<p>Abrupt depth transitions have recently been identified as potential causes of `rogue' or extreme ocean waves. When stationary and (close-to) normally distributed waves travel into shallower water over an abrupt depth transition, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the abrupt depth transition, and new second-order free waves generated due to the abrupt depth transition.</p>
