University of Liverpool Doctoral Thesis Meteotsunami generation, amplification and occurrence in north-west Europe Thesis submitted in accordance with the requirements of the University of Liverpool for the degree of Doctor in Philosophy by David Alan Williams November 2019 ii Declaration of Authorship I declare that this thesis titled “Meteotsunami generation, amplification and occurrence in north-west Europe” and the work presented in it are my own work. The material contained in the thesis has not been presented, nor is currently being presented, either wholly or in part, for any other degree or qualification. Signed Date David A Williams iii iv Meteotsunami generation, amplification and occurrence in north-west Europe David A Williams Abstract Meteotsunamis are atmospherically generated tsunamis with characteristics similar to all other tsunamis, and periods between 2–120 minutes. They are associated with strong currents and may unexpectedly cause large floods. Of highest concern, meteotsunamis have injured and killed people in several locations around the world. To date, a few meteotsunamis have been identified in north-west Europe. This thesis aims to increase the preparedness for meteotsunami occurrences in north-west Europe, by understanding how, when and where meteotsunamis are generated. A summer-time meteotsunami in the English Channel is studied, and its generation is examined through hydrodynamic numerical simulations. Simple representations of the atmospheric system are used, and termed synthetic modelling. The identified meteotsunami was partly generated by an atmospheric system moving at the shallow- water wave speed, a mechanism called Proudman resonance. Wave heights in the English Channel are also sensitive to the tide, because tidal currents change the shallow-water wave speed. To explain meteotsunami growth in a wider range of conditions, a generalised understanding of Proudman resonance is developed through idealised simulations and analytical models. Most surprisingly, wave amplification near predictions of Proudman resonance can occur even if the instantaneous forcing speed deviates from the mean forcing speed by 18%. This amplification can happen if the atmospheric forcing remains over the meteotsunami. Broader context is given to meteotsunami case studies in north-west Europe through an 8-yr climatology. In total, 349 meteotsunamis are identified and 256 associated mesoscale atmospheric systems are classified. Of meteotsunamis between 2010–2017, 79% were smaller than 0.5 m and about half occurred in winter. Of the classified atmospheric systems, 46% were quasi-linear systems and 33% were open-cellular convection. For 45 meteotsunamis in France, the mesoscale atmospheric systems occurred within well-documented synoptic atmospheric conditions, and there is evidence of repeated favourable conditions for Proudman resonance. Finally, a new explanation of how open-cellular convection generates meteotsunamis is developed through synthetic models. Open-cellular convection is modelled as a repeating field of individual cells moving at the shallow-water wave speed. Each individual cell generates an individual wave. When these individual waves form a linear superposition, constructive interference of repeating waves can lead to a larger meteotsunami than would be expected from single individual cells. v vi Contents Declaration of Authorship iii Abstract v List of Figures xii List of Tables xv Acknowledgements xvii Chapter 1 – Introduction 1 1.1 Motivation, Problem and Solution 1 1.2 Thesis approach and structure 3 1.3 A general background of meteotsunamis 4 1.3.1 Addressing common misconceptions 4 1.3.2 Where do meteotsunamis happen? 6 1.3.3 The north-west European continental shelf 12 1.3.4 How are meteotsunamis different to other waves? 15 Chapter 2 – Relevant meteotsunami dynamics 20 2.1 The Navier-Stokes equations and shallow-water equations 20 2.2 The ocean at equilibrium 22 2.3 Forced shallow-water waves 23 2.4 Meteotsunami generation mechanisms 26 2.4.1 Proudman resonance 26 2.4.2 Greenspan resonance 29 2.4.3 Reflection and transmission 30 2.4.4 Shoaling 31 2.4.5 Refraction 32 2.4.6 Currents 33 2.4.7 Seiching 33 vii Chapter 3 – Methods overview 35 3.1 Observational methods 35 3.1.1 Identifying meteotsunamis from sea-level records 35 3.1.2 Atmospheric measurements 38 3.2 Simulating meteotsunamis 41 3.2.1 Finite-difference models 42 3.2.2 Finite-element models 42 3.2.3 Applying boundary conditions and initial conditions 43 3.2.4 Applying an atmospheric forcing 46 Chapter 4 – Paper One 48 4.0 Preamble 48 4.1 Paper Abstract 50 4.2 Introduction 50 4.3 Observations 54 4.3.1 Sea surface observations 54 4.3.2 Atmospheric observations 57 4.3.3 Analysis of observations 60 4.4 Modeling 63 4.4.1 Telemac 63 4.4.2 Atmospheric forcing 63 4.4.3 Best-estimate model 64 4.4.4 Atmospheric forcing ensembles 70 4.4.5 Wind 75 4.4.6 Tides 76 4.5 Conclusions 79 viii Chapter 5 – Paper Two 81 5.0 Preamble 81 5.1 Paper Abstract 83 5.2 Introduction 83 5.3 Methods 86 5.3.1 Hydrodynamic models 86 5.3.2 Synthetic atmospheric forcing 86 5.4 Strict Proudman resonance simulation results and discussion 89 5.5 Oceanographic factors – results and discussion 91 5.5.1 Uniform elevation change (1D-FD) 91 5.5.2 Uniform current (2D-FE) 93 5.5.3 Uniform elevation and current (2D-FE) 96 5.5.4 Bathymetric slope (2D-FE) 97 5.5.5 M2 progressive tides (2D-FE) 100 5.6 Atmospheric factors – results and discussion 103 5.6.1 Average forcing speed (1D-FD) 103 5.6.2 Variable forcing speed (1D-FD) 104 5.6.3 Time-varying amplitude of atmospheric forcing (1D-FD) 107 5.6.4 Forcing aspect ratio (2D-FD) 109 5.7 Conclusions 111 Chapter 6 – Paper Three 117 6.0 Preamble 117 6.1 Paper abstract 119 6.2 Introduction 120 6.3 Data and methods 124 6.3.1 Tide-gauge data 124 6.3.2 Isolating tsunami-like waves 127 6.3.3 NSLOTT classification 128 6.3.4 Meteotsunami classification 129 6.3.5 Classifying atmospheric weather systems 130 ix 6.4 Results and discussion 133 6.4.1 Size-exceedance rates 133 6.4.2 Seasonal and diurnal variation 139 6.4.3 Analyses of coincident mesoscale weather systems 142 6.4.4 Analyses of coincident synoptic environments 146 6.5 Conclusions 155 Chapter 7 – Paper Four 158 7.0 Preamble 158 7.1 Paper Abstract 159 7.2 Introduction 159 7.3 Modelling sea-level pressure perturbations and resultant waves 164 7.4 Results and Discussion 165 7.5 Conclusion 171 Chapter 8 – Conclusions 173 8.1 The dissertation narrative 173 8.2 Study limitations 177 8.2.1 Models 177 8.2.2 Observations 178 8.3 Rising sea levels and a changing climate 179 A Travel-time solution for waves in the English Channel 181 B Supplementary figures to Chapter 5 183 C The finite-difference model 192 D Effective Proudman resonance from an idealised NWP model 195 E The stacking correction 206 F The effect of sub-sampling data 210 Bibliography 212 x xi List of Figures 1.1 Screenshots of May 2017 Dutch meteotsunami. 2 1.2 Reported meteotsunamis around the globe. 10 1.3 The north-west European continental shelf and meteorology. 13 1.4 Surface gravity waves grouped by period. 15 2.1 The inverted barometer effect and wind set-up. 23 2.2 Understanding forced wave dynamics as a forced oscillator. 25 2.3 The fundamentals of Proudman resonant wave growth. 28 2.4 Reflection, transmission, shoaling, refraction and seiching. 31 3.1 A schematic of isolating meteotsunami signals. 36 3.2 A comparison between finite-difference and finite-element domains. 42 4.1 The English Channel study region. 52 4.2 Tide gauge measurements on 23 June 2016. 55 4.3 Radar derived precipitation rates on 23 June 2016. 56 4.4 Surface pressure and 10-m wind speed measurements on 23 June 2016. 58 4.5 Time series of observed and modelled surface pressure anomalies. 65 4.6 Plan view of simulated sea-level elevations. 67 4.7 Time series of observed and modelled sea-level elevations. 69 4.8 Idealised simulations for coastal wave generation mechanisms. 71 xii 4.9 Sea-surface elevation sensitivity to forcing angles and speeds. 72 4.10 Sea-surface elevation sensitivity to wind, amplitude and period. 74 4.11 Sensitivity of the meteotsunami to tides in the model. 77 5.1 Synthetic atmospheric pressure forcings. 88 5.2 Strict Proudman resonance simulation results. 91 5.3 Wave growth when uniformly changing elevation. 93 5.4 Analytical envelopes when including constant currents. 96 5.5 Analytical envelopes including constant currents and elevation. 97 5.6 Sea-level elevation simulations with sloping bottoms. 100 5.7 Sea-level elevation simulations with a dynamic progressive tide. 103 5.8 Sea-level elevation simulations with a variable speed forcing. 106 5.9 Analytical envelopes for a moving forcing that changes amplitude. 109 5.10 Maximum wave amplifications with two-dimensional forcings. 111 6.1 The north-west European continental shelf study region. 126 6.2 The mesoscale atmospheric system classification scheme. 132 6.3 NSLOTT annual size-exceedance rates, grouped by country. 137 6.4 Seasonal variation of meteotsunamis, grouped by country. 140 6.5 Seasonal and diurnal NSLOTT variation across all tide gauges. 141 6.6 Mesoscale atmospheric systems grouped by season and country. 144 6.7 Synoptic composite analyses. 150 6.8 The percentile distribution of Proudman-resonant regions. 152 xiii 7.1 Radar-derived precipitation of isolated cells and open cells. 161 7.2 Simulations with open cells and isolated cells.