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This work addresses the autoregressive modelling of sea level time series from TOPEX/Poseidon satellite al- timetry mission. Datasets from remote sensing applications are typically very large and correlated both in time and space. Multivariate analysis methods are useful tools to summarise and extract information from such large space-time datasets. Multivariate autoregressive analysis is a generalisation of Principal Oscillation Pattern (POP) analysis, widely used in the geosciences for the extraction of dynamical modes by eigen-decomposition of a first order autoregressive model fit- ted to the multivariate dataset of observations. The extension of the POP methodology to autoregressions of higher order, although increasing the difficulties in estimation, allows one to model a larger class of complex systems. Here, sea level variability in the North Atlantic is modelled by a third or- der multivariate autoregressive model estimated by stepwise least squares. Eigen-decomposition of the fitted model yields physically-interpretable seasonal modes. The leading autore- gressive mode is an annual oscillation and exhibits a very ho- mogeneous spatial structure in terms of amplitude reflecting the large scale coherent behaviour of the annual pattern in the Northern hemisphere. The phase structure reflects the seesaw pattern between the western and eastern regions in the trop- ical North Atlantic associated with the trade winds regime. The second mode is close to a semi-annual oscillation. Mul- tivariate autoregressive models provide a useful framework for the description of time-varying fields while enclosing a predictive potential. such large datasets and characterise the dynamical properties of the associated geophysical time series. This work focuses on the autoregressive modelling of time series of sea surface heights from TOPEX/Poseidon satel- lite altimetry mission. Sea level is a key indicator of climate change and an important observational constraint on global climate models. Furthermore, sea level changes have consid- erable environmental, social and economical impacts. The height of the sea surface relative to a geocentric reference ellipsoid is measured from space through radar altimetry. TOPEX/Poseidon (T/P) mission achieved an unprecedented accuracy, yielding a huge, high quality, space-time dataset of precise sea level measurements. A stochastic space-time process {Xs,t} is defined as a col- lection of random variables indexed by parameters (s,t)2R 2 where t indicates time and s a location. Observed values of {Xs,t} from m spatial locations (s=1,...,m) at N times (t=1,...,N ) constitute a realisation of the stochastic process {Xs,t}. The term field is used hereafter to designate a partic- ular realisation and is denoted by

Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry