3.1.1. Observations of Total Velocity Current Maps
As our first example, we analyzed data from two radars located near Usujiri and Kinaoshi, Hokkaido, Japan,
Figure 1(b,c). The radars have a transmit frequency of 42 MHz and a range increment of 0.5 km with a total range of 15 km. The water depth over the total radar coverage area is less than 200 m.
Figure 1(c) shows an example of radial current velocities measured at Kinaoshi. The current flow from 11 March, 14:06 JST to 12 March, 13:54 JST is shown in a video clip (see supplementary media file); the earthquake occurred on 11 March 14:46 JST. The direction and strength of the flow was measured at approximate 4-minute intervals with a cell resolution of 0.5 km × 0.5 km. The maps, which display the tsunami current superimposed on the normal background flow, show the tsunami sweeping in and out of Uchiura Bay. Equation (3) relates the tsunami height and current velocity. In general, to obtain the tsunami height from Equation (3), the long-term trends need to be subtracted from the velocities to reduce the effects of the normal background flow. We chose two times for which the tsunami current appears to dominate the background flow, the first signals the tsunami arrival with inward flow, the second with strong outward flow.
Figure 2 shows the tsunami height superimposed on the total current velocity field at these two times. As noted in
Section 2, the height estimates from Equation (3) are not expected to be accurate very close to the shore.
Figure 2.
The tsunami height superimposed on the total current velocity field measured by radars at Usujiri (blue dot) and Kinaoshi (red dot): (a) 11 March 2011, 15:53 JST; (b) 11 March 2011, 21:00 JST.
Figure 2.
The tsunami height superimposed on the total current velocity field measured by radars at Usujiri (blue dot) and Kinaoshi (red dot): (a) 11 March 2011, 15:53 JST; (b) 11 March 2011, 21:00 JST.
3.1.2. Observations of Radial Velocity Components
The tsunami signal is also visible in the radar return from a single radar site. We use a simplified model to demonstrate the basic behavior. Assuming that the water depth over the radar coverage area can be adequately represented by parallel depth contours, a tsunami will move perpendicular to these contours. To detect the approach, the radial velocity component was resolved perpendicular to the depth contours, as described by Lipa
et al. [
2], averaged over bands parallel to the depth contours and plotted
vs. time from the earthquake for Japan sites, or from a time just prior to arrival for US sites. These velocities were compared with tide gauge measurements of water level.
This method was applied to data from the radar at Kinaoshi,
Figure 3 shows the location of the radar and tide gauge and the offshore bathymetry.
Figure 4(a,b) shows the averaged radial velocity component for Kinaoshi, for six 2-km bands ranging from 2 km to 14 km from the shore. Tidal effects are also evident in the resulting velocity components: the arrival of the tsunami causes marked oscillations, which are superimposed on the normal tidal background.
Figure 4(c) shows the water levels measured by a tide gauge at Hakodate, about 35 km southwest of the radar site; these data were provided by the Japan Meteorological Agency. The details of the radar and tide gauge plots differ, which is to be expected as height and current are not in phase with each other, but are determined by boundary conditions at the coast. In particular, the velocity oscillations begin about 43 minutes before the measured water level oscillations. Reasons for this effect are discussed in
Section 3.3.
Figure 3.
The bathymetry offshore from the radar at Kinaoshi and the tide gauge at Hakodate.
Figure 3.
The bathymetry offshore from the radar at Kinaoshi and the tide gauge at Hakodate.
Figure 4.
Time series of velocity components from the Kinaoshi radar (42 MHz transmitter frequency) and simultaneous water level observations from the Hakodate tide gauge. Radial velocity was resolved perpendicular to the shore, and averaged over bands 2 km wide parallel to the depth contours.
Figure 4.
Time series of velocity components from the Kinaoshi radar (42 MHz transmitter frequency) and simultaneous water level observations from the Hakodate tide gauge. Radial velocity was resolved perpendicular to the shore, and averaged over bands 2 km wide parallel to the depth contours.
Tidal current velocities normal to the depth contours are most evident before the arrival of the tsunami, and as expected increase roughly linearly with range with the weakest current velocities close to the shore, decreasing to zero at the shoreline. The arrival of the tsunami is indicated by the commencement of distinctive oscillations in velocity, which appear to be approximately coherent with a period of about 40 minutes.
We also examined the effect of the tsunami on radial velocities measured on the western US coast and compared the results with tide-gauge measurements of water level obtained by NOAA’s Center for Operational Oceanographic Products and Services (
http://tidesandcurrents.noaa.gov/).
Figure 5 shows the location of the radar at Bodega Bay, California and the offshore bathymetry. A measured radial velocity map is shown, with a reverse flow generated by the tsunami in the inner range cells. The radar has 13 MHz transmit frequency and 2 km range increments.
Figure 6(a,b) shows the component of the radial velocity perpendicular to the shore averaged over four 2-km bands ranging from 0 to 8 km from shore.
Figure 6(c) shows the water levels measured by a tide gauge at Pt. Reyes, about 40 km south of the radar site. The radar detects the tsunami about 12 minutes before the tide gauge, at approximately 16:00 UTC.
As a third example, we analyzed the data from the radar at Trinidad River, California.
Figure 7 shows the location, offshore bathymetry and a measured radial velocity map. We again see the reverse flow generated by the tsunami in the inner range cells. This is a long-range radar with 5 MHz transmit frequency and 6-km range increments.
Figure 8(a,b) shows component of the radial velocity perpendicular to the shore for four 4-km bands ranging from 0 to 16 km from shore.
Figure 8(c) shows the water levels measured by a tide gauge at Crescent City, about 70 km north of the radar site. The radar detects the tsunami about 14 minutes before the tide gauge, at approximately 16:00 UTC, as at Bodega Bay.
Figure 5.
The location of the radar at the Bodega Marine Lab., California, the offshore bathymetry and a measured radial velocity map. Measured radial velocities are for 11 March 2011, 16:52 UTC, and show the reverse flow generated by the tsunami in the inner range calls.
Figure 5.
The location of the radar at the Bodega Marine Lab., California, the offshore bathymetry and a measured radial velocity map. Measured radial velocities are for 11 March 2011, 16:52 UTC, and show the reverse flow generated by the tsunami in the inner range calls.
Figure 6.
Time series of velocity components from the radar at Bodega Bay and simultaneous water level observations from the Point Reyes tide gauge. Radial velocities were resolved perpendicular to the shore, and averaged over bands 2-km wide parallel to the shore.
Figure 6.
Time series of velocity components from the radar at Bodega Bay and simultaneous water level observations from the Point Reyes tide gauge. Radial velocities were resolved perpendicular to the shore, and averaged over bands 2-km wide parallel to the shore.
Figure 7.
The location of the radar at Trinidad River, California, the offshore bathymetry and a measured radial velocity map. Measured radial velocities are for 11 March 2011, 17:36 UTC, and show the reverse flow generated by the tsunami in the inner range calls.
Figure 7.
The location of the radar at Trinidad River, California, the offshore bathymetry and a measured radial velocity map. Measured radial velocities are for 11 March 2011, 17:36 UTC, and show the reverse flow generated by the tsunami in the inner range calls.
Figure 8.
Time-series of radial velocities measured by the long-range radar at Trinidad River and simultaneous water level observations from the Crescent City tide gauge. Radial velocities were resolved perpendicular to the shore, and averaged over bands 4-km wide parallel to the shore.
Figure 8.
Time-series of radial velocities measured by the long-range radar at Trinidad River and simultaneous water level observations from the Crescent City tide gauge. Radial velocities were resolved perpendicular to the shore, and averaged over bands 4-km wide parallel to the shore.