Calculate travel time for a tsunami

Tsunamis can travel vast distances in a short period of time, with disastrous consequences. Unlike typical ocean waves, tsunamis rarely form breaking waves, but they may travel far inland and cause great damage with their strong currents and collected debris.

Most tsunamis are caused by earthquakes, however, they can also be triggered by volcanic eruptions, submarine landslides, explosions, or even meteorite impacts. The East Coast of the United States has a very low tsunami risk. However, tsunamis still occur in the Atlantic Ocean. For example, tsunamis resulted from the 1929 Grand Banks earthquake in Newfoundland, the 1918 San Fermín earthquake in Puerto Rico, and the 1755 Lisbon earthquake in Portugal. Hence, it is valuable to assess tsunami risk and model potential events for hazard management. In this tutorial, you'll investigate three potential tsunamis in the North Atlantic, and calculate the time it would take each one to reach Virginia Beach, Virginia, USA.

This tutorial was last tested on July 17, 2024, using ArcGIS Pro 3.3. If you're using a different version of ArcGIS Pro, you may encounter different functionality and results.

Requirements

• ArcGIS Pro Standard or Advanced (see options for software access)
• ArcGIS Spatial Analyst extension

Calculate speed

Tsunamis begin after an earthquake, landslide, or other triggering event displaces a large volume of water. The potential energy of this vertical displacement is converted into kinetic horizontal energy in the form of waves. As the tsunami radiates outward from the trigger site, its speed is determined by the water's depth: it travels faster over deep water. When the tsunami reaches the shallower waters of a coastal area, its speed slows and its waves grow steeper.

Note:

To learn more about how tsunamis form and change, read Life of a Tsunami.

You'll map the paths taken by three potential tsunamis that could affect Virginia Beach. You'll use a digital elevation model (DEM) of the ocean's floor to calculate the speed each tsunami would travel.

Investigate potential tsunami triggers

In this tutorial, you'll investigate three possible tsunami triggers in the North Atlantic: an earthquake in the Puerto Rico Trench, a landslide on La Palma in the Canary Islands, and an underwater landslide 100 kilometers off the East Coast of the United States.

The data that you need for this analysis is provided in an ArcGIS Pro project package (.ppkx). You'll download the project and use it to examine the locations described above.

1. Download the Tsunami project package.

   A file named Tsunami.ppkx is downloaded to your computer.

   Note:

   A .ppkx file is an ArcGIS Pro project package and may contain maps, data, and other files that you can open in ArcGIS Pro. Learn more about managing .ppkx files in this guide.

2. Locate the downloaded file on your computer. Double-click Tsunami.ppkx to open it in ArcGIS Pro.
3. If prompted, sign in with your ArcGIS account.

   Note:

   If you don't have access to ArcGIS Pro or an ArcGIS organizational account, see options for software access.

   A map appears, showing the bathymetry of the Atlantic Ocean. The map uses the Albers equal area projection. It is important to use an equal area projection when performing analysis with area or distance calculations.

   

   Four locations are marked. You'll visit each of them in turn.

4. On the map, zoom to the blue and yellow dots on the East Coast of the United States.

   

   The blue dot marks Virginia Beach, a city of almost 500,000 people, and the selected impact site for this analysis.

   The yellow dot marks the Currituck Slide, or Currituck Slump. Siting on the edge of the continental shelf, this is the site of a former Submarine Mass Failure (SMF), or underwater landslide. It is estimated that the Currituck SMF occurred between 24,000 and 50,000 years ago, displaced 165 cubic kilometers of water, and caused a tsunami with more than 5 meters of inundation in nearby Norfolk, Virginia. A similar event in this area is possible.

   Note:

   Read more about the Currituck Slide and its tsunami potential in Potential for large-scale submarine slope failure and tsunami generation along the U.S. mid-Atlantic coast.

5. On the map, zoom and pan south to the pink dot in the Caribbean.

   

   The Puerto Rico Trench is the deepest part of the Atlantic Ocean. It lies in the subduction zone between the Caribbean Plate and the North American Plate, putting it at risk of earthquakes and SMFs. A tsunami triggered by the trench would have its most devastating effect on Puerto Rico, but if it was large enough, it could also reach as far north as Virginia Beach.

   Note:

   Read more about the Puerto Rico Trench and its tsunami potential in The Puerto Rico Trench: Implications for Plate Tectonics and Earthquake and Tsunami Hazards.

6. Zoom and pan east to the red dot in the Canary Islands, off the northwest coast of Africa.

   

   La Palma is a volcanic island with a history of recent activity. It is possible that a volcanic eruption could cause a much larger landslide and subsequent tsunami. If the event was large enough, the tsunami could be felt in Virginia Beach, although the chances of damage in North America are unlikely.

   Note:

   Read more about La Palma and its tsunami potential in Volcano Watch — The Canary Islands “mega-tsunami” hypothesis, and why it doesn’t carry water.

7. On the map, click any ocean area.

   A pop-up appears. The value next to Stretch.Pixel Value is the ocean's depth at that location, in meters.

   

   Deeper ocean areas are shown in darker grays and shallower areas are shown in lighter grays. You'll use these ocean depth values to calculate how fast a tsunami will travel.

   Note:

   The AtlanticDEM layer is a subset of the TopoBathy layer on ArcGIS Living Atlas. It was created using the Export Raster pane.

8. Close the pop-up.
9. In the Contents pane, right-click Locations and click Zoom To Layer.

Densify lines

A tsunami caused by any of the three potential causes listed above would spread radially outward and reach many shores. However, for this analysis, you'll only calculate travel time to a specific location: Virginia Beach, USA.

To calculate travel time, you need to draw geodesic lines between each tsunami source and Virginia Beach. A geodesic line is the shortest distance between two points on the curved surface of the earth.

1. In the Contents pane, check the box next to Tsunami Paths to turn the layer on.

   

   The Tsunami Paths layer connects each tsunami source with Virginia Beach. The lines appear straight, but a straight line on a map is not necessarily a straight path on the earth. You'll use the Geodetic Densify tool to create lines that you can be sure are geodesic.

2. On the ribbon, click the Analysis tab. In the Geoprocessing group, click Tools.

   

   The Geoprocessing pane appears.

3. In the search bar, type geodetic densify. In the search results, click Geodetic Densify.

   

   The tool's parameter appears. This tool will create lines with many vertices spaced at defined intervals along its length. These vertices help the line maintain its true shape, regardless of the map's projection.

4. For Input Features, choose Tsunami Paths.
5. For Output Feature Class, replace GeodeticDensify with Geodesic and press Tab.

   Note:

   The new feature class will be stored in Tsunami.gdb, the project's default geodatabase. You can click the Output Feature Class box to reveal the full path.

6. Ensure that Geodetic Type is set to Geodesic and Distance is set to 50 Kilometers.

   

7. Click Run.

   A new layer, named TsunamiPaths_Geodesic, is added to the map.

   

   The line from La Palma to Virginia Beach has more curvature than the same line in the original Tsunami Paths layer.

8. Zoom in to compare the two line layers on the routes from the Puerto Rico Trench and the Currituck Slide.

   These lines also follow slightly different paths in the new layer. Despite how they appear on this map, the curved lines represent the shorter distances.

9. In the Contents pane, right-click Tsunami Paths and click Remove.
10. In the Contents pane, check the box next to TopoBathy Hillshade to turn this layer on.

    Elevation changes on the ocean floor are illuminated by the hillshade. The bathymetry becomes easier to interpret as mountains and ridges. The hillshade layer uses a blend mode so the darks and lights of the DEM layer are still visible underneath.

    

11. Visually follow the path from La Palma to Virginia Beach, noting the changes on the seafloor along its route.

    Question 1: What seafloor features and landforms would a tsunami travel over on its way from La Palma to Virginia Beach? What effects might they have on its speed?

    Note:

    Answers are provided at the end of the tutorial.

Calculate a speed raster based on water depth

The speed of a tsunami can be estimated as the square root of the product of acceleration due to gravity (g) and the depth of the ocean (d), or √(g*d). The standard acceleration due to gravity on Earth (g) is defined as 9.80665 meters per second squared. Water depth values (d) are found in the AtlanticDEM layer. At a location with a depth of 4,000 meters, tsunami speed is √(9.80665m/s² * 4000m), or 198.057 meters per second.

You'll use the Raster Calculator tool to make a new raster layer in which the value of each cell represents the speed of a tsunami in that area.

1. In the Geoprocessing pane, click the Back button.
2. Search for and open the Raster Calculator tool.

   Tip:

   If you see two Raster Calculator options, you can choose either one.

3. In the expression box, type or copy and paste the following: Int(SquareRoot(9.80665*"AtlanticDEM")).

   Tip:

   Alternatively, you can construct this expression by double-clicking items in the Tools and Rasters boxes.

   

   This line calculates the square root of g x d, in which g is 9.80665 and d is the ocean's depth as measured in the AtlanticDEM layer. The expression is wrapped inside an Int function to ensure the output is an integer raster. Later, you'll convert part of this raster to polygons, and that operation requires an integer raster as input.

   In the Contents pane, you can see that the values of AtlanticDEM range from -8,385 to 5,560. The values you are interested in are all negative, representing meters below sea level. However, it's not possible to calculate the square root of a negative number. You'll modify the expression to invert AtlanticDEM values so ocean areas are positive and land areas are negative.

4. In the expression box, replace "AtlanticDEM" with ("AtlanticDEM"*-1).

   The expression now reads Int(SquareRoot(9.80665* ("AtlanticDEM"*-1))). It will calculate a tsunami's speed over ocean areas and return null values for any land areas.

5. For Output raster, type Speed and press Tab.

   

6. Click Run.

   When the tool has finished, a new layer appears on the map. It shows the deepest parts of the ocean (where tsunami speed is fastest) in white and the shallowest parts (where speed is slowest) in black.

7. On the map, click any ocean area.

   A pop-up appears. The number next to Stretch.Pixel Value represents the speed a tsunami would travel over that area, in meters per second.

   You have applied the same calculations everywhere, which is a simplification. As the tsunami reaches the shallower water of coastal areas, its speed will slow and its waves will grow taller and steeper, an effect called shoaling. The tsunami's behavior during shoaling requires more complex equations instead of the one described above. In addition, after hitting land, a tsunami's energy is reflected back to the ocean, resulting in complex behavior and many more waves. Other complicating factors exist at the coast, including funneling, debris, preexisting swell, and tides. A tsunami's behavior along a coast is best described with hydrodynamic modeling. However, for this analysis, you only require a conservative, or earliest arrival time, so applying the simpler, deep water equation to the entire tsunami path will be an acceptable approximation.

8. Close the pop-up.

Extract speed values along tsunami paths

You now have lines representing tsunami paths and a raster layer representing tsunami speeds. To find the travel time for each tsunami, you need to find the speed value along each line segment. You'll use the Extract by Mask tool to extract only those raster cells that intersect with the tsunami path lines.

1. In the Geoprocessing pane, search for and open the Extract by Mask tool.

   Note:

   If you don't have access to the Extract by Mask tool, you can skip to the next section. In the Raster to Polygon tool, use the Speed raster layer as input instead of the smaller PathSpeeds layer. The tool will take longer to process.

2. For Input raster, choose Speed.
3. For Input raster or feature mask data, choose TsunamiPaths_Geodesic.
4. For Output raster, type PathSpeeds and press Tab.
5. Ensure that Extraction Area is set to Inside.

   

6. Click Run.

   A new raster layer appears on the map, although it may not be immediately visible.

7. On the map, zoom to the Virginia Beach and Currituck Slide features.

   

   The new raster contains only those cells that intersect with the line layer. It looks like three jagged lines, each one only one cell wide. You'll change its color scheme to make it more visible against the rest of the map.

8. In the Contents pane, right-click PathSpeeds and click Symbology.

   The Symbology pane appears.

9. In the Symbology pane, click the Color scheme menu and check Show names.

   

10. Scroll a short way down the Color scheme list and choose Cyan to Purple.

    The layer's symbology changes on the map. Cyan cells are areas with slow tsunami speeds and pink cells are areas with fast speeds. The legend shows that values range from 6 to 285 meters per second. This translates to 21.6 to 1,026 kilometers per hour, or 13.4 to 638.5 miles per hour.

    

11. Close the Symbology pane.
12. In the Contents pane, turn off the TsunamiPaths_Geodesic and Speed layers.

    

    Question 2: Which of the tsunami's paths has the greatest range in speed values? Why?

13. On the Quick Access Toolbar, click the Save button to save the project.

    

You have calculated the speed of three potential tsunamis that might reach Virginia Beach. The raster data in this project has a resolution of 5,000 meters, which means that you have a different speed value for every 5 kilometers of each path. Next, you'll use these speed values to calculate travel time.

Calculate travel time

Travel time is equal to distance divided by speed. You now know both of these values, but to perform the calculation, you need to transfer the speed values from the raster layer to the line layer. You'll achieve this with the Raster to Polygon and Intersect tools. The result will be a new line layer in which each segment has a speed value and a length value. You'll use these values to calculate a new travel time field. Finally, you'll summarize the new field to find the total travel time for each tsunami path.

Convert a raster layer to polygons

The first step in transferring speed values is to convert the PathSpeeds raster to a polygon layer.

1. In the Geoprocessing pane, search for and open the Raster to Polygon tool.
2. For Input raster, choose PathSpeeds.

   The input layer must be an integer raster.

3. For Field, choose Value.

   Value represents the speed in meters per second for each 5 km cell.

4. For Output polygon features, type SpeedPolygons and press Tab.
5. Uncheck Simplify polygons.

   This option, if checked, smooths the edges of polygons. For this analysis, it's better to create square-edged polygons that more precisely represent the raster cells.

6. Leave the other parameters blank.

   

7. Click Run.

   Polygons appear on the map. They represent each cell (or group of cells with the same value) in the speed raster.

8. On the map, click one of the polygons.

   A pop-up appears. The gridcode field contains the speed values, in meters per second.

   

9. Close the pop-up.

Intersect lines and polygons

Next, you'll intersect the TsunamiPaths_Geodesic line layer with the SpeedPolygons layer. This will create a new line layer with both speed and distance attributes.

1. In the Geoprocessing pane, search for and open the Pairwise Intersect tool.
2. For Input Features, choose TsunamiPaths_Geodesic and SpeedPolygons.
3. For Output Feature Class, type TsunamiPaths_Speed and press Tab.
4. For Join Attributes, ensure that All attributes is selected.
5. For Output Type, choose Line.

   

   The line will be segmented wherever it crosses a polygon edge. Each new line segment will have an attribute with the speed value from its intersecting polygon.

6. Click Run.

   A new line layer appears on the map.

7. In the Contents pane, right-click TsunamiPaths_Speed and click Attribute Table.

   The attribute table appears below the map. The gridcode field comes from the polygon input layer and contains the speed values. Shape_Length is an autogenerated field that measures the length of each line segment in meters.

   

   Tip:

   To confirm the unit used by the Shape_Length field, right-click TsunamiPaths_Speed in the Contents pane and click Properties. In the Layer Properties window, click the Source tab. Expand the Spatial Reference section and consult the Linear Unit property.

   Shape_Length and gridcode are the fields that you need to calculate travel time.

Calculate travel time for each line segment

You'll add a new field to the TsunamiPaths_Speed layer and calculate it with the travel time for each segment of each line.

1. On the table's toolbar, click the Add Field button.

   

   The Fields view opens, with a new field partially added.

2. In the last row of the table, for Field Name, type TravelTimeHours. For Alias, type Travel time in hours. For Data Type, choose Double.

   

3. Right-click anywhere on the table and click Save.
4. Close the Fields view and return to the attribute table.
5. Scroll to the end of the table to find the new Travel time in hours field.

   The field is empty, containing only null values. You'll calculate the field as the length of each segment divided by its speed value.

6. Right-click the header for the Travel time in hours column and click Calculate Field.

   

7. In the Calculate Field window, for TravelTimeHours =, type or copy and paste !Shape_Length! / !gridcode!.

   Tip:

   Alternatively, build the expression by double-clicking items in the Fields box and the operators below the Helpers box.

   

   This expression returns travel time in seconds. To instead calculate travel time in hours, you'll further divide the number by 3,600.

8. In the TravelTimeHours = box, at the end of the expression, type /3600.

   

9. Click OK.

   The Travel time in hours field is populated with new values, representing the number of hours it would take a tsunami to travel over each segment of the line. The values are very small, since most segments are only 5 kilometers long.

Calculate travel time for each path

To finish the analysis, you'll add the travel times for all segments together to find the total travel time to Virginia Beach for each potential tsunami.

1. In the attribute table, right-click the Travel time in hours column header and click Summarize.

   The Summary Statistics window appears.

2. For Input Table, confirm that TsunamiPaths_Speed is selected.
3. For Output Table, type TsunamiPaths_TravelTime and press Tab.
4. For Field, choose Travel time in hours. For Statistic Type, choose Sum.

   

   The Summary Statistics tool will add all of the values in the Travel time in hours field. It would be more useful to have three totals: one for each tsunami. You'll separate the summary with a Case Field so it returns separate totals for each route.

5. For Case Field, choose Route.
6. Click OK.

   A new table is created with the summarize values.

7. Scroll to the bottom of the Contents pane. Under Standalone Tables, right-click TsunamiPaths_TravelTime and click Open.

   The table has three rows. The SUM_TravelTimeHours field records the total travel time, in hours, for each possible tsunami. A tsunami originating at the Currituck Slide would take 2 hours and 23 minutes to reach Virginia Beach. From La Palma, it would take 9 hours and 24 minutes. From the Puerto Rico Trench, it would take 6 hours and 15 minutes.

   

   Question 3: How might the travel time analysis demonstrated in this tutorial be useful to coastal hazard assessments in a city that is prone to tsunamis?

8. Close both tables. Save the project.

In this tutorial, you calculated travel time for three potential tsunami sources to a defined coastal location. You created geodesic lines to map the most direct route for each tsunami. You used a DEM of the ocean to create a raster that calculates tsunami speeds. You extracted those cells from the speed raster that are along each tsunami's path and converted them into polygon features. You intersected the tsunami path lines with the polygon speed layer. You calculated a new field with travel time values. Finally, you summarized travel time values to find the total travel time for each tsunami.

Note:

You can view travel time maps for historic tsunamis on the Natural Hazards Viewer. In the Layers pane, make a selection under Selected Significant Tsunami Events. You can view travel time maps to selected cities in the Tsunami Travel Times to Coastal Locations Viewer.

Calculating travel time is one aspect of tsunami planning. Advanced tsunami hydrodynamic models are developed to simulate tsunamis from probable triggering events. These models are used to estimate the run-up height and inland extent of tsunamis, and to develop tsunami inundation maps for emergency management and public awareness. The U.S. Tsunami Warning System monitors the oceans to detect tsunamis before they reach coastlines and provide accurate warning messages. The risk of a tsunami in Virginia Beach is very low, but planning for one is still valuable. You are encouraged to repeat this workflow for another location, for example, in the Pacific Ocean.

You can find more tutorials in the tutorial gallery.

Answers

1. What seafloor features and landforms would a tsunami travel over on its way from La Palma to Virginia Beach? What effects might they have on its speed?

   At first, the tsunami would pass over the Canary Basin. These waters are deep, so the tsunami would be traveling fast. Then it would meet some seamounts and tablemounts in the Oceanographer Fracture Zone, which would cause it to slow suddenly. The tsunami would slow again as it passed the Mid-Atlantic Ridge. Then it would have a long stretch of quick travel over the deep water of the North American Basin, including the Sohm Plain. It would be slowed only briefly by the New England Seamount. The tsunami would slow dramatically for the last 125 kilometers of its journey, as it crossed the continental shelf.

2. Which of the tsunami's paths has the greatest range in speed values? Why?

   The path from the Puerto Rico Trench to Virginia Beach has the greatest difference in speed values. The tsunami would begin very fast, since it must first cross the Puerto Rico Trench, the deepest part of the Atlantic Ocean, and it would finish its journey slowly on the very shallow continental shelf.

3. How might the travel time analysis demonstrated in this tutorial be useful to coastal hazard assessments in a city that is prone to tsunamis?

   A city can use this analysis to predict how much time city officials would have to warn residents of an approaching tsunami. A city might plan different evacuation procedures for a tsunami based on the amount of time available.

Acknowledgements

• Locations and Tsunami Paths: manually created by Esri.
• World Oceans Reference: Esri, HERE, Garmin, GEBCO, National Geographic, NOAA, and the GIS User Community.
• World Countries (Generalized): Esri; U.S. Central Intelligence Agency (The World Factbook); National Geographic Society; Garmin International, Inc.
• TopoBathy Hillshade: Esri, Airbus, USGS, NGA, NASA, NOAA, CGIAR, GEBCO, NLS, OS, NMA, Geodatastyrelsen, GSA, GSI and the GIS User Community.
• AtlanticDEM: derived from TopoBathy: Esri, Airbus, USGS, NGA, NASA, NOAA, CGIAR, GEBCO, NLS, OS, NMA, Geodatastyrelsen, GSA, GSI and the GIS User Community.
• Cover image by Dimitris Vetsikas from Pixabay.