Reflection, anyone?

Looks like a reflected wave finding its incident soul mate

Exciting!

WOW! After several pages, I finally derived the analytic expression of the percentage error in depth (Delta h /h) and its dependency on percentage errors in the radian frequency (Delta sigma / sigma), wavenumber (Delta k /k) and wave amplitude (Delta A /A). The surprising feature is that the error in h shows a varying dependency on the value of A.

That is, when A=0 (linear case), the error exhibits a monotonic dependency on kh, ever increasing. But as A increases, the curve shows a a shape that resembles a parabolic curve. If A is large enough, the trend is that for low kh, the error is larger.

Error in Delta h/h as a function of kh, when perturbations are induced in A, sigma, k. Note the strong influence of A on the functional response of the error. However, errors in A induce small errors in h

The figure above shows three amplitude conditions, when evaluated over the DELILAH bathymetry and wave conditions. The influence of A is evident, and suggest that perhaps a measure of nonlinearity needs to be included in the analysis. Ursell anyone?