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 autoreerressive 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.

Abstract
The North Atlantic Oscillation (NAO) is one of the most important climatic patterns in the Northern Hemisphere. Indices based on the normalised pressure difference between Iceland and a Southern station, such as Lisbon or Gibraltar, have been defined in order to describe NAO temporal evolution. Although exhibiting interannual and decadal variability, the signals are statistically rather featureless and therefore it is difficult to discriminate between different types of stochastic models. In this study, Lisbon and Gibraltar NAO winter indices are analysed using the discrete wavelet transform discrete wavelet transform(DWT). A multi-resolution analysis (MRA) is carried out for a scale-based description of the indices and the wavelet spectrum is used to identify and estimate long-range dependence. The degree of association of the two NAO indices is assessed by estimating the wavelet covariance for the two signals. The scale-based approach inherent to the discrete wavelet methodology allows a scale-by-scale comparison of the signals and shows that although the short-term temporal pattern is very similar for both indices, the long-term temporal structure is distinct. Furthermore, the degree of persistence or 'memory' is also distinct: the Lisbon index is best described by a long-range dependent (LRD) process, while the Gibraltar index is adequately described by a short-range process. Therefore, while trend features in the Lisbon NAO index may be explainable by long-range dependence alone, with no need to invoke external factors, for the Gibraltar index such features cannot be interpreted as resulting only from internal variability through long-range dependence. Copyright (C) 2006 Royal Meteorological Society.

Abstract
Sea level is an important parameter in climate and oceanographic applications. In this work the scaling behavior of sea level is analyzed from time series of sea level observations. The wavelet domain is particularly attractive for the identification of scaling behavior in an observed time series. The wavelet spectrum from a scale-by-scale wavelet analysis of variance reproduces in the wavelet domain the power laws underlying a scaling process, allowing the estimation of the scaling exponent from the slope of the wavelet spectrum. Here the scaling exponent is estimated in the wavelet domain for time series of sea level observations in the North Atlantic: at coastal sites from tide gauges, covering 50 years of monthly measurements, and in the open ocean from satellite altimetry, covering 12 years of satellite measurements at 10 days intervals. Both tide gauge and altimetry time series exhibit scaling behavior. Furthermore, the degree of stochastic persistence is spatially coherent and distinct at the coast and in the open ocean. Near the coast, the stochastic structure of the sea level observations is characterized by long-range dependence with a moderate degree of persistence. Larger values of the scaling exponent, consistent with weaker persistence, are concentrated in the northern Atlantic. At mid-latitudes the stochastic dependence of sea level observations is characterized by strong persistence in the form of strong long-range and 1/f dependence.

Abstract
This study addresses the impact of satellite altimetry data processing on sea level studies at regional scale, with emphasis on the influence of various geophysical corrections and satellite orbit on the structure of the derived interannual signal and sea level trend. The work focuses on the analysis of TOPEX data for a period of over twelve years, for three regions in the North Atlantic: Tropical (0 degrees <= phi <= 25 degrees), Sub- Tropical (25 degrees <= phi <= 50 degrees) and Sub-Arctic (50 degrees <= phi <= 65 degrees). For this analysis corrected sea level anomalies with respect to a mean sea surface model have been derived from the GDR-Ms provided by AVISO by applying various state-of-the-art models for the geophysical corrections. Results show that sea level trend determined from TOPEX altimetry is dependent on the adopted models for the major geophysical corrections. The main effects come from the sea state bias (SSB), and from the application or not of the inverse barometer (IB) correction. After an appropriate modelling of the TOPEX A/B bias, the two analysed SSB models induce small variations in sea level trend, from 0.0 to 0.2 mm/yr, with a small latitude dependence. The difference in sea level trend determined by a non IB-corrected series and an IB-corrected one has a strong regional dependence with large differences in the shape of the interannual signals and in the derived linear trends. The use of two different drift models for the TOPEX Microwave Radiometer (TMR) has a small but non negligible effect on the North Atlantic sea level trend of about 0.1 mm/yr. The interannual signals of sea level time series derived with the NASA and the CNES orbits respectively, show a small departure in the middle of the series, which has no impact on the derived sea level trend. These results strike the need for a continuous improvement in the modelling of the various effects that influence the altimeter measurement.

Abstract
This paper addresses the problem of scheduling parallel tasks, represented by a direct acyclic graph (DAG) on heterogeneous clusters. Parallel tasks, also called malleable tasks, are tasks that can be executed on any number of processors with its execution time being a function of the number of processors alloted to it. The scheduling of independent parallel tasks on homogeneous machines has been extensively studied and the case of parallel tasks with precedence constraints has been studied for tree-like graphs. For arbitrary precedence graphs and for heterogeneous machines, the optimization problem is more complex because the processing time of a given task depends on the number of processors and on the total processing capacity of those processors. This paper presents a list scheduling algorithm to minimize the total length of the schedule (makespan) of a given set of parallel tasks, whose dependencies are represented by a DAG.