Sofia Åberg försvarar sin doktorsavhandling

Applications of Rice's formula in oceanographic and environmental problems
 
Abstract
	
This thesis is based on five papers (A-E), all treating various
applications of Rice's formula. The areas of application are
oceanographic and environmental problems.

The first three papers treat properties of encountering waves, that
is, waves that a ship encounters while sailing on the ocean. Paper A a
ddresses the problem of computing the intensity of such waves and, in
particular, the intensity of encountering waves that overtake the sh
ip. A general formula for this intensity is given and it is shown that
for a Gaussian sea it takes an explicit form.  The aim of Paper B is
to compute distributions of properties of the overtaking, encountering
waves in a Gaussian sea. Besides giving integ ral formulas for the
distribution of wave slope and the joint distribution of waveheight
and half-wavelength, we also give interpretation of the results in
terms of wave velocity. The results are illustrated by numerical
examples. Next, in Paper C, the distribution of wavehei ght and
half-wavelength is further explored. More precisely, we propose an
approximation of the distribution, which is inspired by the vel ocity
interpretation in Paper B. This approximation is evaluated for a
Gaussian sea having a Pierson-Moskowitz spectrum.

Paper D is devoted to the study of wave intensity and the distribution
of slope in a Lagrangian sea model. Two different cases are conside
red, namely the sea surface observed at a fixed time point and at a
fixed location, respectively. Formulas for the wave intensity and slop
e are given for these two cases, and the results are compared to the
Gaussian sea model.

In the last paper, Paper E, we consider some aspects of the
statistical quality of air quality standards. More precisely, we want
to illum inate the danger of not taking the spatial variability of the
air pollution concentrations into account in the design of the
standards. Th is is illustrated by computing upper and lower bounds
for the distribution of the maximum of the pollutant concentration in
a region aroun d the site where the measurement is taken. The maximum
is computed conditional on a measurement being exactly at the level
prescribed by t he standard.