 6.6 22 26Ruven Nov. 2013 WM, TS, AS 48 h 990 0.85 3.8 22 -31Ilona Jan. 2014 WM, TS, AS 60 h 991 0.83 3.2 23 8Qendresa Nov. 2014 SM 60 h 986 0.92 10.8 27 -14Xandra Nov./Dec. 2014 WM, TS 84 h 989 0.95 3.6 19 22Stephanie Sep. 2016 BB 54 h 998 0.96 6.0 22 11Trixie Oct. 2016 SM, EM 96 h 1005 0.96 4.9 24 18Numa Nov. 2017 TS, SM, IS 120 h 1002 0.98 5.1 19 20
WM = Western Mediterranean; SM = Southern Mediterranean; EM = Eastern Mediterranean; TS =Tyrrhenian Sea; AS = Adriatic Sea; IS = Ionian Sea; BB = Bay of Biscay.Of the eight storms, four developed or spent a significant part of their lifetime over the WesternMediterranean, three over the Southern Mediterranean and the Ionian Sea: these two regions are indeedhotspots for Medicanes (Cavicchia et al. 2014a). In contrast, storm Stephanie is technically not a Medicane,in that it occurred outside of the Mediterranean Sea. Stephanie has been included in our study as itexhibited the same tropical-like traits as Medicanes (Maier-Gerber et al. 2017), formed under similarlarge-scale circulation patterns and occurred in a region that is geographically and climatologically close tothe Mediterranean. Five of the eight storms occurred in November, the most frequent month in our sample;the three remaining storms occurred in September, October and January, respectively. We note in passingthat this temporal distribution differs from the one relative to the 1948-2011 climatology produced byCavicchia et al. (2014a), which has a maximum in January. I M UZIO ET AL . F I G U R E 3
Tracks of the eight storms. The colour of each circle represents the − V UT value, while its size representsthe MSLP value. The data in Table 1 and the cyclone tracks in Figure 3 show the high heterogeneity of the eight stormsin terms of their duration (Ruven developed rapidly and only lasted 48 hours, Numa remained almoststatically over the Ionian Sea for 36 hours and lasted 120 hours), intensity (almost 20 hPa differencebetween the most intense, Qendresa at 986 hPa, and the least intense, Trixie at 1005 hPa), compactness(Qendresa reached 10.8 hPa/100 km MSLP gradient, Ilona only 3.2 hPa/100 km) and thermal structure(most storms developed a moderate upper-level warm core, yet storms Ruven and Qendresa failed toattain one, with upper-level thermal wind − V UT peaking slightly short of zero). We observe here that even I M UZIO ET AL . 13 though storm Qendresa did not attain an upper-level warm core, it is widely recognised as a Medicane(Pytharoulis et al. 2017; Pytharoulis 2018; Cioni et al. 2018). In fact, a unique, objective definition of whatconstitutes a Medicane has not yet been established in the literature (Fita and Flaounas 2018). However,all storms analysed in this study share some distinctive traits, in that at some point during their life cyclethey shrink notably, acquiring a highly axisymmetric circulation with strong MSLP gradients while quicklymoving towards positive values of upper-level thermal wind (i.e. building a warm core). Another featureshared by most storms is their weakening or even fading after making landfall, which is consistent withthe fact that Medicanes, similarly to tropical cyclones, are strongly influenced by surface fluxes (Fita et al.2007; Tous et al. 2013). | RESULTS
In this section, forecasts of several metrics are analysed, with a focus on the evolution of ensemblestatistics with lead time (hereafter referred to as LT). Forecasts of cyclone occurrence are first examinedin Subsection 4.1. Cyclone position forecasts are then explored in Subsection 4.2. To analyse the storms’thermal structure, upper-level thermal wind forecasts are examined in Subsection 4.3. The kinematicstructure and intensity of the eight storms are finally discussed in Subsection 4.4.Two examples of the evolution of ensemble forecasts are provided in Figure 4, which shows MSLPforecasts for storms Qendresa and Trixie. These two cases illustrate the high variability among bothMedicane features (see also Section 3) and their forecasts. Qendresa is the deepest cyclone amongthe eight cases, with 986 hPa minimum pressure in the ETI. For this storm, the probability of cycloneoccurrence (i.e. the number of storm members) is already high at 7.5 days LT (Figure 4a) and remains highthroughout. Conversely, storm intensity is consistently underpredicted, with the ensemble median up to14 hPa higher than the analysis value. A small but evident dip is seen around 4 days LT for both occurrenceprobability and storm intensity. On the other hand, Trixie is the weakest cyclone in our list, with over 1009hPa, albeit very long-lived, with a lifetime of 96 hours (Table 1). For this storm, occurrence probabilityis much lower than 0.5 at LTs longer than 3 days, with a considerable increase between 2.5 and 1 day LT(Figure 4b). The intensity of Trixie is first overpredicted in early forecasts up to 5 days LT, then slightlyunderpredicted with a greatly reduced spread.In both these cases, the evolution of ensemble forecasts with lead time is far from gradual, with stormintensity forecasts showing little convergence towards the analysis value for Qendresa while an earlyconvergence is followed by a plateau for Trixie; the probability of cyclone occurrence is consistently highfor Qendresa, whereas it is very low for early forecasts, but grows rapidly for late forecasts for Trixie: wename such rapid increases forecast jumps as already noted in Section 1. | Cyclone occurrence forecasts
Medicanes develop because of a combination of factors spanning multiple spatial and temporal scales andare therefore low frequency events (Cavicchia et al. 2014a). Early signals of the occurrence of a cyclone,as seen in ensemble forecasts 5-8 days in advance, are then to be considered a first valuable piece of I M UZIO ET AL . (a) (b) F I G U R E 4
Ensemble forecasts of MSLP for storms Qendresa (left) and Trixie (right). Upper panels: box-percentileplots, with white stripes marking the 25th, 50th (median) and 75th percentiles; the yellow circle shows the controlforecast value (provided it has the cyclone); the dashed line is the operational analysis value. Lower panels: number ofmembers having the cyclone (no cyclone) are represented by blue (gray) bars. prognostic information. For this reason, cyclone occurrence forecasts are examined as a first insight intothe predictability of the eight storms.It is reasonable to expect a gradual increase with lead time of the probability of cyclone occurrence.This is not the case for most storms analysed in the present study, as forecasts often exhibit a distinctlyrapid increase in occurrence probability at some lead times (forecast jump). In order to extract such signals,the difference in the number of storm members between consecutive forecasts is computed and shownin Figure 5. Seven out of eight cases exhibit distinct positive peaks, i.e. a rapid increase in occurrenceprobability over a short interval of lead time: Qendresa (7.5 days LT), Numa (around 7 days), Ruven (6 to 5days), Rolf (around 5.5 days), Ilona (around 5 days), Stephanie (double peak around 5 and 3 days) and Trixie(2 to 1 day). These peaks stand out above the bulk of values which are contained between -1 and 5. Onlyone case, Xandra, shows a gradual increase of occurrence probability throughout all forecasts.We note here that six out of seven occurrence forecast jumps are found at lead times longer than 4days. A notable exception is Trixie, for which occurrence probability does not increase above 50% until2 days LT. These results are consistent with the low atmospheric likelihood of Medicane occurrence andcompatible with the hypothesis that occurrence probability increases significantly only when the forecastmodel’s initial data contain sufficient information on all processes impacting Medicane formation at allscales. This may constitute an instance of predictability barrier, possibly similar to the spring predictabilitybarrier known to impact ENSO predictions (Duan and Wei 2013; Levine and McPhaden 2015) albeit arisingat different temporal scales. I M UZIO ET AL . 15
F I G U R E 5
Difference in the number of storm members (proportional to cyclone occurrence probability) betweencurrent and previous forecast, for each lead time, for all cases. Values are smoothed with a 1-2-1 running mean toreduce noise. | Cyclone position forecasts
The impacts of Medicanes can be considerable (Cavicchia et al. 2014a) but spatially limited to small regions,due to their small size. For this reason, an accurate prediction of their trajectory is key in preventing andmitigating the damages they produce locally. The next step in evaluating ensemble forecasts of the eightstorms is then to examine their predicted position during their mature, tropical-like phase.Cyclone position forecast statistics are shown in Figure 6, where the median of position errors isrepresented as an arrow and forecast spread as an ellipse whose axes (and hence its area) are proportionalto the variance of position errors (see Subsection 2.6). These forecasts appear to converge more graduallycompared to cyclone occurrence forecasts, as demonstrated by the overall slow variation of the size andtilt of both arrows and ellipses over lead time . However, rapid changes of one or more of these quantities(referred to as “position forecast jumps”) are visible at some lead times for some cases. For instance,a sudden decrease in spread, with the ellipse decreasing in size by 30% or more between consecutiveforecasts, is seen for Ilona (3 days LT), Numa (5.5 and 4.5 days), Qendresa (2 days), Rolf (5.5 days), Stephanie The convergence is towards a median and spread value which is very close to zero, but not exactly zero as forecasts are evalu-ated in a time interval. I M UZIO ET AL . (3 days) and Xandra (6 days). Rapid changes in the magnitude of the median error are also apparent, e.g. forIlona (3 days LT), Qendresa (5.5 days), Ruven (5.5 and 4 days), Stephanie (3 days), Trixie (1 day) and Xandra(3.5 days). Position forecast jumps occur in most cases at slightly shorter lead times than occurrenceforecast jumps (difference is 2 days or less for Qendresa, Ilona, Numa, Ruven, Trixie, while the two jumpsoccur at the same lead time for Rolf and Stephanie). This suggests the existence of a causal link betweenincreased occurrence probability and higher accuracy of position forecasts. F I G U R E 6
Statistics of cyclone position forecasts. For any given forecast, only storm members are considered. Thered arrow represents the median of position errors, its components being longitude (horizontal) and latitude (vertical).The blue ellipse is a bivariate normal distribution fit to the position errors, representing their spread; it is scaled so as toencircle 95% of error points. The ellipse is oriented along the direction of maximum variability of the error values andits axes are proportional to their variance in the 2D rotated coordinate system defined by the eigenvectors of theircovariance matrix (see Subsection 2.6). The more storm members, the brighter the colour of both ellipses and arrows.
It is worth noting that the spatial distribution of position errors tends to evolve slowly with lead time.For instance, forecasts exhibit a consistent northwestern bias for Ilona (i.e. the storm is predicted to I M UZIO ET AL . 17 occur too far to the northwest), a southern to southeastern bias for Numa, a southwestern one for Rolf,a northeastern one for Stephanie (at least until 3 days LT) and a large western to southwestern one forTrixie (although in this case with low occurrence probability until 2 days LT). Similarly, position errors areconsistently distributed from west to east for Numa and Trixie, from NW to SE for Qendresa and from SWto NE for Rolf and Xandra. In summary, the region where the cyclone is predicted to occur often tends toremain the same between consecutive forecasts. This implies that early forecasts may already containvaluable prognostic information, in that the actual cyclone position may be approximately estimated earlyon by examining the spatial distribution of position forecasts. One explanation to this may be that certainareas of the Mediterranean Sea are more conducive to Medicane development than others (Tous andRomero 2013; Cavicchia et al. 2014a), so that it is more likely that the cyclone is predicted to spend itsmature phase in these regions. | Thermal structure forecasts
After assessing whether a cyclone is going to occur or not and where it is going to occur, the next step isanalysing its thermal structure. For this reason, we now examine forecasts of upper-level thermal wind,represented by the − V UT parameter, which are shown in Figure 7. The evolution of these forecasts withlead time is generally neither gradual nor monotonic, as already noted with regard to forecasts of cycloneoccurrence (Subsection 4.1). Overall, the forecast spread does not consistently reduce with decreasinglead time, with some cases exhibiting a smaller (Qendresa and Stephanie) or comparable (Ilona, Rolf, Ruven,Xandra) spread at long lead times compared to the latest forecasts. Similarly, in some cases the medianincreasingly deviates from the analysis value with decreasing lead time, only to get closer again in laterforecasts (e.g. Ilona, Numa, Qendresa, Rolf, Stephanie).Storms Rolf and Numa (Figure 7a and 7h, respectively) show a similar evolution, with the forecastmedian − V UT increasingly drifting away from the analysis value and the spread increasing in parallel, untilthe median reaches a minimum and the forecast distribution is entirely below the analysis value (i.e.upper-level thermal wind is underpredicted). The forecast median then converges again towards theanalysis, while the spread first decreases slowly, then much faster to eventually level off at short leadtimes. Storms Ilona and Ruven exhibit instead a contrasting evolution. For Ilona (Figure 7c) the forecastmedian drifts away twice from the analysis value with decreasing lead time, to eventually approach it inthe latest forecasts; the spread oscillates considerably between consecutive forecasts throughout theperiod considered. For Ruven (Figure 7b) the median remains always somewhat close to the analysis valueand the spread does not change considerably throughout the period considered.A peculiar evolution is exhibited by storm Xandra (Figure 7e). Early forecasts consistently underpredictupper-level thermal wind, with very little spread. The spread then increases considerably between 4 and 2days LT while the median − V UT increases slightly. The spread finally decreases again rapidly in the latestforecasts while the median − V UT remains slightly below the analysis value. We interpret this behaviouras follows: with little spread at the longer LTs, ensemble forecasts indicate with high probability thedevelopment of a weaker warm core or a cold core. The increase in spread with decreasing LT indicatesthat new information available in the initial conditions allows the development of a warmer upper-level I M UZIO ET AL . (a) (b) (c) (d) (e) (f) (g) (h) F I G U R E 7
As in Figure 4, but for upper-level thermal wind ( − V UT ) forecasts and for all storms. I M UZIO ET AL . 19 core to occur in some ensemble members. The increase in spread then signifies the increase in probabilityof the Medicane to actually occur.Forecasts of cyclone thermal structure do not appear to be consistently linked to occurrence proba-bility. However, some cases show interesting behaviours: for instance, for Rolf (Figure 7a) the forecastmedian − V UT approaches closely the analysis value only when probability is higher than 0.8; for Stephanie(Figure 7f) the increase in occurrence probability around 4.5 days LT appears to be associated at firstto a broadening of the − V UT forecast distribution and later to its shift towards lower values; for Trixie(Figure 7g) the rapid increase in occurrence probability at 2 days LT is associated to a reduction in the − V UT forecast spread.In all cases, forecasts initialized when the cyclone has already developed have a much lower spreadof upper-level thermal wind than previous forecasts and their median − V UT also tends to be closer to theanalysis value. This is probably explained by the inherently low probability of Medicane occurrence andthe fact that the development of a warm core depends on a variety of factors, including small-scale onessuch as surface fluxes, for which reason a preexisting cyclone constitutes a marked improvement in theinitial conditions. We observe that in most cases the latest − V UT forecast is more accurate than earlierones, in terms of the median − V UT being closer to the analysis value and the spread being lower. For thisforecast, the analysis value lies within the ensemble distribution in all cases. Overall, this is evidence thatthe ECMWF ensemble model can adequately reproduce warm-core cyclones despite its relatively lowhorizontal resolution. | Kinematic structure and intensity forecasts
The last step in our analysis of the ensemble forecasts of the eight storms is assessing how their kinematicstructure and intensity are predicted by examining forecasts of symmetry, compactness and MSLP. Overall,these forecasts also show a non-gradual evolution with lead time, as previously observed for occurrence,position and thermal structure forecasts. Specifically, the forecast median often does not converge gradu-ally and monotonically towards the analysis value, the forecast spread does not always decrease graduallyand monotonically and forecast jumps occur at some lead times for most cases. However, the evolutionof these forecasts is more gradual than that of the forecasts previously examined. For this reason, wefocus here on the overall performance of these forecasts rather than on their evolution with lead time. Fullforecast statistics are only shown for two representative cases, namely Numa for compactness (Figure 8a)and Stephanie for symmetry (Figure 8b).It is apparent that both compactness and symmetry are somewhat underpredicted in these two cases,though with a convergence of forecast distributions towards the analysis value at short lead times. Thesetwo forecasts are representative of compactness and symmetry forecasts for other cases, in that both theunderprediction and the convergence at short lead times are seen in most cases. One could naturally expectcompactness to be underpredicted to some extent, given the low resolution of the ECMWF ensembleprediction model. However, the clear convergence of forecasts at short lead times (in most cases to anextent that the analysis value is well within the interval of the forecast distribution and close to its median)and the fact that the distribution tails reach or exceed the analysis value even at long lead times indicate I M UZIO ET AL . (a) (b) F I G U R E 8
As in Figure 4, but for a) the compactness forecast for Numa and b) the symmetry forecast for Stephanie. that the model is capable of producing high values of compactness. Moreover, compactness and symmetryforecasts appear to be well correlated with each other, so that high values of either metric are associatedto high values of the other. We conclude that the underprediction arises because the occurrence of avery symmetric and compact storm is a highly unlikely event and as such it is by nature near the tail ofthe forecast distribution (especially at long lead times), as observed by Majumdar and Torn (2014). Laterforecasts then tend to converge at short lead times as they benefit from improved initial conditions.Finally, we note that MSLP forecasts, which are overall the most gradually evolving ones with leadtime, do not show any remarkable signal and therefore are not shown here. There appears to be a slighttendency to underpredicting MSLP at long lead times for many storms, which is probably due to the lowprobability of cyclone occurrence in early forecasts. This hypothesis is supported by forecasts of Qendresa,the most intense of the eight storms (see Section 3), which consistently and largely underpredict MSLP,although forecast distribution tails reach the analysis value even at long lead times. Qendresa indeedunderwent an extremely rapid development (more than 15 hPa pressure drop in 18 hours, see Cioni et al.2018) which appears as highly unlikely especially in early forecasts, even though the probability of cycloneoccurrence is high from 7 days in advance (Figure 4). | DISCUSSION AND CONCLUSIONS
Medicanes have been gaining increasing attention in the research community in the last two decades.These storms constitute a major threat in the Mediterranean region, due to intense winds and rainfall.Although the pathway leading to the formation of Medicanes is by now well known, they remain elusive I M UZIO ET AL . 21 characters of the Mediterranean climate in that their frequency of occurrence is low and an objectivedefinition has not yet been found. The predictability of Medicanes is also low due to scarce observationsover the sea and the interplay between the numerous factors influencing their entire life cycle at multiplespatial and temporal scales.In this paper, the predictability of eight southern European tropical-like cyclones, seven of whichMedicanes, is analysed by evaluating ECMWF operational ensemble forecasts against operational analysisdata. We apply an object-based approach that allows focusing on specific storm features, while toleratingtheir shifts in time and space to some extent. Each storm is then treated as an object and its forecasts areevaluated using suitable metrics: MSLP, symmetry, compactness, − V UT which give a measure respectivelyof the cyclone’s intensity, symmetry, pressure gradient and upper-level thermal structure and thereforewell represent tropical-like traits attained during the mature phase of its life cycle. This object-basedapproach has shown strengths in extracting the most relevant information from the data and value incondensing it into intuitive metrics: for these reasons, it could easily be applied to other types of forecastsand atmospheric features. The DTW technique in particular looks promising for further application in theatmospheric sciences due to its intuitiveness and flexibility in providing a meaningful space-time matchingof time series.Findings reveal that the evolution of ensemble forecasts with lead time is far from gradual, generallydiffering from the steady convergence towards the analysis value that may be expected. In particular,rapid increases in the probability of cyclone occurrence ( forecast jumps ) are seen in most cases. Thisbehaviour is compatible with the existence of predictability barriers, similar to the spring predictabilitybarrier observed for ENSO (Duan and Wei 2013), which would only be overcome when initial conditionsadequately represent the variety of factors playing a role in Medicane development at all scales. Cyclonethermal structure forecasts also exhibit a non-gradual evolution in some cases, with the forecast mediandrifting away from the analysis value and spread increasing with decreasing lead time. However, lateforecasts which have been initialized when the storm has already developed tend to be more accuratethan earlier forecasts. This supports previous findings of high sensitivity of Medicane simulations to initialconditions (Cioni et al. 2016).On the other hand, forecasts of cyclone position exhibit a visible tendency to a consistent spatialdistribution of cyclone position uncertainty and bias (i.e. a nonzero median position error) betweenconsecutive forecasts, which may be explained by the fact that some regions of the Mediterranean Sea aremore conducive to Medicane development than others (Tous and Romero 2013; Cavicchia et al. 2014a),thus favouring the occurrence of the cyclone in the same region between consecutive forecasts. Thisimplies that early forecasts may already contain valuable prognostic information on the cyclone’s positionduring its mature phase.Unlike other metrics, compactness and symmetry are consistently underpredicted in most cases,especially at long lead times. A marked improvement of these forecasts is however seen at short leadtimes. In light of these contrasting behaviours, we exclude the presence of any systematic bias that couldbe expected due to the relatively low resolution of the ECMWF ensemble model. We instead deem theunderprediction to be a result of the intrinsically low probability of the occurrence of a Medicane (thatis, a highly axisymmetric and compact storm) in early forecasts, which causes it to be found near the tail I M UZIO ET AL . of the forecast distribution, as observed by Majumdar and Torn (2014). We interpret in the same way aweak tendency to underpredict MSLP that is seen in some cases at long lead times. Considering all metrics,forecasts indicate that the ECMWF ensemble model can adequately reproduce Medicanes in terms oftheir tropical-like traits, albeit only at relatively short lead times.The present work paves the way towards an in-depth investigation of the physical mechanisms under-lying the features revealed by our analysis, in particular the non-gradual evolution of forecasts with leadtime, forecast jumps and the consistent spatial distribution of cyclone position forecasts. A future studywill examine the complex interplay between processes at different spatial and temporal scales leading tothe formation of a Medicane and its impact on their predictability and the evolution of ensemble forecastswith lead time. A C K N O W L E D G E M E N T S
ECMWF is acknowledged for providing the ensemble forecast and operational analysis datasets. Theresearch leading to these results has been carried out within the subproject C3 “Multi-scale dynamicsand predictability of Atlantic Subtropical Cyclones and Medicanes” of the Transregional CollaborativeResearch centre SFB/TRR 165 “Waves to Weather” funded by the German Research Foundation (DFG).
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