**Gothenburg and Varberg, 26-28 September 2007**

Wednesday 26 September: Seminars 10.15-12.00 (MV:L14). Preliminary program for the rest of the workshop can be found below.

**Hidden Markov models for wind time series**

Pierre Alliot and Valerie Monbet, Laboratoire de Statistique Appliquée, Université de Bretagne Sud

Abstract: The fist part of the talk will consist in a brief introduction to Hidden Markov Models (HMM) through various applications of these models to wind time series. After a general introduction, we will focus on HMM with finite hidden state space. These models block time series into consecutive periods of time within which the observations follow a simple regime dependent time series model. Switching between regimes is governed by an unobserved Markov chain. We will see that it leads to simple and open structure which allows direct modelling of various time scales that are present in wind data, as well as opportunities for enhanced interpretation and more physically based models.

In the second part of the talk, we will focus on HMM with non-finite hidden state-space (state-space models). Such models are commonly used to correct the numerical weather predictions. Generally, a linear state-space model is used, the hidden process representing the "error" of the numerical model. Then, the numerical prediction can be corrected using in-situ observations and the Kalman filter. In this talk, a more sophisticated model will be proposed: we will assume that the error can be decomposed in two terms, a level error and a phase error. For example, if we consider a storm passing through, the level error misjudges the severity of the storm and the phase error the time of arrival of the storm. These two terms will be included in the hidden state-space, leading to a non-linear state space model. We will see that this more sophisticated model leads to better prediction, but also

to complicated numerical issues for both parameters and state identification.

**Spatio-temporal modelling of significant wave height**

Anastassia Baxevani, Department of Mathematical Statistics, Chalmers University of Technology.

Abstract: Significant wave height, Hs, is a measure of the variability of the ocean surface and is defined to be four times the standard deviation of the height of the ocean surface. Estimates of Hs can be considered as two dimensional random field that develops over time. We propose a method for constructing models for estimates of Hs based on fitting random field models. The proposed model is parametric and the spatial parameters are estimated applying a new methodology based on total variation on the Hs estimates from the TOPEX-Poseidon satellite.

For the temporal correlation of the field we assume a parametric covariance function, whose parameters are related to those of the spatial correlation through the velocity with which the field is drifting. The spatial and temporal models are then combined to give a stationary spatio-temporal model that is valid over small areas and for short periods of time.

Finally the model is extended to a non-homogeneous one that is valid over large areas of the sea and for time periods up to ten hours.

Program.pdf