Refined computational mesh

For the analysis in this chapter, accurate seabed bathymetry data are used and combined with the seabed deformation representation to run VOLNA and obtain the wave elevations for dif- ferent hypothetical event cases. Information about the bathymetry at each node of a very dense detailed unstructured triangular mesh, which is shown in Figure 5.2 is available, where the number of nodes in the mesh is 1,197,384 corresponding to 2,392,352 triangles.

The public available National Oceanic and Atmospheric Administration and National Geo- physical Data Centre (NOAA/NGDC) bathymetry and topography data sets have been con-

Figure 5.2: Triangular mesh of the Cascadia Subduction Zone, with the coastline indicated by the red colour. The colour scale presents the public available elevation data for the bathymetry and topography.

verted to an adaptive mesh that can be used in VOLNA tsunami model. This conversion was performed by UCL PhD student Xiaoyu Liu and the bathymetry data were kindly provided to me. The NOAA/NGDC data sets are the best available bathymetric and topographic data and they are extracted from the US Geological Survey (USGS) National Elevation Dataset (NED) [Gesch et al., 2014]. NED consists of elevation information3and it is widely used for earth science studies as well as mapping applications. NED is derived from the highest quality USGS digital elevation models (DEMs) or three-dimensional representation of the land’s sur- face. NED is generated using land elevation data for the United States, Alaska, Hawaii, Mexico and Canada. DEMs can be obtained for any place in Earth at several resolutions. NED provides national US coverage at a grid spacing of 1 arc per second, which is approximately 30 metres.

3_{Elevation or geometric height is the height above or below a fixed reference point, usually the Earth’s sea level.}

The elevation data are collected by aerial or bathymetric surveys and they contain information for the Earth’s surface on land and under water.

Chapter 5. Cascadia study using VOLNA evaluations

When new data become available, NED is updated. Also, it is worthy mentioned that NED data are in public domain and they are used for mapping and visualisation, global change research, resource monitoring as well as many other applications [Gesch et al., 2014].

For the generation of the mesh used in the analysis in this chapter, different resolutions of DEMs have been used and they are merged to cover the whole Cascadia Subduction Zone area. Specifically, five different data sources are used, which are the following:

1. ETOPO1 Global Relief Model 1 arc-minute

2. Strait of Juan de Fuca, WA 30 arc-second MHW DEM 3. Strait of Juan de Fuca, WA 5 arc-second MHW DEM 4. US Coastal Relief Model - Northwest Pacific 3 arc-sec 5. US Coastal Relief Model - Central Pacific 3 arc-sec

The cell sizes in the mesh have been calculated using a specific rule which combines the water depth and the slope angle so that the mesh triangles sizes to be smaller at the locations where the waves are travelling more slowly and therefore greater computational accuracy is required. Additionally, for areas where only coarse bathymetry data are available, the mesh size has to be relatively large, whereas in cases where higher resolution data are available, the mesh size is much smaller.

Looking at the generation of the mesh in more detail, the processed followed by Xiaoyu Liu was the following:

1. For areas covered by high resolution DEMs, which are the Strait of Juan de Fuca, WA 5 arc-second, US Coastal Relief Model - Northwest Pacific 3 arc-sec and US Coastal Relief Model - Central Pacific 3 arc-sec, a much more dense mesh is generated compared to lower resolution DEMs areas, which are the ETOPO1 Global Relief Model 1 arc-minute and Strait of Juan de Fuca, WA 30 arc-second MHW DEM.

2. For the case of high resolution DEMs areas: • For the water surface area:

– if the water depth is greater than 250m, which is the area far away from the shoreline and close to the boundaries of the domain, then the mesh cell size is set to be 1000m

– if the water depth is smaller than 10m, which is the area close to the shoreline, the cell size is set to be 200m

– if the water depth is between 10m and 250m, the cell size is obtained by linear interpolation

• For the coast area:

– if the topography height is greater than 50m above the sea level, then the cell size is set to be 1000m

– if the height above the sea level is less then 10m, which is for locations around the coastline, the cell size is set to be 200m

– if the topography height is between 10m and 50m above the sea level, then linear interpolation is used to obtain the mess cell size

3. Similarly, for the areas covered by low resolution DEMs: • For the sea area:

– if the water depth is greater than 3000m, the mesh cell size is set to be 15000m – if the water depth is smaller than 150m or when the bathymetry slope is greater than the 90% upper percentile of all the slopes, then the cell size is set to be 3000m

– if the water depth is between 150m and 3000m, the cell size is obtained by linear interpolation

• For the coast area:

– if the topography is greater than 100m above the sea level, the cell size is set to be 15000m

– if the topography height is less then 50m, the cell size is set to be 3000m – if the topography height is between 50m and 100m above the sea level, then

linear interpolation is used to obtain the mess cell size

Therefore, the mesh is very dense close to the coastline and by moving away from the coast to the boundaries it is getting more sparse, in order to avoid unnecessary detail at locations that are not important. Hence, the particular way of mesh generation saves computational cost. On the other hand, the adaptive mesh gives high resolution at coastal areas and hence more accuracy in inundation predictions, where is the locations we are interested more as they are densely populated.

However, since there are no available data for the coastline location, the coastline coordi- nates have been identified by selecting the triangles that include both sea and coastline. This

Chapter 5. Cascadia study using VOLNA evaluations

is done by checking the bathymetry and topography at all the nodes and collect the triangles that have nodes which have both positive and negative bathymetry. From these triangles, the centres coordinates are obtained and plotted with red nodes in Figure 5.2. This indicates that the coastline location algorithm is not 100% accurate, but it is still very close and it is enough for the purpose of the analysis as no further detail is necessary now. Note that the triangular mesh defines the computational domain for VOLNA. Therefore, it has too be significantly large in order to avoid wave reflections at the boundaries of the domain.