**6.1. Evaluation method**

Using the actual offshore bathymetry, we simulated a tsunami approaching the Portuguese coastline from the west, results are shown in Video 3, available at http://bit.ly/29l4vCx Bathymetry contours are shown in order to understand the tsunami refraction. The epicenter was located more than 200 km to the west of the map. When the source is so distant, the initial condition for solving the PDE can be taken to be a plane wave, corresponding to a ridge of water traveling eastward. This approximation is reasonable whenever the source is distant from the near-field region and is convenient to model for numerical solutions. The domain for the numerical solution consists of the coastline of interest and the open box edges over the ocean. The coastline was assumed to have a Neumann (reflective) boundary condition.

This region was also selected for study because there are three 13.5-MHz SeaSonde HF radars operating at nearby locations, which are shown by green squares in the video. Tsunami observation software is being installed at these sites. The three radars would not see the tsunami if its propagation followed the line of sight from the source because the coast of southern Portugal would shadow those paths. In fact, the model output shows how the tsunami wave refracts and approaches the sites from the south. Reflection of the wave from

Another region of recent interest is the Alboran Sea, which is enclosed on three sides by Gibraltar on the west, Spain on the north and Morocco on the south. There are seismically active regions near tiny Alboran Island that could raise a localized mound of water, which would spread out under the influence of gravity, initially radiating a near-circular tsunami

A point source is another initial condition that is easy to handle in the PDE solution [9].

The tsunami point source is located near Alboran Island (the green square marker) in water that is 1000 m deep. The tsunami radiates in all directions, intensifying in height and velocity as it moves into shallow water, as indicated by the bathymetry contours. As before, background

One can see as the movie progresses how different coastal regions are affected, as the approaching tsunami intensity increases. Offshore reflections and along-shore tsunami vectors are clearly seen from the vectors. The island is small compared to the tsunami wavelength,

This approximate procedure is based on the theory given in Section 2.3. To simulate velocities for a given test radar site over a period of time close to the arrival of a tsunami, band velocities from a real tsunami (termed reference velocities *V*Ref) are superimposed on band velocities measured at the site (termed site velocities *V*Site). Before adding to the site velocities, the reference velocities are adjusted for the site bathymetry using Eq. (7). They are then multiplied

Resulting maps are shown in Video 4 that can be viewed at http://bit.ly/29gMdPA.

color represents normalized height and vector length represents normalized velocity.

the coast is clearly visible.

causing little observable effect.

**5.2. Band-velocity simulation based on Green's Law**

*5.1.2.2. Alboran Sea*

wave.

100 Tsunami

The following steps are used to estimate the size of an approaching tsunami required for detection at the test site.


$$\text{Vdetect} = F\_{\text{dauc}} \, \, ^\ast \mathbf{V}\_{ref}^{\text{list}} \ast \left( \frac{Depth\_{\text{Ref}}}{Depth\_{\text{Sun}}} \right)^{3/4} \tag{12}$$

$$H\_{\text{denoct}} = \sqrt{\frac{\text{Depth}\_{\text{Sike}}}{\text{g}}} V\_{\text{denoct}} \tag{13}$$

where ref init is the magnitude of reference velocity oscillation leading to a detection of the tsunami arrival. Note that in these equations, *V*detect and *H*detect define the values where the band velocities are measured, not values very close to shore in the run‐up zone, that can only be calculated using the highly nonlinear theory.

These steps are repeated using a sliding 5‐h time window, running in the background of an operating radar system. The work described in this section is preliminary in nature and is being further developed in partnership with NOAA.

#### **6.2. Application at two test sites**

We demonstrate the procedure for a single 5‐h time window using as reference band velocities measured by the Kinaoshi radar (A088) during the Tohoku (Japan) tsunami, see **Figure 4**. Test radar sites are located at Bodega Marine Laboratory (BML1) on the US West Coast and Brant Beach (BRNT) on the US East Coast. BML1 has a steep offshore bathymetry profile, that is a narrow continental shelf; it also has low background noise. In contrast, BRNT has a shallow offshore bathymetry profile, that is a wide continental shelf, but this site has higher background noise. Our analysis shows that for these two radar sites, the offshore bathymetry dominates the tsunami detection capability. We compare predictions from the simulation with detections of real tsunamis: at BML1 of the 2011 Tohoku event and at BRNT of the 2013 meteotsunami.

**Figure 17** shows depth vs. distance offshore for the reference site and the two test sites.

Clearly, depths for BRNT are much less than those for BML1, which is advantageous for tsunami detection because it offers longer time from the first alert to the arrival at the coast. However, the signal‐to‐noise ratios for the BRNT antennas were observed to be about 20 dB less than those for BML1, indicating noisy spectra and reduced tsunami detection capability. This is an example of variations in local external noise that are sometimes seen among coastal HF radars.

As the Green's Law approximation applies only when the depth varies slowly compared to the tsunami wavelength, we consider distances from BML1 less than 19 km, which correspond to the edge of the continental shelf, see **Figure 17**. For BRNT, this limit does not apply, as here the continental shelf extends beyond the limits of the radar coverage.

**Figure 17.** Depth vs. distance from shore for A088 (black), BML1 (blue), and BRNT (red).

**• Step 5:** Steps 3 and 4 are repeated for a range of values of the factor *F*. The minimum value of *F*(*F*detect) is sought that will lead to an acceptable detection of the *q*‐factor peak, with an

**• Step 6:** The tsunami velocity (*V*detect) and height (*H*detect) necessary to produce an initial

æ ö <sup>=</sup> ç ÷

*Site detect detect Depth H V*

tsunami arrival. Note that in these equations, *V*detect and *H*detect define the values where the band velocities are measured, not values very close to shore in the run‐up zone, that can only be

These steps are repeated using a sliding 5‐h time window, running in the background of an operating radar system. The work described in this section is preliminary in nature and is being

We demonstrate the procedure for a single 5‐h time window using as reference band velocities measured by the Kinaoshi radar (A088) during the Tohoku (Japan) tsunami, see **Figure 4**. Test radar sites are located at Bodega Marine Laboratory (BML1) on the US West Coast and Brant Beach (BRNT) on the US East Coast. BML1 has a steep offshore bathymetry profile, that is a narrow continental shelf; it also has low background noise. In contrast, BRNT has a shallow offshore bathymetry profile, that is a wide continental shelf, but this site has higher background noise. Our analysis shows that for these two radar sites, the offshore bathymetry dominates the tsunami detection capability. We compare predictions from the simulation with detections of real tsunamis: at BML1 of the 2011 Tohoku event and at BRNT of the 2013 meteotsunami.

**Figure 17** shows depth vs. distance offshore for the reference site and the two test sites.

Clearly, depths for BRNT are much less than those for BML1, which is advantageous for tsunami detection because it offers longer time from the first alert to the arrival at the coast. However, the signal‐to‐noise ratios for the BRNT antennas were observed to be about 20 dB less than those for BML1, indicating noisy spectra and reduced tsunami detection capability. This is an example of variations in local external noise that are sometimes seen among coastal

init is the magnitude of reference velocity oscillation leading to a detection of the

3/4

*<sup>g</sup>* <sup>=</sup> (13)

(12)

*Site*

*Depth*

è ø

detection of the tsunami follow from Green's Law, Eqs (6) and (7):

V \*V \* *init Ref detect ref*

*Depth detect F*

acceptably low false‐alarm rate.

calculated using the highly nonlinear theory.

further developed in partnership with NOAA.

**6.2. Application at two test sites**

where ref

102 Tsunami

HF radars.

**Figure 18.** The multiplicative factor *F*detect required for detection of the initial approach of the simulated tsunami vs. range from the radar. Blue: BML1 and red: BRNT.

With the empirical detection algorithm applied to noisy background velocities, a nonlinear pattern results as the multiplicative factor *F* is varied in Step 5 of the evaluation analysis described in Section 6.1. As *F* is increased from zero, the *q*‐factor increases in stages as different components of the detection methods apply to the band velocities. When the *q*‐factor exceeds the preset limit, this defines the value of *F*(*F*detect) that signals a detection. Preset limits are set to produce minimal false alarms while allowing detection of observed tsunamis. In **Figure 18**, *F*detect is plotted vs. range from the radar: range is defined as the central value for the five 2‐km bands, for example, for bands 1–5 (distance from shore 0–10 km), the central value is 5 km.

Step 6 of the analysis procedure is then applied to estimate for each range the tsunami velocity and height necessary for the detection of the initial tsunami approach. Parameters to insert into Eqs (12) and (13) were estimated as follows: **Figure 7** indicates that the amplitude of the initial A088 (the reference) tsunami velocity oscillation V088 is about 9 cm/s averaged from 0 to 10 km from shore, where the mean depth is approximately 60 m. Substituting these values, the depths from the site and the values of *F*detect shown in **Figure 18**, into Eqs (12) and (13) leads to estimates for the tsunami velocity *V*detect and height *H*detect required for a detection of the initial simulated tsunami approach. **Table 3** shows these values as functions of distance from shore.


**Table 3.** Estimated tsunami velocity and height required for detection vs. range from the radar for the two sample test sites based on simulations using reference tsunami velocities from A088.

From **Table 3**, the height of the simulated tsunami required to trigger a detection is generally larger for BML1 than for BRNT particularly at greater ranges where the water is deeper. This occurs in spite of the lower BRNT signal‐to‐noise ratio, indicating that the shallow offshore bathymetry dominates the tsunami detection capability. We note that values shown in **Table 3** are noisy. Noise reduction will require the analysis of more extended data sets.

#### **6.3. Comparison of test predictions with prior observations of real tsunamis**

In this section, we compare predicted values of tsunami velocity required for a detection (shown in **Table 3**) with observations of real tsunamis at BML1 and BRNT.

#### *6.3.1. BML1*

*F*detect is plotted vs. range from the radar: range is defined as the central value for the five 2‐km bands, for example, for bands 1–5 (distance from shore 0–10 km), the central value is 5 km. Step 6 of the analysis procedure is then applied to estimate for each range the tsunami velocity and height necessary for the detection of the initial tsunami approach. Parameters to insert into Eqs (12) and (13) were estimated as follows: **Figure 7** indicates that the amplitude of the

to 10 km from shore, where the mean depth is approximately 60 m. Substituting these values, the depths from the site and the values of *F*detect shown in **Figure 18**, into Eqs (12) and (13) leads to estimates for the tsunami velocity *V*detect and height *H*detect required for a detection of the initial simulated tsunami approach. **Table 3** shows these values as functions of distance from

**Table 3.** Estimated tsunami velocity and height required for detection vs. range from the radar for the two sample test

From **Table 3**, the height of the simulated tsunami required to trigger a detection is generally larger for BML1 than for BRNT particularly at greater ranges where the water is deeper. This occurs in spite of the lower BRNT signal‐to‐noise ratio, indicating that the shallow offshore

sites based on simulations using reference tsunami velocities from A088.

**Range (km) BML1 BRNT BML1 BRNT** 7.9 11.7 21.6 11.7 11.5 27.4 34.2 30.3 20.8 13.7 65.1 16.4 22.0 17.2 71.0 22.0 10.8 23.2 25.9 31.4 40.6 13.3 129.0 18.9 24.5 23.5 86.2 34.2 84.1 5.6 306.0 8.3 21 5.4 8.2 11.8 18.2 30.6 47.9 21.3 33.9 17.4 28.2 58.5 96.0 33 6.5 10.9 25.9 43.7

**Velocity (cm/s) Height (cm)** 

is about 9 cm/s averaged from 0

initial A088 (the reference) tsunami velocity oscillation V088

shore.

104 Tsunami

About 9 h after the March 11, 2011 Japan earthquake, the Japan tsunami was detected at BML1; see **Figure 19**, which shows the measured band velocities and corresponding *q*‐factors close to the tsunami arrival.

**Figure 19.** BML1 results; start time March 11, 2011, 14:00 UTC: (a) band velocities vs. time. Blue: 0–2 km, red: 2–4 km, black: 4–6 km, and green: 6–8 km; (b) *q*‐factors vs. time obtained from analysis of velocities from five adjacent bands. Blue: 0–10 km, red: 2–12 km, black: 4–14 km, and green: 6–16 km.

Using a threshold of 250, the blue *q*‐factor peak for bands 1–5 indicates a detection of the Japan tsunami arrival at 15:45. **Figure 19(a)** shows that the amplitude of the initial tsunami velocity

oscillation at BML1 was about 7 cm/s. There was no detection of the initial tsunami approach further from shore.

From **Table 3**, the simulation test predicts that the tsunami velocity required for an initial detection at BML1 at a 5‐km range is ∼8 cm/s, which is approximately consistent with the observed velocity (7 cm/s) resulting in the initial detection of the Japan tsunami. The test indicates that larger tsunami velocities are required further from shore for detection to be possible. It also gives credibility to our simulation methodology.
