*3.4.1. Hokkaido, Japan*

**Figure 6** shows the locations of two radars on the Kameda Peninsula, the neighboring tide gauge, and the offshore bathymetry. The water depth is less than 200 m over the radar coverage area; we found that the tsunami signal is visible in the current velocities out to the radar range limits.

**Figure 6.** The location of the radars A087, A088, the tide gauge at Hakodate, and the offshore bathymetry.

**Figure 7.** Perpendicular band velocities from A088 and derived *q*‐factors. (a) Distance from radar: 0–2 km (blue), 2–4 km (red), and 4–6 km (black). (b) The *q*‐factor for range 0–6 km. (c) Distance from radar: 6–8 km (blue), 8–10 km (red), and 10–12 km (black). (d) The *q*‐factor for range 6–12 km.

**Figure 7** shows A088 band velocities obtained over a 5‐h period and the *q*‐factors resulting from application of the analysis described in Section 3.3. About an hour after the earthquake, the tsunami arrived at A088, resulting in distinctive correlated oscillations in the perpendicular band velocities, which lead to a *q*‐factor peak that indicates the tsunami arrival.

Close to shore, part of the tsunami flow is diverted by the steep bathymetry to move parallel to the coast, resulting in a reduced signal in the perpendicular component plotted in **Figure 7**. As discussed in Section 2, this effect can be shown by exact PDE modeling.

The analysis procedure was applied to A087 and A088 for all permutations of three band velocities that contained the tsunami signal, and the resulting *q*‐factors were summed. The *q*‐factor threshold was defined to be 500: the first *q*‐factor to exceed this value was taken as defining the tsunami arrival time. The arrival time at the tide gauge was defined as first tsunami peak in the water‐level reading. Radar and tide gauge arrival times are shown in **Table 1**.


**Table 1.** Tsunami arrival times at the Hokkaido radars and the closest tide gauge.

**Table 1** shows that the arrival times obtained from the radar *q*‐factors reported are in the correct order: the tsunami arrives at Station A087 further from the earthquake location approximately 5 min after it reaches A088. Arrival times measured by the radars preceded those at the neighboring tide gauge by an average of 40 min, due both to the "quadrature relation" between velocity and height (discussed later in Section 4.1) and the tsunami propagation delay between the two observations.
