**4.1. Origin of meteotsunamis and nature of the June 13, 2013 event**

A meteotsunami is generated by an atmospheric pressure disturbance traveling across the sea. An atmospheric anomaly (a low‐ or high‐pressure center) will produce a small peak or trough moving at the same speed on the sea surface beneath it. This results in a freely propagating surface wave that increases in amplitude when the speed of atmospheric anomaly *vaa* matches the shallow‐water wave phase velocity *vph(d)*. This is known as Proudman resonance, see [17]. The speed *vaa* of the June 13, 2013 derecho was about 21.1 m/s [15]. Substituting this value for *vph(d)* into Eq. (5), it follows that the onset of the independent wave occurs at a depth *d* equal to 45 m, which lies about 60 km off the New Jersey coast.

This meteotsunami was unusual because it was generated by a frontal pressure anomaly traveling offshore. Yet coastal sensors including HF radars indicate that the meteotsunami approached the coast. Numerical models [8] indicate that a strong reflection occurred at the shelf edge about 110–120 km offshore, where the depth decreases from 100 to 1200 m over a distance of 20 km. The reflection is greater when a wave interacts with a drop‐off rather than a step‐up with the same slope. Data from New Jersey radars confirm the existence of a wave reflected from the shelf edge back toward the coast. This wave was also detected by coastal tide gauges.

To explain these results, we consider the interaction of the tsunami with a hard boundary, assuming a single pulse of water approaching the coast, that is, a traveling wave. The forward velocity is maximum at the wave crest. As a boundary is approached, there is a hard reflection: the velocity goes to zero and the height doubles. This is known as the Neumann boundary condition. After a period of time from the reflection, a single wave travels outwards, with the crest velocity and height maxima in phase again.

In reality, the situation is more complex. Instead of a single wave or soliton, a series of positive and negative tsunami peaks often resemble a sine wave for height and velocity. The hard‐wall boundary condition causes the height peaks to lag the velocity peaks by as much as a quarter cycle, which is termed the "quadrature effect." After reflection, the height stays positive but the velocity amplitude becomes negative. The interaction of incoming and reflected waves constitutes a more complex partial standing‐wave situation, which is well handled by numer‐ ical model solutions.
