Relationships Between Daily Teleconnection Indices and Oklahoma Tornado Activity

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8-6-2021

Relationships between daily teleconnection indices and Oklahoma tornado activity

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Relationships between daily teleconnection indices and Oklahoma tornado activity

By TITLE PAGE Sean Gabriel Douglas

Approved by:

Christopher M. Fuhrmann (Major Professor) Michael E. Brown Andrew E. Mercer (Committee Member/Graduate Coordinator) Rick Travis (Dean, College of Arts & Sciences)

A Thesis Submitted to the Faculty of Mississippi State University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Geosciences with concentration in Applied Meteorology in the Department of Geosciences

Mississippi State, Mississippi

August 2021

2021

Name: Sean Gabriel Douglas ABSTRACT Date of Degree: August 6, 2021

Institution: Mississippi State University

Major Field: Geosciences with concentration in Applied Meteorology

Major Professor: Christopher M. Fuhrmann

Title of Study: Relationships between daily teleconnection indices and Oklahoma tornado activity

Pages in Study: 61

Candidate for Degree of Master of Science

The phasing of various teleconnection patterns has been linked to variability of tornado activity in various geographic regions. These links have been used to improve long-term tornado forecast models. Oklahoma has been long-considered the center of Tornado Alley, has remained vulnerable to tornado hazards despite mitigation efforts, and as such would benefit greatly from improvements to tornado forecasting.

This study compares phases of four teleconnection patterns considered to be primary climate influencers in North America (El Niño-Southern Oscillation, North Atlantic Oscillation,

Arctic Oscillation, and Pacific/North American Pattern) to tornado activity in Oklahoma.

The phases of these teleconnection patterns were individually compared to Oklahoma tornado day frequency via χ2 statistical testing. It is shown that there are potentially linkages between the negative phases of the North Atlantic Oscillation, the Arctic Oscillation, and the

Pacific-North American Pattern and Oklahoma tornado activity.

Key words: Teleconnections, tornadoes, Oklahoma

DEDICATION

To my incredible wife Shari Lynn Douglas. You have gracefully tolerated my persistent clownery and related tendencies over the course of several decades and have remained not only completely unflappable, but consummately supportive throughout our journey. Honestly, I cannot fathom how you do it. You are indeed The Love of My Life and The Air that I Breathe.

Thank you for being you.

Also, to my dear friends Richard Patrick Barnes, Junior (December 3, 1965–June 4,

2010) and Daniel Thomas Pickersgill (July 13, 1960–April 16, 2020). There simply are not words to express how much I appreciate your unconditional friendship. I love you and miss you every day, Brothers.

ACKNOWLEDGEMENTS

First and foremost, I thank my graduate advisor, Dr. Christopher Fuhrmann, for providing me this opportunity and helping me see it through to completion. I also thank my graduate committee members Dr. Michael Brown and Dr. Andrew Mercer for their time and support.

I also thank my family and friends for your endless love, confidence, and support.

Truthfully, I could not have completed this work without the experiences afforded me by everyone I have had the privilege to interact with throughout my various educational, professional, and interpersonal engagements: this work truly represents a summation of those encounters. In the interest of brevity, I cannot list you all here. Even so, you can rest assured that I am forever grateful for your contributions.

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TABLE OF CONTENTS

DEDICATION ...... ii

ACKNOWLEDGEMENTS ...... iii

LIST OF TABLES ...... vi

LIST OF FIGURES ...... vii

CHAPTER

I. INTRODUCTION ...... 1

Background ...... 1 Statement of Problem ...... 5 Objectives ...... 7

II. REVIEW ...... 8

El Niño-Southern Oscillation ...... 9 North Atlantic Oscillation ...... 15 Arctic Oscillation ...... 18 Pacific-North American Pattern ...... 19

III. DATA AND METHODS ...... 23

Teleconnection Pattern Index Data ...... 23 Tornado Record Data ...... 24 Comparison of the Data ...... 27 Methods ...... 27

IV. RESULTS ...... 31

El Niño-Southern Oscillation ...... 31 North Atlantic Oscillation ...... 33 Arctic Oscillation ...... 35 Pacific-North American Pattern ...... 37

V. DISCUSSION AND CONCLUSIONS ...... 39

El Niño-Southern Oscillation ...... 39 North-Atlantic Oscillation ...... 41 Arctic Oscillation ...... 41 Pacific-North American Pattern ...... 43 Summary ...... 44 Limitations ...... 46 Future Work ...... 50

REFERENCES ...... 53

LIST OF TABLES

Table 1 Summary of links found in research between ENSO, NAO, AO, and PNA activity and Oklahoma tornado climatology compared to findings of this study...... 6

Table 2 Confidence levels, rejection levels, and critical values for χ2 tests (DF = 1) ...... 29

Table 3 Calculations of χ2 and confidence values for ENSO (via ONI)...... 32

Table 4 Calculations of χ2 and confidence values for NAO...... 34

Table 5 Calculations of χ2 and confidence values for AO...... 36

Table 6 Calculations of χ2 and confidence values for PNA...... 38

LIST OF FIGURES

Figure 1 Typical El Niño Winter (NOAA/Climate.gov, n.d., G)...... 11

Figure 2 Typical La Niña Winter (NOAA/Climate.gov, n.d., G)...... 12

Figure 3 Effects of ENSO on tornado/hail frequency (NOAA/Climate.gov, n.d., E)...... 14

Figure 4 NAO in positive phase (Dacula Weather, n.d., B)...... 16

Figure 5 NAO in negative phase (Dacula Weather, n.d., B)...... 17

Figure 6 AO in positive phase (Dacula Weather, n.d., A)...... 19

Figure 7 AO in negative phase (Dacula Weather, n.d., A)...... 20

Figure 8 PNA in positive phase (MO/S IL Weather Center Blog, November 15, 2013)...... 21

Figure 9 PNA in negative phase (MO/S IL Weather Center Blog, November 15, 2013)...... 22

Figure 10 Ratio of US EF0 Tornado Reports to All Tornado Reports (NCEI, n.d., B) ...... 25

Figure 11 US Annual Count of EF15 Tornadoes (NCEI, n.d., B) ...... 26

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CHAPTER I

INTRODUCTION

Background

The United States (US) experiences more tornadoes than any other region on the planet due to its unique combination of geographic features and synoptic influences (NCEI, n.d., E,

Tippett 2018). Throughout history, tornadoes have killed and injured thousands of people and caused billions of dollars in damage (Allen et al. 2015, Ashley 2007, Nouri et al. 2021, Trapp et al. 2007). The hazard they present is particularly high across sections of the Great Plains and

Midwest, so much so that for decades this region has been labeled “Tornado Alley” (Dixon et al.

2011). Despite advances in hazard mitigation (Wood et al. 2017), areas prone to significant tornado activity remain quite vulnerable to it (Dixon and Moore 2012, Doswell III et al. 2012) and as such would benefit from improvements to long-range tornado forecasting.

Oklahoma has long been considered the center of Tornado Alley due to its history of frequent and sustained combinations of key ingredients favorable for the development and growth of severe thunderstorms, supercells, and tornadoes (Dixon et al. 2011). However, there is significant variability in the locations, timings, and intensities of these ingredients, and so there is significant variability in when and where tornadoes occur. Trends in these variabilities influence tornado climatology and cause it to evolve (Ashley 2007, Brooks 2013, Brooks et al.

2014, Concannon et al. 2000, Dixon et al. 2014, Farney et al. 2014, Galway 1977, Gensini and

Brooks 2018, Guo et al. 2016, Moore 2016, Moore 2017, Moore and DeBoer 2019, Moore and

McGuire 2019, Tippett 2014, Tippett et al. 2012). This variability makes long-range tornado forecasting a very difficult problem (Gensini et al. 2020).

Severe weather and tornadoes are primarily mesoscale phenomena that are often set up by synoptic-scale processes (Doswell III et al. 1993). One of the sources of variability in synoptic influences and forcing that affects the US is the various teleconnection patterns observed in the atmosphere (Sheridan and Lee 2012). Their periodic fluctuations, intensities, couplings, and phasings alter temporal and spatial collocation of vertical wind shear, moist instability, and other meteorological factors necessary for the formation of severe thunderstorms and tornadoes (Allen et al. 2015, Cook and Schaefer 2008, Cook et al. 2017). So, there should be linkages between teleconnection patterns and the frequency, intensity, and distribution of tornado activity, and it should follow that increased understanding of these linkages would help improve long-range tornado forecasting.

However, research into these linkages is difficult for several reasons. First, the tornado database contains significant inhomogeneities mainly caused by human biases. Also, teleconnection patterns are nonlinear and variable (Hoerling et al. 1997, Hoerling and Kumar

1997), and are many times tied to, interact, and couple with each other. This can reinforce and/or weaken their effects on tornado activity (Huang et al. 1998, Moore et al. 2018, Moore and

McGuire 2019, Moore and McGuire 2020, Straus and Shukla 2002, Wang et al. 2014).

Moreover, observed signals are not typically strong or explicit or represent any sort of a tornado forecasting "smoking gun". In general, the opposite is more likely to be true: these influences and their markers are quite subtle (Tippett 2018). Finally, any influences of teleconnection patterns on tornado activity will be handed down from the global atmospheric scale down to the mesoscale, which introduces time lags and subjectivity to varying external influences. The result

of all these factors is that it has been difficult to achieve universal consensus across all studies

(e.g., Brown and Nowotarksi 2020, Tippett 2018).

An understanding of the climatology of past tornadoes is key to gaining understanding of the potential for future activity (Elsner et al. 2014). An enormous amount of research into tornado climatology has already been completed dating back to Finley (1888), citing various motivations, utilizing many different techniques and research questions, many times using similar data, and resulting in varied outcomes.

Concannon et al. (2000) found that, for the US, the annual tornado threat generally peaks in the US Southeast in March, and spreads outward to the west, north, and northeast through

July. However, this basic description of US tornado climatology is not necessarily always consistent and reliable. Concannon et al. (2000) also advised that because tornadoes are less frequent toward the northeast US, this description is somewhat less reliable in those areas.

Concannon et al. (2000) also advised that, while the springtime primary maximum of tornadoes in Oklahoma is reasonably consistent from one year to the next, the fall secondary maximum is far less reliable. This contrasts with states in other regions, such as Alabama, whose springtime primary maximum is inconsistent, but the fall secondary maximum is reliable.

Tornado climatology is variable and continuously evolving. Seasonal and geospatial maxima in tornado activity exist, but they differ from region to region, and their exact timings and locations vary (Brooks et al. 2003). The average number of EF151 tornadoes has been more- or-less stable while the number of annual EF15 tornado days has been decreasing and the number of so-called "big tornado days" (i.e., days with large numbers of unrelated tornadoes) has

1 Hereafter, the use of “EF” shall refer to same-number ratings of tornadoes on both the original Fujita Scale and the Enhanced Fujita Scale, and the use of two digits immediately following “EF” shall refer to the inclusive range of ratings between them. For example, “EF15” shall refer to “all tornadoes rated F/EF1 through F/EF5” (or “all tornadoes stronger than F/EF0”). 3

been increasing (Brooks et al. 2014). Another way to say this is that each day has a lower probability of tornado occurrence, but if a tornado does occur there is increased probability that there will be more tornadoes on that day. This has increased annual and monthly variability as well as annual variability in the start of tornado season (Brooks et al. 2014). Concannon et al.

(2000) found that temporal variability could be revealed by subdividing tornado occurrence data at different intervals. For example, 1921–1935 and 1981–1995 show similar rates of significant tornado days, but 1951–1965 contains about 20% more.

Tornado climatology variability is also caused by non-meteorological, mainly human effects (Dixon et al. 2011, Dixon et al. 2014, Doswell III 2007, Doswell III and Burgess 1988,

Doswell III and Burgess 1993, Doswell III et al. 2009, Galway 1977, Nouri et al. 2021, Verbout et al. 2006). Nouri et al. (2021) found that changes in population density contribute to long-term trends in tornado occurrences in the US Southeast, improvements in technology contribute to long-term trends in tornado occurrences in the Great Plains, and both contribute to change in other areas.

Several teleconnection patterns and related mechanisms have already been implicated as having some effect on tornado occurrences and distribution, including El Niño/Southern

Oscillation (ENSO; Allen et al. 2015, Cook and Schaefer 2008, Eichler et al. 2006, Knowles and

Pielke 2005, Lee et al. 2013, Lee et al. 2016, Mayes et al. 2006, Moore 2019), sea-surface temperature (SST) anomalies (Brown and Nowotarski 2020, Chu et al. 2019, Lee et al. 2016,

Marzban and Schaefer 2001, Molina et al. 2016), Madden-Julian Oscillation (MJO; Barrett and

Gensini 2013, Thompson and Roundy 2013), Global Wind Oscillation (GWO), North Atlantic

Oscillation (NAO; Huang et al. 2006), Arctic Oscillation (AO; Nouri et al. 2021), Pacific/North

American (PNA; Muñoz and Enfield 2011) pattern, Eastern Pacific Oscillation (EPO; Brown and

Nowotarski 2020), Western Pacific Oscillation (WPO; Brown and Nowotarski 2020), Atlantic

Multi-decadal Oscillation (AMO; Nouri et al. 2021), and Pacific Decadal Oscillation (PDO;

Nouri et. al 2021). Some statistically significant linkages have been found. Those relevant to the teleconnection patterns examined in this study are summarized in Table 1.

Awareness and understanding of the linkages that have already been discovered between tornadoes and teleconnections such as ENSO (Tippett et al. 2014) and the Global Wind

Oscillation (GWO; Gensini et al. 2019, Gensini et al. 2020) have shown promise in improving tornado forecasts. However, it is important to note that tornadoes can still occur when various teleconnections, such as ENSO, MJO, and GWO, are in phases typically considered unfavorable for tornadic activity (Moore et al. 2018). Also, a favorable environment based on teleconnection phase(s) does not guarantee a large outbreak or big tornado day; no tornadoes or only a small number of tornadoes may occur instead. In these cases, other aspects of the synoptic and/or sub- synoptic environment may exhibit a stronger influence on tornadic activity.

Statement of Problem

This research seeks to mitigate the effects of the difficulties and obstacles concerning the development and improvement of long-range tornado forecasting models, improve understanding of any possible linkages between teleconnection patterns and tornado occurrence, produce results that increase consensus and relieve conflict in the literature, and provide findings that could be used to improve long-range tornado forecasts and models.

Table 1 Summary of links found in research between ENSO, NAO, AO, and PNA activity and Oklahoma tornado climatology compared to findings of this study.

Tornado Sig Sig Sig Pattern Positive Neutral Negative Characteristic Assoc Assoc Assoc

More annually [4] [5] [4] [5] [7] [8]

Less annually [4] [5] [7] [8]

More in AMJ [6] X NAO Less in AMJ [6] X

More in winter [2] AO Less in winter [2]

More in spring [2] [10] X PNA Less in spring [2] [10] X

[1] Allen et al. (2015) [6] Elsner et al. (2016) [2] Childs et al. (2018) [7] Knowles and Pielke (2005) [3] Chu et al. (2019) [8] Marzban and Schaefer (2001) [4] Cook and Schaefer (2008) [9] Mayes et al. (2006) [5] Cook et al. (2017) [10] Muñoz and Enfield (2011)

Objectives

The objective of this research is to detect linkages, correlations, and/or associations between tornado occurrences in Oklahoma and the phases of various global teleconnection patterns. Specifically, the univariate influences of four teleconnection patterns (ENSO, NAO,

AO, and PNA) on tornado activity in Oklahoma will be examined via comparison of Storm

Prediction Center (SPC) tornado data to Climate Prediction Center (CPC) daily teleconnection index values on monthly and annual bases. These four patterns were selected because (1) they are primary influencers of synoptic conditions in the Northern Hemisphere, (2) reliable daily index data were readily available, and (3) previous research has identified links between these patterns and tornado activity (Table 1) that will serve as a baseline against which the methods and results of this study can be compared.

The null hypothesis is that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days for each teleconnection phase.

CHAPTER II

REVIEW

As mentioned, teleconnection patterns have been implicated as influencing tornado activity. Brown and Nowotarksi (2020) found that while teleconnection patterns’ effects are mainly dynamic (e.g., presence of deep shear, positioning of the jet stream), these dynamic influences also force thermodynamic anomalies (e.g., temperature, dewpoint, convective available potential energy, lifting condensation level). Clearly, both dynamic and thermodynamic influences will affect severe thunderstorm and tornado activity. Cook et al.

(2017) found that changes in tornado occurrence during outbreaks are linked to locations of surface lows, low-level jets, and instability axes in addition to the positioning and strength of the subtropical jet, all of which are influenced by teleconnection patterns.

Allen et al. (2015) agrees with previous studies that ENSO influences severe thunderstorm activity in winter but disagrees that such influences would be limited to winter, finding that ENSO influences springtime activity as well. Prolonged –NAO (Elsner et al. 2016) and –PNA (Muñoz and Enfield 2011) phases are both associated with increased tornado activity in the US Southeast. Moreover, a –PNA phase is frequently associated with –ENSO (La Niña) episodes, which have also been shown to foster increased tornado activity (Allen et al. 2015,

Cook et al. 2017). Brown and Nowotarksi (2020) compared daily index values for the NAO,

AO, PNA, EPO, WPO, and Gulf of Mexico (GOM) SST anomalies to severe weather reports over the US Southeast from 1982 to 2017. They found several outbreak patterns aligning with

previous research, especially during springtime. This study also found that prolonged +AO episodes in winter and spring were associated with increased tornado activity in the US

Southeast, as were positive NAO events in winter (contrasting Elsner et al. 2016) and transitions from +NAO to –NAO during spring. However, the period of teleconnection data was limited to only 35 years, so only a small number of pattern cycles could be studied, which creates concerns about the representativeness of the sample (Doswell III 2007).

Nouri et al. (2021) compared index values for several patterns to tornado and population data regionally and at state-level using principal-components analysis, wavelet decomposition, and nested Bayesian modeling. They found that some teleconnection patterns were significant predictors on regional and/or state levels individually and/or in combination with other patterns.

NAO, PDO, and AMO were observed to modulate tornado activity in Oklahoma and Tornado

Alley, AO was observed to affect tornado activity in the US Southeast, and ENSO (via SOI) influenced tornado activity in both regions.

El Niño-Southern Oscillation

The El Niño-Southern Oscillation (ENSO) is a teleconnection pattern that involves the coupling of influences between gradients of atmospheric pressure and SSTs running from

Indonesia and the east-central tropical Pacific Ocean. Neutral ENSO conditions occur with normal trade winds and warmer SSTs/lower pressures to the west. Positive-phase conditions

(referred to as “El Niño”) occur when trade winds weaken, allowing warmer SSTs/lower pressures to extend to the east. This pushes the Pacific jet stream south, which causes winters in the northern US to be drier and warmer and the US Southeast to be wetter and cooler (Figure 1).

Negative-phase conditions (referred to as “La Niña”) occur when trade winds strengthen, pushing warmer SSTs/lower pressures to the west and allowing cold ocean waters to upwell to 9

the surface in the east, where they cool the air, and raises surface pressures (Figure 2). This weakens the Pacific jet stream and pushes it north, which causes winters in the US Pacific

Northwest to be cooler and wetter and the southern US to be warmer and drier. ENSO episodes typically last from several months to a year but have also been seen to last much longer on occasion (NOAA/Climate.gov, n.d., F, NOAA/NOS, n.d.).

When developing any forecasting system based on interactions between the atmosphere and the oceans, it is important to note that El Niño’s effects on North American climate can vary significantly from event to event (Hoerling and Kumar 1997). This is primarily due to atmospheric processes, but also due to SST variations. Banholzer and Donner (2014) found that global average surface temperatures are atypically warm after eastern Pacific El Niño events, but not after central Pacific or mixed occurrences. This study also found that a decrease in the rate of surface warming on a global scale observed since the late 1800s may be tied to decadal variation in the type of El Niño episode observed with each cycle. For example, Lee et al.

(2013) found that positive-phase Trans-Niño Index (TNI) episodes may serve as a long-range climate signal toward predicting US tornado outbreaks, particularly in April and May. TNI represents tropical Pacific SSTs during the onset or decay of ENSO events, i.e., +TNI leads to colder central tropical Pacific temperatures and warmer SSTs in the eastern tropical Pacific.

Models suggest this directional gradient increases the upper westerly and lower southwesterly flows over central and eastern US, which brings in cold/dry upper-level air from the Rocky

Mountain region and warm/moist lower-level air from the Gulf of Mexico. These air masses converge east of the Rockies and increase vertical shear. On the other hand, Marzban and

Figure 1 Typical El Niño Winter (NOAA/Climate.gov, n.d., G).

Schaefer (2001) found a weak correlation between Pacific SSTs and US tornado frequency that varies with the location of SSTs measured and the region of the US affected. The strongest correlation was between cool SSTs in the central tropical Pacific and the number of EF25 tornado days in a region from Illinois to the Atlantic coast, and from Kentucky to Canada.

However, they found only a 53% likelihood of this setup occurring in any month.

Molina et al. (2016) found that SST variability in the Gulf of Mexico, through mechanisms such as the Loop Current and warm-core rings, affects monthly to seasonal severe

Figure 2 Typical La Niña Winter (NOAA/Climate.gov, n.d., G).

weather activity across the US. For instance, increased hail and tornadoes in the southern US are correlated with warmer SSTs in the Gulf of Mexico. The opposite is true for cooler SSTs. This pattern reveals itself through anomalies in low-level specific humidity and mixed-layer convective available potential energy (CAPE). ENSO can enhance or suppress these interactions and patterns, as GOM SST anomalies are typically negative during El Niño due to increased cloud cover resulting from stronger subtropical jets and more cold fronts. The opposite is true during La Niña (Allen et al. 2015).

Weaver et al. (2012) found multidecadal variations in the link between the North

American Low-Level Jet (NA-LLJ) and regional tornado activity. Shifts in SSTs result in spatial

shifts and the strengthening and weakening of the NA-LLJ. Global SST trends may be supporting a shift toward weaker tornadoes in the northern Great Plains, while tornado activity in the US Southeast seems to have no correlation to trends in SSTs. This is contradicted by Molina et al. (2016), however, who found that warmer SSTs in the Gulf of Mexico are correlated with increased hail and tornado activity in the southern US and complicated by ENSO influences as noted above. Lee et al. (2016) found that variability in outbreak likelihood is strongly correlated with ENSO influences on favorable atmospheric processes and that the phases of ENSO and

North Atlantic SST tripole may help general forecasts of US outbreaks.

Mayes et al. (2006) found relationships between several severe weather parameters and

ENSO phase in the north-central US. Allen et al. (2015) also found that the occurrence of tornadoes and hail in the winter and spring is modulated by ENSO (Figure 3). Fewer tornadoes and hail events were observed in the central US during El Niño, while more were observed during La Niña. Since winter ENSO episodes tend to persist into the spring season, these relationships can potentially be used to predict variability in tornadoes and hail during the primary severe weather season. In addition, Cook and Schaefer (2008) found that stronger tornadoes with longer tracks are more likely to occur during La Niña and neutral winters than during El Niño winters. Winters with neutral tropical Pacific SSTs often lead to stronger and more frequent US tornado outbreaks than winters with warm tropical Pacific SSTs (El Niño), while winters with cool Pacific SSTs (La Niña) lie in the middle.

ENSO phase may also affect the geospatial distribution of tornado outbreaks. For neutral phases, tornado outbreaks were more likely across a region spanning Oklahoma-Kansas to the

Carolinas. During La Niña episodes, tornado outbreaks were more likely from southeast Texas

Figure 3 Effects of ENSO on tornado/hail frequency (NOAA/Climate.gov, n.d., E).

to the Illinois-Indiana-Michigan region. During El Niño, tornado outbreaks were more likely in the Gulf states and central Florida (Cook and Schaefer 2008). Cook et al. (2017) found that shifts in tornado frequency are related to ENSO, with La Niña generally favoring more intense and frequent activity than El Niño, especially at higher latitudes. La Niña years (i.e., cooler western US and warmer southern US) tend to produce longer tornado tracks, more violent tornadoes, and have increased probability of outbreaks exceeding 40 tornadoes. During El Niño years, the opposite is observed (i.e., weaker tornadoes, shorter damage paths, smaller outbreaks).

As previously mentioned, there is no consensus on these relationships in the literature, and in

some cases no relationships are found at all, e.g., Knowles and Pielke (2005) found little difference in tornado counts between the strongest El Niño and La Niña events from 1953 to

1989.

ENSO has also been observed to interact with other teleconnections. Huang et al. (1998) found that the NAO occasionally displays multi-annual to multi-decadal coherence with ENSO, a result that was also supported by Wang and Wang (1996). Straus and Shukla (2002) found that

ENSO does not force PNA for warm-event SSTs but could not determine if this is so for cold events. Some of these interactions themselves have also been linked to increased tornado activity. Nouri et al. (2021) found that “interplay” between ENSO and NAO is linked to tornado variability in Tornado Alley.

North Atlantic Oscillation

The North Atlantic Oscillation (NAO) is a main driver of climate variability in the

Northern Hemisphere (Huang et al. 1998, Huang et al. 2016). Strong positive phases of the

NAO cause the eastern US to experience warmer, milder, and wetter winters while northern

Canada is colder and drier (Figure 4). Strong negative phases cause the eastern US to have colder and stormier winters and warmer summers (Figure 5). The NAO’s period varies from days to weeks, but it can remain in one phase for several years (NCEI, n.d., C, NWS/CPC, n.d.,

C, NOAA/Climate.gov, n.d., B).

Huang et al. (2006) found that Atlantic Ocean blocking structures depend on NAO phase, with 67% more blocking days during –NAO (average episode length 11 days) than during

+NAO (6 days). NAO phase is largely responsible for the distribution of surface air temperature anomalies, which are at least partially responsible for the frequency and duration of blocking

Figure 4 NAO in positive phase (Dacula Weather, n.d., B).

episodes. NAO phase is also related to cloud cover: during –NAO, increased cloudiness is observed in the tropics, with lower amounts in the mid-latitudes; during +NAO this is reversed.

Atlantic Ocean cloud cover generally has a negative relationship with surface air temperature, possibly setting up a negative feedback loop.

Huang et al. (1998) found strong alignment between the NAO and SSTs in the Niño3 region (bounded by 5° N and 5° S latitude, 150° W and 90° W latitude) and +PNA, and non-

Figure 5 NAO in negative phase (Dacula Weather, n.d., B).

alignment between NAO and ENSO when Niño3 SST anomalies are weak, typically with –NAO and an east-shifted –PNA.

Links between tornado activity and the NAO are well-explained by the nature of the

NAO pattern. Normally, there is lower pressure over the northern North Atlantic Ocean

(Icelandic Low) and higher pressure over the central North Atlantic Ocean (Azores High).

During +NAO, the Icelandic Low and the Azores High are both stronger than average, increasing the zonal gradient between them. This strengthens the Atlantic jet stream and shifts storm tracks

to the north. Higher pressure extends into eastern North America, creating warmer conditions.

During –NAO, the Icelandic Low and Azores High are both weaker than average, decreasing the zonal gradient between them and subsequently weakening the jet stream and shifting storm tracks to the south. Lower pressure extends into eastern North America, allowing for more cold- air excursions and stormier conditions (Durkee et al. 2008).

Arctic Oscillation

The Arctic Oscillation (AO) is a mid-to-high latitude pattern that affects the positioning of the mid-latitude jet stream. Positive phases manifest when lower pressure occurs over the

Arctic and higher pressure occurs over the north Atlantic and Pacific Oceans, which pushes the jet stream to the north. This causes storm tracks to be steered further north and traps cold air in the polar regions, resulting in warmer and drier conditions in the mid-latitudes (Figure 6).

During negative phases, the pressure polarity is reversed, the jet stream and storm tracks migrate to the south, and cold air moves out of the polar regions. This results in colder temperatures and increased storm activity in the mid-latitudes, particularly during the winter months (Figure 7). The AO’s period runs from a few days to a few weeks (NCEI, n.d., A,

NOAA/Climate.gov, n.d., A).

Childs et al. (2018), Nouri et al. (2021), and Brown and Nowotarski (2020) found that

+AO episodes in winter were associated with increased tornado activity in the US Southeast.

Brown and Nowotarski (2020) also found an association between +AO and increased tornado activity in spring. The AO also influences ENSO episodes: when AO during spring and the preceding November are in phase, the spring AO exerts significant influence on the subsequent winter ENSO primarily via constructive superposition of SST anomalies induced in various

Figure 6 AO in positive phase (Dacula Weather, n.d., A).

regions of the Pacific Ocean. When the spring AO and preceding November AO are out of phase, this linkage in not apparent (Chen et al. 2018).

Pacific-North American Pattern

The Pacific-North American Pattern (PNA) is a principal source of climate variability in the Northern Hemisphere mid-latitudes (Dai et al. 2017). Positive PNA phases are often

Figure 7 AO in negative phase (Dacula Weather, n.d., A).

associated with El Niño episodes, resulting in deeper troughs and cooler temperatures over the eastern US and stronger ridges and warmer temperatures over the western US (Figure 8).

Negative phases are often associated with La Niña, and the opposite effects are observed (Figure

9). The PNA’s period runs from a few weeks to several months (NCEI, n.d., D, NWS/CPC, n.d.,

D, NOAA/Climate.gov, n.d., D, NOAA/Climate.gov, n.d., H).

Figure 8 PNA in positive phase (MO/S IL Weather Center Blog, November 15, 2013).

Chu et al. (2019) found that global SSTs in April are linked to the start of –PNA and the annual increase in tornado frequency in the southern Great Plains. During this time, atmospheric circulation anomalies can steer moisture advection northward from the Gulf of Mexico, increasing support for increased supercell and tornado activity. The seasonality of the PNA and associated moisture availability prevent this linkage at other times of the year. Muñoz and

Enfield (2011) found that one mode of variability of the Inter-Americas Sea Low-Level Jet (IA-

LLJ) is linked mainly to the PNA and controls the pressure in the US Southeast, leading to

Figure 9 PNA in negative phase (MO/S IL Weather Center Blog, November 15, 2013).

increased precipitation in the lower Mississippi, Tennessee, and Ohio River basins (MORB).

Tornado activity in this region is significantly linked to the IA-LLJ and the PNA index in March, along with the PDO and ENSO indices. Even broader, decadal-scale shifts in MORB activity may be related to decadal shifts in the IA-LLJ.

CHAPTER III

DATA AND METHODS

Teleconnection Pattern Index Data

Datasets describing daily index values for NAO, AO, and PNA covering the period from

1950 through 2020 are readily available from CPC (NWS/CPC, n.d., A, NWS/CPC, n.d., E).

Acquiring data for ENSO is not as straightforward. Because ENSO is influenced by many climatological factors, meteorological authorities have devised several different indices to describe them, such as the Multivariate ENSO Index (MEI), Oceanic Niño Index (ONI), the

Trans-Niño Index (TNI), the Southern Oscillation Index (SOI), and the Japanese Meteorological

Agency’s ENSO Index. This work will utilize the ONI to describe ENSO conditions. The ONI is the leading indicator used by operational forecasters in the US to monitor ENSO conditions

(Glantz and Ramirez 2020, NOAA/Climate.gov, n.d., C). However, the ONI is determined monthly using a 3-month rolling average using the preceding and following months (e.g., the historical monthly index for January is calculated using December, January, and February).

Because ENSO evolves slowly, these monthly averages should be applicable to their constituent days. So, the recorded ONI indices for a given month were assigned to all days within that month, creating a proxy for a daily index.

The bidirectionality of the teleconnection indices (i.e., positive and negative) is an important consideration in this work. The phase of weak index values (i.e., those close to zero) could be questioned as they may fall within margins of error associated with the production of

these values. To limit the influence of these values on calculations, this work will follow previous studies that applied notch filtering to the daily teleconnection indices. The basic effect of this notch filtering is to create a range of index values that will indicate a neutral phase (as opposed to a single value of 0). Previous studies have utilized notch widths ranging from ±0.25 to ±1.00, which create wider neutral notches and increasingly suppresses weak-index effects

(Allen et al. 2015, Childs et al. 2018, Durkee et al. 2008). However, because tornado and non- tornado days associated with these notched index values will not be included in sampling, increasing notch widths also have the effect of decreasing sample sizes. This could negatively affect statistical testing. To balance these issues, this study will utilize a notch width of ±0.50 across all testing.

Tornado Record Data

This study utilized a subset of the SPC tornado record data for Oklahoma (NWS Forecast

Office, Norman OK, n.d.). There are several well-known and documented problems with these data. They are quite noisy and inconsistent, suffering from several inhomogeneities caused primarily by anthropogenic biases (Kelly et al. 1978, Schaefer and Edwards 1999). The most oft-cited issue is that there has been a significant increase in the EF0 counts, while EF15 tornado counts have remained relatively stable, as illustrated in Figures 10 and 11. This trend is not necessarily supported by meteorology or climatology, but is instead explained by improvements in tornado forecasting, technological advances, and population increases (Brooks et al. 2014,

Dixon et al. 2011, Fuhrmann et al. 2014, Guo et al. 2016, Lee et al. 2013, Tippett et al. 2012,

Verbout et al. 2006). A second issue reported by Coleman and Dixon (2014) concerns tornadoes that occurred prior to the 1973 implementation of the Fujita Scale. These tornadoes were rated retroactively, and it is believed that the surveyors’ use of media photographs focusing on the 24

Figure 10 Ratio of US EF0 Tornado Reports to All Tornado Reports (NCEI, n.d., B)

worst damage led them to rate them too high. Other issues include changes and differences in building standards, limitations of and changes made to the Fujita/Enhanced Fujita Scales, lack of standardized data collection methods, differences in observers and spotters, variability in radar observations, evolution of population density, waxing and waning of media and public interest in tornadoes, and lack of separation between meteorological and non-meteorological effects (Allen et al. 2015, Brooks and Doswell III 2001, Brooks et al. 2014, Chu et al. 2019, Dixon et al. 2011,

Doswell III 2007, Doswell III and Burgess 1988, Fuhrmann et al. 2014, Gensini and Brooks

2018, Guo et al. 2016, Lee et al. 2013, Marzban and Schaefer 2001, Moore and DeBoer 2019,

Schaefer et al. 1986, Verbout et al. 2006, Wood, et al. 2017). 25

Figure 11 US Annual Count of EF15 Tornadoes (NCEI, n.d., B)

Nevertheless, the SPC tornado record continues to be widely used by researchers, who frequently filter and/or subset the data to address these issues. Many studies, such as Chu et al.

(2019), Guo et al. (2016), and Moore and DeBoer (2019), removed EF0 tornadoes. Lee et al.

(2013) focused only on EF35 tornadoes. Doswell III (2007) and Fuhrmann et al. (2014) considered clusters of tornadoes (e.g., tornado days or “outbreaks”, with the latter smoothing the subset of EF15 tornadoes). Allen et al. (2015), Brooks et al. (2014), and Gensini and Brooks

(2018) developed and/or used covariates and/or proxies for the data. Lee et al. (2013) and

Marzban and Schaefer (2001) constrained the data spatially, while Allen et al. 2015, Brooks et al. (2014), and Guo et al. (2016) limited the data temporally. Chu et al. (2019) did both. Tippett

et al. (2012) and Verbout et al. (2006) detrended the data using linear regression, with the latter dropping the first few years of the dataset beforehand. This study will filter the tornado day by utilizing EF15 tornado days.

Comparison of the Data

This study, as with any study attempting to draw conclusions from the comparison of short-fuse data (tornadoes) and long-term data (teleconnection indices), has the challenge of ensuring that enough cycles of the long-term phenomena are sampled so that robust conclusions can be drawn (Brooks et al. 2014, Doswell III 2007, Doswell III and Burgess 1988). This becomes more difficult as teleconnection periods increase and their index time series decrease.

To ensure that any correlations detected were indeed robust, it was important that the data go back far enough in time so that as many cycles as possible were considered for each teleconnection pattern. The periods of the teleconnection patterns involved in this work range from a few weeks to (rarely) a few years, meaning that even considering the shortest of the time series analyzed (1979–2020), enough cycles of the teleconnections examined will have been sampled.

Methods

Oklahoma tornado data from SPC was used to generate monthly and annual counts of

EF15 tornado and non-tornado days for the period of record (1950–2020). For each of these sets of counts, a climatological frequency for each month and year was determined simply by dividing the number of tornado days by the number of possible days for that month and year over the period of record. Then, all counts of tornado days and non-tornado days were separated into groups associated with positive, neutral (±0.50), and negative phases of ENSO (via ONI), NAO,

AO, and PNA. These counts represent the observed frequency of tornado days by teleconnection and phase. Adjusted climatological frequencies of each teleconnection were also determined to account for only those tornado days associated with positive and negative phases. Using these adjusted climatological frequencies, expected frequencies of tornado and non-tornado days were then determined for each teleconnection’s positive and negative phases.

These observed and expected frequencies were derived from counts of nominal data. A chi-squared (χ2) test was used to assess whether the distributions of the observed and expected tornado days varies with teleconnection phase. The χ2 test and applications are described in detail in Wilks (2019). The χ2 test does not assume an underlying data distribution; the χ2 test is used to examine whether two datasets have the same distribution. This is done by categorizing the two datasets into histograms, determining the frequencies for their categories, and then comparing the results to make inferences about whether the two datasets have the same or different distributions. The χ2 test is readily used to evaluate discrete data but can also be used for continuous data once those data have been categorized. The χ2 test can be used to see what kind of distribution a dataset has simply by comparing that dataset to datasets with known distributions.

The χ2 statistic is calculated using Equation 1:

푘 (푂 − 퐸)2 휒2 = ∑ , (1) 퐸 푖=1

where O represents the number (of tornado or non-tornado days) observed, E represents the number expected, and k represents the total number of days contained within the sample. It is easy see that when observed values equal expected values, the numerator goes to zero, and so the 28

χ2 statistic becomes zero and the distributions have the same shape. Thus, smaller χ2 values indicate more similarity between the distributions, and larger χ2 values indicate less similarity between the distributions.

Because there were two outcomes for each of the compared statistics, these χ2 tests had 1 degree of freedom (DF), meaning that the null hypothesis could be considered for rejection at critical values corresponding to increasing confidence levels as indicated in Table 2. If the χ2 test for a teleconnection phase produced a statistic that is larger than the critical value for a particular confidence level, there was statistically significant difference at that confidence level between the shapes of the observed and expected distributions, and the null hypothesis that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days can be rejected.

Table 2 Confidence levels, rejection levels, and critical values for χ2 tests (DF = 1)

Confidence Level Rejection Level (α) Critical Value

90% 0.1 2.706

95% 0.05 3.841

97% 0.03 4.709

98% 0.02 5.412

99% 0.01 6.635

99.9% 0.001 10.827

It is important to consider that some errors are always possible with hypothesis testing.

The type of error most often associated with hypothesis testing is a false rejection of the null hypothesis, which is known as a “Type I” error. The likelihood of making of a Type I error

typically corresponds to the rejection level of the test. Another kind of possible error involves failing to reject the null hypothesis when it should be rejected (a “Type II” error), the likelihood of which is usually very difficult to quantify. In general, when the likelihood of making a Type I error increases, the likelihood of making a Type II error decreases, and vice-versa. To balance these likelihoods, a rejection level of 0.05 is often used. For this study, confidence levels of 95% or higher were considered statistically significant and represented cases where the null hypothesis would be considered for rejection. Confidence levels below 95% were used for detecting weaker associations to support the robustness of more significant results.

It is also important to note that the results of χ2 tests are highly dependent on sample size; the validity of the χ2 tests becomes questionable when sample sizes are very small. The χ2 test assumes that the sample sizes in 80% of the cells of its input contingency matrices all have a value of at least five (McHugh 2013). To account for this, when any one of the four observed or expected values placed into any of the 2×2 contingency matrices was less than 5, the resulting χ2 value was not considered valid. This was only an issue with the computation of the monthly χ2 values; the likelihood of such cases was eliminated with the aggregation of the monthly counts into annual counts.

CHAPTER IV

RESULTS

El Niño-Southern Oscillation

The results for ENSO (via ONI) are displayed in Table 3. It is noted that the distributions of observed and expected tornado days were different at the 90% confidence level for February and September. While both February and September are noted to have a higher frequency of tornado days during –ENSO than during +ENSO, the differences noted between their observed and expected distributions were not at a confidence level high enough to reliably reject the null hypothesis that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days for each teleconnection phase.

Table 3 Calculations of χ2 and confidence values for ENSO (via ONI).

ADJ: Adjusted CONF: Confidence FREQ: Frequency NEU: Neutral POR: Period of Record TOR: Tornado CLIM: Climatological EXP: Expected NEG: Negative OBS: Observed POS: Positive TOT: Total

Calculation of χ2 statistics and confidence values:

* W = ((J – Q)2 / Q) + ((K – R)2 / R) + ((N – S)2 / S) + ((P – T)2 / T) ** X is based on 1 degree of freedom; 2.706 → 90%; 3.841 → 95%; 4.709 → 97%; 5.412 → 98%; 6.635 → 99%; 10.827 → 99.9%

Red digits indicate cases where χ2 contingency matrix inputs are less than 5 (resulting in an invalid χ2 test). Thick box borders indicate confidence values associated with valid χ2 tests (i.e., no contingency matrix inputs less than 5). Purple shading indicates the greater of the positive (U) and negative (V) observed tornado day frequencies.

North Atlantic Oscillation

The results for NAO are displayed in Table 4. It is noted that the distributions of observed and expected tornado days were different at the 98% confidence level for April, at the

99% confidence level for May, and at the 99.9% confidence level annually. These differences are strong enough to reliably reject the null hypothesis that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days for each phase. All three of these periods are noted to have a higher frequency of tornado days during –NAO than during +NAO. It is further noted that the distributions of observed and expected tornado days for November are possibly different at the

98% confidence level. While November is noted to have a higher frequency of tornado days during +NAO than during –NAO, this determination is not considered valid because the number of observed negative-phase tornado days used to compute this χ2 statistic was less than 5. So, the

χ2 test statistic cannot be used to reject the null hypothesis in this case.

Table 4 Calculations of χ2 and confidence values for NAO.

ADJ: Adjusted CONF: Confidence FREQ: Frequency NEU: Neutral POR: Period of Record TOR: Tornado CLIM: Climatological EXP: Expected NEG: Negative OBS: Observed POS: Positive TOT: Total

Calculation of χ2 statistics and confidence values:

Arctic Oscillation

The results for AO are displayed in Table 5. It is observed that the distributions of observed and expected tornado days for –AO events were different at the 95% confidence level for October. This difference is strong enough to reliably reject the null hypothesis that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days for each phase. October is noted to have a higher frequency of tornado days during –AO than during +AO. It is further noted that the distributions of observed and expected tornado days for December are possibly different at the

90% confidence level. However, this determination is not considered valid because the number of observed negative-phase tornado days, expected positive-phase tornado days, and expected negative-phase tornado days are all less than 5. Even if these values were all at least 5, and while December is noted to have a higher frequency of tornado days during +AO than during –

AO, the difference noted between their observed and expected distributions was not at a confidence level high enough to reliably reject the null hypothesis.

Table 5 Calculations of χ2 and confidence values for AO.

ADJ: Adjusted CONF: Confidence FREQ: Frequency NEU: Neutral POR: Period of Record TOR: Tornado CLIM: Climatological EXP: Expected NEG: Negative OBS: Observed POS: Positive TOT: Total

Calculation of χ2 statistics and confidence values:

Pacific-North American Pattern

The results for PNA are displayed in Table 6. It is noted that the distributions of observed and expected tornado days were different at the 99% confidence level for both April and May, and at the 99.9% confidence level annually. These differences are strong enough to reliably reject the null hypothesis that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days for each phase. All three of these periods are noted to have a higher frequency of tornado days during –PNA than during +PNA. It is further noted that the distributions of observed and expected tornado days for January are possibly different at the 99% confidence level. While

January is noted to have a higher frequency of tornado days during –PNA than during +PNA, this determination is not considered valid because the numbers of observed positive-phase tornado days, expected positive-phase tornado days, and expected negative-phase tornado days used to compute this χ2 statistic were all less than 5. So, the χ2 test statistic cannot be used to reject the null hypothesis in this case.

Table 6 Calculations of χ2 and confidence values for PNA.

ADJ: Adjusted CONF: Confidence FREQ: Frequency NEU: Neutral POR: Period of Record TOR: Tornado CLIM: Climatological EXP: Expected NEG: Negative OBS: Observed POS: Positive TOT: Total

Calculation of χ2 statistics and confidence values:

CHAPTER V

DISCUSSION AND CONCLUSIONS

El Niño-Southern Oscillation

In general, previous studies have concluded that –ENSO (+ENSO) is generally more likely to increase (decrease) Oklahoma tornado days, particularly in winter and spring. This is explained by the shifting of the jet stream over North America during –ENSO (+ENSO), which modulates upper-level wind fields, increasing (decreasing) low-pressure system frequency in the

US Great Plains during –ENSO (+ENSO) and significantly increasing (decreasing) moisture advection from the Gulf of Mexico into the Great Plains, increasing (decreasing) both CAPE and

SRH values and decreasing (increasing) lifting condensation levels. These ingredients and processes increase (decrease) the likelihood of tornado activity (Allen et al. 2015).

Annual increases (decreases) in tornado activity during –ENSO (+ENSO) were noted by

Cook and Schaefer (2008), Cook et al. (2017), Knowles and Pielke (2005), and Marzban and

Schaefer (2001). This study does not support these findings, as no statistically significant differences between the annual distributions of observed and expected tornado days for –ENSO or +ENSO were observed.

Increased (decreased) tornado activity in winter during –ENSO (+ENSO) episodes was noted by Allen et al. (2015), Childs et al. (2018) and specifically in January and February by

Cook et al. (2017). These findings are not supported. While there was a difference noted between observed and expected distributions of tornado days for –ENSO in February, this was

only noted at the 90% confidence level, which is not sufficiently high to reliably reject the null hypothesis. However, –ENSO is associated with an 80.0% increase in tornado day frequency (as compared to climatology) in February and +ENSO is associated with a 30.0% decrease in tornado frequency, so this result merits further study.

Increased (decreased) tornado activity in spring during –ENSO (+ENSO) episodes was noted by Allen et al. (2015), and specifically in March and April by Cook et al. (2017). These findings are not supported. No differences were noted between observed and expected distributions of tornado days during any of the spring (March, April, and May) months.

Elsner et al. (2016) found that the positive (negative) phase of ENSO was associated with increased (decreased) tornado activity in meteorological spring (MAM). This finding is not supported, as no statistically significant differences between the distributions of observed and expected tornado days for +ENSO were noted in March, April, or May.

While the effects of ENSO on tornado activity are typically limited to winter and spring,

Mayes et al. (2006) found that there is also increased (decreased) tornado activity during the summer and fall months (MJJ-SON) when ENSO is in a negative (positive) phase. This finding is also not supported. While there was a difference noted between observed and expected distributions of tornado days for –ENSO in September, this was only noted at the 90% confidence level, which is not sufficiently high to reliably reject the null hypothesis. However,

However, –ENSO is associated with a 55.6% increase in tornado day frequency (as compared to climatology) in September and +ENSO is associated with a 24.9% decrease in tornado frequency, so this result merits further study.

North-Atlantic Oscillation

As with ENSO, associations between tornado activity and the NAO have also been established in the literature. Elsner et al. (2016) found that the presence of a –NAO (+NAO) was associated with increased (decreased) tornado activity in late spring and early summer. This finding is partially supported, given that the distributions observed and expected tornado days for

–NAO events were different at the 98% confidence level in April and the 99% confidence level in May. Compared to climatology, –NAO is associated with increased tornado day frequency in

April (19.8%) and May (19.4%), and +NAO is associated with decreased tornado days frequency in April and May (25.6% for both months). Annually, –NAO is associated with a 18.5% increase in tornado day frequency and +NAO is associated with a 21.6% decrease in tornado day frequency.

That –NAO is associated with increased Oklahoma tornado days in April and May and annually is not necessarily surprising, as it is associated with higher heights over Iceland and lower heights over the subtropics. These lower heights are most significantly observed in the US

Southeast, with some influence extending into the Great Plains (Dacula Weather, n.d,, B, Elsner et al. 2016).

With respect to the weak signal noted for positive NAO episodes in November, while

+NAO is associated with a 51.1% increase in tornado day frequency over climatology and –

NAO is associated with a 58.0% decrease, this test statistic is invalid and cannot be relied upon.

However, the result does merit further study.

Arctic Oscillation

The AO has also been found to influence tornado activity in the US. Childs et al. (2018) found that the presence of a +AO (–AO) was associated with increased (decreased) tornado 41

activity in winter. The current study did not find any valid, statistically significant associations that could corroborate this finding. However, a single, invalid, non-significant association was found for December, when +AO has a higher frequency of tornado days than –AO. So, this finding of Childs et al. (2018) is not supported. However, +AO is associated with a 66.0% increase in tornado day frequency (as compared to climatology) in December and –AO is associated with a 56.0% decrease in tornado frequency, so this result merits further study.

The statistically significant (at the 95% confidence level) association noted for October was unexpected. Also surprising was the lack of other associations throughout the year. It may be that teleconnections like the AO, when closer to neutral, do not exhibit a particularly strong or consistent influence on the regional climate, much like what we see with ENSO. In these cases, other teleconnections or aspects of the planetary to synoptic-scale circulation may be playing a more important role. Tornadoes can certainly occur with a different mix of atmospheric conditions regardless of the influence of any single teleconnection pattern and may not always be synoptically evident. Therefore, the associations with dominant teleconnection patterns may be more muted or out of phase with the associations typically seen with tornadoes. Even so, –AO is associated with a 37.4% increase in tornado day frequency (as compared to climatology) in

October and +AO is associated with a 41.8% decrease in tornado frequency, so this result also merits further study.

Relationships between the AO and tornado activity can be explained by the prevailing circulation. The AO is driven by changes in pressure over the Arctic and over the northern

Atlantic and Pacific Oceans. During +AO, there is lower pressure over the Arctic and higher pressure over the mid-latitudes. This causes a northward shift of the jet stream, leading to warmer temperatures in the mid-latitudes with fewer cold-air outbreaks. During –AO, there is

higher pressure over the Arctic and lower pressure over the mid-latitudes. The jet stream is weaker and shifted to the south, leading to cooler temperatures in the mid-latitudes and increased cold-air outbreaks, as well as the potential for severe weather (Dacula Weather, n.d., A).

Pacific-North American Pattern

Childs et al. (2018) and Muñoz and Enfield (2011) found that the presence of –PNA

(+PNA) was associated with increased (decreased) tornado activity in spring. These findings are supported, given that the distributions observed and expected tornado days for –PNA events were different at the 99% confidence level in both April and May. Compared to climatology, –

PNA is associated with increased tornado day frequency in April (12.6%) and May (24.2%), and

+PNA is associated with decreased tornado days frequency in April (37.9%) and May (24.6%).

Annually, –PNA is associated with a 17.4% increase in tornado day frequency and +NAO is associated with a 22.7% decrease in tornado day frequency.

As with NAO, that –PNA is associated with increased Oklahoma tornado days in April and May is not necessarily surprising. The PNA is driven by varying pressures over Hawaii, the

Rocky Mountains, the North Pacific Ocean south of Alaska, and the US Southeast. During –

PNA, the first two regions experience lower pressures while the other two regions experience higher pressures. This weakens and splits the East Asian jet stream, resulting in a blocking pattern in the northern North Pacific. Pressures trend lower over Canada, resulting in warmer and wetter conditions across the south-central US. –PNA episodes are routinely associated with

La Niña episodes (Dacula Weather, n.d,, C).

During +PNA, the pressure regime is reversed, with higher pressures over Hawaii and the

Rockies and lower pressures over the Northern Pacific Ocean south of Alaska and the US

Southeast. The resulting pressure gradient strengthens the East Asian jet stream and results in 43

anomalously high pressures over Canada, which causes western North America to be warmer and south-central and southeast US to be cooler. During winter, +PNA brings drier conditions to the Pacific Northwest as well as the eastern US. +PNA episodes are routinely associated with El

Niño episodes.

With respect to the weak signal noted for positive NAO episodes in November, while –

PNA is associated with a 224.4% increase in tornado day frequency over climatology, this test statistic is invalid and cannot be relied upon. The tornado day frequency for +PNA could not be calculated due to a no observed instances of positive-phase tornado days. For this reason, this signal is considered spurious.

Summary

Based on these results, it can be concluded that, in general, the positive phases of the

ENSO, NAO, AO, and PNA, taken individually, are not linked to Oklahoma tornado activity on a monthly or annual basis. A pair of weak signals involving positive phases were observed: one in November for +NAO and one in December for +AO. The association for +NAO in

November, while strong at 98%, is an invalid test statistic based on insufficient sample sizes, and this association is not explained by meteorology. The association for +AO in December was not strong enough to reject the null hypothesis and was also an invalid test statistic based on insufficient sample sizes. However, the findings of Child et al. (2018) corroborate this association. It is likely that the filtering used on the tornado data (EF15 tornado days) and teleconnection index data (±0.50 neutral notch) were too strong to allow the χ2 statistic to be properly computed and sufficiently strong for this teleconnection.

These results are generally supported by established circulation patterns associated with each of these teleconnections. For example, the positive phase of the ENSO typically results in a 44

southward migration of the jet stream, which inhibits moisture advection from the Gulf of

Mexico, a key ingredient for tornadic activity in the central Plains. The positive phase of the

NAO brings higher pressure to North America, while the positive phase of the AO results in fewer cold-air outbreaks over North America. Finally, the positive phase of the PNA warms the western states and cools the southeast states. These conditions are generally unfavorable for the development of severe thunderstorms and tornadoes.

On the other hand, the negative phases of these four teleconnections are linked to increased tornado days in several monthly and annual cases. This is most notably observed with strong (i.e., >98%) associations in April and May as well as annually for –NAO and –PNA.

This is also observed with –AO in October, although this association (95%) is not as strong.

Weak signals (90%) were also observed for –ENSO in February and September, and an invalid result (99%) was noted for –PNA in January. The monthly associations for –NAO are corroborated by the findings of Elsner et al. (2016), and the monthly associations for –PNA are corroborated by Childs et al. (2018) and Muñoz and Enfield (2011). The weak monthly associations for –ENSO are not necessarily corroborated by any of the literature reviewed herein, except perhaps indirectly by Cook and Schaefer (2008), Cook et al. (2017), Knowles and Pielke

(2005), and Marzban and Schaefer (2001), all of which found that these episodes generally result in more tornadoes annually.

For –NAO, –AO, and –PNA, there is sufficient support for rejecting the null hypothesis that there are no linkages, correlations, associations, and no statistically significant differences between observed and expected frequencies of tornado days and these teleconnections phases in

Oklahoma. For the other patterns and phases, there is not sufficient evidence to reject the null hypothesis. For –ENSO, while there may indeed be an association with increased Oklahoma

tornado activity, this study did not produce sufficient evidence to reliably conclude that this is the case. As with the positive phases, these results are in line with much of the existing literature and established circulation patterns (i.e., negative phases typically increase support for severe thunderstorms and tornadoes).

Limitations

The tornado data used to produce this study are widely known to be problematic and, as with many previous studies, filtering was applied prior to analysis to mitigate the effects of human-created trends and biases. The teleconnection index data also required filtering to suppress the influence of weakly positive or negative phases. Each filtering technique has advantages and disadvantages. The specific filters applied were consistent across all teleconnection patterns studied. It is possible that varying the size of the neutral notches applied to each teleconnection (as in Childs et al. 2018) may present more appropriate results. The use of a single notch across all patterns may not be a good fit in all cases. For this study in particular, filtering caused reduction of sample sizes, which can decrease reliability of the χ2 statistical test utilized.

Despite the slow evolution of the ENSO and the use of 3-month rolling averages to generate monthly index values, the extension of this monthly data to create proxy data from monthly values for ONI could result in introduction of errors into the analyses of this study.

The χ2 test simply confirms or denies that the distributions of these parameters are similar, which only allows for inferences of whether there are links between them (Wilks 2019).

The χ2 test does not allow for inferences related to tornado or tornado day counts, intensities, outbreaks, seasons, track lengths/widths, or any other quantitative factors. To make quantitative

inferences, additional evaluation using different types of testing, such as evaluations of the differences of means, would have to be completed.

Another problem with this kind of hypothesis testing is known as the multiplicity problem for independent tests (Wilks 2019). This concerns this collective influence of an accumulation of potential Type I errors, the probability of which is given by α. The potential for bias to be introduced into results grows with the number of tests performed (i.e., the more tests performed on a data set, the more the overall α increases). A failure to account for multiplicity could result in some findings that are falsely considered statistically significant. As this study did not involve a significant number of calculations and was primarily exploratory, multiplicity is not as much of a problem for these results. However, if a very large number of calculations were involved or more specific inferences were to be made, some measure of controlling or adjusting for multiplicity would have to be employed.

The atmosphere, its features, and its interactions are constantly in motion, influencing each other continuously on several different, necessarily overlapping and not necessarily fixed, scales. Oke (2002) describes the classification of atmospheric characteristics and processes into size (and time) ranges as being fraught with significant disagreement; Oke (2002) instead describes the “meso-scale” as “reasonable consensus” ranging between 10 and 200 km, overlapping ranges both larger/smaller and longer/shorter. Emanuel (1986) seems to eschew the idea of differing scales, instead concluding that atmospheric processes represent a continuous spectrum. Within this spectrum, processes of all sizes, from the global scale down to the molecular level, from beyond the tropopause down to (and even below) the surface (Brown and

Arnold 1998), and from centuries and millennia down to milliseconds are all so interrelated that attempting to discretize the atmosphere on any level may be inappropriate.

Fujita (1986) cautions that given the human impact of mesoscale phenomena, it is important to recognize, analyze, and forecast these processes separately from those at larger scales. Within larger scales, mesoscale signals would not likely be observable; when they are, they may be disregarded as errors or “noise”. Fujita (1986) cited the range of 10 to 100 km as generally and practically comprising the “center” of the mesoscale while recognizing that this was not necessarily a fixed range. Regardless of this lack of consensus, all three of these works agree that mesoscale processes are not necessarily completely constrained within any discrete range. Neither are the influences that affect mesoscale processes nor are the effects of mesoscale processes.

Remembering that atmospheric processes define these scales and not vice-versa is vitally important to gaining an understanding of mesoscale phenomena. This idea creates a vast overall domain from which experimental results must be extracted by carefully selecting constraints such as domain edges, initial conditions, variable subgroups, parameterizations, resolutions, and datasets/subsets. Any such constraints used in this vast domain, no matter how few are employed or how carefully they are applied, create an enormous number of opportunities to criticize (positively or negatively) any study simply by tweaking constraints or by using different constraints. The use of constraints also allows error to creep in and open the door to an enormous number of questions that can create opportunities for further research, all of which should be tempered by real-world applicability, capability, and affordability.

This study involved testing of the phases of teleconnection patterns on an individual basis. However, as noted above, meteorological processes are continuous and do not occur in a vacuum. Every point in both datasets is subject to varying external inputs. Teleconnection patterns do not occur individually, and their various couplings have been found to affect local

weather. For example, during La Niña events when there is also a strong –PNA phasing, it is typically cotemporal with +NAO (Pozo-Vázquez et al. 2001, Pozo-Vázquez et al. 2005). During late El Niño winters, the opposite is regularly observed: a strong +PNA is associated with –

NAO (Moron and Gouirand 2003). It is recognized that this study parameterized these data to perform testing and analysis and that these parameterizations are likely to have introduced error into the analyses and results.

No adjustment was made to account for the differences in influence between the teleconnection patterns tested. The influences of individual teleconnection patterns are known to vary geospatially and temporally: how, how much, when, and how often each teleconnection pattern influences Oklahoma will vary from teleconnection to teleconnection.

The propagation of effects and influences through sequences of meteorological processes does not occur instantaneously. These events take time, and the amount of time involved with propagation of effects varies but is generally expected to increase as more mechanisms are added to the sequence and as the sequence spans additional levels of scale. This creates a variable lag between the onset and/or arrival of a teleconnection phase and the production of tornadoes.

Teleconnection patterns generally occur on the global atmospheric scale. They influence synoptic conditions, which in turn influence mesoscale conditions. However, the categorization of data into temporal bins (e.g., the necessary parameterizations into data into tornado days and daily index values) smooths over these aspects of the real atmosphere and ignores this variable lag time. This certainly introduces the possibility of error into the analyses performed in this study.

Future Work

While this research aligns well with established relationships between teleconnections and tornado activity, it also leads to new questions. Because teleconnections occur simultaneously and influence each other as well as the overall circulation regime (like gears in a machine or engine), future research should involve similar testing of multivariate combinations of these daily predictors. Of particular interest would the well-known connections between AO and NAO as well as the various relationships between ENSO, NAO, AO, and PNA mentioned previously. These comparisons should also be repeated for univariate and multivariate combinations of these and other predictor teleconnections for which monthly index values are available (e.g., EPO, WPO, AMO, PDO). This work could also be extended to other states and/or regions and incorporate the use of geospatial tools and analysis to improve results. For example, geographic domains could be defined by grids of varying resolutions (rather than by state borders) and tornado days could be tabulated by point and path data (as opposed to simple occurrences). Gridded tornado days density surfaces could then be created using kernel density estimation (as in Dixon et al. 2011, Coleman and Dixon 2014, Fuhrmann et al. 2014, and many others) or via other techniques. These surfaces could then be compared to teleconnection index data to check for significant associations.

Future work should also consider linkages, associations, and relationships with the

Madden-Julian Oscillation (MJO) and Global Wind Oscillation (GWO). The MJO is a tropical teleconnection pattern described in 8 phases that involves a persistent convective disturbance moving eastward around the Earth with an average period of 30 to 60 days. It has been observed to influence mid-latitude thunderstorm and tornado activity as well as wintertime outbreaks of

Arctic air across the central and eastern US (Moore and McGuire 2020).

Barrett and Gensini (2013) found that April tornado days are more likely during MJO phases 6 and 8 and less likely during phases 3, 4, and 7, while May tornado days are more likely during phases 5 and 8 and less likely during phases 2 and 3. This work also found that in MJO phases that support increased likelihood of tornado days, positive anomalies of CAPE, bulk shear, and storm-relative helicity (SRH) are seen in the central US, and that during phases that supported decreased likelihood of tornado days, the opposite was found. These anomalies are believed to be linked to the MJO due to changes in the circulation of the troposphere. Barrett and Henley (2015) found hail day variability for different phases of the MJO. In April, hail days were most likely in the south-central US during phase 5. In May, hail days were least likely in the north-central US during phase 3. In June, hail days were most likely in west Texas and least likely over the central US during phase 8. Thompson and Roundy (2013) found that the frequency of violent tornado outbreaks more than doubles during MJO phase 2 as compared to other phases. Phase 2 also induces the most supportive low-frequency circulation pattern preceding tornado outbreaks.

The GWO is a way of describing how the Earth’s relative atmospheric angular momentum varies in terms of the MJO, ENSO, and some additional mid-latitude processes with a subseasonal period on the order of 1–2 months using 8 phases (Gensini and Marinaro 2016,

Gensini and Allen 2018, Weickmann and Berry 2009). Gensini et al. (2019) and Gensini et al.

(2020) documented successes of the Extended-Range Tornado Activity Forecast (ERTAF) project utilizing the GWO to produce skillful, increased-range (i.e., 2–3 weeks) tornado forecasts. Moore (2018) found that phases of the GWO vary with a period of 20–25 years and that tornado frequency is weakly correlated with positive phases 2, 3, and 4 as well as negative phases 6, 7, and 8 in winter, spring, and fall. Winters and springs with more days in phases 2, 3,

and 4 and fewer days in phases 6, 7, and 8 have more tornadoes. Winters and springs with more days in phases 2, 3, and 4 have a higher probability of increased tornado activity. Taken together, seasons with more days with lower atmosphere angular momentum typically experience increased activity, especially in winter and spring. Moore and McGuire (2020) found that springtime tornado days cluster in phases 2 and 3 of the GWO, and the greatest number of days occurs when the MJO is in phases 1, 2, or 3. Springtime tornado days are most common in phase 5 of the MJO, and this is enhanced when GWO is in phases 5, 6, 7, or 8.

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