Space-time prediction of ocean winds

Anders Malmberg

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology

ISBN 91-628-6489-0

The topic of this thesis is inspired by an experiment in which a vessel, laying a submarine cable, was provided with forecasts overlaid with satellite observations of significant wave height. During the
operation, the vessel was close to an adverse weather area and the personnel on board could confirm that the forecast was not as close to the "ground truth" as the satellite observation was. One of the outcomes of this experiment was the suggestion to develop a method providing forecasts merged with satellite observations. In this thesis such a method is developed for near-surface ocean winds.
The thesis consists of four papers (Paper A-D). The contribution of Paper A and B is the development of a statistical framework, in which forecasts and satellite observations in a bounded area are merged and a measure of uncertainty is provided. A dimension-reduced Kalman filter is used as an emulator of the atmospheric dynamics. This is considered in Paper A. The method of merging Kalman filter forecasts with satellite measurements is developed in Paper B.
Closely related to Paper A and B is the problem of modelling the covariance structure of residuals taken as differences between forecasts and satellite measurements. Two isotropic covariance functions belonging to the Mat\'{e}rn family are used. However, neither of the functions seem to properly model the residual field. The contribution of Paper C is an explorative study and it forms a basis for further research.
Finally, Paper D models the dynamics of a spatio-temporal process based on an image warping approach. Image warping models the dynamics through the movement of a set of control points. As well as allowing affine transformations, the model also allows for non-linear dynamics. The main contribution of this paper is the formulation of a penalised likelihood which is used to estimate the model.
Space-time Kalman filtering; near-surface ocean winds;
real-time assimilation; residual wind speed; variogram parameters;
image warping; thin-plate splines.