Spatial Interpolation of Wave Fields Based on Limited Spatial Measurements

In experimental campaigns investigating space-time varying signals, e.g., evolving wave fields, it is common for the spatial resolution not to be as high as desired to properly capture the spatial variability of propagating water waves. This is often due to unavoidable experimental, technical, and cost constraints. To overcome this limitation, we present a relatively simple procedure (called S-interp) to interpolate wave fields at spatial locations where no measurements are available. S-interp consists of the interpolation of wave fields along points being at the same phase. The main hypothesis of S-interp is that the wave field follows a linearlike evolution along points being at the same phase. Therefore, along these points, differences between the interpolated and the actual wave fields are minimal. We use S-interp to successfully reconstruct missing areas of experimental nonbreaking wave conditions. These wave conditions are focused wave events recorded by video cameras, whose wave fields are measured by surface detection analysis of the video images. Overall, the hypothesis of S-interp is seen to be valid even at the focal wave crest, where the performance of S-interp is assessed in terms of the normalized error. The main source of error for S-interp is seen to be the spacing between the probes, whereas the nonlinear effects of the wave fields seem secondary. The recommended spacing between probes when using S-interp is at most 10${\%}$ of the characteristic wavelength to guarantee an upper limit of the error below 5${\%}$. The potential application of S-interp to random sea-states is discussed.