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

Abstract

Abstract. This work addresses the autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry 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 fitted 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 order multivariate autoregressive model estimated by stepwise least squares. Eigen-decomposition of the fitted model yields physically-interpretable seasonal modes. The leading autoregressive mode is an annual oscillation and exhibits a very homogeneous 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 tropical North Atlantic associated with the trade winds regime. The second mode is close to a semi-annual oscillation. Multivariate autoregressive models provide a useful framework for the description of time-varying fields while enclosing a predictive potential.

Using multiple time series analysis for geosensor data forecasting

“…Considering the multivariate analysis, De Luna and Genton [10] propose a suitable VAR model identification strategy, taking advantage of the spatial location of the different time series, which is particularly useful when data is rich in the time dimension but sparse in the spatial dimension, and the main objective is to provide time-forward predictions (as in our case). A strategy based on multivariate VAR models is discussed in [5] as well.…”

Composite Analysis-Based Machine Learning for Prediction of Tropical Cyclone-Induced Sea Surface Height Anomaly

“…For example, in the Eastern Equatorial Pacific, a polynomial-harmonic model with the least-squares method was proposed to predict the gridded SSHA [16]. Along the mid-Atlantic, based on the empirical model decomposition, in the North Atlantic, a multivariate autoregressive method was proposed to predict the seasonal SSHA variability [17]. Data-driven approaches can predict the SSHA very well with a lower demand of prior knowledge.…”

Shifts in the Spatiotemporal Dynamics of Schistosomiasis: A Case Study in Anhui Province, China

“…We first implement a multivariate autoregressive model to assess the changes in schistosoma infection in Anhui Province of China, using annual county-level prevalence data for the period 1997–2010. We employed the principal oscillation pattern (POP) analysis, a multivariate technique to empirically infer the characteristics of the space-time variations of a possibly complex system [ 15 ], to detect the spatio-temporal variation of schistosomiasis risk over our study period. Concluding remarks are finally presented with regards to the results.…”