**5.1. Simulation based on solution of the fundamental equations of motion**

To simulate tsunami height and velocity, Eqs (2) and (3) are solved numerically within the radar coverage area, typically out to ∼50 km from the coast. The offshore bathymetry is included as the depth variable, *d*(*x*,*y*), and the coastline becomes a boundary for the domain. First, the scalar Eq. (3) is solved for the tsunami wave height. Then, velocity is obtained by integrating the left side of Eq. (2) over time, after linearization as described in Section 2.1. This establishes the relations between the orbital velocity measured by the radar and the tsunami wave height, as well as provides the time of arrival at the coast from any point in the near‐field region.
