Validating the diffusion model for long-term coastal profile evolution

Abstract

An algorithm for the simultaneous determination of two coefficients in an inverse problem for equations of the parabolic type is studied. The model under investigation has been proposed by H. de Vriend and M. Capobianco to describe the long-time coastal profile evolution. The iterative inversion procedure is based on the minimization of a suitable cost functional. Results of numerical tests are shown to illustrate the performance of the algorithm. The real measured data of the coastal profile evolution have been numerically processed to validate the aforementioned diffusion type model.

Modelling and predicting coastal zone depth profile evolution: a survey

“…In Figure 2, a 3D plots of the profiles, p dir (z, t) = u comp (z, t) + p(z, 0) and p exp (z, t) = u meas (z, t) + p(z, 0) (p(z, 0) being the depth profile at the initial time moment) for the Delfland data are shown. Summarizing, one can conclude that (see [13,23] for details):…”

“…A formal Fourier-type transform (or a formal Laplace-type transform as in [23]) was used to reduce the problem dimension. More precisely, to solve the original problem, the Fourier-type (or Laplacetype)representation ( 5)…”

“…In [23,30], a first attempt was made to address the 2D problem, that is to study the evolution of both, the shoreline and the depth profiles. Several 1D problems, treated as was described in Section 3 for a single 1D case, at several fixed y i 's, for i = 1, 2, .…”

“…In [23] the problem for equation ( 2) was considered applying a discrete version of the Laplace type transform (see (5)). First, the coefficients, D(z) and B(z), were supposed equal at all 30 observation points along the coast.…”