Abstract
The characterisation and quantification of long-term sea-level variability is of considerable interest in a climate change context. Long time series from coastal tide gauges are particularly appropriate for this purpose. Long-term variability in tide gauge records is usually expressed through the linear slope resulting from the fit of a linear model to the time series, thus assuming that the generating process is deterministic with a short memory component. However, this assumption needs to be tested, since trend features can also be due to non-deterministic processes such as random walk or long range dependent processes, or even be driven by a combination of deterministic and stochastic processes. Specific methodology is therefore required to distinguish between a deterministic trend and stochastically-driven trend-like features in a time series. In this chapter, long-term sea-level variability is characterised through the application of (i) parametric statistical tests for stationarity, (ii) wavelet analysis for assessing scaling features, and (iii) generalised least squares for estimating deterministic trends. The results presented here for long tide gauge records in the North Atlantic show, despite some local coherency, profound differences in terms of the low frequency structure of these sea-level time series. These differences suggest that the long-term variations are reflecting mainly local/regional phenomena. © 2008 Springer-Verlag Berlin Heidelberg.

Abstract
Sea level is a key variable in the context of global climate change. Climate-induced variability is expected to affect not only the mean sea level but also the amplitude and phase of its seasonal cycle. This study addresses the changes in the amplitude and phase of the annual cycle of coastal sea level in the extra-tropical North Atlantic. The physical causes of these variations are explored by analysing the association between fluctuations in the annual amplitude of sea level and in ancillary parameters [atmospheric pressure, sea-surface temperature and North Atlantic Oscillation (NAO) winter index]. The annual cycle is extracted through autoregressive decomposition, in order to be able to separate variations in seasonality from long-term interannual variations in the mean. The changes detected in the annual sea level cycle are regionally coherent, and related to changes in the analysed forcing parameters. At the northern sites, fluctuations in the annual amplitude of sea level are associated with concurrent changes in temperature, while atmospheric pressure is the dominant influence for most of the sites on the western boundary. The state of the NAO influences the annual variability in the Southern Bight, possibly through NAO-related changes in wind stress and ocean circulation.

Abstract
Quantile regression is applied for characterizing long-term sea-level variability in the Baltic Sea from long tide gauge records. The approach allows to quantify not only variability in the mean but also in extreme heights and thus provides a more complete description of regional sea-level variability. In the Baltic, slopes in minima are similar to the classical mean-based ordinary least squares slope, but maxima exhibit larger trends, particularly at the northernmost stations, in the Gulf of Bothnia, likely associated with changes in north Atlantic atmospheric circulation and particularly regional wind patterns. Citation: Barbosa, S. M. ( 2008), Quantile trends in Baltic sea level, Geophys. Res. Lett., 35, L22704, doi: 10.1029/2008GL035182.

Abstract

Abstract
In this article, we introduce an iterative subspace system identification algorithm for MIMO linear parameter-varying systems with innovation-type noise models driven by general inputs and a measurable white noise time-varying parameter vector. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state-space approximations, thus considered a Picard-based method. Such methods have proven to be convergent for the bilinear state-space system identification problem. Their greatest strength lies on the dimensions of the data matrices that are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.

Abstract
In this paper a successive approximation approach for MIMO linear parameter varying (LPV) systems with affine parameter dependence is proposed. This new approach is based on an algorithm previously introduced by the authors, which elaborates on a convergent sequence of linear deterministic-stochastic state-space approximations. In the previous algorithm the bilinear term between the time varying parameter vector and the state vector is allowed to behave as a white noise process when the scheduling parameter is a white noise sequence. However, this is a strong limitation in practice since, most often than not, the scheduling parameter is imposed by the process itself and it is typically a non white noise signal. In this paper, the bilinear term is analysed for non white noise scheduling sequences. It is concluded that its behaviour depends on the input sequence itself and it ranges from acting as an independent colored noise source, mostly removed by the identification algorithm, down to a highly input correlated signal that may be incorrectly assumed as being part of the system subspace. Based on the premise that the algorithm performance can be improved by the noise energy reduction, the bilinear term is expressed as a function of past inputs, scheduling parameters, outputs, and states, and the linear terms are included in a new extended input.