Observed northward shift of large hailstorms in the eastern United States since 2000

Given its high population density and degree of urbanization, the eastern United States (US) is a region vulnerable to the impacts from hailstorms. Small changes in hail activity may indicate large impacts on the potential hail risks faced by the region. While contrasting hailstorm-favorable environmental changes between the northeastern and southeastern US have been documented, the meridional shift of hail activity in the eastern US has not been directly revealed based on observed hailstorm records. In this letter, using the official hailstorm database, we find a significant northward migration of hail activity (+0.33° N decade−1) in the eastern US since 2000, which is mainly contributed by the increasing proportion of large hailstorm events (hail size 0.75–2.0 inch) hitting the northeast in July and August (+0.93° N decade−1). The spatially inhomogeneous climatic mean state changes over the past two decades contribute a leading role: the intensified Bermuda High and the eastward shift of upper-level jet stream over the central US tended to moisten (dry) the atmosphere over the northeastern (southeastern) US by enhancing the low-level poleward moisture transport. This not only provides more moisture for hailstorm formation in the northeast but also destabilizes (stabilizes) the atmosphere in the northeast (southeast) under an overall increase in dry instability over the eastern US. These factors together lead to a northward shift of large hailstorms toward the northeastern US, where hailstorms were relatively seldom reported. Incorporating this shift in knowledge may improve contingency and risk management strategies of both the public and private sectors in the future.


Introduction
Hailstorms are a typical category of meteorological disaster that may lead to fatalities, property destruction, automobile damage, and economic losses.Depending on the storm durations and hailstone sizes, a hailstorm event can lead to more than $1 billion losses (Brooks and Dotzek 2008, Tang et al 2019, Raupach et al 2021).Climatologically, hailstorms occur more frequently over the central United States (US), or the 'Hail Alley' 5 (Elmore et al 2022); however, hail disasters may also be serious in regions 5 The 'Hail Alley' is a region in the central US where climatic and topographic conditions create an environment conducive to frequent and intense hailstorms.This region includes states such as Colorado, Wyoming, Nebraska, North Dakota, South Dakota, Oklahoma and Texas, Nebraska, Colorado, and Wyoming.(https:// nssl.noaa.gov/education/svrwx101/hail/)outside of the 'Hail Alley.'In addition to the characteristics of the hailstorm itself, damage caused by a hailstorm also depends on other human factors, such as the population, degree of social development and emergency system response (Prein andHolland 2018, Battaglia et al 2019).The eastern US, a highly populated and developed region to the east of the Mississippi River (∼90 • W) (figure S1(a)), is relatively vulnerable to hailstorms.While the eastern US receives fewer reports of hail each year (Cintineo et al 2012, Murillo et al 2021), the same degree of hail activity change may cause much larger impacts on the region compared with other regions.Thus, great attention should be given to understanding the changes in hailstorm activity over the eastern US and the corresponding mechanism.
The changing climate has led to variability in environmental factors that support hailstorms (Diffenbaugh et al 2013, Johnson and Sugden 2014, Li et al 2016, Rädler et al 2019, Tang et al 2019, Raupach et al 2021), which has affected US hailstorms in terms of their occurrence, intensity and spatial distribution in recent years (Changnon and Changnon 2000, Xie et al 2008, Kapsch et al 2012, Allen and Tippett 2015, Mohr et al 2015, Punge and Kunz 2016, Brimelow et al 2017).For instance, while no apparent hailstorm trend has been found for the US, records of significantly increasing hailstorm events were documented in the High Plains and central Rockies (Changnon and Changnon 2000, Cao 2008, Raupach et al 2021).Although the hailstorm trend is partly contributed by the increasing number of hailstorm reports due to various non-meteorological factors (Allen and Tippett 2015), the variation in hailstormfavoring environments also is a contributing factor (Diffenbaugh et al 2013, Brimelow et al 2017, Tang et al 2019, Raupach et al 2021).A recent study shows an increase in days with environments favorable to large hailstorms in the central and eastern US since 1979.In particular, the trends in large hail-favoring (LHP) days over the northeastern US are apparently larger than those over the southeastern US (Tang et al 2019).These changes may lead to changes in the meridional distribution of hail activity in the eastern US, which signifies a change in the probability that a region is affected by hailstorms and increases the potential risk of hail disasters over regions that have seldom experienced hailstorms in the past.
Meanwhile, numerous studies have already reported the impacts of climate change on the meridional position of different atmospheric systems.For instance, the position of tropical cyclone genesis and lifetime-maximum intensity have been moving away from the tropics recently (Kossin et al Given the vulnerability of the eastern US to hailstorms (Kerschner 2009), determining the changes in the spatial distribution of hail activity is of enormous importance to society.As mentioned above, hailfavorable environments have been observed more frequently in the northeastern US (Tang et al 2019); however, their conclusions were made based on environmental proxies computed from reanalyses (Raupach et al 2021).Although the response of hailstorms to climate change has drawn much attention from the scientific community, to our knowledge, there has not been research directly studying the latitudinal shift of the eastern US hail activity based on hailstorm records.Hence, this study aims to explore the meridional shift of hail activity over the eastern US and its major triggers from 2000-2022, where hail observations are more temporally homogeneous (see supplementary materials), based on official hail event records.Particular attention is given to the eastern US, where larger average loss costs take a heavy toll because of its high population density (Battaglia et al 2019).

Data and methods
In the following analyses, the spatial change in hail activity is analyzed based on the US Storm Events Database (Schaefer and Edwards 1999).The database offers a comprehensive and official record of hail activity by collecting all hail reports from different sources.The limitations and validity of this hail database for studying the long-term changes in hail activity have been discussed in previous publications (Smith 1999, Doswell et al 2005, Cintineo et al 2012, Paulikas 2014, Allen and Tippett 2015).In order to reduce anthropogenic signals of hail activity change, it is recommended to use data after 2000 for climate studies of hail activity (Allen and Tippett 2015), so this study focuses on year 2000-2022.In addition, each hail episode is referred to as a single hail event, regardless of the number of hail reports, so as to avoid spurious signals due to the spatially inhomogeneous population distribution.During 2000-2022, total 7290 hail episodes were observed in the eastern US, thus 7290 hail events were analyzed in this study The seasonality of hail activity in the eastern US lasts from March to August, peaking in May (figure S1(b)); thus, the following analyses are based on these six months (March to August).Throughout the text, the eastern US is referred to as the region to the east to 90 • W. The southeastern US is the region to the east of 90 • W and to the south of 38 • N, while the northeastern US is the region to the east of 90 • W and to the north of 38 • N, according to the changes in spatial distribution of hail events (later shown in section 3.1 and figure 1).
Changes in the spatial distribution of hail activity were examined by applying the probability density function (PDF, or image histogram) and spatial PDF (SPDF) (Chen et al 2002, Leung et al 2022, Gan et al 2023) to the hailstorm reports, by neglecting the overall hail occurrence trend of the eastern US.Then, we quantitively estimate the contributions of (1) changes in the occurrence probability of hail-favoring synoptic circulation patterns and (2) changes in the climatic mean state, respectively, to the northward shift of eastern US hail activity, based on the North American Regional Reanalysis (NARR) (Mesinger et al 2006).More details about the about the data, definitions, and methodology can be found in the supplementary materials.Unless otherwise stated, all tendencies reported in the following analyses are statistically significant.

Overall northward shift of hail activity in the eastern US
Based on the US Storm Events Database, there was an overall drop in all eastern US hail event counts in terms of hail size (d hail , unit: inch) larger than 0.75, with the decreasing tendency in the southeastern US larger than that in the northeastern US (figure 1(a)).This results in a significantly increasing tendency (+0.75 • N decade −1 ) in the average latitude over all hail events with d hail ⩾ 0.75 since 2000, indicating a northward shift of hail events in the eastern US.This northward shift is evident in the significant PDF change of event counts from 2000-2010 to 2012-2022.Comparing the two 11 year periods, the PDF peak jumped from 35.1 • N to 39.9 • N, with apparent increasing (decreasing) tendencies of hail events to the north (south) of 38 • N (figure 1(a)).Hence, for simplicity, 38 • N is taken as the boundary (black dashed line in figure 1(a)) between the northeastern and southeastern US in the following discussion.
Further analyses show that the northward shift of eastern US hail activity is mainly contributed by that of large hail events (0.75 ⩽ d hail < 2).The changing pattern of sub-severe hail event (0.75 ⩽ d hail < 1.25) frequency is generally consistent with the variation in all hail events (d hail ⩾ 0.75) because of the larger proportion of sub-severe hailstorms compared to others.Namely, the reduced occurrence of sub-severe hailstorms, which is attributed to mid-low tropospheric warming (Dessens et al 2015, Brimelow et al 2017), explains the overall reduction in eastern US hailstorms.In addition, a larger decreasing tendency of sub-severe hail frequency is observed in the southeastern US, which causes the hail latitude mean (PDF peak) to jump from 36.6 In contrast, opposite signs of severe hail event (1.25 ⩽ d hail < 2) tendencies are evident between the southeastern and northeastern US.Importantly, more frequent severe hailstorm events are observed in the northeastern US, especially in New York, Massachusetts, West Virginia, and Wisconsin, where hailstorms were relatively seldom reported historically (Gensini andAshley 2011, Cintineo et al 2012).This, together with the decreasing tendencies in the southeastern US, pushes the average latitude of severe hails from 36.8 • N to 38.1 • N and the PDF peak from 35.1 • N to 39.6 • N (figure 1(c)).On the other hand, no significant meridional shift is observed for both very large hail events (2 ⩽ d hail < 3) and giant hail events (d hail ⩾ 3) (figure S2).
In other words, among all categories, significant increasing latitudinal tendencies are only observed for large hail events, i.e. the combination of sub-severe and severe hail events.Moreover, the largest tendencies come from July's severe events (+1.19 • N decade −1 ), and August's sub-severe (+1.26 • N decade −1 ) and severe (+1.24 • N decade −1 ) hail events (figure 1(d)).Taking both July and August into account, a net northward shift is observed for large hail events in the eastern US, as indicated by the SPDF of hail activity (figures 1(e) and (f)).The average latitude of large hail events in July and August rises from 37.5 • N to 38.7 • N from 2000-2010 to 2012-2022 at a rate of +1.11 • N decade −1 .The results implies that the increasing latitude tendencies of large hail events in July and August are the main contributor for the northward shift of hail activity in the eastern US.
The above analyses confirmed that the increasing proportion of large hail over the northeastern US in July and August leads to an overall poleward migration of the eastern US hail activity.The next question is: what are the main reasons for the northward shift of the eastern US large hail event in July and August?

Changes in the occurrence probability of hail-favoring synoptic circulation patterns
The spatial distribution of hailstorms may be affected by changes in synoptic activities and the varying atmospheric climatic mean states.  of the above two factors.In this section, we first examine the changes in the occurrence of different weather patterns that favor hail formation and their impacts on the changes in eastern US hail activity.Focus is placed on the large hailfall events in July and August, the key contributors to the northward shift of eastern US hailfall events.
The typical hail-favoring synoptic patterns were identified by applying the K-Means clustering method (Hartigan and Wong 1979) to the 500 hPa geopotential field when large hail events occurred during July-August from 2000-2022.According to the silhouette method (figure S3), five hail-related weather types were obtained from the K-Means algorithm (see supplementary materials for details).The five hail-related weather types are all characterized by a 500 hPa trough over eastern Canada and the eastern US but of slightly different positions and strengths.The slight differences in the mid-level trough are amplified in the lower troposphere and determine the spatial pattern of hail activity by modulating the low-level convergence and moisture distribution (figures 2(a)-(c)).
Specifically, Type 1 has a rather evenly distributed hail distribution; Type 2 hail storms more likely occur in the west part of the northeast, centered over Ohio, Wisconsin, and Illinois; Type 3 features hail activity covering a larger area of the southeastern US; Type 4 favors more hailstorms over the northeast, centered over New York State, Connecticut, and Massachusetts; Type 5 is more concentrated along the East Coast.Overall, the average latitudes of Types 3 (37.7 • N) and 5 (37.6 • N) hail events are the lowest, while the highest average latitudes are observed for Type 1 (38.5 • N) and Type 2 (38.4 • N) (figure 2(a)).
As different weather types favor hail formation over different regions, variation in the occurrence of the five weather types implies a changing spatial pattern of hail activity (Kapsch et al 2012, Li et al 2016) and may have an impact on the average latitude of eastern US hail events.We find that significant negative tendencies are observed in Type 2 since 2000 (−9.00%/decade); in contrast, positive tendencies are found in Type 1 (+4.76%/decade) and Type 3 (+4.75%/decade)(figure 2(d)), while tendencies of Types 4 and 5 are negligible.
The contrasting tendency slightly reduces hailstorms over the central part of northeastern US, mainly over Ohio and West Virginia; meanwhile, hail activity over Mississippi, Tennessee, and Pennsylvania is slightly enhanced.This, however, does not cause a net meridional shift in eastern US hail activity.By considering the effects caused by the relative occurrence fraction change in the five hail-favoring weather types alone (see supplementary materials), the average latitude of the eastern US large hailfall remains

Moistening effect of the northeastern US atmosphere
Further analyses indicate the northward shift of eastern US hail events is primarily due to the decadal change in the atmospheric climatic mean state.We find significant northward shift (ranging from 0.57-1.95• N decade −1 ) of eastern US hail events from 2000-2010 to 2012-2022 for all weather types (figure S4).Negative SPDF tendencies are observed in the southeastern US, generally to the south of 38 • N, while positive SPDF tendencies are found in the northeastern US.The contrasting tendency in the SPDF of hail events agrees with that shown in figure 1(f), which suggests the overall northward shift of the eastern US hail activity is more likely caused by the atmospheric background change rather than the occurrence probability of the hail-favoring weather types.
The environmental conditions that favor hail events include (1) atmospheric moisture that supports storm development and provides water molecules for hail production, (2) atmospheric instability that influences the occurrence and strength of convective storms, and (3) vertical atmospheric temperature profiles that determine the altitudes at which hailstones form, grow, congregate, and eventually melt (Raupach et al 2021, Taszarek et al 2021).Thus, we further analyze the decadal changes in these conditions between the southeastern and northeastern US from 2000-2010 to 2012-2022 and discuss their impacts on the northward shift of the eastern US hail activity.
First, there has been an atmospheric moistening effect in the northeastern US since 2000.The average atmospheric precipitable water (PW) increases from 28.9 mm to 29.1 mm, with its PDF peak jumping from 27.5 mm to 28.1 mm, although the PDF change is statistically insignificant.There is also an apparent increase in the occurrence probability of extreme PW (⩾35 mm), which upon further analysis indicates that more moisture has been provided for thunderstorm formation during extremely wet days in the northeastern US (figure 3(a)).However, such an atmospheric moistening tendency is not observed in the southeastern US, where the PW PDF has no apparent changes in its shape, position, or mean value (figures 3(b) and (c).
The atmospheric moistening in the northeastern US is a combined result of the intensifying Bermuda High and eastward shift of jet stream over the US continent.The Bermuda High was enhanced in recent decades (Hasanean 2004, Li et al 2011).The intensification of Bermuda High and the westward displacement of its western ridge strengthened the warm moist low-level southerly flow and the northward low-level moisture flux over the eastern US, which transported more water vapor from the low latitudes to the north (red vectors in figure 3(c)) (Li et al 2011).In addition, apparent decadal changes in the jet stream are observed.There is an eastward shift of the jet stream entrance in the past two decades.This, by favoring the upper-level divergence over the northeastern US, enhances moisture flux convergence in the lower troposphere over the northeastern US (figure 3(d)) and consequently provides more water for hailstorm formation (Sinclair 1993).
The spatial difference in PW change suggests the decadal atmospheric moisture change favors a greater increase in hail activity in the northeastern US than in the southeastern US.Although the moistening effect over the northeastern US is not statistically significant, the northeastern US is a rather marginal region where the relatively dry atmosphere is a key limiting factor for hailstorm formation (Hurlbut and Cohen 2014, Brimelow et al 2017, Tang et al 2019) (figure 2(b)), which implies that even a slight increase in atmospheric water content could enhance the probability of hail events.

Contrasting tendencies in atmospheric instability over the eastern US
In addition, the atmosphere becomes more unstable (stable) in the northeastern (southeastern) US.The Total Totals Index (TT) (Miller 1967, Peppler and Lamb 1989, Haklander and Van Delden 2003) PDF in the northeast shows a rightward shift with its mean value rising from 41.2 • C to 41.6 • C, indicating an overall increase in the northeastern US atmospheric instability; however, opposite changes are observed in the southeastern US, where the average TT slightly decreases from 43.5 • C to 43.3 • C (figures 4(a), (d) and S5(a)).Similar changes are observed for convective available potential energy (figures not shown).Given the faster lower tropospheric warming in the past decades (figure 4(g)), the dry static instability increases over the whole eastern US as indicated by the enlarging Vertical Totals index (VT) (figure S5(b)).However, the warming atmosphere with a relatively constant water vapor (figures 3(a) and (b)) tends to lower the relative humidity (figure 4(h)) (Murray 1967) (see supplementary materials) and thus reduces the moist static stability in the southeastern US, as indicated by the decreasing Cross Totals index (CT) (figure S5(c)).As a result, the enhanced dry static instability is offset by the CT decrease, resulting in an overall drop in the TT in the southeastern US (figures 4(e) and (f)).On the other hand, because relative humidity is less sensitive to air temperature change in the cooler and drier northeastern US, there is a smaller reduction in relative humidity and relative humidity, and the canceling effect is thus comparatively smaller (figures 4(b) and (c)).In addition, the slight moistening effect in the northeastern US also offsets the decrease in moist static stability caused by the warming atmosphere.Overall, these effects together lead to an increase in atmospheric instability over the northeastern US, favoring the formation of more large-sized hail.

Impacts of tropospheric warming on the hail growth zone (HGZ) and melting level height (MLH)
Apart from the above two factors, changes in the HGZ and MLH also have a role in the northward migration of eastern US hailstorms (Tang et al 2019, Raupach et al 2021).It has been documented that mid-low tropospheric warming tends to increase both the HGZ and MLH (Li et al 2016, Prein and Heymsfield 2020, Raupach et al 2021).Figure S6 show that the overall MLH in the eastern US rises as the lower tropospheric temperature increases.Although the average MLH increase is similar when comparing the northeastern and southeastern US, there is a larger increase in the occurrence probability of extremely large MLH in the southeast; meanwhile, the average MLH increase in the northeast is mainly due to the dropping occurrence of extremely small MLH (figures S6(a) and (c)).This leads to a greater chance that hailstones melt before hitting the ground in the southeast compared to the northeast.
In the meantime, the HGZs of the two regions have no significant differences in the mean value change but the variances do change.The northeastern US HGZ PDF flattens between the two periods, with the variance increasing from 405.6 m 2 to 665.1 m 2 , indicating that extremely large and small HGZs are more frequently observed in 2012-2022.In contrast, the southeastern US HGZ variance decreases from 563.0 m 2 to 439.2 m 2 (figures S6(b) and (d)).As a result, a larger number and a greater size of hailstones can be produced in the northeastern US compared to the southeastern US, if other factors remain unchanged.The above two factors together provide better conditions for hail production in the northeast than in the southeast.Meanwhile, the decadal change in the vertical wind shear does not contribute to the northward shift of eastern US hail activity (figure S7).
Overall, the spatially heterogeneous changes in the atmospheric climatic mean state provide a better moisture and thermodynamic environment for hail formation in the northeastern US than in the southeastern US.In contrast to the insignificant meridional shift of hail activity caused by the varying occurrence of hail-favoring weather types (figures 5(a) and (b)), the changes in the climatic mean state cause a significant net northward shift of eastern US hailstorms.If considering these climatic mean state changes alone (see supplementary materials), a significant increase in the proportion of hail events is observed in Wisconsin, Michigan, Pennsylvania, Maryland, and New York state.Meanwhile, a significant decrease is observed in Florida, Georgia, Alabama, and South Carolina.This results in a net northward shift of eastern US hail activity.The average latitude of large hails rose from 37.4 • N to 38.9 • N from 2000-2010 to 2012-2022 at a rate of +1.28 • N decade −1 (figure 5(c)).The result aligns with the SPDF change in large hailfall events in July and August (figure 1(f)), indicating that the changes in the atmospheric climatic mean state play a major role in the northward shift of eastern US hail risks, and is unlikely a result of anthropogenic signal (see supplementary materials).

Conclusions and discussion
The analyses presented here illustrate a northward shift of the eastern US hail activity since 2000.Although the number of hail reports overall decreases due to the warming atmosphere, there is an apparent rise in the proportion of hailstorms affecting the northeastern US.Based on reanalysis and observational data, our results show that the northward migration of hailstorms mainly comes from the change in the spatial distribution of large hailfall in July and August.By quantifying the impacts caused by the varying occurrence of hail-favoring weather types and the impacts caused by climatic mean state changes, we find that the latter is the key contributor to the northward migration of eastern US hailstorms.This conclusion is in line with previous research showing a contrasting long-term variation in the LHP over the eastern US (Tang et al 2019).
As summarized in figure 5(d), in the past two decades, the intensified Bermuda high and the eastward shift of upper-level jet stream over the central US tended to moisten (dry) the atmosphere over the northeastern (southeastern) US by enhancing the low-level poleward moisture transport and the moisture flux convergence over the northeastern US.This not only provides more moisture for hailstorm formation in the northeast but also destabilizes (stabilizes) the atmosphere in the northeast (southeast) despite an overall increase in dry instability over the eastern US.In addition, more frequent extremely large HGZ occurrences and smaller extremely low MLH occurrence probabilities both provide better conditions for hailstone production in the northeastern US than in the southeastern US.These spatially inhomogeneous changes in the climatic mean state factors together lead to the northward migration of eastern US risks.With only 23 years of data, this study cannot definitively attribute the observed northward shift of eastern US hail events to anthropogenic climate change or internal variability.While other research has revealed that the Bermuda is intensified by anthropogenic warming (Li et al 2011), future research and data refinement are needed to better understand the historical change in hail activity and its potential drivers over longer timescales.
Hail disasters are one of the most destructive types of weather events.This study, based on official hail event records, directly shows an increasing probability that large hail events hit the northeastern US, where hailstorms are less frequently reported.Given the projected stronger Bermuda High in the future climate due to anthropogenic warming (Song et al 2018, Zhou et al 2021), the presented research suggests that the insurance industry may be expected to face more bills for hail-related claims over the northeastern US.Government emergency departments may need to update contingency plans for hail threats, especially in places vulnerable to hail disasters, to ensure a timely, effective, and decisive response to hailstorms and humanitarian aid to those who are affected.
2014, Altman et al 2018, Daloz and Camargo 2018, Murakami et al 2020, Huang et al 2023), which is attributed to the poleward expansion of the tropics and the Hadley circulation (Hu and Fu 2007, Johanson and Fu 2009, Lucas et al 2014, Sharmila and Walsh 2018).Additionally, poleward shifts in the agro-climate zones (King et al 2018, Ceglar et al 2019), precipitation and extratropical weather systems, etc. (Cai and Cowan 2013, Bukovsky et al 2017) are also documented.In particular, extratropical jet streams and storm tracks have been reported shifting to higher latitudes (Yin 2005, Tamarin-Brodsky and Kaspi 2017, Li et al 2019, Balaguru et al 2023), which may modulate the large-scale environmental circulation affecting hail activity (Xie et al 2008, Brooks 2013).
While the former influences the chances of atmospheric circulation patterns triggering the development of hailstorms (Kapsch et al 2012, Li et al 2016), the latter controls the background conditions that favor hail production (Brimelow et al 2017, Tang et al 2019).To understand the causes of the poleward migration of the eastern US large hails, we quantitatively estimate the impacts

Figure 1 .
Figure 1.Spatial distribution of tendencies in occurrence frequency (shading, unit: counts decade −1 , with meshed areas denoting significant tendencies at the 95% confidence level) for hail events with (a) d hail ⩾ 0.75, (b) 0.75 ⩽ d hail < 1.25 (sub-severe events), and (c) 1.25 ⩽ d hail < 2 (severe events).Inset includes the average latitude time series (bottom-right, unit: • N) and the differences (bars) of the PDFs (unit: %) between 2000-2010 (blue curves) and 2012-2022 (red curves) (top-left).The black dashed lines denote the boundary (38 • N) between the northeastern and southeastern US.(d) Average latitude tendencies (unit: • N decade −1 ) of hail events of different categories for each month, with numbers denoting the linear tendency and asterisks indicating the confidence levels (1 asterisk = 90%, 2 asterisks = 95%, and 3 asterisks = 99%).(e) Same as (c) except for hail events with 0.75 ⩽ d hail < 2 (large hails) in July and August only.(f) SPDF tendency (shading, unit: % decade −1 , with meshed areas denoting significant tendencies at the 95% confidence level) for large hail events in July and August.Inset includes the average latitude time series (bottom-right, unit: • N) and the differences of the PDFs (unit: %) between 2000-2010 (blue curve) and 2012-2022 (red curve) (top-left).The PDF differences in all panels are statistically significant at the 99% confidence level.Analysis of the results indicate an increase in the average latitude of eastern US hail activity from 2000-2022, which was mainly contributed by the northward shift of large hailstorms in July and August.

Figure 2 .
Figure 2. (a) SPDF of hail activity (shading, unit: %) and 500 hPa geopotential composite (contour, unit: gpm) of the five weather types identified by the K-Means clustering method.Numbers with (without) bracket on the right-hand corner denote the proportion of occurrence of each cluster (number of hail events being assigned to each cluster).(b) Precipitable water (shading, unit: mm), 850-hPa geopotential (contour, unit: gpm), and 850 hPa wind (vector, unit: m s −1 ) composites of each weather type.(c) Same as (b), except for anomalies of variables relative to the climatological mean over 2000-2022.(d) Time series of occurrence probability (unit: %) of each weather type, with numbers denoting the linear tendency and asterisks indicating the confidence levels (1 asterisk = 90%, 2 asterisks = 95%, and 3 asterisks = 99%).The results show that the changes in the occurrence probability of the five hail-favoring weather types is not the primary reason of the northward shift in eastern US hail activity.

Figure 3 .
Figure 3. PDFs of PW (unit: mm) over the (a) northeastern and (b) southeastern US in 2000-2010 (blue line) and 2012-2022 (orange line).The green curve denotes their differences.The changes in PDFs in (a) and (b) are both statistically insignificant.(c) Changes in 700-1000 hPa average wind field (vector, unit: m s −1 ) and 700-1000 hPa column integrated water vapor (shading, unit: kg m −2 ) and 500 hPa geopotential (contour, unit: gpm) from 2000-2010 to 2012-2022.(d) Same as (c) except for 700-1000 hPa column integrated moisture flux (vector, unit: kg m −1 hPa −1 s −1 ) and moisture flux convergence (shading, unit: 10 −6 kg m −2 hPa −1 s −1 ).The green (yellow) contour denotes the jet stream region, defined by a 200-hPa horizontal wind speed exceeding 25 m s −1 , in 2000-2010 (2012-2022).Red vectors, black and green hatch marks denote significant changes in variables plotted in vectors, contours, and shading, respectively, at the 95% confidence level.The results show that the intensified Bermuda high and eastward shift of jet stream over the central US together bring more water vapor source to the northeastern US, favoring hailstorm formation there.

Figure 4 .
Figure 4. PDFs of (a) TT (unit: • C), (b) VT (unit: • C), (c) and CT (unit: • C) over the northeastern US in 2000-2010 (blue line) and 2012-2022 (orange line).The green curves denote their differences.(d)-(f) same as (a)-(c), except over the southeastern US.The changes in PDFs in (a), (b) and (d)-(f) are statistically significant at the 95% confidence level.(g) Changes in air temperature at 850 hPa (shading, unit: • C) and 500 hPa (contour, unit: • C) from 2000-2010 to 2012-2022.(h) Same as (g) except for 850 hPa dew temperature (shading, unit: • C) and 850 hPa relative humidity (contour, unit: %).Black and green hatch marks denote significant changes in variables plotted in contours and shading, respectively, at the 95% confidence level.Analysis of the results show the vertical tropospheric warming gradient and the northeastern moistening effect together enhance the atmospheric instability over the northeastern US but not over the southeastern US.

Figure 5 .
Figure 5. (a) Scatter plot visualizing the relationship among the occurrence probability tendency (x-axis, unit: % decade −1 ), hail event latitude tendency (y-axis, unit: • N decade −1 ), average occurrence probability (dot size, unit: %), and average hail event latitude (dot color, unit: • N) of each weather type from 2000-2022.(b) SPDF tendency (shading, unit: % decade −1 , with meshed areas denoting significant tendencies at the 95% confidence level) of July and August sub-severe and severe hail events by considering the impacts of varying occurrence of hail-favoring weather types only.Inset includes the average latitude time series (bottom-right, unit: • N) and the differences (bars) of the PDFs (curves, unit: %) between 2000-2010 and 2012-2022 (top-left).(c) Same as (b), except by considering the impacts of climatic mean state change only.The PDF differences in (c) are statistically significant at the 99% confidence level.(d) Schematic diagram summarizing the mechanism of the northward migration of the eastern US hail activity.The intensified Bermuda High (black contour) and eastward shift of jet stream (red arrow at the top layer) over the central US enhance low-level poleward moisture transportation (blue horizontal arrows) and moisture flux convergence in the northeastern US (blue vertical arrows).This, on the one hand, moistens and destabilizes the atmosphere over the northeastern US; on the other hand, it dries and stabilizes the atmosphere over the southeastern US (shadings of the middle two layers indicate, from bottom to top, the low-level specific humidity and TT).These changes in the climatic state finally lead to the poleward shift of hail activity in the eastern US (shading of the bottom layer).