Exploring Spatial Patterns of Virginia Tornadoes Using Kernel Density and Space-Time Cube Analysis (1960–2019)

Round 1

Reviewer 1 Report

Review of "Exploring Spatial Patterns of Virginia Tornadoes using Kernel Density and Space-Time Cube analysis (1951-2018)"

Recommendation: Minor revision

The authors examined the spatial patterns of tornadoes in Virginia and trends  of tornadoes. Since those are important informations, the paper will be acceptable after minor revisions.

1. Why the authors focused on Virginia in the US ? Please clarify what are special features in this region and are different from other regions in the US.
2. The authors discussed that upward frequency trends of tornadoes in Virginia are due to the passing of larger number of tropical cyclones. However, the increase of tornado reports are largely influenced by inhomogeneities in time and space in procedures for collecting tornado reports that may lead to large non-meteorological impacts in the record (Brooks 2013).

Author Response

Response to Reviewer Evaluations

Allen et al.  Exploring Spatial Patterns of Virginia Tornadoes using Kernel Density and Space-Time Cube Analysis (1960 – 2019).  To facilitate review, author responses are in bold. 

Reviewer 1

Recommendation: Minor revision

The authors examined the spatial patterns of tornadoes in Virginia and trends of tornadoes. Since those are important informations, the paper will be acceptable after minor revisions.

1. Why the authors focused on Virginia in the US ? Please clarify what are special features in this region and are different from other regions in the US.

 

Leonard and Law (2019) note “….a subregional-scale spatial analysis is more appropriate for analyzing trends in tornado variability”.  This analysis builds necessary understanding within the Commonwealth of Virginia as to tornado risk and frequency.  Presently, there is no such analysis for Virginia though regional and nearby states (West Virginia., Leonard and Law 2019) exist.  We also added additional context, highlighting other regional analyses as recommended by another Reviewer. 

 

 

2. The authors discussed that upward frequency trends of tornadoes in Virginia are due to the passing of larger number of tropical cyclones. However, the increase of tornado reports are largely influenced by inhomogeneities in time and space in procedures for collecting tornado reports that may lead to large non-meteorological impacts in the record (Brooks 2013).

 

While we note possible mechanisms than influence tornado climatology, this manuscript does not intend to explain why the changes have occurred.  We have added the reference to further support the various factors that contribute to the observed changes and outline the documented database deficiencies: 

• Brooks, H. E. (2013). Severe thunderstorms and climate change. Atmospheric Research, 123, 129-138.
• Verbout, S. M., Brooks, H. E., Leslie, L. M. & Schultz, D. M. Evolution of the US tornado database: 1954–2003. Weather Forecast.21, 86–93 (2006).

Reviewer 2 Report

See attached.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer Evaluations

Allen et al.  Exploring Spatial Patterns of Virginia Tornadoes using Kernel Density and Space-Time Cube Analysis (1960 – 2019).  To facilitate review, author responses are in bold. 

Reviewer 2

Summary: This is a potentially valuable study, but there is one major limitation that I believe must be addressed prior to publication. Briefly, the potential effect of reporting bias has not been seriously considered in the analysis, making some of the major conclusions of the study (especially the purported increasing frequency of Virginia tornadoes) tenuous. I also noted a lot of redundancy throughout the manuscript that impedes the reader; I’ve noted the most egregious instances below but recommend that the authors try to eliminate all redundancies in the revision.

The authors have reviewed the manuscript for redundancies. 

Recommendation: Accept pending Major

Major Comments While the spatial patterns and trends found in VA tornado frequency are intriguing, especially given the plausible atmospheric and topographical explanations provided by the authors, it is unclear what effects reporting bias may be having. The authors acknowledge this concern (e.g., lines 180-183) but do not address it in their analysis, aside from including tornado days (which are less sensitive than tornado counts to reporting bias) in Fig. 3. Given the typical magnitude of this effect within the U.S. (e.g., Elsner et al. 2013; Potvin et al. 2019), and the fact that at least a moderate correlation can be subjectively diagnosed between population density and tornado frequency/trend in the present study (Figs. 1b, 6, 7a), I believe the authors should present at least a simple analysis of this reporting bias within their study domain. For example, a plot of mean tornado counts versus population density as in Fig. 3a of Potvin et al. (2019) and a comparison of the trends in tornado occurrence and population density would be very helpful in assessing how much of the analyzed spatial and temporal gradients are spurious versus meteorological. If the authors choose not to perform this additional analysis, the most important conclusions of the paper – that tornado activity is higher in eastern VA and is increasing with time – will need to be heavily qualified/weakened.

We present the distribution pattern of tornadoes in multiple ways, individual decadal plots and summative mapping via kernel density mapping.  The summative pattern is not suggestive of a direct correlation between population density and tornado abundance. If this were the case, we would expect to find more tornado observations occurring in areas of moderate to relatively dense Coastal Plain and Piedmont locations (e.g., the Interstate 95 corridor between Richmond and northern Virginia and, especially, the interior Peninsula of Hampton Roads, between Hampton/Newport News and Williamsburg). Rather, these areas indicate lower than surrounding tornadic activity.  Furthermore, an area of relatively low population in the interior coastal plain has nonetheless a relatively high reported tornado activity (south of Richmond and Petersburg focusing on Dinwiddie, Prince George and Sussex Counties.)  If human population density is the overarching driver of tornado reports, then we would not expect to see an associated cluster of tornadoes in this location.  Rather, outside of a few of the isolated wilderness areas of the George Washington and Jefferson National Forests (themselves topographically rugged and unfavorable to tornadogenesis), the human population and settlement pattern of Virginia retains a moderate density which is supportive of observation and reporting.

Nonetheless, the authors concur that a more statistically controlled and nuanced approach to controlling for observational bias could corroborate our inferences.  We have also added the following references as recommended:

• Elsner, J. B., L. E. Michaels, K. N. Scheitlin, and I. J. Elsner, 2013: The decreasing population bias in tornado reports. Wea. Climate Soc., 5, 221–232, doi:https://doi.org/10.1175/WCAS-D12-00040.1.
• Potvin, C. K., C. Broyles, P. S. Skinner, H. E. Brooks, and E. Rasmussen, 2019: A Bayesian hierarchical modeling framework for correcting reporting bias in the U.S. tornado database. Wea. Forecasting, 34, 15–30, https://doi.org/10.1175/WAF-D-18-0137.1
• Verbout, S. M., Brooks, H. E., Leslie, L. M. & Schultz, D. M. Evolution of the US tornado database: 1954–2003. Weather Forecast.21, 86–93 (2006).
• Gensini, V.A. and H.E. Brooks. 2018. Spatial trends in United States tornado frequency. npj Climate and Atmospheric Science 1 (38). https://doi.org/10.1038/ s41612-018-0048-2.
• Moore, T. W. Annual and seasonal tornado trends in the contiguous United States and its regions.  J. Climatol.38, 1582–1594 (2018).

 

Minor Comments

Lines 39-40: Need a ref(s) showing how large-scale topography and its effect on mesoscale vorticity can increase tornadogenesis frequency.

Topographical influence on the formation of vertical instability is well documented within the meteorological literature.  Near-surface vorticity can be modified on the leeward mountain side.  We have added the following references: 

• Elsner, J. B., Fricker, T., Widen, H. M., Castillo, C. M., Humphreys, J., Jung, J., ... & Dixon, P. G. (2016). The relationship between elevation roughness and tornado activity: A spatial statistical model fit to data from the central Great Plains. Journal of Applied Meteorology and Climatology, 55(4), 849-859.
• Holden, J., & Wright, A. (2004). UK tornado climatology and the development of simple prediction tools. Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, applied meteorology and physical oceanography, 130(598), 1009-1021.

Line 111 and elsewhere: More accurate to say “begin and end points”, since many tornadoes do not develop “top-down” or decay “bottom-up” (e.g., French et al. 2013).

We have modified the text accordingly. 

Lines 128-136: This section is redundant and should be considerably shortened.

This comment refers to the latter portion of Section 2.2:  Tornado track mapping.  We have modified some of the text, but maintain the text is necessary to explain the methodological approaches used in the study. 

Lines 145-156: The authors should add figures illustrating this analysis or remove this portion of the paper.

The methodological approach outlined provides necessary detail to the study.  We believe the cross-validation of the single tornado track is worth highlighting. 

Lines 153-154: Need a ref(s) showing that stronger tornadoes tend to have longer tracks.

We have removed this portion of the sentence for clarity. 

Line 165: What type of kernel was used (e.g., Gaussian)?

“After iterative computation with KDE bandwidths between 1km to 10km, we ultimately implemented a 4km bandwidth very close to the default 1/30^th ratio of the maximum divided by the minimal length-width ratio of the study area (Commonwealth of Virginia) and similarly implemented by Cai et al. (2013)”.

Section 2.4: Unless readers are expected to already be familiar with space-time cubes, please briefly describe this analysis method. Also, what is the motivation for binning into hexagons rather than squares?

Square or rectangular tesselations also tend to break-up or distort curvilinear patterns owing to acute angles. There is also an inherent benefit to using hexagons to reduce spatial sampling bias of phenomena, since they have a low perimeter-area ratio. Since our study included the relatively large area of Virginia (east-west ~690km), hexagons would also show less distortion owing to the curvature of the earth as compared to a fishnet or grid tessellation.  Per Birch et al. 2007, hexagonal tessellation provides for an equidistant measurement between centroids versus square or rectangular tessellations, which also tend to break-up or distort curvilinear patterns owing to acute angles. There is also an inherent benefit to using hexagons to reduce spatial sampling bias of phenomena, since they have a low perimeter-area ratio. Since our study included the relatively large area of Virginia (east-west ~690km), hexagons would also show less distortion owing to the curvature of the earth as compared to a fishnet or grid tessellation. 

We have added the reference to the text:

• Birch, C. P., Oom, S. P., & Beecham, J. A. (2007). Rectangular and hexagonal grids used for observation, experiment and simulation in ecology. Ecological modelling, 206(3-4), 347-359.

Lines 191-204: This section is redundant and should be considerably shortened.

We have modified this section. 

Lines 269-271: Is this sentence redundant with the previous one?

We have modified this section. 

Lines 282-284: How was statistical significance of the trends computed?

Our implementation of space-time cube trend analysis includes a test for a monotonic trend in tornado frequency in selected hexbin tessellation (Birch et al. 2007; ESRI 2021). For each bin in the cube, a time-incremented count is tallied, accumulating a score value for each step increase or decrease. A z-score and p-value are used to determine significance of the test (null hypothesis is there exists no monotonic trend.) Although the Mann-Kendall test is often computed as a non-parametric test, a z-score (positive indicating increasing trend; negative indicating decrease) can be computed from the ranked correlations, number of ties, number of time periods and an expected sum (zero) to gauge statistical significance.  

Future alternative approaches could explore space-time semi-variograms to assess these dependences. However, the simplified use of a Mann-Kendall trend test (often used in low sample populations and non-parametric approaches) provides a first-order estimate of predominate trends across space and time in the bins.

ESRI presents a detailed summary of how spatial statistics are calculated using space-time cubes.  We have added the reference, accordingly: 

ESRI. How Create Space Time Cube by Aggregating Points works. Available online: https: //desktop.arcgis.com/en/arcmap/latest/tools/space-time-pattern-mining-toolbox/learnmorecreatecube. htm#ESRI_SECTION1_F1EA94A3BA8940E0B56AB08A302D1C08 (accessed on 18 April 2021)

Table 1: Double-check the widest tornado width; 6858 m would be wider than the world-record 31 May 2013 El Reno, OK, tornado.

Thank you for noting this computing error.  We have modified the Table and verified other statistics. 

Fig. 2: I recommend labeling each panel with the respective decade so that the reader needn’t keep referencing the caption.

We have modified Figure 2 accordingly. 

Reviewer 3 Report

Exploring Spatial Patterns of Virginia Tornados using Kernel Density and Space-Time Cube Analysis (1951—2018)

Allen et al.

The authors present a spatial climatology of Virginia tornadoes over the period 1951–2018. Using a suite of geographic methods and techniques, they find that the majority of Virginia tornadoes occurred in the eastern portion of the state—along the Piedmont and Coastal Plain—that tornadoes and tornado days have increased in the state, and that most tornadoes occurred during the warm season and in the afternoon and early evening hours.

I believe that the authors are presenting a valuable, targeted study. State-level tornado climatologies are not a new undertaking, but they have taken a back seat to national- or regional-level climatologies in the recent decades. That said, there are several issues I have with the introduction—-or literature review—section of the study, as well as results section that I feel need to be addressed before the manuscript is suitable for publication.

Major Concerns:

(1) Literature review. I believe that the authors have done a nice job in describing and writing out the general understanding of tornadoes and climate in the Introduction, but are missing several spatial climatologies that weaken the grounding of this paper.

Firstly, as a manuscript that is providing a spatial climatology of tornadoes, the absence of a Grazulis (1990), Brooks et al. (2003 WAF), and more recently Elsner et al. (2016 PLOS) is alarming. These works need to be woven into the introduction to provide a more complete overview of our spatial understanding of tornado behavior.

Secondly, the lack of a paragraph highlighting other state-level climatologies is surprising. The authors have several state-level studies cited in the manuscript (Davis et al. 1997, Leonard and Law, 2019), but fail to frame this research along those lines. I suggest a paragraph devoted to state-level climatologies that can make use of work such as: Grazulis (1990), Pryor and Kurzhal (1997 Phys. Geo), Nese and Forbes (1998 JSTOR), Bounds and Soule (1986 Southeastern Geo), etc.

Lastly, I think adding a sentence or two on the potential impacts of tornadoes (casualties and property loss) would help support the aim of enhancing severe weather and climate hazard awareness. Studies like Ashley (2007 WAF), Fricker et al. (2017 Geom. Nat. Haz. and Risk), and Fricker and Elsner (2019 Annals) might help here. The Fricker and Elsner paper identifies several tornadoes in the southeastern portion of Virginia that caused more casualties than we might otherwise expect, getting after the question of vulnerability in the area.

(2) Figure 2 . I am curious as to why Figure 2 is added in the data and methods section of the manuscript. It seems to me that the mapping of tornado tracks would be a result of this work, rather than a method. If it is meant to show the data used, here, then why separate the tracks into decadal subplots?

(3) Results. Again, I believe the authors have done a nice job in thinking through the results section of this manuscript. That said, there are two main issues I have with the written results that I feel need to be addressed.

First, the authors mention an increase in the number of tornadoes and number of tornado days in the state when comparing earlier and more recent time periods. However, they only provide a summary statistic (average) of the two time periods. Why not provide a simple regression across the entire time period? This would get after the question of changing tornado risk in the same way the summary statistic does and provide more robust evidence of changing tornado behavior in the state. Beyond this, the authors also state that the changes in tornado counts and tornado days might be caused by tropical cyclone activity but do not evaluate whether or not that is the precise reason (stating it is beyond the scope of the present research). To me, this is not good enough. There are datasets containing tropical cyclone tornadoes that would easily answer whether or not the shift in the number of tornadoes and tornado days can be attributed to tropical cyclone activity. Todd Moore and Roger Edwards are two excellent contacts for this information.

Second, the authors write out that Virginia has a minor “Tornado Alley” (seen in Figure 7b). Not only is the establishment of this problematic from a public perception of risk standpoint, but it fails to account for the scientific description of “Tornado Alley” as written in Brooks et al. (2003). My guess is that the authors are using the term “Tornado Alley” to describe an area with the highest number of tornadoes without accounting for the seasonality component attached to “Tornado Alley” in the scientific community. While this may seem a small difference, I do think it warrants consideration for the removal of the term. I see no benefit from telling the people of Virginia they are part of a mini “Tornado Alley” when many of those storms are likely driven by tropical cyclones and the annual rate of tornadoes in the entire state is ~11 tornadoes.

Minor Concerns:

(1) Time Period: Why are tornadoes from 1950 not included in this study? The historical tornado record begins in 1950 and there are no scientific reasons I can think of for excluding 1950 data while including 1951 data.

(2) Figure 4 and Figure 5: Can the 3D-effect of this bars be removed from the figures? In addition, I recommend thinking about the diurnal cycle (Figure 5) as a circular barplot rather than a linear one.

(3) Table 1: Can Table 1 be updated to show only the top 5 in each of these categories? As is, I do not think this table helps any stakeholders make sense of tornado behavior in the state. For example, half of the deadly tornado days only have 1 death associated with them. Is this information really needed here?

Author Response

Response to Reviewer Evaluations

Allen et al.  Exploring Spatial Patterns of Virginia Tornadoes using Kernel Density and Space-Time Cube Analysis (1960 – 2019).  To facilitate review, author responses are in bold. 

Reviewer 3

The authors present a spatial climatology of Virginia tornadoes over the period 1951–2018. Using a suite of geographic methods and techniques, they find that the majority of Virginia tornadoes occurred in the eastern portion of the state—along the Piedmont and Coastal Plain—that tornadoes and tornado days have increased in the state, and that most tornadoes occurred during the warm season and in the afternoon and early evening hours.

I believe that the authors are presenting a valuable, targeted study. State-level tornado climatologies are not a new undertaking, but they have taken a back seat to national- or regional-level climatologies in the recent decades. That said, there are several issues I have with the introduction—-or literature review—section of the study, as well as results section that I feel need to be addressed before the manuscript is suitable for publication.

Major Concerns:

(1) Literature review. I believe that the authors have done a nice job in describing and writing out the general understanding of tornadoes and climate in the Introduction, but are missing several spatial climatologies that weaken the grounding of this paper.  Firstly, as a manuscript that is providing a spatial climatology of tornadoes, the absence of a Grazulis (1990), Brooks et al. (2003 WAF), and more recently Elsner et al. (2016 PLOS) is alarming. These works need to be woven into the introduction to provide a more complete overview of our spatial understanding of tornado behavior.

We have modified the introduction and added additional references to the manuscript: 

• Elsner, J. B., Jagger, T. H., & Fricker, T. (2016). Statistical models for tornado climatology: Long and short-term views. PloS one, 11(11), e0166895.

Secondly, the lack of a paragraph highlighting other state-level climatologies is surprising. The authors have several state-level studies cited in the manuscript (Davis et al. 1997, Leonard and Law, 2019), but fail to frame this research along those lines. I suggest a paragraph devoted to state-level climatologies that can make use of work such as: Grazulis (1990), Pryor and Kurzhal (1997 Phys. Geo), Nese and Forbes (1998 JSTOR), Bounds and Soule (1986 Southeastern Geo), etc.

We frame the paper with two recent and nearby state climatologies:  Leonard and Law (WV) and Montz et al. (North Carolina).  We have added context to include other state-level tornado references: 

• Gaffin, D.M. and S.S. Parker. 2006. A climatology of synoptic conditions associated with significant tornadoes across the Southern Appalachian Region. Wea. Forecasting 21: 735–751.
• Daoust, Mario. 2003. An analysis of tornado days in Missouri for the period 1950–2002. Physical Geography 24 (6): 467–487. https://doi.org/10.2747/0272- 3646.24.6.467.

Lastly, I think adding a sentence or two on the potential impacts of tornadoes (casualties and property loss) would help support the aim of enhancing severe weather and climate hazard awareness. Studies like Ashley (2007 WAF), Fricker et al. (2017 Geom. Nat. Haz. and Risk), and Fricker and Elsner (2019 Annals) might help here. The Fricker and Elsner paper identifies several tornadoes in the southeastern portion of Virginia that caused more casualties than we might otherwise expect, getting after the question of vulnerability in the area.

Thank you for the suggestions.  We have added a few sentences on associated impacts, drawing attention to Fricker and Elsner (2020).  An important caveat to note is the dataset clusters economic impacts into rather large groups earliy in the time period.  For example, the coding groups damages between $5,000 and $50,000 into a single group.  Thus, we avoided being over detailed with impacts framing within the manuscript and focused on the diurnal and season patterns of tornadoes.  The manuscript Table highlights the tornadoes contributing to death.  We have added the following references, per this recommendation: 

• Ashley, W. S. (2007). Spatial and temporal analysis of tornado fatalities in the United States: 1880–2005. Weather and Forecasting, 22(6), 1214-1228.
• Fricker, T., Elsner, J. B., Mesev, V., & Jagger, T. H. (2017). A dasymetric method to spatially apportion tornado casualty counts. Geomatics, Natural Hazards and Risk, 8(2), 1768-1782.
• Fricker, T., & Elsner, J. B. (2020). Unusually devastating tornadoes in the United States: 1995–2016. Annals of the American Association of Geographers, 110(3), 724-738.

(2) Figure 2 . I am curious as to why Figure 2 is added in the data and methods section of the manuscript. It seems to me that the mapping of tornado tracks would be a result of this work, rather than a method. If it is meant to show the data used, here, then why separate the tracks into decadal subplots?

We have modified Figure 2’s placement. 

(3) Results. Again, I believe the authors have done a nice job in thinking through the results section of this manuscript. That said, there are two main issues I have with the written results that I feel need to be addressed.  First, the authors mention an increase in the number of tornadoes and number of tornado days in the state when comparing earlier and more recent time periods. However, they only provide a summary statistic (average) of the two time periods. Why not provide a simple regression across the entire time period? This would get after the question of changing tornado risk in the same way the summary statistic does and provide more robust evidence of changing tornado behavior in the state.

We have modified the manuscript accordingly.  We also modified the study period to represent a more traditional climatological, 30-year period.  While evidence may suggest changing tornado behavior, the confounding factors that contribute to increases (or decreases) in tornado frequency are well documented.

Figure 3 provides a visual representation of how tornadoes and tornado days have changed.  The 30-year climatology provides a climatological comparison.  We added a trendline to Figure 3 to assist in this recommendation. 

Beyond this, the authors also state that the changes in tornado counts and tornado days might be caused by tropical cyclone activity but do not evaluate whether or not that is the precise reason (stating it is beyond the scope of the present research). To me, this is not good enough. There are datasets containing tropical cyclone tornadoes that would easily answer whether or not the shift in the number of tornadoes and tornado days can be attributed to tropical cyclone activity. Todd Moore and Roger Edwards are two excellent contacts for this information.

The authors believe the casual mechanisms are beyond the scope of this study.  We modified the phrasing of the outlined sentences to provide additional context and clarity.  

Second, the authors write out that Virginia has a minor “Tornado Alley” (seen in Figure 7b). Not only is the establishment of this problematic from a public perception of risk standpoint, but it fails to account for the scientific description of “Tornado Alley” as written in Brooks et al. (2003). My guess is that the authors are using the term “Tornado Alley” to describe an area with the highest number of tornadoes without accounting for the seasonality component attached to “Tornado Alley” in the scientific community. While this may seem a small difference, I do think it warrants consideration for the removal of the term. I see no benefit from telling the people of Virginia they are part of a mini “Tornado Alley” when many of those storms are likely driven by tropical cyclones and the annual rate of tornadoes in the entire state is ~11 tornadoes.

In the revised manuscript, we still draw attention to this area of higher tornado frequency but agree with this suggestion.  We have removed the problematic term.  

Minor Concerns:

• Time Period: Why are tornadoes from 1950 not included in this study? The historical tornado record begins in 1950 and there are no scientific reasons I can think of for excluding 1950 data while including 1951 data.

To the initial comment, 1950 is not included in the initial analysis because no tornadoes were reported in Virginia.  Following Reviewer comments, we have modified the study period to reflect a more traditional climatology period (1960 – 2019).  The two 30-year periods allow for more direct long-term comparison and address the data quality concerns highlighted by other Reviewers (Agee and Childs, 2014).  2019 was not originally included but has since become available through the Storm Prediction Center dataset.  While we are more than willing to expand the dataset to encompass 1950 – 2019, the statistical trends and spatial patterns remain near the same.

• Figure 4 and Figure 5: Can the 3D-effect of this bars be removed from the figures? In addition, I recommend thinking about the diurnal cycle (Figure 5) as a circular barplot rather than a linear one.

We removed the 3D-effect.  The diurnal cycle plots mirror National Weather Service graphics: 

https://www.weather.gov/lot/tornadoclimatology

(3) Table 1: Can Table 1 be updated to show only the top 5 in each of these categories? As is, I do not think this table helps any stakeholders make sense of tornado behavior in the state. For example, half of the deadly tornado days only have 1 death associated with them. Is this information really needed here?

We highlighted all tornado-related deaths in the Commonwealth of Virginia.  We feel it is important to highlight any tornado that contributed to a death.  We have modified the table. 

Reviewer 4 Report

 Referee report on - Exploring Spatial Patterns of Virginia Tornadoes using Kernel Density and Space-Time Cube Analysis (1951 – 2018)

The work analyzes spatial patterns and trends in the occurrence of tornadoes in Virginia using methods derived from Kernel Density estimators and a tool derived from this method (Space-Time Cube Analysis). In general, I believe that the work has a relevant contribution to the spatial analysis of the occurrence of tornadoes, introducing a class of statistical methods for the spatio-temporal analysis of these events. I believe the methods used are correct, the results are consistent (noting the limitation placed in comment 1 below), and the presentation of the article is clear and allows a reproduction of the results for potential interested researchers. So, my recommendation is to publish the article after including a discussion on the two important questions I ask below.

Specific Points

1 - A relevant question is about changes in tornado detection/annotation methods. As discussed in Agee and Childs (2014) there is an undercount of tornadoes in years of 1951-1953 problem. Another relevant point is that part of the increases in the number of tornadoes, especially EF0 rating tornadoes, can be attributed to non-climatic factors. As discussed in Valente and Laurini (2020) in their analysis of the occurrence of tornadoes in the USA using the same database: 

“Considering (E)F0 tornadoes, it is possible to observe a growth pattern in the trend component between 1962 and 2000, whereas between 2000 and 2016 it remains stable. From 2016 can be seen a growth pattern again. This result is consistent to results commonly found in the literature and, as discussed by Moore (2017), part of this effect can also be attributed to non-meteorological factors such as changes in reporting practices, reporting procedures, and observing technology. As argued by Brooks and Doswell III (2001), information about tornadoes comes from untrained witnesses, which may have led to basic errors in reporting practice. Weaker tornadoes are likely to be missed in the reporting since they have short lifetimes and path lengths, while stronger tornadoes may be more reliably reported (Brooks and Doswell III 2001; Kunkel et al. 2013; Verbout et al. 2006). An additional component of the increase trend in the F0 tornadoes is likely due to the policy change in 1982 which have established that all tornadoes that did not have rated damage must be classified as (E)F0 (Brooks 2004). “
Authors should discuss the results obtained based on the limitations noted above.

2 - Methods based on kernel density estimators are very sensitive to the amount of data available (the curse of dimensionality) and to the methods of bandwidth selection. The authors use an ad hoc choice for the bandwidth used, but they should comment on the robustness of the results to this choice, and also the problems of using KDE for higher rating tornadoes, which have a very small number of occurrences. 

References

Agee, Ernest, and Samuel Childs. 2014. Adjustments in tornado counts, f-scale intensity, and path width for assessing significant tornado destruction. Journal of Applied Meteorology and Climatology 53: 1494–1505
Brooks, Harold E. 2004. On the relationship of tornado path length and width to intensity. Weather and Forecasting 19: 310–19. 
Brooks, Harold, and Charles A. Doswell III. 2001. Some aspects of the international climatology of tornadoes by damage classification. Atmospheric Research 56: 191–201.
Kunkel, Kenneth E., Thomas R. Karl, Harold Brooks, James Kossin, Jay H. Lawrimore, Derek Arndt, Lance Bosart, David Changnon, Susan L. Cutter, Nolan Doesken, and et al. 2013. Monitoring and understanding trends in extreme storms: State of knowledge. Bulletin of the American Meteorological Society 94: 499–514.
Moore, Todd W. 2017. On the temporal and spatial characteristics of tornado days in the United States. Atmospheric Research 184: 56–65.
Valente, F.; Laurini, M. Tornado Occurrences in the United States: A Spatio-Temporal Point Process Approach. Econometrics 2020, 8, 25. https://doi.org/10.3390/econometrics8020025
Verbout, Stephanie M., Harold E. Brooks, Lance M. Leslie, and David M. Schultz. 2006. Evolution of the us tornado database: 1954–2003. Weather and Forecasting 21: 86–93.

Author Response

Reviewer 4

Referee report on - Exploring Spatial Patterns of Virginia Tornadoes using Kernel Density and Space-Time Cube Analysis (1951 – 2018)

The work analyzes spatial patterns and trends in the occurrence of tornadoes in Virginia using methods derived from Kernel Density estimators and a tool derived from this method (Space-Time Cube Analysis). In general, I believe that the work has a relevant contribution to the spatial analysis of the occurrence of tornadoes, introducing a class of statistical methods for the spatio-temporal analysis of these events. I believe the methods used are correct, the results are consistent (noting the limitation placed in comment 1 below), and the presentation of the article is clear and allows a reproduction of the results for potential interested researchers. So, my recommendation is to publish the article after including a discussion on the two important questions I ask below.

Specific Points

1 - A relevant question is about changes in tornado detection/annotation methods. As discussed in Agee and Childs (2014) there is an undercount of tornadoes in years of 1951-1953 problem. Another relevant point is that part of the increases in the number of tornadoes, especially EF0 rating tornadoes, can be attributed to non-climatic factors. As discussed in Valente and Laurini (2020) in their analysis of the occurrence of tornadoes in the USA using the same database:

“Considering (E)F0 tornadoes, it is possible to observe a growth pattern in the trend component between 1962 and 2000, whereas between 2000 and 2016 it remains stable. From 2016 can be seen a growth pattern again. This result is consistent to results commonly found in the literature and, as discussed by Moore (2017), part of this effect can also be attributed to non-meteorological factors such as changes in reporting practices, reporting procedures, and observing technology. As argued by Brooks and Doswell III (2001), information about tornadoes comes from untrained witnesses, which may have led to basic errors in reporting practice. Weaker tornadoes are likely to be missed in the reporting since they have short lifetimes and path lengths, while stronger tornadoes may be more reliably reported (Brooks and Doswell III 2001; Kunkel et al. 2013; Verbout et al. 2006). An additional component of the increase trend in the F0 tornadoes is likely due to the policy change in 1982 which have established that all tornadoes that did not have rated damage must be classified as (E)F0 (Brooks 2004). “
Authors should discuss the results obtained based on the limitations noted above.

 

Thank you to the reviewer for the thoughtful comment.  We recognize the data limitations associated with the early period and have included additional context on this matter as recommended.  Our hope this additional context provides adequate justification. 

On the larger issue, the authors modified the study time period to be more reflective of traditional, 30-year climatology period.  This allows for more direct comparison between early (1960 – 1989) and late (1990 – 2019) time periods while also addressing the larger issue raised above.   

• Agee, E., & Childs, S. (2014). Adjustments in tornado counts, F-scale intensity, and path width for assessing significant tornado destruction. Journal of Applied Meteorology and Climatology, 53(6), 1494-1505.
• Valente, F., & Laurini, M. (2020). Tornado Occurrences in the United States: A Spatio-Temporal Point Process Approach. Econometrics, 8(2), 25.
• Moore, T. W. (2017). On the temporal and spatial characteristics of tornado days in the United States. Atmospheric Research, 184, 56-65.
• Brooks, H., & Doswell III, C. A. (2001). Some aspects of the international climatology of
• Verbout, Stephanie M., Harold E. Brooks, Lance M. Leslie, and David M. Schultz. 2006. Evolution of the us tornado database: 1954–2003. Weather and Forecasting 21: 86–93.

2 - Methods based on kernel density estimators are very sensitive to the amount of data available (the curse of dimensionality) and to the methods of bandwidth selection. The authors use an ad hoc choice for the bandwidth used, but they should comment on the robustness of the results to this choice, and also the problems of using KDE for higher rating tornadoes, which have a very small number of occurrences.

After iterative computation with KDE bandwidths between 1km to 10km, we ultimately implemented a 4km bandwidth very close to the default 1/30^th ratio of the maximum divided by the minimal length-width ratio of the study area (Commonwealth of Virginia) and similarly implemented by Cai et al. (2013). This selection of bandwidth provided for visual discrimination within counties and along potential patterning to capture topographic influences, such as the Blue Ridge Mountains, Ridge and Valley Province, and the Fall Zone. A coarser bandwidth may overly smooth the density of tornado patterns along these features, while a finer scale visually obscured subregional trend.

Round 2

Reviewer 2 Report

Thanks to the authors for addressing my comments.

Author Response

No comments

Reviewer 3 Report

The authors have provided a much improved version of their previous manuscript. They have acknowledged and responded to each of my concerns and while there are a few aspects of the manuscript (tropical cyclone tornadoes, etc.) I feel could be further evaluated, I am happy with the overall result.

Author Response

The comment is by no means a definitive cause factor except to say there could be a prevalence of tornadoes in the east related to these storms; they may reflect a different track and orientation as compared to frontal or other synoptic tornadogenesis.  Detailing their role would require further analysis that go beyond the scope of the manuscript. We do note future research may explore such issues.