An original method for characterizing internal waves

An empirical orthogonal function analysis is applied to the data. The first two spatial empirical modes represent over 99% of the variability, and their corresponding time-dependent expansion coefficients take higher absolute values during internal wave events. In order to check how the expansion coefficients vary during an internal wave event, their time derivative, called here changing rates, are computed. It shows that each wave of an internal wave train is characterized by a double oscillation of the changing rates. At the front of the wave, both changing rates increase in absolute value with opposite sign, and then decrease to become null at the maximum amplitude of the wave. At the rear of the wave, the changing rates describe another period, again with opposite sign. This double oscillation can be used as a detector of internal waves, but it can also give information on the width of the wave, by measuring the length of the oscillation, as this information may sometimes be hard to read straight out of the data. When plotting the changing rates one versus another, the resulting scatter diagram puts on a butterfly shape that illustrates well this behaviour.