Aerospace and Electronic Systems Magazine March 2018 - 49

questions have arisen regarding the extension of its capabilities to
include offshore tsunami detection. With this in mind, concepts associated with the optimal spatial and temporal scales necessary for
tsunami detection on the continental shelf and at its edge using this
technology are considered in this section.

ROBUST DETECTION OF SMALL TSUNAMI SURFACE
CURRENTS
When a tsunami wave train propagates across the open ocean as
a shallow water gravity wave with a speed of about 200 m/s, it is
guided by the Coriolis effect and refraction due to gradients in the
bathymetry on scales longer than the tsunami wavelength, which
may range to hundreds of kilometers in deep water. When the wave
meets steep gradients at the edges of continental shelves, the wave
speed decreases significantly. Generally speaking, the distance offshore at which the tsunami signatures can
be detected, which, in turn, determines the
warning time delivered, depends on the bathymetry: the wider the shallow continental
shelf, the greater the warning time.
Following linear wave theory [11], the
maximum orbital velocity, i.e., surface current velocity, of a wave as it moves from
a depth D with the initial elevation a(D) to
another depth d is given by
Vo ( d ) = a ( D )

VThr =

c
,
2 f TCI

(2)

where c is the speed of light. All tsunami-induced current velocities with values above these thresholds have a nonzero probability

g D 4
  ,
d d 

(1)

where g is the gravitational acceleration
and d is the changing water depth. Hence,
while the tsunami wave is approaching the
continental shelf, the surface current pattern
changes from small magnitudes in deep water to more significant values in the shelf
area, as shown in [12].
Results of the application of linear wave
theory for tsunami phase velocity and maximum orbital velocity, as a function of water depth, appear in Figure 1 for a tsunami
MARCH 2018

wave, with an initial elevation of 20 cm at a water depth of 4,000
m. Surface current velocities induced by a tsunami are many orders
of magnitude smaller than the phase velocity of tsunami propagation. Nevertheless, these current velocities can be accurately measured with high spatial and temporal resolution by using the phased
array HF ocean radar technology in real time. The sensitivity of the
radar in resolving the surface current velocities strictly depends
on the operating radar frequency f and coherent integration time
(CIT) TCI, as indicated in Figure 1 by horizontal lines. The lines
mark velocity resolution thresholds derived from different radar
characteristics, i.e.,

Figure 1.

Phase velocity of tsunami propagation (black line) and the maximum horizontal orbital velocity
(surface current velocity) in a tsunami wave (green line). The boundaries for velocity resolution to
detect tsunami at different water depths using HF radar with different operation frequencies and
CIT (horizontal lines).

IEEE A&E SYSTEMS MAGAZINE

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine March 2018