A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

The nearly continuous 3.5 years of altimeter data in the western North Atlantic Ocean from the GEOS 3 mission (April 1975 to November 1978) have been used to study the seasonal variability of the Gulf Stream. The differences between altimetric measurements of sea surface height made at satellite ground track intersections, called crossovers, are utilized to construct time series of sea level variations. The results indicate that the Gulf Stream in the region off Cape Hatteras has a pronounced seasonal variability. The peak-to-peak amplitude of the seasonal cycle in terms of cross-stream sea level difference is about 15 cm, with a maximum in April and a minimum in December. The result is in good agreement with historic hydrographic observations and recent direct measurements of the Gulf Stream. The mechanisms responsible for the observed seasonal variability are discussed.

Seasonal variability of the Gulf Stream from satellite altimetry

Recent progress in the application of satellite altimetry from Seasat and GEOS 3 to the observation of the oceanic mesoscale variability and general circulation is reviewed. The lack of accurate geoid models has been the major obstacle in the study of the general ocean circulation from altimetry. The use of geoid-independent methods that utilize the temporal differences in altimetric measurements taken at fixed locations, however, has made significant contributions to our knowledge of the mesoscale variability of the ocean. The mesoscale energies of the sea surface height and geostrophic current have been mapped on a global basis. Their distributions in wave number space have also been analyzed. Because of many of the deficiencies of existing altimeter data (short duration, inadequate orbit, poor accuracy, etc.) most of these results describe only a small portion of the frequency-wave number spectrum of the variability, but they have nonetheless demonstrated the great value of an optimally designed altimetric mission in advancing our knowledge of the global mesoscale variability. The current technology allows satellite altimetry to detect oceanic variability at periods from a few days to 3–5 years, and wavelengths from 50 to 10,000 km. Determining the time-averaged general ocean circulation from altimetry is more problematic because an accurate geoid is indispensable. The currently available global geoid models have useful accuracies only at wavelengths greater than about 7000 km. There have been several attempts at mapping the global ocean circulation at those scales using existing altimeter data and geoids. When these results are compared with hydrographic surveys, some qualitative agreement can be observed, but the quantitative differences are mostly inconclusive because of the geoid and orbit errors. It has been suggested, however, that an altimetric mission that is optimally designed with the current technology, when complemented by a state-of-the-art gravimetric mission to map the earth's gravity field, is able to determine the ocean circulation quantitatively at scales from the ocean basin to about 200 km.

Recent progress in the application of satellite altimetry to observing the mesoscale variability and general circulation of the oceans

The synthesizing information, achieving understanding, and deriving insight from increasingly massive, time-varying, noisy and possibly conflicting data sets are some of most challenging tasks in the present information age. Traditional technologies, such as Fourier transform and wavelet multi-resolution analysis, are inadequate to handle all of the above-mentioned tasks. The empirical model decomposition (EMD) has emerged as a new powerful tool for resolving many challenging problems in data processing and analysis. Recently, an iterative filtering decomposition (IFD) has been introduced to address the stability and efficiency problems of the EMD. Another data analysis technique is the local spectral evolution kernel (LSEK), which provides a near prefect low pass filter with desirable time-frequency localizations. The present work utilizes the LSEK to further stabilize the IFD, and offers an efficient, flexible and robust scheme for information extraction, complexity reduction, and signal and image understanding. The performance of the present LSEK based IFD is intensively validated over a wide range of data processing tasks, including mode decomposition, analysis of time-varying data, information extraction from nonlinear dynamic systems, etc. The utility, robustness and usefulness of the proposed LESK based IFD are demonstrated via a large number of applications, such as the analysis of stock market data, the decomposition of ocean wave magnitudes, the understanding of physiologic signals and information recovery from noisy images. The performance of the proposed method is compared with that of existing methods in the literature. Our results indicate that the LSEK based IFD improves both the efficiency and the stability of conventional EMD algorithms.

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Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel

Since the last quadrennial report, new satellite altimeter data have not been generally available. Nevertheless, important progress has been made from analyses of Geos 3 and Seasat data. The marine gravity field has been determined to an extraordinary resolution and accuracy, and important solid earth geophysical interpretations made. In the area of oceanography, statistical estimates of the variability of dynamic topography have been published, methods for incorporating altimeter data into numerical models have been developed and applied, and tentative, but interesting determinations of the mean circulation have been made. In addition, altimeter waveform analysis has made it possible to use altimeter data to determine elevations of major ice fields. Finally, important new insights into the nature of satellite ephemeris error and its influence on altimetrically derived sea surface topography have been achieved.

Oceanographic and geophysical applications of satellite altimetry

Altimeter data obtained from GEOS-3 during the three year period 1975-78 for a region of the western North Atlantic which includes a portion of the Gulf Stream system and part of the open ocean area of the subtropical gyre are analyzed by a new technique which utilizes all the points along the satellite tracks. The physical phenomenon studied are the time-variable but almost geostrophic currents, or mesoscale eddies, so that geoid errors contaminate the scientific signal minimally and the dynamical interpretation is direct. Results presented include the spatial distribution of geostrophic eddy kinetic energy and examples of a synoptic map of the eddy field (April 1977) and of a time series at a point. These results are compared to and synthesized with a diverse and select set of existing measurements and observations obtained in situ by a variety of instrumental techniques. The agreement is generally good, and the altimeter data analyzed provides new information on features in the map of mean eddy kinetic energy. The implications are that satellite altimetry will serve as a powerful quantitative tool in eddy current research and that even presently archived data contains further useful scientific information.

C. D. Leitao

Papers

A Study of the Variability of Ocean Currents in the Northwestern Atlantic Using Satellite Altimetry