**3. HF radar observations of the 2011 Japan tsunami leading to an empirical detection algorithm**

Radar echoes are produced by reflection of the radar wave from ocean waves with wavelengths half that of the radar; such waves have periods between 1.5 and 4.5 s. In contrast, the tsunami wave period lies between 20 and 50 min, corresponding to wavelengths between 400 and 800 km in the open ocean. Tsunami orbital velocities add to the shortwave radial velocities producing the radar echo; in deep water, tsunami velocities are too small to be seen by the radar, but they increase as the tsunami moves onto the continental shelf and the water depth decreases below 200 m and can then be observed by radars located on the coast.

Radial current velocities are obtained from the first‐order radar echo spectra measured at individual radar sites [13, 14]. In usual practice, several radar echo spectra are averaged over time before analysis. As time resolution is critical for local tsunami detection, unaveraged spectra are analyzed. The Doppler shift from the ideal Bragg frequency defines the radial current speed; spectral values at that frequency are interpreted to give the azimuth angles at which this speed occurs. Together with range defined by the time delay, estimates follow for the radial current velocity at locations spaced 1° apart around a circular range cell centered on the radar site.

error estimate of about 25% when using Green's Law for estimating tsunami height change

Solving Eqs (2–3) provides both the tsunami height and orbital velocity profiles as the wave approaches the coast, as impacted by the decreasing depth on the journey toward shore. This yields the most accurate estimate for the arrival time from any offshore point along its path and is useful in near field of the coastal radar because the computational effort is manageable. However, for an approach from much farther out, or in order to get a quick, rough estimate of the tsunami arrival time, the phase velocity *vph*(*d*) at depth *d*, time *t*, and distance *s* along a

> ( ) *ph <sup>s</sup> v d*

> > 0

*t*

Eqs (5) and (9) lead to the following approximate solution for the elapsed time Δ*T* for the

( ) *<sup>s</sup> <sup>s</sup> <sup>T</sup>*

*gd s*

Because of inherent smoothing of the integration process, the depth profile need not be defined to great resolution, allowing quick use of Eq. (10) over large ocean distances to give rough

**3. HF radar observations of the 2011 Japan tsunami leading to an empirical**

Radar echoes are produced by reflection of the radar wave from ocean waves with wavelengths half that of the radar; such waves have periods between 1.5 and 4.5 s. In contrast, the tsunami wave period lies between 20 and 50 min, corresponding to wavelengths between 400 and 800 km in the open ocean. Tsunami orbital velocities add to the shortwave radial velocities producing the radar echo; in deep water, tsunami velocities are too small to be seen by the radar, but they increase as the tsunami moves onto the continental shelf and the water depth

Radial current velocities are obtained from the first‐order radar echo spectra measured at individual radar sites [13, 14]. In usual practice, several radar echo spectra are averaged over time before analysis. As time resolution is critical for local tsunami detection, unaveraged spectra are analyzed. The Doppler shift from the ideal Bragg frequency defines the radial

decreases below 200 m and can then be observed by radars located on the coast.

¶ <sup>=</sup> ¶ (9)

¶ D = ò (10)

due to sharp depth changes.

tsunami great‐circle ray path can be expressed as follows:

tsunami arrival at distance *S* from the start:

estimates of the tsunami arrival time.

**detection algorithm**

**2.5. Tsunami arrival time**

80 Tsunami

Total current velocities are obtained by combining radial velocities from the radar sites [13]. A grid is formed over the radar coverage area and averaging circles form surrounding each grid point. Total velocity vector components are calculated by fitting to radial velocities from the different radar sites that fall within the averaging circle.

On March 11, 14:46 2011 Japan Standard Time (JST), a magnitude‐9 earthquake off Sendai, Japan, unleashed a large tsunami that was observed by HF radars around the Pacific Rim, see **Figure 1**. The earthquake and resulting tsunami are known as the Tohoku event. As our first example, we show current velocities measured by two SeaSonde radars located near Usujiri and Kinaoshi, Hokkaido, Japan during the 2011 Tohoku tsunami.

**Figure 1.** (a) The North Pacific Ocean showing the location of the radars that detected the tsunami. Abbreviated radar field names are as follows; corresponding geographic locations are given in Section 1. Japan: A087 and A088. USA: STV2, SEA1, YHS2, TRIN, GCVE, BML1, PREY, COMM, ESTR, and LUIS. (b) The location of the Japan earthquake and the radars in Hokkaido. (c) The bathymetry offshore from the radars and radial velocities measured by the Kinaoshi radar, March 11, 2011, 21:00 JST.

The radars had a transmit frequency of 42 MHz and a range increment of 0.5 km. The water depth over the entire radar coverage area is less than 200 m. The 42 MHz frequency band is used for high‐resolution, short‐range current observations and results in a radar range less than 15 km, due to significant attenuation of the surface wave passing across the sea at these higher HF frequencies.

### **3.1. Total velocity current maps**

The direction and strength of the flow were measured at approximate 4‐min intervals with a cell resolution of 0.5 km × 0.5 km. **Figure 2** shows total current‐velocity maps, the first

**Figure 2.** Tsunami current velocity vectors with the tsunami height shown in colors. Radar measurements from A087 (blue circle) and A088 (red circle) made on March 11, 2011 (a) the tsunami arrival at 15:53 JST and (b) outward flow occurring later at 21:00 JST.

demonstrating the arrival of the tsunami, indicated by strong inward flow, the second an example of outward flow. Eqs (6) and (7) relate the tsunami height to the current velocity; heights are displayed in colors superimposed on the velocity vectors shown by the arrows. As noted in Section 2.3.2, the accuracy of Green's Law estimates of height decreases close to shore.

A video showing the current velocity/height flow from March 11, 14:06 JST to March 12, 13:54 JST is shown in Video 1, available at http://bit.ly/29lOdXw

Time in JST is given in each frame of the movie. The video shows the tsunami arriving at 15:53 JST and then sweeping in and out of Uchiura Bay.
