Frequency-Domain Stochastic Modeling of Stationary Bivariate or Complex-Valued Signals

There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. In this paper we provide a joint framework for all three representations in the context of frequency-domain stochastic modeling. This framework allows us to extend many established statistical procedures for bivariate vector time series to complex-valued and rotary representations. These include procedures for parametrically modeling signal coherence, estimating model parameters using the Whittle likelihood, performing semi-parametric modeling, and choosing between classes of nested models using model choice. We also provide a new method of testing for impropriety in complex-valued signals, which tests for noncircular or anisotropic second-order statistical structure when the signal is represented in the complex plane. Finally, we demonstrate the usefulness of our methodology in capturing the anisotropic structure of signals observed from fluid dynamic simulations of turbulence.Comment: To appear in IEEE Transactions on Signal Processin

A Power Variance Test for Nonstationarity in Complex-Valued Signals

We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in O(NlogN) time, where N is the length of the observed signal. The test procedure examines the second-order structure and contrasts the observed power variance - i.e. the variability of the instantaneous variance over time - with the expected characteristics of stationary signals generated via the bootstrap method. Our algorithmic procedure is capable of learning different types of nonstationarity, such as jumps or strong sinusoidal components. We illustrate the utility of our test and algorithm through application to turbulent flow data from fluid dynamics

Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories

Drifters deployed in close proximity collectively provide a unique observational data set with which to separate mesoscale and submesoscale flows. In this paper we provide a principled approach for doing so by fitting observed velocities to a local Taylor expansion of the velocity flow field. We demonstrate how to estimate mesoscale and submesoscale quantities that evolve slowly over time, as well as their associated statistical uncertainty. We show that in practice the mesoscale component of our model can explain much first and second-moment variability in drifter velocities, especially at low frequencies. This results in much lower and more meaningful measures of submesoscale diffusivity, which would otherwise be contaminated by unresolved mesoscale flow. We quantify these effects theoretically via computing Lagrangian frequency spectra, and demonstrate the usefulness of our methodology through simulations as well as with real observations from the LatMix deployment of drifters. The outcome of this method is a full Lagrangian decomposition of each drifter trajectory into three components that represent the background, mesoscale, and submesoscale flow

The Evolution and Propagation of Quasigeostrophic Ocean Eddies

The long-term evolution of initially Gaussian eddies is studied in a reduced-gravity shallow-water model using both linear and nonlinear quasigeostrophic theory in an attempt to understand westward-propagating mesoscale eddies observed and tracked by satellite altimetry. By examining both isolated eddies and a large basin seeded with eddies with statistical characteristics consistent with those of observed eddies, it is shown that long-term eddy coherence and the zonal wavenumber–frequency power spectral density are best matched by the nonlinear model. Individual characteristics of the eddies including amplitude decay, horizontal length scale decay, and zonal and meridional propagation speed of a previously unrecognized quasi-stable state are examined. The results show that the meridional deflections from purely westward flow (poleward for cyclones and equatorward for anticyclones) are consistent with satellite observations. Examination of the fluid transport properties of the eddies shows that an inner core of the eddy, defined by the zero relative vorticity contour, contains only fluid from the eddy origin, whereas a surrounding outer ring contains a mixture of ambient fluid from throughout the eddy’s lifetime.Keywords: Quasigeostrophic models, Eddies, Ocean circulation, Satellite observation

Will extreme climatic events facilitate biological invasions?

Copyright © 2012 Ecological Society of AmericaExtreme climatic events (ECEs) – such as unusual heat waves, hurricanes, floods, and droughts – can dramatically affect ecological and evolutionary processes, and these events are projected to become more frequent and more intense with ongoing climate change. However, the implications of ECEs for biological invasions remain poorly understood. Using concepts and empirical evidence from invasion ecology, we identify mechanisms by which ECEs may influence the invasion process, from initial introduction through establishment and spread. We summarize how ECEs can enhance invasions by promoting the transport of propagules into new regions, by decreasing the resistance of native communities to establishment, and also sometimes by putting existing non-native species at a competitive disadvantage. Finally, we outline priority research areas and management approaches for anticipating future risks of unwanted invasions following ECEs. Given predicted increases in both ECE occurrence and rates of species introductions around the globe during the coming decades, there is an urgent need to understand how these two processes interact to affect ecosystem composition and functioning.National Science Foundatio

Global change, global trade, and the next wave of plant invasions

Copyright © 2012 Ecological Society of AmericaMany non-native plants in the US have become problematic invaders of native and managed ecosystems, but a new generation of invasive species may be at our doorstep. Here, we review trends in the horticultural trade and invasion patterns of previously introduced species and show that novel species introductions from emerging horticultural trade partners are likely to rapidly increase invasion risk. At the same time, climate change and water restrictions are increasing demand for new types of species adapted to warm and dry environments. This confluence of forces could expose the US to a range of new invasive species, including many from tropical and semiarid Africa as well as the Middle East. Risk assessment strategies have proven successful elsewhere at identifying and preventing invasions, although some modifications are needed to address emerging threats. Now is the time to implement horticulture import screening measures to prevent this new wave of plant invasions.National Science Foundatio

The debiased Whittle likelihood

The Whittle likelihood is a widely used and computationally efficient pseudolikelihood. However, it is known to produce biased parameter estimates with finite sample sizes for large classes of models. We propose a method for debiasing Whittle estimates for second-order stationary stochastic processes. The debiased Whittle likelihood can be computed in the same O(n log n) operations as the standard Whittle approach. We demonstrate the superior performance of our method in simulation studies and in application to a large-scale oceanographic dataset, where in both cases the debiased approach reduces bias by up to two orders of magnitude, achieving estimates that are close to those of the exact maximum likelihood, at a fraction of the computational cost. We prove that the method yields estimates that are consistent at an optimal convergence rate of n(-1/2) for Gaussian processes and for certain classes of non-Gaussian or nonlinear processes. This is established under weaker assumptions than in the standard theory, and in particular the power spectral density is not required to be continuous in frequency. We describe how the method can be readily combined with standard methods of bias reduction, such as tapering and differencing, to further reduce bias in parameter estimates

Will Extreme Climatic Events Facilitate Biological Invasions?

Extreme climatic events (ECEs) – such as unusual heat waves, hurricanes, floods, and droughts – can dramatically affect ecological and evolutionary processes, and these events are projected to become more frequent and more intense with ongoing climate change. However, the implications of ECEs for biological invasions remain poorly understood. Using concepts and empirical evidence from invasion ecology, we identify mechanisms by which ECEs may influence the invasion process, from initial introduction through establishment and spread. We summarize how ECEs can enhance invasions by promoting the transport of propagules into new regions, by decreasing the resistance of native communities to establishment, and also sometimes by putting existing non-native species at a competitive disadvantage. Finally, we outline priority research areas and management approaches for anticipating future risks of unwanted invasions following ECEs. Given predicted increases in both ECE occurrence and rates of species introductions around the globe during the coming decades, there is an urgent need to understand how these two processes interact to affect ecosystem composition and functioning