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

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 by an arbitrary factor *F* that can be varied to adjust the height of the simulated tsunami approaching the test site. This process is encapsulated in Eq. (11) for a given band:

$$V\_{\rm Sun} = V\_{\rm Sun} + F \ast V\_{\rm Rf} \ast \left( \begin{matrix} \text{Depth}\_{\rm Rf} \\ \text{ } \end{matrix} \bigg/ \text{Depth}\_{\rm Sn} \right)^{\text{3/4}} \tag{11}$$

where *V*Sim is the simulated velocity that for *F* = 1 would be observed if the reference tsunami approached the test site and DepthSite and DepthRef are the average depths across the band for the test and reference sites. Increasing/decreasing the value of *F* will increase/decrease the size of the simulated velocity.

Simulated band velocities calculated using this approximate method are currently used to evaluate the suitability of radar sites for tsunami detection, as described in the next section.
