A Statistical Analysis of the Solar Phenomena Associated with Global EUV Waves

Solar eruptions are the most spectacular events in our solar system and are associated with many different signatures of energy release including solar flares, coronal mass ejections, global waves, radio emission and accelerated particles. Here, we apply the Coronal Pulse Identification and Tracking Algorithm (CorPITA) to the high-cadence synoptic data provided by the Solar Dynamics Observatory (SDO) to identify and track global waves observed by SDO. 164 of the 362 solar flare events studied (45%) were found to have associated global waves with no waves found for the remaining 198 (55%). A clear linear relationship was found between the median initial velocity and the acceleration of the waves, with faster waves exhibiting a stronger deceleration (consistent with previous results). No clear relationship was found between global waves and type II radio bursts, electrons or protons detected in situ near Earth. While no relationship was found between the wave properties and the associated flare size (with waves produced by flares from B to X-class), more than a quarter of the active regions studied were found to produce more than one wave event. These results suggest that the presence of a global wave in a solar eruption is most likely determined by the structure and connectivity of the erupting active region and the surrounding quiet solar corona rather than by the amount of free energy available within the active region.


Introduction
Global waves in the low solar corona (commonly called "EIT waves") were first observed using the Extreme ultraviolet Imaging Telescope (EIT; Delaboudinière et al., 1995) on board the Solar and Heliospheric Observatory (SOHO; Domingo, Fleck, and Poland, 1995). Initially identified as fast-mode MHD waves (e.g. Dere et al., 1997;Moses et al., 1997;Thompson et al., 1998), this interpretation was questioned following observations of stationary bright fronts at coronal hole boundaries and anomalously low measured kinematics (cf. Delannée and Aulanier, 1999). This led to the development of two distinct families of theories to describe this phenomenon; that they are alternatively waves (either linear or non-linear waves) or pseudo-waves (i.e. a brightening resulting from the restructuring of the coronal magnetic field during the eruption of a coronal mass ejection). Note that a more detailed overview of the different theories proposed to explain the "EIT wave" phenomenon may be found in the recent reviews by Liu and Ofman (2014) and Warmuth (2015). However, the advent of high-cadence observations with the launch of the Solar Terrestrial Relations Observatory (STEREO; Kaiser et al., 2008) and Solar Dynamics Observatory (SDO; Pesnell, Thompson, and Chamberlin, 2012) spacecraft has begun to refine our understanding of this phenomenon. Recent work comparing the predictions made by each of these theories with observations suggests that they are best described as large-amplitude waves initially driven by the rapid lateral expansion of a CME in the low corona, before propagating freely (cf. Long et al., 2017).
Although our understanding of the origin and physical properties of global waves has progressed since they were first observed, their relationship with other solar phenomena such as solar flares, CMEs, solar energetic particles (SEPs) and radio bursts continues to be a source of investigation. Global EIT waves have traditionally been studied using single event case studies, making it difficult to draw general conclusions about the nature of their relationship with these phenomena. Recognising this issue, a catalogue of global EIT waves observed by SOHO/EIT was assembled by Thompson and Myers (2009), with each wave event identified "by eye" and classified using a quality rating system. This catalogue was subsequently used to investigate the link between global EIT waves and other solar phenomena including type II radio bursts, solar flares and CMEs (e.g. Biesecker et al., 2002;Warmuth and Mann, 2011). More recent work has extended this systematic approach to observations from the Extreme UltraViolet Imager (EUVI; Wuelser et al., 2004) on board STEREO (Muhr et al., 2014;Nitta et al., 2014) and SDO/AIA (Nitta et al., 2013). In each of these cases the global waves were identified using semi-automated techniques; Muhr et al. (2014) defined the direction into which the wavefront propagated and used a perturbation profile technique to fit the leading edge of the wavefront while Nitta et al. (2013Nitta et al. ( , 2014 used 2D intensity stack plots produced by a series of arc sectors to visually identify the leading edge of the wavefront. Each approach requires manual input from the user, potentially making them susceptible to user bias. In addition, the catalogues created using observations from SOHO/EIT and STEREO/EUVI may have been subject to the lower temporal resolution of both instruments, which could have led to a systematic under-estimation of the kinematics of the global waves (cf. Byrne et al., 2013).
Despite these issues, the catalogues developed by Thompson and Myers (2009) (in particular), Muhr et al. (2014) and Nitta et al. (2013) have been widely used to study the relationship between global waves and other solar phenomena such as type II radio bursts, solar flares and CMEs. Although initially ambiguous, the relationship between global waves and CMEs is now well defined, with Biesecker et al. (2002) showing that every wave has an associated CME, although not every CME has an associated wave. Type II radio bursts have long been observed in the solar corona associated with solar eruptions (e.g. Payne-Scott, Yabsley, and Bolton, 1947;Wild and McCready, 1950) and it was generally accepted that both type II bursts and Moreton-Ramsey waves (first observed in the 1960s by Moreton, 1960;Moreton and Ramsey, 1960) were signatures of the same driving process (Uchida, 1968). However, the much lower measured speeds and other discrepancies between Moreton-Ramsey and global EIT waves complicated extending this assumption to EIT waves. Instead, Klassen et al. (2000) found that 90% of type II bursts identified in 1997 were associated with EIT waves. In contrast, Biesecker et al. (2002) used the wave event list compiled by Thompson and Myers (2009) to show that only 29% of the waves in the list had an associated type II radio burst. This percentage was supported by an analysis of 60 global EUV waves observed by STEREO/EUVI and studied by Muhr et al. (2014), who found that 22% of the global waves studied had an associated type II radio burst. However, a study of 138 global waves identified by Nitta et al. (2013) using SDO/AIA found that 54% of the waves were associated with a type II radio burst. The exact nature of the connection between global waves and type II radio bursts therefore remains subject to investigation.
The energy release during a solar eruption (either as a flare or through acceleration of a CME) can also result in solar energetic particles (SEPs) being accelerated into the heliosphere. SEPs are known to fall into two general categories, impulsive (typically associated with particle acceleration in a small area such as a solar flare) and gradual (associated with particle acceleration over a broad area, such as from a CME) as described by Reames (1993). Release of gradual SEPs tends to occur close to the Sun, where the CME shocks as it propagates outwards into the heliosphere (e.g. Kahler, 1994). This process can also occur in the low corona, with the lateral expansion of the CME shock front accelerating SEPs (e.g. Rouillard et al., 2012) as it propagates through the low corona. The result of this impulsive lateral expansion is best observed as a global EUV wave (cf. Long et al., 2017). Despite this, there is no clear relationship between global EUV waves and SEP events, with most previous work tending to focus on individual case-study events (e.g. Kozarev et al., 2011;Prise et al., 2014). The measured SEP detection time is then typically used to infer the time and location that the particles (both protons and electrons) were released on the Sun, which can be compared to the tracked evolution of the global wave in the low corona (e.g. Rouillard et al., 2012;Prise et al., 2014). This approach was also used by Miteva et al. (2014) to study 179 SEP events between 1997 and 2006, finding that protons detected in situ were related to the global EUV waves, but that there was no correlation between the waves and electrons.
Here we describe the application of an automated algorithm to observations from SDO/AIA to identify and characterise global EUV waves and relate them to other solar phenomena such as flares, CMEs, SEP events and type II radio bursts. The various data-sets and how the measurements were made are described in Section 2, with the results of the statistical analysis described in Section 3. The results are then discussed and some conclusions drawn in Section 4. Note that the complete table used for the analysis described here is also included in the Appendix.

Observations and Data Analysis
The list of global EUV waves identified by Nitta et al. (2013) was used as a starting point for this investigation to maximise the number of global wave events and associated phenomena that could be studied in detail. In each case, the location of the flare associated with each eruption was used as the source of the global wave, with the start time of the flare used as the reference point for analysing the EUV, radio and in situ data.

Global Wave Characterisation and Analysis
The events listed in the wave list of Nitta et al. (2013) were processed using the Coronal Pulse Identification and Tracking Algorithm (CorPITA; Long et al., 2014). CorPITA is an automated code designed to identify, track and analyse global EUV waves using science quality data from the SDO/AIA 211 Å passband. Although global waves have previously been characterised using each of the eight extreme ultraviolet (EUV) passbands observed by SDO (Liu et al., 2011), previous work has shown that they are best observed using either the 193 Å or 211 Å passbands . The 211 Å passband was used here as it observes slightly hotter plasma than the 193 Å passband and as a result does not have as much emission from the background corona, making the global wave easier to identify and characterise.
Percentage base-difference images are used to identify the wave pulse, with the pre-event image defined as the image 2 minutes prior to the start time of the flare. A series of 360 arc sectors, each of 10 • wide and offset by 1 • , centered on the flare location are then used to define a series of intensity profiles. The wave pulse is identified using these intensity profiles and fitted using a Gaussian function which allows the position (i.e. the centroid of the Gaussian), peak intensity and full-width at half-maximum to be recorded in each arc sector for each time step. The CorPITA code then identifies the pulse in each arc sector by finding the largest section of contiguous data-points exhibiting increasing distance away from the source point. This section of data-points is then fitted using a quadratic function which provides an estimate of the initial pulse velocity and acceleration. The temporal variation in pulse distance from the source point for the 7 June 2011 event is shown in Figure 1a. Although this technique ensures a consistent approach to estimating the initial pulse velocity and acceleration of the pulse, the accuracy can be affected by sudden jumps in pulse position (e.g. due to the algorithm becoming confused by bright points or small-scale loop oscillations). The accuracy of the measurement in each arc sector is therefore quantified in each case using a quality rating system, with the pulse scored according to the number of images used to identify it, the fitted initial velocity and acceleration and the uncertainty in identifying the pulse (cf. Long et al., 2014). Figure 1b shows the estimated quality rating for each of the arc sectors studied for the 7 June 2011 event. A wave is then identified by CorPITA if more than 10 adjacent arc sectors detect a moving pulse with a quality rating greater than 60%. The measured parameters of the wave identified by CorPITA are then stored for future use (as listed in Table 1). In addition to the location of the source, start time of the wave and fitted kinematics, CorPITA also records the number of arcs in the largest segment in which CorPITA has identified a wave (corresponding to the column Num. arcs in Table 1) and the central arc of this segment in degrees clockwise from solar north (Central arc angle). Note that Central arc angle uses the central angle of the segment to indicate the mean direction of the identified wave pulse, and does not necessarily correspond to the highest rated arc within that segment.
Although a more detailed description of the CorPITA technique may be found in the paper by Long et al. (2014), it should be noted that the code has since been updated to address issues found during an initial attempt at the work described here. Data is now downloaded in 20 minute chunks to speed up processing rather than an initial 10 minute chunk followed by single image downloading as before. This increase in time over which to search for a wave provides a better opportunity to identify the wave pulse, particularly for gradual flare events where the starting time of the wave and starting time of the flare may not be well correlated. The code has been rewritten for stability and to ensure a more rigorous analysis, while the colour table has also been updated to make it more accessible and easier to understand (as shown in Figure 1).

Solar Energetic Particle Analysis
The SEP events associated with each global wave event were identified using measurements from the 3D EESA/PESA (Lin et al., 1995) instrument on board the Wind spacecraft. The data for electrons of energies between ≈ 1.3 keV and ≈ 27 keV and protons of energies between ≈ 195 keV and ≈ 4.4 MeV were examined for 24 hours around (8 hours before and 16 hours after) the start time of the associated solar flare. In each case, the data were obtained from the NASA Coordinated Data Analysis Web (CDAW) website. 1 The presence of an SEP event in each energy band was determined by first smoothing the flux data using a Savitsky-Golay filter to reduce the effect of small-scale variations. The flux was then examined to find the point at which it began to increase rapidly, with data prior to this point defined as the background. The onset times were then calculated using a Poisson cumulative sum (CUSUM) method (cf. Huttunen-Heikinmaa, Valtonen, and Laitinen, 2005). The CUSUM method is widely used in industry to identify changes in running processes, with a Poisson-CUSUM approach used if the data has a Poisson distribution. This approach works by cumulating the difference between an observed count Y i and a reference value, where μ a is the mean of the background flux and μ d is μ a plus twice the standard deviation of the background flux. If this cumulation exceeds a threshold value h (chosen to minimise the effect of small point-to-point fluctuations while retaining sensitivity to large-scale particle events), then an out-of-control signal is given. In this case, a particle event was identified by looking for 300 out-of-control signals in a row. The onset time of particle detection at the spacecraft was then defined by the time of the first out-of-control signal. Once an onset time was determined for each energy level, a velocity dispersion analysis was used to determine the release time of the particles from the Sun (e.g. Reames, 2009). This was also used to confirm the presence of an SEP event, with an event defined to have occurred if the velocity dispersion analysis gave a realistic physical release time from the Sun, i.e. the release time was before the onset time. An example of two events with realistic and unrealistic release times is shown in Figure 2. In the realistic case, the onset time at each energy can be identified by the sudden increase in particle flux, which corresponds to a valid estimate of release time and travel distance using the velocity dispersion plot. However, no such increase may be discerned in the unrealistic case, leading to the physically impossible estimates of release time and travel distance in the resulting velocity dispersion plot. Velocity dispersion analysis is a commonly used technique that assumes both that particles at all energies are released at the same time and that particle scattering is energy independent. However, energy dependent particle scattering can greatly affect particle arrival times, meaning that propagation through the heliosphere is not a simple trajectory along the Parker spiral. Therefore, to ensure consistency, each event was initially processed using this approach with the resulting plots examined "by eye" for confirmation.

Identification and Characterisation of Type II Radio Bursts
The type II radio bursts associated with each global wave event were identified using the daily lists of radio bursts collated by the Space Weather Prediction Centre located at the National Oceanic and Atmospheric Administration (NOAA/SWPC). A window 90 minutes either side of the start time of the global wave was used to look for associated events in the NOAA/SWPC list. This choice of time window was motivated by the fact that type II radio bursts can be seen up to 15 minutes before or after the first instance of an EUV wave observation (Park et al., 2013;Warmuth, 2010;Miteva et al., 2014); the larger time window used here was chosen to account for any anomalous events. For each candidate radio burst associated with a global wave, the SWPC list provides an associated start time, an end time, the observatory used to make the observation, the frequency range of the burst and the estimated drift speed. It should be noted that the drift speeds used in this analysis are the values provided by NOAA/SWPC, which are obtained using the standard approach of converting drift rate to speed via a density model of the solar corona (Mann and Classen, 1995;Miteva and Mann, 2007). However, it should be remembered that the absolute values of these bursts are known to be subject to large uncertainty given the often arbitrary nature of the models and the differences between individual observatories (Magdalenić et al., 2008(Magdalenić et al., , 2012. This estimation also assumes a radially propagating shock driver, whereas it has been shown that shocks can often propagate non-radially (Mancuso and Raymond, 2004;Magdalenić et al., 2012). Nonetheless, given the goal of trying to find a statistical correlation between radio burst properties and various other phenomena, we believe that the uncertainties associated with using the quoted type II burst speeds should be acknowledged but are not of major concern.

Results
Due to limitations inherent to the approach taken by CorPITA, it was not possible to analyse all of the events identified by Nitta et al. (2013) as they originated either too close to or beyond the solar limb. CorPITA requires a source point from which to track the pulse and so it cannot study events that do not originate on disk. As a result, of the 410 wave events identified by Nitta et al. (2013), only 362 could be analysed using CorPITA. 164 events were classified as having global waves by CorPITA, with no waves found for the remaining 198 events. The output from CorPITA for all events studied is listed in Table 1.

Wave Kinematics
The global waves identified here exhibited a wide variety in their kinematics, both from arc to arc within each event and from event to event. For a given event, CorPITA is designed to examine each arc sector separately, allowing the directional variation in pulse position to be identified and studied. Although this provides a more accurate estimate of how the wave evolves, it makes event-to-event comparison difficult as it raises the question of which velocity and acceleration values should be used. For every event studied here, the initial velocity and acceleration were calculated for each arc by first identifying the largest section of contiguous data-points exhibiting increasing distance away from the source point and fitting these points using a quadratic function (as illustrated in Figure 3 of Long et al., 2014). The medians of the initial velocity and acceleration values across all arc sectors with a sufficiently high quality rating were then chosen as being most representative of the kinematics of that event. Panels a and b of Figure 3 show the median initial velocity and acceleration, respectively, of all events studied plotted with respect to the peak GOES X-ray flux of the associated flare in each case. It is clear that there is a broad spread in both the median initial velocity and the acceleration of the waves studied, with the maximum median initial velocity peaking at ≈ 950 km s −1 and the maximum median acceleration peaking at ≈ −750 m s −2 .
To determine whether the median initial velocity and acceleration of the waves was most appropriate for comparing events, the maximum initial velocity and acceleration of the wave events were also examined. These were taken as the maximum of the initial velocity and acceleration values derived across all arc sectors with a sufficiently high quality rating for a given event. Panels c and d of Figure 3 show the maximum initial velocity and acceleration, respectively, of all events studied plotted with respect to the peak GOES X-ray flux of the associated flare in each case, similar to panels a and b of Figure 3. Although the maximum initial velocity and acceleration are clustered around ≈ 2000 km s −1 and ≈ −2000 m s −2 , respectively, there is a much larger spread in both, as apparent from panels c and d of Figure 3.
Finally, the initial velocity and acceleration were plotted against each other for both the median and the maximum values to try and identify any trends comparable to those previously found by Warmuth (2010), Warmuth and Mann (2011) and Muhr et al. (2014). Panel e of Figure 3 shows the median initial velocity plotted against median acceleration for each event studied. It is possible to identify a clear trend in this case, with faster (slower) waves exhibiting a stronger (weaker) negative acceleration. This is consistent with the results of both Warmuth and Mann (2011) and Muhr et al. (2014), who plotted the initial velocity against acceleration, and with Warmuth (2010), who plotted the average velocity against acceleration. The approach was repeated for the maximum initial velocity and acceleration (shown in Figure 3f), but consistent with panels c and d, the plot shows a much broader spread. Although a slightly decreasing trend can be discerned, with faster (slower) waves again exhibiting a stronger (weaker) negative acceleration, this trend is much weaker than that apparent for the median initial velocity and acceleration data shown in panel e. This suggests that the maximum initial velocity and acceleration are poor indicators of the overall wave kinematics and the median initial velocity and acceleration should be used when trying to characterise a given wave event using a single kinematic value.
Previous work by Warmuth and Mann (2011) used the wave catalogue of Thompson and Myers (2009) to suggest that there were three kinematic classes of global EUV waves. Class 1 referred to initially fast waves with a strong deceleration, class 2 waves had moderate and nearly constant speeds while class 3 referred to slow waves with an erratic kinematic profile. The results shown in Figure 3e are generally consistent with the results of Warmuth and Mann (2011), but it is not possible to distinguish three independent kinematic classes of global waves in this case. This may be due to the larger number of events used (164 here compared to 61 for Warmuth and Mann, 2011) or alternatively the higher cadence of SDO/AIA compared to SOHO/EIT and STEREO/EUVI in Warmuth and Mann (2011). However, when the data in Figure 3e were fitted using a linear relation, an intercept of 180 km s −1 was found, consistent with the cutoff value of ≈ 170 km s −1 used by Warmuth and Mann (2011) to define the difference between linear waves and those features possibly due to magnetic reconfiguration. However, this value was slightly lower than the intercept found by Muhr et al. (2014) using STEREO/EUVI observations. The consistency between the results presented here and by Warmuth (2010), Warmuth and Mann (2011) and Muhr et al. (2014) indicates that these features are large-amplitude events as outlined by Long et al. (2017).
Although the catalogue of Nitta et al. (2013) was used as a starting point for this work, it is worth noting that the analysis of the pulse kinematics described here and shown in Figure 3 do not match the results presented in Nitta et al. (2013). This is most likely due to the different approaches used to identify the wave pulse and measure its kinematics. Whereas Nitta et al. (2013) tracked the leading edge of the wavefront in a 2-dimensional time-distance plot, here a 1-dimensional intensity profile of the wavefront was fitted using a Gaussian, with the centroid of the Gaussian taken as the position of the wavefront at each point in time. This approach removes the effect of pulse broadening on the identified pulse position (see, e.g. Long et al., 2014, for a more detailed discussion). In addition, both the velocity and the acceleration of the pulse were simultaneously measured here for each pulse using a single quadratic fit to the temporal variation in pulse position. This is in contrast to Nitta et al. (2013), who used both linear and quadratic fits independently applied to the temporal variation in pulse position to estimate the velocity and deceleration of the pulse, respectively.

Relationship with Solar Flares and Active Regions
When global EIT waves were first observed there was a lot of discussion regarding their origin, with the debate focusing on whether they were initially driven by the associated flare or coronal mass ejection (e.g. Cliver et al., 2005;Vršnak et al., 2006). Since then, the general consensus has been reached that they are initially driven by the rapid lateral expansion of the erupting CME in the low corona; a conclusion strongly supported by the SDO observations reported by Patsourakos, Vourlidas, and Stenborg (2010). A detailed discussion of the predictions made by the different theories and how recent observations support this conclusion may be found in the recent paper by Long et al. (2017).
As shown in panel a of Figure 4, all of the events studied here originated in the activity belts, consistent with previous observations (e.g. Muhr et al., 2014). However, 14 of the events studied had no associated flare. The vast majority of the waves also tended to start after the start time of the associated flare, as indicated by panel b of Figure 4, although 10 events studied did start before the flare. While most of the waves identified were first observed by CorPITA within 10 minutes of the start of the flare, some were not observed until up to 30 minutes after the flare (as defined by the NOAA GOES catalogue). Panel c of Figure 4 indicates a broad spread in the size of the flares associated with each wave studied. Although the vast majority of waves were associated with M-and C-class flares, more than 10 waves were associated with both B-and X-class flares respectively.
These results suggest that the flare plays little-to-no role in the initiation or even existence of a wave, indicating that some other criteria must be fulfilled before a solar eruption pro- Figure 5 Panel a The relationship between the start time of the CME as defined by the linear fit to the temporal variation in CME position obtained from the LASCO CDAW catalogue and the start time of the wave detected by CorPITA. Panel b The relationship between the median initial wave velocity measured by CorPITA and the linear starting velocity of the CME measured by CDAW. duces a wave. While the relationship with CMEs is examined more closely in Section 3.3, panel d of Figure 4 suggests that the active region from which the wave originates may be important. Over 25% of active regions produced more than one wave during their time on disk, with two active regions producing six waves each. This suggests that the magnetic structure of the active region or its relationship with the surrounding quiet solar corona may determine the ability of the active region to produce a wave during a solar eruption.

Relationship with CMEs
A comparison was also made between the identified waves and their associated coronal mass ejections as identified by the LASCO CDAW catalogue. 2 Global waves have historically been strongly associated with CMEs, with Biesecker et al. (2002) in particular suggesting that every wave has an associated CME while not every CME has an associated wave. However, a direct comparison between the on-disk global wave and the erupting CME is complicated by the fact that CMEs are best seen when in the plane of the sky (so when associated with eruptions close to the limb) whereas global waves are best observed and tracked on disk.
As shown in Figure 5, there is no clear correlation between the start time of the global wave and the start time of the associated CME predicted by the linear fit to the temporal variation in CME position obtained from the LASCO CDAW catalogue (panel a). Similarly, there is no clear correlation between the median initial wave velocity and the fitted linear velocity of the CME (panel b). While initially concerning, both of these results are consistent with our current understanding of global waves and CMEs and their relationship; a point worth discussing in more detail.
The CDAW catalogue uses LASCO observations to identify and measure CMEs and, as a consequence of the location of SOHO/LASCO at the L1 Lagrange point, is biased towards Figure 6 Panel a The offset time between the start of the global wave and the associated type II radio burst. The relationship between the median velocity (panel b) and median acceleration (panel c) of the wave as measured by CorPITA and the drift speed of the type II radio burst. Panel d Histogram showing the variation in median wave velocity for wave events with and without type II radio bursts.
CMEs erupting from the solar limb as seen from Earth. As a result, CMEs associated with global waves observed by SDO/AIA tend to be observed as halo CMEs, which are difficult to identify and measure. The velocity and starting time values used here were also taken from the linear fits to the temporal variation of the CME distance, with the result that any acceleration or deceleration of the CME was ignored, which may account for the spread in projected CME start times. Finally, the predicted mechanism by which the waves are produced by the lateral expansion of the erupting CME in the low corona suggests that there should be no direct correlation between the velocity of the wave and the forward velocity of the CME (which is what is typically measured when studying CMEs). As a result the lack of any correlation shown in Figure 5 is to be expected.

Relationship with Type II Radio Bursts
With the growing consensus on the interpretation of global coronal waves as large-amplitude waves initially driven by the lateral expansion of a CME in the low corona, a natural comparison can be made between global waves and type II radio bursts. Type II bursts are strongly associated with MHD shock waves (cf. Nelson and Melrose, 1985) and as a result the relationship between them and global waves has long been hypothesised and investigated (e.g. Cliver, Webb, and Howard, 1999;Biesecker et al., 2002;Nitta et al., 2014). However, their relationship remains inconclusive.
Despite the strong relationship between type II radio bursts and MHD shock waves and the interpretation of global EUV waves as large-amplitude or shock waves, a comparable number of wave events were identified with and without associated radio bursts. 66 wave events had an associated type II burst, with 98 wave events having no associated type II radio signature detected at Earth, meaning that 40% of the waves in our sample have an associated type II burst. This is higher than the 22% association rate reported by Muhr et al. (2014), but comparable to the 43% association rate reported by Biesecker et al. (2002) for waves with a high quality rating (> 50% using the classification of Thompson and Myers, 2009). However, this is much lower than the 100% associated rate between type II bursts and EUV waves with an associated Hα Moreton-Ramsey wave reported by Warmuth et al. (2004) and Warmuth (2010). It should be noted that no comparison was made in this paper between global waves observed in EUV and Hα passbands; given the relative lack of recent synoptic studies of Moreton-Ramsey waves in Hα data we leave a more detailed analysis of the relationship between these two phenomena for a dedicated future work.
As shown in Figure 6d, there is no relationship between the median velocity of the wave and whether or not it had an associated type II burst, with very fast wave events exhibiting no type II emission while a significant number of very slow events had associated radio emission. This is most likely related to the fact that type II radio burst generation is related to conditions in the upper corona at > 1.2 R (Mann et al., 2003), while the global wave propagates lower down in the corona (at ≈ 70 -100 Mm, cf. Kienreich, Temmer, and Veronig, 2009;Patsourakos and Vourlidas, 2009).
For those events which had an associated type II radio burst, the start of the radio emission was observed after the start of the wave in the vast majority of cases (see Figure 6a), similar to the relative start times of waves and radio bursts reported by Miteva et al. (2014) and Warmuth (2010). This delay between the start time of the global wave and the associated type II burst is likely due to the time taken for the disturbance to either become super-Alfvénic (as modelled by Vršnak and Lulić, 2000), or the time taken for the driver to reach regions of low ambient Alfvén speed in the corona (Mann et al., 2003;Zucca et al., 2014); in some cases this can take up to 30 minutes after detection of the wave. The duration of the radio bursts was also observed to be at most 35 minutes, with most radio bursts lasting less than 20 minutes, consistent with the lifetime of the observed waves. However, a number of events had associated radio emission which was observed to start prior to the first detection of the global wave, suggesting that the radio emission in those cases may have been due to either the rapid expansion of the CME rather than the wave, or the CME driving a shock radially before any lateral expansion produced the wave. In either case, the difference in start time of up to 30 minutes between the waves and associated type II radio bursts means that while they may originate from a common MHD disturbance in the corona, they most likely belong to spatially separated parts of this disturbance.
There is also no clear relationship between either the median initial velocity or acceleration of the identified waves and the drift speed of the associated radio bursts. Panels b and c of Figure 6 show that most of the events identified tended to have drift velocities of 0 -2000 km s −1 , with two notable exceptions in both cases. Some of the events also had quite high drift velocities of ≈ 2000 km s −1 despite estimated median velocities lower than 200 km s −1 . Even when accounting for the size of the associated flare, there is still no clear relationship between median initial wave velocity and drift speed of the associated type II burst, with the flare size in panels b and c of Figure 6 indicated by the colour of the datapoint.
This lack of a clear relationship between the drift velocity of the type II burst and the median initial velocity of the identified wave is at odds with the conclusions of Warmuth (2010), who found a linear relationship between these parameters. Several individual case studies have also reported a kinematical relationship between type IIs (e.g. Vršnak et al., 2006;Pohjolainen, Hori, and Sakurai, 2008;Grechnev et al., 2011;Kozarev et al., 2011;Ma et al., 2011). However, there may be several reasons for the lack of such a relationship that we find here. Firstly, as mentioned above, while the type II radio burst and the global wave are most likely different manifestations of the same shock in the corona, they may belong to separate parts of this shock, i.e. the wave propagates laterally or parallel to the solar surface, while the type II burst may propagate (semi-)radially (Grechnev et al., 2011). Second, there is no guarantee that these speeds will be the same. In fact, the discrepancy between the type II drift speed and the wave speed means that expansion of the MHD disturbance is most likely anisotropic, with no relationship between lateral and radial expansion speed. Thirdly, a major issue with relating these two speeds concerns the reliability of the type II speed itself. This speed is derived from one of the many density models used in radio physics, which are often chosen arbitrarily and may not represent the density environment of the event (Magdalenić et al., 2008). This analysis also assumes radial radio source propagation, which may not be the case. Finally, Warmuth (2010) focused on global EUV waves with associated Hα Moreton-Ramsey waves. Given the supposed mechanism by which these phenomena are thought to be related (i.e. the coronal EUV wave has a sufficiently large downward impulse that allows its footprint to be observed as a Moreton-Ramsey wave; see, e.g. Warmuth, 2010Warmuth, , 2015, for more details), this indicates that the waves observed by Warmuth (2010) were large-amplitude shocks. Although a similar mechanism may have produced the global waves studied here, these waves may not have been sufficiently strong to produce a radio signature. This suggests that a more granular study, focusing on strong EUV waves with associated Hα Moreton-Ramsey waves might provide a higher correlation between global EUV waves and type II radio emission (comparable to Warmuth et al., 2004;Warmuth, 2010).

Relationship with Solar Energetic Particle Events
Similar to the predicted relationship with type II radio bursts, as large-amplitude and sometimes weakly shocked waves, global waves would be expected to accelerate solar energetic particles as they propagate across the Sun. However, of the 164 events with identified global waves, only 21 were found to have any evidence of an associated proton event, whereas only 14 events were found to have any evidence of an associated electron event (of which 12 had an associated proton event). While there are several probable reasons for this discrepancy, it is most likely due to a lack of connectivity between the field lines along which the particles could be accelerated and the spacecraft detecting the particles. In a simplistic interpretation, only events erupting from solar west would be expected to have any connectivity with the detecting spacecraft due to the Parker spiral, a suggestion consistent with the fact that 19 of the 23 events found here were associated with flares that originated on the western hemisphere.
However, recent studies have shown that even events on the far side of the Sun can produce particle detections at Earth, with studies by Rouillard et al. (2012) and Lario et al. (2016) suggesting that the global waves travelled across the Sun and eventually encountered field lines connected to Earth/L1. It has also been shown that particles can be detected despite being produced far from the footpoint of a magnetic field line connected to the spacecraft as a result of either super-radial spreading of field lines throughout the corona (e.g. Klein et al., 2008), or very high levels of lateral diffusion in a turbulent solar wind (e.g. Laitinen et al., 2016). The large spatial extent of global waves and their ability to accelerate particles far from the erupting active region therefore suggests that more SEP events should have been identified. However, only four events were found here that were associated with active regions located in the eastern solar hemisphere.
This lack of identified events may be due to the configuration of the coronal magnetic field into which the wave is propagating. Although previous work by Park et al. (2013Park et al. ( , 2015 compared wave propagation to a potential field source surface extrapolation of the solar corona to compare the time at which the wave encountered a connected field line with the inferred SEP release times, this approach is rarely taken. However, the results described here suggest that a full understanding of the ability of a global wave to accelerate SEPs must combine the propagation of the wave with a full understanding of the coronal and heliospheric magnetic field. Although this approach is beyond the scope of the statistical path taken here, we hope to return to it in a dedicated future work.

Discussion and Conclusions
In this manuscript, we have applied the Coronal Pulse Identification and Tracking Algorithm (CorPITA) to the list of global coronal waves assembled by Nitta et al. (2013) and compared the output with a variety of other solar phenomena. Of the 410 events identified as waves by Nitta et al. (2013), only 362 could be processed using this approach due to requirements on the location of the source point of the wave. Of these 362 events processed, 164 were classified as having associated global waves, with CorPITA finding no waves for the remaining 198 events. This indicates a significant disconnect between the systematic automated approach to identifying and characterising global coronal waves and the traditional "by-eye" approach. Although most of these issues can and should be overcome through advanced image and signal processing and feature tracking, some may be due to the different definitions used to identify the wave pulse. For example, CorPITA uses a series of 1-dimensional intensity profiles obtained from percentage base-difference images to identify and fit the wave using a Gaussian model, whereas Nitta et al. (2013) used 2-dimensional distance-time stack plots to identify the leading edge of the pulse.
With the waves identified and tracked, the next step was to examine the variation in wave kinematics. As CorPITA uses a series of 360 10 • arc sectors to identify and track the waves, each wave can be represented by a range of velocity and acceleration values which may not be representative of the large-scale motion of the wave. The maximum velocity and acceleration in particular are poorly representative of the overall wave motion as they can be strongly affected by anomalous measurements. However, the median velocity and acceleration provide a much better representation of the large-scale kinematics and should always be used when wishing to describe a wave using a single kinematic value. The median velocity and acceleration of the measured waves were also found to be correlated (consistent with the previous work of Warmuth and Mann, 2011). Although the spread in values increased with both velocity and acceleration, faster waves tend to have a stronger deceleration. However, no clear relationship could be determined for the maximum velocity and acceleration, suggesting that they are not representative of the overall kinematics of the wave.
There was also no clear relationship between the global waves and the associated solar flares. Neither the maximum or median velocities or accelerations showed any relationship with the class of the associated flare, with C-class flares associated with the waves that exhibited both the highest and the lowest median velocity. Similarly, there was no clear correlation between the wave parameters described here and the properties of the associated CMEs as measured by the LASCO CDAW catalogue. However, this is most likely due to instrumental and measurement effects rather than the lack of any underlying physical relationship and is unsurprising given the statistical approach taken here. A more thorough analysis would require measurements of CMEs taken away from the Sun-Earth line and would measure the lateral expansion velocity rather than the forward motion of the CME. It was possible to observe CMEs propagating along the Sun-Earth line using the STEREO spacecraft, with the instruments on both spacecraft deliberately designed to have overlapping fields-of-view in the low corona which could allow the lateral expansion of the CME to be measured. However, the low temporal cadence of the instruments makes it difficult to disentangle the wave from the expanding CME, while the gradual progression of STEREO behind the Sun during the period of this project complicates a direct comparison between the global wave and the associated CME. Finally, no correlation was found between the global waves and SEPs, with only 21 of the events exhibiting any SEP signature. This is most likely because only Wind data were used in this analysis, but the ability of global waves to accelerate particles far from their erupting active region suggests that the structure of the coronal magnetic field into which the wave propagates should be accounted for when trying to study the acceleration of SEPs by global waves in the solar corona.
The lack of any clear statistical correlation between the different solar phenomena studied here indicates that determining the criteria required to produce a global wave is not a simple task. Although the majority of waves identified here were associated with both flares and CMEs, the parameters measured show no correlation, suggesting that the free energy available within an active region to produce a flare and accelerate the CME does not determine the presence of a wave in the subsequent eruption. However, it was found that over 25% of active regions produced multiple wave events, with two active regions producing six wave events each. This suggests that the structure of the erupting active region and its connectivity with the surrounding quiet solar corona may be much more important for determining the presence of a global wave in a solar eruption. Understanding the criteria required to produce a global wave therefore requires a more detailed examination of an active region producing multiple wave events, which we hope to continue in a dedicated future work. Table 1 below outlines the complete list of global wave events identified by Nitta et al. (2013) and processed by the CorPITA code for this paper. t_flare refers to the start time of the flare as defined by the GOES classification. t_wave refers to the time of the first observation of the wave by CorPITA. Num. arcs refers to the number of arcs in the largest segment in which CorPITA has identified a wave, with Central arc referring to the central arc of this segment in degrees clockwise from solar north. Median velocity is given in km s −1 and median acceleration is given in m s −2 . The complete list is also available as a comma separated value list attached to the online version of this paper.