Abstract

An algorithm for the detection of horizontal wind shear at low levels was developed. The algorithm makes use of data collected by all radars from the Application Radar à la Météorologie Infra-Synoptique (ARAMIS) operational network, in order to build a complete mosaic of wind shear over metropolitan France. The product provides an estimation of the maximum horizontal wind shear detected in the low levels, between 0 and 2 km AGL. Examination of the wind shear mosaic for different cases shows that the product is able to retrieve small-scale wind shear signatures that can be linked to either convergence lines ahead of convective cells, which are indicative of gust fronts, or strong convergence areas inside intense cells. A statistical evaluation of the wind shear mosaic was performed, by comparing horizontal wind shear observed inside the area defined by convective objects with wind gusts recorded along their trajectory by weather stations. A link between those different observations was clearly established.

Therefore, the use of wind shear for wind gust prediction was tested in combination with other parameters: an estimation of the energetic potential of density currents, the cell surface with reflectivity over 51 dBZ, relative helicity, and cell propagation speed. Different wind gust warning rules were tested on 468 convection nowcasting objects (CONOs). The results clearly highlighted the benefits of using wind shear for wind gust estimation, and also demonstrated the improvement in forecasting skill when combining different parameters. The wind shear mosaic will be produced operationally before the end of 2013 and will be used to improve wind gust warnings provided to end users.

1. Introduction

Wind shear is a difference in wind speed or direction over a relatively short distance in the atmosphere. Its horizontal component, horizontal wind shear, is commonly observed at the low levels within severe phenomena caused by thunderstorms, such as microbursts, gust fronts, or mesocyclones. As these phenomena can cause significant damage, in particular to aircrafts during landing or taking off, it is essential for forecasters to have synthesis tools to help them detect their occurrence and their level of severity, in order to improve warnings.

Doppler radar data are an essential source of information for measuring horizontal wind shear inside precipitation at high spatial and temporal resolutions. Well-trained forecasters can directly interpret radial velocity images in order to detect wind shear features indicative of the presence of gust fronts or mesocyclones, for example, but automatic detection provides additional help and avoids overwhelmingly large amounts of data. Significant efforts have been dedicated over the past few decades, especially in the United States, to develop efficient warning tools for use by air traffic controllers and forecasters to detect and describe areas of strong horizontal wind shear at low levels.

Low-level wind shear detection algorithms based on Doppler radar data are often dedicated to specific phenomena such as gust fronts or mesocyclones. Uyeda and Zrnić (1986) first developed a gust front algorithm based on the tracking of radial velocity gradients along radials (i.e., radial convergence combined with the detection of azimuthal shear). Merritt et al. (1989) improved this algorithm for the U.S. Terminal Doppler Weather Radars (TDWRs), by checking the vertical continuity of the shear between two low-level elevation angles (typically 0.5° and 1°) in order to reduce the false alarm rate. They also added a technique for estimating horizontal winds ahead of and behind detected gust fronts, which was further improved by Hermes et al. (1993). Eilts et al. (1991) implemented the identification of reflectivity thin lines, which proved to be useful for the detection of gust fronts oriented along a radial and therefore having a weak radial convergence. Although the accuracy of these algorithms increased from year to year, a number of limitations were found. For example, the vertical continuity technique does not always improve the quality of the algorithm, because vertical continuity cannot always be established, particularly for shallow gust fronts at long ranges (over 60 km), as explained by Hermes et al. (1993), or close to the radar when the lowest elevation sweep is contaminated by ground clutter and cannot be compared to the following sweep. Moreover, vertical wind shear erroneously interpreted as radial convergence was found to be responsible for many false alarms within the gust front algorithm. Consequently, none of these algorithms reached the level of a well-trained forecaster.

A significant improvement was made with the development of the machine intelligent gust front algorithm (MIGFA; Delanoy and Troxel 1993; Evans and Weber 2000), which was first applied to Airport Surveillance Radar (ASR-9) Weather Systems Processor (WSP) before being adapted to TDWRs. This algorithm relies on a machine intelligence approach with object detection and recognition techniques. This new approach allowed a significant increase in the probability of detection as well as a decrease in the false detection rate (Evans and Weber 2000). The algorithm was consequently adapted afterward for the Next Generation Weather Radar (NEXRAD) system (Smalley et al. 2005).

In parallel to developments dedicated to gust front detection, many algorithms have also been developed for the detection of mesocyclones, which also induce strong low-level wind shear. Zrnic et al. (1985) first developed an automatic mesocyclone detection algorithm for NEXRAD, based on the detection of pattern vectors, which are azimuthal runs of increasing velocities along a fixed range. This algorithm was improved by Stumpf et al. (1998) and was also adapted to other radar networks like the Canadian (Bellon and Zawadzki 2003) and Spanish networks (Elizaga et al. 2007). More recently, the National Severe Storms Laboratory (NSSL) created a product called rotation tracks, which derived from the merging of azimuthal shear data from multiple radars and the accumulation of the maximum values on Cartesian grids over time (Miller et al. 2012). The product was improved by quality control methods (Lakshmanan et al. 2013), taking advantage of spatial and temporal coherence in order to remove nonmeteorological echoes whose impact is amplified due to time accumulation.

The method presented in this paper makes use of data collected by all radars within the Application Radar à la Météorologie Infra-Synoptique (ARAMIS) operational network (Fig. 1a) in order to build a complete mosaic of wind shear over France, as is done for the rotational tracks described by Miller et al. (2012). In areas where there is overlap between different radars, the probability of nondetection due to unfavorable geometrical configurations (i.e., when the wind shear line is parallel to the radar beam) is hence reduced, provided that the different radars can sample the wind shear pattern from different angles. The algorithm provides an estimation of the maximum horizontal wind shear at low levels, between 0 and 2 km above ground level (AGL) as is done by Miller et al. (2012) for the 0–3 and 3–6 km AGL layers. A difference from the approach proposed by Miller et al. is that all kinds of horizontal wind shear are considered and not only azimuthal shear. This allows for the detection of all phenomena generating horizontal wind shear, such as gusts fronts, convergence lines, or mesocyclones. With this product, it will also be possible to estimate the range of horizontal wind shear values that can be observed in France, as well as the nature of various phenomena that lead to wind shear, as was done by Hobson et al. (2012), who uses wind shear among other parameters to categorize storm types. An original product evaluation is proposed: wind shear values are directly compared to gust records measured by weather stations, in an object-oriented mode.

Fig. 1.

(a) The French ARAMIS radar network. North points straight up (as is the case for all other spatial figures). Large circles indicate a distance of 100 km from the radar and smaller circles (for X-band radars) indicate a distance of 60 km from the radar. All C- and S-band radars (24) are operational while the two X-band radars in the Alps will be operational in 2013. (b) Wind shear mosaic 1536 × 1536 km2 domain. Colors indicate the number of elevation angles for all radars scanned during the 5-min cycle and available inside the vertical column from 0 to 2 km AGL. Example given for 1030 UTC 1 Jul 2012.

Fig. 1.

(a) The French ARAMIS radar network. North points straight up (as is the case for all other spatial figures). Large circles indicate a distance of 100 km from the radar and smaller circles (for X-band radars) indicate a distance of 60 km from the radar. All C- and S-band radars (24) are operational while the two X-band radars in the Alps will be operational in 2013. (b) Wind shear mosaic 1536 × 1536 km2 domain. Colors indicate the number of elevation angles for all radars scanned during the 5-min cycle and available inside the vertical column from 0 to 2 km AGL. Example given for 1030 UTC 1 Jul 2012.

This paper is organized as follows: the French Doppler radar network is briefly described in section 2, then the algorithm steps of the wind shear mosaic are detailed in section 3. Three cases illustrating the product are presented in section 4, as is a summary of forecasters' feedback for a few cases. In section 5, a statistical evaluation of the link between wind shear and wind gusts, which was conducted within the area defined by the convective cell tracks, is presented. And in section 6, an indicator of wind gust risk using wind shear in combination with other parameters is evaluated. Finally, possible improvements to the product and its operational perspectives are discussed in section 7.

2. Radar network

The French radar network presently consists of 24 operational radars (6 S band and 18 C band) plus two X-band radar in the Alps that should become operational in 2014. All radars have Doppler capability, and cover most of the metropolitan territory (Fig. 1a). The introduction of Doppler processing within this network is quite recent: a staggered triple pulse repetition time (PRT) Doppler scheme (Tabary et al. 2006) was first developed in 2004, and was then gradually introduced. This scheme allows measurements without ambiguity (the Nyquist velocity is equal to 60 m s−1) simultaneously with reflectivity up to a range of 250 km. Doppler data are assimilated operationally in the French Applications of Research to Operations at Mesoscale (Applications de la recherche à mésoéchelle, AROME) numerical weather prediction (NWP) model (Montmerle and Faccini 2009) and are also used to retrieve 3D wind fields in real time, in areas with sufficient radar density (Bousquet et al. 2008).

The quality of the initial Doppler scheme was assessed by Tabary et al. (2006) in a variety of situations (clear air, convection, stratiform precipitation, etc.). A mean dealiasing success rate of 90% was estimated for all pixels of all plan position indicator (PPI) scans collected during 1 month of data (August 2004) by the Trappes radar in north-central France. However, this success rate decreases in convective situations because of the higher spectral widths due to turbulence or wind shear. Improvements in the Doppler scheme have subsequently been proposed, by increasing the PRFs and choosing optimum ratios between the three PRFs (Augros and Tabary 2009). A new PRFs triplet was tested and then introduced for the 10 most-recent C-band radars (shown in Table 1 in comparison with the low-PRF triplet). The quality of the radial velocity improved significantly thanks to the new PRF triplet, with a reduction by a factor of 2–3 in the percentage of dealiasing errors. However, it was possible to introduce the new triplet only for the most recent C-band radars, because the electronic components of the older radars cannot support such high PRFs due to duty-cycle constraints. This is why an error filter as well as a median filter, whose principles are given in the following section, must be applied to raw radial velocity data in order to remove spurious data ensuing from dealiasing errors.

Table 1.

Values of the PRFs for low- and high-PRF modes, with their associated “mean” PRFs, being the inverse of the mean PRT, with the associated extended Nyquist velocities (VNEs) and the ratios of PRF2 over PRF1 and PRF3 over PRF1.

Values of the PRFs for low- and high-PRF modes, with their associated “mean” PRFs, being the inverse of the mean PRT, with the associated extended Nyquist velocities (VNEs) and the ratios of PRF2 over PRF1 and PRF3 over PRF1.
Values of the PRFs for low- and high-PRF modes, with their associated “mean” PRFs, being the inverse of the mean PRT, with the associated extended Nyquist velocities (VNEs) and the ratios of PRF2 over PRF1 and PRF3 over PRF1.

3. Algorithm description

a. Preprocessing

Radial velocity is estimated with the pulse-pair technique: complex correlations are calculated for each pulse pair and each range gate and directly projected onto a Cartesian grid, as explained in Tabary et al. (2006). PPIs of raw radial velocity data consist therefore of Cartesian spatial grids of 512 × 512 km2 with 1-km2 resolution. No radial velocity in polar coordinates is currently available, which is why we use these Cartesian grids of radial velocity.

Data are typically available for six elevation angles every 5 min, for each network radar. Only the lower-elevation angles (typically below 2.7°) are repeated every 5 min and a few higher-elevation angles are added in order to form a complete volume in a “supercycle” of 15 min. An example of the scanning strategy for the Trappes radar is illustrated in Table 2. For the wind shear mosaic, as interest lies in the low levels (below 2 km) and because high temporal resolution is needed, only the elevation angles that are repeated every 5 min are used.

Table 2.

Scanning strategy for the Trappes radar.

Scanning strategy for the Trappes radar.
Scanning strategy for the Trappes radar.

In the current state of the signal processing, no ground clutter filter is implemented. Therefore, in the first step of the preprocessing, all echoes that are not due to precipitation (noise, ground clutter, clear air, etc.) need to be removed. For conventional (i.e., nonpolarimetric) radars, spurious reflectivity echoes are removed through the use of a threshold on reflectivity pulse-to-pulse fluctuations following Sugier et al. (2002). On polarimetric radars, a fuzzy-logic algorithm proposed by Gourley et al. (2007) is applied in order to separate precipitating from nonprecipitating echoes. To ensure that no ground clutter echo remains, the pixels whose radial velocities are under a threshold of 1 m s−1 are removed.

Likewise, the pixels having reflectivity values under the 15-dBZ threshold are also classified as invalid, in order to ensure that no clear-air echo remains, since these echoes usually have higher dealiasing error rates that can induce erroneous shear. These echoes have a particularly poor Doppler quality when they are mixed up with ground clutter. Work is currently underway to remove ground clutter thanks to an adaptive filtering technique suitable for our triple-PRT system. This new technique should lead to an improvement in the Doppler data quality for weak reflectivity values in ground clutter regions. In addition, clear-air echoes might also not be representative of the actual wind, as no distinction is currently made between insects and birds. Whereas insects are usually good tracers of the wind, this is not the case for birds because they can have their own direction and speed. For this reason, it was preferred not to use clear-air echoes in the first version of the wind shear mosaic. Dual-polarization technology is being gradually implemented in the French operational network and may allow for a differentiation between insects and birds in the future, leading to a drop in the 15-dBZ threshold for a future version of the wind shear mosaic.

For wind shear estimation a very high quality of Doppler data is essential; therefore, an error filter is then applied in order to discard potential spurious velocities resulting from dealiasing failures: if the mean radial velocity gradient between one pixel and its surrounding neighbors is over a certain threshold (25 m s−1 km−1), or if all surrounding pixels are invalid, the pixel is defined as invalid. The threshold of 25 m s−1 km−1 was adjusted after a few sensitivity tests, in order to remove potential errors without removing too many good data points. For comparison, this threshold is higher than the maximum shear (24.5 m s−1 km−1) observed by Zrnić et al. (1985) when analyzing 40 mesocyclones observed in the United States in 1977.

After the error filter, a median filter is applied to smooth the radial velocity field and to eliminate remaining dealiasing errors: if at least 20% of the pixels (16 pixels) inside a 9 km × 9 km neighborhood around a pixel are valid, the median of these pixels is applied to the pixel and if not, the pixel is declared invalid. Such a large median filter size is needed only for the radars that have the poorest Doppler data quality (because they have low PRFs), in order to retrieve a smoothed field. But for the sake of homogeneity, the same filter size is applied to all radars.

To retrieve only the storm-relative radial velocities, the advection field is subtracted from the velocity field in the last step of preprocessing. This advection field is calculated for each radar from the successive reflectivity composites following the approach of Tuttle and Foote (1990), as adapted and explained in Tabary (2007).

b. Calculation of wind shear for individual scans

Because raw velocity PPIs are not produced in polar coordinates, calculations of velocity gradients along radials or along azimuths, which are classically used for gust front and mesocyclone detection algorithms, cannot be directly performed in our case. From the smoothed Cartesian radial velocity field (V), the wind shear (WS) at each point is calculated as the maximum value of the gradients between the surrounding pixels (N, NE, E, SE, S, SW, W, and NW; as seen in Fig. 2a):

 
formula

where V(N) is the radial velocity of the northern pixel and dN–S is the distance between the centers of the northern and southern pixels.

Fig. 2.

(a) Scheme representing one pixel (red) with its surrounding neighbors in the Cartesian 1 × 1 km2 projection. The associated wind shear is calculated as the maximum value of gradients between neighbors (south–north, northeast–southwest, east–west, southeast–northwest). (b) Illustration of the selection of the maximum wind shear value inside a vertical column from 0 to 2000 m AGL from different scans corresponding to different elevation angles and different radars.

Fig. 2.

(a) Scheme representing one pixel (red) with its surrounding neighbors in the Cartesian 1 × 1 km2 projection. The associated wind shear is calculated as the maximum value of gradients between neighbors (south–north, northeast–southwest, east–west, southeast–northwest). (b) Illustration of the selection of the maximum wind shear value inside a vertical column from 0 to 2000 m AGL from different scans corresponding to different elevation angles and different radars.

For the estimation of the maximum, each of the four gradients is considered only if it is lower than the threshold of 25 m s−1 km−1. If none of the gradients verifies this condition, the pixel is defined as invalid. The value of this threshold was chosen after tests on a few cases and spurious data were removed without eliminating too much good data. This threshold is adjusted to the spatial width of the median filter that was previously applied, but could be revisited for other types of Doppler data.

Figure 3 illustrates the steps in the creation of one wind shear PPI from raw Doppler data, for the Bollene radar at 0.8° elevation, at 0000 UTC 7 August 2011. This situation is explained in detail in section 4. The raw radial velocity and reflectivity PPIs in Figs. 3a and 3b show many ground clutter echoes. These echoes are clearly removed in Figs. 3c and 3d after ground clutter elimination. Figure 3e, which is obtained after applying the error and median filters, is very clean and is more appropriate for wind shear estimation than is the raw radial velocity image. Moreover, although the image has been smoothed in order to remove dealiasing errors, a significant wind shear feature south of the radar is still clearly visible. Figure 3g is retrieved after the subtraction of the advection field shown in Fig. 3f. Finally, the corresponding wind shear PPI is shown in Fig. 3h.

Fig. 3.

PPIs at 0.8° elevation for the Bollene radar, at 0000 UTC 7 Aug 2011. Black circles indicate a distance of 100 km from the radar. Shown are (a) raw reflectivity (dBZ); (b) raw radial velocity (m s−1) following the negative away, positive toward (NAPT) convention; (c) reflectivity (dBZ) and (d) radial velocity (m s−1) after ground clutter elimination; (e) radial velocity after all filters (ground clutter elimination, velocity and reflectivity thresholds, error filter, 9 × 9 km2 median filter); (f) radial component of advection field (m s−1); (g) as in (e), but with subtraction of radial component of advection field (m s−1); and (h) corresponding horizontal wind shear (m s−1 km−1) estimation.

Fig. 3.

PPIs at 0.8° elevation for the Bollene radar, at 0000 UTC 7 Aug 2011. Black circles indicate a distance of 100 km from the radar. Shown are (a) raw reflectivity (dBZ); (b) raw radial velocity (m s−1) following the negative away, positive toward (NAPT) convention; (c) reflectivity (dBZ) and (d) radial velocity (m s−1) after ground clutter elimination; (e) radial velocity after all filters (ground clutter elimination, velocity and reflectivity thresholds, error filter, 9 × 9 km2 median filter); (f) radial component of advection field (m s−1); (g) as in (e), but with subtraction of radial component of advection field (m s−1); and (h) corresponding horizontal wind shear (m s−1 km−1) estimation.

After the wind shear PPIs have been produced for all selected radar elevations, they are synchronized with respect to the ending time of the considered 5-min cycle period using the advection field, to account for the asynchronous measurements.

c. Calculation of the national wind shear mosaic

Wind shear values from all PPIs of all radars are projected inside a 3D grid representing the final domain over France, with a 1536 × 1536 km2 horizontal extension. The final wind shear mosaic is calculated from this 3D grid by selecting for each pixel the maximum value inside the column from the ground to a height of 2 km AGL (Fig. 2b). The altitude of the selected pixel is recorded, as well as the number of elevation angles of all radars that were available inside the vertical column. An example of this field is shown in Fig. 1b. It constitutes a primary version of the quality index, considering that the risk of wind shear underestimation for geometrical reasons decreases with increasing numbers of radars and elevation angles taken into account. Although this field is calculated dynamically, it is not supposed to vary too much providing that all the network radars are operating normally.

The wind shear mosaic is produced in real time every 5 min in the 1536 × 1536 km2 domain, at a 1 km × 1 km horizontal resolution. This product is complementary to the national three-dimensional (3D) multiple-Doppler wind field that is produced in real time using a dual-Doppler technique (Bousquet et al. 2008; Bousquet et Tabary 2013), since it covers low levels, whereas the 3D wind field, which requires at least two radars for wind vector retrieval, covers heights only above 1500 m in many areas. Moreover, the wind shear mosaic has a higher spatial resolution (1 km instead of 2.5 km) and a shorter time resolution than the 3D multiple-Doppler wind field (5 min instead of 15 min) because it uses only the lower-elevation angles, repeated every 5 min, whereas the 3D multiple-Doppler wind field also uses the higher-elevation angles available only once every 15 min.

4. Case studies

a. A tornado case observed in northern France

During the night of 23 August 2010, a tornado formed in the Nord-Pas-de-Calais region within an intense convective line propagating in the south-southwesterly direction. The tornado, observed at 0150 UTC near the village of Humbert in the Pas-De-Calais department, produced severe damage and was classified as category 2 on the enhanced Fujita scale (EF2).

For this situation, a persistent line of shear can be seen in the wind shear mosaic, shown in Figs. 4c and 4d for 0050 and 0130 UTC, respectively. This line is already visible more than 1 h before the tornado was recorded. The shear values within the line are very strong: over 5 m s−1 km−1, with maxima greater than 8 m s−1 km−1.

Fig. 4.

Illustration of the 23 Aug 2010 event in the Nord-Pas-de-Calais region, at (left) 0050 and (right) 0130 UTC (right), by (a),(b) the reflectivity mosaic (dBZ), (c),(d) the wind shear mosaic (m s−1 km−1), and (e),(f) the radial velocity PPI observed by the Abbeville radar at 0.8° elevation (m s−1, NAPT convention). The location where the tornado was observed at 0150 UTC is indicated by a red point. In (a)–(d), the different colored lines indicate the coast (thick white line), the department boundaries (thin white lines), and the Belgium–France border (green line). The white cross indicates the position of the Abbeville radar. In (e),(f), the colored lines represent the coast and the Belgium–France border (black lines), the departments boundaries (brown lines), and the main rivers (blue lines). The location of the Abbeville radar is indicated by a black circle. Arrows indicate strong convergence within the thunderstorm in which the tornado formed.

Fig. 4.

Illustration of the 23 Aug 2010 event in the Nord-Pas-de-Calais region, at (left) 0050 and (right) 0130 UTC (right), by (a),(b) the reflectivity mosaic (dBZ), (c),(d) the wind shear mosaic (m s−1 km−1), and (e),(f) the radial velocity PPI observed by the Abbeville radar at 0.8° elevation (m s−1, NAPT convention). The location where the tornado was observed at 0150 UTC is indicated by a red point. In (a)–(d), the different colored lines indicate the coast (thick white line), the department boundaries (thin white lines), and the Belgium–France border (green line). The white cross indicates the position of the Abbeville radar. In (e),(f), the colored lines represent the coast and the Belgium–France border (black lines), the departments boundaries (brown lines), and the main rivers (blue lines). The location of the Abbeville radar is indicated by a black circle. Arrows indicate strong convergence within the thunderstorm in which the tornado formed.

In this case, the wind shear line is likely due to the strong convergence within the convective cell that is also visible in the radial velocity data from the Abbeville radar, as seen in Figs. 4e and 4f. When this event occurred, the product was not available in real time. Had it been available, forecasters could have detected the strong and persistent convergence in advance and, therefore, anticipated the potential severity of the thunderstorm, although the wind shear algorithm does not specifically identify the tornado.

However, not all wind shear lines that are visible in this mosaic can be associated with severe phenomena. In Fig. 4c, for example, other shear lines can be seen northwest of the radar. These lines are due to gradients in the radial velocity field but are not associated with severe weather. They also have different characteristics than the wind shear line associated with the thunderstorm that produced the tornado: they are not very organized and are not persistent.

In cases with strong vertical wind shear, shear lines can also appear in the horizontal wind shear mosaic. Gradients of radial velocity can even be amplified in comparison with the real wind because of failures in the dealiasing algorithm, which produces false alarms in the wind shear mosaic. Examples of these features are given and explained in detail in Fabry et al. (2013).

Based on this first example, it appears that the low-level horizontal wind shear mosaic provides some benefit in helping detect wind shear: it was able to identify the strong convergence area within the thunderstorm that generated the tornado in this case. However, two limitations are already perceivable: vertical wind shear is sometimes erroneously interpreted as radial shear, and second, the approach does not distinguish between gust fronts, mesocyclones, or other types of phenomena that produce horizontal wind shear.

b. An MCS case, associated with a bow echo and strong wind gusts

In the late afternoon of 12 July 2011, a mesoscale convective system (MCS) formed in the Limousin region, within a very convective southwesterly flow. The MCS produced very strong gusts, in particular between 1900 and 2000 UTC. The maximum gusts recorded during this time period in the Limousin region are shown in Fig. 5. Two weather stations recorded gusts over 100 km h−1, and one station recorded a gust of 91 km h−1. The signature of the convective cell in the reflectivity mosaic and in the low-level wind shear mosaic is shown in Fig. 6 at 1930, 1940, and 1950 UTC. A thick line with high reflectivities (over 60 dBZ) can be seen. This line progressively adopts a bow shape, clearly visible at 1950 UTC. A wind shear line is also present, ahead of the cell, with very high values (greater than 8 m s−1 km−1). Like the reflectivity line, the wind shear line gradually forms a bow shape, which is characteristic of the presence of strong downdrafts as documented by Fujita (1978), Weisman (1993), and Davis et al. (2004) during the Bow Echo and MCV Experiment (BAMEX). The wind shear line is very likely due to the convergence ahead of the cell, between downdrafts associated with the cold pool and environmental air.

Fig. 5.

Maximum gusts recorded between 1900 and 2000 UTC 12 Jul 2011 by weather stations in the Limousin region. Black lines represent the department boundaries.

Fig. 5.

Maximum gusts recorded between 1900 and 2000 UTC 12 Jul 2011 by weather stations in the Limousin region. Black lines represent the department boundaries.

Fig. 6.

Mesoscale system observed in the Limousin region on 12 Jul 2011: (left) reflectivity mosaic (dBZ) and (right) wind shear mosaic (m s−1 km−1) observed at (a),(b) 1930, (c),(d) 1940, and (e),(f) 1950 UTC. A white cross indicates the position of the Grèzes radar. White lines indicate the French department boundaries.

Fig. 6.

Mesoscale system observed in the Limousin region on 12 Jul 2011: (left) reflectivity mosaic (dBZ) and (right) wind shear mosaic (m s−1 km−1) observed at (a),(b) 1930, (c),(d) 1940, and (e),(f) 1950 UTC. A white cross indicates the position of the Grèzes radar. White lines indicate the French department boundaries.

In this case, the wind shear mosaic clearly identifies the strong and persistent convergence ahead of the storm, which is also very consistent with strong reflectivities. The bow echo is visible at the same time in the reflectivity field and in the low-level horizontal wind shear field, meaning that the wind shear signature can serve as an additional indication of strong gusts.

c. An MCS case with heavy rainfall but moderate gusts

The case studied in this section is also an MCS, which formed during the evening of 6 August 2011 with the enlargement of a convective line in southeastern France and moved in a west-southwesterly flow until the end of the night of 7 August 2011. This MCS produced heavy rainfall, with hourly accumulations of over 50 mm recorded at a few surface weather stations. The signature of the storm in the low-level wind shear mosaic is shown in Fig. 7 with the corresponding reflectivity fields at 0000 and 0030 UTC. The shear line is thick and curved, and high values (over 10 m s−1 km−1) persist for more than 1 h. However, no significant gusts were recorded by surface stations in the vicinity of the storm. The maximum values recorded were only 48 and 52 km h−1 at two different stations, as indicated in Fig. 8. Yet, the absence of strong gust records by the surface network does not necessary mean that no strong gusts occurred but could also be explained by the absence of ground stations in the area where the storm was particularly intense, as indicated by the black rectangle in Fig. 8.

Fig. 7.

Signature of a mesoscale system observed in the Bouches-du-Rhône department on 7 Aug 2011: reflectivity mosaic (dBZ) at (a) 0000 and (b) 0030 UTC and low-level wind shear mosaic (m s−1 km−1) at (c) 0000 and (d) 0030 UTC. White crosses indicate radars positions: Nîme (south) and Bollène (north). Thin white lines indicate department boundaries and the thick white line is the coastline.

Fig. 7.

Signature of a mesoscale system observed in the Bouches-du-Rhône department on 7 Aug 2011: reflectivity mosaic (dBZ) at (a) 0000 and (b) 0030 UTC and low-level wind shear mosaic (m s−1 km−1) at (c) 0000 and (d) 0030 UTC. White crosses indicate radars positions: Nîme (south) and Bollène (north). Thin white lines indicate department boundaries and the thick white line is the coastline.

Fig. 8.

Maximum gusts recorded by wind surface stations in the Bouches-du-Rhône department on 7 Aug 2011 between 0000 and 0100 UTC. The gusts associated with the MCS are circled in black. A black rectangle indicates an area with no weather stations and where the storm was particularly intense. The gray lines represent the department borders and the black line is the coastline. The black crosses indicate the position of the radars: Nîmes (south) and Bollène (north).

Fig. 8.

Maximum gusts recorded by wind surface stations in the Bouches-du-Rhône department on 7 Aug 2011 between 0000 and 0100 UTC. The gusts associated with the MCS are circled in black. A black rectangle indicates an area with no weather stations and where the storm was particularly intense. The gray lines represent the department borders and the black line is the coastline. The black crosses indicate the position of the radars: Nîmes (south) and Bollène (north).

To better understand this case, a multiple-Doppler analysis of radar data (Bousquet et al. 2008; Bousquet and Tabary 2013) was performed, within a 200 × 200 km2 domain centered on the Nîmes radar, using eight radars from southeast France. The 3D reflectivity, wind, and divergence fields were reconstructed with a 2-km horizontal resolution from 500 to 12 000 m AGL. In this case, the comparison between both products can be conducted because the region around the Nîmes radar is particularly well covered by different radars (as shown in Fig. 1b). The reflectivity and divergence fields at 1.0 km MSL are shown in Fig. 9 for 0000 and 0030 UTC.

Fig. 9.

Wind direction (vectors) superimposed on the (a),(b) the reflectivity (dBZ) and (c),(d) divergence fields (m s−1 km−1) at 1.0 km MSL in the Bouches-du-Rhône region, as derived from multiple-Doppler analysis of radar data at (a),(c) 0000 and (b),(d) 0030 UTC 7 Aug 2011. A purple line represents the coast, blue lines indicate main rivers, and the brown lines are the department boarders.

Fig. 9.

Wind direction (vectors) superimposed on the (a),(b) the reflectivity (dBZ) and (c),(d) divergence fields (m s−1 km−1) at 1.0 km MSL in the Bouches-du-Rhône region, as derived from multiple-Doppler analysis of radar data at (a),(c) 0000 and (b),(d) 0030 UTC 7 Aug 2011. A purple line represents the coast, blue lines indicate main rivers, and the brown lines are the department boarders.

An area with strong and persistent convergence can be seen inside the storm. The strong wind shear signature, visible in the low-level wind shear mosaic, is likely due to this significant convergence. The low-level wind shear mosaic is therefore consistent with the reconstructed divergence field.

This example shows that the wind shear mosaic clearly identifies the strong convergence inside the storm, and could help the forecasters anticipate its severity and long duration. The moderate intensity of the gusts can possibly be explained by the relatively moderate speed of the storm (around 40 km h−1) compared to many other cases with strong gusts and storm speeds exceeding 70 km h−1.

d. Summary of forecaster feedback on cases from the summer of 2011

In the summer of 2011, a real-time evaluation of the wind shear mosaic was organized for Météo-France forecasters. They were given the opportunity to see the wind shear mosaic in real time or for older situations. For each case they selected, they were asked to

  • provide their opinions about the relevance of the wind shear signatures,

  • indicate if these are collocated with wind gusts,

  • indicate the presence of nonmeteorological signatures (false alarms),

  • offer their insight into the usefulness of the product, and

  • suggest necessary improvements before operational use.

From June to September 2011, forecaster comments could be collected for only 15 cases. For the majority of these cases, the forecasters noticed a good level of agreement between gusts and wind shear signatures. However, they also detected some cases with strong gusts and no wind shear or conversely strong wind shear without gusts. For some of the cases with wind shear and no gusts, the wind shear was likely due to the vertical wind shear being erroneously interpreted as radial shear. This phenomenon is illustrated and explained in Fabry et al. (2013). Forecasters therefore requested to have the possibility to see the altitude of the maximum wind shear value (between 0 and 2 km AGL) assigned to each pixel, to help them differentiate low-level radial shear from vertical wind shear.

Overall, the forecasters found the information of low-level horizontal wind shear to be useful, although they pointed out the absence of a direct link between the intensity of the wind shear and the intensity of the gusts. It was thus suggested to use the wind shear information not alone but in association with other parameters to confirm the wind gust diagnostics.

5. Statistical evaluation of the link between wind shear and gusts

a. Evaluation objective

A statistical evaluation of the link between wind shear estimations and gust risk was carried out using the values of wind gusts recorded by the French weather stations network (about 500 stations distributed over the 550 000 km2 of the French territory). This evaluation was conducted within the area defined by the tracks of convective cells that were determined by convection nowcasting objects (CONOs: Moisselin et al. 2012). The main principle was to build a database (structured by object) and then to determine the relationship between, on the one hand, the low-level horizontal wind shear observed by the radar network and, on the other hand, the gusty winds associated with thunderstorms, in terms of intensity and frequency.

b. Definition of CONOs

CONOs are an object-oriented diagnosis for convective clouds. They are built from the French radar composite of reflectivity and also incorporate lightning data (Météorage network): thunderstorm objects are created from areas with a reflectivity greater than 35 dBZ and at least one lightning impact or from areas with a reflectivity greater than 41 dBZ. For this study, only the reflectivity threshold of 41 dBZ was used to define the cells, in order to select the most intense cases. A tracking algorithm links the convective objects of consecutive radar composite images and takes merges and splits of cells into account. An illustration of CONOs is shown in Fig. 10. The smoothed outlines of the convective objects are superimposed onto the thresholded reflectivity mosaic, and are also superimposed onto the 10.8-μm IR channel image from the Meteosat Second Generation (MSG). Different features are estimated for each CONO throughout their lifetime and the following can be visualized by forecasters: motion speed and direction, relative helicity, maximum precipitation intensity, estimation of the maximum associated gusts, number of associated lightning impacts, maximum reflectivity, the threshold of reflectivity defining the cell, the cell surface and its trend, all gusts measured by weather stations along the trajectory of the cell, etc. For the statistical evaluation, the information of low-level wind shear estimated from the radar network was also added in the CONOs database: for each time step of the trajectory, the 99th percentile of the wind shear inside the area defined by each CONO was associated with the other features. A schema illustrates the life cycle of a CONO and its associated parameters in Fig. 11. CONOs are a component of a warning service that provides messages to end users through a Short Message Service (SMS) or e-mails, concerning the thunderstorm risk (Brovelli et al. 2009).

Fig. 10.

Visualization of the CONO objects with the Météo-France forecasters' tool Synergie. The background image is the thresholded reflectivity mosaic superimposed on the 10.8-μm IR channel MSG image. CONO contours are shown as thick black lines and their associated motion vector, which is the expected gravity center displacement in the next hour, is shown as a purple arrow. The past trajectory of the gravity center of each object is displayed as a thin blue line. Diagnosed characteristics of the selected cell (green contour), such as its propagation direction and speed, its associated rainfall intensity, its estimated risk of hail, its risk of gust, its number of lightning impacts, its horizontal surface extension, and its relative helicity, are displayed on the right.

Fig. 10.

Visualization of the CONO objects with the Météo-France forecasters' tool Synergie. The background image is the thresholded reflectivity mosaic superimposed on the 10.8-μm IR channel MSG image. CONO contours are shown as thick black lines and their associated motion vector, which is the expected gravity center displacement in the next hour, is shown as a purple arrow. The past trajectory of the gravity center of each object is displayed as a thin blue line. Diagnosed characteristics of the selected cell (green contour), such as its propagation direction and speed, its associated rainfall intensity, its estimated risk of hail, its risk of gust, its number of lightning impacts, its horizontal surface extension, and its relative helicity, are displayed on the right.

Fig. 11.

Life cycle of a CONO with its associated parameters. The cell or CONO is represented by the ellipse at its first time step (t0), at a given time t, and at its last time step tend.

Fig. 11.

Life cycle of a CONO with its associated parameters. The cell or CONO is represented by the ellipse at its first time step (t0), at a given time t, and at its last time step tend.

c. Data and methodology

The comparison between low-level horizontal wind shear observed by the radar network and the gusts recorded by weather stations was conducted at the CONO scale for the complete life cycle of each cell: the maximum of the 99th percentile of the wind shear registered during the lifetime of each CONO was compared to the maximum gust recorded along its trajectory.

All wind shear values and all gust records collected during the lifetime of each CONO were combined, rather than comparing the values at each time step, in order to maximize the number of gust records for each object. The wind surface station network does not indeed perfectly cover all of France and there are therefore many time steps for which no gust records can be associated with the CONOs.

For the wind shear estimation at each time step, the 99th percentile inside the area of the object was chosen after a few tests with other parameters like the 98th percentile or the maximum shear. As the values of high shear appear to be concentrated in a rather limited area inside a convective object, a very selective criterion proved to be more efficient. Rather than considering the maximum wind shear value, the 99th percentile was preferred as a compromise to maintain a high detection rate while limiting the number of possible false alarms.

Case studies of severe weather were analyzed for 21 events between August 2009 and September 2011. Days were selected manually for the presence of intense convection, MCSs, convective lines, tornadoes, or thunderstorm-producing strong wind gusts. The selected events are listed in Table 3. Many of the cases were suggested by forecasters, who evaluated the benefits of the low-level wind shear mosaic during the real-time experimentation that was organized during summer 2011. The three cases illustrated in section 4 are included in the dataset. For each event, all CONOs associated with at least one gust record along their trajectory were selected. Finally, a total number of 1007 CONOs were analyzed.

Table 3.

Selected events for the statistical comparison between wind shear and gusts.

Selected events for the statistical comparison between wind shear and gusts.
Selected events for the statistical comparison between wind shear and gusts.

d. Results

The selected CONOs were split into four classes, related to the maximum value of the gusts recorded along their trajectory: less than 60 km h−1, between 60 and 80 km h−1, between 80 and 100 km h−1, and greater than 100 km h−1. These thresholds are typically used operationally by forecasters for classifying the severity of gusts. CONOs without wind speed measurement along their trajectory were removed from the sample.

The graph in Fig. 12 shows the normalized distribution of wind shear values (maximum of the 99th percentiles estimated inside the areas of the CONOs during their lifetime), for the four classes of maximum gusts recorded along the trajectory of the cells. The peaks in the distribution are shifted toward higher wind shear values for higher classes of gusts, especially for gusts over 80 km h−1 and for gusts over 100 km h−1. The peak of the distribution for the lowest class of gusts (less than 60 km h−1) is centered on the wind shear value of 1 m s−1 km−1, whereas the peak of the distribution for the highest class of gusts (greater than 100 km h−1) is centered on the wind shear value of 8 m s−1 km−1. This shows that there is a link between the horizontal shear observed in the low levels and the occurrence of gusts.

Fig. 12.

Normalized distributions of the maximum values of the 99th percentile of wind shear (m s−1 km−1) estimated inside the areas of the CONOs during their lifetime, for four classes of maximum gusts, recorded along the trajectory of the CONOs: <60 km h−1; [60, 80 km h−1[; [80, 100 km h−1[; and ≥100 km h−1.

Fig. 12.

Normalized distributions of the maximum values of the 99th percentile of wind shear (m s−1 km−1) estimated inside the areas of the CONOs during their lifetime, for four classes of maximum gusts, recorded along the trajectory of the CONOs: <60 km h−1; [60, 80 km h−1[; [80, 100 km h−1[; and ≥100 km h−1.

To quantify this link, a contingency table was created (Table 4). CONOs were distributed into two classes of wind shear: less or more than 6 m s−1 km−1 and in the four classes of gusts described previously. For the three classes of gusts with maximum values less than 100 km h−1, the number of CONOs having a maximum wind shear below 6 m s−1 km−1 is always greater than the number of CONOs with a maximum wind shear greater than 6 m s−1 km−1. However, the relative difference between those numbers decreases with the increase of the gusts classes, and the number of CONOs with a maximum wind shear higher than 6 m s−1 km−1 becomes the greatest for gusts higher than 100 km h−1. To test the hypothesis of independency of the two variables, a chi-squared test (Greenwood and Nikulin 1996) was performed. Since there are three degrees of freedom for this table, the value that would be exceeded in only 5% of the cases in the χ2 table if the variables were independent is 7.82. The observed χ2 value is 89.4, which is clearly more than 7.82 and proves that there is a statistical link between horizontal wind shear values and gusts recorded under the tracks of the convective objects.

Table 4.

Contingency table for the 1007 selected CONOs, distributed by row into four classes of gusts (km h−1) and by column into two classes of wind shear (m s−1 km−1).

Contingency table for the 1007 selected CONOs, distributed by row into four classes of gusts (km h−1) and by column into two classes of wind shear (m s−1 km−1).
Contingency table for the 1007 selected CONOs, distributed by row into four classes of gusts (km h−1) and by column into two classes of wind shear (m s−1 km−1).

To evaluate the strength of the link between the wind shear and gusts, the Tschuprow coefficient T was calculated (Tschuprow 1939). This coefficient is the square root of the ratio of the observed χ2 and maximum χ2 that would be obtained if the variables were independent:

 
formula

with N being the total number of CONOs (1007) and z the degrees of freedom in Table 3. The quantity T equals zero when variables are independent and one if there is perfect dependence. In this case, T = 0.226, which means that the dependence is significant but not very strong.

6. Toward an operational use of wind shear for gust estimation

a. Current state of gust risk estimation

To help forecasters assess the severity of each CONO, different characteristics are estimated throughout their lifetime, as explained in the previous section. One of these characteristics is an estimation of the highest wind gusts that can potentially be associated with the CONO. In the current operational version of CONOs, wind gust values are initialized by an index of gusts, called the indice de Rafale d'Orage (IRO), which estimates the energetic potential of density currents from the output of the Action de Recherche Petite Echelle Grande Echelle (ARPEGE) atmosphere model (Déqué et al. 1994). The index is proportional to the difference between the minimum wet bulb potential temperature in the air surrounding the thunderstorm and the potential temperature at the surface, multiplied by the wind speed at the altitude of the minimum wet-bulb potential temperature. Its value is modified if the observed gusts associated with the CONO are higher or if the area of CONO with reflectivity over 51 dBZ is larger than 50 km2. This criterion is historically used by Météo-France nowcasting tools for estimating severe phenomena associated with thunderstorms, like hail or gusts.

b. New methodology

Since a link between wind shear and wind gusts was highlighted in the case study and in the statistical evaluation, a new methodology for wind gust estimation was tested, using wind shear in combination with other parameters: IRO, the storm area with reflectivity over 51 dBZ, relative helicity, and cell propagation speed. These parameters were tested for the estimation of wind gusts over 80 km h−1, which is the threshold from which damage may occur. Gust forecasting rules were built first for each parameter separately and then for combinations of parameters. All rules are presented in Table 5. For the wind shear rule, an integrated wind shear value was calculated for each CONO at each time step: it is the minimum value, during the previous three time steps (10 min), of the 99th percentile of the wind shear inside the area of the CONO. With this integrated wind shear, only persistent and high wind shear values are taken into account.

Table 5.

Rules for the estimation of wind gusts greater than 80 km h−1.

Rules for the estimation of wind gusts greater than 80 km h−1.
Rules for the estimation of wind gusts greater than 80 km h−1.

From the list of events presented in Table 3, all events starting from August 2011 were considered for the evaluation of wind gust forecasting rules. Events prior to this month were not selected because relative helicity was not available. From the seven selected events, only CONOs associated with at least one wind record during their lifetime and having a lifetime longer than 15 min were retained, in order to be able to calculate the integrated wind shear for each CONO. After these steps, a total of 468 CONOs remained.

The evaluation of the different prediction rules was conducted at the CONO scale for the complete life cycle of each cell. For a given rule, the wind gust estimation for a CONO was considered a “hit” if the maximum gust associated with the CONO during its lifetime was over 80 km h−1 and if the rule estimated a wind gust to be over 80 km h−1 for at least one time step of the CONO On the contrary, if the rule estimated a gust to be over 80 km h−1 for at least one time step of the CONO and if no gusts over 80 km h−1 were recorded during its entire lifetime, it was considered a “false alarm.”

c. Results

The forecast skill of all warning rules is measured in terms of the probability of detection (POD), false alarm ratio (FAR), and true skill statistic (TSS):

 
formula
 
formula
 
formula

The TSS score, also called the Hanssen–Kuipers skill score (Hanssen and Kuipers 1965), is the difference between the probability of detection and the probability of false detection. Perfect forecasts receive a score of 1, random forecasts receive a score of 0, and forecasts inferior to random forecasts receive a negative score.

Figure 13 summarizes the results regarding the warning rules based on one parameter only. The wind shear rule has the best probability of detection (46%) and the best true skill statistic (19%). However, its false alarm ratio is very high (87%), and is slightly above those of the helicity and reflectivity rules. The high false alarm ratios of all estimation rules reveal the difficulties involved with estimating wind gusts. The wind shear rule offers an advantage over other warnings rules in terms of probability of detection only.

Fig. 13.

POD, FAR, and TSS for wind gust warning rules described in Table 5, based on one of the following parameters only: IRO, reflectivity, propagation speed, or wind shear.

Fig. 13.

POD, FAR, and TSS for wind gust warning rules described in Table 5, based on one of the following parameters only: IRO, reflectivity, propagation speed, or wind shear.

The results of wind gust forecasting rules combining different parameters are shown in Fig. 14. The three first rules (on the left) combine all individual rules except the wind shear rule. Not surprisingly, the probability of detection increases when the minimum number of necessary criteria to estimate wind gusts decreases. When only one out of four criteria has to be met to estimate gusts over 80 km h−1, the probability of detection reaches a value of 54%. The true skill statistic for this rule performs the best (19%) among the rules not using wind shear. However, the false alarm ratio for this rule is high (88%), but on the order of those of the other rules. Rules using wind shear have, in comparison, a higher probability of detection with a maximum of 62% when only one out of five criteria has to be met to estimate gusts over 80 km h−1. But the false alarm ratio for this rule is also the highest (90%). In terms of true skill statistic, the best rule is when at least two criteria out of five are met to forecast wind gusts over 80 km h−1, with a value of 22%. This value is also higher than the true skill statistic of the wind shear rule, which is the best score for rules using only one parameter.

Fig. 14.

POD, FAR, and TSS for wind gust warning rules described in Table 5, based on different combinations of the parameters.

Fig. 14.

POD, FAR, and TSS for wind gust warning rules described in Table 5, based on different combinations of the parameters.

Although false alarm ratios of all rules are very high, these results highlight the benefit of using wind shear for wind gust estimation, in order to improve the probability of detection. They also demonstrate the improvement in the estimation skill when combining different parameters.

7. Conclusions and operational implementation

An algorithm for the detection of horizontal wind shear at low levels has been developed. The algorithm makes use of data collected by all radars from the French operational network, in order to build a complete mosaic of wind shear over metropolitan France. The examination of the wind shear mosaic on different cases shows that the product is able to retrieve small-scale wind shear signatures that can be linked to either convergence lines ahead of convective cells indicative of gust fronts, or strong convergence areas inside intense cells, contributing to their high intensity and long duration. The product also detects “false” wind shear signatures, such as those due to vertical wind shear. Solutions will need to be proposed in the future to mitigate these errors. A primary improvement could be the use of time continuity to differentiate persistent wind shear lines from nonpersistent ones. For example, the algorithm used for the tracking of convective objects on reflectivity data could be adapted in order to track wind shear signatures in an object-oriented mode, such as is done in Hobson et al. (2012), with an automated technique to categorize storm types from different kinds of radar data, including wind shear. The algorithm could also be improved by adding a differentiation of the phenomena inducing wind shear, in particular for mesocyclones or gust fronts. This will be easier when radial velocity data are available in polar coordinates. Better raw radial velocity data quality, thanks to the introduction of ground clutter filtering or to higher PRFs, will increase the quality of the wind shear mosaic as well.

A comparison between wind shear values observed inside the area defined by convective objects and wind gusts recorded along the trajectory of the cells was conducted. The aim of this comparison was to characterize the relationship between low-level horizontal wind shear observed by the radar network and gusty winds associated with thunderstorms, in terms of intensity and frequency. A link between those different observations has clearly been established: the distribution of the wind shear values inside the CONOs is shifted toward higher values for higher classes of gusts, and a χ2 test demonstrated the statistical link.

As a consequence, the use of wind shear for wind gust estimation was tested. A 99th percentile of the wind shear inside the CONO above 6 m s−1 km−1 during at least three consecutive time steps (10 min) was required to estimate wind gusts of greater than 80 km h−1. This warning rule was evaluated together with other rules using the following parameters: an estimation of the energetic potential of density currents, the cell surface with reflectivity over 51 dBZ, relative helicity, and cell propagation speed. A total of 468 CONOs were analyzed for this evaluation. From the wind gust forecasting rules using only one criterion, the wind shear rule has the best true skill statistic (19%). Forecasting rules combining different parameters with or without wind shear were also evaluated. The best rule results from the combination of all parameters including wind shear and requiring that two out of five criteria are met. Its true skill statistic is 22%. The results clearly highlighted the benefit of using wind shear for wind gust estimation, and also demonstrated the improvement of forecasting skill when combining different parameters. However, false alarm ratios remain very high (over 80%) and there is still room for improvement. To better understand under which circumstances each parameter is more efficient, the evaluation will be carried out again for more cases, in order to classify the results related to storm type, as was done by Guillot et al. (2008) when classifying the forecast skill of tornado forecast.

The wind shear mosaic is about to be produced operationally and the objective is to use this new product to improve wind gust warnings provided to end users.

Acknowledgments

Thanks to Pierre-Emmanuel Gallerand and Matthieu Chevillard, who contributed with enthusiasm to this study during their training. Great thanks to Jeff Beck for correcting and improving the English in this paper. This paper also benefited from the very insightful comments of the reviewers.

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