Emily M. Lane

A mechanism for switching near a heteroclinic network

We describe an example of a robust heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling due to complex eigenvalues in the flow linearized about one of the equilibria common to all cycles in the network. We construct and use return maps to investigate the asymptotic stability of the network, and show that switching is ubiquitous near the network. Some of the unstable manifolds involved in the network are two-dimensional; we develop a technique to account for all trajectories on those manifolds. A simple numerical example illustrates the rich dynamics that can result from the interplay between the various cycles in the network.

Tsunami runup and tide-gauge observations from the 14 November 2016 M7.8 Kaikōura earthquake, New Zealand

The 2016 Mw 7.8 Kaikōura earthquake was one of the largest earthquakes in New Zealand’s historical record, and it generated the most significant local source tsunami to affect New Zealand since 1947. There are many unusual features of this earthquake from a tsunami perspective: the epicentre was well inland of the coast, multiple faults were involved in the rupture, and the greatest tsunami damage to residential property was far from the source. In this paper, we summarise the tectonic setting and the historical and geological evidence for past tsunamis on this coast, then present tsunami tide gauge and runup field observations of the tsunami that followed the Kaikōura earthquake. For the size of the tsunami, as inferred from the measured heights, the impact of this event was relatively modest, and we discuss the reasons for this which include: the state of the tide at the time of the earthquake, the degree of co-seismic uplift, and the nature of the coastal environment in the tsunami source region.

Initialising Landslide-Generated Tsunamis for Probabilistic Tsunami Hazard Assessment in Cook Strait

The Cook Strait Canyon is a submarine canyon which lies within 10 km of Wellington, the capital city of New Zealand. The canyon flanks are scarred with the evidence of past landslides that may have caused large local tsunamis. City planning and civil defence management require information on the magnitude and frequency of these tsunamis to adequately plan for them. Submarine-landslide-generated tsunamis are by nature local features. While they may be catastrophic in the near field, they are generally far smaller scales than co-seismic tsunamis and their energy does not travel very far. Including them within a comprehensive tsunami hazard assessment requires accounting for a large number of potential landslide sources. Unless we only use simple rules of thumb to approximate tsunami height, this requires considerable computing power. This article describes a technique for expanding two-dimensional vertical-slice tsunami generation by landslide modelling into a two-dimensional horizontal surface which can be used for tsunami propagation and inundation modelling. As such, it spans the gap between full three-dimensional modelling of the landslide and simple initialisation.

Towards a Spatial Probabilistic Submarine Landslide Hazard Model for Submarine Canyons

The Cook Strait Canyon of central New Zealand was identified as a priority area to quantify landslide-generated tsunami hazard in a national study in 2005. Therefore the canyon system has seen increasing research interest over the last decade. Landslide scars have been mapped throughout the whole of the Cook Strait Canyon area and analysis of landslide morphology demonstrates that the majority of landslides have some dependence on the topography of the canyon system. Axial downcutting destabilising lower canyon walls is proposed as the principal factor preconditioning slopes for failure. The canyons occur in an active tectonic environment and earthquakes are inferred to be the overriding failure triggering mechanism.

Probabilistic Hazard of Tsunamis Generated by Submarine Landslides in the Cook Strait Canyon (New Zealand)

Cook Strait Canyon is a submarine canyon that lies within ten kilometres of Wellington, the capital city of New Zealand. The canyon walls are covered with scars from previous landslides which could have caused local tsunamis. Palaeotsunami evidence also points to past tsunamis in the Wellington region. Furthermore, the canyon’s location in Cook Strait means that there is inhabited land in the path of both forward- and backward-propagating waves. Tsunamis induced by these submarine landslides pose hazard to coastal communities and infrastructure but major events are very uncommon and the historical record is not extensive enough to quantify this hazard. The combination of infrequent but potentially very consequential events makes realistic assessment of the hazard challenging. However, information on both magnitude and frequency is very important for land use planning and civil defence purposes. We use a multidisciplinary approach bringing together geological information with modelling to construct a Probabilistic Tsunami Hazard Assessment of submarine landslide-generated tsunami. Although there are many simplifying assumptions used in this assessment, it suggests that the Cook Strait open coast is exposed to considerable hazard due to submarine landslide-generated tsunamis. We emphasise the uncertainties involved and present opportunities for future research.

Coupled Modelling of the Failure and Tsunami of a Submarine Debris Avalanche Offshore Central New Zealand

Evidence of previous submarine mass failures in the form of excavation scars has been widely documented in the Cook Strait Canyons of New Zealand. Recent bathymetry surveying has identified a well-defined submarine landslide scar and its associated debris deposit on the northern slope of southern Hikurangi Trough. The newly acquired multi-beam data allowed determination of the location and extent of the deposit, estimation of its volume, as well as reconstruction of both the pre-failure bathymetry and the initial state of the mass failure. A dynamically coupled two-layer model was used to numerically investigate this submarine debris avalanche and its resulting tsunami impact on the coasts of central New Zealand. The modeling results show a fairly good overall agreement with the observed debris deposition and also suggest that tsunami associated with the debris avalanche quite possibly inundated the coasts of central New Zealand, with maximum run-up elevations of between 3 and 5 m in several nearby locations.

Tsunami inundation modelling using RiCOM

Abstract The New Zealand coastline faces the risk of tsunami from a variety of sources, including remote and local earthquakes, submarine landslides, and volcanoes. Palaeotsunami studies indicate New Zealand has undergone periods of catastrophic tsunami activity, such as in the 1500s. It is important to be able to quantify the hazard posed by tsunamis. In this paper we detail the process of modelling tsunami propagation and inundation from source to destination using RiCOM, a finite element coastal hydrodynamic model on an unstructured grid. We give examples of model outputs, such as maps of tsunami inundation depth, maximum speeds, wave arrival times and time spent inundated, which can be used to quantify the hazard. We also perform sensitivity analysis of the response of the tsunami to the average slip on, and length and width of, the fault surface while keeping the moment magnitude and all other parameters constant. Larger average slip is shown to produce larger tsunamis. The width/aspect ratio of the slip has a more variable effect on the size of the tsunami, which depends upon the local coastal geometry. This information can be used to identify risk areas, plan escape routes, protect people and infrastructure and, more generally, to inform the public as to the tsunami risk in their region.

Verification of RiCOM for Storm Surge Forecasting

RiCOM is an unstructured-grid finite-element coastal ocean model. It is used to provide storm surge forecasts as part of a larger suite of environmental forecasting models known collectively as EcoConnect. RiCOM is forced with surface pressure and with 10 m winds forecast by the weather prediction model, NZLAM-12. Our objective is to evaluate the RiCOM forecasts, to understand the strengths of the model, and to identify improvements that can be made. The verification process involves comparison of the predicted sea level with data gathered from the New Zealand-wide sea level network managed by NIWA. Predicted time series for each site are built up from successive 48-hour forecasts. Different forcing and frequency components of the real and model time series are then compared. Historical mooring data are also used to evaluate RiCOMs ability to capture flows. Tidal and low frequency components of RiCOM are seen to compare well with sea level network data. There are some situations where RiCOM does not perform as well. Velocity forecasts have only been basically evaluated due to a lack of current data. Future additions and improvements to the model have been identified such as improving the wind stress formulation, extending the model to three dimensions, and adding baroclinic circulations and coupling the model with a wave model.

Forecasting Extreme Sea Level Events and Coastal Inundation from Tides, Surge and Wave Setup

Abstract A new marine forecasting system for the New Zealand region has been developed, including global and regional wave models, and regional tide and storm surge models. These form part of an integrated weather-related hazards forecasting capability, which also includes an accurate, data-assimilating high-resolution weather forecasting system and a national-scale flood forecasting system. Predicted variations in sea surface height and depth-averaged current due to tides and storm surge are provided in twice-daily 48-hour regional forecasts. Storm surge is predicted for the New Zealand region using the RiCOM hydrodynamic model on an unstructured grid in depth-averaged mode, using semi-implicit integration in time and a semi-langrangian scheme for advection. The model reproduced the storm surge event resulting from the passage of cyclone “Funa” across New Zealand during January 2008. Root-mean-square (RMS) errors in predicted storm surge height were 4-13 cm. For a second simulated storm, which occurred in Marlborough in late July/early August 2008, the model predicted the storm surge height with RMS errors at Kaikoura and Lyttelton of 7 and 4 cm, respectively. Wave-breaking also contributes to sea levels close to the coast through radiation stresses. The forecast system runs Wavewatch III on nested global and regional structured grids, providing twice-daily 48-hour forecasts. Model developments incorporating wave radiation stresses into the hydrodynamic model forcing are described, and some investigations into the effects of wave forcing on surface setup and coastal inundation are presented. A case study of inundation around the fringes of Hawkes Bay in response to extreme sea levels exacerbated by wave-induced stresses is presented. The case study used the SWAN wave model to provide the near-shore wave characteristics and radiations stresses, and demonstrates the ability of the coupled tide-surge-wave model to simulate and predict coastal flooding on a spatial resolution of a few metres.

Submarine mass movements and their consequences : progress and challenges

This sixth edition of the Submarine Mass Movements and Their Consequences volume, coincident with the seventh eponymous conference includes 61 papers that span a variety of topics and are organized into nine parts as follows: (1) Submarine mass movement in margin construction and economic significance; (2) Failure dynamics from landslide geomorphology; (3) Geotechnical aspects of mass movement; (4) Multidisciplinary case studies; (5) Tectonics and mass movement processes; (6) Fluid flow and gas hydrates, (7) Mass transport deposits in modern and outcrop sedimentology; (8) Numerical and statistical analysis; and, (9) Tsunami generation from slope failure. The breath and quality of this body of work underpins a positive outlook and our enthusiasm for the future direction of research in this area of science as it moves towards ever more detailed analysis and monitoring. We also emphasize in this volume the need to look at mountain-scale outcrops to better understand our seismic imaging, to carry out statistical studies that draw on global data sets to better constrain broad behavioural characteristics, and to undertake numerical modelling to understand the sensitivity of a range of natural slopes.