Modelling Sea Surface Dynamics Using Crossing Distributions
Centre for Mathematical Sciences
The thesis deals mainly with modelling sea surface dynamics. We consider
two different scales. The short-term scale,known as sea state, in which the
sea surface over a restricted time period and space can be modelled as a
stationary random field, and the long-term scale in which we study the evolution
of wave characteristics like the significant wave height H_s, over long periods
of time and at great geographic regions.
The main statistical tools are crossing distributions, which are given by
a generalisation of Rice's formula which is valid under mild conditions.
In the short-term scale, we consider the sea surface as a Gaussian stationary
random field. Study of the motion of such a surface should include the notion
of velocity. Different velocities, that capture different aspects of the
sea dynamics, are defined and their statistical distributions are obtained.
Also of interest is the effect the wave kinematics have on the distribution
of global maximum. It is observed that taking into account time dynamics
of spatial characteristics results in distributions different than those
obtained for the static case.
Satellites orbiting around the earth provide with global spatial coverage
of the ocean surfaces. The logarithmic values of H_s are modelled as a locally
stationary Gaussian random field. The mean value varies seasonally and
geographically and the covariance structure is modelled as a sum of two
independent sources, one in a coarser and one in a finer scale. To capture
the temporal variability velocities, that enter the covariance structure
as parameters, are used. Wave climate of H_s is of importance for different
applications, like for example estimation of the fatigue accumulated by a
vessel sailing a certain route.
Gaussian random fields, level crossings, Rice formula, global maximum, velocities