Estimating Tsunami Travel Times

Want to know how long you have until a tsunami generated in Chile reaches your doorstep? To figure it out you need two things: the speed of the wave generated and the great circle distance between you and the location of tsunami origin.

Wave speed (c) is related to the depth (H) of the water body the wave is moving through:

c = √(gH)

 

where g is acceleration due to gravity = 9.8 m/s² and H is in meters. The average wave speed in open ocean is approximately 200 m/s. This is fine to use in back of the envelope calculations such as this.

 

To find the great circle distance between two points you need the radius of the earth (approximately 6370 km) and the spherical angle (ψ) between the points, given by: 

ψ = arcos [ sin(φ₁)sin(φ₂) + cos(φ₁)cos(φ₂)cos(θ₂ – θ₁) ]

where φ₁ and φ₂  are the latitudes of the starting and ending points respectively. θ₁ and θ₂ are the longitudes of the starting and ending points respectively.

From there, use the spherical angle and radius to find arc length (s): s=rψ. Once you have that, you can find the travel time of the tsunami: t = s/c. Keep in mind that this is very general and rough!

I've generated a Matlab script calculating the travel time for a tsunami generated in Santiago, Chile to reach Honolulu, Hawaii (~11.5 hrs according to my script). If you want to pick different starting or ending points, just mess with the latitudes and longitudes.

Interested in tsunamis? Check out these sites:
Violent Hawaii: Deadly Tsunamis
NOAA Tsunami Website
 

%Long Gravity Wavesclose all

clear all

c = 200; % speed of propagation (m/s)
r = 6370; % radius of Earth (km)
r2 = r*1000; % radius of Earth (m)

lat1 = -35.846; % Latitude of santiago, Chile -33
lat2 = 21.467; % Latitude of Honolulu, Hawaii 22
lon1 = -72.719; % Longitude of Santiago, Chile -71
lon2 = -157.983; %Longitude of Honolulu, Hawaii -158

cosangle = sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos(lon2 - lon1);

angle = (acos(cosangle))*(180/pi); % angle in degrees

arclength = 2*pi*r2*(angle/360) % arclength between locations (m)

time = (arclength/c)*(1/60)*(1/60) % travel time (hr)