Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models

Mukhin, Dmitry; Kondrashov, Dmitri; Loskutov, Evgeny; Gavrilov, Andrey; Feǐgin, A. M.; Ghil, Michael

doi:10.1175/jcli-d-14-00240.1

Cited by 34 publications

(22 citation statements)

References 48 publications

(70 reference statements)

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“…The dynamics of the unobserved variables {u(t k , ξ j )} j∈I\J is thus lacking and the main issue is to derive an efficient parameterization of the interactions between the resolved and unresolved -i.e., roughly speaking, the observed and unobserved -variables in order to derive equations that model the evolution of the field U J with reasonable accuracy. Furthermore, the scalar field 2 Note that, in some sense, the EMR methodology can also be viewed as an extension of hidden Markov models (HMMs) [70,71] or of artificial neural networks (ANNs) [72,73,74], since the latter are generally nonlinear but do not involve the memory effects inherent in the EMR methodology; see [24,44]. 3 Here δt denotes the sampling interval of the data.…”

Section: The Closure Problem From Partial Observations and Its Emr Somentioning

confidence: 99%

Data-driven non-Markovian closure models

Kondrashov

Chekroun

Ghil

2015

Physica D: Nonlinear Phenomena

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121

178

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This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a very broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The approach is applied to conceptual nonlinear models borrowed from climate dynamics and population dynamics. In both cases, it is shown that the resulting closure models are able to capture the main statistical features of the dynamics, even in presence of weak time-scale separation.Comment: 47 pages, 7 figure

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Section: The Closure Problem From Partial Observations and Its Emr Somentioning

confidence: 99%

Data-driven non-Markovian closure models

Kondrashov

Chekroun

Ghil

2015

Physica D: Nonlinear Phenomena

Self Cite

121

178

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“…Also, there are several spatio-temporal extensions of those techniques, based on multichannel singular spectral analysis (MSSA)151617 taking into account time-lag correlations in data. In recent papers advances of MSSA-based expansion for empirical forecast of complex system1819 as well as for studying synchronization and clustering in multivariate dynamics20 were demonstrated. Papers2122 suggest a method for principal mode extraction combining data rotation and system’s evolution operator construction.…”

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confidence: 99%

Principal nonlinear dynamical modes of climate variability

Mukhin

Gavrilov

Feǐgin

et al. 2015

Sci Rep

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We suggest a new nonlinear expansion of space-distributed observational time series. The expansion allows constructing principal nonlinear manifolds holding essential part of observed variability. It yields low-dimensional hidden time series interpreted as internal modes driving observed multivariate dynamics as well as their mapping to a geographic grid. Bayesian optimality is used for selecting relevant structure of nonlinear transformation, including both the number of principal modes and degree of nonlinearity. Furthermore, the optimal characteristic time scale of the reconstructed modes is also found. The technique is applied to monthly sea surface temperature (SST) time series having a duration of 33 years and covering the globe. Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for ENSO variability, and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed.

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“…SSA utilizes time‐lagged information associated with inherent memory effects; therefore, it is particularly fit for the Earth system modeling. This was demonstrated by Mukhin et al [] for predicting dynamical transitions in the coupled ocean‐atmosphere model and by Chen et al [] who developed nonlinear generalization of SSA for low‐order modeling of the atmosphere. In this study (section 3) we use ST‐PCs of SSA to construct a low‐order model of the oceanic LFV.…”

Section: Models and Methodsmentioning

confidence: 94%

Stochastic modeling of decadal variability in ocean gyres

Kondrashov

Berloff

2015

Geophysical Research Letters

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Decadal large-scale low-frequency variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper presents a novel fully data driven approach that addresses this challenge. Proposed is non-Markovian low-order methodology with stochastic closure and use of mode decomposition by multichannel Singular Spectrum Analysis. The multilayer stochastic linear model is obtained from the coarse-grained eddy-resolving ocean model solution, and with high accuracy it reproduces the main statistical properties of the decadal variability. The proposed methodology does not depend on the governing fluid dynamics equations and geometry of the problem, and it can be extended to other ocean models and ultimately to the real data. BackgroundMidlatitude atmosphere and ocean possess not only significant interannual variability but also several large-scale variability modes on decadal and interdecadal timescales: North Atlantic Oscillation, Atlantic Multidecadal Oscillation, and Pacific Decadal Oscillation. Oceanic evidence of these modes is found in the sea surface temperature [Hansen and Bezdek, 1996], hydrography [Qiu and Joyce, 1992], and altimetry [Qiu and Chen, 2005], and it is mostly expressed in structural changes of the eastward jet extensions and the adjacent recirculation zones of the main western boundary currents, such as the Gulf Stream and Kuroshio. Physical origins of these large-scale low-frequency variability (LFV) modes remain unclear, and it is not even known to what extent these origins are intrinsic atmospheric, intrinsic oceanic, or coupled oceanic-atmospheric. One of the reasons, why coupled ocean-atmosphere comprehensive general circulation models (GCMs) cannot distinguish between these scenarios, is inability of their oceanic model components to simulate mesoscale eddies and their impact on the large-scale currents accurately and for a long time. On the other hand, seasonally forced, eddy-resolving ocean-only GCMs exhibit significant intrinsic LFV variability of mesoscale activity [Penduff et al., 2011], intergyre heat transport [Hall et al., 2004], sea level height [Cabanes et al., 2006], western boundary currents [Taguchi et al., 2007], and meridional overturning circulation [Biastoch et al., 2008]. This suggests that not only significant part of the LFV is intrinsic to the ocean but also oceanic mesoscale eddies could play significant role in driving it.Present theoretical understanding of the intrinsic LFV of the ocean starts from the null hypothesis that the ocean integrates high-frequency atmospheric forcing and responds in terms of the red variability spectrum [Hasselman, 1976]. However, over the last 20 years it became evident that in the presence of stochastic, seasonal, or constant atmospheric forcing, the most significant intrinsic LFV of the ocean is not red but operates on interannual-to-interdecadal time scales. One idea is that this variability can be understood in terms of early bifurcations...

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Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models

Cited by 34 publications

References 48 publications

Data-driven non-Markovian closure models

Data-driven non-Markovian closure models

Principal nonlinear dynamical modes of climate variability

Stochastic modeling of decadal variability in ocean gyres

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