Velocities for Random Surfaces
Anastassia Baxevani, Krzysztof Podgórski, Igor Rychlik
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2002
ISSN 14039338

Abstract:

For a stationary twodimensional random field evolving in time, we derive
statistical distributions of appropriately defined velocities.The results
are based on a generalization of the Rice formula. We discuss importance
of identifying the correct form of the distribution which accounts for the
sampling bias. The theory can be applied to practical problems where evolving
random fields are considered to be adequate models. Examples include changes
of atmospheric pressure, variation of air pollution, or dynamical models
of the sea surface elevation. We study the last application in more detail
by applying

the derived results to Gaussian fields representing irregular sea surfaces.
In particular, we study statistical properties of velocities both for the
sea surface and for the envelope field based on this surface. The latter
is better fitted to study wave group velocities and is of particular interest
for engineering applications. For wave and wave group velocities, numerical
computations of distributions are presented and illustrated graphically.

