Copyright © 2010 Esteban Flores and José R. León R. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We apply Rice's multidimensional formulas, in a mathematically rigorous
way, to several problems which appear in random sea modeling. As a first example, the probability
density function of the velocity of the specular points is obtained in one or two dimensions as well
as the expectation of the number of specular points in two dimensions. We also consider, based on a
multidimensional Rice formula, a curvilinear integral with respect to the level curve. It follows that its
expected value allows defining the Palm distribution of the angle of the normal of the curve that defines
the waves crest. Finally, we give a new proof of a general multidimensional Rice formula, valid for all
levels, for a stationary and smooth enough random fields .