Climatology of Severe Convective Wind Gusts in Australia

Alessio Cosmo Spassiani M.Sc., B.Sc. (Hons.)

A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2020 School of Civil Engineering

Abstract Severe convective wind storms are responsible for billions of dollars in damage to global infrastructure each year. This suggests there are systematic deficiencies in the way that structures are designed to withstand this type of event and that there is a need to better understand the hazard convective wind storms pose to infrastructure. In order to quantify this risk, it is necessary to have a reliable and spatially complete climatology of their occurrence. Given no such climatology exists for Australia, this research sought to develop such a climatology based on recent observational records, as well as examining how climate change may impact the severe convective wind storm climate into the future. Severe weather records (including wind gusts) in the Australian Bureau of Meteorology’s Severe Storm Archive are spatially and temporally incomplete and are therefore inadequate for developing a reliable climatology. In contrast, approximately 600 Automatic Weather Stations (AWS) around the country now produce 1-minute data records for several atmospheric variables (including wind speed and direction). These records offer a source of data that can be reliably analysed. However, analysis of these data presents challenges, primarily including, a) identifying the weather mode (e.g., convective, frontal, strong pressure gradients, pressure systems) responsible for each extreme gust, and b) overcoming the incomplete spatial coverage of the network. To overcome these challenges, this work utilises Self-Organizing Maps (SOM) as an automated method for classifying the mode of each observed gust, and then applies hierarchical Bayesian statistics to extend the analysis to regions where no AWS records exist. With the increasing use and acceptance of SOM algorithms for classifying atmospheric data, this machine learning technique was used to objectively identify severe wind storms from 1- minutre AWS data. The SOM algorithm was applied to a small subset of AWS stations so that the SOMs could be trained, and their performance verified. Given the large number of free parameters built into the SOM algorithm, it was first essential to conduct a proper sensitivity analysis to determine the set up for the SOM. Upon selecting the best combination of free parameters to run the SOMs, different combinations of atmospheric variables were explored, including: wind speed, change in wind direction, temperature, mean sea-level pressure, precipitation and equivalent potential temperature. Various statistical tools were used to determine how well the SOM algorithm was able to identify convective events compared to a manual identification of events. It was found that by considering wind speed alone, the SOM was able to perform well compared to methods that combine other variables such as temperature, pressure, and change in wind direction.

ii To extend this station-based analysis and facilitate the development of a spatially complete convective wind storm climatology across the Australian continent, observational and global reanalysis data are coupled to determine the probability of severe wind storms occurring in different parts of Australia, even where there is no observational data available. A Bayesian hierarchical framework was used to develop the relationship between the SOM identified AWS convective events and severe weather indices calculated from ERA-Interim reanalysis data, while minimizing the impact of the spatial and temporal biases inherit to the AWS data. Using this model, the expected number of severe wind storms occurring in all parts of Australia was estimated. The Bayesian model was run using data between 2005-2015 and showed that there are significantly more severe convective wind storms occurring in northern Western Australia, southern Northern Territory and western Queensland than observational datasets show. Resampling techniques minimised the effects of the short observational period and helped determine the index or indices that best relates the observational and reanalysis data. These relationships were then used to extend the length of the observed dataset over the entire ERA- Interim reanalysis period (1979-2015). The flexibility of the Bayesian Hierarchal model allows the ERA-Interim reanalysis data to be replaced by other global datasets, including global climate models. Here, the Bayesian model is run with CMIP5 data to estimate how the climatology of severe convective wind storms might change under different climate scenarios. The BOM-CSIRO ACCESS-CM 1.3 under the RCP8.5 scenario was used. Mean severe weather indices were calculated for the projection period of 2090-2100 and the historical period from 1990-2000. Using this global model input for the Bayesian model, the change in the severe convective wind storm event counts from 1990-2000 to 2090-2100 were examined. To understand potential changes to convective wind storm hazard under an Intergovernmental Panel on Climate Change (IPCC) climate change scenario, large-scale global climate model environmental parameters (i.e. CAPE, Wind Shear) used in the stochastic model to estimate convective wind storm frequency were studied. Running the stochastic model with these “changed” environments showed that an increase in the number of severe convective wind storms can be expected during the spring, summer, and autumn, especially over northern Western Australia, and Queensland. This resulting data can be used to generate hazard maps and stochastic event sets to inform wind- resistant design standards and facilitate risk-based decision making by government and industry.

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Declaration by author

This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis.

I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, financial support and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my higher degree by research candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award.

I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School.

I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis and have sought permission from co- authors for any jointly authored works included in the thesis.

Alessio Spassiani Doctor Matthew Mason January, 2020 January, 2020

Publications included in this thesis

No publications included.

Submitted manuscripts included in this thesis

No manuscripts submitted for publication.

Other publications during candidature Conference Abstracts

Spassiani, A.C., M. Mason, R.J. Krupar III, V. Cheng. “An Australian Climatology of Severe Convective Wind Storms Using Bayesian Hierarchical Modelling.” Oral presentation as part of the 29th Conference on Severe Local Storms, Stowe, VT., October 2018.

Spassiani, A.C., M. Mason, R.J. Krupar III. “Bayesian statistical approach for developing a convective wind storm climatology of Australia.” Oral presentation as part of the AMOS 2018 Conference, Sydney, NSW., February 2018.

Spassiani, A.C., M. Mason, R.J. Krupar III. “Estimating severe wind storm occurrence across Australia using Bayesian modelling.” Poster presentation as part of the ECSS 2017 Conference, Pula, Croatia., September 2017.

Spassiani, A.C., M. Mason, R.J. Krupar III. “A probabilistic method for estimate severe weather event occurrence frequency using Bayesian statistics.” Oral presentation as part of the AMOS 2017 Conference, Canberra, ACT., February 2017.

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Contributions by others to the thesis

This thesis is part of a larger project originally designed by Dr. Matthew Mason, titled “Characterising the hazard, structure and impacts of severe convective wind storms”.

Statement of parts of the thesis submitted to qualify for the award of another degree

No works submitted towards another degree have been included in this thesis.

Research Involving Human or Animal Subjects

No animal or human subjects were involved in this research.

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Acknowledgements

First and foremost, I would like to thank my parents, Angelina and Alessandro Spassiani, for all their love and support over the years, especially during my academic years abroad. Without them none of this would have been possible. I would also like to thank my siblings and their partners for always being there, Gian-Paolo and Elise Spassiani, Dr. Natasha Spassiani and Richard Pasquire, Lucas Spassiani and Alicia Marchini. Even though you were far away your support has meant a lot to me. I would have not gotten to the submission line without the help and support from the people I have met during my time at the University of Queensland (UQ). Especially without the help of my advisors, Dr. Matthew Mason and Dr. Richard Krupar III. Thank you both for your guidance and feedback throughout these four years. Thank you to the Wind Engineering Research group, Thomas Klöetzke, Ting Yang, Junwei Lyu, Razib Hussan and Nipun Mudiyanselage, for sitting and listening to me speak for countless hours about everything I did not understand. Thanks to all the friends I made during my time at UQ: Scott Lines, Marcello Llano, Denise Lotti, Thierry Bore, Carmen Gorska, Massi Rahbar Nodehi, Ryan Beecroft, Craig Heatherington, Nick Hutley, Mitchell Baum, and Nathaniel Deering. You have all helped to make rough patches during the past four years bearable. Thank you to Dr. Vincent Cheng for all of your help in teaching me about Bayesian statistical modelling. A very big thank you to my friends who generously, and probably ignorantly, said yes to reading through chapters of my thesis, Christopher Needles and Andrew Schwartz. I cannot ever repay you for that favour. I’ve have been lucky enough to meet some amazing people during my time living in Australia. Thank you to Kat Juergens, Bryce Kahlert, Shannon Lines, Adam Lines, Sean Gordon, and Gerard Gasparin for the fun times exploring Brisbane with me. Thank you to all of my friends back home in Canada and around the world for your support. And a very special thank you to those who came all the way to Australia to visit: Amanda De Monte, Justin Catania, Andrea Catania, Alice Wood, and Aitor Atencia. It meant a lot to have some familiar faces come say hello.

Financial support

This research was supported by the Australian Government through the Discovery Early Career Award (Award Number: DE150101347).

I acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC). Cette recherche a été financée par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG). (Application Number: PGSD3-502271-2017) Keywords

Climatology, Wind Storm, Self-Organising Maps, Bayesian Statistics, Climate Change, Australia. Australian and New Zealand Standard Research Classifications (ANZSRC)

ANZSRC code: 040105, Climatology, 50% ANZSRC code: 090599, Civil Engineering not elsewhere classified, 25% ANZSRC code: 961099, Natural Hazards not elsewhere classified, 25% Fields of Research (FoR) Classification

FoR code: 0905, Civil Engineering, 50% FoR code: 0401, Atmospheric Sciences, 50%

Dedications

This thesis is dedicated to my nephews and niece, Oliver, Gabriella, and Felipe. Wishing you all the success in pursuing what you love to do.

Abbreviations

AWS Automatic Weather Stations BMU Best Match Unit BOM Bureau of Meteorology BSS Brier Skill Score dCAPE Downdraft CAPE DMI Dry Microburst Index DVWS Deep Vertical Wind Sheer ECMWF European Centre for Medium-Range Weather Forecasts EL Equilibrium Level ERA-Interim European Reanalysis-Interim FFD Forward Flank Downdraft GUSTEX Gust Index LFC Level of Free Convection LFC-EL Height difference between the LFC and EL LI100 100hPa Lifted Index LI50 50hPa Lifted Index LIs Surface Lifted Index MAE Mean Absolute Error MBrst Microburst Index MCMP Microburst Composite Index MDPI Microburst Day Potential Index mlCIN Mixed Layer Convective Inhibition muCAPE Most Unstable Convective Available Potential Energy muCIN Most Unstable Convective Inhibition PDF Probability Density Function RCM Regional Climate Models RFD Rear Flank Downdraft sbCAPE Surface Based Convective Available Potential Energy SHERBE Severe Hazards In Environments with Reduced Buoyancy SHR6 0-6km Shear SigSev Significant Severe SOM Self-Organising Maps SRH1 1km Storm Relative Helicity SRH3 3km Storm Relative Helicity SSA Severe Storm Archive SST Sea Surface Temperature SVWS Shallow Vertical Wind Sheer SWI Severe Weather Indices SWS Severe Weather Section TeD Theta-E Deficit UD Updraft WBZ Wet Bulb Zero WINDEX Wind Index

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WMAE Weighted Mean Absolute Error WNDG Wind Damage Parameter

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Table of Content Front Matter

Abstract ...... ii

Declaration by author ...... iv

Publications included in this thesis ...... v

Submitted manuscripts included in this thesis ...... vi

Other publications during candidature ...... vii

Conference Abstracts ...... vii

Contributions by others to the thesis ...... viii

Statement of parts of the thesis submitted to qualify for the award of another degree ...... viii

Research Involving Human or Animal Subjects...... viii

Acknowledgements ...... ix

Financial support ...... x

Keywords ...... x

Australian and New Zealand Standard Research Classifications (ANZSRC) ...... x

Fields of Research (FoR) Classification ...... x

Dedications ...... xi

Abbreviations ...... xii

Table of Content ...... xiv

List of Figures ...... xix

List of Tables ...... xxvi

Chapter 1: Introduction ...... 29

1.1. Motivation ...... 30

1.2. Objective ...... 31

Chapter 2: Literature Review ...... 33

2.1. Meteorological Overview of Severe Wind Generating Systems ...... 34

2.1.1. Synoptic Weather Systems ...... 34

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2.1.2. Mesoscale Weather Systems ...... 38

2.1.3. Microscale Weather Systems ...... 44

2.2. Climates of Australia ...... 48

2.2.1. Air Masses...... 49

2.2.2. Seasonal Variability ...... 50

2.3. Thunderstorm Climatologies ...... 51

2.3.1. Observational Datasets Limitations ...... 51

2.3.2. Current Solutions ...... 52

2.3.3. Australian Thunderstorm Climatologies ...... 55

2.3.4. Australian Convective Wind Storm Climatologies ...... 58

2.4. Event Classification ...... 62

2.4.1. Statistically Identifying Events ...... 63

2.4.2. Meteorologically Identifying Events ...... 64

2.5. Convective Wind Storms and Climate Change ...... 66

2.6. Literature Summary ...... 69

Chapter 3: Classifying wind gust typologies using Self-Organising Maps...... 71

3.1. Introduction ...... 72

3.2. Data and methods ...... 74

3.2.1. Automatic Weather Station data and analysis...... 74

3.2.2. Extracting Wind Storms ...... 75

3.2.3. Quality Controlling 1-min Wind Storms ...... 77

3.2.4. Manual Event Classification for SOM Training ...... 78

3.2.5. Self-Organizing Maps ...... 82

3.2.5.1. Introduction to Self-Organizing Maps ...... 82

3.2.5.2. Input Variables and Preprocessing ...... 86

3.2.5.3. Assessing SOM performance ...... 88

3.2.5.4. Matching Events to SOM ...... 92

3.3. Results and Discussion ...... 94

3.3.1. SOM Sensitivity Analysis ...... 94

3.3.2. SOM Selection ...... 94

3.3.3. SOM Climatology ...... 100

3.4. Conclusions ...... 105

Chapter 4: Australian convective wind gust climatology using Bayesian hierarchical modelling ...... 107

4.1. Introduction ...... 108

4.2. Data and methods ...... 111

4.2.1. Observation Data ...... 111

4.2.2. Reanalysis Data ...... 114

4.2.3. Bayesian Hierarchical Model ...... 116

4.2.3.1. Observation Model ...... 117

4.2.3.2. Explanatory Model ...... 118

4.2.3.3. Parameter Model ...... 120

4.2.3.4. Model Performance ...... 120

4.3. Results and Discussion ...... 122

4.3.1. Model Comparison ...... 122

4.3.1.1. Autumn ...... 123

4.3.1.2. Winter ...... 126

4.3.1.3. Spring ...... 129

4.1.3.4. Summer ...... 132

4.3.2. Probability of Detection ...... 135

4.3.3. Climatologies ...... 137

4.3.3.1. 2005-2015 ...... 137

4.3.3.2. 1979-2015 ...... 147

4.4. Conclusion ...... 149

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Chapter 5: Climate Change Impacts on the Climatology of Convective Wind Storms in Australia ...... 151

5.1. Introduction ...... 152

5.2. Data and Methods ...... 154

5.2.1. ACCESS-CM Dataset ...... 154

5.2.2. Calculating Severe Weather Indices ...... 156

5.2.3. Bayesian Model ...... 157

5.2.4. Change in Climatology ...... 158

5.3. Results and discussion...... 159

5.3.1. Changes in Severe Weather Indices ...... 159

5.3.2. Change in Climatology ...... 168

5.4. Conclusion ...... 173

Chapter 6: Conclusions and Recommendations ...... 175

6.1. Summary and Significance of Findings ...... 176

6.1.1. Objective 1 ...... 176

6.1.2. Objective 2 ...... 177

6.1.3. Objective 3 ...... 178

6.2. Recommendations and Areas for Future Research ...... 178

References...... 181

Appendix A: Severe Weather Indices Descriptions ...... 209

A.1. Downdraft CAPE (dCAPE) ...... 210

A.2. Dry Microburst Index (DMI) ...... 210

A.3. LFC-EL Height (LFC-EL) ...... 210

A.4. GUSTEX ...... 211

A.5. Lifted Index (Surface, 50hPa, 100hPa) ...... 211

A.6. Microburst Composite (MCOMP) and Microburst Index (MBurst) ...... 212

A.7. Microburst Day Potential Index (MDPI) ...... 212

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A.8. Most Unstable CAPE (muCAPE) ...... 213

A.9. Most Unstable CIN (muCIN) ...... 213

A.10. Significant Severe (SigSev) ...... 213

A.11. SHERBE ...... 214

A.12. Theta-E Deficit (TeD) ...... 214

A.13. Storm Relative Helicity (1km, 3km) ...... 214

A.14. Wet-Bulb Zero (WBZ) ...... 215

A.15. WINDEX ...... 215

A.16. Wind Damage Parameter...... 216

A.17. Wind Shear (Shr6, DVWS, SVWS)...... 216

Appendix B: Additional Bayesian Results...... 243

B.1. Introduction...... 244

B.2. Autumn-Winter ...... 245

B.3. Spring-Summer ...... 246

B.4. Year ...... 249

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List of Figures

Figure 2.4: An idealised atmospheric sounding, showing areas of CAPE and CIN. The summation of the areas between the temperature profile (solid red line) and the air parcel trajectory (solid black line) is equivalent to the values of CAPE and CIN. (The COMET Program, 2006). ………………………………………………….40

Figure 2.5: A vertical cross-section of a typical evolution of a multi-cell thunderstorm. (Markowski and Richardson, 2010). ……………………………………………..41

Figure 2.6: The mature stage of a supercell thunderstorm in the northern hemisphere, where the FFD is the Forward Flank Downdraft, the RFD is the Rear Flank Downdraft, and UD is the Updraft. (Lemon and Doswell, 2010). ………………………...…..42

Figure 2.7: Vortex lines demonstrating how a tornado can form when (a) there is no pre-existing vertical vorticity at the surface and a downdraft is needed to aid in the formation of vertical vorticity at the ground and (b) when pre-existing vertical vorticity is present at the ground and convergence along can result in the generation of a tornado. (Markowski and Richardson 2010). ………………………………………….…..45

Figure 2.8: The five regions of a tornado vortex. (Markowski and Richardson, 2010). ………46

Figure 2.9: Cross-section of a microburst (Markowski and Richardson, 2010). ...……………48

Figure 2.11: From Dowdy and Kuleshov (2014) showing the remotely sensed ground-flash lighting observation density (flashes km-2year-1) for the period 2005-2015. …..57

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(22/3–21/9). Adapted from Geerts and Noke-Raico (1995). (e) Total density of Bureau STA sourced tornado reports from 1795 to 2014, aggregated on a 75 × 75 km grid and overlaid with point report locations. (f) Reanalysis of observed tornadoes in Australia from historical archives gridded analogously to panel e for the period 1795–1910 (Allen and Allen, 2014). ……………………..……….…61

Figure 3.1: The 306 AWS across Australia examined for this work. The size of the marker indicates the periods of good data in years and the colour indicates the number of 6-hourly wind storms above 70 km h-1 per year at each station. ……………...... 74

Figure 3.2: Example of 1-min data during different type severe wind storms where (a) is representative of a wind only event, (b) is during frontal rain band or transition event, (c) would be considered a convective event and (d) a general event. ….....79

Figure 3.4: Illustrates the different possible inputs for some of the free parameters that can be specified for the SOM. This includes the use of a (a) hexagon lattice or a (b) square lattice, whether the neighbourhood function is (c) bubble, (d) Gaussian, (e) cut Gaussian, or (f) Epanechicov, and how (g) the learning rate changes as a function of the number of steps or training length. (adapted from Kohonen, 2001).……..85

Figure 3.5: Proportion of SOM training database with each storm mode classification. ……...90

Figure 3.6: The observed convective wind storm counts, above 70 km h-1, at the 13 training stations compared to the expected counts calculated for the W-D-T-P-P 4X4 SOM and the W-T-P 4X4 SOM using the four different counting methods. ………..….95

Figure 3.7: The Sammon map for the 4x4 W-T-P SOM where the axes describe the distances between the nodes from each other in variance scaled values. …………………...97

Figure 3.8: The 4x4 SOM for the Wind-Temperature-Pressure variable combination. The solid blue line shows the average normalised wind speed over the 4 hr period for each node. The grey lines show the normalised wind speed values for each event from the 13 training stations that were sorted into the node. The dotted orange line shows the mean normalised pressure for the node, while the dash orange line shows the mean normalised temperature for the node. The hits above each node shows the number of events that contribute to each node. ………………………...... ……...98

Figure 3.9: The number of each event type that falls into the nodes for the 4x4 Wind- Temperature-Pressure SOM. The left y-axis gives the count of the wind storm types while the right y-axis shows the percentage difference of each event type in the node when compare compared to the overall event counts for the events from the 13 stations used to train the SOMs. ..………………………………………...99

Figure 3.10: Yearly average expected convective wind storm counts above 70 km h-1 for the 4X4 Wind-Temperature-Pressure SOM using the 1st and 2nd counting methods for (a) the entire year, (b) spring, (c) summer, (d) autumn, and (e) winter. …….102

Figure 3.11: Yearly average expected convective wind storm counts above 90 km h-1 for the 4X4 Wind-Temperature-Pressure SOM using the 1st and 2nd counting methods for (a) the entire year, (b) spring, (c) summer, (d) autumn, and (e) winter. …….103

Figure 3.12: Shows the yearly average expected convective event counts, over the entire year, at each station as determined by the 4X4 W-D-T-P-P SOM for (a) events above 70 km h-1 and (b) events above 90 km h-1. ……………………………………..104

Figure 3.13: (a) shows the average annual thunder-day map of Australia (Kuleshov et al., 2002)) and (b) the 2000 years return period for non-cyclonic gust (m s-1) for Australia (Wang et al, 2013). ……………………………………………….…105

Figure 4.1: Number of days with at least one convective event observed within a grid cell between 2005 and 2015 for southern hemisphere a) autumn, b) winter, c) spring, d) summer………………………………………………………………………112

Figure 4.2: Mean yearly AWS density for each grid cell over Australia from 2005-2015. ….113

Figure 4.3: Shows the distributions of the two chains for the (a) WNDG model and the (b) MDPI model. The first column is a0, the second a1, the third αStationD and the fourth βStationD. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively. ………………….……...125

Figure 4.4: Shows the distributions of the two chains for the (a) WNDG model and the (b) DMI model (c) is Li100-Shr6 model and (d) is the WINDEX model. For the 1 index models the first column is a0, the second a1, the third αStationD and the fourth βStationD. For the two index models the first column is a0, the second a1, the third is a2, the fourth is αStationD and the fifth is βStationD. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively...... 128

Figure 4.5: Shows the distributions of the two chains for the (a) LiSfc-Shr6-lfcel model and the (b) LiSfc-SVWS-lfcel model. The first column is a0, the second a1, the third is a2, the fourth is a3, the fifth αStationD and the sixth βStationD. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively. …………………………………………………………....131

Figure 4.6: Shows the distributions of the two chains for the (a) Li100-Shr6-dCAPE model and the (b) LiSfc-Shr6-dCAPE model and (c) Li100-SVWS-dCAPE. The first column is a0, the second a1, the third is a2, the fourth is a3, the fifth αStationD and the sixth βStationD. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively. …………………….…...134

Figure 4.7: The probability of detection (POD) curves for the models that appear to perform the best for each season. Where the blue-square curve shows the POD for the MDPI model in autumn, the orange-triangle curve shows the POD for the Li100- Shr6 model for winter, the grey-circle line shows the POD curve for the Li100-

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SVWS-dCAPE curve for summer, and the green- circle line shows the POD curve for the LiSfc-SVWS-lfcel for spring……………………………………….…..136

Figure 4.8: Output from the MDPI autumn model from 2005-2015 for (a) the mean expected number of days on which at least one convective event (Elatent) will occur within a grid cell (0.75°X0.75°), (b) the standard deviation of Elatent, (c) the mean probability of detection (POD) at each grid cell, (d) the standard deviation of POD, (e) the mean conditional autoregressive (CAR) term at each cell, and (f) the standard deviation of CAR………………………………………………….….138

Figure 4.9: Output from the Li100-Shr6 winter model from 2005-2015 for (a) the mean expected number of days on which at least one convective event (Elatent) will occur within a grid cell (0.75°X0.75°), (b) the standard deviation of Elatent, (c) the mean probability of detection (POD) at each grid cell, (d) the standard deviation of POD, (e) the mean conditional autoregressive (CAR) term at each cell, and (f) the standard deviation of CAR……………………………..…..….140

Figure 4.10: Output from the LiSfc-SVWS-lfcel spring model from 2005-2015 for (a) the mean expected number of days on which at least one convective event (Elatent) will occur within a grid cell (0.75°X0.75°), (b) the standard deviation of Elatent, (c) the mean probability of detection (POD) at each grid cell, (d) the standard deviation of POD, (e) the mean conditional autoregressive (CAR) term at each cell, and (f) the standard deviation of CAR……………………………………142

Figure 4.13: Shows the percentage of events that occur in the four seasons (a) autumn, (b) winter, (c) spring, (d) summer………………………………………….…...…146

Figure 4.14: Shows the climatology for the number of days with a severe convective wind storm above 90 km h-1 per year between 1979-2015 for (a) autumn (MDPI- Autumn model), (b) winter (Li100-Shr6-Winter model), (c) spring (LiSfc-SVWS- lfcel-Spring model), and (d) summer (Li100-SVWS-dCAPE)-Summer model) using the mean values of the indices calculated using ERA-Interim data between 1979-2015…………………………………………………………………..…148

Figure 5.1: Mean MDPI values for autumn for (a) the historical period (1990-2000) and (b) the projected RCP8.5 period (2090-2100). ……………………………………...…159

Figure 5.2: Difference in MDPI for autumn between RCP8.5 scenario (2090-2100) and the historical period (1990-2000). …………………………………………………160

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Figure 5.3: Mean Li100 values for winter for (a) the historical period (1990-2000) and (b) the projected RCP8.5 period (2090-2100) and the mean Shr6 for (c) the historical period (1990-2000) and (d) the projected RCP8.5 period (2090-2100)………….161

Figure 5.4: Difference in (a) Li100 and (b) Shr6 for winter between RCP8.5 scenario (2090- 2100) and the historical period (1990-2000)…………………………………….162

Figure 5.5: Mean LiSfc values for spring for (a) the historical period (1990-2000) and (b) the projected RCP8.5 period (2090-2100), the mean SVWS for (c) the historical period (1990-2000) and (d) the projected RCP8.5 period (2090-2100), and the mean lfcel for (e) the historical period (1990-2000) and (f) the projected RCP8.5 period (2090- 2100)………………………...……………………………………..………...…163

Figure 5.6: Shows the difference in (a) LiSfc, (b) SVWS, and (c) lfcel for spring between RCP8.5 scenario (2090-2100) and the historical period (1990-2000)……….….164

Figure 5.8: Shows the difference in (a) Li100, (b) SVWS, and (c) dCAPE for summer between RCP8.5 scenario (2090-2100) and the historical period (1990-2000)…….…….167

Figure 5.11: The change in the most unstable CAPE calculated using ACCESS-CM 1.3 during the summer months (December-February) between the periods of 2090-2100 and 1990-2000. …………………………………………………………………....172

Figure A.1: Mean Downdraft CAPE (dCAPE) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 217

Figure A.2: Mean Dry Microburst Index (DMI) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 218

Figure A.3: Mean LFC-EL Height (LFC-EL) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 219

Figure A.4: Mean GUSTEX calculated between 2005-2015 for a) the entire year, b) spring- summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer. .... 220

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Figure A.5: Mean Surface Lifted Index (LiSfc) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 221

Figure A.6: Mean 50hPa Lifted Index (Li50) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 222

Figure A.7: Mean 100hPa Lifted Index (Li100) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 223

Figure A.8: Mean Microburst Composite (MCOMP) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 224

Figure A.9: Mean Microburst Index (MBURST) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 225

Figure A.10: Mean Microburst Day Potential Index (MDPI) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 226

Figure A.11: Mean most unstable CAPE (muCAPE) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 227

Figure A.12: Mean Convective Inhibition (CIN) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 228

Figure A.13: Mean Significant Severe (SigSev) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 229

Figure A.14: Mean SHERBE calculated between 2005-2015 for a) the entire year, b) spring- summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 230

Figure A.15: Mean Theta-E Deficit (TeD) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 231

Figure A.16: Mean 0-1km Storm Relative Helicity (SRH1) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 232

Figure A.17: Mean 0-3km Storm Relative Helicity (SRH3) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 233

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Figure A.18: Mean Wet Bulb Zero (WBZ) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 234

Figure A.19: Mean WINDEX calculated between 2005-2015 for a) the entire year, b) spring- summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 235

Figure A.20: Mean Wind Damage Parameter (WNDG) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 236

Figure A.21: Mean 0-6km Shear (SHR6) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 237

Figure A.22: Mean Deep Vertical Wind Shear (DVWS) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 238

Figure A.23: Mean Shallow Vertical Wind Shear (SVWS) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer...... 239

Figure B.1: Shows the distributions of the two chains for the (a) MCMP model and the (b) WNDG model. The first column is a0, the second a1, the third αStationD and the fourth βStationD...... 246

Figure B.2: Shows the distributions of the two chains for the (a) LiSfc -Shr6-TeD model and the (b) muCAPE-Shr6-TeD model. The first column is a0, the second a1, the third a2, the fourth is a3, the fifth αStationD and the sixth βStationD...... 248

Figure B.3: Shows the distributions of the two chains for the (a) MCMP model and the (b) Li100-Shr6- SRH3model (c) is Li50-Shr6- TeD model (d) is the Li50-Shr6- dCAPE model (e) is the muCAPE-Shr6-SRH3 (f) is the LiSfc-SVWS-TeD model and (g) is the Li100-SVWS-SRH3 model. For the 1 index models the first column is a0, the second a1, the third αStationD and the fourth βStationD. For the three index models the first column is a0, the second a1, the third is a2, the fourth is a3, the fifth is αStationD and the sixth is βStationD...... 250

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List of Tables

Table 3.1: POD and FAR for different combinations of N and Cspike...... 78

Table 3.2: The SOM models and sizes with well organised Sammon maps that performed best according to the metric used to assess their performance...... 91

Table 3.3: The MAE (counts) and WMAE (%) for the SOM models shown in Table 3.2 using the four different methods for counting the number of expected convective events above 70 km h-1 ...... 93

Table 4.1: List of the indices used in the Bayesian explanatory models Section 4.2.3.2...... 115

Table 4.2: List the models for autumn that converged according to the Gelman-Ruben score, along with Total CAR value for each model, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of the metrics...... 124

Table 4.3: The two autumn models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 124

Table 4.5: The four winter models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 127

Table 4.6: List the models for spring that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of each metric...... 130

Table 4.7: The two spring models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 131

Table 4.8: List the models for summer that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of the metrics...... 133

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Table 4.9: The five summer models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 134

Table 4.10: Shows the mean and standard deviation (StdDev) values for the ∝StationD, βStationD parameters for each of the models that perform the best for the four seasons...... 135

Table 5.1: List of indices used to explain the rate of severe convective wind occurrence in the Bayesian model. Indices calculated using the SHARPpy package are noted...... 156

Table A.1: The 76 explanatory models used and the severe weather indices used for each model. …………………………………………………………………………...240

Table B.2: The five autumn-winter models with the percent difference for the three metrics less than 20% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 246

Table B.4: The five spring-summer models with the percent difference (Δε) for the three metrics less than 20% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 247

Table B.6: The five year models with the percent difference for the three metrics less than 20% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models...... 249

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Chapter 1: Introduction

Introduction Chapter 1

1.1. Motivation

Weather and climate have a high impact on global infrastructure. Munich Re (2016) reports that more than 94 percent of all disasters are linked to severe weather events such as floods, cyclones or local convective storms. Severe convective wind storms (i.e. thunderstorm outflows) alone are responsible for billions of U.S. dollars of damage to global infrastructure each year (Munich Re, 2014). More specifically to Australia, 50% of all wind related damage to buildings are caused by local convective wind storms (Blong, 2005). While damage can occur to new and old structures, alike, the continued occurrence of damage suggests that there may be deficiencies in the way structures are designed to withstand these types of wind storms. A key reason for this is that the hazard associated with convective wind storms are poorly understood and convective wind storms are not explicitly designed for in most wind-resistant design standards. A better understanding of the risk convective wind storms pose to infrastructure in Australia is therefore necessary to properly mitigate the impacts of future events. A major component of this is to understand when, where, and how often these events occur so that convective wind storm hazard maps can be developed. When wind engineering was an emerging field of research two types of wind storm were suggested to be of engineering importance (tropical or extratropical cyclones and convective thunderstorms or frontal squalls) (Davenport, 1960). However, despite this wind-resistant design only assumes stationary large-scale storms to be representative of design wind storms around the globe. This is problematic for two reasons. Firstly, Holmes (2002) shows that convective and synoptically driven wind storms produce different exceedance probability curves. As such, unless these different wind storms are treated separately, inappropriate levels of risk will be assumed for any given gust wind speed. Secondly, the spatio-temporal structure of these two types of wind storm, and potentially any sub-classes of storm within them, are vastly different (Letchford et al., 2002). In the 1980s, large-scale observational programs were undertaken in the U.S.A. to systematically characterise the structure of convective wind storms (e.g. Fujita, 1981; Wilson et al., 1984; Hjelmfelt, 1988; Atkins and Wakimoto, 1991; Wakimoto, 2001). Despite showing the stark differences between convective and synoptic wind storm structure, the resolution of this data was inadequate for describing wind characteristics (i.e. mean and variance at a point) in a manner useful to structural engineers. More recent research has been able to obtain new information on thunderstorm outflow wind profile evolution (Gunter and Schroeder, 2015), as well as, structural details of the wind flow within tornadoes (e.g., Wurman et al., 2013) through

Introduction Chapter 1 the use of mobile research Doppler radars. Gunter and Schroeder (2013) looked at three outflow events and noted significant variations between the events and in the evolution of the instantaneous dual-Doppler wind speed and direction profiles. The limited number of events studied, along with the significant variation between individual storm structures, highlights the difficulty in characterising the structure of convective wind storms. Less work has been undertaken to quantify the regional importance of convective wind storms, particularly in Australia. From an engineering point of view, this is as important as understanding the evolution and structure of the wind. A solid understanding of the hazard convective wind storms pose ensures design methods derived for dealing with them are applied in areas where they are of the greatest risk. Convective wind storm reports can be found in peer-reviewed literature (e.g., Kuleshov et al., 2016) or in the Bureau of Meteorology’s (BOM) Severe Storm Archive (SSA; BOM, 2015), but incomplete datasets of storm reports make it difficult to get a complete geographical picture of the convective wind storm hazard. Some research has used large-scale environmental parameters to fill the gaps in the observational dataset (e.g., Brooks et al., 2003; Allen et al., 2011), but this method, thus far, has not provided the detailed information on wind speed frequency and severity required by engineers for design. Individual anemometer records can be used to get information on wind speed frequency and severity at a location (Holmes, 2002; Wang et al., 2013), but a uniform national assessment of convective wind storm hazard cannot be made from this dataset alone due to the sparsity of wind observations. A similar issue exists when estimating the wind hazard associated with tropical cyclones, but in that case stochastic event-based modelling techniques have been developed to overcome such data limitations (e.g., Harper, 1999; Vickery et al., 2009). These use large-scale environmental parameters to complement statistical analysis of observations to develop spatially complete estimates of wind hazard risk. A similar approach is adopted in this thesis to define convective wind storm risk in a spatially complete manner across Australia. 1.2. Objective

The main objective of this research is to develop a convective wind gust climatology for Australia. Greater confidence in the estimates of the expected maximum gust wind speed in areas known to be dominated by convective wind storms is required so that appropriate design wind speeds can be defined in these regions. This research seeks to provide estimates of the frequency of convective wind hazard in areas where observations exist, but also extend this to areas with little to no direct observational data. Further, it will explore how large-scale changes to the climate might impact convective wind storm hazard across Australia. This work expands

Introduction Chapter 1 limited existing research that explores relative convective storm risk across Australia using large-scale weather and climate information (i.e. reanalysis data), but more directly applies this to wind hazard assessment and the generation of information useful for engineering design. The research presented in this thesis can be broken up into three main aims: 1) Develop an objective and automated method for the identification of convective wind gusts from 1-minute Automatic Weather Station (AWS) data records. In particular, this approach must identify events from records measured in regions of mixed wind climate and be able to classify the meteorological phenomena responsible for the event. 2) Create a spatially complete climatology of severe convective wind storms across Australia that accounts for spatio-temporal biases and limitations in observational records. 3) Explore how the severe convective wind storm climatology of Australia might change under expected climate change scenarios. This thesis is laid out as follows. Chapter 2 provides a detailed literature review that gives background information on the current understanding of different types of convective wind storms. It discusses existing climatologies of severe convective storms in Australia, as well as the limitations associated with these climatologies. Moreover, it highlights the gaps that still exist with respects to the understanding of severe convective wind storms, which this thesis looks to address. The next three chapters look at addressing each of the three aims listed above. Chapter 3 examines the use of the machine learning technique of Self-Organising Maps as a new method to identify convective wind gust from 1-minute AWS data. Chapter 4 utilises Bayesian statistical modelling to build a spatial complete climatology of severe convective wind gusts in Australia using AWS data and ERA-Interim reanalysis data while limiting biases inherit to the AWS observations. Chapter 5 looks at using the models developed in chapter 4 to develop an understanding of how the climatology of severe convective wind gusts in Australia may change under the IPCC RCP8.5 climate scenario. These three chapters each have their own introduction that discusses the current work and limitations related to the particular aim of the chapter and how it will be addressed. This is then followed by a detailed methodology used to achieve the aim of the chapter. The results are given and discussed in detail and finally the findings and their significance are summarised in the conclusion of the chapters. Chapter 6 concludes the thesis by summarises the main outcomes of each of these chapters and detailing how these outcomes can be used to advance future research related to understanding the risk and hazard associated with severe convective wind storms in Australia and globally under both current and future climate. 32

Chapter 2: Literature Review

Literature Review Chapter 2

2.1. Meteorological Overview of Severe Wind Generating Systems

The Bureau of Meteorology (BOM) defines a severe wind storm to be one that has a wind gust of 90 km h-1 or more. Several different weather phenomena generate severe wind gusts. These events can be broken down into broad categories based on their scale. This includes synoptic, mesoscale, and microscale events (Markowski and Richardson, 2010). In wind engineering, events are typically broken down into large-scale stationary events and non- stationary events (Davenport, 1960). It is important to also note that smaller-scale phenomena (i.e., supercells) can be embedded within a large-scale system such as extratropical cyclones that produce tornadoes (Lin and Smith, 1979) as well as tropical cyclones that can produce tornadoes (Edwards, 2012). Current understanding of these different scale events and the weather phenomena associated with them are described in this section. 2.1.1. Synoptic Weather Systems In meteorology synoptic refers to large-scale atmospheric disturbances. These weather systems tend to be on the order of several hundred kilometres to several thousand kilometres in size. Moreover, they have lifetimes of a few days up to a week or more. They include high- and low-pressure systems, extratropical cyclones, and can even include tropical cyclones. Although these large systems are complex to explain mathematically, scale analysis is a technique often used to simplify the governing equations, i.e., the momentum equation (Eqn. 2.1), the continuity equation (Eqn. 2.2), and the thermodynamic equation (Eqn. 2.3) for a particular type of motion:

퐷풗 = − 1 ∇푝 − 푔풌 − 푓풌 × 풗 + 푭풓 = 0 , (2.1) 퐷푡 휌

퐷휌 + 휌∇ ∙ 푣⃗ = 0 , (2.2) 퐷푡

퐶 퐷휃 = 휃 푄̇ , (2.3) 푝 퐷푡 푇

Where, 푡 is time, 풗 is the wind speed, 푝 is pressure, 휌 is the density of air, 푔 is the mean gravitational acceleration, 푓 is the Coriolis force, 풌 is the three dimensional unit vector, 푭풓 is the friction vector, 휃 potential temperature, 푄̇ is the entropy, 푇 is temperature, and 퐶푝 is the specific heat capacity of air at constant pressure. The momentum equation, in terms of

Literature Review Chapter 2 meteorology, explains the motion of an air parcel of unit mass on a rotating sphere. It states that the change in position of a parcel of air in the troposphere is equal to the summation of the pressure gradient force, Earth’s gravitational pull, the Coriolis force, and friction. Similarly, for meteorology the continuity equation states that air cannot be created or destroyed in the troposphere. Moreover, it explains that the rate of change of mass in a volume can only occur through 3-D convergence or divergence. The thermodynamic equations explain the conservation of energy, stating that heat added (removed) to (from) an air parcel goes into the increase (decrease) in internal energy as well as into work done on the surrounding air through expansion (compression). Scale analysis works by defining characteristic scales of the field variables based on observations and removing variables that are of orders of magnitudes smaller than the other variables within the equations. On the synoptic scale, several terms (e.g., vertical acceleration) in the governing equations can safely be ignored since they are insignificant on this scale compared to other terms, i.e., the pressure gradient force and Coriolis force. Extratropical cyclones form in the mid and high latitudes. The development of an extratropical cyclone occurs when a pre-existing vorticity maximum aloft interacts with a pre- existing low-level baroclinic zone, resulting in surface cyclogenesis (Petterssen, 1939; Petterssen and Smebye, 1971). A baroclinic atmosphere refers to an atmosphere in which density is a function of both pressure and temperature. Therefore, a surface of constant pressure would intersect with a surface of constant density. Baroclinic instability is a wave instability that is related to the vertical shear of the mean flow. This instability increases as it converters potential energy from the mean horizontal temperature gradient. Diabatic heating can also play an important role in the development of extratropical cyclones, where latent heat release can provide a local source of available potential energy (APE) in the presence of enhanced baroclinic zones ( Krishnamurti, 1968; Johnson and Johnson, 1970; Johnson et al., 1976). Extratropical cyclones have fronts associated with them (Bjerknes, 1919) that can be thought of as transition layers with discontinuities in temperature and velocity (Palmén, 1948) and even moisture (Wallace and Hobbs, 2006). Surface fronts are known to provide an environment conducive to the generation of mesoscale instabilities (Dorian et al., 1988) and observational studies have shown a strong relationship between the formation of some convective storms and the diagnosed surface frontogenesis (Berry and Bluestein, 1982; Koch, 1984). Frontogenesis refers to the process in which fronts are generated (Holton, 2004) and has been shown to enhance the vertical velocities and initiate convection (Koch and McCarthy, 1982).

Literature Review Chapter 2

Figure 2.1: Schematic of the conveyor-belt model developed by Carlson (1980) showing the Cold Conveyor Belt (CCB), warm conveyor belt (WCB) and the dry conveyor belt (DCB). (The COMET Program, 2014) Carlson (1980) developed the conveyor-belt conceptual model of extratropical cyclones. In this model, three airstreams are described, the dry conveyor belt, the warm conveyor belt, and the cold conveyor belt (Figure 2.1). The warm conveyor belt and the cold conveyor belt are two regions where strong low-level winds can occur (Martínez-Alvarado et al., 2012). The warm conveyor belt is an extensive region of relatively strong surface winds located in the warm sector of the cyclone, south of the storm centre (in the northern hemisphere) and can persist through most of the cyclone’s life cycle. During the mature stage of an extratropical cyclone, the cold conveyor belt can produce strong surface winds when it curves around the cloud head. A third region has also been identified as a localised region of strong winds, the ‘sting jet’ (Browning, 2004). Sting jets are defined as accelerating drying winds that descend from the cloud head in the mid-troposphere toward the top of the boundary layer, which conserves wet-bulb potential temperature (Martinez-Alvarado et al., 2012). Moreover, momentum from the sting-jet can be transferred to the surface via boundary layer processes, such as turbulent mixing. However, sting jets are not frequent, as suggested by statistical studies (Parton et al., 2010; Martínez-Alvarado et al., 2012). The structure of the winds

Literature Review Chapter 2 associated with extratropical cyclone differ from those associated with systems that develop in the tropics. Another type of synoptic system considered by wind engineers are tropical cyclones. While these storms are usually not considered to be of synoptic scale with respect to meteorology, the wind profile for tropical cyclones are treated the same as extratropical cyclones for wind engineering purposes. A tropical cyclone is defined as a low-pressure system that forms over a tropical ocean and has a closed circulation (Glickman, 2000). The main energy source of a tropical cyclone is through the latent heat release of water vapour (Gray, 1968). Conditions necessary, but not sufficient, for the formation of a tropical cyclone include: a sea surface temperature (SST) greater than 26.5°C, a large enough Coriolis force to allow for low-level convergence to generate relative vorticity, weak vertical wind shear of the horizontal wind and the presence of an existing disturbance ( Gray, 1968; Emanuel, 1989; Zehr and Milton, 1992; DeMaria, 1996). Tropical cyclones consist of a warm-core vortex (Elsberry, 1995) with winds that are cyclonic throughout most of the system except near the top of the storm where they become anticyclonic (Frank, 1977; Emanuel, 2003). Maximum ascent in a tropical cyclone occurs in the eyewall, a ring of deep convective clouds near the centre of the storm where the radius of maximum winds is found (Emanuel, 2003). A well-developed tropical cyclone will have an eye (a nearly cloud-free region in the centre of the storm), where air slowly subsides (Emanuel, 2003). Figure 2.2 shows a cross-section of an idealised tropical cyclone and summarised the motion and energy cycle through a tropical cyclone TC.

Figure 2.2: An idealised radial cross-section of a tropical cyclone depicting the flow through the cyclone, contours of equivalent potential temperature on the left, θe (red dashed contours) and azimuthal wind speed (black solid contours) and angular momentum (blue solid contours) on the right (Wallace and Hobbs, 2005). The strongest surface winds in a tropical cyclone can be found to the right (left) of the cyclone, following the storm’s motion, in the northern hemisphere (southern hemisphere). Most simply, this is a result of the sum of the motion vector and the circulation of the cyclone

Literature Review Chapter 2

(Kepert, 2010). Moreover, winds tend to increase toward the centre of the cyclone with the radial surface winds strongest just outside the eyewall of the tropical cyclone and nearly zero at the eyewall, while the tangential component of the wind is strongest at the eyewall itself (Wallace and Hobbs, 2006). The wind speeds increase towards the centre of the cyclone as a result of the advection of angular momentum by the frictional inflow, maintaining strong near- surface winds (Kepert, 2010). This effect is strongest where both the inflow and radial gradient of angular momentum are the strongest, near the eyewall. While tropical cyclones have been discussed here under synoptic weather systems, to be consistent with the two main groups of weather systems considered by wind engineering, it is important to note that there are significant mesoscale processes and features that take places within these types of systems. For example, mesovortices can exists within the eyewall of tropical cyclones. They are known to have strong wind anomalies that can increase the potential for wind damage if they are extended to the ground (Kepert, 2010). 2.1.2. Mesoscale Weather Systems The term mesoscale was introduced in the 1940s to describe weather phenomena smaller than the synoptic scale but larger than the microscale (phenomena with scales less than a few kilometres, like tornadoes, dust devils, and turbulence). For mesoscale systems, the full complexity of the governing equations (Eqns. 2.1, 2.2, 2.3) must be considered (Doswell, 1987). Unlike extratropical cyclones that are almost solely driven by baroclinic instability, mesoscale systems can be topographically forced or driven by a combination of instability (e.g., thermal instability, symmetric instability, and barotropic instability). Thermal instability is a type of instability that can be generally described as an instability that occurs when a parcel of air is warmed to a point when it becomes positively buoyant compared to the surrounding environmental air and rises. Symmetric instability is a two-dimensional form of baroclinic instability that results if a parcel is displace along a slantwise path, instead of just vertically or horizontally, even if conditions for static (vertical) and inertial (horizontal) stability are satisfied individually. Unlike a baroclinic atmosphere, a barotropic atmosphere is one in which density is a function of pressure alone. This means that the temperature field is uniform on a pressure surface and therefore, there is no temperature advection on a pressure surface. Like baroclinic instability, barotropic instability is also a wave instability that grows by extracting kinetic energy from the mean-flow field.

Literature Review Chapter 2

The dominant instability, for any given day, is dependent on the local state of the atmosphere, which can be driven by synoptic scale motions (Markowski and Richardson, 2010). The mesoscale includes thunderstorms (single-cell, multicellular, and supercellular) and other convective systems known as mesoscale convective systems (MCSs). There are three necessary conditions for thunderstorms to occur: moisture, instability, and a trigger (Doswell et al., 1996; Doswell, 2001). The lifecycle of a single-cell thunderstorm is shown in Figure 2.3, where the thunderstorm initiates, becomes mature and precipitates, and then dissipates as the precipitation and downdraft suppress the updraft.

Figure 2.3: The three stages of an ordinary cell thunderstorm: (a) towering cumulus stage, (b) mature stage, (c) dissipating stage (Markowski and Richardson, 2010 [adapted from Byers and Braham, 1949]). For a thunderstorm to initiate, an air parcel must reach the level of free convection (LFC; Appendix A.3) through some sort of lift/trigger, and subsequently remain positively buoyant over a significant vertical depth. The LFC is the level at which a lifted air parcel becomes warmer than the surrounding environmental temperature and is therefore positively buoyant. The presence of low-level moisture has been shown to lower the height of the LFC (Crook et al., 1989) and leads to larger values of convective available potential energy (CAPE; Appendix A.8), which is a measure of the vertical integration of buoyancy, and lower values of convective inhibition (CIN; Appendix A.9), which is a measure of stability near the surface to the LFC (Davies, 2002). Figure 2.4 shows an idealised atmospheric sounding, where CAPE and CIN can be calculated from the areas highlighted in orange and blue respectively. CAPE values below 1000 Jkg-1 signify weak instability whereas values greater than 2500 Jkg-1 refers to strong instability (Markowski and Richardson, 2010). CIN values less than 10 Jkg-1 are

Literature Review Chapter 2

considered to be weak while values greater than 50 Jkg-1 are large and may impede thunderstorm development (Markowski and Richardson, 2010). The release of latent heat from low-level moisture is a good source of energy for thunderstorms, and it is important this source of energy is available through a large depth of the atmosphere (e.g., Austin, 1948; Byers and Hull, 1949; Chalker, 1949; Braham, 1952). Therefore, the presence of low-level moisture as well as instability is essential for convection to initiate. However, these two conditions are not always sufficient.

Vertical wind shear, the vector difference between the winds at two levels of the atmosphere, while not a necessary condition for convective initiation, plays an important role in defining the type of storm that will form. The presence of vertical wind shear can result in a thunderstorm being severe, where a severe thunderstorm is defined by the Bureau of Meteorology as a thunderstorm which produces large hail (2 cm in diameter or greater), damaging wind (90 km h-1 or greater), tornadoes, and/or heavy rainfall conducive to flash flooding. Vertical wind shear can promote storm organisation and longevity by reducing the interference of precipitation and outflow with the updraft by displacing them further away from the updraft as the shear increases. In addition, the development of dynamic vertical pressure

Literature Review Chapter 2 gradients can lead to the lifting of environmental air along the gust front and trigger new cells (i.e., multicell convection) (Markowski and Richardson, 2010). However, too much shear in environments with little instability and a weak updraft can be unfavourable for thunderstorm development. Figure 2.5 shows the idealised life-cycle of a multicellular thunderstorm that results from the presence of moderate 0 to 6 km vertical wind shear (Shr6; Appendix A.17) (approximately 10-20 m s-1) where cell 1 is the oldest cell in the system and 4 and 5 are newer cells initiated by the gust front of older cells.

Figure 2.5: A vertical cross-section of a typical evolution of a multi-cell thunderstorm. (Markowski and Richardson, 2010)

In contrast to multicell thunderstorms, supercells are long-lived (1-4 h lifetimes, up to 8 h have been observed) convective thunderstorms that require strong wind shear and have only a single dominant updraft that appears quasi-steady within a deep mesocyclone (a region of vertical vorticity of width 3-8 km and magnitude of O(10-2) s-1 (Markowski and Richardson, 2010). Unlike multicellular convective thunderstorms that propagate in space by the triggering of new cells on the gust front as well as through advection by the mean flow, supercells propagate through advection by the mean wind and are displaced right or left of the mean wind by vertical pressure gradients extending over a deep layer, usually between 0-6 km. Supercells contain two main downdrafts, the rear-flank downdraft (RFD) and the forward-flank downdraft (FFD) (Markowski and Richardson, 2010). The RFD forms when dry mid- and upper-level

Literature Review Chapter 2 winds encroach upon the backside of the updraft resulting in evaporative cooling and negative buoyancy. This may be the result of a downward-directed vertical pressure gradient force on the upshear flank of the storm. The FFD is a result of evaporation of rain and the melting and sublimation of ice from the deposit of hydrometeors on the forward flank of the updraft. The inflow into a supercell updraft can be strong, with speeds greater than 20 m s-1, and is associated with a dynamic pressure minimum of 1-3 hPa. A three-dimensional schematic of supercell structure and airflow, in the northern hemisphere, is shown in Figure 2.6.

Even when atmospheric conditions are conducive to the formation of severe convective thunderstorms through the availability of instability, large amounts of moisture, and significant vertical wind shear, a thunderstorm still might not materialise if there is not forced ascent of air to the LFC. This lift can be provided by air mass boundaries such as drylines, synoptic fronts, outflow boundaries, and sea breezes. Initiation can also be triggered by orographic

Literature Review Chapter 2 circulations or forced ascent by topography (Markowski and Richardson, 2010). The use of severe weather indices can help to determine the availability of moisture, instability and shear in the local environment. However, they do not determine if there will be a trigger present to help realise the potential for thunderstorm formation. A mesoscale convective system (MCS) is an ensemble of thunderstorms producing adjoining precipitation areas that can stretch for 100 km or more. They are large enough that the Coriolis force can be significant (Markowski and Richardson, 2010). These storms can develop immediately following convective initiation or several hours after initial convective development because of the formation of a large cold pool created by the outflows of the earlier convection, which acts to initiate new cells along its length. Most MCSs can be thought of as multicellular convection, that the gust fronts continuously trigger the formation on new cells, resulting in a system of cells that outlive any individual cell. MCSs include squall lines, bow- echo (where the entire MCS is bow shaped or the bow-echo is a sub-squall-line structure), and mesoscale convective complexes (MCCs). Squall lines are defined as any line or narrow band of thunderstorms and generally last several hours. Rotunno et al. (1988) found two basic types of long-lived squall lines: lines of ordinary thunderstorms that continually grow and decay and lines of nearly steady supercells. The former appears to be more common and occur with strong, deep shear perpendicular to the squall line, whereas the latter type occurs with strong, deep shear at an angle to the squall line. Bow-echoes usually originate as a single, large, and strong convective cell that evolves into a bow-shaped line segment of cells as the surface winds develop, with the strongest winds occurring at the apex of the bow (Weisman, 2001). Fujita (1978) notes that they are commonly associated with downbursts and hypothesised that there must also be a strong rear-inflow jet, with its core at the apex of the bow. MCCs are a subset of MCSs that have distinct anvils. Their anvils are a cold cloud shield that are large, circular, and long-lived. MCCs are favoured in broad middle- and upper- tropospheric ridging, when a short-wave trough moves through the longer-wavelength ridge (Markowski and Richardson, 2010). They tend to, but do not always, initiate on the cold side of synoptic fronts and their inflow is drawn from above the stable nocturnal boundary layer. After a few hours from initiation, the Coriolis acceleration becomes significant, a warm-core structure develops and the MCC generates a mesohigh with divergent, anticyclonic outflow near the tropopause (Maddox, 1980). A low-pressure with convergent, cyclonic eddy is produced below the level of maximum convective heating and is called a mesoscale convective vortex (MCV) (Chen and Frank, 1993). MCVs will likely outlive the parent MCC (Menard and 43

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Fritsch, 1989) when the environmental vertical wind shear is weak and can result in the initiation of new convection on subsequent days. 2.1.3. Microscale Weather Systems Microscale meteorology refers to short-lived atmospheric phenomena, smaller than the mesoscale and generally a few kilometres or less in scale (Markowski and Richardson, 2010). These phenomena include tornadoes, and microbursts. When examining phenomena on the microscale, terms such as the Coriolis force and even on occasion the horizontal pressure gradient force can be neglected (Eqn. 2.1, 2.2, 2.3). Tornadoes are violently rotating columns of air that are often associated with a funnel- shaped cloud extending from the base of the parent cumulonimbus updraft to the ground. Tornadoes were originally rated on the Fujita scale (F-scale) where an F1 tornado has a 3- second gust of about 20-35 m s-1 up to F5 with wind speeds of 117-142 m s-1. This rating was later replaced by the Enhanced Fujita Scale (EF-scale) where an EF1 tornado has a 3-second gust of about 29-38 m s-1 up to an EF5 with wind speeds greater than 75m s-1 (Wind Science and Engineering Center, 2006). The EF-scale has not been adopted by all countries. Furthermore, different building standards will affect the usefulness of the rating system. Tornadoes are usually O(100 m) in diameter but can measure up to 4 km and generally persist for less than 10 minutes. In some instances, tornadoes have been observed to last up to one hour or more. Tornadoes can occur with all types of deep moisture convection (DMC) but the most significant and violent tornadoes are associated with supercells (Kelly et al., 1978). For tornadogenesis to occur, large vertical vorticity must arise at the ground (Figure 2.7b). When pre-existing vertical vorticity near the ground is negligible so is the vorticity stretching. Therefore, vertical vorticity must come from either the tilting of horizontal vorticity or from advection aloft towards the surface. It is unlikely that the tilting of horizontal vertical vorticity gradients alone can produce vertical vorticity at the surface (Markowski and Richardson, 2009). However, with the descent of a downdraft the vertical vorticity can be advected towards the surface where it can be stretched to form a tornado (Figure 2.7a) (Davies-Jones and Brooks, 1993; Davies-Jones et al., 2001). Numerous numerical simulations have shown that the downdraft in supercells likely plays a role in producing a tornado vortex that stretches to the surface (e.g., Rotunno and Klemp, 1985; Walko, 1993; Grasso and Cotton, 1995; Adlerman et al., 1999). Markowski (2002) makes notes of many observations of RFDs being located near tornadoes however, the precise dynamical relationship between the two is still not known.

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Figure 2.7: Vortex lines demonstrating how a tornado can form when (a) there is no pre- existing vertical vorticity at the surface and a downdraft is needed to aid in the formation of vertical vorticity at the ground and (b) when pre-existing vertical vorticity is present at the ground and convergence along can result in the generation of a tornado. (Markowski and Richardson 2010)

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The structure of a tornado can be broken down into 5 regions: (1) the outer region comprising of inward spiralling air that approximately conserves angular momentum, (2) the core region that extends from the tornado axis to the radius of maximum wind and is in cyclostrophic balance and centrifugally stable, (3) the corner regions where part of the boundary layer flow turns upwards, (4) the boundary layer flow region that is turbulent as a result of the interaction with the ground, and (5) the rotating updraft region where the larger- scale parent updraft above the tornado is located (Snow, 1982; Davies-Jones, 1986) (Figure 2.8).

Figure 2.8: The five regions of a tornado vortex. (Markowski and Richardson, 2010) In contrast to tornadoes, a downburst results from downdrafts that strike the ground and can cause strong and often highly divergent horizontal winds (Figure 2.9). A downburst is arbitrarily defined to have an outflow diameter of less than 10 km with ones less than 4 km known as microbursts (Fujita, 1981). Downdrafts are associated with relatively high-pressure at the surface because of the deceleration of the impinging column of air as it approaches the ground. Both dynamical and thermodynamical forcing can be important in the occurrence of a downburst, but thermodynamical forces probably play a more dominant role, except in the case of the occlusion downdraft of supercell thunderstorms (Markowski and Richardson 2010). The

Literature Review Chapter 2 thermodynamical forcing is related to the creation of negative buoyancy that results from latent cooling and hydrometeor loading (Squires, 1958; Emanuel, 1981). The evaporation of liquid water, melting of ice, and sublimation of ice all contribute to latent cooling. A dry boundary layer is favourable for the creation of negative buoyancy as raindrops evaporate as they fall into a deep layer of unsaturated air. Moreover, entrainment of dry mid-level air into the storm can produce negative buoyancy aloft (Fujita, 1981; Atkins and Wakimoto, 1991; Wakimoto, 2001). Microburst events can be divided into three different types (wet, dry, and hybrid) that are driven by different processes. Wet microbursts are characterised by a low cloud base, heavy precipitation, and reduced visibility. They are mainly forced through the entrainment of mid- level dry air and precipitation loading (Fujita, 1981; Atkins and Wakimoto, 1991; Ellrod et al., 2000; Wakimoto, 2001). In contrast, dry microbursts have a high cloud bases and little or no precipitation at the surface. Dry microburst result from the latent cooling beneath the thunderstorm cloud base through evaporation, melting, and/or sublimation (Wakimoto, 1985; Atkins and Wakimoto, 1991; Ellrod et al., 2000; Wakimoto, 2001). Hybrid microburst result from processes that occur in both wet and dry microburst (Ellrod et al., 2000). That is, they occur due to both dry air entrainment and/or precipitation loading in the mid-level as well as latent cooling in the low-level. The melting and sublimation of ice can contribute to the creation of negative buoyancy, but where the sublimation rate increases with a decrease in the relative humidity, melting rates will decrease. This is because melting will only occur once the wet-bulb temperature is nearly freezing. Also, the height of the wet-bulb-zero level is lower in dry environments, resulting in less time for ice to melt as it falls to the ground and therefore less cooling. Thus, it is important to note that even though a dry environment can result in the initiation of a downdraft, its intensity does not necessarily escalate with increased dryness (Markowski and Richardson, 2010). Dynamical effects, such as pressure perturbations and their vertical gradients, play a more important role in environments with large vertical wind shear. High-pressure perturbations are often found aloft, upshear of the updraft in supercells. Below this high- pressure perturbation the pressure decreases closer to the surface resulting in a downward acceleration forcing positively buoyant air downwards (Weisman and Klemp, 1984; Fujita, 1985; Kessinger et al., 1988;).

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Figure 2.9: Cross-section of a microburst (Markowski and Richardson, 2010) 2.2. Climates of Australia

There are several different climate regions across Australia, many with subclasses of their own. Therefore, it is important to understand differences between climate regions in Australia and what the implications of these differences are for the generation of severe wind gusts. Following British settlement, the first assessment of climate regions was likely conducted by Surveyor-General Goyder in 1865. He plotted boundaries of native vegetation greatly affected by a bad drought to determine regions suitable for growing wheat. Since then, there have been many attempts to delineate between the various climate zones and regions of Australia all the way back to the Aborigines who distinguished between wet and dry regions, cold and warm regions, and regions where the wind was too cold or dusty (Gentilli, 1972). This includes determining regions using a single raw climate element such as seasonal rainfall, regions based on integrated climatic elements (e.g., duration and range of temperature as well as annual rainfall) and methods that look at frequency and duration of climate elements. Figure 2.10 shows the many different classes and subclasses of climate regions in Australia as determined using the Köppen classification system. The vast diversity of climate regions across Australia suggests that the dominate weather system affecting the various climate regions may be different. Therefore, it is not possible to assume that the distribution of weather systems responsible for generating severe wind gusts is the same in different parts of the country. It is important to be able to objectively determine the weather systems irrespective of climate regions.

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Figure 2.10: Climate zones and regions as determined from the BOM based on a modified Koppen classification system, with means based on standard 30-year climatology (1961 to 1990). (BOM 2014) 2.2.1. Air Masses Air masses play an important role in influencing the climate regions of Australia. In general there are 8 major air masses that affect Australia as described by (Tapper and Hurry, 1993). Six air masses are sourced from the surrounding oceans. The first is the modified polar maritime air mass that is very cold, moist, and unstable. It originates over the Southern Ocean, just off the coast of Antarctica, and affects southern Australia occasionally in the winter during the passage of strong cold fronts. The southern maritime air mass originates over the Southern Ocean. This air mass is cold, moist, and unstable at low levels but stable aloft. It influences the weather of southern Australia year-round, bringing cool, moist weather. Orographic lifting of this air mass can result in storms that are more significant. The tropical maritime Tasman air mass originates over the north Tasman Sea and is warm, unstable, and moist to high levels. It brings warm, drizzly weather to the coastal regions of eastern Australia for most of the year with less of an influence towards the south in the winter. The orographic lifting of this air mass can also result in more significant weather. The tropical maritime Pacific air mass is warmer than the tropical maritime Tasman air mass originating over the Coral Sea and western Pacific Ocean. This air mass can also be influenced by the presence of significant topography. It affects the North Queensland coast for most of the year. The equatorial air mass comes from the maritime area north and west of Australia. It is very warm, moist, and unstable and associated

Literature Review Chapter 2 with the monsoon. It affects the north and north-west coast of Australia only in the summer, but can affect areas as far south as 30°S. The tropical maritime Indian air mass is similar to the tropical maritime Pacific but its source is in the eastern Indian ocean and affects the north- western coast of Australia. The remaining two air masses originate over the continent. The first being the tropical continental originating over central Australia. This air mass is very hot, dry and unstable during the summer months. The upper extent of the instability is limited by the lack of moisture in the air mass as well as by the trade wind inversion in the mid-troposphere. This air mass affects north-central Australia throughout the year but can also cause heatwave conditions for southern Australia in summer when strong northerly flow is present. The second continental air mass is the subtropical continental, which originates over south-central Australia. This air mass is warm and dry. It dominates inland southern Australia mostly in the winter. The movement of these air masses and their interactions with one another can play a vital role in the development of conditions necessary for convection to occur (i.e. instability, moisture, shear, trigger) that can result in the occurrence of convective wind storms. 2.2.2. Seasonal Variability During the summer months, there is a shift in the predominant high-pressure systems that tend to sit over the Indian and Pacific Oceans towards the south. This results in the westerlies sitting well south of Australia. A trough tends to sit between the two high-pressure systems and typically has weak cold fronts associated with it that do not tend to affect north of 40°S (Tapper and Hurry, 1993). Southeastern Australia shifts from warm northerlies, resulting from the tropical Tasman maritime and even subtropical continental air masses, to cool, moist south- westerlies of the southern maritime air mass. On the east coast, south-easterly trade winds bring warm, moist tropical maritime Tasman and Pacific air onshore, bringing wet stormy weather to the region, especially in North Queensland. While on the west coast, easterly winds bring hot, dry tropical and subtropical continental air masses. In these middle-latitude regions, extreme winds are produced by severe thunderstorms during the summer months (Gentilli, 1972). In north Australia, there is a system of lows, typically a monsoon depression between two heat lows, the Pilbara low to the west and the Cloncurry low to the east (Sturman and Trapper, 1996). This brings the moist equatorial maritime air mass inland. Tropical cyclones are the main wind hazards in the tropics and can occasionally extend as far south as New South Wales (NSW) on the east coast, and the Perth region on the west coast (Walsh et al., 2016). In the winter, the two main high-pressure areas over the Indian and Pacific Oceans move equatorward. A cooler continent interior results in the absence of heat-induced lows. In

Literature Review Chapter 2 southern Australia, the air motion is largely westerly, bringing cool, moist southern maritime air onshore. This is usually associated with frequent frontal passages. The northward motion of the highs results in a stronger influence from mid-latitude low-pressure systems and their fronts often bringing very cold modified polar maritime air masses. Coastal low-pressure systems can bring heavy rain, strong winds, and large waves to the southeast coast of Australia (Speer et al., 2009), especially during the winter months, and even autumn and spring. Generally, these East Coast Lows (ECLs) cause a significant amount of damage each year. These systems and their fronts can even penetrate well into Queensland (QLD). North Australia is influenced by strong subsidence and a steady south easterly trade wind resulting in dry, warm, and cloud free weather. Along the tropical east coast of Australia there is little storm activity since the trade winds, with the moist tropical maritime Pacific air mass, are parallel to the coast and not lifted orographically. 2.3. Thunderstorm Climatologies

2.3.1. Observational Datasets Limitations Developing an accurate climatology of thunderstorms or severe thunderstorms is difficult. An adequate and reliable dataset of observed events is crucial but these events are rare at any given location and are often dependent on manual observation systems to document their occurrence (Brooks et al., 2003). Thunderstorms require an observer or an Automatic Weather Station (AWS) to observe an event and a system to record these witnessed reports. Moreover, Doswell et al. (2005) note that given the spatial dimension and variability in both space and time it is unlikely that observations are recording the max intensity of an event. This leads to problems in the interpretation of events statistics, such as perception-based intensity assessments of damage from tornadoes and convective winds, which have non-meteorological factors affecting the records (Brooks et al., 2003; Trapp et al., 2006; Allen et al., 2011; Tippett et al., 2015; Allen and Tippett, 2015). There can also be inconsistencies in reporting standards and even reports of fictitious events (Forbes and Wakimoto, 1983; Doswell and Burgess, 1988). Examples of this problem have been shown by Doswell et al. (2005) with respect to differences in the reporting practices of non-tornadic thunderstorms in the U.S. and by King (1997) who examined the impacts of population on tornado reporting in Ontario, Canada. Biases and errors in observational datasets have previously been documented (e.g., Doswell and Burgess, 1988; Brooks and Doswell, 2001; Weiss et al., 2002; Doswell et al., 2005). They result from meteorological (e.g., King et al., 2003) and non-meteorological factors, such as the type of monitoring network, proximity to population centres and/or observational equipment

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(i.e., Doppler radar), and even terrain and topography (Schaefer and Galway 1982; Grazulis and Abbey Jr., 1983; King, 1997; Ray et al., 2003). With respect to non-meteorological factors, population density has been shown to significantly contribute to observation bias in severe thunderstorms records in North America (e.g., Snider, 1977; Schaefer and Galway, 1982; Tescon et al., 1983; Etkin and Leduc, 1994; Paruk and Blackwell, 1994; King, 1997; Ray et al., 2003; Doswell et al., 2005; Anderson et al., 2007). However, Doswell et al. (2005) show that the severe thunderstorm report database in the U.S. contains inhomogeneities that are not simply a reflection of population biases. The issue of observation bias for severe thunderstorm records in Australia is of particular concern given the majority (85%) of Australia’s population resides within 50 km of the coast. In Australia, the Severe Storm Archive (SSA; BOM, 2015) contains data on hail, tornadoes, and damaging convective winds as early as 1795 up to the present day. In this dataset there is a strong bias, and even an over reporting of events, towards urban areas and the coast or along road networks (Schuster et al., 2005b; Allen et al., 2011; Tippett et al., 2015; Allen and Tippett, 2015, Allen and Allen, 2016). Similarly, due to the sparse population in regional areas, along with the relatively small scale of severe thunderstorms, there is an under reporting of events in these rural areas resulting in a lack of understating of severe thunderstorms (Kelly et al., 1985; Hales, 1993; Griffiths et al., 1993; Geerts and Noke-Raico, 1995; Mills and Colquhoun, 1998; Doswell, 2001). In addition, comparisons of events through space and time is difficult because of different collection methods and changes in these methods with time (Brooks et al., 2003b). For example, prior to the Australian BOM establishing the severe weather section in 1987 there was no formal collection mechanism, which led to temporal inconsistencies (Hales, 1993; Griffiths et al., 1993). This resulted in noticeable increase in the number of hailstorms over this period producing an artificial positive trend and questionable spatial distributions of hail occurrence (Allen and Allen, 2016). Because of this, the SSA is a short and inconsistent dataset prior to 1987 and it is therefore challenging to make report-based climatology periods longer than a couple of decades. Moreover, it makes it difficult to quantify the interannual variability, which has proven difficult for Australia (Schuster et al., 2005a). 2.3.2. Current Solutions The use of severe weather indices (Brown and Murphy, 1996) has proven to be a useful solution to some of the problems faced when creating a climatology of thunderstorms (e.g., Brooks et al., 2003a; Allen et al., 2011; Allen and Karoly, 2014). A severe weather index is a parameter developed by meteorologists to aid in forecasting thunderstorms. They typically use

Literature Review Chapter 2 a combination of parameters (i.e., CAPE and wind shear) to determine if conditions are favourable for thunderstorm development. They originally were simple, using atmospheric variables like temperature and humidity and looked at the state of the atmosphere to determine the likelihood an air mass could become unstable when subjected to processes such as surface heating and horizontal convergence (Boyden, 1963). Severe weather indices can be divided into broad categories that describe conditional instability, latent instability, potential instability, and/or a combination of conditional and potential instability. Some instability indices will also consider kinematic properties (i.e., wind shear) or moisture. Not all severe weather indices look specifically at instability. For example, some parameters look at downdraft potential, the amount of shear present in the atmosphere, or the risk of hail occurring, while other indices look at a combination of severe weather threats. The indices that look specifically at the potential for downdrafts to occur will be important for this work as this mechanism is largely responsible for the occurrence of severe winds at the surface during convective storms. Severe weather indices have been used to separate environments that are likely to produce non-severe thunderstorms and those that are likely to produce severe thunderstorms (Brooks, 2009; Allen et al., 2011). This is done by the association of environmental ingredients and reports. These indices make it possible to find connections between environmental conditions that are well observed in the atmosphere to specific weather events that are not well observed. The idea is to develop a relationship between meteorological variables and the occurrence of severe weather in an area with good reporting of events (Brooks et al., 2003b). With this relationship it is possible to estimate the occurrence of severe weather in areas with poor reporting of events (Brooks et al., 2003b). Moreover, they can also be used to estimate and evaluate the overall climatology of severe thunderstorm environments for periods longer than the available reports (Brooks, 2009; Allen et al., 2011). Many studies have looked at determining the best discriminators to distinguish between severe and non-severe thunderstorms. Brooks (2009) found that in both the US and Europe, high values of CAPE and shear were important for severe convection to develop. However, he notes that the large-scale forecast problem may be different for the two regions. Grünwald and Brooks (2010) also show that the quantitative relationship between CAPE and the 0 to 6km wind shear (Shr6) is different for the US and Europe even though they are both important in the two regions. Allen et al. (2011) derived a set of environmental ingredients associated with severe thunderstorms reported in Australia. Similar to Brooks (2009) they determined CAPE and Shr6 to be the better indices for distinguishing between severe and significant severe thunderstorm environments. These studies have not included the presence of a trigger to build their climatologies. 53

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Severe weather indices can be useful when creating climatologies of environments conducive to the development of severe weather events and assessing the risk associated with them, even in areas with large uncertainty in the observational dataset. While many studies have looked at possible relationships (e.g., Brooks et al., 2003b; Carey et al., 2003), most have not considered observational biases. Other studies do not consider possible spatial correlation between observations (e.g., King, 1997), but the explicit consideration of error covariance in space is important to obtain correct statistical inference and to identify factors unaccounted for by a statistical model (Wikle and Anderson, 2003; Anderson et al., 2007). Previously, population sampling bias in the reporting of tornadoes have been accounted for with statistical models that correct observations in areas with low population density by using nearby sites with high population density and reliable observational records (Twisdale, 1982; Tescon et al., 1983; King, 1997; Ray et al., 2003). Unfortunately, these statistical methods assume that the tornado climatology is homogeneous or that there is enough areal coverage of reliable sites to derive accurate adjustments (e.g., King 1997; Ray et al., 2003; Anderson et al., 2007). This assumption is not valid in countries where vast areas have unreliable data, such as Canada and Australia, and thus the observational uncertainty can be significant (Cheng et al., 2013). Bayesian modelling has also been shown to be useful in addressing the issue of observational biases (Cheng et al., 2013, 2015, 2016). It provides an unbiased approach to incorporate the uncertainty associated with the forecasting of thunderstorms (Arhonditsis et al. 2007, 2008a,b). Also, the use of Bayesian hierarchical modelling has been shown to a provide a conceptually plausible way to address complex natural systems (Clark, 2005; Cheng et al., 2010). The approach sorts out complex environmental patterns, utilises different sources of data, incorporates different spatiotemporal scales, and explicitly considers unknown or unmeasurable quantities ( Clark, 2005; Clark and Gelfand, 2006; Zhang and Arhonditsis, 2009). Wikle and Anderson (2003) used a Bayesian spatiotemporal model to analyse tornado report counts in the U.S. They looked at the spatiotemporal distribution of tornado reports and the relationship to the Niño3.4 index of the El Niño/Southern Oscillation phenomenon. They demonstrate the usefulness of this approach in modelling complicated spatiotemporal processes and provide insight into climatological and meteorological diagnostic analyses. They also show the ability for this method to provide uncertainty in data, model, process and parameters when performing inference on complicated physical processes. Although not considered in their model they note that the statistical approach is flexible and can be adapted for more complicated scenarios such as to explicitly account for observational uncertainty and sampling 54

Literature Review Chapter 2 bias. In later work, Anderson et al. (2007) examine the influence of population on the reporting of tornado events in several U.S. cities. Their results indicated that some of the spatial variability in tornado reports may be attributed to population density. In addition, they found that population density effects have regional variability which they attribute to the quality of construction, rural construction density, or variability in reporting standards. Cheng et al. (2013) used Bayesian hierarchical modelling to predict tornado occurrence across Canada by first considering the covariance between lightning flash density climatology and tornado occurrence. The authors then postulated that the likelihood of observing a tornado was related to population density. Cheng et al. (2015) similarly used Bayesian hierarchical modelling to improve the tornado climatology of Canada but examined the combination of severe weather indices instead of lightning flash density. Cheng et al. (2016) continue this work by using a Bayesian hierarchical model framework to depict the causal linkage between the annual or seasonal tornado occurrence across North America. In addition, they explicitly account for the role of regional variability in the occurrence of tornadoes, which they note has not be considered in predictive frameworks before. Cheng et al. (2016) proposed that the delineation of local regions of homogenous physical processes can be determined from patterns in the local model error. Their model is configured to include a gridcell-specific conditional autoregression (CAR) term that considers the variability unaccounted for by the use of severe weather indices. The CAR term account for factors such as the spatiotemporal variability of the physical mechanisms responsible for severe thunderstorm formation, differences in the scales at which these processes occur and the resolution they are studied at, local climate and geographic processes that can influence the convective initiation of events, as well as regional and seasonal climate regimes that can violate the assumption of a spatial homogenous parametrization. This CAR term can be determined for different temporal resolutions such as seasons or months. 2.3.3. Australian Thunderstorm Climatologies The majority of mesoscale meteorology climatologies have focused on thunderstorm activity in general and not on specific thunderstorm hazards. Kuleshov et al. (2002) used 300 observation stations across Australia to identify thunderdays as being most prevalent across the tropics, during the summer and into early autumn corresponding to the development of the monsoon, with secondary maxima in the interior and in southeast Australia. Further research (Kuleshov and Jayaratne, 2004; Kuleshov, 2004; Kuleshov et al., 2006, 2009; Dowdy and Kuleshov, 2014) showed there is a bi-modal behaviour in the southeast with the expected spring

Literature Review Chapter 2 and summer peak, as well as a secondary peak over the east coast associated with intense extratropical cyclone development during the winter months. While thunderdays suggest that the greatest occurrence of thunderstorms is in the tropical regions (Figure 2.11), the Australian tropics usually lack vertical wind shear to promote the development of strong and long-lived severe thunderstorms (Barnes, 2001). The presence of high relative humidities in the lower layers would inhibit the production of damaging convective winds, while the lack of vertical wind shear reduces the likelihood of supercellular tornado events (Allen and Allen, 2016). However, the presence of a strong cumulus updrafts along with relatively weak surface flow would support non-supercellular tornadoes (Allen and Allen, 2016). The lack of these conditions favourable for severe thunderstorm development in the tropics would suggest that thunderstorms that produce more than just lightning are more likely to occur in the mid-latitude regions of Australia (Barnes, 2001; Allen and Karoly, 2014), which is similar to observations made in other locations worldwide (e.g., Brooks et al., 2003). Most of the severe thunderstorm climatologies in Australia have focused around the southeast and east coast of the continent (Yeo et al., 1999; Buckley et al., 2001; Leigh and Kuhnel, 2001; Schuster et al., 2005a; Yeo, 2005). However, severe thunderstorms are known to occur throughout Australia (Hanstrum and Foley, 1990; Allen, 2012; Richter et al., 2014). Brooks et al. (2003) and later Brooks and Dotzek (2007) estimated favourable severe thunderstorm environments frequency in Australia using a U.S.-derived discriminant for reanalysis data. Their results showed a peak frequency over eastern Australia (Queensland, New South Wales, and Victoria) and across the north of the continent (Northern Territory and Western Australia). Allen and Karoly (2014) built on their work and extended the climatology over the entire continent independent of observations. They used an environmental discriminant to develop a 32-year climatology using a different reanalysis and found high frequencies extending along the Great Dividing Range, across northern Australia (Queensland, Northern Territory, and Western Australia) and down into southern WA. A peak frequency in favourable severe thunderstorm environment was also observed over the northern sub-tropics and tropics, which have little observations in existing records, but due to the small population density in this area, they note the need to further investigate the occurrence of severe thunderstorms in that region (Allen and Allen et al., 2016).

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Figure 2.11: From Dowdy and Kuleshov (2014) showing the remotely sensed ground-flash lighting observation density (flashes km-2year-1) for the period 2005-2015.

The majority of severe thunderstorms and their favourable environments occur between midday and 7 p.m. local time (Griffiths et al., 1993; Schuster et al., 2005a; Allen et al., 2011; Allen and Karoly, 2014). Like much of the rest of the world, thunderstorms typically peak with the diurnal cycle of surface temperature and the maximum availability of heating which is associated with potential updraft strength (Kelly et al., 1985). As identified by Allen and Allen (2016) there are two main seasons for severe thunderstorms in Australia. The first are warm season severe thunderstorms that typically occur between September and April (Fig. 5a, Harper et al., 2000; Tucker, 2002; Niall and Walsh, 2005; Schuster et al., 2005a; Allen et al., 2011; Allen and Karoly, 2014) and the second are cool season severe thunderstorms between May and September (Griffiths et al., 1993; Hanstrum et al., 2002; Mills, 2004; Kounkou et al., 2009). Given size of Australia there are latitudinal variations in the seasonal distribution of severe thunderstorms (Allen and Allen, 2016). As a result of the regularity of synoptic systems passing towards the south of the continent, the peak severe thunderstorm activity occurs earlier in QLD (October to January) with a second peak in March (Yeo, 2005) as opposed to further south

Literature Review Chapter 2 where the peak occurs in the spring and summer (Allen and Karoly, 2014). However, there is a high degree of inter-annual variability in severe thunderstorm occurrence both temporally and spatially (Allen and Allen, 2016). The spatial and temporal of severe thunderstorms climatologies make understanding risk, variability, and potential trends over the last few decades difficult. 2.3.4. Australian Convective Wind Storm Climatologies There are few climatologies of severe wind gusts for Australia. The ones that have been conducted tend to only focus on specific regions of the country. Geerts (2001) developed a climatology for NSW using 9 anemometers. Their study found that damaging convective wind storms occurred on or west of the Great Dividing Range from November to December and mainly resulted from dry microbursts. This work contrasts what has been found over southeast QLD, east of the Great Dividing Range, where severe winds tend to occur from hybrid microburst events, especially high precipitation supercells (Eyre, 1992; Colquhoun, 1995; Richter et al., 2014). Holmes (2002) considered the distribution of damaging convective winds occurrence statistically and determined 500-year return period gusts for non-tropical cyclone regions of Australia. Their work showed that for each of Australia’s state capitals, with the exception of Perth, convective winds were more dominant than synoptic winds at this level of occurrence probability. Subsequent work, using reanalysis data that was downscaled to 14km resolution over Tasmania, found that the 500-year return levels for severe convective winds across the state were less than those generated by synoptic events, but still reached up to 37 m s-1 in northwest part of the state (Sanabria and Cechet, 2010; Cechet et al., 2012). The current Australian structural design standard for wind actions, AS.NZS 1170.2:2011, was developed using historical data from a select number of AWS data up until 1998. Wang et al. (2013) re-examined the wind gust hazards for the consideration of vulnerability and design of buildings and infrastructure in Australia using AWS wind gust data from 1939 to 2007 and hazard modelling. They note that the lack of surface measurements required for calibration of wind-field models will affect the accuracy that can be achieved with their model. Through the use of a probabilistic and statistical approach for wind hazard modelling, Wang et al. (2013) showed that when considering gust wind speeds from convective thunderstorms, along with the tropical cyclone gusts, the current design standards are only adequate for the coastal regions of northern Western Australia (WA). They found that the 2000-year hazard map shows areas where the gust speeds can reach up to 60 m s-1 whereas the Standard specified regional design wind speed is 48 m s-1. The effect of possible changes to the climate on wind gusts was also

Literature Review Chapter 2 considered by Wang et al. (2013) but only for synoptic events. They note that climate change research related to gusts from tropical cyclones and thunderstorms is important for reducing uncertainty of future climate conditions and is likely an important consideration for revisions to the Standards used for the design of buildings and infrastructure. For tornadoes specifically, there have been many case studies of events but climatologies of these events are limited (Fujita, 1973; Goliger and Milford, 1998; Allen and Allen, 2016) and do not always tend to agree with one another. It has long been suggested that tornado occurrence is rare in Australia and that when they do occur they are weak compared to those that occur in the U.S. (Fujita, 1973; Minor et al., 1980; Allen, 1980; Geerts and Noke-Raico, 1995). However, there is evidence in the Australia Severe Storm Archive (SSA) of strong, damaging tornadoes (Holcombe and Moynihan, 1978; Plukss, 1979; Minor et al., 1980). Clarke (1962) used documentary records and newspapers to identify 167 tornado events from January 1950 to June 1961 and calculated the frequency of tornadoes in QLD and WA to be similar to those states in the U.S. with the highest rates of tornado occurrence but found them to be of lesser intensity. For NSW, Evesson (1970) examined the newspaper record from 1805-1966 and then extrapolated the frequency over the populated coastal areas over the rest of the state. They estimated 15 tornadoes per year over NSW which contrasted the 14.6 tornadoes events estimated per year over all of Australia by Clarke (1962). Fujita (1973) challenged these two studies and through the post-analysis of Clarke’s data suggested a frequency of tornado occurrence in Australia, compared to the U.S. to be an order of magnitude less. Minor et al. (1980) looked at numerous case studies as well as Evesson’s climatology and found Australian tornadoes to have similar characteristics to American tornadoes, including their intensity, suggesting little difference in the potential strength of tornadoes between the two continents. Moreover, they suggested that after taking into account population density the frequency in parts of Australia matched some parts of the U.S. Another study by Geerts and Noke-Raico (1995) used the SSA from 1960-1992 to find an average of 29 tornadoes occurring on average across the continent. Despite them acknowledging that population density alone might not explain the distribution of observed tornadoes they suggested that tornado occurrences in the interior of the continent were rare. Geerts and Noke-Raico (1995) also revealed a seasonal cycle in tornado frequency over Australia that differed from the U.S. in that it is bi-modal, with an early spring/summer peak and a second peak in the early winter months. The cool-season tornadoes made up a significant amount of the overall tornado climatology and were focused around southwestern WA, southern SA, and western VIC. Furthermore, the Perth Bureau of Meteorology office studied the impacts of significant 59

Literature Review Chapter 2 tornadoes along the southwest coast of Australia for the winter months and found that almost half of reported tornadoes occurred in these months between 1987-1996, mainly on the southwest coast of Western Australia and the southeast coast of South Australia. More recent studies have looked at environmental proxies over Australia and found modest frequencies of favourable tornado environments over eastern Australia but non-zero probabilities over most of the continent (Brooks et al., 2003; Brooks and Dotzek, 2007; Tippett et al., 2015). This is consistent with estimates derived from observations that suggest tornado frequency in Australia is low when compared to the U.S. (Allen and Allen 2016). However, while studies have typically applied a single criterion that was developed for the U.S. (e.g., Brooks et al., 2003) Allen and Allen (2016) showed from their analysis of tornadoes in 2013 that a wide range of environments can results in the formation of tornadoes in Australia, highlighting a higher risk of tornadoes in Australia may be possible. Hanstrum et al. (2002) used environment-based parameters to find approximately 8 days per year where conditions were favourable for the development of cool-season tornadoes.

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Figure 2.12: A compilation of tornado climatologies of Australia over the years put together by Allen and Allen (2016). (a) 167 tornadoes from 1950 to 1961, adapted from Clarke (1962). (b) Areas with tornado frequency comparable to the active states of the U.S., adapted from Minor et al. (1980). (c) Gridded 2 × 2-degree density of tornadoes from 1950 to 1959, adapted from Allen (1980). (d) Distribution of the Bureau STA record of 348 tornadoes reported during 1960–1992. The triangles were used to denote summer events (22/9–21/3) and the circles winter events (22/3–21/9). Adapted from Geerts and Noke-Raico (1995). (e) Total density of Bureau STA sourced tornado reports from 1795 to 2014, aggregated on a 75 × 75 km grid and overlaid with point report locations. (f) Reanalysis of observed tornadoes in Australia from historical archives gridded analogously to panel e for the period 1795–1910 (Allen and Allen, 2014). 61

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A limitation of these climatologies, some of which are shown in Figure 2.12, has been the inadequate observational data to properly assess the risk of severe convective wind storms and tornadoes across Australia. There is a need to improve and update the SSA using historical records similar to what was done by Grazulis (1993) in the U.S. Given the risk these events pose to heavily populated urban areas (Geerts and Noke-Raico, 1995; Allen and Allen, 2016) there is a need to better understand the intensity and occurrence of all convective wind storms for Australia since such events are rarely assessed in the field. Given the discussion in Section 2.3.2 it may be possible that the use of severe weather indices and reanalysis can help to provide additional data, specifically where there is limited or no observations, when trying to create a severe wind gust climatology. Moreover, exploring the applications of these environmental parameters can make it possible to examine the risk over an extended period and improve understanding of the environments favourable to their development across the continent (Allen and Allen, 2016). The use of severe weather indices could also be helpful in determining the effects of climate change on the frequency of convective wind gusts, as will be discussed in Section 2.5. 2.4. Event Classification

A major challenge with weather observations, especially severe wind storms, is the classification of their meteorological origin. In meteorology this usually means separating and classifying them into two main groups, synoptic and convective events, or stationary and non- stationary for wind engineers (Gomes and Vickery, 1976; Kasperski, 2002; Lombardo et al. 2009; Solari, 2014). In Australia, studies that look at convective winds have mainly focused on the use of anemometer records and manually exclude non-convective events (e.g., Geerts, 2001). Wang et al. (2013) highlight that while this is an issue when analysing anemometer data, it also is an issue when analysing data from the SSA. It is important to distinguish between the two types of events because winds from different meteorological origins exhibit different statistical characteristics (Holmes, 2002). Extreme value theory can be used to consider the distributions of severe convective wind occurrence statistically (Holmes, 2002). Recently, extreme value theory has been coupled with downscaled reanalysis data over Tasmania to approximate the 500-year return levels for convective winds (Sanabria and Cechet, 2010; Cechet et al., 2012). More detailed analysis may even look at subdividing those two groups into more specific weather events. However, it can be difficult to estimate the occurrence of specific convective storm types using environments (Geerts, 2001) given the vast range of environments that support the formation of wet, dry, and hybrid microbursts responsible for

Literature Review Chapter 2 severe convective winds (Wakimoto, 2001). Moreover, it is limited by the quality of the observational record and the assumptions of extreme value theory (Sanabria and Cechet, 2010). The separation of event types into homogenous families is especially important in mixed wind climates, so that reliable distributions of severe wind storms can be determined and used to conduct refined analyses of different phenomena and their contributions to wind loading of structures (De Gaetano et al., 2014). To do this it is important to consider both the records detected by wind monitoring network and the weather scenarios responsible for the event. Currently, the use of synthetic indicators and expert judgments are still the main tools used to separate and classify an extensive amount of data and process of wind velocity records (Gomes and Vickery, 1976; Riera and Nanni, 1989; Twisdale and Vickery, 1992; Choi, 1999; Choi and Hidayat, 2002; Kasperski, 2002; Duranona et al., 2006; Lombardo et al., 2009). 2.4.1. Statistically Identifying Events The first method is a statistical analysis that looks to systematically separate and classify measurements of large wind datasets. This approach has the main goal of understanding extreme wind velocities’ effects on structures, since different storms are known to influence the response of structures differently (Kwon and Kareem, 2009, 2013). Mixed populations were first dealt with by Thom (1967) who used two combined distributions for extratropical and tropical cyclones and then showed that one-third of the yearly peak wind velocities in the United States occur during thunderstorms (Thom, 1968). In Australia, Gomes and Vickery (1976) separated thunderstorm from non-thunderstorm winds, determined their distributions and derived a so-called mixed distribution. Subsequent research explored separate analysis of different weather phenomena like extratropical pressure systems, thunderstorms, hurricanes and tornadoes, which showed increase in the accuracy of separating events (Gomes and Vickery, 1977/1978). However, Kasperski (2002) notes that it is not possible to clearly separate thunderstorms from fronts due to the occurrence of what the author calls gust fronts with intermediate properties. The work by Gomes and Vickery (1977/1978) was extended to a more general framework by Cook et al. (2003) who focused on wind-excited response of structures and separated different phenomena by their association to stationary or non-stationary and Gaussian or non-Gaussian properties. The different behaviour of single-degree-of-freedom (SDOF) systems that are subjected to non-stationary thunderstorm and stationary synoptic events was studied by Choi and Hidayat (2002b), Chen and Letchford (2004) and Chay and Albermani (2005). Solari et al. (2013) then looked at the dynamic response of SDOF systems to different types of wind storms with a focus on the behaviour of the structure to these events.

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Although this method assesses the risk associated with convective winds it does not provide information about the occurrence of convective winds, particularly the occurrence of widespread damaging squall lines or derechos (Corfidi et al., 2015). Due to the amounts of data involved with the analysis of anemometer data, a detailed understanding of the meteorology responsible for generating the gust events is typically avoided. Instead, synthetic information based on the available data is used to make the process as automated as possible. Gomes and Vickery (1976) and Twisdale and Vickery (1992) assumed that the daily peak wind velocity was convective if it occurred on a day that thunder was reported by a meteorological observer, but Holmes (1999) notes that this assumption is often wrong. Kasperski (2002) used the mean wind velocity, the peak wind velocity and gust factor to divide the data into frontal depressions, thunderstorms and intermediate events, or gust fronts. For 20 years of wind data from towers in Australia, Rowcroft (2011) first extracted peak wind velocities greater than 40 m s-1 measured at 2 to 4 different heights ranging from at least 10m and up to 80m. They then determined the events to be convective if they satisfied the follow 4 conditions: (1) they last between 5 and 30 min; (2) the temperature has a drop of 1.51C or more; (3) there is an increase in wind speed at more than one height of the towers; (4) the wind speed differential, the difference between the maximum receding and maximum approaching radial velocities, is greater than 10 m s-1. De Gaetano et al. (2014) separated events recorded by anemometers into three categories, stationary Gaussian extratropical cyclones, non-stationary non-Gaussian thunderstorm outflows, and stationary non-Gaussian intermediate events. This procedure was applied in Solari et al. 2014 and Zhang et al. 2018. While the use of synthetic information provides some deeper understanding of the recorded gust there is a need to better understand the environmental climatology conducive to the formation of these events given the wide array of favourable meteorological environments in which these events occur. 2.4.2. Meteorologically Identifying Events The second approach used to identify gust origins looks at specific weather phenomena of interest through the detailed inspection and reconstruction of the meteorological conditions responsible for each given event type. This includes the use of surface measurements, radar, satellite, soundings and any other data that helps explain the atmospheric set up during an event. For example, Charba (1974) used anemometers, thermometers, barometers, hygrometer and radar images to examine an intense gust front in Oklahoma on 31st May 1969. Goff (1976) used similar instruments to analyse 20 thunderstorm outflows in Oklahoma from 1971 to 1973. In

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Australia, Sherman (1987) used wind observations recorded on a transmission tower at 4 different levels as well as surface measurements of temperature, pressure, humidity, and radar images to give a detailed description of a downburst that struck Bald Hills in Queensland on 5th November 1977. Similar kinds of analysis were also conducted by Fujita (1990), Gast and

Schroeder (2003), Holmes et al. (2008), and Gunter and Schroeder (2013). Loredo-Souza et al. (2019) calculated a range of severe weather indices (Caracena et al., 1989; Gilmore and Wicker, 1998) from atmospheric soundings during the occurrence of severe wind gusts in Brazil to determine if the damaging gust was a downburst event. Their approach started by taking gusts greater than 10 m s-1 (Garstang et al., 1998) to account for events where the maximum wind speeds might not have been observed by an anemometer. To be classified as a downburst, the event required the presence of precipitation, along with an abrupt decrease of the equivalent potential temperature (θe), between 4.00 K and 18.74 K, and an instantaneous decrease of specific humidity greater than 3.5 g kg-1 air (Garstang et al., 1998). In addition, Loredo-Souza et al. (2019) looked for a pressure increase greater than 2.4 hPa, a threshold that was based on work by Fujita (1985), Caracena and Maier, (1987), and Garstang et al., (1998). These identification methods can be tedious, require significant resources, and requires human intervention. A more automatic method would be necessary to be able to look at larger dataset of severe weather events. Recently, machine learning has become more widely used in atmospheric science, especially the use of Self-Organising Maps (SOM). The SOM algorithm was first introduced by Kohonen (1982). It uses competitive machine learning, a type of machine learning, to classify large volumes of data into a two-dimensional grid of map nodes with a predetermined number of archetypes. The algorithm organises the data based on their similarities. This method is used in many disciplines and as noted by Huth et al. (2008) is gaining popularity in the atmospheric sciences. SOMs have been used to classify proximity soundings by Nowotarski and Jensen (2013) to improve the forecasting of supercells and tornadoes. Their results showed that SOMs can be used as a classification technique for research as well as for creating conditional probability forecast products. In addition, they suggest it can be used for hodographs to classify different storm types, such as supercellular and nonsupercellular. The use of SOMs for the wind storm classification has merit because it can efficiently process large datasets while being relatively objective in the process and can consider more detailed data than through manual classification methods.

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2.5. Convective Wind Storms and Climate Change

There has been a significant increase in global temperature because of anthropogenic emission of carbon dioxide (IPCC, 2014). Current trends in thunderstorm occurrence are difficult to analyse due to the sparse and sporadic nature of their occurrence, as discussed in Kuleshov et al. (2002). Environment-based studies have been used to project trends for thunderstorm activity (Kunkel et al., 2013; Brooks, 2013; Hermida et al., 2013). Kunkel et al. (2013) and Brooks (2013) found that currently, there is no significant trends in thunderstorm environments for the United States as well as other parts of the world. In Europe, Hermida et al. (2013) found no trend when looking at networks of hailpads. However, using a statistical model, Rädler et al. (2018) finds that the occurrence severe weather (lightning, hail, and wind) has increase over large parts of Europe, apart from the southwest, for the period of 1979-2016. This was attributed to an increase in the instability found in the reanalysis data and not by changes in midtropospheric moisture or wind shear. In Australia, outside of the natural variability (i.e., ENSO), a lack of trend has been noted in both the occurrence of thunderdays and environmental climatology over the past three decades (Davis and Walsh, 2008; Allen and Karoly, 2014). However, the lack of long-term records in Australia, and therefore reliable trend analysis, continues to be a significant gap in our knowledge (Walsh et al., 2016). These issues persist when trying to determine future trends in the occurrence of thunderstorms and their associated hazards. Climate models are limited in their capacity to simulate convective environments. Many of these models poorly resolve mesoscale processes (Trapp et al., 2007; Del Genio et al., 2007). For example, the convective parameterization schemes used are known to eliminate energy from the atmosphere and have difficulty in dealing with convective inhibition (Gettelman et al., 2002; Marsh et al., 2007; Allen et al., 2014a). Also, the resolution used by these models makes it difficult to resolve sub grid scale processes as well as topographic influences that affect values of CAPE (Iorio et al., 2004; Niall and Walsh, 2005; Allen et al., 2014a). However, GCMs are shown to be useful in the simulation of large-scale features and synoptic systems that favour the development of thunderstorms. (Trapp et al., 2007; Del Genio et al., 2007; Marsh et al., 2007, 2009; Trapp et al., 2009; Van Klooster et al., 2009; Gensini et al., 2014; Diffenbaugh et al., 2013). Using the discriminator from Brooks et al. (2003), Marsh et al. (2007, 2009) showed that GCMs could produce reasonable spatial distributions of severe thunderstorms in the U.S. and Europe, but not necessarily the magnitudes. While some attention has been given to aspects of weather events (i.e., temperature, flooding, drought), in assessment reports by the Intergovernmental Panel on

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Climate Change (IPCC) and the United States Climate Change Science Program (CCSP) (IPCC 2007, 2012; CCSP, 2008) little attention has been given to the effects of climate change on severe convective wind storms. This is likely a result of the difficulties in data collection and the small horizontal scale of these events compared to the resolution of global models (Brooks, 2013). Current research, for future trends, has shown that a warming climate would lead to an increased occurrence of favourable thunderstorm environments as well as thunderstorms. This was mainly due to the increase in CAPE (Trappet al., 2007; Brooks, 2013; Diffenbaugh et al., 2013; Tippett et al., 2015). Brooks (2013) showed that most climate model simulations they examined suggest an increase in global temperature and boundary layer moisture will result in an increase in CAPE but also a decrease in Shr6. Moreover, they find that the increase in CAPE will more than offset the decrease in Shr6 over the U.S., which would increase the occurrence of environments conducive to thunderstorms. However, increase in CAPE may not necessarily correspond to the largest decrease in deep-layer shear (Brooks et al., 2007; Brooks, 2013; Diffenbaugh et al., 2013) and therefore the overall change in severe thunderstorm occurrence may be small or have a seasonal shift (Allen et al., 2014b) instead of an actual increase or decrease. Nonetheless, a decrease in the occurrence of environments favourable to produce thunderstorms might occur, over the U.S. and Europe, as a result of the poleward shift of synoptic patterns and the decrease in the thermal gradient (Del Genio et al., 2007; Marsh et al., 2009; Brooks, 2013; Diffenbaugh et al., 2013). With respect to storm intensity, Diffenbaugh et al. (2013) suggested there would be more intense storms in the eastern U.S., as they found the increase in days with high CAPE would coincide with low CIN. However, because of the high vertical resolution required to resolve CIN (Brooks 2009, 2013), it is difficult to know the effects of a warming climate on CIN as well as the occurrence of synoptic systems associated with both initiation and deep-layer shear (Allen et al., 2014b). A recent study by Chen et al. (2020) suggests that CIN will become stronger over most land areas while becoming weaker over the oceans. They suggest the increase in CIN over land would inhibit the onset of weak to moderate moist convection, allowing for more intense CAPE to develop and likely result in less frequent but more intense moist convection. Yet, models also show little change in the occurrence of initiating features (i.e., fronts, troughs, dry lines). This combined with an increase in CAPE means that it is possible to see more days with strong shear while also having high CAPE (Trapp et al., 2009; Diffenbaugh et al., 2013; Gensini et al., 2014; Púcik et al., 2017; Hoogewind et al., 2017).

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In Australia, there was early analysis using three single mixed-layer global climate models that suggested decreases in the frequency of hail (McMaster, 1999). Subsequent work, for two stations in southeast Australia, supported these results using the CSIRO Mk3 model, which suggested decreases in the number of days with sufficient CAPE for severe hail, and an increase in the intensity of hail events when they do occur (Niall and Walsh, 2005). Even with the limitations that GCMs face when resolving convective storms, Allen et al. (2014a) showed that they can simulate the occurrence of favourable environments similar to reanalysis models. Allen et al. (2014b) show that low CAPE environments would decrease over Australia, while high CAPE environments would increase. In addition, low and moderate Shr6 would be relatively unchanged, while high Shr6 would decrease. Allen et al. (2014b) find that, over Australia, a warmer climate will result in an increase in thunderstorm environments over northern and eastern Australia. This is similar to work by Abbs et al. (2007) and Leslie et al. (2008) that found an increase in these environments over the east coast of Australia. Two factors that will play a role in how the occurrence of severe weather in Australia will change as a result of a warmer climate are (1) the availability of moisture and (2) the response of the jet stream (Allen et al., 2014b). Allen et al. (2014b) looked at the performance of two global climate models, the CSIRO Mk3.5 and Cubic-Conformal Atmospheric Mode (CCMA) in Australia. They showed a poleward shift of synoptic patterns, resulting in decrease in Shr6, as well as a decrease in the thermal gradient between the midlatitudes and the poles. However, they also showed higher sea-surface temperatures and advected moisture resulting in the increase in high CAPE environments. Their work suggested there would be an increase in severe thunderstorm environments under a highly warmed future climate scenario, especially for the east coast of Australia. However, their analysis showed a significant sensitivity in severe thunderstorm environments due to model physics specifically related to moisture advection and convective parameterizations, likely a result of how the models resolved topographic features and the resulting effect on moisture advection. The influence of a warming climate on cool-season tornadoes, that form in low-instability environments, has not been considered globally (Kounkou et al., 2007). Timbal et al. (2010) suggest that they will be less likely to occur because of the thermal stabilization of the lower troposphere over southern Australia in the winter months, this is opposite to their warm season counterparts. In the state of Tasmania specifically, Cechet et al. (2012) finds that there is no large change in the hazard associated with thunderstorms when looking at the years 2050 and 2090, however this is using the

Literature Review Chapter 2 assumption that the intensity of thunderstorms remains constant and only considers changes in thunderstorm frequency. Research into the influence of a warming climate on Australian severe thunderstorms is limited. In addition, nothing can be known with a high level of certainty because processes important to determining the frequency and intensity of convective storms are of a smaller scale than resolved by GCMs (Allen et al., 2014b). Given the large discrepancies between climate models, it is important to consider a larger suite of models when analysing potential changes. In addition, there is a need to determine how the initiation of these events may change and how to improve the model physics and better incorporate topographical features important to the severe thunderstorm environment in Australia (Allen and Allen, 2016). One such approach may be that used by Gensini and Mote (2015) who made use of dynamical downscaling over the U.S. to directly simulate storm occurrence instead of favourable environments. Despite the stated limitations, it remains a useful exercise to attempt to quantify the potential changes to convective wind hazards due to climate change using GCM derived environments, given these are the best data and methods currently available. The use of different climate change scenarios will help to quantify some of the uncertainty associated with these results. To the author’s knowledge, no research has looked at the potential change to convective wind storm hazard with climate change in Australia except for the work of Cechet et al. (2012) who looked only at the impacts to Tasmania. 2.6. Literature Summary

Convective winds have been shown to have a large social and economic impact around the world, including in Australia. These winds originate from many different atmospheric phenomena. They largely result from mesoscale and microscale events, but have been shown to occur in larger scale, synoptic events. Research has looked at the hazard posed by severe wind gusts to buildings and infrastructure around the world, but little research has focused specifically on severe wind gust generated by convective wind storms. Work has been done to improve the forecasting of such events through the use of severe weather indices. These indices look at large-scale atmospheric parameters to help determine the potential for thunderstorm formation. The use of severe weather indices along with techniques such as Bayesian statistics can help to improve the reliability of observational datasets. This work looks to extend the earlier research conducted that was discussed in this chapter. Specifically, focus is put on developing a new method for separating and classifying severe wind storms from anemometer records. Specifically, building on the two main methods,

Literature Review Chapter 2 statistically and meteorologically, that have previously been used by numerous studies that date back to the 60s and have been discussed in detail by De Gaetano et al. (2014). In addition, the work conducted here looks to build on previous climatologies of severe convection in Australia, which Allen and Allen (2016) discuss in detail, by building what is believed to be the first severe convective wind storm climatology for Australia. Moreover, this work looks to improve the method used in previous thunderstorm climatologies where most are spatially incomplete and do not correct for reporting biases with observational datasets. Finally, this work builds on the previous research done by Allen et al. (2014a,b) into the effects of climate change on thunderstorm environments across Australia by examining the impacts of climate change specifically on the occurrence of severe convective wind storms. The development of a national convective wind gust climatology helps to inform national hazard and risk assessments associated with the severe wind storms in the present climate as well as in the next 50 to 100 years.

Chapter 3: Classifying wind gust typologies using Self-Organising Maps

Classifying wind gust typologies using Self-Organising Maps Chapter 3

3.1. Introduction

Fifty percent of all wind related damage to buildings in Australia are the result of local convective wind storms (Blong, 2005). A key reason for this is that in Australia, as in all other regions of the world, wind resistant design standards do not explicitly consider these events within their provisions. A better understanding of the risk convective wind storms pose to infrastructure is necessary to mitigate impacts of future events. A major component of this is to understand when, where, and how often these events occur. This will allow for the development of convective wind storm hazard maps. To build a convective wind gust climatology, an observational dataset that provides accurate and reliable information on the occurrence of these events is required. Unfortunately, many observational datasets do not specify the storm mode responsible for the severe wind storm. In Australia, the Commonwealth Bureau of Meteorology (BOM) now records all severe local storms reported by storm spotters, the public and any of its Automatic Weather Stations (AWS). This dataset is known as the Severe Storm Archive (SSA) and includes wind storms where the peak gust was measured or estimated to be greater than 90 km h-1. Unfortunately, this dataset contains inconsistences, specifically relating to the location and timing of events. It is also prone to biases caused by temporal changes in population density and location. This makes it difficult to build a robust and reliable climatology using this dataset. Fortunately, the BOM has an extensive record of wind data from AWS located across Australia. Unlike the full SSA database, the AWS provides reliable information on the location, magnitude and timing of wind gust occurrence. However, this dataset has its own challenges. The dataset is large, comprising of almost 600 stations across Australia and does not provide any information about the storm modes responsible for each individual gust. In order to develop a climatology of severe convective wind gusts it is crucial to know which observed gust resulted from convective storms. Given the size of the dataset, it is difficult and time consuming to identify each storm mode manually. Identifying storm mode is a major challenge when building a severe convective wind storm climatology (Gomes and Vickery, 1976; Kasperski, 2002; Lombardo et al., 2009; Wang et al., 2013; Solari, 2014). The separation of event types into homogenous families is especially important in mixed wind climates, so that sound distributions of severe wind storms can be determined and used to conduct refined analyses of different phenomena and their contributions to wind-excited response of structures (De Gaetano et al., 2014). To do this, it is

Classifying wind gust typologies using Self-Organising Maps Chapter 3 important to consider both the records detected by wind monitoring network and the weather scenarios responsible for the event. In Australia, studies that look at convective winds have mainly focused on the use of anemometer records that manually exclude non-convective events (Geerts, 2001). Alternatively, extreme value theory can be used to consider the distributions of severe convective wind occurrences statistically (Holmes, 2002). Currently, the use of synthetic indicators and expert judgments are still the main tools used to separate and classify an extensive amount of data and process wind velocity records (Gomes and Vickery, 1976; Riera and Nanni, 1989; Twisdale and Vickery, 1992; Choi, 1999; Choi and Hidayat, 2002; Duranona et al., 2006; Kasperski, 2002; Lombardo et al., 2009). However, this method avoids a detailed understanding of the meteorology responsible for the events. Another method looks at specific weather phenomena of interest through the detailed inspection and reconstruction of the meteorological conditions responsible for the specific event type. This includes the use of surface measurements, radar, satellite, soundings and any other data that helps explain the atmospheric set up during an event. For example, in Australia, Sherman (1987) used wind observations recorded on a transmission tower at 4 different levels as well as surface measurements of temperature, pressure, humidity, and radar images to give a detailed description of a downburst that struck Bald Hills in QLD on 5th November 1977. However, this method can be tedious, require significant resources, and requires human intervention. A more automatic method would be necessary to be able to look at larger dataset of severe weather events. In this paper, machine learning is examined as an efficient and objective method to differentiate between wind gusts generated by convective and non-convective storms. For this work convective storms are defined as events that originate from convective weather systems and have small temporal and spatial scales. In comparison, non-convective storms are on a larger temporal and spatial scale. Specifically, the Self-Organising Maps (SOM) algorithm, introduced by Kohonen (1982), is utilised. This method has been used in many disciplines and as noted by Huth et al. (2008) it is becoming more widely used in the atmospheric sciences. Within this field, the SOM algorithm has been used to classify synoptic weather types in Australia using geopotential height data (Jiang et. al., 2013a; 2013b; Jiang et, al., 2015). SOMs have also been used to classify proximity soundings to improve the forecasting of supercells and tornadoes (Nowotarski and Jensen, 2013; Nowotarski and Jones, 2018). These studies have shown that SOMs can successfully be used as a classification technique for research as well as creating conditional probability forecast products. Given this, it is proposed here that a similar 73

Classifying wind gust typologies using Self-Organising Maps Chapter 3 technique involving SOMs can be used to classify the meteorological origin of wind gusts from 1-minute data records. This paper outlines the proposed approach for developing, training and applying a SOM classification model using meteorological data with the aim of identifying the meteorological origin of recorded wind gusts. This model is then applied to all available 1- minute wind gust data in Australia for the period 2005-2015 and a national convective wind gust climate for this period developed. 3.2. Data and methods

3.2.1. Automatic Weather Station data and analysis The BOM observation network includes staffed and cooperative observer stations as well as AWS. Standard BOM AWSs record data at 1-minute intervals, and the wind data recorded includes 1-minute mean wind speed, peak 3-second gust within each 1-minute period and mean wind direction. In addition, each station records 1-minute temperature, dew-point temperature, wet-bulb temperature, mean sea-level pressure, sea-level pressure, vapour pressure, and saturated vapour pressure. For this work the wind speed, wind direction, temperature, mean sea-level pressure, and precipitation data records are utilised. This 1-minute data has been obtained for 599 stations across Australia, with variable start and end dates for each station, Years Events

Classifying wind gust typologies using Self-Organising Maps Chapter 3 with the maximum data availability from 1995 to 2015. Only stations with at least 5 years of 1-minute data were examined for this work to limit the influence of stations with short record periods. Figure 3.1 shows the 306 AWS with at least 5 years of data used for the analysis. 3.2.2. Extracting Wind Storms The first step in the analysis procedure is to extract wind gusts of interest from AWS records. For this analysis, all wind gusts exceeding 70 km h-1 are identified at every station. So that only a single value is recorded for each gust event, where multiple exceedances are observed within a given 6-hour time block (00-06Z, 06-12Z, 12-18Z, and 18-00Z) only the maximum gust value is retained. While the choice of 6-hour time blocks is somewhat arbitrary, this period is chosen to ensure that multiple events that occur on the same day, but may have resulted from different types of storms, can be identified and included in the dataset. Using the time each gust occurs, all 1-minute data (i.e., wind speed and direction, temperature, dew-point temperature, wet-bulb temperature, mean sea-level pressure, sea-level pressure, vapour pressure, and saturated vapour pressure) 2 hours before and after the gust event are extracted and stored. Gust wind speeds are then corrected to account for topographic influences. This is done by calculating the topographic multiplier (Mt) at each station for the eight cardinal and primary intercardinal directions (i.e., North, Northeast, East, Southeast, South, Southwest, West, and Northwest) following the approach specified in AS/NZS1170.2 (Standards Australia, 2012). ~30m resolution elevation data, sourced from Geoscience Australia (2011), was used to define topographic slopes for these calculations. The corrected wind speed is calculated as follows:

푢0 푢푐표푟푟 = , (3.1) 푀푡

where u0 is the measured wind gust and ucorr is the corrected wind gust value after applying

푀푡. For Tasmania (TAS), above 500 meters the topographic multiplier is defined as,

푀푡 = 푀ℎ(1 + 0.00015퐸), (3.2)

where 푀ℎ is the hill shape multiplier and E is the site elevation above mean sea level, in meters. For the rest of Australia, the topographic multiplier is defined as:

푀푡 = max (푀ℎ, 1). (3.3)

Classifying wind gust typologies using Self-Organising Maps Chapter 3

The hill shape multiplier is calculated as follows:

퐻 a. For < 0.05, 푀ℎ = 1.0, 2퐿푢 b. For 0.05 ≤ 퐻 < 0.45, 2퐿푢 퐻 |푥| 푀ℎ = 1 + ( ) (1 − ), (3.4) 3.5(푧+퐿1) 퐿2 c. For 퐻 ≥ 0.45 and within the separation zone, 2퐿푢 |푥| 푀ℎ = 1 + 0.71 (1 − ), (3.5) 퐿2

Not in the separation 푀ℎ zone follows (3.4)

where, H is the height of the hill, Lu is the horizontal distance upwind from the crest of the hill to a level half the height below the crest, x is the horizontal distance upwind or downwind to the crest of the hill, L1 is the length scale to determine the vertical variation of Mh, and L2 is the length scale to determine the horizontal variation of Mh (Standards Australia, 2012).

Wind gusts from any direction where Mt is larger than 1.3 (upwind slope of > 25°) are removed. This is done to minimise the influence of steep topography where there is uncertainty in the application of this procedure (Holmes et al., 2012). If removing these data results in the loss of more than 25% of events for any given station, that site is removed from any further analysis so overall statistics are not adversely affected. This resulted in the removal of 22 stations from the dataset, mainly located in the Australian Alps and Tasmania. Applying Eqn. 3.1 implicitly assumes that the type of event generating a wind gust does not influence Mt values, which in this procedure were developed assuming atmospheric boundary layer (ABL) winds (Holmes et al., 2012). Evidence suggests this may not be the case for microburst-scale convective events (e.g., Mason et al., 2010), but given no consensus yet exists on how topography influences wind gusts during these, or any other non-ABL wind event, the assumption that Mt is independent of event type is applied here. A further assumption this correction procedure makes is that the influence of differing surface terrain (i.e. effective aerodynamic roughness) between directions or sites can be ignored. This is not strictly correct, but given relatively short data records were available at many sites, automated effective roughness calculation procedures such as those proposed by Masters et al. (2010) and Lombardo and Krupar (2015) were unable to be uniformly applied. Further, given the primary objective of this research is to understand the convective wind gust climate, the prevailing

Classifying wind gust typologies using Self-Organising Maps Chapter 3 wisdom that surface roughness influences peak gusts during convective events to a lesser degree than ABL events (Holmes et al., 2012), suggests this is an acceptable assumption to make. In the instances where 1-minute data samples were missing in the extracted 4-hour data blocks, a smoothing is applied to the time series for each variable and missing data replaced with the smoothed value. This is done to minimise the number of events discarded for either training or applying the SOM model. The smoothing was applied using both a 5-minute and 10-minute averages to see if there was any sensitivity to the smoothing used. 3.2.3. Quality Controlling 1-min Wind Storms When manually identifying events for training the SOM algorithm (Section 3.2.4), all wind speed time histories were manual assessed and spurious data removed from these records. This approach was unrealistic when analysing the entirety of the AWS dataset. As such, here the de- spiking method of Højstrup (1993) is applied, which was shown by Suomi et al. (2017) to effectively remove unrealistically high wind speeds from anemometer records. In brief, the method uses the previous data point (i − 1) to predict the next data point, i, in a time series. The forecast wind speed at the time of event is calculated as:

푢푓푐푠푡(𝑖) = 푐표푣푖(휏)푢퐿(𝑖 − 1) + (1 − 푐표푣푖(휏))̅푢̅퐿̅(𝑖), (3.6) where, cov(τ) is the autocovariance with time lag (τ) equal to the resolution of the measurements

(i.e., Δt) and ̅푢̅퐿̅(𝑖) is the mean observed wind speed. The autocovariance and mean observed wind speed are calculated using a fixed number of data points, N, as done by Suomi et al. (2017). The event is then considered to be spurious if the absolute value of the forecast value minus the actual value is greater than the threshold for spike detection (Cspike) times the standard deviation of the last N observations:

|푢푓푐푠푡,푖 − 푢퐿,푖| > 퐶푠푝푖푘푒 휎푖. (3.7)

The fixed number of data points, N, and the value of Cspike used for this work were determined after a sensitivity analysis comparing the events removed manually from the 13 training stations discussed in Section 3.2.4 to the events removed using the de-spiking method.

Values of N = 100 and Cspike = 3 were found to have the best performance with a probability of

Classifying wind gust typologies using Self-Organising Maps Chapter 3 detection (POD) of 73% and a false alarm rate (FAR) of 15%. Table 3.1 shows the different

POD and FAR for different combinations of N and Cspike.

Table 3.1: POD and FAR for different combinations of N and Cspike. Cspike = 2.5 Cspike = 3 Cspike = 3.5 POD FAR POD FAR POD FAR N = 120 73 31 67 17 47 22 N = 100 73 27 73 15 53 20

N = 70 73 21 3 15 53 20

3.2.4. Manual Event Classification for SOM Training In order to train the SOM algorithm, extracted gusts for a selection of stations were manually classified. Training stations were chosen from across Australia so the SOM could account for any regional variations in time history characteristics within a given storm type that may exist. Stations were chosen near BOM weather radars. Of the stations used, most have over 10 years of 1-minute AWS data available with only three having just 5 years of data. However, the period that was used was also limited by the length of the radar data available which usually did not extend further back than 2005. For each training station, each extracted wind gust was manually assigned a storm mode using a mix of radar data (BOM, 2019b), synoptic maps (BOM, 2019a), the Southern Hemisphere Tropical Cyclone Data Portal (SHTCDP) (BOM, 2019c.), and lightning data (GPATS, WWLLN). The lightning data specifies the occurrence of lightning during 6hr time blocks (00-06Z, 06-12Z, 12-18Z, and 18-00Z) in 0.25-degree grid cells across Australia. Using all available data for each particular site, each gust event was categorised into one of four types; Convective, Transitioning, General, and Wind Only. Events were labelled as Wind Only events if the recorded wind was consistently “high” over the extracted 4-hour period, with little to no change in any of the other weather variables (e.g., Figure 3.2a). These events were typically associated with strong pressure gradients and little to no radar reflectivity. If there was a distinct front or air mass change visible on the synoptic maps, or on the radar imagery, along with features in the 1-minute weather data that are typically expected with a change in airmass (i.e. a sharp, distinct and lasting change in the wind direction and/or temperature, e.g., Figure 3.2b) then the event was labelled as a Transitioning event. Events were considered Convective (e.g., Figure 3.2c) if there was a distinct increase in wind speed at the time of event that was associated with an increase in pressure (Loredo-Souza

Classifying wind gust typologies using Self-Organising Maps Chapter 3

et al., 2016) and decrease in temperature, equivalent potential temperature, and mixing ratio (Garstang et al., 1998). This follows the approach used by Loredo-Souza et al. (2019) who analysed wind related damage that resulted from downbursts in Brazil. The presence of lightning was also taken into consideration but the presence or absence of lightning was not a deciding factor in determining if an event was convective or not. The presence of a convective radar signature (i.e. high reflectively, hook echo etc.) was also considered. All remaining events were classified as General (e.g., Figure 3.2d). These events were severe wind storms that had a relatively short increase in wind speed but were not associated with a significant increase in pressure or drop in temperature at the time of the event. They typically lacked a convective radar signature or lightning. These events, therefore, were not specifically associated with convection or directly related to a front or change in air mass. To finalise event classification,

a) b)

c) d)

Classifying wind gust typologies using Self-Organising Maps Chapter 3 the SHTCDP was used to determine whether extracted gusts were associated with a tropical cyclone. Any gust events found to be so were sorted into the General category for this work. Also, for the sake of consistency, any events found to be caused by embedded convection within a front were classified as Transitioning. Figure 3.3 shows the location of the 13 stations that were used for SOM training. The gross proportion of each event type is also indicated for each site, with the size of the pie charts scaled to the total number of events at each station. Figure 3.3a shows these proportions for events throughout the year. In the northern parts of Australia, the majority of events mainly fall into two storm modes, Convective or General. The exceptions being Cairns and Townsville, where there appears to be a bigger than expected influence by the Wind Only mode. This is likely a result of the small number of events observed at these stations making it difficult to give an accurate representation of the dominate storm modes at these locations. Whereas further south, there is more of a mix of the four storm modes, with the Convective making up a smaller percentage. The exceptions being in central Australia, Alice Springs and Roxby Downs, and in the eastern parts of Australia at Oakey. Looking at how this picture changes during different times of the year the events are split into two periods, Spring-Summer (September, October, November, December, January, February) in Figure 3.3b and Autumn- Winter (March, April, May, June, July, and August) in Figure 3.3c.

Classifying wind gust typologies using Self-Organising Maps Chapter 3

b) c)

Figure 3.3: Map of Australia showing the location of the 13 stations where 6-hourly wind storms above 70 km h-1 were manually categorised into four categories. The pie charts next to each station show the percentage of each storm type identified at the station, where blue represents Wind Only, green is General, orange is Transitioning, and red is Convective. The size of the pie charts are representative of the number of events observed at each station. Similar proportions are seen during the Spring-Summer months as are seen during the entire year especially for the stations in northern and central Australia. This may be because the majority of events at these stations tend to occur during these months. During the Autumn and Winter months there is a decrease in the overall number of events at all stations, specifically at the central and northern Australia stations with only 1 event at both the Weipa and Cairns stations, but a slight increase at the Jandakot and Adelaide stations. Most stations see a

Classifying wind gust typologies using Self-Organising Maps Chapter 3 reduction in the percentage of events originating from Convective modes except for Darwin and Smithton. The increase at Darwin may just be reflective of the small number events reported during these months with only 8 events recorded in almost 14 years of available data. The larger portion of convective events at Smithton during the Autumn-Winter months is not easily explained, but with only 5 years of data available at this station it is difficult to make any conclusion about the climatology there. 3.2.5. Self-Organizing Maps

3.2.5.1. Introduction to Self-Organizing Maps

Self-Organizing Maps (SOM) use competitive machine learning to characterise patterns within a dataset into a two-dimensional grid of map nodes. This allows large volumes of data to be classified into a set number of archetypes that are sorted based on their similarities. The algorithm is an iterative process by which the training data are used to train a SOM that represents the distribution of data. The training algorithm works by repeated comparison of training data vectors to the SOM nodes. Where each SOM node has an associated model vector, m, of length equal to the dimension of the training data vectors. The best matching unit (BMU) is found to be the SOM node that has the smallest Euclidean distance between its model vector, m, and a given training data vector x. The BMU and surrounding nodes are then updated using the following equation,

푚푖(푡 + 1) = 푚푖(푡) + 훼(푡)ℎ퐵푀푈푖(푟(푡))[푥(푡) – 푚푖(푡)] , (3.8)

where t is time, α is the learning rate parameter, and hBMUi is the neighbourhood function around the BMU with the neighbourhood radius, r, for the ith SOM node. The learning rate parameter defines how the map is updated and the neighbourhood function explains the relationship between adjacent nodes. The SOM algorithm used here is explained in detail by Kohonen (2001) and the MATLAB function package is available through Vesanto (2000). A key advantage of using SOM for event classification is that no initial assumptions or information about what the final map will look like is required. The training data is analysed objectively because the SOM only knows the values of the training data at different time steps and nothing about the storm modes themselves. The greatest advantage of using SOMs over the more traditional analysis of empirical orthogonal functions (EOFs) is the lack of restrictions of orthogonality and stationarity of identified patterns (Gervais et. al., 2016). However, this leads to large numbers of free parameters, variables in the SOM that must be manually

Classifying wind gust typologies using Self-Organising Maps Chapter 3

specified, which result in some subjectivity in the resulting SOM. To minimise the impact of this subjectivity a sensitivity analysis is performed on 8 of the free parameters. These include, the lattice, SOM (map grid) size, neighbourhood function hBMUi, radius of influence r, initialization, learning rate function α, the training length T, and the algorithm. These 8 free parameters are discussed below. While the SOM algorithm supports map grids of any dimensions, the focus here is on 2- dimensional maps since they are simpler to visualise and understand. The nodes can be arranged in a hexagonal (Figure 3.4a) or rectangular lattice (Figure 3.4b). The hexagonal lattice is recommended since all 6 neighbours of a node will be the same distance apart, as opposed to the 4 neighbours on a rectangle lattice, but is mostly a matter of personal preference (Kohonen, 2001; 2014). The size of the SOM determines the number of nodes that will be used to represent the data. The mapping is not negatively affected if the number of nodes exceeds the number of input vectors, as long as the neighbourhood function is chosen appropriately. However, larger SOM maps can be computationally expensive. Here, 7 different SOM sizes are investigated: [2 × 2], [2 × 5], [3 × 3], [3 × 4], [3 × 5], [4 × 4], and [6 × 6]. Each node within the SOM is related to the nodes adjacent to it. The neighbourhood function explains the relationship of a node to its adjacent nodes. The neighbourhood function and the number of nodes controls the smoothness and generalization of the mapping. The SOM algorithm used (Vesanto, 2000) allows for four different neighbourhood function: bubble (Figure 3.4c), Gaussian (Figure 3.4d), cut Gaussian (Figure 3.4e), and Epanechicov (Figure 3.4f). The different neighbourhood functions are dependent on a radius of influence, which is the maximum distance away from the BMU where the training data still has influence. Kohonen (2001) suggest beginning training with a radius equal to the diameter of the SOM to ensure all nodes are updated at the start, and then allow the radius of influence to decrease with training time. Examples of the radius of influence are shown in Figure 3.4a and 3.4b by the hexagon and square lines drawn around the centre point, where 0 refers to a radius of influence of 0, 1 refers to radius of influence of 1 and so forth. The use of four different radius of influence are explored here. A radius, r, of zero, an r that starts at 1 and goes to 0, as well as an r that starts at 2 and ends at 0, and finally an r that starts at 3 and ends at 0. Prior to the SOM training, the SOM is initialised either randomly or linearly. Random initialisation involves the model vector of each node being initialised with smaller random values, whereas the linear initialisation has the model vectors initialised along the linear subspace between the two principal eigenvectors of the training dataset. The Gram-Schmidt procedure is used to calculate the eigenvectors. 83

Classifying wind gust typologies using Self-Organising Maps Chapter 3

The training of the SOM is dependent on the learning rate, α(t), as well as the training length,

T. Training is done in two phases; it begins with rough training, Trough, with a large radius of influence and learning rate, and then fine-tuning training, Tfine, with a small radius of influence and learning rate. The learning rate specifies how the weight vector changes during SOM learning. Three different learning rate functions are used, linear, inverse-of-time, and a power series. Examples of what the learning rate as a function of number of steps looks like is shown in Figure 3.4g, where the solid line is the linear learning rate function, the dash-dot line in the inverse-of-time function, and the dash line is the power series function. Moreover, three different training lengths, or number of training steps, are examined; (1,1), (2,8), and (20,80).

The first number refers to the training steps of Trough, to first tune the SOM to be approximately in the same space as the input data, and the second number refers to the training steps of the of

Tfine, to fine-tune the SOM map. The SOM algorithm can use either, the sequential, batch, or SOMPAK training method. The sequential method trains the SOM iteratively where one training data vector (or gust event) is randomly chosen and the distance between it and the model vectors of the SOM are determined. The SOM map is then updated at the end of each iteration following Eqn. 3.8. The batch algorithm works by running all training data vectors at once. The SOM map is then updated with the net effect of all samples. The model vectors are updated following a modified version of Eqn. 3.8,

푛 ∑푗=1 ℎ퐵푀푈(푗)(푡)푥푗 푚푖(푡 + 1) = 푛 , (3.9) ∑푗=1 ℎ퐵푀푈(푗)(푡)

where BMU(j) is the best matching unit for the input data vector, xj,, and n is the number of input vectors. An additional method that was tested is SOMPAK training, which is the MATLAB version of an earlier release of the SOM function package created for Unix by Kohonen et al. (1996). This training method follows that of the sequential training method, Eqn. 3.8. A sensitivity analysis was conducted with the different possible combination of the 8 free parameters discussed above. This includes assessing three built in error quantification tools in the SOM toolbox; the Sammon mapping algorithm (Sammon, 1969), the quantization error (QE), and the topographic error (TE) (Vesanto, 2000). The Sammon map is a nonlinear mapping of the SOM from higher to lower dimensions, which is representative of the Euclidean distance between map nodes onto a two-dimensional field. An example of what a Sammon map

Classifying wind gust typologies using Self-Organising Maps Chapter 3

looks like can be seen in Figure 3.7. It can be used to determine the topology or spatial relationship between map nodes, or how similar map nodes are to one another. If the SOM is well constructed it should have a flat Sammon map (Kohonen, 2001), that is, it should look a two-dimensional square grid structure. The QE is the average Euclidean distance between each data vector and its corresponding BMU. It is a measure of how similar the data are to the BMU. The TE is the percentage of data vectors that do not have their second-BMU adjacent to its BMU. It is a measure of the organisation of the SOM. A combination of a low QE, a low TE, and a well- ordered Sammon map will be important when determining which free parameters should be used for the SOM.

a) b)

c) d) e) f)

Classifying wind gust typologies using Self-Organising Maps Chapter 3

3.2.5.2 Input Variables and Preprocessing

Although the AWS provides nine different 1-min weather variables (Section 3.2.1) focus is put on the combination of four of variables: wind speed, change in wind direction, temperature and pressure. Precipitation is also considered in one test case since the manual identification of events showed it to be a useful variable with potential to distinguish between event types. However, the available precipitation data tended to have more missing data points than some of the other variables so its use was limited here. Equivalent potential temperature was also calculated to determine if it might perform better than temperature alone. The change in wind direction was calculated by subtracting the wind direction at each time step by the mean wind direction measured in the first ten minutes of the four hour time series. This is done by breaking the wind down into its u (zonal) and v (meridional) components as follows:

푢 = −푼 ∗ sin(퐷𝑖푟 ∗ ( 휋 )) , (3.10) 푇푟푢푒푁표푟푡ℎ 180 푣 = −푼 ∗ cos(퐷𝑖푟 ∗ ( 휋 )) , (3.11) 푇푟푢푒푁표푟푡ℎ 180

where U is wind speed and Dirtruenorth is the wind direction from true north. The mean direction is then calculated from the mean u and v wind components during the first ten minutes in the time series following:

arctan (−푢) 𝑖푓 푣 > 0, −푣 −푢 arctan ( ) + 휋 𝑖푓 푣 < 0 푎푛푑 푢 ≥ 0, −푣 −푢 180 arctan ( ) − 휋 𝑖푓 푣 < 0 푎푛푑 푢 < 0, ( ) ∗ −푣 , 휋 휋 + 𝑖푓 푣 = 0 푎푛푑 푢 > 0, 2 − 휋 𝑖푓 푣 = 0 푎푛푑 푢 < 0, 2 {푢푛푑푒푓𝑖푛푒푑 𝑖푓 푣 = 0 푎푛푑 푢 = 0. 퐷𝑖푟푇푟푢푒푁표푟푡ℎ = 푢 . (3.12) arctan ( ) 𝑖푓 푣 > 0, 푣 푢 arctan ( ) + 휋 𝑖푓 푣 < 0 푎푛푑 푢 ≥ 0, 푣 푢 180 arctan ( ) − 휋 𝑖푓 푣 < 0 푎푛푑 푢 < 0, 270 − ( ) ∗ 푣 , 휋 휋 + 𝑖푓 푣 = 0 푎푛푑 푢 > 0, 2 휋 − 𝑖푓 푣 = 0 푎푛푑 푢 < 0, 2 { {푢푛푑푒푓𝑖푛푒푑 𝑖푓 푣 = 0 푎푛푑 푢 = 0.

Classifying wind gust typologies using Self-Organising Maps Chapter 3

The absolute value of the change in direction, wrapped between -180 to 180 degrees, is then used. Equivalent potential temperature is calculated following equation 2.36 in Rogers and Yau (1989):

2675푤 ( ) 푇 휗푒 = 휗 푐 , (3.13)

where, θe is the equivalent potential temperature, θ is the potential temperature, w is the mixing ratio and Tc is the temperature at the isentropic condensation level. The isentropic condensation temperature can be calculated from equation 2.33 in Rogers and Yau (1989),

푝푐 푘 푇푐 = 푇0( ) , (3.14) 푝0

where k is a constant equal to 0.286, and T0 is the temperature and p0 is the pressure and pc is the isentropic pressure. The isentropic pressure is calculated by rearranging equation 2.18 in Rogers and Yau (1989) and substituting the vapour pressure and missing ratio with the saturation vapour pressure and saturation mixing ratio. This gives,

휀+푤푠 푝푐 = 푒푠 ( ), (3.15) 푤푠

where ws is the saturation mixing ratio, es is the saturation vapour pressure, and 휀 is a constant equal to 0.622. Prior to running the SOM algorithm, the input variables are normalised. For this work the wind speed and precipitation are normalised by dividing each event by the maximum wind speed and precipitation rate recorded within the extracted 4-hour data period, respectively. The absolute change in wind direction is normalised by dividing by 180°. The temperature, pressure, and potential temperature are normalised by subtracting each event by the minimum value of the variable and then dividing by the difference between the maximum and minimum value of the variable. These normalizations mean that each input variable is a time history of values ranging between 0 and 1. This is done to help improve the discriminating of the events. The following 10 input variable combination are explored to identify the best performing combination for the SOM algorithm:

Classifying wind gust typologies using Self-Organising Maps Chapter 3

1. Wind Speed Only (W) 2. Wind Speed and Change in Wind Direction (W-D) 3. Wind Speed and Temperature (W-T) 4. Wind Speed and Pressure (W-P) 5. Wind Speed, Temperature and Pressure (W-T-P) 6. Wind Speed, Change in Wind Direction, and Pressure (W-D-P) 7. Wind Speed, Change in Wind Direction, and Temperature (W-D-T) 8. Wind Speed, Change in Wind Direction, Temperature, and Pressure (W-D-T-P) 9. Wind Speed, Change in Wind Direction, Temperature, Pressure, and Precipitation (W-D-T-P-P) 10. Wind Speed and Potential Temperature (W-Te) 3.2.5.3 Assessing SOM performance

The performance of each SOM is tested following an approach similar to Nowotarski and Jensen (2013). In this approach, forecast skill scores are used as a way of examining the ability of a SOM to predict wind storm types. It is important to note that this does not strictly verify the performance of the SOM since the same data is being used for both the training and verification. However, it has been shown to be a good way to assess the relative skills of the SOM in an idealised forecasting scenario. For this work the Brier Skill Score is also used (BSS; Brier, 1950; Wilks, 2006; 2010). In general, the BSS works as follows. For each event, i, within an event set of length n there are c possible categories that can occur. For a given event the forecast probabilities for each category to occur are fi1, fi2, … fic, for categories 1, 2, . . . c, respectively. The classes are chosen to be mutually exclusive and exhaustive so that:

푐 ∑푗=1 푓푖푗 = 1 , i = 1, 2, 3, … 푛. (3.16)

The Brier Score (BS) is then defined to be:

1 푟 푛 2 퐵푆 = ∑ ∑ ( 푓 − 퐸 ) , (3.17) 푛 푗=1 푖=1 푖푗 푖푗

where Eij, takes the value 1 or 0 according to whether the event occurred in class j or not. A perfect forecast will have a BS equal to zero, and the worst possible forecast will have a value of c. The BSS is commonly used for dichotomous events (i.e., either the storm type in question

Classifying wind gust typologies using Self-Organising Maps Chapter 3 occurs or it does not) as done by Wilks (2006) and Nowotarski and Jensen (2013). In this case, Eqn. 3.17 simplifies to:

1 푛 2 퐵푆 = ∑ ( 푓 − 퐸 ) . (3.18) 푛 푖=1 푖 푖

The BS is calculated for each SOM where the forecast probabilities for each event type corresponds to the percentage of each storm type within the node an individual event is sorted into. A climatological BS, BSclim, is also calculated, which for this work is calculated using the forecast probabilities equal to the percentage of each storm type used for the event input dataset. The forecast skill is then defined to be the BSS which scales the BS with respect to a perfect

BS and BSclim, such that the BSS is calculated as:

퐵푆 퐵푆푆 = 1 − . (3.19) 퐵푆푐푙푖푚

The BSS is therefore useful in assessing the ability of a SOM to forecast the individual storm modes. To calculate the BSS, each time series is assumed to represent an individual forecast and the forecast probability vector is generated from the probability density function (PDF) of the node in the SOM to which that profile is matched. The BSclim is generated using the PDF of the entire dataset of 13 stations examined (Figure 3.5). The dichotomous BSS for each of the four categories is calculated with a focus on the ability of the SOM to correctly identify convective storms above all else. However, the cumulative BSS, i.e., c = 4, is also calculate since a successful SOM should ideally be able to successfully classify all storm categories. In addition to picking a SOM with a BSS closest to 1 for convective events alone and overall, it is important to make sure that the SOM has both a relatively small QE and TE compared to other SOM. This is to ensure that not only does the SOM have skill when classifying event types, but also that the nodes are well organised. A well-organised Sammon map is a measure of how well the SOM is constructed and therefore shows if it is robust and reliable. Nowotarski and Jensen (2013) also looked at two other measures to assess the quality of their SOMs. First, they looked at the change in variance of the events before and after applying the SOM algorithm. The variance between the events, for each variable considered, is calculated at each time step and averaged over the 4h period. This is done for all events used to train the SOM as well as for the events sorted into each. The average variance of each node is compared to the average variance for all events used to train the SOM. Since the SOM is

Classifying wind gust typologies using Self-Organising Maps Chapter 3 designed to group similar time series together into the same node, a successful SOM will be one in which the variance of each individual node is smaller than the variance of the entire training dataset.

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 Wind Only Transtion Convective General

Figure 3.5: Proportion of SOM training database with each storm mode classification. Moreover, a well-constructed SOM should not just reduce the variance, it should also be able to distinguish between the characteristics common to the different storm modes if it is to be used as a tool to classify different storm categories. To assess this, Nowotarski and Jensen (2013) looked at the difference between the percentage of a storm mode in each node to that of the same storm mode in the entire SOM. If the percentage difference is positive (negative) in any node, then an event that the SOM places in that node is more (less) likely to produce the storm type in question. The predictive ability of the SOM for each storm type is evaluated by looking at the difference between the maximum percentage difference minus the minimum percentage difference for each storm type. They called this the percentage difference spread. A large (small) percentage difference spread would suggest the SOM is good (bad) at distinguishing between events associated with that give storm type. The average percentage

Classifying wind gust typologies using Self-Organising Maps Chapter 3 difference spread between the four storm modes can be taken to determine how well the SOM can distinguish between all storm modes. Considering that there are multiple ways to assess SOM performance (not all of which will agree), to facilitate choosing an appropriate SOM, the importance of each metric for its use here is ranked. The ranking is as follows: 1. BSS Convection 2. Overall BSS 3. Topographic Error 4. Quantisation Error 5. Variance Reduction 6. Percentage Difference Spread The top SOM model for each SOM size is chosen for each of the 10 atmospheric variable combinations tested (Section 3.2.5.2). As a final check to make sure that the best performing SOM is chosen, the Sammon map (Sammon 1969) is manually examined to make sure that it is flat with the nodes well organised and not folded over one another. Only the SOMs with a well organised Sammon map are chosen and are listed in Table 3.2 along with their corresponding metric values. In general, it is important to find a SOM with a good ability to “forecast” the storm type of individual events which is characterised by a BSS score close to 1. Since this work is most concerned with identifying convective events, the focus is on the convective BSS. In addition, the TE and QE should be relatively small, and there should be little variance as well as a decrease in the variance from the entire event training data to the nodes in the SOM. And lastly, there should be a relatively large percent difference spread. It is with these 10 models that will be analysed to see how well their “forecast” match reality.

Table 3.2: The SOM models and sizes with well organised Sammon maps that performed best according to the metric used to assess their performance. Average Average BSS BSS Topographic Quantization Average Percent Variance Convective Overall Error Error Variance Difference Difference Model Type SOM Spread

W 2×2 0.4735 0.2899 0.0011 1.8645 0.0163 -0.0223 0.5579 W 4×4 0.5040 0.3462 0.1378 1.6006 0.0120 -0.0266 0.7029 W-D 3×5 0.4959 0.3715 0.1509 2.3142 0.0148 -0.0237 0.7413 W-D-T-P-P 4×4 0.5034 0.3846 0.0486 5.2669 0.0254 -0.0222 0.8263 W-P 3×5 0.5357 0.3419 0.0101 3.6047 0.0267 -0.0284 0.7316 W-T 3×4 0.5127 0.3870 0.0511 3.3478 0.0258 -0.0287 0.7139 W-T-P 4×4 0.5280 0.3783 0.2246 2.6472 0.0185 -0.0412 0.8125 W-Te 3×3 0.5046 0.3491 0.0214 4.4048 0.0309 -0.0327 0.6732

Classifying wind gust typologies using Self-Organising Maps Chapter 3

3.2.5.4. Matching Events to SOM

Upon choosing the SOMs that best sort the 13-station training dataset, they are applied to classify wind gust events at the 306 stations examined across Australia between 1995 and 2015. To do this, the BMU for each event is calculated at each node within the SOM, and the event assigned to the node that displays the smallest BMU. The SOM will look something like the one shown in Figure 3.8 which is a 4×4 SOM resulting in 16 different nodes that an event can be matched. The event is then assigned the conditional probability of each storm type for the given node. The conditional probability follows the forecast probability defined earlier, that is the percentage of each storm mode within a node is the conditional probability that an event sorted into that node will be any one of the four storm modes. Once all gust events are assigned to a node, four different approaches for determining the number of convective events are explored. In the first approach, if the conditional probability of an event being convective is above 50%, that is there is a greater chance of an even being convective than any of the other three modes combined, then it is considered to be convective. The second approach classifies an event as convective if the conditional probability of the event being convective is the largest of the four event types within the node it is assigned. The third approach is to sum the number of events put into a node at a given station, then multiply that by the convective conditional probability of that node. The sum of the statistical event counts for all nodes is taken to get the expected number of connective events over the sample duration. The final approach follows the third, but only does the final summation using nodes where the convective conditional probably if it is ≥ 25%. Of these four counting approaches, the first two are capable of assigning an event type explicitly to each event, while the latter two produce statistical convective event counts without classifying individual events. The different counting methods are explored to determine the best approach to go from the conditional probabilities assigned by the nodes to a single event count value. For the SOMs chosen in Section 3.2.5.3, the convective gust event counts using the four methods described above are calculated. To assess which counting methods worked best, the total number of convective events manually identified, observed, at the 13 training stations is compared to the number of convective events calculated, expected, using the SOM. The mean absolute error (MAE) is calculated for each counting method. In addition, the weighted mean absolute error (WMAE) is assessed by dividing the absolute error at each station by the observed number of events for the given station. This was done on three different time scales, yearly, seasonally for (southern hemisphere) summer (DJF), autumn (MAM), winter (JJA), and spring

Classifying wind gust typologies using Self-Organising Maps Chapter 3

(SON), and then biyearly for spring-summer and autumn-winter. The average MAE was taken for the four seasons (autumn, winter, spring, summer (A/W/S/S)) and the two combined seasons (spring-summer (S-S), autumn-winter (A-W)). The MAE and WMAE for the SOM models and the counting methods are shown in Table 3.3. These results will be discussed in Section 3.3.2.

Table 3.3: The MAE (counts) and WMAE (%) for the SOM models shown in Table 3.2 using the four different methods for counting the number of expected convective events above 70 km h-1 Count MAE MAE MAE WMAE WMAE WMAE Model Type SOM Method Yearly A/W/S/S S-S/A-W Yearly A/W/S/S S-S/F-W W 2×2 1 0.57 0.16 0.3 26 36 37 2 0.34 0.11 0.2 33 40 41 3 0.27 0.08 0.14 21 33 30 4 0.39 0.11 0.21 20 29 31 W 4×4 1 0.27 0.08 0.15 27 28 29 2 0.27 0.08 0.15 27 28 29 3 0.31 0.09 0.16 22 33 30 4 0.34 0.09 0.18 18 28 27 W-D 3×5 1 0.36 0.1 0.19 24 31 36 2 0.21 0.08 0.13 20 32 32 3 0.32 0.1 0.17 23 36 33 4 0.28 0.08 0.15 17 31 29 W-D-T-P-P 4×4 1 0.25 0.07 0.13 15 23 25 2 0.24 0.09 0.17 23 41 31 3 0.33 0.1 0.17 24 42 30 4 0.24 0.08 0.13 15 27 22 W-P 3×5 1 0.3 0.09 0.15 17 28 22 2 0.23 0.08 0.13 20 36 35 3 0.41 0.11 0.21 23 40 33 4 0.29 0.1 0.17 15 31 27 W-T 3×4 1 0.22 0.08 0.15 22 28 29 2 0.22 0.08 0.15 22 28 29 3 0.27 0.08 0.14 19 28 25 4 0.33 0.1 0.18 17 27 28 W-T-P 4×4 1 0.26 0.1 0.16 11 24 26 2 0.26 0.1 0.16 11 24 26 3 0.33 0.1 0.18 21 37 31 4 0.38 0.12 0.21 18 30 28 W-Te 3×3 1 0.41 0.12 0.21 24 35 34 2 0.41 0.12 0.21 24 35 34 3 0.28 0.08 0.14 20 34 30 4 0.34 0.1 0.18 16 30 30

Classifying wind gust typologies using Self-Organising Maps Chapter 3

3.3. Results and Discussion

3.3.1. SOM Sensitivity Analysis When analyzing the different metrics used to assess the performance of the different SOM models (Section 3.2.5.1), no specific combination of free parameters was found to perform significantly better than others. However, there are some general trends. The BSS, variance, variance difference, and percent difference spread tend to increase with increasing SOM size. Whereas, the quantization error decreases with increasing SOM size. The type of algorithm, learning rate (α) and SOM size does not appear to impact the topographic error. Linear initialization tends to have a smaller topographic error compared to random initialization, but if the radius of influence is large enough, then random initialization can give similar topographic errors, or even reduce them. A hexagon lattice also tends to give smaller topographic errors. Using a Gaussian neighborhood function has larger QE, if the training length is too short, but a smaller TE. In general, the QE will decrease if the training length is increased. The TE generally decreases with larger radius of influence. Increasing the radius of influence usually decreases the variance or variance difference but does not seem to affect the BSS or percent difference spread. Increasing the training length also tends to increase the BSS and the percent difference spread. Moreover, the algorithm, learning rate, initialization, lattice, smoothing, and neighborhood function do not tend to affect the BSS, percent difference spread, variance, variance difference, or the quantization error. Based on the parameter combinations tested for this work, the main conclusion from the sensitivity analysis is the importance of a long training length, which for the data used for this work was a total training length of at least 100 steps (20 in the rough phase and 80 in the fine-tuning phase). Furthermore, it is important to use a SOM size that minimised both the TE and the QE. 3.3.2. SOM Selection We can see in Table 3.2 (Section 3.2.5.3) the 8 SOM models, out of 70 that were examined, which displayed well organised Sammon maps. Of the eight, there was no weather variable combination that consistently perform well irrespective of the SOM size. Similarly, there was no SOM size that appears to work consistently well irrespective of the weather variables used. However, the 4×4 SOM size had the most models with well-sorted Sammon maps. None of the 2x5 or 6x6 SOMs had well sorted Sammon maps like those seen in the other SOM sizes. These eight models also had some of the best error metric values of the 70 tested models that were examined but none is the best by all metrics.

Classifying wind gust typologies using Self-Organising Maps Chapter 3

Figure 3.6: The observed convective wind storm counts, above 70 km h-1, at the 13 training stations compared to the expected counts caluclated for the W-D-T-P-P 4X4 SOM and the W-T-P 4X4 SOM using the four different counting methods.

Calculating the convective storm counts for these 8 models allows for the comparison between the expected event counts for the 13 test stations and their observed counts (Figure 3.6). Examining Table 3.3 (Section 3.2.5.4), does not show any particular counting method to consistently perform better or worse than any other. The counting method and SOM model used both seem to play an important role in determining the expected convective gust counts. Focusing on the WMAE shows the 4×4 SOM for the Wind-Temperature-Pressure (W-T-P) model using counting method 1 or 2 has the smallest WMAE when looking at the overall yearly event counts. This model is also within 5% of the smallest WMAE when looking at the four- seasons yearly event counts but has a 20% larger WMAE for the bi-seasonal yearly event counts when compared to the model and count method with the smallest bi-seasonal WMAE. The 4×4 SOM for the Wind-Direction-Temperature-Pressure-Precipitation (W-D-T-P-P) using the 1st counting method has the smallest WMAE when looking at the four-seasons yearly counts, but has a 30% and 15% higher WMAE for the overall yearly event counts and bi- seasonal yearly event count, respectively. The other SOMs and counting methods typically have larger errors when looking at these three time periods. Therefore, the two models believed to be the best to move forward with are the 4×4 W-T-P and the 4×4 W-D-T-P-P, where their convective event counts above 70 km h-1 compared to the observed event counts are compared at each station. The 4×4 SOM appears to be an ideal size to explain the various types of severe wind storms and potential subcategories that can occur across Australia, and likely globally, 95

Classifying wind gust typologies using Self-Organising Maps Chapter 3 without over classifying the events. The W-T-P combination is believed to work well for distinguishing convective events because it covers two main characteristics of a convective event; the temporary increase in pressure and the decrease in temperature at the time of an event. Moreover, the W-D-T-P-P takes into account those two characteristics as well as the wind direction, that typically changes drastically at the time of event, and the occurrence of short duration, sometimes intense, rainfall that may also be associated with these events. Taking these two SOMs, it was also examined how well they matched observations when only considering gust events above 90 km h-1. This larger threshold is commonly used in meteorology to designate a wind storm event as severe (BOM, 2016a) and is approximately the threshold for onset of damage to residential structures in many parts of the world (Ginger et al., 2010). Here the 4×4 W-T-P model was found to have the smallest WMAE for the overall yearly event counts, and a 29% and 14% larger error than the smallest WMAE for the four- seasons and bi-seasonal yearly event counts. While the 4×4 W-D-T-P-P has a 54%, 70% and 38% larger WMAE for the overall, four-seasons, and bi-seasonal yearly event counts, respectively. Given this, it was decided to use the 4×4 W-T-P model using either the 1st and 2nd counting method to continue the analysis. For this case, the 1st and 2nd counting method end up giving the exact same event count because the convective conditional probability is greater than 50% in the nodes where it has the highest probability of occurring. The challenge with the W-D-T-P-P, which may affects its ability to perform as well as the W-T-P SOM, could be because the precipitation data was not as readily available as the other variables, in addition to the challenges in characterizing the various way the wind direction can change during a convective wind storm. Looking at this model in detail shows that its Sammon map is flat with its 16 nodes well organised and evenly spaced (Figure 3.7). The SOM itself is shown in Figure 3.8, where the mean value of the normalised wind speed (solid blue line), temperature (dashed orange) and pressure (dotted orange) values are shown for each node. The “hits” above each node refers to the number of events sorted into the node, with each node having at least 20 events sorted into them. The normalised wind speed values for each individual event, from the training dataset, in the node is shown by the dashed grey lines. In the top left node, the wind speed is relatively low and rapidly increases at the time of the event followed by a relatively quick decrease to a wind speed similar to that before the event. The temperature rapidly decreases at the time of the event and slowly recovers but to a temperature less than that before the event occurred. There is also an overall decrease in the pressure with time except for a quick increase when the event occurs before continuing to decrease. Moving across the top row of nodes, there is a 96

Classifying wind gust typologies using Self-Organising Maps Chapter 3

Figure 3.7: The Sammon map for the 4x4 W-T-P SOM where the axes describe the distances between the nodes from each other in variance scaled values. progressively slower return to the original wind speed after the event occurs. Moving down the rows there is a decrease in the ratio between the peak wind speed at the time of the event compared to the start and finish wind speed. This decrease in ratio occurs quickly and occurs more slowly for progressive columns. With respect to the pressure, moving across the first row there appears to be a slow reversal where the pressure before the event is relatively high and after the event is relatively low, to the pressure being relatively low before the event occurs and being relatively high after the event. Moving down the rows, the more dramatic change in the pressure that occurs around the time of the events becomes less pronounced to the point where there is a relatively gradual decrease in pressure in the bottom left node and a relatively gradual increase in pressure in the bottom right node. With the temperature, the decrease that occurs at the time of the event tends to increase moving across the first row, in addition, the slight recovery that occurs in the far left node slowly disappears towards the far right node. Moving down the rows, the drop in temperature gets smaller, to the point in the bottom right node the temperature slowly increase from before the event to after the event. Compared to the bottom right node where there is a temporary increase in temperature before the event occurs, before a sudden decrease and a small recovery. The gradual evolution seen in the three variables

Classifying wind gust typologies using Self-Organising Maps Chapter 3

moving down and across the SOM verifies what was seen in the Sammon map (Figure 3.7), that is the SOM is well constructed and organised. The characteristics of the top row suggest these events are likely characteristic of convective events with the potential for transition events to top right part of the SOM, whereas the bottom left nodes suggest more wind only events and the bottom right suggest more general events. Figure 3.9, discussed below, verifies these findings.

Figure 3.8: The 4x4 SOM for the Wind-Temperature-Pressure vairable combination. The solid blue line shows the average normalised wind speed over the 4 hr period for each node. The grey lines show the normalised wind speed values for each event from the 13 training stations that were sorted into the node. The dotted orange line shows the mean normalised pressure for the node, while the dash orange line shows the mean normalised temperature for the node. The hits above each node shows the number of events that contribute to each node.

Examining Figure 3.9 the count of each storm type sorted into each node can be seen. It shows that the top row of nodes is dominated by convective events with most being sorted in the top right node. There are less convective events moving towards to the left side of the SOM. Moving down to the next row of nodes, there is more of a mix of events sorted into these nodes. But with the left two nodes having more wind only and general events and the right two nodes having more general and transition events. In the bottom two rows of nodes, it is evident that

Classifying wind gust typologies using Self-Organising Maps Chapter 3 more wind only events occur in the far left nodes, and more general events in the far right nodes. These counts of event types in the nodes match the mean characteristic of the wind speed, temperature, and pressure variables of each node shown in Figure 3.8. This provides some confidence that this SOM has skill in sorting the four storm modes. In addition, from percent difference, also shown in Figure 3.9, this SOM appears to perform well when sorting out convective events, compared to using the statistical climatology of the training dataset. This is shown by the large positive percent differences for convective events in the top row of the SOM. Moreover, there are also large positive percentage differences for wind only events in the first node of the third and fourth row and large positive percent difference for general events in the last node of the third and fourth row. Finally, it can be seen that the third and fourth node in the second row have large positive percent difference for transition events.

Classifying wind gust typologies using Self-Organising Maps Chapter 3

While this SOM model and event count method appears to perform the best for convective events out of all the SOM analyses it does not have the smallest error for the other three storm modes. Looking at the overall BSS of the SOMs shown in Table 3.2 (Section 3.2.5.3), the overall skill is lower than the convective skill alone, suggesting while these SOMs work well at distinguishing convective events they do not perform as well when it comes to the other storm modes. When looking at the BSS specific to the wind only, general, or transition, they each had different SOM that worked better. This may suggest the need to use a different SOM to analyse the other severe wind storms. Since the focus of this work is to identify the convective events those SOMs that performed well with that task above all else were picked. However, it is not quite clear why there was not a SOM that appeared to perform equally well across the four storm modes. It may be because different storm modes require more variables to explain the characteristic associated with them such that the SOM can better identify them or the use of additional variables adds unnecessary details that may make it harder for the SOM to sort events. 3.3.3. SOM Climatology Expanding the 4×4 W-T-P SOM to all stations, the average annual number of convective wind gusts exceeding 70 km h-1 across the country is estimated, Figure 3.10. Over the entire year, Figure 3.10a, there are a large number of events shown to be occurring in-land, specifically over Western Australia (WA) and along the coast in northern WA. A smaller maximum of events is also shown to occur over northeast New South Wales (NSW) as well as over inland Queensland (QLD). Patterns start to emerge when looking at the individual seasons, Figure 3.10b-e. How this breaks down for each season can be seen in Figure 3.10. The largest number of events occur during the summer months (Figure 3.10c) with these mainly occurring over the northern part of WA and extending inland to a smaller extent. Those smaller peaks are also evident over the northeast part of NSW and inland QLD. The number of events decreases across the country in autumn (Figure 3.10d) with the largest number of yearly events occurring at a station in southeastern WA and almost no events in northern QLD. There is a minimum in the number of events in the winter (Figure 3.10e), with the few events that do occur mostly limited to the southern part of the country corresponding to the dry season for the tropical northern part of the country. Events begin to increase during the spring months (Figure 3.10b) with them mainly occurring in central Australia at to a lesser extent southeast QLD and northeast NSW.

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Looking at just events above 90 km h-1 (Figure 3.11) a similar picture can be seen for both the yearly counts as well as for each season compared to 70 km h-1 (Figure 3.10) but with overall less events. There are some noticeable differences in the distributions of events above 90 km h-1 compared to those above 70 km h-1. The first one is the extent of the more severe events in inland WA is not as pronounced, with the peak number of events occurring in central WA being below 90 km h-1. The peaks over northeast NSW and inland QLD are still present but shifted slightly closer to the coast in NSW and less prominent in QLD. A more evident peak also emerges over inland South Australia. The same seasonal shift of events can also be seen in Figures 3.10b to 3.10e. It is important to note here that the majority of stations, almost 200, have less than 10 years of available 1-min data, which make it difficult to say much about the distribution and frequency of events above 70 km h-1 or 90 km h-1. This emphasizes the fact that the observational climatology shown here should only be taken as an approximate convective wind gust climatology, and not be considered conclusive. Moreover, given that events at the stations are only observed at a single fixed point in space, there may be significant local and regional effects, such as topography or bodies of water, that may considerably increase or decrease the number events at any given station compares to the average for that area or region. This highlights the need to explore other techniques to expand this kind of climatology to build a more robust and spatial complete climatology of convective wind storms. Using the output from the W-D-T-P-P 4×4 SOM the distribution of convective counts at each of the station show very much the same distribution across the country (Figure 3.12) with a couple differences. For events above 70 km h-1 (Figure 3.12a), the most noticeable difference is a reduction in the number of events per year for the interior of the country, specifically in WA. This reduction is about 1 or 2 events per year at some stations. There is also a small increase in the number of events per year at some of the coastal stations across the country, most noticeable in TAS. This increase is on the order of 1 event per year. These differences are also apparent for events above 90 km h-1 (Figure 3.12b) where there is a decrease in the convective event count at stations in WA on the order of about half an event per year, and a small increase at some stations in TAS of about a quarter of an event per year.

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b) c)

d) e)

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b) c)

d) e)

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To see how this compares to previous work, research by Kuleshov et al. (2002) who examine thunderstorm distribution and frequency in Australia is looked at. They show that the majority of thunder-days, up to 80 per year, occur mainly in northeast WA, northern NT and to a lesser extent, approximately 60 thunder-days, in northern QLD. In addition, they show pockets of 30- 40 thunder-days extending down into central WA, much of NSW, and southeast QLD (Figure 3.13a). While this agrees to what is shown in Figures 3.9 and 3.10, a maximum in convective wind storms in northern NT or in northern QLD is not seen. Moreover, there is one station in southeast WA reporting a significant number of events, compared to other stations, especially above 90km h when it is associated with only about 10-15 thunder-days according to Kuleshov et al. (2002). It is important to note, that while lightning can be a good indicator of convective storms, it does not necessarily mean that a severe convective wind will occur. Comparisons can also be made by looking at work from Wang et al. (2013) who analysed daily non-cyclonic gust maxima at 122 sites with at least 10 years of data. They find the non-cyclonic gust hazard was 104

Classifying wind gust typologies using Self-Organising Maps Chapter 3

greatest around southeast QLD and northeast NSW and would extend west across the county towards the northern part of WA (Figure 3.13b). While this is something shown here, the extent of the hazard in Wang et al. (2013) is not as extensive as found here. Wang et al. (2013) also found there is less of a hazard posed by non-cyclonic winds in Northern QLD which corresponds to the minimum in convective wind storms found at stations in that part of the country.

a) b)

The SOM algorithm is shown to be a promising machine learning technique that can be utilised to categorize severe wind storms quickly and in an objective way. Although no clear combination of SOM free parameters performed better than others, the importance of setting a long enough training length, and setting a large enough radius of influence - especially for the larger SOMs (4×4, 6X6) – was clear. Larger SOMs tended to better sort events into the four storm modes, having large BSS value compared to the smaller SOM sizes. This may be because the additional nodes allow the SOM to sort out the many different sub-categories that appear to exist within the four categories examined for this work. It is also interesting to note that using just the wind speed only provides a SOM that performs as well as some of the other index combinations. From the SOMs that were flat and well organised, it was possible to expand beyond the training stations to all stations across Australia. Through this technique, it is possible to estimate the expected number of convective wind gusts across Australia at the BOMs AWS sites. It showed that the interior of the country has a

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Classifying wind gust typologies using Self-Organising Maps Chapter 3

significant amount of convective wind storm events. Moreover, it allowed for the visualisation of how the occurrence of these events evolve through the year. It would also be possible to do similar climatologies for Wind Only, General, and Transitioning wind storms using this method. Although, only four broad categories of severe winds were examined it may be possible to expand this method to include more specific storm modes, specifically distinguish between dry and wet microburst, supercells, sting jets, etc. This would likely involve expanding the subset of the AWS dataset to include more examples of each specific storm type. Future work will look to improve the training of the SOMs using more manually identified stations as well as a separate set of manually identified stations to verify SOM performance. Moreover, it will be important to experiment with different definitions of the wind storm type categories in hopes of developing a more universal SOM that works well for all types of wind storm. This may require the use of additional training data to complement the use of the 1-min AWS data. Such data would include additional variable combinations as well as calculating other, more informative, meteorological variables from the ones measured by the AWS. In addition, incorporating other datasets into the SOM like the lightning or radar data as well as topographic data may prove to be useful as well.

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Chapter 4: Australian convective wind gust climatology using Bayesian hierarchical modelling

Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.1. Introduction

The current Australian structural design standard, AS/NZS1170.2:2011 (Standards Australia, 2011), was developed with historical wind gust data from around the country using weather station data up until 1998. Wang et al. (2013) re-examined these data using Automatic Weather Station (AWS) wind gust data from 1939 to 2007 with the aim of developing hazard models and mapping extreme wind gusts for both the current and likely future climate. They note that the lack of surface measurements across the country affected the accuracy they could achieve with their model. Through the use of a probabilistic and statistical approach for wind hazard modelling, Wang et al. (2013) showed that when considering gust wind speeds from convective thunderstorms, the current design standards are only adequate for the coastal regions of northern Western Australia. To determine the hazard posed by any type of natural catastrophe it is necessary to know the, when, where, and how often these events occur at any given location. A spatially complete climatology of severe convective wind storms, based on robust and reliable data, is essential for improving the understanding of the risk and hazard associated with severe convective wind storms. However, to do this there needs to be high fidelity data that is collected over a period of at least 30-50 years. Unfortunately, these events are rare at any given location, have a small spatial and temporal scale, and are often dependent on a human observer or AWS to observer and document their occurrence (Brooks et al., 2003a). Therefore, the availability of high fidelity convective wind storm data is rare in Australia given the sparse population density along with the small spatial and temporal scales of convective events. Moreover, the available observations do not identify the storm mode. For severe wind storms it is important to distinguish if a given wind gust is convective or synoptically driven. This is because convective and synoptically driven events produce different exceedance probability curves as shown by Holmes (2002). Distinguishing between these two storm modes will help to better understand national wind hazard. Knowing the storm mode of individual reports of events will allow for the statistical analysis of these separated climates and understanding of their different characteristics. Separating and classifying weather observations, especially severe wind storms, into two main groups, synoptic and convective events for meteorologist or stationary and non-stationary for wind engineers (Solari, 2014; Lombardo et al. 2009; Gomes and Vickery 1976; Kasperski, 2002) is a major challenge. The issues with classifying events and current approaches are discussed in detail in Section 2.4. Wang et al. (2013) highlights that this is an issue especially

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling for anemometer data. The separation of event types into homogenous families is especially important in mixed wind climates, so that independent wind gust distributions can be determined and used to conduct refined analyses of different phenomena and their contributions to wind-excited response of structures (Gaetano et al., 2014). To do this it is important to consider both the records detected by wind monitoring network and the weather scenarios responsible for the event. Due to the amounts of data in these datasets, classification schemes typically do not consider the meteorology responsible for the events. Synthetic information, such as the gust factor, are used to make the process as automated as possible. Alternatively, meteorologists tend to look at specific weather phenomena of interest through the detailed inspection and reconstruction of the meteorological conditions responsible for the specific event type. However, this classification approach is tedious, requires significant resources, and requires human intervention. The Self-Organising Map (SOM) approach developed in Chapter 3 is used to provide a more automatic method to help utilised large severe weather event datasets. Biases and errors in observational datasets result from meteorological (e.g., King et al., 2003) and non-meteorological factors. These limitations are discussed in Section 2.3.1 of the literature review. These biases and errors are an issue since they lead to problems in the interpretation of events statistics. The issue of observation bias for thunderstorm records in Australia is of particular concern given the majority (85%) of Australia’s population resides within 50 km of the coast, which is reflected in the Bureau of Meteorology’s (BOM) Severe Storm Archive (SSA) having a strong bias towards urban areas and the coast (Allen et al., 2011). Also, comparisons of events through space and time is difficult because of different collecting methods (e.g. different instrumentation, reporting practices), and changes in these methods with time (Brooks et al. 2003c). For example, each state in Australia has its own Severe Weather Section (SWS) responsible for recording severe thunderstorms. Brooks and Doswell (2001) make note of similar issues when building a climatology of tornado events in the U.S.. They make note of the limited number of observations for given locations and dates, as well as, the accuracy and temporal consistency of reports. Inconsistencies in reports includes: errors in recording the time and location information, changes in the nature of detailed damage surveys, population changes, increased public awareness, and even the use of video cameras. These are issues that also occurs in the BOM SSA. Past research has dealt with the lack of event data by looking at the environments that produce severe weather (e.g., Brooks et al., 2003b; Grunwald and Brooks, 2011) to develop relationships for areas where severe weather observations are reliable and extend it to areas 109

Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling with similar climates that have less reliable severe weather observations, or none at all. To do this researchers look at the large scale state of the environment through covariates or indices (Brown and Murphy, 1996) and calculated with global reanalysis databases (e.g., ECMWF ERA-Interim, NCEP/NCAR Reanalysis I, NCEP/DOE Reanalysis II) as a spatially uniform and reliable pseudo-measure of global atmospheric conditions. The use of meteorological covariates (Brown and Murphy, 1996) has proven to be a useful solution to some of the problems faced when creating a climatology of thunderstorms (e.g., Allen and Karoly 2014; Allen et al. 2011; Brooks et al. 2003a). However, it is difficult to find indices or combinations of indices that capture all the necessary conditions for severe thunderstorm development. Typically, an index threshold is set and all environments that exceed that level are deemed environments that may produce a severe thunderstorm or one of its sub-hazards (e.g., convective winds). There are however two limitations with this type of climatological analysis; (1) it is only useful for analysing the relative storm hazard between areas as it does not fully account for the fact that meeting a threshold does not guarantee the development of a storm, and (2) it assumes the same covariate threshold is applicable across a range of climatological regions. Further detail on previous research that utilises this approach can be found in Section 2.3.1 and 2.3.2. of the literature review. While many studies have looked at possible relationships (e.g., Brooks et al., 2003b; Carey et al., 2003) most have not considered observational biases or possible spatial correlation between observations (e.g., King, 1997). Anderson et al. (2007) examine the influence of population on the reporting of tornado events in several U.S. cities found some of the spatial variability in tornado reports may be attributed to population density and that population density effects have regional variability. Wikle and Anderson (2003) demonstrate the usefulness of hierarchical Bayesian spatiotemporal model in modelling complicated spatiotemporal and physical processes and its ability to provide estimates of uncertainty in data, model, process, and parameters. Bayesian hierarchical modelling has also been shown to be useful in addressing the issue of observational biases (Cheng et al. 2013; 2015; 2016). Cheng et al. (2013) used Bayesian hierarchical modelling to predict tornado occurrence across Canada and postulated that the likelihood of observing a tornado was related to population density. Cheng et al. (2015) similarly used Bayesian hierarchical modelling to improve the tornado climatology of Canada using the combination of severe weather indices. Cheng et al. (2016) continues this work by using a Bayesian hierarchical model framework to depict the causal linkage between the annual or seasonal tornado occurrences across North America. In addition, they explicitly accounts for the role of regional variability in the occurrence of tornadoes, which 110

Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling they note has not be considered in predictive frameworks before. Section 2.3.2 gives an in- depth discussion on using Bayesian hierarchical modelling for developing climatologies. The objective of this chapter is to build a spatially complete climatology of severe convective wind storms for Australia. This is done using a modified version of the Bayesian hierarchal model described in Cheng et al. (2016). Bayesian statistics will be used to develop relationships between Severe Weather Indices (SWI) calculated from ERA-Interim reanalysis data and AWS data to predict severe convective wind storm occurrence across Australia for different months and different seasons. These include, the four southern hemisphere meteorological seasons; summer (December – February), spring (March – May), winter (June – August), autumn (September – November), two broader seasons of summer-spring and autumn-winter, in addition to the entire year. This chapter continues with the use of the BOM network of AWS as the observational dataset, which was used in Chapter 3 to develop the SOM method. More specifically, the SOM selected in Section 3.3.2 is used. This AWS data experience similar biases that human-based report datasets do, as mentioned previously. The methods are discussed in detail in Section 4.2. Results output from the different Bayesian models (i.e. the use of different SWI combinations) are presented in Section 4.3. Section 4.4 discusses these results and identifies the models that provide the most realistic climatology for each season. The work is than summarised in Section 4.5. 4.2. Data and methods

4.2.1. Observation Data The BOM AWSs data, described in detail in Section 3.2.1, is the same observational data used for this chapter. Unfortunately, the AWS dataset is sparse across Australia, with higher concentrations around metropolitan areas. Furthermore, the frequency and extent of observations collected by any given station and method used to collect these data can change with time. In addition, the AWS can only observe events at a point location and many stations have collected data for only a short time period, might have been decommissioned or moved to a different location. This results in a short dataset that is spatial incomplete and contains two types of bias. The first bias is the influence of station density on report distribution. Rural areas with fewer stations or areas with no stations will have an artificial minimum in reports. The second is an artificial increase in severe weather reports with time. This is a result of an increase in the number of AWS stations in the observational network with time. These biases will be dealt with using Bayesian statistics similar to how population biases were accounted for in previous studies (Anderson et al., 2007; Wikle and Anderson, 2003; Cheng et al., 2013; 2015;

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 2016). Gust wind speeds are then corrected to account for topographic influences following the approach specified in AS/NZS1170.2 (Standards Australia, 2012) which is outlined in Section 3.2.1.1.

a) b)

c) d)

Figure 4.1: Number of days with at least one convective event observed within a grid cell between 2005 and 2015 for southern hemisphere a) autumn, b) winter, c) spring, d) summer.

The events, above 90 km h-1, at each of the 311 stations with at least 5 years of data, are then classified using the 4X4 W-T-P SOM developed in Chapter 3. This SOM takes into account the wind speed, temperature, and pressure of each event. Events are considered convective if they are sorted into a node where the convective probability of that node is the highest out of the four storm modes. The number of severe wind storms, within each of the ERA-Interim 0.75 grid cell over Australia, is calculated. Since the main interest is whether the atmospheric environment in a grid cell is conducive to the occurrence of a severe convective wind storms it is only necessary to include one wind storm even if multiple stations within a grid-cell record a severe wind gust on the same day. Therefore, “redundant” events are removed and the number of days where gusts > 90 km h-1 occurred for 6 different seasons, as well as the entire year are determined. These include, the four southern hemisphere meteorological seasons; summer (December – February), spring (March – May), winter (June – August),

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling autumn (September – November), two broader seasons of summer-spring and autumn-winter, in addition to the entire year. From here on, event count, or rate of event occurrence, refers to the number of days that there is at least one severe convective wind gust above 90 km h-1 occurring. Figure 4.1 shows the event counts over the period from 2005 to 2015 for the four meteorological seasons. The first bias that results from the AWS network being dense around population centres and spares in rural areas can be seen in Figure 4.1, with the majority of event counts being focused around the major metropolitan areas of Australia.

Figure 4.2: Mean number of yearly AWS per grid cell (~5625km2) over Australia from 2005- 2015. In addition to determine convective event counts for each ERA-Interim grid cell, it is also necessary to get the mean station density for each cell over the same period. This is done by taking into account not only the presence of a station during a given period but also determining the percentage of time each station was recording reliable data. All stations were first quality controlled to have extended periods of erroneous data removed from the 1-minute wind speed record. This was done through visual inspection of the wind speed time series of each station, looking for data that was elevated above unrealistic values or constrained below certain values for extended periods of time. Then the percentage of 1-minute time steps that had data available was determined for every month, over the period, at each station. Each station was then

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling multiplied by the percentage of time it was recording reliable data. Total station counts are determined for each of the 6 seasons considered as well as the entire year, for each year between 2005-2015 and averaged over the entire period, Figure 4.2. These data are used within the Bayesian hierarchal model. 4.2.2. Reanalysis Data In addition to the observational dataset mentioned above, the European Centre for Medium- Range Weather Forecasts (ECMWF) European Reanalysis-Interim (ERA-Interim) dataset is used for this work (Berrisford et al., 2011; Dee et al., 2011). ERA-Interim was chosen, over other global reanalysis datasets, for use in this thesis because it utilises four-dimensional variational data assimilation which tends to give more realistic assessment of observed conditions (Dee et al. 2011). The ERA-Interim is a global reanalysis dataset that assimilates historic observations of the atmosphere, ocean, and land surface into a numerical model that reconstructs past climate and weather systems (Dee et al. 2011). It provides 6-hourly atmospheric fields available on 37 vertical pressure levels from 1000hPa to 1hPa. The reanalysis data used here are the air temperature, relative humidity, u and v wind components, geopotential height, relative vorticity, and sea-level pressure between 1000 hPa and 100 hPa, as well as at the surface (2 m for temperature and 10 m for winds), interpolated to a regular, 0.75 degree, latitude/longitude grid from January 1st, 1979 to December 31st, 2015. These data allowed a suite of environmental indices to be calculated. For this chapter multiple combinations of 22 different severe weather indices examined are summarized in Table 4.1. Each parameter is calculated for 6-hour time steps between 1979- 2015 and for all ERA-Interim grid cell over Australia. Average values of the indices are calculated for the period from 2005-2015 for the 6 seasons as well as for the entire year. The mean values between 2005-2015 are normalised for each season prior to being used as input in the Bayesian models. This is mainly important for the Bayesian models that use multiple indices so that they may be comparable and allow the model to converge more easily. The period of 2005-2015 is used because this is the period where 1-min AWS data is available for the majority of stations. Some indices are calculated using the SHARPpy open source sounding and hodograph analysis routines (Blumberg et. al., 2017). The intersection of the pressure levels with the surface was dealt with using logarithmic interpolation between the two levels that intersected the surface. Indices calculated using SHARPpy had the 1000hPa level assumed to be the surface. More detailed explanations of the indices used, along with figures of the mean values of the indices over Australia for the different seasons can be found in Appendix A.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Table 4.1: List of the indices used in the Bayesian explanatory models Section 4.2.3.2. Parameter Abbreviated Formula Calculated Reference Name Name Using SHARPpy

Lifted Index LiSfc, Li50, 푇500ℎ푃푎 − 푇푖 →500ℎ푃푎 Galway (1956) Li100 (𝑖 = 푠푓푐, 50ℎ̅̅̅̅̅̅푃푎̅̅̅, 100ℎ̅̅̅̅̅̅̅푃푎̅̅̅) 푧퐸퐿 Most Unstable muCAPE 휃퐸푝 − 휃퐸푒 Yes Moncrieff and Convective 푔 ∫ 푑푧 Miller (1976) 푧 휃퐸푒 Available 퐿퐹퐶 Potential Energy

Theta-e deficit TeD theta-emax - theta-emin Ellrod et al. (2000) Wet Bulb Zero WBZ ℎ𝑖푒푔ℎ푡 표푓 푡ℎ푒 푧푒푟표 푤푒푡 푏푢푙푏 푡푒푚푝푒푟푎푡푢푟푒 Miller (1972) Height Height lfcel 퐸퐿 − 퐿퐹퐶 Yes difference between the EL and LFC Significant Sig.Sev. 푚푢퐶퐴푃퐸 ∗ 퐷퐿푆 Yes Brooks et al. Severe (2003b) Downdraft dCAPE 푝퐿퐹푆 Yes Gilmore and Wicker CAPE − ∫ (훼푝 − 훼푒)푑푝 (1998) 푝푠푓푐 SHERBE 푆퐻퐸푅퐵퐸 훾2푚−3푘푚 훾700−500ℎ푃푎 퐸퐵푊퐷 Sherburn and Parker ( )( )( ) 5.2 5.6 27 (2014) Microburst MCOMP 0 퐿퐼푠푓푐 > −8 Entremont et al. Composite 0 푚푢퐶퐴푃퐸 < 3100 1 𝑖푓 퐿퐼 ≤ −8 (2018) {1 𝑖푓 3100 ≤ 푚푢퐶퐴푃퐸 ≤ 3999} + 푠푓푐 2 퐿퐼푠푓푐 ≤ −9 2 푚푢퐶퐴푃퐸 ≥ 4000 { 3 퐿퐼푠푓푐 ≤ −10} 0 푉푇 < 27 0 𝑖푓 훾 ≤ 8.4 1 𝑖푓 푉푇 ≥ 27 + { 2푚−3푘푚 } + { } + 1 훾2푚−3푘푚 > 8.4 2 푉푇 ≥ 28 3 푉푇 ≥ 29 0 푑퐶퐴푃퐸 < 900 1 𝑖푓 푑퐶퐴푃퐸 ≥ 900 −5 𝑖푓 푃푊푉 ≤ 1.5 { } + { } 2 푑퐶퐴푃퐸 ≥ 1100 0 푃푊푉 > 1.5 3 푑퐶퐴푃퐸 ≥ 1300 Gust Index GUSTEX 훼푊퐼 + 0.5푈500ℎ푃푎 Geerts (2001) 2 0.5 Wind Index WINDEX 5(퐻푚푅푞(Γ − 30 + 푞1 − 2푞푚)) McCann (1994)

Deep Vertical DVWS 2 2 2 2 Wind Shear √푢500 + 푣500 − √푢1000 + 푣1000

Shallow SVWS 2 2 2 2 Vertical Wind √푢850 + 푣850 − √푢1000 + 푣1000 Shear Dry Microburst DMI Γ500−700ℎ푃푎 + (푇 − 푇푑)700 − (푇 − 푇푑)500 Ellrod and Nelson Index (1998)

0-6km Shear Shr6 2 2 2 2 √푢6푘푚 + 푣6푘푚 − √푢2푚 + 푣2푚

푧퐿퐹퐶 Convective muCIN 휃퐸푝 − 휃퐸푒 Gilmore and Wicker Inhibition −푔 ∫ 푑푧 (1998) 0 휃퐸푒 Microburst Day MDPI 푀푎푥휃 (푆퐹퐶 − 850ℎ푃푎) − 푀𝑖푛휃 (650− < 500ℎ푃푎) Atkins and 푒 푒 Potential Index 30푘푡푠 Wakimoto (1991) 1푘푚,3푘푚 Storm Relative SRH1, SRH3 푑푽푬풏풗풊풓풐풏풎풆풏풕 Yes Davies-Jones et al. Helicity − ∫ 푘(푽푬풏풗풊풓풐풏풎풆풏풕 − 푽푺풕풐풓풎)푥 푑푧 (1990) 0 푑푧 Wind Damage WNDG 푚푢퐶퐴푃퐸 훾 푽 푚푢퐶퐼푁 + 50 Yes ( )( 2푚−3푘푚)( ퟏ−ퟑ.ퟓ풌풎)( ) Parameter 2000 9 15 40 Microburst MBURST −5 푠푏퐶퐴푃퐸 < 2000 Yes Blumberg et. al.

0 푠푏퐶퐴푃퐸 ≥ 2000 Index 0 𝑖푓 휃 ≥ 355 (2017) { 푒 } + 1 𝑖푓 푠푏퐶퐴푃퐸 ≤ 3300 + 1 휃푒 < 355 2 푠푏퐶퐴푃퐸 ≥ 3700 {4 푠푏퐶퐴푃퐸 ≥ 4300} 0 퐿퐼푠푓푐 > −7.5 1 𝑖푓 퐿퐼 ≤ −7.5 0 𝑖푓 훾 ≤ 8.4 푠푓푐 + { 2푚−3푘푚 } + 2 퐿퐼푠푓푐 ≤ −9 1 훾2푚−3푘푚 > 8.4

{3 퐿퐼푠푓푐 ≤ −10} 0 푉푇 < 27 0 푃푊푉 ≤ 1.7 1 𝑖푓 푉푇 ≥ 27 { } + { 0 𝑖푓 푑퐶퐴푃퐸 ≤ 900 + 푃푊푉 ≥ 1.7} + 2 푉푇 ≥ 28 1 푑퐶퐴푃퐸 > 900 + 푃푊푉 > 1.7 3 푉푇 ≥ 29 −3 𝑖푓 푃푊푉 ≤ 1.5 1 𝑖푓 푇푒퐷 ≥ 35 { } + { } 0 푃푊푉 > 1.5 0 푇푒퐷 < 35

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.2.3. Bayesian Hierarchical Model Hierarchical models allow complex environmental processes to be broken down into a series of conditional models linked together by simple probability rules (Wilke, 2003). Such models can be considered from a classical or Bayesian perspective, but Bayesian methods becomes necessary when systems are complex (Wilke, 2003, Anderson et al. 2007), as is the case here. Unfortunately, the posterior distributions cannot be calculated analytically, but the development and use of a Markov Chain Monte Carlo (MCMC) simulation approaches has made the implementation of Bayesian statistics possible (Wilke, 2003; Anderson et al., 2007). The freely available WinBUGS software (Lunn et al., 2000) is used for this work as it has been used with previous studies that have also looked at correcting similar biases in severe weather datasets (Anderson et al., 2007; Cheng et al., 2013; Cheng et al., 2016). Bayesian hierarchal modelling is used to determine a relation between the SWI and the rate of severe wind occurrence while correcting for biases that result from AWS density influence on the report of severe weather events across Australia. The approach adopted here extends the approach adopted by Cheng et al. (2016) when estimating tornado frequency across North America. Knowing that the number of days with at least one convective wind gusts above 90 km h-1 observed per cell (Eobs) is unlikely to be the true number, it is assumed that the reported number of events are an “undercount” of the true number of days with at least one convective wind gusts above 90 km h-1 per cell (Elatent) that occur. This process considers that the probability of detecting (POD) an event is less than one. Anderson et al. (2007) based their POD relationship between population density and the underreporting of tornadoes on the distance sampling method used to estimate animal density in ecological research (Buckland et al., 2001; Williams et al., 2002). The basic hierarchical formulation of the classical distance-sample model developed by Royle et al. (2004) was implemented by Anderson et al. (2007) and is the basis of what is used here for the POD relationship. The Bayesian model is run using 76 different combinations of the 22 variables listed in Table 4.1. Table A.1 in Appendix A lists all 76 explanatory variable combinations that were tested within the Bayesian model. These combinations are run for all 6 of the seasons and the entire year. Each model starts with two different initialization points and results in output of two MCMC chains. These two chains are used to test for convergence of the model as well as the model performance. For each combination run, an initial 5,000 iteration is used. This is referred to as the burn-in since these iterations are discarded. These iterations are typically prior

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling to convergence and done to allow the model to continue from a uniformed initialisation point. Following the burn there is an additional 50,000 iterations performed. This is to ensure that enough iterations are run so that the different Bayesian models can converge, while making the process of running 76 different combinations as automated as possible. Then a final 7,500 iterations are applied so that samples can be draw from and used for the results. This final set of iterations is done because of a limitation in WinBUGS that limits the amount of memory that can be stored. It was therefore not possible to sample from the previous 50,000 iterations. The convergence of the models for each season are determined according to the Gelman-Ruben score followed by the use of three metrics (Total CAR, deviance, and MAE) and visual analysis of the two MCMC chains. The method of testing for convergence is discussed in detail in Section 4.2.3.4. The implemented Bayesian Hierarchal model is composed of three sub-models; (1) the observation error model that accounts for the non-meteorological factors affecting the fidelity of severe thunderstorm counts in the dataset (i.e. what is discussed above), (2) the explanatory model that considers the meteorological components causally linked to thunderstorm formation and evolution, and (3) the parameter model that quantifies the uncertainty in the parameter values. 4.2.3.1. Observation Model

The observation model implemented here follows that of Anderson et al. (2007) and Cheng et al. (2016). The model first specifies a binomial distribution for the reported number of events,

Eobsi, for a given area or grid cell, i, and time period, conditional on the expected number of events, Elatenti, for the same area and time period. The binomial distribution is a discrete distribution (Bain and Engelhardt, 1992) that is commonly used where Eobsi can be thought of as the number of “successes” in Elatenti independent Bernoulli trails, with pi(훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷), the probability of detecting an event for the given density effect parameters, 훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷, where 푆푡푎푡𝑖표푛퐷 represents AWS density explained in Section 4.2.1. This relationship is:

(퐸표푏푠푖|퐸푙푎푡푒푛푡푖, 휆푖, 푝푖(훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷))~퐵𝑖푛표푚𝑖푎푙[퐸푙푎푡푒푛푡푖푝푖(훼푆푡푎푡푖표푛퐷,훽푆푡푎푡푖표푛퐷)]. (4.1)

The probability of detection in a given cell, pi , is a function of 푆푡푎푡𝑖표푛퐷푖. Cheng et al. (2016) defined this relationship using an exponent model. Preliminary tests found the use of their exponent model led to unrealistic values for 푝푖 for the current application. This is believed

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling to occur as a result of the assumption of the model that there are cells in which 푝푖 would be 1 for a given 푆푡푎푡𝑖표푛퐷 which would not be the case for the Australian AWS dataset. This is likely because these events are relatively small when compared to the grid cells used. Given this and the fact that the AWS can only observe events at a point it is likely that events are passing between stations and are not recorded in the observational record. This is likely the case even with the highest AWS density available in Australia (approximately 9 stations per grid or 1 station for every 635 km2). The relationship for the Bayesian models is given as:

훽푆푡푎푡푖표푛퐷 StationD푖 푝푖(훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷 ) = 1 − 푒푥푝(−1 ∗ ( ) ), (4.2) 훼푆푡푎푡푖표푛퐷

th where 푠푡푎푡𝑖표푛퐷푖 is the station density of the i area. The 훽푆푡푎푡푖표푛퐷 parameter affects the shape of the pi curve, where as 훼푆푡푎푡푖표푛퐷 determines the slope or rate of increase of the pi curve. In addition, the value of 훼푆푡푎푡푖표푛퐷 is constrained between 0.0027 and 0.000356 to help the model find a realistic pi curve. This equation therefore allows for greater flexibility in defining the relationship between the probability of detecting an event (pi) and AWS density (푆푡푎푡𝑖표푛퐷푖).

Eqn. 4.2 results in a POD of 1 for large 푆푡푎푡𝑖표푛퐷푖 and approaches zero for a small or zero

푆푡푎푡𝑖표푛퐷푖. The final component to the observational sub-model is to account for the chance of irregular th spatial variation within each i area. The true climatological event count, Elatenti, is therefore modelled as a Poisson process (Bain and Engelhardt 1992) conditioned on a climatological event frequency per cell, 휆푖:

(퐸푙푎푡푒푛푡푖|휆푖)~푃표𝑖푠푠표푛(휆푖). (4.3)

Elatenti is bounded by zero and will be greater or equal to Eobsi but never smaller.

4.2.3.2. Explanatory Model

The explanatory model is the logarithm of the expect event frequency, λi, as a linear function of several explanatory variables x:

log (휆푖) = 훼0 + 훼1푥푖1 + 훼2푥푖2 + ⋯ + 훼푘푥푖푘 + 퐶퐴푅푖, (4.4)

where 푥푖푘 is the value of the explanatory variable k (e.g., muCAPE, muCIN, etc.) and 훼푘 are regression coefficients corresponding to the ith explanatory variable. In addition to the

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling explanatory variables an additional, conditional autoregressive term, 퐶퐴푅푖, is added to Eqn.

4.4. The 퐶퐴푅푖 term is a gridcell-specific, random effect term that is designed to capture variability of severe convective wind storm occurrence that is not explicitly considered by the explanatory variables. Moreover, through the use of this term, it is possible to address the issue that the globally common parameterizations used in the model may be violated on a smaller, regional scale (Cheng at al., 2016). For example, orographic influence on the formation of thunderstorms (Taylor et al., 2011) or possible lake or sea-breeze convergence-influenced convective processes (King et al., 2003). Given this, Cheng et al. (2016) assume the 퐶퐴푅푖 term to have regional characteristics and therefore to be spatially correlated. This term is based on the Bayesian conditional autoregressive model (Besag et al., 1991) where each grid cell term is jointly distributed as a multi-variate normal distribution with mean zero and an unknown covariance matrix (Besag and Kooperberg, 1995). In addition, the model assumes each 퐶퐴푅푖 depends only on the neighbouring cells and that all of the neighbours have equal influence (weight of 1). The term is therefore defined as:

휎2 퐶퐴푅푖 ~ 푁표푟푚푎푙(휇푖, ), (4.5) 푛푖 where,

1 ∑ 휇푖 = 푗휖푁푖 퐶퐴푅푖, (4.6) 푛푖 and 푛푖 is the number of adjacent grid cells. This research will test models that use 1, 2 or 3 explanatory variables within Eqn. 4.4 to determine which combination of explanatory variables best explain the expected event frequency, λi, across all cells. The explanatory models with 1 variable will utilise composite indices, these are indices that have been created to include multiple measures of the state of the atmosphere into a single value. These include the GUSTEX, WINDEX, Dry Microburst Index, Microburst Day Potential Index, the Significant Severe index, SHERBE, Microburst Composite Index, Microburst Index, and the Wind Damage Parameter. The 2 indices models will incorporate an instability index with a shear index. The four different instability indices considered include the most unstable CAPE, the surface, 50hPa, and 100hpa Lifted Index. While the different shear indices include the 0km to 6km shear, as well as the Deep Vertical Wind Shear, and the Shallow Vertical Wind Shear. Finally, the 3 variable models will look at

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling one of the four instability indices in combination with one of the shear indices and a third variables that measures a different quantity. This third variable used will be one of the following, the height difference between the Level of Free Convection and the Equilibrium Level, the Wet Bulb Zero height, the 1km and 3km Storm Relative Helicity, the Theta-E deficit, the Convective Inhibition, and the Downdraft CAPE. All of these explanatory variables are necessary ingredients for severe thunderstorm formation. 4.2.3.3. Parameter Model

The parameter model treats each parameter as a random variable rather than a fixed quantity

(Anderson et al., 2007). The parameters (훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷, and 훼푘) are estimated using the Bayesian approach of assigning prior distributions. Prior distributions are assigned to be non- informative by making them “flat”. The data will then determine the shape of the posterior distributions. The regression coefficients, 훼푘, are assigned a normal distribution (Bain and Engelhardt, 1992) with a mean of 0 and variance of 10,000 (implying that the prior distribution is non-informative). Similarly, the density effect parameters, 훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷 , are assigned a normal distribution with a mean of 1 and variance of 10,000:

훼푆푡푎푡푖표푛퐷 ~ 푁표푟푚푎푙(1, 10 000), (4.7)

훽푆푡푎푡푖표푛퐷 ~ 푁표푟푚푎푙(1, 10 000), (4.8)

훼푘 ~ 푁표푟푚푎푙(0, 10 000), (4.9) 휎2 ~ 퐼푛푣푒푟푠푒 퐺푎푚푚푎(0.01, 0.01). (4.10)

The Bayesian model is run using the mean SWI calculated the period from 2005 to 2015 to determine the mean model parameters values, along with their distributions. 4.2.3.4. Model Performance

The first step in selecting the optimal combinations of indices for use in Eqn. 4.4 is to ensure any given combination results in convergence of the Bayesian model. Convergence of the model is checked using the Gelman-Rubin convergence diagnostic (Gelman and Rubin, 1992; Brooks and Gelman, 1998), which is based on the “chain” (i.e., the time series) showing the evolution of each parameter when started from two different initialization points. This convergence diagnostic works by comparing the estimated variance between chains, how similar the chains are to each other, and the variance within chains (mean variance of each chain) for each model parameter. Brooks and Gelman (1998) suggest a Gelman-Rubin score of less than 1.2 is required for all model parameters (i.e., 훼0, 훼1, (훼2, 훼3), 훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷,

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 푑푒푣𝑖푎푛푐푒, σ ) to be confident that convergence has occurred. The models found not to meet this criterion were discarded and further analysis conducted only on the remaining set of models. The ability of each model to calculate the number of days with at least one convective wind -1 gusts above 90 km h per cell (EobsMiy) for the individual years, y, within the observation period was then assessed. That is, the actual number of days with at least one convective wind -1 gust above 90 km h observed per cell (Eobsiy) from the AWS is compared with the EobsMiy calculated by running the Bayesian models for each year, y, from 2005-2015. In these tests, instead of using the 2005-2015 average indices values as the explanatory input, the mean seasonal values for the individual year was used. However, the parameter distributions determined by the trained models are utilised. Monte-Carlo simulations using the Bayesian parameters is performed using a sample size of 20,000 for each parameter. The distributions of the indices coefficients are then randomly sampled to solve for the expected rate of event occurrence, 휆푖푦, Eqn. 4.4 determined by each model. Elatentiy is then solved by sampling from the Poisson distribution of 휆푖푦. Similarly, the distributions for 훼푆푡푎푡푖표푛퐷 and 훽푆푡푎푡푖표푛퐷 are randomly sampled to solve for the probability of detecting an event, piy, of each grid-cell for the station density for the given year, since this density tends to increase over time, so will piy.

EobsMiy is then determine by multiplying piy by Elatentiy. This is done by using the mode of the two variables’ distributions. Three metrics were used to test the performance of all models that “converged”. They are, the Mean Absolute Error (MAE), the deviance, and the total conditional autoregressive (Total

CAR) term. The MAE is calculated by taking the absolute error between the EobsMiy value for each cell and the corresponding Eobsiy for the same cell and year. The absolute error is then averaged over all ERA-Interim cells that have AWS for a given year and then averaged over the 11-year period. The 푑푒푣𝑖푎푛푐푒 or Deviance Information Criterion (DIC) is a measure of how well the model fits the data, where the smaller the deviance is the better the model fits the data. It is defined as −2 ∗ 푝(푦|휃) where 푦 comprises the observed data (i.e., Eobs) and 휃 comprises the distributions of the variables which 푦 depends (i.e.,

퐸푙푎푡푒푛푡, 휆푖, 훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷 ) (Spiegelhalter et al., 2002). The sum of the absolute value of the CAR terms over all cells is also calculated as a Total CAR value. Since the CAR term accounts for things not accounted for by the explanatory variables within the Bayesian model the Total CAR would give an idea of how well the explanatory variables can explain 휆푖. A small

Total CAR would suggest they explain 휆푖 well while a large Total CAR would suggest they do

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling not do a good job of explaining 휆푖 on their own. The models, for each season, that have deviance, Total CAR, and MAE values within 25% of the model that have the smallest value, referred to here as the percent difference, for each metric are then analysed further. The percent difference, Δε, is defined as:

ε퐸,푖 Δε퐸 = 100 ∗ ( − 1), (4.11) ε퐸,1

th where ε퐸 is the error term for one of the three metrics, E, (i.e. εtCAR, εdev, εMAE), i is the i combination being assessed, and ε퐸,1 indicates the first ranked (i.e. lowest error) model error value. All remaining models were then individually assessed to ensure that the distributions for the coefficients and the 훼푆푡푎푡푖표푛퐷 , 훽푆푡푎푡푖표푛퐷 terms, for the two chains initialised in the Bayesian model, did in fact converged as suggested by the Gelman-Ruben score. In addition, the values assigned to the coefficient of each of the indices for each model was checked to ensure it was consistent with the physical understanding of the index and how it related to the occurrence of severe convection. 4.3. Results and Discussion

4.3.1. Model Comparison In general, the Total CAR are smallest for autumn and spring and largest during winter and summer. This suggests that while there are some severe weather indices that explain event occurrence rate well for the spring and autumn, the CAR term plays an increasingly important role for winter and summer. As for the deviance, terms are smallest in winter and largest in summer, with the deviance for the autumn and spring models sitting in between. The deviance appears to be smaller in winter due to the low number of observed events during this season for the model to fit to, as opposed to the summer months, which have the largest number of reported events across Australia. The MAE follows a similar pattern to the deviance, with the smallest MAE in winter and the largest in summer. Given the deviance and MAE both measure how well the model fits the observational data, this similarity is somewhat expected. It is also generally observed that MAE is similar for many of the models, this is likely attributed to use of the CAR term in Eqn. 4.4, which is there to correct results for what the explanatory variables cannot explain. This is apparent across all seasons shown in Sections 4.3.1. While the Gelman- Rubin score gives a quick metric to know if the individual Bayesian models converged it is beneficial to perform a visual analysis of the two chains used to initialise the model to help

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling decide which model or models perform best for each season. A model that has converged well will have chains with similar distributions that overlap each other. The output for these models are then analysed in Section 4.3.3. While this analysis was conducted for the 6 different seasons listed above plus the entire year, the results for only the four traditional seasons (Autumns, Winter, Spring, Summer) are shown in this section. The analysis for the Autumn-Winter, Spring-Summer, and the entire year did not yield a model that converged to a point where the results were believed to be reliable. However, these results can be found in Appendix B out of curiosity. It is believed these seasons did not produce reliable models due to the spatial distributions between the four traditional seasons being different enough, that their mean indices values were not good representations of the event occurrence rate. 4.3.1.1.Autumn

For the autumn season, which goes from March to May, 17 of the 76 models are considered to have converged according to the Gelman-Ruben score. These 17 models are shown in Table 4.2, with their corresponding Total CAR, deviance, MAE values and percent difference compared to the model with the smallest Total CAR, deviance, or MAE. There is a mix of 1, 2, and 3 indices models that met the convergence criteria set out in Section 4.2.3.4. However, only two models, both 1 index models have a percent difference value, for all three of the

metrics (ΔεtCAR, Δεdev, ΔεMAE) less than 25%. These are the Wind Damage Parameter Model (WNDG) and the Microburst Day Potential Index (MDPI). While most models shown in Table 4.2 have comparable deviance and MAE values, all less than 15% greater than the first ranked Deviance (Li100-Shr6-SRH1) and MAE (Li50-Shr6-TeD) models, the Total CARs show more

variability. In fact, with the third ranked model (Sig.Sev.) has a ΔεtCAR of 56% when compared with the WNDG model. The coefficient parameters of the models, WNDG and MDPI, are examined to verify that the Bayesian model gives a result that agrees with the reasoning behind the indices. The coefficients are shown in Table 4.3 where both models have a mean a0 value close to 1 and a1 of 0.38 for WNDG and 0.42 for MDPI. These values make sense since for larger values of WNDG and MDPI a greater chance for severe convective wind storms to occur would be

expected. Given this, the distributions of the parameters in Eqn. 4.2 (훽푆푡푎푡푖표푛퐷, 훼푆푡푎푡푖표푛퐷) and the coefficients in Eqn. 4.4 are visually examined to verify that the chains converged as predicted by the Gelman-Ruben score.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Table 4.2: List the models for autumn that converged according to the Gelman-Ruben score, along with Total CAR value for each model, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of the metrics.

Model Total CAR Deviance MAE ΔεtCAR Δεdev ΔεMAE

WNDG 112.95 213.20 2.67 0 6 14

MDPI 122.89 213.50 2.62 9 6 11

Sig.Sev. 175.72 213.90 2.70 56 6 15

Li100-SVWS-dCAPE 186.90 216.80 2.45 65 8 4

muCAPE-SVWS 213.89 215.90 2.53 89 7 8

GUSTEX 223.23 212.50 2.57 98 6 9

Li50-SVWS 240.23 213.50 2.51 113 6 7

Li50-SVWS-SRH3 262.56 206.00 2.46 132 2 5

LiSfc-Shr6 271.07 214.70 2.49 140 7 6

WINDEX 283.11 211.90 2.45 151 5 4

Li100-SVWS-SRH3 300.66 209.40 2.39 166 4 2

LiSfc-Shr6-CIN 321.72 213.10 2.38 185 6 1

Li50-Shr6-TeD 356.44 203.30 2.35 216 1 0

Li100-Shr6-SRH1 428.23 201.20 2.39 279 0 2

Li50-SVWS-SRH1 431.24 208.70 2.37 282 4 1

LiSfc-SVWS-WBZ 459.60 211.50 2.36 307 5 1

Li100-SVWS-SRH1 467.47 202.50 2.35 314 1 0

WNDG 0.94 0.55 0.38 0.11 - - - -

MDPI 1.15 0.47 0.42 0.17 - - - -

Figure 4.3a shows the parameter and coefficient distributions for the WNDG model and Figure 4.3b shows these for the MDPI model. The blue distributions represent the MCMC chain output from the first initialization point and the orange distributions represent the MCMC chain output from the second initialization point. For each figure, the first column shows the probability density function (PDF) of the a0 chains, the second shows the PDF for the a1

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling chains, while the third and fourth columns shows the PDFs for the chains from 훼푆푡푎푡푖표푛퐷 and

훽푆푡푎푡푖표푛퐷 chains, respectively. The chains showed are from the final 7,500 iterations of which are sampled. While the distributions for most of the parameters in both models look similar, there is a noticeable difference between the chains for 훼푆푡푎푡푖표푛퐷 in the WNDG model. This suggests that the 훼푆푡푎푡푖표푛퐷 parameter in the POD may not have converged as well as first appears. Given this, of the indices tested, it is felt that the MDPI model provides the most informed explanation of severe convective wind gust occurrence rate during autumn. This model is therefore used for the final climatology, shown in Section 4.3.3, of severe convective wind storms during autumn.

Figure 4.3: Shows the distributions of the two chains for the (a) WNDG model and the (b) MDPI model. The first column is a0, the second a1, the third 훼푆푡푎푡푖표푛퐷 and the fourth 훽푆푡푎푡푖표푛퐷. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.3.1.2.Winter

There were only 4 models that converged according to the Gelman-Ruben score during the winter months (June-August). It is believed that this may be a result of the low observed event counts during these months that make it challenging for the model to converge to a solution. Another issues may be that the typical indices used to explain the occurrence of severe weather may not be entirely appropriate in the winter months. More tailored indices for the kind of convective events that occur in the winter months may need to be developed. These four models are the WNDG model, Dry Microburst Index (DMI) model, the WINDEX model, and the 100hPa Lifted Index, 0km to 6km Shear (Li100-Shr6) model. No three-index model was found to converge. Table 4.4 shows the value of the three metrics for the winter models. All four models had Δε values less than 10% for each metric.

Table 4.4: List the models for winter that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of the metrics. Model Total CAR Deviance MAE ΔεtCAR Δεdev ΔεMAE WNDG 567.26 122.30 1.52 0 3 0 DMI 584.33 118.90 1.53 3 0 1 Li100-Shr6 614.50 119.00 1.52 8 0 0 WINDEX 622.96 121.90 1.53 10 3 1

The coefficient values for the four models are shown in Table 4.5. All models have a negative value for the a0 coefficient, which likely is a result of the low number of events that occur during the winter across Australia. Despite this, the WNDG, DMI, and Li100-Shr6 model all have coefficients that make physical sense. For the 1-index models, a0 is positive for both suggesting the frequency of events will increase with larger values. For the 2-index model a0 is -0.18. This value intuitively makes sense, giving larger negative values of Li100 represents a more unstable atmosphere increasing the probability of convection occurring. Moreover, a2 is 0.16, where larger shear values tend to be associated with more severe convective storms. Since WINDEX is a measure of the gust potential it would be expected that the larger WINDEX is, the more likely severe convective wind gusts would occur. However, the coefficient for WINDEX is negative in the model, which is not what would be expected and questions the suitability of that model.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Table 4.5: The four winter models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models. Model a0 a0 a1 a1 a2 a2 a3 a3 Mean StdDev Mean StdDev Mean StdDev Mean StdDev

WNDG -0.34 1.15 0.17 0.22 - - - -

DMI -1.00 0.91 1.12 0.39 - - - -

Li100-Shr6 -0.71 0.92 -0.18 0.24 0.16 0.54 - -

WINDEX -0.31 0.86 -0.30 0.34 - - - - When looking at the parameter distribution of the two chains for the four models in Figure 4.4 only the Li100-Shr6 model appears to have distributions that are comparable with only small difference. With the other three models, 훼푆푡푎푡푖표푛퐷 , is different for the two chains, especially for the WNDG model, with the peak being shifted from one another. For the DMI and WINDEX models, they both have chains that are relatively flat. These observations suggest these three models were unable to converge to a specific value. Therefore, these models may not be reliable ones to consider. The Li100-Shr6 model is used for the final climatology, shown in Section 4.3.3, of severe convective wind storms during winter.

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Figure 4.4: Shows the distributions of the two chains for the (a) WNDG model and the (b) DMI model (c) is Li100-Shr6 model and (d) is the WINDEX model. For the 1 index models the first column is a0, the second a1, the third 훼푆푡푎푡푖표푛퐷 and the fourth 훽푆푡푎푡푖표푛퐷. For the two index models the first column is a0, the second a1, the third is a2, the fourth is 훼푆푡푎푡푖표푛퐷 and the fifth is 훽푆푡푎푡푖표푛퐷. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.3.1.3. Spring

For the season of spring (September to November) there are a larger number of models found to meet the Gelman-Ruben convergence score (Table 4.6). However, only two out of the 43 models have all three metric values with Δε less than 25%. These are both 3-indices models. The first is the Surface Lifted Index, 0km to 6km Shear, and height difference between Level of Free Convection and the Equilibrium Level (LiSfc-Shr6-lfcel). The second model using two of the same indices but with the Shr6 variable replaced by the Shallow Vertical Wind Shear (LiSfc-SVWS-lfcel). The coefficients for the two 3-indices models are given in Table 4.7. Where the a0, a1, a2, and a3 values for the LiSfc-Shr6-lfcel are 2.53, 0.69, 0.39, and 0.95 respectively. For the LiSfc- SVWS-lfcel model they are, 2.62, 0.53, -0.35, and 0.50. The spring models have large values of a0, likely related to the overall increased number of observed events compared to autumn or winter. The two models both have positive values for the LiSfc index, which goes against intuition. Looking at the mean value of the index, Figure A.5 in Appendix A, for the spring months as well as Figure 4.1c, showing the observed number of events during the spring, it is evident that the cells with the most observed events, along the southeastern parts of Australia, are associated with positive values of LiSfc, just above zero. This may be why the coefficient is found to be positive for the models. The coefficient for Shr6 is consistent with the physical understanding of severe convection, with increased shear resulting in increasingly severe convection. In contrast, the coefficient for SVWS is negative, going against the understanding of the relationship between shear and severe convection. However, Markowski and Richardson (2006) note that the lack of numerical simulations to resolve the lower layers of the atmosphere make it difficult to know the importance of vertical wind shear in this layer. Finally, a positive a3 in relation to the lfcel is seen in both models. This is expected given the larger the height difference the larger the depth of the atmosphere for an air parcel to rise freely.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Table 4.6: List the models for spring that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of each metric. Model Total CAR Deviance MAE ΔεtCAR Δεdev ΔεMAE LiSfc-Shr6-lfcel 170.34 370.80 6.53 0 8 7 LiSfc-SVWS-lfcel 199.06 368.70 7.15 17 7 17 muCAPE-SVWS-WBZ 223.53 360.60 6.87 31 5 13 Li100-Shr6-lfcel 247.65 361.00 6.38 45 5 5 Li50-SVWS-CIN 249.65 356.90 6.51 47 4 7 LiSfc-SVWS 289.54 354.20 6.65 70 3 9 SHERBE 291.84 352.60 6.43 71 2 5 LiSfc-Shr6-dCAPE 292.39 352.10 6.34 72 2 4 LiSfc-Shr6-CIN 297.99 362.40 6.46 75 5 6 LiSfc-SVWS-SRH3 304.12 352.60 6.47 79 2 6 LiSfc-SVWS-dCAPE 306.85 351.40 6.61 80 2 8 Li50-Shr6-CIN 309.57 358.70 6.47 82 4 6 LiSfc-SVWS-WBZ 323.92 357.00 6.53 90 4 7 LiSfc-SVWS-SRH1 338.07 358.00 6.62 98 4 9 LiSfc-SVWS-TeD 338.12 351.00 6.35 99 2 4 Li50-SVWS-SRH3 358.19 354.90 6.60 110 3 8 WNDG 365.21 351.60 6.49 114 2 6 Li50-SVWS-SRH1 367.22 349.80 6.49 116 2 6 Li100-dvws 369.62 349.40 6.63 117 1 9 muCAPE-SVWS-SRH1 375.56 352.10 6.53 120 2 7 mcmp 375.89 353.40 6.74 121 3 11 GUSTEX 376.80 352.30 6.51 121 2 7 Li100-SVWS-dCAPE 377.00 351.00 6.51 121 2 7 muCAPE-Shr6-SRH1 377.76 351.40 6.49 122 2 6 muCAPE-SVWS 382.84 348.60 6.58 125 1 8 muCAPE-SVWS-TeD 387.45 354.50 6.34 127 3 4 Li100-Shr6-SRH3 401.23 345.60 6.27 136 0 3 Li100-SVWS-TeD 412.64 348.40 6.38 142 1 5 Li100-Shr6-SRH1 415.38 348.20 6.41 144 1 5 muCAPE-SVWS-SRH3 415.41 348.70 6.40 144 1 5 Sig.Sev. 429.19 352.90 6.30 152 2 3 Li100-Shr6-TeD 431.86 347.90 6.10 154 1 0 Li50-Shr6-TeD 431.97 352.10 6.28 154 2 3 LiSfc-Shr6 433.50 346.70 6.33 154 1 4 WINDEX 442.47 348.30 6.30 160 1 3 Li50-Shr6-WBZ 450.48 344.40 6.55 164 0 8 muCAPE-Shr6 463.11 347.70 6.26 172 1 3 Li50-Shr6 463.20 344.80 6.44 172 0 6 muCAPE-Shr6-TeD 470.21 350.30 6.37 176 2 5 Li100-Shr6 470.71 350.20 6.36 176 2 4 muCAPE-Shr6-WBZ 518.64 347.30 6.41 204 1 5

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Table 4.7: The two spring models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models. Model a0 a0 a1 a1 a2 a2 a3 a3 Mean StdDev Mean StdDev Mean StdDev Mean StdDev

LiSfc-Shr6-lfcel 2.53 0.50 0.69 0.22 0.39 0.28 0.95 0.23

LiSfc-SVWS-lfcel 2.62 0.38 0.53 0.19 -0.35 0.16 0.50 0.19 Finally, the two chains for each model are visually compared in Figure 4.5. In the LiSfc- Shr6-lfcel there are some discrepancy seen in the distribution of the a0, a1, and a2 coefficient as well as for 훼푆푡푎푡푖표푛퐷, particularly the relatively flat distribution in the one chain for

훼푆푡푎푡푖표푛퐷. The chains are comparably more similar in LiSfc-SVWS-lfcel with some difference in 훼푆푡푎푡푖표푛퐷. Despite the small difference the LiSfc-SVWS-lfcel looks to be the model that would give the most reliable output of event counts. The LiSfc-SVWS-lfcel model is therefore used for the final climatology (Section 4.3.3) of severe convective wind storms during spring.

Figure 4.5: Shows the distributions of the two chains for the (a) LiSfc-Shr6-lfcel model and the (b) LiSfc-SVWS-lfcel model. The first column is a0, the second a1, the third a2, the fourth is a3, the fifth 훼푆푡푎푡푖표푛퐷 and the sixth 훽푆푡푎푡푖표푛퐷. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.1.3.4. Summer

Lastly, summer from December to February is examined. There are 18 models that converge for summer according to the Gelman-Ruben score (Table 4.8). Of which, 3 models have all three metric values with Δε less than 25%. These three models are the 100hPa Lifted Index, 0km to 6km Shear, and downdraft CAPE (Li100-Shr6-dCAPE), the same model with Li100 replaced by the Surface Lifted Index (LiSfc-Shr6-dCAPE), and Li100, the Shallow Vertical Wind Shear, and downdraft CAPE (Li100-SVWS-dCAPE). The coefficients for the summer models are shown in Table 4.9. All three models have an a0 value close to or great than 3, associated with the season that has the largest number of observed events of the four seasons. The Li100-Shr6-dCAPE and LiSfc-Shr6-dCAPE models both have a negative a1 and positive a2 associated with their lifted index and Shr6 indices respectively. As mentioned previously these coefficient signs are what would intuitively be expect for these indices. The Li100- SVWS-dCAPE model unfortunately has a positive a1 for Li100 and a negative a2 for SVWS, however this is consistent with what was seen for the coefficient for LiSfc and SVWS in the spring model. Comparing the distribution of observed days with events during the summer (Figure 4.1d) with the mean values of Li100 during the summer (Figure A.7) it is clear that the relationship between the two would be complex. There are multiple cells across Australia that observe numerous days with severe convective wind storms that are associated with different values of Li100, both negative and positive. It may be possible that when taking into account the SVWS and dCAPE that a more stable atmosphere as defined by the 100hPa lifted index better explains the occurrence of these severe convective wind storms. Looking at case studies in different parts of Australia, that focus on these indices, might better explain this relation. Each model has dCAPE as an explanatory variable, all three with their a3 coefficient being positive. A large dCAPE is associated with greater potential for the occurrence of a downdraft, so therefore would expect a positive coefficient so that a larger mean dCAPE would result in a greater event occurrence rate. The distributions for the three summer models can be compared in Figure 4.6. The Li100-

Shr6-dCAPE model has very visible differences in most of the coefficients except for βStationD. Better agreement is seen between the parameter chains for the other two models. However, they both seem to have some disagreement with the a3 coefficient for the dCAPE variable, with both having one chain that looks slightly bimodal. However, the LiSfc-Shr6-dCAPE model has a much larger MAE while the Li100-SVWS-dCAPE model has the smallest MAE of all the models that were found to converge for summer. Therefore, the Li100-SVWS-dCAPE

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling model is believed to be the model that is most reliable at explaining the rate of event occurrence during the summer months for Australia and is used for the summer climatology shown in Section 4.3.3.

Model Total CAR Deviance MAE ΔεtCAR Δεdev ΔεMAE

Li100-Shr6-dCAPE 305.30 436.80 9.17 0 6 12

LiSfc-Shr6-dCAPE 313.70 431.80 9.64 3 5 17

Li100-SVWS-dCAPE 354.83 424.00 8.21 16 3 0

MDPI 429.54 426.50 8.46 41 4 3

LiSfc-Shr6-WBZ 613.11 429.90 9.50 101 4 16

Li50-SVWS-SRH3 684.97 429.70 9.03 124 4 10

muCAPE-SVWS-SRH3 700.74 426.70 9.42 130 4 15

LiSfc-SVWS-SRH1 704.69 431.00 9.26 131 5 13

Li50-Shr6-SRH1 715.47 413.10 8.47 134 0 3

LiSfc-SVWS 722.77 422.10 8.78 137 3 7

Li100-SVWS 731.56 428.30 8.76 140 4 7

Li100-SVWS-SRH1 749.96 424.90 8.99 146 3 9

WNDG 770.49 430.50 8.74 152 5 6

Li100-dvws 776.25 416.20 8.55 154 1 4

Li50-Shr6 780.65 423.00 8.45 156 3 3

Sig.Sev. 798.24 411.80 8.65 161 0 5

muCAPE-Shr6-lfcel 815.47 422.70 8.66 167 3 6

LiSfc-Shr6-CIN 881.78 428.00 8.55 189 4 4

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Table 4.9: The five summer models with the percent difference for the three metrics less than 25% and their corresponding coefficient mean and standard deviations as determined by the Bayesians models. Model a0 a0 a1 a1 a2 a2 a3 a3 Mean StdDev Mean StdDev Mean StdDev Mean StdDev

Li100-Shr6-dCAPE 3.36 0.39 -0.015 0.25 0.45 0.32 1.26 0.20

LiSfc-Shr6-dCAPE 3.17 0.38 -0.11 0.24 0.44 0.34 1.2 0.20

Li100-SVWS-dCAPE 2.91 0.32 0.15 0.19 -0.21 0.17 0.87 0.26

Figure 4.6: Shows the distributions of the two chains for the (a) Li100-Shr6-dCAPE model and the (b) LiSfc-Shr6-dCAPE model and (c) Li100-SVWS-dCAPE. The first column is a0, the second a1, the third a2, the fourth is a3, the fifth 훼푆푡푎푡푖표푛퐷 and the sixth 훽푆푡푎푡푖표푛퐷. Where the blue and orange distributions are the MCMC chain outputs from the first and second initialization points, respectively.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.3.2. Probability of Detection Using the model that performed best for each of the four seasons, the Probability of Detection (POD) is plotted as a function of the number of AWS per grid cell. The mean POD curves are shown in Figure 4.7. Each curve generally follows the same shape. There is a relatively sharp increase in the POD as the number of stations increase to a few stations per cell. Afterwards, the increase in POD slows as it approaches one. The point at which the rate of increase in POD begins to slow is different for the four models, or seasons. The autumn and summer POD curves reach 0.5 between 4-5 stations per grid cell. Whereas, the winter and spring curves reach 0.5 between 6-7 stations per grid cell. Similarly, the POD curves reach 0.99 by 17, 22, 30, and 18 for the autumn, winter, spring, and summer months respectively. The need for less stations in the autumn and the most number of station in spring is evident in the two parameters values (∝푆푡푎푡푖표푛퐷 , 훽푆푡푎푡푖표푛퐷) found in the POD equations. In Table 4.10,

∝푆푡푎푡푖표푛퐷, is largest for the spring POD equation and it is found furthest to the right along the x-axis, as opposed to the autumn POD curve which has the smallest ∝푆푡푎푡푖표푛퐷, and is found furthest to the left along the x-axis. Similarly, the autumn POD equation has the largest

훽푆푡푎푡푖표푛퐷 with the steepest rate of increase in POD whereas, the spring POD equation has the smallest 훽푆푡푎푡푖표푛퐷 and shows the least steep rate of increase in POD.

Table 4.10: Shows the mean and standard deviation (StdDev) values for the ∝푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷 parameters for each of the models that perform the best for the four seasons. Model ∝푆푡푎푡푖표푛퐷 ∝푆푡푎푡푖표푛퐷 훽푆푡푎푡푖표푛퐷 훽푆푡푎푡푖표푛퐷 Mean StdDev Mean StdDev

MDPI – Autumn 1.014E-3 5.585E-4 1.453 0.2629

Li100-Shr6 – Winter 1.290E-3 6.214E-4 1.383 0.3014

LiSfc-SVWS-lfcel – Spring 1.526E-3 5.476E-4 1.248 0.1476

Li100-SVWS-dCAPE – Summer 1.076E-3 4.357E-4 1.342 0.1826

It is not immediately clear why the POD curves would vary for the different seasons. However, it is hypothesised here that the difference in convective storm sizes and differences in the severity of events during different periods of the year might impact the AWS density required to observe severe convective wind storm above 90 km h-1. With respects to different sizes of convective storms it would be expected that larger convective system (e.g., linear convective systems) would be more likely observed by the AWS than more isolated convective system (e.g., multicellular, supercells) and thus require a less dense network of AWS to detect

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling them. Similarly, stronger convective systems, such as supercells that may have more intense outflows, would likely have a higher chance of being observed as a severe convective wind storm by an AWS than a weaker system whose outflow decays below the 90 km h-1 threshold before it is observed by an AWS. The less intense severe convective systems would therefore require a denser network of AWS to be observed. The use of a more detailed SOM that considers different type of convective events, as suggested in Chapter 3, would make it possible to see which types of convective events are dominate during the different seasons and see if storm types do in fact play a role in the ability of the AWS network to observe events. The use of radar data may be able to provide some useful information about the “true” strength of severe convective winds not directly near an AWS to see if the intensity of convective systems has a seasonal dependency that affects the POD of the AWS network.

1.2

0.8

0.6 POD

0.4

MDPI - Autumn

Li100-Shr6 - Winter 0.2 Li100-SVWS-dCAPE - Summer

LiSfc-SVWS-lfcel - Spring

0 0 5 10 15 20 25 30 35 40 Number of stations per cell Figure 4.7: The probability of detection (POD) curves for the models that appear to perform the best for each season. Where the blue-square curve shows the POD for the MDPI model in autumn, the orange-triangle curve shows the POD for the Li100-Shr6 model for winter, the grey-circle line shows the POD curve for the Li100-SVWS-dCAPE curve for summer, and the green- circle line shows the POD curve for the LiSfc-SVWS-lfcel for spring.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling 4.3.3. Climatologies From the chosen models for each season, the spatially complete climatology for autumn (MDPI), winter (Li100-Shr6), spring (LiSfc-SVWS-lfcel) and summer (Li100-SVWS- dCAPE) are discussed here. The climatologies between 2005-2015 are shown and discussed in Section 4.3.3.1. Moreover, the flexibility of the models created allow for this climatology to be extended using the entire ERA-Interim reanalysis data from 1979-2015. The mean annual event counts (i.e. at least one gust > 90 km h-1 on a given day in a 75x75km grid cell) for the seasons over this extended, 37-year period, are shown and discussed in Section 4.3.3.2.

4.3.3.1. 2005-2015

Since the Bayesian models were developed using the ERA-Interim reanalysis data between 2005-2015, this period was a good place to start to visualise what the climatology of severe convective wind storms across Australia might look like. Specifically, the expected number of days in which at least one severe convective event occurs within a grid cell (Elatent). In addition, it provides spatially complete outputs for the probability of detecting (POD) an event in a given cell and conditional autoregressive term (CAR) for a given cell. The following figures, (Figures 4.8-4.11) show the outputs for the autumn model (Figure 4.8), winter model (Figure 4.9), spring model (Figure 4.10), and summer model (Figure 4.11). Each figure specifically shows the mean values for (a) Elatent, (c) CAR, and (d) POD as well as the standard deviation for (b) Elatent, (d) CAR, and (f) POD. Looking first at autumn, Figure 4.8a shows that the MDPI model estimates there is at most 1.5 days with a severe convective event expected per year across Australia. This is mainly around the northern half of Western Australia (WA), particularly the northeast part of WA. The model suggests less than 0.5 event days (i.e. one day where a severe wind storm occurs would be expected every 2 years) for most of the rest of the country with the exception on northeast New South Wales (NSW) where it is closer to 1 event day per year. The standard deviation values for Elatent at each cell (Figure 4.8b) suggest that the model has the greatest uncertainty around the northeast part of WA with standard deviations up to 3 event days per year. The POD across Australia is as expected, and closely follows the number of stations shown in Figure 4.2. The highest PODs are near the major cities, while most of the country has a POD of zero due to there being no AWS, with at least 5 years of data, in those cells at any point between 2005- 2015. This is also evident for the other seasonal models (Figure 4.9c, 4.10c, 4.11c). The CAR term (Figure 4.8e) shows that for the most part it is near zero, or slightly positive. This suggests

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling that the MDPI index requires only minor adjustments to explaining the event occurrence rate and in some places slightly underestimates the rate at which events occur.

a) b)

c) d)

e) f)

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling Looking next at winter, the spatial distribution of events changes (Figure 4.9a). The output from the Li100-Shr6 model suggests there are little to no convective wind storms occurring throughout most of Australia in the winter months. The northern most coast of Australia has a small number of days, less than 0.25 event days per year (i.e. one day where a severe wind storm occurs would be expected every 4 years), occurring. Similar counts are shown in the southern half of Australia with the exception of southwest WA and Tasmania (TAS), where there is closer to 1 to 1.5 event days per year occurring. The contrast in event days between north and south Australia is likely explained by the moving of the two predominate high- pressure systems in the Indian and Pacific Oceans moving equatorward. This results in strong subsidence in the north and a lack of orographic lifting as the trade winds move the moist tropical maritime Pacific air mass parallel to the coast (Tapper and Hurry, 1993). While in the south, costal low-pressure systems and their cold fronts are less likely to affect the interior of the continent, mainly affecting the southern parts of Australia. The less frequent passage of cold fronts in the interior of Australia during the winter could play a role in why severe convective wind storms are not as common in the interior during this time by removing a potential source of lifting and convective initiation. There is however significant standard deviation in Elatent, up to 3 event days, for several cells along the south coast of Australia and even a few along the coast of northern WA (Figure 4.9b). This suggests the model struggles to determine the expected number of event days in these cells. Figure A.7 shows the mean value of Li100. Large positive values are seen to the north, suggesting a very stable atmosphere, and Li100 can be seen to gradually decrease towards the south, suggesting the atmosphere is becoming more unstable. There is also a small area of increased instability right along the southern coast. This thin coastal area of instability could be responsible for the large standard deviation seen in Elatent, making it difficult for the model to explain the relationship uniformly well across the country even with the use of the CAR term. The CAR term (Figure 4.9c) also shows a contrast between the northern and southern parts of Australia, with negative values to the north, especially along the coast of Queensland, and positive values to the south. These values are larger than seen in the other seasons and has a different scale here than in Figures 4.8c, 4.10c, and 4.11c. The negative values would suggest that the two indices overestimate the event occurrence in those areas while the positive values suggest the indices under estimate the event occurrence in the south of Australia. In addition, the under reporting of event days in the south of the country would suggests there is some other factor aside from Li100 and Shr6 that explains the occurrence of

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling events in the south and that this factor is likely different to what is inhibiting events in the north that Li100 and Shr6 do not explain.

a) b)

c) d)

e) f)

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling In spring an increase in the number of event days that occur across the county can be seen (Figure 4.10a). This increase is likely associated with the shift in synoptic weather patterns as the high-pressure systems over the Indian and Pacific Oceans start to move south (Tapper and Hurry, 1993). The maximum number of severe convective wind storm days appear to occur in the interior of the continent, with event days dropping off around the coast, more so towards the south. Up to 4.5 event days per year can be seen in central Northern Territory (NT) and east into Queensland (QLD). In the northern parts of Australia, the increase in events is likely associated with the monsoonal depression starting to return and the formation of heat lows. There is also a small maximum, similar in amplitude in northeast NSW. This small maximum likely relates to return of the south-easterly trade winds bringing warm, moist Pacific and Tasman maritime air to this region (Tapper and Hurry, 1993). The standard deviation of Elatent (Figure 4.10b) suggest that this area of maximum event days is associated with some uncertainty with standard deviation values approach 3 days. However, the CAR term (Figure 4.10c) decreases across most of the country compared to winter, but not as near zero as autumn. Moreover, the standard deviation of the CAR term (Figure 4.10d) is relatively uniform across the country, aside from cells located over the ocean. Therefore, while the model finds some uncertainty over the value of Elatent, in the parts of the country with the highest event days, it does not find a significant need to correct for factors not accounted for by LiSfc, SVWS, and lfcel. There are small positive values along the southeastern coast of Australia suggesting the LiSfc-SVWS-lfcel model slightly underestimates the number of event days that part of the county. There also appear to be slight overestimation in the number of event days in central NT, around Adelaide in SA and tropical north Queensland.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling

a) b)

c) d)

e) f)

The largest event day counts are shown to occur in the summer months (Figure 4.11a). It is important for the reader to note that the scale in Figure 4.11a is different from those shown for the other seasons in Figures 4.8a, 4.9a, and 4.10a. These day counts are significantly higher compared to the three other season, reaching up to 15 event days per year over northern WA. The increase in events across the country may be attributed to the large-scale weather patterns

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling that are typically present throughout the summer and are more favourable to the formation of convection. In the summer, the intertropical convergence zone can be found over the northern part of Australia. It is associated with convergence and uplift of very moist air, which is favourable for convective storms to develop. Frequency of these thunderstorms tends to decrease moving away from the coast but exceptions have been noted over inland Western Australia where ‘dry’ thunderstorms are common (Kuleshov et al. 2002). In WA the general wind pattern is easterly bringing hot, dry continental air into the region. However, there is also the recurring of trade winds that bring warm, moist tropical maritime air from the Indian ocean into northern WA (Tapper and Hurry, 1993). The interaction of these two different air masses could have the potential to create severe convective weather, specifically these ‘dry’ thunderstorms, that may be responsible for the large number of severe convective wind events in this region. Like in spring, the east coast of Australia experiences south-easterly trade winds that bring warm, moist Pacific and Tasman maritime air to this region and with it the potential for convection that is aided by orographic lifting of the great dividing range. While the mean Elatent values does appear high, it is important to note that the grid cells are reasonably large and cover an area of approximately 5,625km2. Given that, almost all of these grid cells, with large Elatent values, occur in very sparsely populated area making it difficult to verify through other datasets if these values have merit. It may be possible to look at the BOM Severe Storm Archive (SSA) but significant quality control would be needed prior to comparing event day counts or running a similar Bayesian model using events from the SSA. Examining additional outputs from the model, the standard deviation of Elatent (Figure 4.11b) is found to be significant over northern WA and even parts of western QLD. This is not surprising giving the magnitude of the mean Elatent values as well as the sparsity of cells with nonzero POD values in these regions (Figure 4.11e). In contrast, the small maximum of Elatent over northeast NSW has a much smaller standard deviation for Elatent. The standard deviation of CAR (Figure 4.12b) shows a distinction between the cells where AWSs are present and the cells that do not have any AWSs. The mean CAR term in summer (Figure 4.11c) shows for the most part the model underestimates the event day counts, especially over the northeast part of WA and some cells along the southeast parts of Australia. There is better confidence in the CAR term for the cells that have AWS. While this may be expected, it is interesting how stark the contrast is in the summer. Since the counts are significantly higher than the other seasons, and not closer to the counts seen in spring, it is suggested these results be taken with caution.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling

a) b)

c) d)

e) f)

Figure 4.11: Output from the Li100-SVWS-dCAPE summer model from 2005-2015 for (a) the mean expected number of days on which at least one convective event (Elatent) will occur within a grid cell (0.75°X0.75°), (b) the standard deviation of Elatent, (c) the mean probability of detection (POD) at each grid cell, (d) the standard deviation of POD, (e) the mean conditional autoregressive (CAR) term at each cell, and (f) the standard deviation of CAR. An aggregated count of the number of days per year, with a severe convective event, over the entire year is shown in Figure 4.12. This is done by combining the outputs of the four seasonal models. Figure 4.12 shows that the majority of days with a severe convective wind storm appears to occur over the north half of WA, with about 15-20 event days per year, and extends to a lesser degree into the south half of the NT and western QLD with about 10 event 144

Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling days per year. The rest of the country see about 1-5 event days with a severe convective wind storm, with the exception of a couple cells over northeast NSW that have about 10-12 event days per year. Looking at the contribution of each season to the entire year, Figure 4.13, it is clear that the majority of events occurring during the summer. With cells over northern Western Australia having up to 80% of their event days occurring in the summer. Cells east of Western Australia have about 40% of their event days occurring in the spring, whereas most cells have 10-20% of their event days in autumn. In the winter, most cells have less than 10% of their event days occurring with the exception of cells over the southern Australian coast and Tasmania where the percentage can reach up to 60%.

Figure 4.12: Shows the climatology for average number of days with at least one severe convective wind storm above 90 km h-1 per year between 2005-2015 over the entire year through the summation of the of the outputs from the four seasonal models shown in Figure 4.8a-4.11a. The climatology shown in Figure 4.12 can be compare to what is seen from the climatology based on solely the AWS data in Figure 3.11 (Section 3.3.3) which covers the same period between 2005-2015. It is important to note that the results here show a per year count for the number days with at least one convective wind storm within an entire ERA-Interim cell, whereas the climatology in Chapter 3 shows the yearly, 6-hourly event count at an individual AWS. Aside from the climatology in Figure 3.11 not being spatially complete, one of the big

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling differences is that there are a significantly less number of events per year shown in Figure 3.11, with at most 3.5 occurring at a station, compared to up to 20 event days with a severe convective event in a cell shown in Figure 4.12. Since each AWS only picks up events at that station, the POD in the Bayesian model tries to account events that are missed. The POD in the model corrects the results to get all the events in a cell, which is much larger than the size of many convective storms. Aside from these differences, there are similarities seen between these two climatologies. Specifically, that is there are a large number of events occurring over northern WA as well as the interior of Australia. Moreover. Both climatologies show a small peak over northern NSW. These similarities provide some confidence in the results obtained from the two methods developed. a) b)

c) d)

Figure 4.13: Shows the percentage of events that occur in the four seasons (a) autumn, (b) winter, (c) spring, (d) summer.

4.3.3.2. 1979-2015

In order to accurately determine the hazard associated with any type of severe weather event, including severe convective wind storms, a long enough period of observations is necessary. While the results from the models discussed above give a spatially complete climatology with the effects of AWS biases minimised it is only done so for a short 11 year period. Here, those

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling relationships developed in Section 4.2.3 and discussed in Section 4.3.1 are extending through the use of the entire ERA-Interim period (37 years), to estimate the number of event days per year from 1979-2015. Eqn. 4.4 is solved, for each season, through the use of a Monte-Carlo simulation using the distribution of each parameter (a0, a1, a2, a3, CARi), from the models chosen in 4.3.1, and the mean indices value between 1979-2015. A random sampling of 20,000 times is used to give a distribution for the event occurrence rate, λi, at each ERA-Interim grid cell i. Elatent is then solved in the Monte-Carlo simulation by taking the Poisson distribution of λi. Results of this analysis are shown in Figure 4.14 where yearly seasonal event occurrence is shown for autumn, winter, spring, and summer. When interpreting this figure it is important to note that the scale for summer is different from those used for autumn, winter, and spring. Comparing the climatology over the extended period of 1979-2015 with the period the Bayesian models were develop using (2005-2015), only minor differences are noted. In autumn, Figure 4.14a, there is a slightly larger area in northeast WA where there is expected to be greater than 1.5 event days per year when compared with what is seen in Figure 4.8a. There is a more noticeable difference in winter, Figure 4.14b, with a significant increase in event occurrence around northeast TAS, and along the southwest coast of WA. The reasons for this might be that numerous cells around the southern parts of Australia have large standard deviations in Elatent, as shown in Figure 4.9b. This suggests that the model developed might be struggling to explain the event occurrence rate in those cells. This could be impacting the Monte-Carlo simulation for 1979-2015 such that when samples are taken from the distributions, from those cells, there is an over estimation in the number of days that experience a severe convective wind storm in the winter. An increase in events throughout the continent can again be seen in spring (Figure 4.14c) with almost an extra event day per year occurring over central NT and the western most part of QLD. Summer (Figure 4.14d) has a significant number of events, however, the event count is slightly higher than in Figure 4.11 over WA, with counts closer to 16 event days per year on average.

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling

a) b)

c) d)

Figure 4.14: Shows the climatology for the number of days with a severe convective wind storm above 90 km h-1 per year between 1979-2015 for (a) autumn (MDPI-Autumn model), (b) winter (Li100-Shr6-Winter model), (c) spring (LiSfc-SVWS-lfcel-Spring model), and (d) summer (Li100-SVWS-dCAPE)-Summer model) using the mean values of the indices calculated using ERA-Interim data between 1979-2015.

Compared to previous climatology of thunderstorms in Australia there are some similarities as well as some differences to what is shown here. Dowdy and Kuleshov (2014) showed, through the use of lightning data, that the majority of lightning occurs along the northeast coast of Western Australia and into northern Northern Territory with a gradually decrease towards the south. There is also a smaller maximum shown along the eastern QLD-NSW boarder and one over QLD, south of the Gulf of Carpentaria. Looking at the mean annual severe environments from 1979 to 2012, Allen and Karoly (2014) found that there was up to 50 days favourable for severe convection across much of tropical Australia and extending down the east coast into NSW. In this work specific to severe convective wind storms, the majority of events are found to occur over the northern parts of WA and to a lesser extent across the NT into QLD. These events are not realised to the same extent over Cape York as the other two climatologies might suggest. The lack of severe convective wind events over Cape York may be explained by large amounts of moisture in the boundary layer due to sea breezes from both

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling the Gulf of Carpentaria and the Coral Sea. This would prevent the occurrence of dry air entertainment and thus limits the potential for downdrafts to occur. Severe convective wind events also do not occur at similar rates along the QLD-NSW boarder as they do in tropical WA. Interestingly, the winter Bayesian model does suggest the occurrence of the occasional severe convective wind storms over the tropics during the winter, when no AWS observed such an event. Dowdy and Kuleshov (2014) show that cold season (May-October) lightning events do occur most frequently over the tropics, especially WA and NT, suggesting these results may have some merit. Although, it is hard to make a direct comparison given these previous studies consider thunderstorms in general or look at the environments conducive to the formation of a thunderstorm and do not specifically look at the occur of severe convective wind storms. 4.4. Conclusion

This chapter looked at developing a spatially complete climatology of severe convective wind storms across Australia. Furthermore, it attempts to correct for three major biases found in typical report-based climatologies. That is, an artificial maximum in event counts located near population centers, an artificial minimum located in rural parts of the country and an artificial increase in event counts with time as new AWS stations are added to the network. These biases are common to most observational datasets. To correct for these biases Bayesian hierarchal modelling was utilised to relate global reanalysis data (ERA-Interim) to the number of observed severe convective wind storms, while taking into account the change in AWS density. This method proved useful in similar applications used elsewhere (e.g., Cheng et al. 2016) and was adapted to work in Australia using AWS data. Through the testing of 22 different severe weather indices, that examine environmental conditions from the instability of the atmosphere to the storm relative helicity, models were developed to explain the rate of severe convective wind event days occurrence from 2005-2015 for four different seasons (autumn, winter, spring, summer). Results suggest that there are more severe convective wind storms occurring across Australia than are being observed. This is especially true in the interior of the continent, and in northern Western Australia. There is also a seasonal change in the event day occurrence rate with a minimum number of event days occurring during the winter months, an increase in events during the spring months to a maximum in the summer, and a decrease in events in autumn as winter approaches. In addition to the changes in the event day occurrence rate, there is also a shift in where the event days occur. Event days are confined to the southern parts of Australia in the winter, as two main high-pressure systems sit over the Indian and Pacific Oceans and the northern parts of the

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Australian convective wind gust climatology Chapter 4 using Bayesian hierarchical modelling country experience their dry season. With event days mainly along the southern coast of Australia likely resulting from coastal low-pressure systems (e.g., extratropical cyclones) that with their fronts can cause embedded convection. There is then a shift of event days north in the spring as the high-pressure systems that tend to sit over the Indian and Pacific Oceans move south, bringing stormy weather to the mid-latitudes. In addition, the monsoon depressions begin to move south into northern Australia bringing stormy weather to Australia’s tropics. There is a small shift in the event maximum to the east in the summer, followed by a further retreat south in autumn. The method used does however have its limitations, which include the use of a short observational period which makes it difficult to capture all the natural variability in the event occurrence rate at a given location. In addition, only a small number of severe weather indices and combinations were considered, limiting the ability to find indices that best explain the event occurrence rate and the physics behind the phenomena. Some of the models found to perform well had coefficient values, established by the Bayesian approach, that did not always agree with what might be expected given current understanding of the physics behind the development of these events. This may suggest that a given index may not be physically tied to the occurrence rate of convective wind gust for the particular seasons used or that, there is a compensation effect of the model approach. That is, if one of the predictors in the model is generating an excess or deficit of the phenomena that the model maybe be trying to find a term to offset this effect. Although it was challenging to find models that converged and performed well for all seasons, this method proved to be a useful tool in correcting the biases within the AWS dataset. Future research would look at improving the convergence of the models and in turn the reliability of their results. This can be done through different means, such as testing other indices combinations or even using more fundamental atmospheric variables that some of the indices are based upon. The idea being that the indices can be better tailored to suit the Australian climate. In addition, the use of non-meteorological indices might prove helpful, such as a topography input. But, it would be most helpful to have an extended observational dataset to work with, extending the observational dataset to 2019 would increase the time period at most station by an additional 4 years resulting in close to 10 years of data from the 5 years minimum used for this work. Furthermore, with the recent release of ERA5 (Hersbach et al., 2019) the increased reanalysis resolution might help to better relate the event occurrences to more accurate index values. However, this would require significantly more computational expense. 150

Chapter 5: Climate Change Impacts on the Climatology of Convective Wind Storms in Australia

Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia 5.1. Introduction

There has been a significant increase in global temperature over the last 60 years because of anthropogenic emission of carbon dioxide (IPCC, 2014). Moreover, a recent special report by the Intergovernmental Panel on Climate Change (IPCC) states that human activities have caused an estimated 1.0°C of global warming above pre-industrial levels and there is high confidence that between 2030 and 2052 warming is likely to reach 1.5°C if CO2 continues to increase at current rates (IPCC, 2018). The report goes on to note that there is medium to high confidence that this increase in temperature may result in increases to the mean temperature in most land and ocean regions, hot extremes in most inhabited regions, heavy precipitation in several regions, and increase to the probability of drought and precipitation deficits in some regions. The most recent report does not say much about the impact of this increase in temperature on the occurrence of severe thunderstorms or more specifically severe convective wind storms. While some attention has been given to certain aspects of weather events (i.e. temperature, flooding, drought) and thunderstorms in general, assessment reports by the IPCC and the United States Climate Change Science Program (CCSP) (IPCC 2007, 2012; CCSP, 2008) give little attention to the effects of climate change on severe convective wind storms. This is likely a result of the difficulties in data collection and the small horizontal scale of these events compared to the resolution of global models (Brooks, 2013). Given that these wind storms are known to cause billions of dollars in damages to infrastructure in Australia alone (Blong, 2005) it is important to understand how increased global warming may impact the occurrence of these wind storms in Australia. To help understand future trends in the occurrence of severe convective events it is important to understand first whether trends exist in current or historic data. Unfortunately, current trends in thunderstorm occurrence have been difficult to analyse due to the sparse and sporadic nature of these records (e.g. Kuleshov et al., 2002). However, past research has noted a lack of trend, outside of the natural variability (i.e. ENSO), in both the occurrence of thunder- days and environmental climatology over the past three decades in Australia (Davis and Walsh, 2008; Allen and Karoly, 2014). A similar lack of trend in thunderstorm environments is found by Kunkel et al. (2013) and Brooks (2013) for the United States as well as other parts of the world. However, the lack of long-term records in Australia, and therefore reliable trend analysis, continues to be a significant gap in our knowledge (Walsh et al. 2016). These issues persist when trying to determine future trends in the occurrence of thunderstorms and their associated hazards.

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia Climate models are faced with limitations when trying to simulate convective environments. Many of these models poorly resolve mesoscale processes (Trapp et al., 2007; Del Genio et al., 2007). For example, the convective parameterization schemes used are known to eliminate energy from the atmosphere and have difficulty in dealing with convective inhibition (Gettelman et al., 2002; Marsh et al., 2007; Allen et al., 2014a). Also, the resolution used by these models makes it difficult to resolve sub grid scale processes as well as topographic influences that affect values of CAPE (Iorio et al., 2004; Niall and Walsh, 2005; Allen et al., 2014a). However, Global Climate Models (GCMs) are shown to be useful in the simulation of large-scale features and synoptic systems, which favour the development of thunderstorms. (Trapp et al., 2007; Del Genio et al., 2007; Marsh et al., 2007, 2009; Trapp et al., 2009; Van Klooster et al., 2009; Gensini et al., 2014; Diffenbaugh et al., 2013). Using the discriminator from Brooks et al. (2003), Marsh et al. (2007, 2009) showed that GCMs could produce reasonable spatial distributions of severe thunderstorms in the U.S. and Europe, but not necessarily the magnitudes. More recently, higher-resolution Regional Climate Models (RCMs) are used to complement GCMs (Allen, 2018) by adding further details to global climate analyses when it comes to understanding future projections using severe weather parameters (Púčik et al., 2017). In addition, the use of dynamic downscaling has proven a useful tool when exploring future projections (Griffiths et al., 1993; Trapp et al., 2007b; Trapp et al., 2011, Gensini and Mote, 2014) especially its ability to consider terrain features (Viceto et al., 2017) Limited research has been conducted specifically related to severe convective wind storms. Cechet et al. (2012) used downscaling to estimate the projections of these hazards under climate change but only for Tasmania. Fortunately, there has been some more extensive work on thunderstorms in general. In Australia, even with the limitations that CGMs face when resolving convective storms, Allen et al. (2014a) showed that they can simulate the occurrence of favourable environments similar to reanalysis models. However, their analysis showed a high level of sensitivity when calculating severe thunderstorm environments, specifically due to model physics related to moisture advection and convective parameterizations. They note that this is likely a result of how the models resolved topographic features and the resulting effect on moisture advection. In addition, Allen et al. (2014b) showed that low CAPE environments would decrease over Australia, while high CAPE environments would increase. They also showed that low and moderate 0-6 km shear would be relatively unchanged, while high 0-6 km shear would decrease. Allen et al. (2014b) find that, over Australia, a warmer climate will result in an increase in thunderstorm environments over northern and eastern 153

Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia Australia. This is similar to work by Abbs et al. (2007) and Leslie et al. (2008) that found an increase in these environments over the east coast of Australia. Two factors that will play a role in how the occurrence of severe weather in Australia will change as a result of a warmer climate are (1) the availability of moisture and (2) the response of the jet stream (Allen et al. 2014b). Allen et al. (2014a) looked at the performance of two global climate models, the CSIRO Mk3.5 and Cubic-Conformal Atmospheric Model (CCMA) in Australia. They showed a poleward shift of synoptic patterns, resulting in a decrease in SHR6, as well as a decrease in the thermal gradient between the midlatitudes and the poles. However, they also showed higher sea-surface temperatures and advected moisture resulting in the increase of high CAPE environments. Their work suggested there would be an increase in severe thunderstorm environments under a highly warmed future climate scenario, especially for the east coast of Australia. Research into the influence of a warming climate on Australian severe thunderstorm is limited. The work in this chapter looks to expand this limited research by examining the potential influence of a warming climate on severe convective wind storms specifically. The Bayesian models developed in the previous chapter (Chapter 4), for the four seasons (autumn, winter, spring, summer) are used to estimate any potential change in the occurrence of severe convective wind storms in the Representative Concentration Pathways (RCP) 8.5 climate scenario. RCP8.5 assumes no climate mitigation target and that greenhouse gas emissions and concentrations will increase considerably over time to a radiative forcing of 8.5 W m-2 by the end of the century. This will be done through the use of the CSIRO-BOM ACCESS-CM 1.3, as a case study for the prosed methods in Section 5.2, comparing the period between 2090- 2100 to the historical period between 1990-2000. 5.2. Data and Methods

5.2.1. ACCESS-CM Dataset For this chapter, the Australian Community Climate and Earth System Simulator coupled model (ACCESS-CM) (Bi et. al., 2013), developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and the Bureau of Meteorology (BOM) at the Centre for Australian Weather and Climate Research (CAWCR) is used. The model was built by coupling the UK Met Office atmospheric unified model (UM), to the ACCESS ocean model. The goals of this climate model were to participate in phase five of the Coupled Model Inter- comparison Project (CMIP5) while providing a state-of-the-art climate modelling capacity to support Australian research. The two versions of the model, ACCESS1.0 and ACCESS1.3

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia share the same ocean sea-ice model, with the exception of a few parameters, but have different atmospheric and land surface components. The ACCESS1.0 is configured with the UK Met Office HadGEM2 (r1.1) atmospheric physics and the Met Office Surface Exchange Scheme land surface model version 2. ACCESS1.3 uses atmospheric physics similar to the UK Met Office Global Atmosphere 1.0 including modifications implemented by CAWCR and the CSIRO Community Atmosphere Biosphere Land Exchange land surface model version 1.8. Both versions of the model are run with a 1.25° latitude by 1.875° longitude grid, using a staggered Arakawa C grid. They have 38 hybrid height levels with atmospheric parameters available, 3-hourly, 6-hourly, daily, and monthly. The overall skill of ACCESS-CM, both globally and for the Australian region, is significantly improved when compared with its predecessor the CSIRO Mk3.5 model developed for CMIP3 (Bi et. al., 2013). Bi et. al. (2013) find that the two versions of ACCESS- CM generally simulate similar global average annual mean climate for both preindustrial and the reconstructed historical atmospheric forcing conditions. Moreover, the results are close to the observations, reanalysis estimations, or comparable to the results of other CMIP5 models (e.g. Watterson et al., 2013). For these models, Bi et. al. (2013) find that the global average annual mean surface air temperature, across the 500-year preindustrial control integrations, has a climate drift of +0.35 °C and +0.04 °C in ACCESS1.0 and ACCESS1.3, respectively. Climate drifts are long-term trends found in climate models that cannot be attributed to natural variability. These drifts can arise due to perturbations to the climate system on coupling component models together and deficiencies in model physics and numerics (Sen Gupta, 2012). ACCESS1.3 shows nearly no drift in the global average annual mean surface air temperature for the preindustrial control simulations. ACCESS1.0 however has a climate drift of 0.07 °C/century but the climate drift found in the ACCESS1.0 piControl simulation had little effect on the climate change signals simulated in the historical and RCP forcing scenario runs (Dix et al. 2013). Specifically for this work, the historical period of 1990-2000 is used for ACCESS1.3. The focus is put on ACCESS1.3 since it has the smaller climate drift. In addition, the climate scenario RCP8.5 is used for the forecast period of 2090-2010. The RCP8.5 scenario is used since it will give an idea of just how much things may change. These 10-year period is similar to those used by Trapp and Hoogewind (2016), with the exception that they looked only at the month of May. The data used includes the 6-hourly eastward wind (ua), northward wind (va), air temperature, surface pressure, specific humidity, as well as the orography data. Due to the use of the Arakawa C grid the ua and va vector components are located mid-way between the 155

Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia scalar grid points. As a result, the u grid points are displaced ½ a grid box in longitude and the v grid points are displaced ½ a grid box in latitude. A bicubic interpolation is used to find the value of u and v at the same latitude and longitude as the scale grid points. The data was then converted from the 38 hybrid height levels to pressure levels using the following equation:

( ) ( ) P(k) = P(k − 1) ∗ exp ( − g ∗ z k – z k−1 ) (5.1) Rgas ta(k)

Where, P is the pressure, g is the gravitational constant, Rgas is the ideal gas constant, z is the geopotential height, ta and is the temperature.

5.2.2. Calculating Severe Weather Indices Using the ACCESS-CM 1.3 data, indices are calculated for the historical period from 1990- 2000 and the forecast period from 2090-2100 for RCP8.5 scenario. The indices used in this chapter are, the surface and 100hPa Lifted Index (LiSfc, Li100), the height difference between the EL and LFC (lfcel), the downdraft CAPE (dCAPE), the shallow vertical wind shear (SVWS), the 0-6km shear (Shr6), and the Microburst Day Potential Index (MDPI). Both the lfcel and dCAPE are calculated using the SHARPpy algorithm. The equations for the indices can be found in Table 5.1, which is a subset of those presented in Table 4.1. Table 5.1: List of indices used to explain the rate of severe convective wind occurrence in the Bayesian model.

Parameter Abbreviated Formula Calculated Reference Name Name Using SharpPy

Lifted Index LiSfc, Li100 푇500 − 푇푖 →500ℎ푃푎 Galway (𝑖 = 푠푓푐, 100ℎ̅̅̅̅̅̅̅푃푎̅̅̅) (1956) Height lfcel 퐸퐿 − 퐿퐹퐶 Yes difference between the EL and LFC Downdraft dCAPE 푝퐿퐹푆 Yes Gilmore and CAPE − ∫ (훼푝 − 훼푒)푑푝 Wicker 푝 푠푓푐 (1998)

Shallow SVWS 2 2 2 2 Vertical √푢850 + 푣850 − √푢1000 + 푣1000 Wind Shear

0-6km Shear Shr6 2 2 2 2 √푢6푘푚 + 푣6푘푚 − √푢2푚 + 푣2푚 Microburst MDPI 푀푎푥휃 (푆퐹퐶 − 850ℎ푃푎) − 푀𝑖푛휃 (650− < 500ℎ푃푎) Atkins and 푒 푒 Day Potential 30푘푡푠 Wakimoto Index (1991)

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia 5.2.3. Bayesian Model The four Bayesian models found in Chapter 4 to work best for each season, are used in this chapter to explore the influence of climate change on the number of severe convective wind storm event days per year. That is, the Microburst Day Potential Index (MDPI) model for autumn, the 100hPa Lifted Index and 0km to 6km shear (Li100-Shr6) model for winter, the Surface Lifted Index, Shallow Vertical Wind Shear, and height difference between the Level of Free Convection and the Equilibrium level (LiSfc-SVWS-lfcel) model for spring, and the 100hPa Lifted Index, Shallow Vertical Wind Shear and downdraft CAPE (Li100- SVWS - dCAPE) model for summer. This is done by solving the expected rate of event occurrence equation for each model using the ACCESS1.3 model data, and their corresponding historical and RCP8.5 scenarios. The equation for the MDPI autumn model is, log (휆푖) = 1.15 + 0.42 ∗ 푀퐷푃퐼푖 + 퐶퐴푅푖 (5.2)

The equation for the Li100-Shr6 winter model is,

log (휆푖) = −0.71 − 0.18 ∗ 퐿𝑖100푖1 + 0.16 ∗ 푆ℎ푟6푖 + 퐶퐴푅푖 (5.3)

The equation for the LiSfc-SVWS-lfcel spring model is, log (휆푖) = 2.62 + 0.53 ∗ 퐿𝑖푆푓푐푖 − 0.35 ∗ 푆푉푊푆푖 + 0.5 ∗ 푙푓푐푒푙푖 + 퐶퐴푅푖 (5.4)

The equation for the Li100-SVWS-dCAPE summer model is, log (휆푖) = 2.91 + 0.15 ∗ 퐿𝑖100푖 − 0.21 ∗ 푆푉푊푆푖 + 0.87 ∗ 푑퐶퐴푃퐸푖 + 퐶퐴푅푖 (5.5)

Where for each equation, 퐶퐴푅푖, is the conditional autoregressive term unique to each grid cell for each model and was discussed in detail in Section 4.2.3. The mean values for each index are used in the calculation of 휆푖 for the two periods and the indices are normalised by the mean and standard deviation of the mean values calculated from ERA-Interim used to train the original models. While the mean values of the parameters (a0, a1, a2, a3) are shown in Eqn. 5.2-5.5, the equations are solved through the use of a Monte-Carlo simulation using each parameter distribution. That is the combination of the parameter distributions from Section 4.3.3.2 (Figure 4.3, 4.4, 4.5, 4.6). A 20,000 realisation random sample is used to give a distribution for the event occurrence rate at each ACCESS-CM grid cell i. Elatent is solved in

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia the Monte-Carlo simulation by taking the Poisson distribution of 휆푖. The main limitation of this approach comes from the assumption that the parameters and their distributions obtained in Chapter 4, using the ERA-Interim reanalysis data, is representative of the of the indices that are calculated from CSIRO ACCESS-CM 1.3 model. This is especially true given the ERA- Interim data used was for the period of 2005-2015 while the ACCESS-CM 1.3 model was used for the period of 1990-2000. Comparing the mean ACCESS-CM 1.3 indices values shown in this chapter (Figures 5.1, 5.3, 5.5, and 5.7) to the mean ERA-Interim indices values shown in Appendix A would suggest this assumption is not completely accurate. This assumption is necessary because of the lack of observational data available for the climate model’s historical period of 1990-2000 to be able to retrain the Bayesian models. Normalising the indices prior to running the Bayesian model, as well as looking only at the change in the event counts between the projected period of 2090-2100 and the historical period of 1990-2000, are done to minimise the potential impacts the using a different data than that used to train the Bayesian model. 5.2.4. Change in Climatology To analyse the impact of the different climate change scenarios on the occurrence of severe convective wind storms across Australia, the method of Diffenbaugh et al. (2013) is followed. For their work, they looked at the difference in severe thunderstorm environments between the 2070-2099 period of the RCP8.5 and the 1970-1999 baseline, calculated as 2070-2099 minus 1970-1999. In this chapter, using ACCESS1.3, the difference between the number of expected events for the 2090-2099 (Elatentrcp8.5) with the number of expected events 1990-1999 historical run (Elatenthist) is calculated (ΔElatent). That is:

훥퐸푙푎푡푒푛푡 = 퐸푙푎푡푒푛푡푟푐푝8.5 − 퐸푙푎푡푒푛푡ℎ푖푠푡 (5.6)

This is done for all four seasons, using their corresponding Bayesian models. The 훥퐸푙푎푡푒푛푡 of each season is analysed in Section 5.3.2 to see how the event counts may change under the RCP8.5 scenario.

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia 5.3. Results and discussion

5.3.1. Changes in Severe Weather Indices The mean values of the indices used in each season’s model are first analysed. That is, for autumn (Eqn. 5.2), winter (Eqn. 5.3), spring (Eqn. 5.3), and summer (Eqn. 5.4). This is done by looking at the mean values of each of these indices, during their corresponding seasons, and calculating the difference between the historical period (1990-2000) and the future period (2090-2100). Figure 5.1 shows the mean MDPI during autumn for the two periods, while Figure 5.2 shows the difference from 1990-2000 to 2090-2100. For both periods, the largest values of MDPI are to the north and they gradually decrease to the south with lower values extending from the south into southern Australia. Under RCP8.5 there is an increase in MDPI to the north and decreases to the south with a small decrease along the Queensland coast. When comparing the historical autumn MDPI calculated in this chapter (Figure 5.1a) to the values calculated in Chapter 3 (Figure A.10d) they are found to be similar in the magnitude and spatial distribution of the index. This suggests that the autumn model from Chapter 3 should work well for MDPI calculated with ACCESS-CM 1.3.

a) b)

Figure 5.1: Mean MDPI values for autumn for (a) the historical period (1990-2000) and (b) the projected RCP8.5 period (2090-2100).

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia

Figure 5.2: Difference in MDPI for autumn between RCP8.5 scenario (2090-2100) and the historical period (1990-2000).

In the winter, both the Li100 and Shr6 are found to be important in explaining the rate of event occurrence. The mean values of both indices for the historical and future period are shown in Figure 5.3 with the difference between the two periods shown in Figure 5.4. It is important to note that the color bar for Li100 is reversed given that larger negative number refer to larger instability, this is the case for the figures showing LiSfc as well. The smallest values of Li100, which is associated with a more unstable environment, are located around the coast of Australia, with the most unstable value found in the northern part of the country. This pattern is similar for both periods. One of the most noticeable difference between the two time periods is the increase in stability over the Northern Territory that then extends into northern Western Australia in the future period. This is verified in Figure 5.4, where it can also be seen that instability has increased for the most part over Queensland, especially along its coast, as well as the southern coast of Western Australia and South Australia. Large value of Shr6 are seen across most of Australia with the northern most part having some of the lowest values. In the future period it can be seen that overall the Shr6 decreases, but the peak values appear to shift further north. This shows up in Figure 5.4 as an increase in Shr6 over the northern part of the country while the rest of the country has a noticeable decrease in Shr6.

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia a) b)

k k c) d)

m s-1 m s-1

Figure 5.3: Mean Li100 values for winter for (a) the historical period (1990-2000) and (b) the projected RCP8.5 period (2090-2100) and the mean Shr6 for (c) the historical period (1990- 2000) and (d) the projected RCP8.5 period (2090-2100).

The winter historical Li100 (Figure 5.3a) and the winter Li100 from Chapter 3 (Figure A.7e) have similar distributions and magnitudes. They both show higher stability in the northern interior of the country and decreases in stability towards the coast. The biggest difference is that the Li100 from Chapter 3 has a thin area along the southern coast of Australia with much more unstable values of Li100. This could have an effect on the output here shown in Section 5.3.2. The winter historical Shr6 (Figure 5.3c) and the winter Shr6 from Chapter 3 (Figure A.21e) have only minor difference. These differences are slightly lower values in Shr6 from ERA-Interim in the north of Australia and slightly higher values in Shr6 from ERA-Interim in the south of Australia. The overall spread in Shr6 values is comparable for both datasets and is unlikely to affect the performance of the model developed in Chapter 3 here.

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a) b)

k m s-1

Figure 5.4: Difference in (a) Li100 and (b) Shr6 for winter between RCP8.5 scenario (2090- 2100) and the historical period (1990-2000).

The event occurrence rate during the spring is determined using the LiSfc, the SVWS, and the lfcel indices (Figure 5.5). The LiSfc shows the atmosphere to be most unstable over Australia in the tropics and along the eastern coast of the country. This instability appears to increase in the tropics (Figure 5.6) in the future period but decrease for many parts of the interior of the continent, specifically, inland Queensland and slightly inland from the southern coast of Australia. The largest values of SVWS in the spring appear to be in the tropics over the Northern Territory as well as along much of the southern coast of Australia and Tasmania. This does not appear to change much in the future climate. Figure 5.6 shows little change in SVWS between the two periods with some cells along the coast seeing an increase in SVWS of up to 3 m s-1. The height difference between the level of free convection and the equilibrium level (lfcel) appears to be highest along the northern coast of Australia and extend, to a lesser degree, south into the interior of the country with the exception of a part of northern Northern Territory. The smallest lfcel exist along the east coast of Queensland and the southern coast of Australia. A similar pattern is seen in the future climate but with increases in the lfcel through a large portion of the continent. More specifically over New South Wales, the eastern parts of South Australia and along the Northern Territory-Queensland boarder.

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia a) b)

k k c) d)

m s-1 m s-1 e) f)

m m

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia The spring historical LiSfc (Figure 5.5a) and the spring LiSfc from Chapter 3 (Figure A.5f) have similar magnitudes but the distributions are slightly different. The ERA-Interim LiSfc has a uniform north-south increase and the ACCESS-CM 1.3 LiSfc has more variability as it increases from north to south. The spring historical SVWS (Figure 5.5c) is slightly higher overall but lacks the increases seen along the west and east coast of Australia in ERA-Interim (Figure A.23f). The biggest difference in the indices for the spring model can be seen in the lfcel index. The lfcel calculated using ACCESS-CM 1.3 (Figure 5.5e) has a spatial distribution that follows that seen in the ERA-Interim lfcel (Figure A.3f), however it is not as smooth. The more significant difference is the magnitude, with the ERA-Interim lfcel having values significantly larger, up to 4,000 m larger. This difference could be underestimating the impact of lfcel in calculating the number of event days using ACCESS-CM 1.3 especially since the RCP 8.5 lfcel index is less than that seen in the ERA-Interim values.

a) b)

k m s-1

Figure 5.6: Shows the difference in (a) LiSfc, (b) SVWS, and (c) lfcel for spring between RCP8.5 scenario (2090-2100) and the historical period (1990-2000).

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia In the summer Li100, SVWS, and dCAPE help to explain the rate at which severe convective wind storms occur. Figure 5.7 shows the mean values of these three indices for both periods. The difference in the two periods is then shown in Figure 5.8. During the summer the Li100 is negative for most of the tropical parts of Australia, values become more positive (more stable) towards the south. There is a small region of more stable air that extends into South Australia. Compared with the historical period, Li100 is more unstable along much of the northern and eastern coasts of Australia. In addition, most of Queensland and New South Wales are also slightly more unstable. The southern parts of the country appear to be slightly more stable compared to the historical period. During the summer months the SVWS follows a similar pattern to that seen in the spring but to a lesser extent. Values are a few m s-1 less than seen in spring and the areas of increased SVWS are not as extensive. The same pattern is seen for the future climate between 2090-2100 with changes in the magnitude of SVWS being limited to less than 1 m s-1 for most of the country. The dCAPE for both the historical and future period are very similar in their distributions. However, the future period has larger values of dCAPE, which in some parts of the country exceed 600 kJ kg-1. The increase is mainly in the northern half of the country and along the west and east coasts, while the south coast and small parts of Western Australia and South Australia remain relatively unchanged.

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia a) b)

k k c) d)

m s-1 m s-1 e) f)

J kg-1 J kg-1

Figure 5.7: Shows the mean Li100 values for summer for (a) the historical period (1990-2000) and (b) the projected RCP8.5 period (2090-2100), the mean SVWS for (c) the historical period (1990-2000) and (d) the projected RCP8.5 period (2090-2100), and the mean dCAPE for (e) the historical period (1990-2000) and (f) the projected RCP8.5 period (2090-2100). Like was seen comparing the spring, LiSfc between ACCESS-CM and ERA-Interim, the summer historical Li100 (Figure 5.7a) and the summer Li100 from Chapter 3 (Figure A.7g) have similar magnitudes but the ERA-Interim Li100 has a uniform north-south increase and the ACCESS-CM 1.3 Li100 has more variability as the stability increase from north to south. The summer historical SVWS (Figure 5.7c) is similar in both magnitude and distribution

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia compared to the ERA-Interim SVWS (Figure A.23g). However, there are small SVWS values along the west and south coast of Australia in the ACCESS-CM 1.3 dataset. The dCAPE values for ACCESS-CM (Figure 5.7e) and ERA-Interim (Figure A.1g) follow each other closely. The spatial distributions show large values of dCAPE towards the north of Australia, extending from northern Western Australia across into western Queensland with maximum values around 1200 J kg-1. The main difference is that the ERA-Interim maximum over Queensland is not as high as it is over Western Australia whereas, ACCESS-CM 1.3 has these two maximums are of similar magnitude. The differences in the indices, for the four seasons, will have an impact on the results shown here. This impact is minimised by considering the change in event days between 2090-2100 and 1990-2000 instead of the counts found for each period separately.

a) b)

k m s-1

J kg-1

Figure 5.8: Shows the difference in (a) Li100, (b) SVWS, and (c) dCAPE for summer between RCP8.5 scenario (2090-2100) and the historical period (1990-2000).

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia 5.3.2. Change in Climatology Using the mean values of the indices shown in Section 5.3.1 and the equations introduced in Section 5.2.3 it is possible to get the expected rate of event occurrence (Elatent) for the two periods, 2090-2099 (Elatentrcp8.5) and 1990-1999 (Elatenthist). Taking the difference between

Elatentrcp8.5 and Elatenthist gives (ΔElatent). This difference is shown in Figure 5.9 for the four seasons, autumn, winter, and spring, which have the same event count scale, and summer which has a larger scale. The combined difference in event days over the entire year is shown in Figure 5.10. These figures show the average expected increase per year in the number of days in which at least 1 severe convective event is expected to occur in a given grid cell (1.25° X 1.875°, ~23,500km2). Figure 5.9 suggests that there would be a small increase in the number of days with a severe wind storm during autumn. This increase is less than about 0.5 days per year (or an extra day with a severe convective wind storm every 2 years) for the northern parts of Australia, mainly along the northern coast of Western Australia, as well as western Queensland and inland along the Queensland-New South Wales boarder. An increase up to an extra 2 days per year is shown in at least one cell in northern Western Australia. This corresponds with cells that have the largest increase in MDPI in the future climate. The cells where the number of events decreases are negligible. There are a few cells over Cape York Peninsula, in Queensland, where the drop in events is about 0.1 days (or 1 event every 10 years). In winter, it is suggested that on average there would not be an increase in the number of days with a severe convective wind storm. This is likely in related to the increase in shear, Shr6, being collocated in areas shown by a decrease in instability through the Li100 index. Moreover, areas with an increase in the instability seem to be collocated with areas of decrease shear (Figure 5.4). There is however one cell off the coast of Queensland where there is an increase of approximately 0.5 event days per year. While there does not seem to be much in the increase of events during the winter, there are a few cells over Tasmania with decreases in events of about 0.1 event days per year and one cell on the boarder of South Australia and Victoria with a decrease of about 0.5 event days. This may be attributed to the increase in stability over this area shown in Figure 5.4.

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia

a) b)

c) d)

Figure 5.9: Shows the increase in the number of days where at least one severe wind gust above 90 km h-1 will occur in a given grid in 2100-2090 compared to 1990-2000 for (a) autumn (MDPI), (b) winter (Li100-Shr6), (c) spring (LiSfc-SVWS-lfcel), and (d) summer (Li100- SVWS-dCAPE). In the spring, most of the country sees an increase in days where a severe convective wind storm occurs. This increase is between 0.5-1 days. The biggest increase can be seen in the southeast corner of the Northern Territory. The pattern of increased in event days looks to follow the change in the surface lifted index (LiSfc) (Figure 5.6), where the increases appear in cells where the LiSfc has increased. This is expected given that the spring Bayesian model finds a positive relationship between LiSfc and the event occurrence rate. The tropics and the east coast of Australia do not see an increase in the number of days during the spring. In these areas, there is a slight decrease in events days of about 0.1-0.3 days per year. This again appears to follow the change in LiSfc from the historical to future period. In summer, a significant increase in days with severe convective wind storms is expected for parts of the country. This increase is mainly focused around the northern part of the country with the largest increases occurring over northern Western Australia with increase on the order of an extra 25 days with at least 1 severe convective wind storm per grid cell occurring. These

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia large increases extend into parts of the Northern Territory and the western parts of Queensland, where increases of greater than 15 days of severe convective wind storms are expected by the end of the century. While these increases appear to be quite significant, especially compared to those seen in the other seasons, they looked to be related to the large increase in dCAPE from 1990-2000 to 2090-2100. The increase in dCAPE is not clear. Research by Nolan and Rappin (2008) used numerical modelling to examine the impact of increase sea surface temperature (SST) on the occurrence of tropical cyclogenesis. Although the study was for tropical cyclogenesis, they showed in their model increase SST resulted in an increase in dCAPE and that this was mainly related to the higher altitude in which the mid-level relative humidity minimum was occurring at. In the ACCESS-CM 1.3 model, Rashid et al. (2013) shows that towards the end of the century, the relative humidity decreases in the tropical upper troposphere as well as the mid to upper troposphere over the tropic and subtropics in both hemispheres. However, these decreases are shown for the northern hemisphere summer and would need to be verified for the southern hemisphere summer. These decreases in the relative humidity could be resulting in the increase in altitude at which the mid-level relative humidity minimum is occurring and therefore resulting in an increase to dCAPE in the summer. There are no areas, during the summer, where the number of days with a severe convective event, decreases. A yearly picture of the change in event day counts between 2090-2100 and 1990-2000 can be seen in Figure 5.10. The increase to the average yearly event counts over the entire year follows closely to that seen during the summer, since this is where the largest increase in events appears to occur. From Figure 5.10 increases in events can be seen across the country with at least 1 extra day with a severe convective wind storms occurring in most cells. The biggest increases are seen in Western Australia, along its west coast and more so in the northern part of the state, as well as in the Northern Territory and in Queensland. Almost every cell over Australia, using the ACCESS-CM, shows that throughout the year there will be some kind of increase to the number of days in which a severe convective wind storm will occur. The exception to this is along the South Australia coast, outside of Spencer and St. Vincent Gulf.

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Figure 5.10: Shows the increase in the number of day where at least one severe wind gust above 90 km h-1 will occur in a given grid in 2100-2090 compared to 1990-2000 for the entire year. While previous work has suggested an increase in instability, through CAPE (Brooks et al., 2007; Allen et al., 2014b; Brooks, 2013; Diffenbaugh et al., 2013), would occur under future climate scenarios, this has not been as clear cut in what has been shown here. An increase in the MDPI is seen during autumn, which would suggest an increase in the instability of the atmosphere. However, in winter, spring, and summer, where the lifted index provides the influence of instability in those models, the increase in instability appears to be focused around the coasts with some area inland showing increases in instability mixed with other areas in between showing a decrease in the instability. While CAPE is not examined here, since it was not one of the indices used for any of the seasonal models, it is shown here in Figure 5.11 to provide a comparison to what can be seen in previous work. Here, the ACCESS-CM 1.3 suggest increases in the most unstable CAPE over parts of northern Australia (up to 500 J kg- 1) and southward with increase in southeast Australia (up to 200 J kg-1). Allen et al. (2014b), using mixed layer CAPE, finds that the CSIRO Mk3.6 climate model shows large decreases (up to 500 J kg-1) in the mean CAPE during summer in the interior of the country as well as the northwest and northeast. This model also suggests that the mean summer CAPE will increase

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia over eastern Australia (up to 300 J kg-1) and northern Australia (up to 500 J kg-1). In contrast, Allen et al. (2014b) finds the CCAM (Cubic-Conformal Atmospheric Model) model suggest smaller increases (up to 200 J kg-1) over northern Australia that extend further south than CSIRO Mk3.6 shows. Even though different CAPE calculations are used there are some similarities between ACCESS-CM 1.3 and CCAM with respect to the spatial distribution of the increase. While this gives some confidence in the distribution of the change in instability given by the ACCESS-CM 1.3 model, it highlights the importance of considering multiple climate models.

Figure 5.11: The change in the most unstable CAPE calculated using ACCESS-CM 1.3 during the summer months (December-February) between the periods of 2090-2100 and 1990-2000. These previous works (Brooks et al., 2007; Brooks, 2013; Diffenbaugh et al., 2013; Allen et al., 2014b) also suggested a decrease in 0 to 6km shear under climate change. This is also shown here, for winter, where Shr6, is found to decrease across most of the country. It is less clear what will happen to the shallow vertical wind shear (SVWS). With respects to the SVWS shown here, there is no significant change in both the spring and summer. In the spring there are some areas with a slight increase to the SVWS, mainly along the coasts of the continent. In

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia the summer there is a slight decrease seen in the SVWS seen over the northern Northern Territory and over Tasmania. When it comes to the number of events that occur, Allen et al. (2014b) suggested that the increase might be small or be a seasonal shift. While a seasonal shift cannot be seen here, due to the 3 months seasons considered in this work, there is a small increase for autumn and winter and a slightly larger increase in events for parts of the country during spring with a more significant increase in events in summer. Abbs et al. (2007) and Leslie et al. (2008) found an increase thunderstorm environments over the east coast of Australia. Allen et al. (2014a) also suggested there would be an increase in severe thunderstorm environments under a highly warmed future climate scenario, especially for the east coast of Australia. Similarly, Allen et al. (2014b) finds that a warmer climate will result in an increase in thunderstorm environments over northern and eastern Australia. In this work, which is more specific to severe convective wind storms as opposed to thunderstorm environments in general, the increase in events over the east coast of Australia is not as evident as what is seen in the interior of the country. The biggest increases are western Queensland, and northern Western Australia during the summer, and northern South Australia in the spring. The increase in events during the summer looks to be related to the larger increase in dCAPE that is shown to occur between 2090-2100 and 1990- 2000. The dCAPE is largest over northern Western Australia and across into western Queensland but decreases closer to the Queensland coast and southeastern Australia. This would explain why the increase in severe convective wind storms is not as apparent on the east coast of Australia as previous research into climate change effects on thunderstorm might suggest. In addition, the relatively coarse resolution of ACCESS-CM and its depiction of the topography of eastern Australia may impact the ability of the model to accurately resolve dCAPE in this region. While it is difficult to know if this large increase in dCAPE will be realised in a future climate the use of an ensemble of GCMs might provide insight into how realistic this change is to the atmosphere’s state. The increase in spring events over South Australia appears to be located in an area where the instability (LiSfc) does not change much, but there is a decrease in SVWS, and an increase in the lfcel collocated together. According to the Eqn. 5.4 developed in the previous chapter this would result in an increase in events. 5.4. Conclusion

Using the seasonal Bayesian models, developed in Chapter 4, with the Australian global climate model as input, has provided some insight into the possible impacts that climate change may have on severe convective wind storms in Australia. While only one model was used, for

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Climate Change Impacts on the Climatology of Chapter 5 Convective Wind Storms in Australia one potential scenario, it is suggested that throughout the year there will be an increase in the number of days with severe convective wind storms in 2090-2100 when compared with 1990- 2000. These increases in events mainly appear to occur during the summer months and are focused around northern Western Australia and east into western Queensland. While some of the findings here agree with previous research, such as the increase in instability through parts of Australia associated with decrease in shear and increase in convective type events in northern Australia, the significant increase in convective events over eastern Australia does not appear to translate into severe convective wind storms. However, the results presented here may not be statistically significant. Statistical significance testing is required before any conclusions can be drawn. Since climate models are known to have large discrepancies between them, and and due to the fact that only one model has been studied within this thesis, it is not possible to know where the results shown in this chapter are significant. This is especially true given that the resolution of Global Climate Models (GCMs) are too large to model the storms explicitly, and the microphysics do not simulate the physics of the storm well enough (Allen et al. 2014b). It will be important for future work to consider a larger suite of models when analyzing potential changes. In addition, there is a need to determine how to deal with improving the model physics important to the severe thunderstorm environment in Australia (Allen and Allen, 2016). It will also be important to consider other potential scenarios in future work. However, given these limitations this chapter demonstrates the potential for this method to help determine how the occurrence rate of convective events may change under climate change. This method would benefit greatly from the upcoming CMIP6 project to help understand the impacts of climate change on the occurrence of severe convective wind storms. CMIP6 will provide additional models with improved microphysics schemes as well as finer resolution. In addition, the availability of new updated scenarios gives an opportunity to expanded this method. Running this method, with an ensemble of GCM will help to improve the understanding of the uncertainty in the results, specifically in understanding how the different microphysics scheme might be influencing the different indices calculation and therefore the rate of event occurrence calculations. This will help to better understand the physics behind the different changes that are seen during the different seasons. Furthermore, one of the benefits of the CMHIP6 would be the availability of historical data that overlaps with the available 1- minute AWS data that is available. This would make it possible to re-train the models developed in Chapter 4 using the GCM data so that the coefficients are better suited to the indices calculated using those datasets. 174

Chapter 6: Conclusions and Recommendations

Conclusion and Recommendations Chapter 6

6.1. Summary and Significance of Findings

The overall aim of this thesis was to expand current understanding of the occurrence frequency of severe convective wind storms around Australia. This was important because of the significant threat these events pose to infrastructure across Australia along with the desire to incorporate them into wind-resistant design standards. Ultimately, this thesis developed what is likely the first spatially complete climatology, for all of Australia, of convective wind storms for both the current climate and a potential future climate scenario. Specifically, this thesis addressed three research objectives; (1) the development of an objective and automatic method for the identification of convective wind gust events from Automatic Weather Station (AWS) data, (2) the creation of a spatially complete climatology of severe convective wind gust across Australia, and (3) understanding how the severe convective wind gust climatology of Australia might change as a result of climate change. Through the use of novel and underutilised methods (i.e. Self-Organising Maps and Bayesian statistics) along with large-scale weather datasets it was possible to examine these objectives. This made it possible to build on the limited existing research and provided a better understanding of when, where, and how frequently these events occur across Australia. Each objective was addressed in its own chapter within the thesis. The key outcomes and conclusions for each are outlined in the following sections.

6.1.1. Objective 1 In order to develop the climatology in Chapter 4 using AWS data it was first necessary to develop a method in which severe convective wind gusts could be extracted from this dataset, in an efficient and effective manner. The AWS provides reliable information about when and where severe wind gusts (defined in Chapter 3 as a recorded gust greater than 70 km h-1) occur around the country. However, AWS data in Australia does not provide explicit information about the weather event responsible for generating any given severe wind gust. In order to create a climatology of severe wind gusts of convective origin it was first necessary to identify which of the recorded gusts in the AWS dataset were generated by these events. This required the development of an objective and automatic method for the identification of convective wind storm events from 1-minute AWS data. Unlike existing classification approaches, this approach

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Conclusion and Recommendations Chapter 6 explicitly takes into account the meteorology of the event, and is especially useful for stations located in mixed wind climates. It was found that using Self-Organising Maps (SOM), specifically one that considers the wind speed, temperature, and mean sea-level pressure, was capable of identifying wind gusts in the AWS dataset that were generated by convective storms. Moreover, SOMs that consider wind speed alone were able to perform as well, if not better, than SOMs that considered the wind speed, change in wind direction, temperature, mean sea-level pressure, and precipitation together. In addition, this method provides uncertainty in the event type by assigning conditional probabilities to each event for the different types of meteorological set up considered in the SOM. The method made it possible to identify the events at almost 600 AWS objectively and efficiently while taking into consideration the meteorological set up associated with the individual events. Previous methods would avoid detailed consideration of the meteorological set up due to the size of the data associated with the AWS dataset, while methods that took into consideration the meteorological set up were only able to do so for a small number of events. 6.1.2. Objective 2 Having high fidelity data collected over at least 30 years is generally considered necessary to create a reliable climatology (Mason and Klotzbach, 2013). Unfortunately, this length of data does not yet exist uniformly across Australia for convective wind storms, so it was necessary to find an alternative method to develop a climatology of these gusts. In Chapter 4, an estimated spatially complete climatology of severe convective wind gust across Australia was developed through the creation of a Bayesian Hierarchal model that incorporated the ERA- Interim Reanalysis dataset and the AWS dataset. Anemometer records have traditionally been used to get information on wind speed frequency and severity (Holmes, 2002; Wang et al., 2013). In addition, large-scale environmental parameters have been used to fill the gaps in the observational dataset (e.g., Brooks et al., 2003; Allen et al., 2011). However, to-date they have not been used together with statistical analysis techniques to develop a spatially complete climatology of severe convective wind gusts in Australia. The method allowed for the consideration of both the temporal and spatial biases in the AWS dataset. The climatology developed showed 20 days in which a severe convective wind storm are expected to occur over the northern parts of Western Australia and that this extends to a lesser degree across the southern parts of the Northern Territory and the western parts of Queensland. Up to 80% of these days were found to occur during the summer months (December, January, February) with

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a few also occurring in the Spring (September, October, November) while little to no events were found to occur during the winter (June, July, August) except for the southern most parts of the country. Like all methods and models there are uncertainties associated with them, the main source of uncertainty associated with the results discussed here is the short observational record that is available. The short AWS record make it difficult to capture all the natural variability in the rate of event occurrence and more importantly makes it challenging to objectively train and test the models. 6.1.3. Objective 3 The final research objective of the thesis was to develop insight into how the severe convective wind gust climatology of Australia developed in Chapter 4 might be modified under expected climate change scenarios. The ACCESS-CM1.3 dataset was utilised along with the Bayesian Hierarchal models developed in Chapter 4. As discussed in Chapter 5, the RCP8.5 scenario was used to examine the change in the occurrence of severe convective wind storms over the 100 years between 2090-2100 and 1990-2000. This was done through the calculation of the mean severe weather indices using ACCESS-CM 1.3 RCP8.5 data for these two period. Using this data and the rate of event occurrence equations develop previously, a Monte-Carlo simulation was run to calculate the number of event days. From this analysis it was found that there is little to no change expected in the number of event days during the winter months. During spring, summer, and autumn though, an increase in event days is projected. The largest increases were noticed in summer, with up to an additional 25 days of storm activity observed in northern Western Australia and western Queensland. Autumn saw increase of about 1-2 event days per year over the same region, while spring saw an increase of about 1 event day per year over much of the country. However, there is uncertainty in these results resulting from the use of only one global climate model within this thesis. Like most studies that examine the impacts of climate change there is uncertainty in the global climate model outputs and the use of an ensemble of global climate models is necessary to understand and quantify this uncertainty. Uncertainly also exists in the methods used here since the models were trained on a different dataset using a period different from the historical climate model period. 6.2. Recommendations and Areas for Future Research

Ultimately, the climatology developed in this thesis fills the gaps in the observational datasets in Australia. However, the SOM and Bayesian methods developed here are applicable

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Conclusion and Recommendations Chapter 6 globally and provide a solid foundation for future research into severe convective wind storms in Australia and around the globe. Although there are a limited number of case studies on convective wind storms they have shown that there is significant variation between individual storm structures (Gunter and Schroeder, 2013). This highlights the difficulty in characterising the structure of convective wind storms. It will be necessary to create a novel spatial-temporal wind field model that can characterising the non-stationary gust structure of the different types of convective wind storms. While the work in the thesis did not look at different types of convective wind storms the SOMs developed showed to be helpful in distinguishing between convective and non-convective events. There is the potential to expand the method developed to look at different types of convective events. Expanding the analysis of severe convective wind storms to consider subclasses of wind storms may help to provide more accurate climatologies, for both the current and future climate. In addition, it will further improve our understanding of these events and the risk and hazard associated with them. While a spatially complete climatology of severe convective wind gusts for Australia was developed in this thesis, having reliable and extensive observational data is still invaluable. In order to build on and improve the work conducted in this thesis it will be important to continue to expand the available observational data. This will make it possible to better validate the results of the SOM method and the Bayesian hierarchal model. Specifically, more detailed case studies and field campaigns around actual events will help to improve understanding of the physical mechanism responsible for the formation of severe convective wind storms and help to better explain the rate and severity of these event occurrences in different parts of the country. Moreover, it would help to improve the understanding of the findings from the climatology developed in this thesis. Specifically, the large number of events seen to be occurring in northern Western Australia during the summer and spring as well as the more than insignificant number of events that do still occur in the winter months for the southern parts of the country. Improved observational datasets will also improve the reliability of models developed through this method when extending the models to look at climate change. The most valuable aspect of this thesis and its contribution to future research is its flexibility. The flexibility of the methods and models developed makes it possible to extend them to other parts of the globe. Moreover, they have the potential to be used to examine different types of hazards beyond just wind storms such as hail, rain, and lightning strikes. With the SOM method demonstrating the need for only wind speed, temperature, and mean sea-level pressure to distinguish between convective and non-convective wind storm it should be possible to develop

179

Conclusion and Recommendations Chapter 6 a similar SOM for other parts of the globe where this 1-minute data is available. In addition, there may be the potential to develop a universal SOM that works well globally. The Bayesian method used, which was adapted from a similar method for building a tornado climatology in North America (Cheng et al., 2016), has proven its ability to be adaptive for different weather hazards and regions. Furthermore, it has been shown here to be a useful tool when considering the applications involved in understanding the impacts of climate change. The potential of these two methods and their numerous applications make them invaluable tools in understanding weather events and their hazards for both meteorologist and engineers.

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Appendix A: Severe Weather Indices

Descriptions

Severe Weather Indices Descriptions Appendix A

A.1. Downdraft CAPE (dCAPE)

Gilmore and Wicker (1998) defines downdraft CAPE (dCAPE) as the maximum increase in kinetic energy (per unit mass) that could result from the evaporative cooling of air as it descends from a source height to the ground. The kinetic energy gained during descent is proportional to the area between the moist adiabat of a saturated descending parcel and the environmental temperature curve on a skew T-logP graph (Normand 1938). It is calculated by taking the integral of the difference between the potential temperature of the environment and the downdraft parcel from the height from which the parcel starts to descend to the surface. The descent height of the downdraft is determined following the method outlined in Gilmore and Wicker (1998), who use the method suggested by Brancato (1942) and Rasmussen (1994), who ultimately use the level of the minimum wet-bulb potential temperature as the starting parcel height. The reasoning for this is because air will, in theory, be the driest and will provide the greatest evaporative cooling and largest negatively temperature perturbation on the sounding (Gilmore and Wicker 1998). Figure A.1 shows the mean dCAPE values for the period of 2005- 2015 for the different seasons analysed in Section 4.3. A.2. Dry Microburst Index (DMI)

The Dry Microburst Index (DMI) was created by Ellrod and Nelson (1998) to address the high convective cloud bases and strong evaporational cooling in the sub-cloud layer common during dry microbursts (Ellrod et al., 2000; Wakimoto, 1985). The index looks at the 700- 500hPa lapse rate, and the 700hPa and 500hPa dewpoint depressions. Ellrod et al. (2000) found a threshold for the occurrence of dry microburst to be a value of DMI greater or equal to 6. They also suggest that DMI together with CAPE would be helpful in evaluating the potential risk of dry microburst. Figure A.2 shows the mean DMI values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.3. LFC-EL Height (LFC-EL)

The Lifted Condensation Level (LCL) is the height at which a parcel of air lifted from the surface, dry adiabatically, becomes saturated. It is a good approximation for cloud base height and is calculated by subtracting the surface dew-point temperature from the surface temperature (Barnes, 1968). The level at which a parcel of air lifted dry adiabatically to the LCL and then moist-adiabatically from the surface become lighter than the surrounding air and begins free ascent is the Level of Free Convection (LFC). The lower the LFC the more likely convection will occur. Convective thunderstorms are more likely to initiate and be maintained

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Severe Weather Indices Descriptions Appendix A if the LFC is below 3,000 m (Thompson et al. 2012). The Equilibrium Level (EL) is used to estimate the height of the anvil of deep convection. It is the level where an air parcel becomes negatively buoyant and stops rising. The Lifted Parcel Level (LPL) is the height of the most unstable air parcel used in muCAPE to determine the highest level of CAPE. The smaller the difference between the LCL and LFC the more likely deep convection will occur as a result of the small distance the air parcel would have to rise freely. This is similar to CIN (Colby, 1984). The larger the difference between the LFC and the EL (LFC-EL) the more likely deep convection will occur. This is a result of the larger depth of the atmosphere an air parcel will freely rise before reaching a stable layer. This is similar to CAPE (Moncrieff and Miller, 1976). Figure A.3 shows the mean LFC-EL values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.4. GUSTEX

The GUSTEX is a modified version of the WlNDEX which was designed to forecast gust speeds for wet or dry microbursts (McCann 1994). However, Geerts (2001) notes that thunderstorms may have additional wind-producing mechanisms not present in microbursts making it unrealistic to expect the WlNDEX to forecast all strong surface winds that may result from all convective situations. Furthermore, they show that the downward transfer of horizontal momentum is shown to play an important role in the generation of strong surface winds. Therefore, they look to modify WINDEX to also incorporate the vertical transfer of horizontal momentum along with the downburst. Building on work by McCann (1994) and Foster (1958) the GUSTEX, given in kts, is designed to incorporate the WINDEX and the midtropospheric wind. It is found to be a better predictor of maximum gust strength than WINDEX for thunderstorms in NSW. Although, it is noted that its usefulness may depend on the quality of the local gust climatology. This suggests that it may need to be tailored to different parts of the globe. In addition, while it is shown to be a good predictor for the occur of severe surface wind gust when a thunderstorm does occur it is not necessarily a good indicator that a thunderstorm will occur. Figure A.4 shows the mean GUSTEX values for the period of 2005-2015 for the different seasons analysed in Section 4.3.

A.5. Lifted Index (Surface, 50hPa, 100hPa)

The Lifted Index (Galway 1956) is a measure of the instability of the atmosphere. It is calculated as the temperature difference between the observed 500hPa temperature and the assumed 500hPa temperature of a parcel lifted from the surface, the 50hPa or 100hPa mean

211

Severe Weather Indices Descriptions Appendix A mixed layer near the surface. The index value is negative for parcel temperatures which are warmer than the environment. The more negative the index is the more unstable the atmosphere is believed to be. Values around -2 suggest weak severe weather potential, values between -3 and -5 suggest moderate severe weather potential and value less than -6 suggest strong severe weather potential. Figure A.5 shows the mean surface Lifted Index (LIsfc) values between 2005-2015 for the different seasons. Figure A.6 shows the mean 50hPa Lifted Index (LI50) values between 2005-2015 for the different seasons. Figure A.7 shows the mean 100hPa Lifted Index (LI100) values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.6. Microburst Composite (MCOMP) and Microburst Index (MBurst)

The Microburst Composite (MCOMP) is a composite index created at the Storm Prediction Centre in the United States to improve the prediction of microburst and severe weather events. This index is a weighted sum of the surface-based CAPE (SBCAPE) (the most unstable CAPE

(muCAPE) is used for this work) the surface Lifted Index (LIsfc), the lapse rate, the Vertical Total (VT), the Downdraft CAPE (dCAPE) and perceptible water. It is used to determine the likelihood of a microburst occurring. A value of 3-4 is interpreted to mean a “slight chance” of a microburst, 5-8 a “chance” of a microburst and ≥ 9 that a microburst is “likely” (Entremont et al., 2018). Figure A.8 shows the mean MCOMP values between 2005-2015 for the different seasons. The Microburst Index (MBurst) is an alternative form of MCOMP calculated by the

SHARPpy program that incorporates the value of the equivalent potential temperature (θe) and the θe difference. Figure A.9 shows the mean MBurst values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.7. Microburst Day Potential Index (MDPI)

The Applied Meteorology Unit’s (AMU) and 45h Weather Squadron’s created the Microburst Day Potential Index (MDPI) using data collected by Atkins and Wakimoto (1991) in the Microburst and Severe Thunderstorm (MIST) project (Wheeler, 1995). It is the difference between the maximum equivalent potential temperature (θe) in the lowest 150hPa and the minimum θe between 650hPa and 500hPa divided by a critical threshold of 30°K. Values of MDPI greater or equal to one suggest a high probability of a wet microburst occurring. The MDPI is found to have good skill in alerting a forecaster of potential wet microbursts occurring but possesses a reasonable false alarm rate (Applied Meteorology Unit,

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Severe Weather Indices Descriptions Appendix A

1996). Figure A.10 shows the mean MDPI values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.8. Most Unstable CAPE (muCAPE)

One of the most widely used indices for instability is called the Convective Available Potential Energy (CAPE). It is a measure of the buoyance force of a rising air parcel due to temperature difference between the parcel and its environment. It is calculated between the LFC and the EL. There are several versions of CAPE but due to time constraints and the computation cost of calculating CAPE, only one form of CAPE is utilised. This work makes use of the muCAPE where the LPL is used instead of the LFC and represents the height of the most unstable parcel. Focus is put on this version of CAPE because the main interests is the maximum potential for convection occurring. Since the vertical momentum equation can be written in terms of buoyance it is easy to calculate the parcel’s maximum vertical velocity from CAPE, this is known as WMAX (Markowski and Richardson 2010). Figure A.11 shows the mean muCAPE values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.9. Most Unstable CIN (muCIN)

Convective Inhibition (CIN) is the energy required to lift an air parcel to its LFC. In this work it is the most unstable CIN that is used to complement the muCAPE. It is important that CIN is non-zero for vigorous deep convection to occur but not too large that it prohibits deep convection from occurring altogether. If significant amounts of CAPE are present in the atmosphere in association with Large CIN values an external forcing, large enough to overcome the CIN, is required for deep convection to be realised (Wallace and Hobbs 2006). Figure A.12 shows the mean muCIN values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.10. Significant Severe (SigSev)

Brooks et al. (2003b) found that while individual parameters did not discriminate well between severe and non-severe thunderstorms, they did find that when considering both instability and shear together an improvement in the distinguishment of severe events from non-severe events was possible. They created the Significant Severe Index (SigSev). This index is calculated through the product of mixed layer CAPE (mlCAPE) and 0 to 6 km shear (m3s-3). Craven and Brooks (2004) suggested a thresholds of 10,000m3s-3 for a severe event, a threshold of 20,000m3s-3 for a significant hail/wind storm, and a threshold of 30,000m3s-3 for a significant

213

Severe Weather Indices Descriptions Appendix A tornado. For this work however, the muCAPE is used in place of the mlCAPE. Figure A.13 shows the mean SigSiv values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.11. SHERBE

The Severe Hazards in Environments with Reduced Buoyancy parameter using the Effective shear magnitude (SHERBE) is shown to discriminate between High Shear-Low Cape (HSLC; muCAPE ≤ 1000 J kg-1 and shear ≥ 18 m s-1) significant severe reports versus nulls across all environment in the U.S., with little variation between regions (Sherburn and Parker 2014). It is noted that the index does lose skill where CAPE is small or zero. SHERBE incorporates the 0-3 km lapse rate (oC km-1) and the 700-500hPa lapse rate (oC km-1) with the effective bulk wind difference (EBWD) (m s-1). Like most indices, SHERBE is designed to diagnose the likelihood of significant severe convection not to forecast the initial development of convection (Sherburn and Parker 2014). A threshold of 1 is used to distinguish between areas where convection will occur (Sherburn and Parker 2014). Figure A.14 shows the mean SHERBE values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.12. Theta-E Deficit (TeD)

The Theta-e Deficit (TeD) is defined as the maximum vertical difference in equivalent potential temperature (θe) from the surface to the middle troposphere (Ellrod et al. 2000). Research by Atkins and Wakimoto (1991) and later by Wheeler and Roeder (1996), found similarity in soundings on days in which a microburst occurred. These similarities included difference in the vertical θe and a θe minimum located between 650 and 500 mb.

The θe minimum aloft indicates the presence of a layer in the atmosphere that is favorable for the production of large negative buoyancy due to evaporative cooling. If a precipitation core within a thunderstorm reaches this layer, evaporative cooling takes place as dry air is entrained into the thunderstorm cell. The result is the generation of large negative buoyancy and the formation of a strong downdraft that becomes a downburst when reaching the surface (Atkins and Wakimoto 1991). While the reginal adjustment is necessary for TeD, a threshold of around 20-30K is typical for the occurrence of microbursts. Figure A.15 shows the mean TeD values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.13. Storm Relative Helicity (1km, 3km)

The Storm Relative Helicity (SRH) is a measure of the potential for cyclonic updraft rotation in right-moving supercells and is typically calculated for the lowest 1-km and 3-km layers

214

Severe Weather Indices Descriptions Appendix A above ground level (Davies-Jones et al. 1990). More specifically, it is proportional to the streamwise vorticity and storm-relative winds, considering both the ground-relative wind vector and the storm motion. There is no clear threshold value for SRH when forecasting supercells, since the formation of supercells appears to be related more strongly to the deeper layer vertical shear. However, larger values of SRH do suggest an increased threat of tornadoes with supercells. The threshold is typically greater than 250m2s-2 and 100 m2s-2 for SRH3 and SRH1 respectively. Figure A.16 shows the mean SRH1 values for the period of 2005-2015 for the different seasons analysed in Section 4.3. and Figure A.17 shows the mean SRH3 values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.14. Wet-Bulb Zero (WBZ)

The wet-bulb-zero (WBZ) height is the height where the wet-bulb temperature goes to 0oC. The WBZ height, above the surface, has been shown in many cases to be a good index to determine when severe weather (i.e. tornadoes, hail, and wind gusts) will occur at the surface (Miller, 1972). Miller (1972) shows that severe weather at the surface is found when the WBZ height is greater than 3.2 km but notes that it alone cannot be used as a unique predictor. A higher WBZ height suggests mid- and upper-level stability and a large melting area for hail, whereas lower WBZ heights means the low-level atmosphere is too cool and stable to support large hail. The melting of hail, associated with a high WBZ height, cools the surrounding air resulting in negative buoyancy that supports downdrafts that can produce severe wind storms at the surface (Doswell 1982). Figure A.18 shows the mean WBZ values for the period of 2005- 2015 for the different seasons analysed in Section 4.3. A.15. WINDEX

The WlNDEX is designed to forecast gust speeds for wet or dry microbursts (McCann 1994). It is based on the studies of the dynamics of microburst production, using soundings known to have been taken in microburst environments. The WINDEX takes into account the height of the melting level above the ground, the mixing ratio in the lowest 1km above the surface as well as at the melting level, and the lapse rate. It is found to better assess the potential for microbursts than indices such as Lifted Index. Like most stability indices it is conditional on convection occurring. However, thunderstorms may have additional wind-producing mechanisms not present in microbursts so it is unlikely that the WlNDEX would be able to forecast strong surface winds in all convective situations. Figure A.19 shows the mean WlNDEX values for the period of 2005-2015 for the different seasons analysed in Section 4.3.

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Severe Weather Indices Descriptions Appendix A

A.16. Wind Damage Parameter

The Wind Damage Parameter (WNDG) is a non-dimensional composite parameter that was created by the SPC. It is used to identify areas where large CAPE, steep 0-3km lapse rates, enhanced flow in the low-mid levels (between 1-3.5km above the surface), and minimal CIN are co-located. Values of WNDG greater than 1 were found to favour an enhanced risk for scattered damaging outflow gusts with multicell thunderstorm clusters, primarily during the afternoon in the summer (SPC; http://www.spc.noaa.gov/exper/soundings/help/index.html). Figure A.20 shows the mean WNDG values for the period of 2005-2015 for the different seasons analysed in Section 4.3. A.17. Wind Shear (Shr6, DVWS, SVWS)

Wind shear is the change of wind with height in both direction and magnitude. It is common that only the change in magnitude is used when determining the shear of a specific layer of the atmosphere. In general, higher values of shear tend to result in more organised and persistent thunderstorms. The 0-6 km wind shear (Shr6) is used for identifying the likelihood of supercell thunderstorms. Typically, these storms are associated with 0-6 km wind shear values over 20 m s-1 in the U.S. (Rasmussen and Blanchard 1998). The 0-1 km shear, also known as the shallow vertical wind shear (SVWS), can help determine the longevity of convection. Higher values of SVWS suggest longer lasting convection. Moreover, SVWS has been used to distinguish between tornadic and non-tornadic supercell thunderstorms (Rasmussen and Blanchard 1998). For this work the SVWS is taken as the wind shear between 850hPa and the surface and an additional deep vertical wind shear (DVWS) is taken as the wind shear between 500hPa and the surface since these are roughly equivalent to 0-1km and 0-6km levels. Figure A.21 shows the mean 0-6km Shear values for the period of 2005-2015 for the different seasons analysed in Section 4.3. Figure A.22 shows the mean DVWS values for the period of 2005- 2015 for the different seasons analysed in Section 4.3. Figure A.23 shows the mean SVWS values for the period of 2005-2015 for the different seasons analysed in Section 4.3.

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Severe Weather Indices Descriptions Appendix A

J kg-1

b) c)

J kg-1 J kg-1 d) e)

J kg-1 J kg-1 f) g)

J kg-1 J kg-1

Figure A.1: Mean Downdraft CAPE (dCAPE) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.2: Mean Dry Microburst Index (DMI) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

m m d) e)

m m f) g)

m m

Figure A.3: Mean LFC-EL Height (LFC-EL) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

kt kt d) e)

kt kt f) g)

kt kt

Figure A.4: Mean GUSTEX calculated between 2005-2015 for a) the entire year, b) spring- summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

k k d) e)

k k f) g)

k k

Figure A.5: Mean Surface Lifted Index (LiSfc) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

k k d) e)

k k f) g)

k k

Figure A.6: Mean 50hPa Lifted Index (Li50) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

k k d) e)

k k f) g)

k k

Figure A.7: Mean 100hPa Lifted Index (Li100) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.8: Mean Microburst Composite (MCOMP) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.9: Mean Microburst Index (MBURST) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.10: Mean Microburst Day Potential Index (MDPI) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

J kg-1

b) c)

J kg-1 J kg-1 d) e)

J kg-1 J kg-1 f) g)

J kg-1 J kg-1

Figure A.11: Mean most unstable CAPE (muCAPE) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

J kg-1

b) c)

J kg-1 J kg-1 d) e)

J kg-1 J kg-1 f) g)

J kg-1 J kg-1

Figure A.12: Mean Convective Inhibition (CIN) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

m3 s-3

b) c)

m3 s-3 m3 s-3 d) e)

m3 s-3 m3 s-3 f) g)

m3 s-3 m3 s-3

Figure A.13: Mean Significant Severe (SigSev) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.14: Mean SHERBE calculated between 2005-2015 for a) the entire year, b) spring- summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

k k d) e)

k k f) g)

k k

Figure A.15: Mean Theta-E Deficit (TeD) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

m2 s-2

b) c)

m2 s-2 m2 s-2 d) e)

m2 s-2 m2 s-2 f) g)

m2 s-2 m2 s-2

Figure A.16: Mean 0-1km Storm Relative Helicity (SRH1) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

m2 s-2

b) c) J kg-1

J kg-1

J kg-1 m2 s-2 m2 s-2

d) e) J kg-1

J kg-1

-1 m2 s-2 J kg m2 s-2 f) g) J kg-1

J kg-1

2 -2 2 -2 m s J kg-1 m s

Figure A.17: Mean 0-3km Storm Relative Helicity (SRH3) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter,J kg f)-1 spring, and g) summer.

233 J kg-1

J kg-1 Severe Weather Indices Descriptions Appendix A

b) c)

km km d) e)

km km f) g)

km km

Figure A.18: Mean Wet Bulb Zero (WBZ) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.19: Mean WINDEX calculated between 2005-2015 for a) the entire year, b) spring- summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

b) c)

d) e)

f) g)

Figure A.20: Mean Wind Damage Parameter (WNDG) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

m s-1

b) c)

m s-1 m s-1 d) e)

m s-1 m s-1 f) g)

m s-1 m s-1

Figure A.21: Mean 0-6km Shear (SHR6) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) summer.

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Severe Weather Indices Descriptions Appendix A

a)a)

-1 m ms-1 - s1 a) m s

b) c) mm s -s1- 1 a)

m s-1- 1 a) m s

-1-1 -1 mm s s -1 a) m s m s

d) e) mm s -s1- 1 a)

mm s -s1- 1 a)

-1 -1 m s mm s -s1- 1 m s a) f) g)

mm s -s1- 1 a)

m s-1 m s-1 mm s -s1- 1 a) Figure A.22: Mean Deep Vertical Wind Shear (DVWS) calculated between 2005-2015 for a) the entire year, b) spring-summer, c) autumn-winter, d) autumn, e) winter, f) spring, and g) mm s -s1- 1 summer. a)

238 mm s -s1- 1 a)

mm s -s1- 1 a) Severe Weather Indices Descriptions Appendix A

-1 mm s- 1s

b) c) b) c) m s-1

b) c) m s-1

b) c) -1 -1 m s -1 m sm-1 s m ms-1 s

d)d ) e)e ) b) c) -1 m s

m s-1 m s-1 d) e) b) c) m s-1

d) e) m s-1 m s-1 b) m s-1 c) -1 m s-1 m s-1 m s m s-1

f)f ) g)g ) d) e) b) c) -1 m s m s-1 m s-1 m s-1 m s-1 f) g) d) e) b) c) -1 m s

f) m s-1 g) m s-1 -1 -1 d) m s -1 e) m s -1 -1 b) m-1 s c) m ms s m s m s-1

Figure A.23: f)Mean Shallow Vertical Wind Shearg) (SVWS) calculated between 2005-2015 for e) d) -1 m s-1 a) the entire year,b) b) spring-summer, c) autumnm s -winter,c) d) autumn, e) winter,-1 f) spring, and g) m s-1 m s m s-1 summer. m s-1 Figu

f) g) re d) e) b) 239c) m s-1 A.1 -1 -1 m s 6m: s m s-1 m s-1 f) m s-1 g) Me d) e) b) c) an m s-1 Shal Severe Weather Indices Descriptions Appendix A

Table A.1: The 76 explanatory models used and the severe weather indices used for each model.

Model Name Severe Weather Severe Weather Severe Weather Index 1 Index 2 Index 3 DMI Dry Microburst Index - - GUSTEX Gust Index - - MCOMP Microburst Composite - - MDPI Microburst Day Potential Index - - MBURST Microburst Index - - Sig.Sev. Significant Severe Index - - SHERBE SHERBE - - WINDEX Wind Index - - WNDG Wind Damage Potential - - muCAPE -Shr6 Most Unstable CAPE 0-6km Shear - muCAPE -SVWS Most Unstable CAPE Shallow Vertical Wind Shear - muCAPE -DVWS Most Unstable CAPE Deep Vertical Wind Shear - LiSfc-Shr6 Surface Lifted Index 0-6km Shear - LiSfc -SVWS Surface Lifted Index Shallow Vertical Wind Shear - LiSfc -DVWS Surface Lifted Index Deep Vertical Wind Shear - Li50-Shr6 Mean Mixed 50hPa Lifted 0-6km Shear - Index Li50-SVWS Mean Mixed 50hPa Lifted Shallow Vertical Wind Shear - Index Li50-DVWS Mean Mixed 50hPa Lifted Deep Vertical Wind Shear - Index Li100-Shr6 Mean Mixed 100hPa Lifted 0-6km Shear - Index Li100-SVWS Mean Mixed 100hPa Lifted Shallow Vertical Wind Shear - Index Li100-DVWS Mean Mixed 100hPa Lifted Deep Vertical Wind Shear - Index LiSfc-Shr6-lfcel Surface Lifted Index 0-6km Shear Height difference between the LFC and EL LiSfc-Shr6-WBZ Surface Lifted Index 0-6km Shear Wet Bulb Zero height LiSfc-Shr6-SRH1 Surface Lifted Index 0-6km Shear 0-1km Storm Relative Helicity LiSfc-Shr6-SRH3 Surface Lifted Index 0-6km Shear 0-3km Storm Relative Helicity LiSfc-Shr6-TeD Surface Lifted Index 0-6km Shear Theta-E Deficit LiSfc-Shr6-muCIN Surface Lifted Index 0-6km Shear Most unstable Convective Inhibition LiSfc-Shr6-dCAPE Surface Lifted Index 0-6km Shear Downdraft CAPE LiSfc-SVWS-lfcel Surface Lifted Index Shallow Vertical Wind Shear Height difference between the LFC and EL LiSfc- SVWS -WBZ Surface Lifted Index Shallow Vertical Wind Shear Wet Bulb Zero height LiSfc- SVWS -SRH1 Surface Lifted Index Shallow Vertical Wind Shear 0-1km Storm Relative Helicity LiSfc- SVWS -SRH3 Surface Lifted Index Shallow Vertical Wind Shear 0-3km Storm Relative Helicity LiSfc- SVWS -TeD Surface Lifted Index Shallow Vertical Wind Shear Theta-E Deficit LiSfc- SVWS -muCIN Surface Lifted Index Shallow Vertical Wind Shear Most unstable Convective Inhibition LiSfc- SVWS -dCAPE Surface Lifted Index Shallow Vertical Wind Shear Downdraft CAPE LiSfc- DVWS -lfcel Surface Lifted Index Deep Vertical Wind Shear Height difference between the LFC and EL LiSfc- DVWS -WBZ Surface Lifted Index Deep Vertical Wind Shear Wet Bulb Zero height LiSfc- DVWS -SRH1 Surface Lifted Index Deep Vertical Wind Shear 0-1km Storm Relative Helicity LiSfc- DVWS -SRH3 Surface Lifted Index Deep Vertical Wind Shear 0-3km Storm Relative Helicity LiSfc- DVWS -TeD Surface Lifted Index Deep Vertical Wind Shear Theta-E Deficit LiSfc- DVWS -muCIN Surface Lifted Index Deep Vertical Wind Shear Most unstable Convective Inhibition LiSfc- DVWS -dCAPE Surface Lifted Index Deep Vertical Wind Shear Downdraft CAPE Li50-Shr6-lfcel Mean Mixed 50hPa 0-6km Shear Height difference between the Lifted Index LFC and EL Li50-Shr6-WBZ Mean Mixed 50hPa 0-6km Shear Wet Bulb Zero height Lifted Index

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Li50-Shr6-SRH1 Mean Mixed 50hPa 0-6km Shear 0-1km Storm Relative Helicity Lifted Index Li50-Shr6-SRH3 Mean Mixed 50hPa 0-6km Shear 0-3km Storm Relative Helicity Lifted Index Li50-Shr6-TeD Mean Mixed 50hPa 0-6km Shear Theta-E Deficit Lifted Index Li50-Shr6-muCIN Mean Mixed 50hPa 0-6km Shear Most unstable Convective Lifted Index Inhibition Li50-Shr6-dCAPE Mean Mixed 50hPa 0-6km Shear Downdraft CAPE Lifted Index Li50-SVWS-lfcel Mean Mixed 50hPa Shallow Vertical Wind Shear Height difference between the Lifted Index LFC and EL Li50- SVWS -WBZ Mean Mixed 50hPa Shallow Vertical Wind Shear Wet Bulb Zero height Lifted Index Li50- SVWS -SRH1 Mean Mixed 50hPa Shallow Vertical Wind Shear 0-1km Storm Relative Helicity Lifted Index Li50- SVWS -SRH3 Mean Mixed 50hPa Shallow Vertical Wind Shear 0-3km Storm Relative Helicity Lifted Index Li50- SVWS -TeD Mean Mixed 50hPa Shallow Vertical Wind Shear Theta-E Deficit Lifted Index Li50- SVWS -muCIN Mean Mixed 50hPa Shallow Vertical Wind Shear Most unstable Convective Lifted Index Inhibition Li50- SVWS -dCAPE Mean Mixed 50hPa Shallow Vertical Wind Shear Downdraft CAPE Lifted Index Li50- DVWS -lfcel Mean Mixed 50hPa Deep Vertical Wind Shear Height difference between the Lifted Index LFC and EL Li50- DVWS -WBZ Mean Mixed 50hPa Deep Vertical Wind Shear Wet Bulb Zero height Lifted Index Li50- DVWS -SRH1 Mean Mixed 50hPa Deep Vertical Wind Shear 0-1km Storm Relative Helicity Lifted Index Li50- DVWS -SRH3 Mean Mixed 50hPa Deep Vertical Wind Shear 0-3km Storm Relative Helicity Lifted Index Li50- DVWS -TeD Mean Mixed 50hPa Deep Vertical Wind Shear Theta-E Deficit Lifted Index Li50- DVWS -muCIN Mean Mixed 50hPa Deep Vertical Wind Shear Most unstable Convective Lifted Index Inhibition Li50- DVWS -dCAPE Mean Mixed 50hPa Deep Vertical Wind Shear Downdraft CAPE Lifted Index Li100-Shr6-lfcel Mean Mixed 100hPa 0-6km Shear Height difference between the Lifted Index LFC and EL Li100-Shr6-WBZ Mean Mixed 100hPa 0-6km Shear Wet Bulb Zero height Lifted Index Li100-Shr6-SRH1 Mean Mixed 100hPa 0-6km Shear 0-1km Storm Relative Helicity Lifted Index Li100-Shr6-SRH3 Mean Mixed 100hPa 0-6km Shear 0-3km Storm Relative Helicity Lifted Index Li100-Shr6-TeD Mean Mixed 100hPa 0-6km Shear Theta-E Deficit Lifted Index Li100-Shr6-muCIN Mean Mixed 100hPa 0-6km Shear Most unstable Convective Lifted Index Inhibition Li100-Shr6-dCAPE Mean Mixed 100hPa 0-6km Shear Downdraft CAPE Lifted Index Li100-SVWS-lfcel Mean Mixed 100hPa Shallow Vertical Wind Shear Height difference between the Lifted Index LFC and EL Li100- SVWS -WBZ Mean Mixed 100hPa Shallow Vertical Wind Shear Wet Bulb Zero height Lifted Index Li100- SVWS -SRH1 Mean Mixed 100hPa Shallow Vertical Wind Shear 0-1km Storm Relative Helicity Lifted Index Li100- SVWS -SRH3 Mean Mixed 100hPa Shallow Vertical Wind Shear 0-3km Storm Relative Helicity Lifted Index Li100- SVWS -TeD Mean Mixed 100hPa Shallow Vertical Wind Shear Theta-E Deficit Lifted Index Li100- SVWS -muCIN Mean Mixed 100hPa Shallow Vertical Wind Shear Most unstable Convective Lifted Index Inhibition Li100- SVWS -dCAPE Mean Mixed 100hPa Shallow Vertical Wind Shear Downdraft CAPE Lifted Index Li100- DVWS -lfcel Mean Mixed 100hPa Deep Vertical Wind Shear Height difference between the Lifted Index LFC and EL Li100- DVWS -WBZ Mean Mixed 100hPa Deep Vertical Wind Shear Wet Bulb Zero height Lifted Index Li100- DVWS -SRH1 Mean Mixed 100hPa Deep Vertical Wind Shear 0-1km Storm Relative Helicity Lifted Index Li100- DVWS -SRH3 Mean Mixed 100hPa Deep Vertical Wind Shear 0-3km Storm Relative Helicity

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Lifted Index Li100- DVWS -TeD Mean Mixed 100hPa Deep Vertical Wind Shear Theta-E Deficit Lifted Index Li100- DVWS -muCIN Mean Mixed 100hPa Deep Vertical Wind Shear Most unstable Convective Lifted Index Inhibition Li100- DVWS -dCAPE Mean Mixed 100hPa Deep Vertical Wind Shear Downdraft CAPE Lifted Index

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Appendix B: Additional Bayesian Results

Additional Bayesian Results Appendix B

B.1. Introduction

This appendix shows the tables and figures, similar to those shown in Section 4.3.1 for the autumn-winter (March to August) season, Section B.2, the spring-summer (September to February) season, Section B.3, and for the entire year, Section B.4. Tables B.1, B.3, and B.5 listed the Bayesian models that converged according to the Gelman-Ruben score. Moreover, they show the values, and percent difference for the three metrics (Total CAR, deviance, MAE) used to analysis each model for autumn-winter, spring-summer, and the year respectively. Tables B.2, B.4, and B.6 lists the models with the smallest percent difference for Total CAR, deviance, and MAE (ΔεtCAR, Δεdev, ΔεtMAE) along with them mean and standard deviation values of their coefficient from Eqn. 4.4 for autumn-winter, spring-summer, and the year respectively. Figures B.1, B.2, and B.3 show the distributions from the two MCMC chains for the parameters (a0, a1, a2, a3, 훼푆푡푎푡푖표푛퐷, 훽푆푡푎푡푖표푛퐷 ) for autumn-winter, spring-summer, and the year respectively.

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B.2. Autumn-Winter

Table B.1: List the models for autumn-winter that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of the metrics. Model Total CAR Deviance MAE ΔεtCAR Δεdev ΔεMAE mcmp 239.44 274.50 3.99 0 6 12 WNDG 294.75 268.40 3.95 23 3 11 MDPI 302.56 261.30 3.84 26 1 8 Li50-SVWS 363.83 273.10 3.97 52 5 11 muCAPE-Shr6 376.72 265.40 3.69 57 2 3 Li100-dvws 384.20 263.90 3.79 60 2 6 gstx 384.86 268.70 3.85 61 4 8 LiSfc-SVWS 387.68 268.70 3.92 62 4 10 Li100-Shr6-dCAPE 392.61 267.50 3.66 64 3 3 LiSfc-SVWS-dCAPE 395.20 262.10 3.71 65 1 4 Li100-SVWS-dCAPE 397.32 260.70 3.74 66 0 5 muCAPE-SVWS-CIN 401.40 262.50 3.68 68 1 3 wndx 402.58 271.20 3.80 68 4 6 Li100-Shr6-CIN 402.96 267.80 3.69 68 3 3 dmi 407.65 259.90 3.67 70 0 3 muCAPE-Shr6-TeD 407.83 262.10 3.68 70 1 3 SHERBE 408.24 262.20 3.83 71 1 7 Li50-SVWS-WBZ 411.44 267.20 3.70 72 3 4 Li100-Shr6-SRH3 419.94 259.60 3.66 75 0 3 Li50-SVWS-dCAPE 422.46 266.10 3.71 76 3 4 Li50-SVWS-SRH3 425.20 265.00 3.70 78 2 4 Li50-Shr6-dCAPE 427.96 260.80 3.64 79 0 2 Li50-SVWS-CIN 431.13 263.30 3.66 80 1 3 Li100-Shr6-TeD 435.25 262.10 3.66 82 1 2 LiSfc-Shr6-SRH3 439.20 261.60 3.67 83 1 3 LiSfc-Shr6-TeD 446.81 266.40 3.66 87 3 2 LiSfc-Shr6-dCAPE 453.07 263.70 3.65 89 2 2 Li50-Shr6-SRH1 457.97 262.40 3.57 91 1 0 Li50-SVWS-SRH1 461.50 261.90 3.68 93 1 3 LiSfc-Shr6-SRH1 464.39 264.50 3.75 94 2 5 muCAPE-SVWS-TeD 480.74 264.70 3.67 101 2 3

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MCMP 1.26 0.54 0.55 0.23 - - - - WNDG 1.11 0.52 0.34 0.11 - - - -

Figure B.1: Shows the distributions of the two chains for the (a) MCMP model and the (b) WNDG model. The first column is a0, the second a1, the third 훼푆푡푎푡푖표푛퐷 and the fourth 훽푆푡푎푡푖표푛퐷.

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B.3. Spring-Summer

Table B.3: List the models for spring-summer that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference of the three metrics for each model compared to the model with the smallest values of the metrics. Model Total CAR Deviance MAE ΔεtCAR Δεdev ΔεMAE LiSfc-Shr6-TeD 399.07 522.90 12.79 0 2 0 muCAPE-Shr6-TeD 413.82 526.70 13.32 4 3 4 SHERBE 604.78 512.40 13.40 52 0 5 muCAPE-SVWS-TeD 617.32 527.30 13.14 55 3 3 wndx 618.47 521.10 13.44 55 2 5 muCAPE-SVWS 650.16 530.50 13.46 63 4 5 Li100-dvws 668.60 527.20 13.95 68 3 9 LiSfc-Shr6-lfcel 690.52 524.20 13.65 73 2 7 Li50-Shr6 751.92 517.20 13.16 88 1 3

LiSfc-Shr6-TeD 3.56 0.48 0.19 0.20 0.72 0.28 1.41 0.22 muCAPE-Shr6-TeD 3.57 0.43 0.24 0.16 1.12 0.34 1.45 0.28

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B.4. Year

Table B.5: List the year models that converged according to the Gelman-Ruben score, along with each models Total CAR value, their deviance values, and weighted mean absolute error (MAE). In addition, it shows the percent difference (Δε) of the three metrics for each model compared to the model with the smallest values of the metrics. Model Total Deviance MAE ΔεtCAR Δεdev ΔεMAE CAR MCMP 376.60 592.90 15.03 0 3 5 Li100-Shr6-SRH3 388.71 598.60 15.23 3 4 6 Li50-Shr6-TeD 392.73 584.00 14.33 4 2 0 Li50-Shr6-dCAPE 412.21 582.50 15.67 9 1 8 muCAPE-Shr6-SRH3 423.74 589.10 15.28 13 2 6 LiSfc-SVWS-TeD 441.48 585.90 16.14 17 2 11 Li100-SVWS-SRH3 469.08 582.60 16.40 25 1 13 Li100-SVWS-TeD 485.44 589.80 15.54 29 3 7 Li100-SVWS-dCAPE 521.12 577.20 14.66 38 0 1 Li100-SVWS 524.34 589.40 16.30 39 2 13 Li100-Shr6 578.84 585.30 15.16 54 2 5 muCAPE-SVWS-SRH3 600.39 592.90 15.39 59 3 6 LiSfc-Shr6 605.94 575.20 14.97 61 0 3 muCAPE-SVWS-TeD 615.51 579.20 14.48 63 1 0 Li50-Shr6-WBZ 617.81 584.70 15.63 64 2 5 muCAPE-SVWS-lfcel 622.39 594.50 14.90 65 3 0 gstx 627.41 584.00 16.66 67 2 10 LiSfc-Shr6-CIN 639.42 576.70 15.69 70 0 3 Sig.Sev. 715.51 577.20 15.80 90 0 4 muCAPE-Shr6 775.07 587.60 15.20 106 2 0

MCMP 3.97 0.47 0.77 0.12 - - - - Li100-Shr6- SRH3 3.97 0.22 0.33 0.14 0.34 0.19 -0.56 0.17 Li50-Shr6- TeD 3.918 0.54 0.46 0.17 0.38 0.23 0.84 0.20 Li50-Shr6-dCAPE 3.56 0.25 0.26 0.17 0.37 0.21 0.93 0.21 muCAPE-Shr6-SRH3 3.47 0.37 0.085 0.23 0.59 0.29 -0.69 0.17 LiSfc-SVWS-TeD 3.80 0.26 0.55 0.18 -0.08 0.13 0.65 0.19 Li100-SVWS-SRH3 3.48 0.28 0.38 0.13 -0.32 0.12 -0.31 0.16

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b) c)

d) e)

Figure B.3: Shows the distributions of the two chains for the (a) MCMP model and the (b) Li100-Shr6- SRH3model (c) is Li50-Shr6- TeD model (d) is the Li50-Shr6-dCAPE model (e) is the muCAPE-Shr6-SRH3 (f) is the LiSfc-SVWS-TeD model and (g) is the Li100-SVWS- SRH3 model. For the 1 index models the first column is a0, the second a1, the third 훼푆푡푎푡푖표푛퐷 and the fourth 훽푆푡푎푡푖표푛퐷. For the three index models the first column is a0, the second a1, the third is a2, the fourth is a3, the fifth is 훼푆푡푎푡푖표푛퐷 and the sixth is 훽푆푡푎푡푖표푛퐷.

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