2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, 2009
ABSTRACT Wavelet ridge analysis is a technique for estimating the time-varying properties of a mo... more ABSTRACT Wavelet ridge analysis is a technique for estimating the time-varying properties of a modulated oscillatory signal from a contaminated observation. Here this technique is extended to the multivariate case, that is, to a set of N real-valued time series. The bivariate case is illustrated with an application to a set of freely-drifting oceanographic floats. A freely distributed software package implementing this algorithm is available online at http://www.jmlilly.net.
A modulated oscillation in two or three dimensions can be represented as the trajectory traced ou... more A modulated oscillation in two or three dimensions can be represented as the trajectory traced out in space by a particle orbiting an ellipse, the properties of which vary as a function of time. Generalizing ideas from signal analysis, the signal variability can be described in terms of kinematic quantities, the instantaneous moments, that formalize our intuitive notions of time-varying frequency and amplitude. On the other hand, if we observed an ellipse evolving in space we would seek to describe it in terms of its physical moments, such as angular momentum, moment of inertia, etc. The main result of this paper is to show that the two sets of moments are identical. Most significantly, an essential physical quantity---the circulation---is the same as the product of the two most important kinematic quantities, the instantaneous frequency and the squared instantaneous amplitude. In addition to providing a rich set of geometric tools for the analysis of nonstationary oscillations in t...
The mechanisms by which oceanic heat is delivered to Antarctic ice shelves are a major source of ... more The mechanisms by which oceanic heat is delivered to Antarctic ice shelves are a major source of uncertainty when assessing the response of the Antarctic ice sheet to climate change. Here, we combine observations below the Fimbul Ice Shelf with high resolution ocean modeling to study the heat exchange of the ice shelf cavity with the open ocean and quantify ice shelf basal melting. Situated at the prime meridian, the Fimbul Ice Shelf is the sixth largest ice shelf in Antarctica, being fed by Jutulstraumen, the largest ice stream in western Dronning Maud Land. Its oceanographic configuration is typical for the ice shelves along the coast of the Eastern Weddell Sea, where only a narrow continental shelf protects the glaciated coast from intrusions of Warm Deep Water and estimates of melting has varied widely over a number of studies. Our results reveal an unexpected level of complexity to supply of oceanic heat for basal melting. Two different water masses reach the ice base at differ...
A method for diagnosing the physical properties of a time-varying ellipse is presented. This esse... more A method for diagnosing the physical properties of a time-varying ellipse is presented. This essentially involves extending the notion of instantaneous frequency to the bivariate case. New complications, and possibilities, arise from the fact that there are several meaningful forms in which a time-varying ellipse may be represented. A perturbation analysis valid for the near-circular case clarifies these issues. Diagnosis of the ellipse properties may then be performed using wavelet ridge analysis, and slowly-varying changes in the ellipse structure may be decoupled from the fast orbital motion through the use of elliptic integrals, without the need for additional explicit filtering. The theory is presented in parallel with an application to a position time series of a drifting subsurface float trapped in an oceanic eddy.
... of deep convection reaching a depth of over 2 km during some winters, is of particular import... more ... of deep convection reaching a depth of over 2 km during some winters, is of particular importance for its influence on the θ/S and potential vorticity structure of the North Atlantic (Talley and McCartney ... The present work is the second involving the Bravo mooring; the first (Lilly et al ...
... Corresponding author address: Lucia Bunge, Department of Oceanography, The Florida State Univ... more ... Corresponding author address: Lucia Bunge, Department of Oceanography, The Florida State University, Tallahassee, FL 32306-4320. ... dans l'Atlantique Equatorial-Seasonal Equatorial Atlantic Experiment (FOCAL-SEQUAL) (198284) (eg, Garzoli 1987; Houghton and Colin ...
ABSTRACT The mechanisms by which heat is delivered to Antarctic ice shelves are a major source of... more ABSTRACT The mechanisms by which heat is delivered to Antarctic ice shelves are a major source of uncertainty when assessing the response of the Antarctic ice sheet to climate change. Direct observations of the ice shelf-ocean interaction are extremely scarce and in many regions melt rates from ice shelf-ocean models are not constrained by measurements. Our two years of data (2010 and 2011) from three oceanic moorings below the Fimbul Ice Shelf in the Eastern Weddell Sea show cold cavity waters, with average temperatures of less than 0.1°C above the surface freezing point. This suggests low basal melt rates, consistent with remote sensing-based, steady-state mass balance estimates for this sector of the Antarctic coast. Oceanic heat for basal melting is found to be supplied by two sources of warm water entering below the ice: (i) eddy-like bursts of Modified Warm Deep Water that access the cavity at depth for eight months of the record; and (ii) fresh surface water that flushes parts of the ice base with temperatures above freezing during late summer and fall. This interplay of processes implies that basal melting at the Fimbul Ice Shelf cannot simply be parameterized by coastal deep ocean temperatures, but instead appears directly linked to both solar forcing at the surface as well as to the dynamics of the coastal current system.
Accepted 1995 March 23. Received 1995 March 13; in original form 1994 August 14 ... SUMMARY We pr... more Accepted 1995 March 23. Received 1995 March 13; in original form 1994 August 14 ... SUMMARY We present an algorithm, based on the wavelet transform and multiple taper spectral analysis, for providing a low-variance spectrum estimate of a non-stationary data process. ...
2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, 2009
ABSTRACT Wavelet ridge analysis is a technique for estimating the time-varying properties of a mo... more ABSTRACT Wavelet ridge analysis is a technique for estimating the time-varying properties of a modulated oscillatory signal from a contaminated observation. Here this technique is extended to the multivariate case, that is, to a set of N real-valued time series. The bivariate case is illustrated with an application to a set of freely-drifting oceanographic floats. A freely distributed software package implementing this algorithm is available online at http://www.jmlilly.net.
A modulated oscillation in two or three dimensions can be represented as the trajectory traced ou... more A modulated oscillation in two or three dimensions can be represented as the trajectory traced out in space by a particle orbiting an ellipse, the properties of which vary as a function of time. Generalizing ideas from signal analysis, the signal variability can be described in terms of kinematic quantities, the instantaneous moments, that formalize our intuitive notions of time-varying frequency and amplitude. On the other hand, if we observed an ellipse evolving in space we would seek to describe it in terms of its physical moments, such as angular momentum, moment of inertia, etc. The main result of this paper is to show that the two sets of moments are identical. Most significantly, an essential physical quantity---the circulation---is the same as the product of the two most important kinematic quantities, the instantaneous frequency and the squared instantaneous amplitude. In addition to providing a rich set of geometric tools for the analysis of nonstationary oscillations in t...
The mechanisms by which oceanic heat is delivered to Antarctic ice shelves are a major source of ... more The mechanisms by which oceanic heat is delivered to Antarctic ice shelves are a major source of uncertainty when assessing the response of the Antarctic ice sheet to climate change. Here, we combine observations below the Fimbul Ice Shelf with high resolution ocean modeling to study the heat exchange of the ice shelf cavity with the open ocean and quantify ice shelf basal melting. Situated at the prime meridian, the Fimbul Ice Shelf is the sixth largest ice shelf in Antarctica, being fed by Jutulstraumen, the largest ice stream in western Dronning Maud Land. Its oceanographic configuration is typical for the ice shelves along the coast of the Eastern Weddell Sea, where only a narrow continental shelf protects the glaciated coast from intrusions of Warm Deep Water and estimates of melting has varied widely over a number of studies. Our results reveal an unexpected level of complexity to supply of oceanic heat for basal melting. Two different water masses reach the ice base at differ...
A method for diagnosing the physical properties of a time-varying ellipse is presented. This esse... more A method for diagnosing the physical properties of a time-varying ellipse is presented. This essentially involves extending the notion of instantaneous frequency to the bivariate case. New complications, and possibilities, arise from the fact that there are several meaningful forms in which a time-varying ellipse may be represented. A perturbation analysis valid for the near-circular case clarifies these issues. Diagnosis of the ellipse properties may then be performed using wavelet ridge analysis, and slowly-varying changes in the ellipse structure may be decoupled from the fast orbital motion through the use of elliptic integrals, without the need for additional explicit filtering. The theory is presented in parallel with an application to a position time series of a drifting subsurface float trapped in an oceanic eddy.
... of deep convection reaching a depth of over 2 km during some winters, is of particular import... more ... of deep convection reaching a depth of over 2 km during some winters, is of particular importance for its influence on the θ/S and potential vorticity structure of the North Atlantic (Talley and McCartney ... The present work is the second involving the Bravo mooring; the first (Lilly et al ...
... Corresponding author address: Lucia Bunge, Department of Oceanography, The Florida State Univ... more ... Corresponding author address: Lucia Bunge, Department of Oceanography, The Florida State University, Tallahassee, FL 32306-4320. ... dans l'Atlantique Equatorial-Seasonal Equatorial Atlantic Experiment (FOCAL-SEQUAL) (198284) (eg, Garzoli 1987; Houghton and Colin ...
ABSTRACT The mechanisms by which heat is delivered to Antarctic ice shelves are a major source of... more ABSTRACT The mechanisms by which heat is delivered to Antarctic ice shelves are a major source of uncertainty when assessing the response of the Antarctic ice sheet to climate change. Direct observations of the ice shelf-ocean interaction are extremely scarce and in many regions melt rates from ice shelf-ocean models are not constrained by measurements. Our two years of data (2010 and 2011) from three oceanic moorings below the Fimbul Ice Shelf in the Eastern Weddell Sea show cold cavity waters, with average temperatures of less than 0.1°C above the surface freezing point. This suggests low basal melt rates, consistent with remote sensing-based, steady-state mass balance estimates for this sector of the Antarctic coast. Oceanic heat for basal melting is found to be supplied by two sources of warm water entering below the ice: (i) eddy-like bursts of Modified Warm Deep Water that access the cavity at depth for eight months of the record; and (ii) fresh surface water that flushes parts of the ice base with temperatures above freezing during late summer and fall. This interplay of processes implies that basal melting at the Fimbul Ice Shelf cannot simply be parameterized by coastal deep ocean temperatures, but instead appears directly linked to both solar forcing at the surface as well as to the dynamics of the coastal current system.
Accepted 1995 March 23. Received 1995 March 13; in original form 1994 August 14 ... SUMMARY We pr... more Accepted 1995 March 23. Received 1995 March 13; in original form 1994 August 14 ... SUMMARY We present an algorithm, based on the wavelet transform and multiple taper spectral analysis, for providing a low-variance spectrum estimate of a non-stationary data process. ...
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