2007

Gaffney, Scott J., Andrew W. Robertson, Padhraic Smyth, Suzana J. Camargo, and Michael Ghil. 2007. “Probabilistic clustering of extratropical cyclones using regression mixture models.” Climate Dynamics 29 (4). Springer: 423–440.

PDFShprits, Yuri, Dmitri Kondrashov, Yue Chen, Richard Thorne, Michael Ghil, Reiner Friedel, and Geoff Reeves. 2007. “Reanalysis of relativistic radiation belt electron fluxes using CRRES satellite data, a radial diffusion model, and a Kalman filter.” Journal of Geophysical Research: Space Physics 112 (A12). Wiley Online Library.

PDFKondrashov, Dmitri, and Michael Ghil. 2007. “Reply to T. Schneider's comment on "Spatio-temporal filling of missing points in geophysical data sets".” Nonlinear Processes in Geophysics 14 (1): 3–4.

PDFSushama, L., Michael Ghil, and K. Ide. 2007. “Spatio-temporal variability in a mid-latitude ocean basin subject to periodic wind forcing.” Atmosphere-ocean 45 (4). Taylor & Francis: 227–250. Abstract

The mid-latitude ocean's response to time-dependent zonal wind-stress forcing is studied using a reduced-gravity, 1.5-layer, shallow-water model in two rectangular ocean basins of different sizes. The small basin is 1000 km $\times$ 2000 km and the larger one is 3000 km $\times$ 2010 km; the aspect ratio of the larger basin is quite similar to that of the North Atlantic between 20$\deg$N and 60$\deg$N. The parameter dependence of the model solutions and their spatio-temporal variability subject to time-independent wind stress forcing serve as the reference against which the results for time-dependent forcing are compared. For the time-dependent forcing case, three zonal-wind profiles that mimic the seasonal cycle are considered in this study: (1) a fixed-profile wind-stress forcing with periodically varying intensity; (2) a wind-stress profile with fixed intensity, but north–south migration of the mid-latitude westerly wind maximum; and (3) a north–south migrating profile with periodically varying intensity. Results of the small-basin simulations show the intrinsic variability found for time-independent forcing to persist when the intensity of the wind forcing varies periodically. It thus appears that the physics behind the upper ocean's variability is mainly controlled by internal dynamics, although the solutions’ spatial patterns are now more complex, due to the interaction between the external and internal modes of variability. The north–south migration of wind forcing, however, does inhibit the inertial recirculation; its suppression increases with the amplitude of north–south migration in the wind-stress forcing. Model solutions in the larger rectangular basin and at smaller viscosity exhibit more realistic recirculation gyres, with a small meridional-to-zonal aspect ratio, and an elongated eastward jet; the low-frequency variability of these solutions is dominated by periodicities of 14 and 6–7 years. Simulations performed in this setting with a wind-stress profile that involves seasonal variations of realistic amplitude in both the intensity and the position of the atmospheric jet show the seven-year periodicity in the oceanic circulation to be robust. The intrinsic variability is reinforced by the periodic variations in the jet's intensity and weakened by periodic variations in the meridional position; the two effects cancel, roughly speaking, thus preserving the overall characteristics of the seven-year mode.

Deloncle, Axel, Richard Berk, Fabio D'Andrea, and Michael Ghil. 2007. “Weather regime prediction using statistical learning.” Journal of the Atmospheric Sciences 64 (5): 1619–1635.

PDF2006

Kondrashov, Dmitri, S. Kravtsov, and M. Ghil. 2006. “Empirical Mode Reduction in a Model of Extratropical Low-Frequency Variability.” Journal of the Atmospheric Sciences 63 (7): 1859-1877. Publisher's Version

Kravtsov, S, P Berloff, William K. Dewar, M Ghil, and James C. McWilliams. 2006. “Dynamical origin of low-frequency variability in a highly nonlinear midlatitude coupled model.” Journal of Climate 19 (24). Abstract

A novel mechanism of decadal midlatitude coupled variability, which crucially depends on the nonlinear dynamics of both the atmosphere and the ocean, is presented. The coupled model studied involves quasigeostrophic atmospheric and oceanic components, which communicate with each other via a constant-depth oceanic mixed layer. A series of coupled and uncoupled experiments show that the decadal coupled mode is active across parameter ranges that allow the bimodality of the atmospheric zonal flow to coexist with oceanic turbulence. The latter is most intense in the regions of inertial recirculation (IR). Bimodality is associated with the existence of two distinct anomalously persistent zonal-flow modes, which are characterized by different latitudes of the atmospheric jet stream. The IR reorganizations caused by transitions of the atmosphere from its high- to low-latitude state and vice versa create sea surface temperature anomalies that tend to induce transition to the opposite atmospheric state. The decadal–interdecadal time scale of the resulting oscillation is set by the IR adjustment; the latter depends most sensitively on the oceanic bottom drag. The period T of the nonlinear oscillation is 7–25 yr for the range of parameters explored, with the most realistic parameter values yielding T \approx 20 yr. Aside from this nonlinear oscillation, an interannual Rossby wave mode is present in all coupled experiments. This coupled mode depends neither on atmospheric bimodality, nor on ocean eddy dynamics; it is analogous to the mode found previously in a channel configuration. Its time scale in the model with a closed ocean basin is set by cross-basin wave propagation and equals 3–5 yr for a basin width comparable with the North Atlantic.

Kondrashov, Dmitri, S Kravtsov, and M Ghil. 2006. “Empirical mode reduction in a model of extratropical low-frequency variability.” Journal of the Atmospheric Sciences 63 (7): 1859–1877. Abstract

This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model's phase space has a dimension of O(104). The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model's probability density function (PDF). In particular, the reduced model's PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog. An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model's deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model's multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.

Kao, Jim, Dawn Flicker, Kayo Ide, and Michael Ghil. 2006. “Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter.” Journal of Computational Physics 214 (2). Elsevier: 725–737.

PDFKravtsov, S., Andrew W. Robertson, and Michael Ghil. 2006. “Multiple regimes and low-frequency oscillations in the Northern Hemisphere's zonal-mean flow.” Journal of the Atmospheric Sciences 63 (3): 840–860.

PDFBellon, G., Michael Ghil, and H. Le Treut. 2006. “Scale separation for moisture-laden regions in the tropical atmosphere.” Geophysical Research Letters 33 (1). Wiley Online Library.

PDFKondrashov, Dmitri, and Michael Ghil. 2006. “Spatio-temporal filling of missing points in geophysical data sets.” Nonlinear Processes in Geophysics 13 (2): 151–159. Abstract

The majority of data sets in the geosciences are obtained from observations and measurements of natural systems, rather than in the laboratory. These data sets are often full of gaps, due to to the conditions under which the measurements are made. Missing data give rise to various problems, for example in spectral estimation or in specifying boundary conditions for numerical models. Here we use Singular Spectrum Analysis (SSA) to fill the gaps in several types of data sets. For a univariate record, our procedure uses only temporal correlations in the data to fill in the missing points. For a multivariate record, multi-channel SSA (M-SSA) takes advantage of both spatial and temporal correlations. We iteratively produce estimates of missing data points, which are then used to compute a self-consistent lag-covariance matrix; cross-validation allows us to optimize the window width and number of dominant SSA or M-SSA modes to fill the gaps. The optimal parameters of our procedure depend on the distribution in time (and space) of the missing data, as well as on the variance distribution between oscillatory modes and noise. The algorithm is demonstrated on synthetic examples, as well as on data sets from oceanography, hydrology, atmospheric sciences, and space physics: global sea-surface temperature, flood-water records of the Nile River, the Southern Oscillation Index (SOI), and satellite observations of relativistic electrons.

2005

Moore, JC, Aslak Grinsted, and S Jevrejeva. 2005. “New tools for analyzing time series relationships and trends.” Eos, Transactions American Geophysical Union 86 (24). Wiley Online Library: 226–232. Abstract

Geophysical studies are plagued by short and noisy time series. These time series are typically nonstationary contain various long-period quasi-periodic components, and have rather low signal-to-noise ratios and/or poor spatial sampling. Classic examples of these time series are tide gauge records, which are influenced by ocean and atmospheric circulation patterns, twentieth-century warming, and other long-term variability. Remarkable progress recently has been made in the statistical analysis of time series. Ghil et al. [2002] presented a general review of several advanced statistical methods with a solid theoretical foundation. This present article highlights several new approaches that are easy to use and that may be of general interest.

Kravtsov, S., Andrew W. Robertson, and Michael Ghil. 2005. “Bimodal behavior in the zonal mean flow of a baroclinic beta-channel model.” Journal of the Atmospheric Sciences 62 (6): 1746–1769.

PDFZhang, Yunyan, Bjorn Stevens, and Michael Ghil. 2005. “On the diurnal cycle and susceptibility to aerosol concentration in a stratocumulus-topped mixed layer.” Quarterly Journal of the Royal Meteorological Society 131 (608). Wiley Online Library: 1567–1583.

PDFKondrashov, Dmitri, S Kravtsov, Andrew W. Robertson, and Michael Ghil. 2005. “A hierarchy of data-based ENSO models.” Journal of climate 18 (21): 4425–4444. Abstract

Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset’s statistics. These inverse models assume that the system’s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset’s leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance. The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models’ simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies. Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The “spring barrier” of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

Simonnet, Eric, Michael Ghil, and Henk Dijkstra. 2005. “Homoclinic bifurcations in the quasi-geostrophic double-gyre circulation.” Journal of Marine Research 63 (5). Sears Foundation for Marine Research: 931–956. Abstract

The wind-driven double-gyre circulation in a rectangular basin goes through several dynamical regimes as the amount of lateral friction is decreased. This paper studies the transition to irregular flow in the double-gyre circulation by applying dynamical systems methodology to a quasi-geostrophic, equivalent-barotropic model with a 10-km resolution. The origin of the irregularities, in space and time, is the occurrence of homoclinic bifurcations that involve phase-space behavior far from stationary solutions. The connection between these homoclinic bifurcations and earlier transitions, which occur at larger lateral friction, is explained. The earlier transitions, such as pitchfork and asymmetric Hopf bifurcation, only involve the nonlinear saturation of linear instabilities, while the homoclinic bifurcations are associated with genuinely nonlinear behavior. The sequence of bifurcations—pitchfork, Hopf, and homoclinic—is independent of the lateral friction and may be described as the unfolding of a singularity that occurs in the frictionless, Hamiltonian limit of the governing equations. Two distinct chaotic regimes are identified: Lorenz chaos at relatively large lateral friction versus Shilnikov chaos at relatively small lateral friction. Both types of homoclinic bifurcations induce chaotic behavior of the recirculation gyres that is dominated by relaxation oscillations with a well-defined period. The relevance of these results to the mid-latitude oceans' observed low-frequency variations is discussed. A previously documented 7-year peak in observed North-Atlantic variability is shown to exist across a hierarchy of models that share the gyre modes and homoclinic bifurcations discussed herein.

Dijkstra, Henk A., and Michael Ghil. 2005. “Low-frequency variability of the large-scale ocean circulation: a dynamical systems approach.” Reviews of Geophysics 43. Abstract

Oceanic variability on interannual, interdecadal, and longer timescales plays a key role in climate variability and climate change. Paleoclimatic records suggest major changes in the location and rate of deepwater formation in the Atlantic and Southern oceans on timescales from millennia to millions of years. Instrumental records of increasing duration and spatial coverage document substantial variability in the path and intensity of ocean surface currents on timescales of months to decades. We review recent theoretical and numerical results that help explain the physical processes governing the large-scale ocean circulation and its intrinsic variability. To do so, we apply systematically the methods of dynamical systems theory. The dynamical systems approach is proving successful for more and more detailed and realistic models, up to and including oceanic and coupled ocean-atmosphere general circulation models. In this approach one follows the road from simple, highly symmetric model solutions, through a “bifurcation tree,” toward the observed, complex behavior of the system under investigation. The observed variability can be shown to have its roots in simple transitions from a circulation with high symmetry in space and regularity in time to circulations with successively lower symmetry in space and less regularity in time. This road of successive bifurcations leads through multiple equilibria to oscillatory and eventually chaotic solutions. Key features of this approach are illustrated in detail for simplified models of two basic problems of the ocean circulation. First, a barotropic model is used to capture major features of the wind-driven ocean circulation and of the changes in its behavior as wind stress increases. Second, a zonally averaged model is used to show how the thermohaline ocean circulation changes as buoyancy fluxes at the surface increase. For the wind-driven circulation, multiple separation patterns of a “Gulf-Stream like” eastward jet are obtained. These multiple equilibria are followed by subannual and interannual oscillations of the jet and of the entire basin's circulation. The multiple equilibria of the thermohaline circulation include deepwater formation near the equator, near either pole or both, as well as intermediate possibilities that bear some degree of resemblance to the currently observed Atlantic overturning pattern. Some of these multiple equilibria are subject, in turn, to oscillatory instabilities with timescales of decades, centuries, and millennia. Interdecadal and centennial oscillations are the ones of greatest interest in the current debate on global warming and on the relative roles of natural and anthropogenic variability in it. They involve the physics of the truly three-dimensional coupling between the wind-driven and thermohaline circulation. To arrive at this three-dimensional picture, the bifurcation tree is sketched out for increasingly complex models for both the wind-driven and the thermohaline circulation.

Kravtsov, S, Dmitri Kondrashov, and M Ghil. 2005. “Multilevel regression modeling of nonlinear processes: Derivation and applications to climatic variability.” Journal of Climate 18 (21): 4404–4424. Abstract

Predictive models are constructed to best describe an observed field’s statistics within a given class of nonlinear dynamics driven by a spatially coherent noise that is white in time. For linear dynamics, such inverse stochastic models are obtained by multiple linear regression (MLR). Nonlinear dynamics, when more appropriate, is accommodated by applying multiple polynomial regression (MPR) instead; the resulting model uses polynomial predictors, but the dependence on the regression parameters is linear in both MPR and MLR. The basic concepts are illustrated using the Lorenz convection model, the classical double-well problem, and a three-well problem in two space dimensions. Given a data sample that is long enough, MPR successfully reconstructs the model coefficients in the former two cases, while the resulting inverse model captures the three-regime structure of the system’s probability density function (PDF) in the latter case. A novel multilevel generalization of the classic regression procedure is introduced next. In this generalization, the residual stochastic forcing at a given level is subsequently modeled as a function of variables at this level and all the preceding ones. The number of levels is determined so that the lag-0 covariance of the residual forcing converges to a constant matrix, while its lag-1 covariance vanishes. This method has been applied to the output of a three-layer, quasigeostrophic model and to the analysis of Northern Hemisphere wintertime geopotential height anomalies. In both cases, the inverse model simulations reproduce well the multiregime structure of the PDF constructed in the subspace spanned by the dataset’s leading empirical orthogonal functions, as well as the detailed spectrum of the dataset’s temporal evolution. These encouraging results are interpreted in terms of the modeled low-frequency flow’s feedback on the statistics of the subgrid-scale processes.

Koo, Seongjoon, Andrew W. Robertson, and Michael Ghil. 2005. “A Multiple-Regime Approach to Atmospheric Zonal-Flow Vacillation”.

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