2018

Kondrashov, Dmitri, Mickaël D. Chekroun, Xiaojun Yuan, and Michael Ghil. “Data-Adaptive Harmonic Decomposition and Stochastic Modeling of Arctic Sea Ice.” In Advances in Nonlinear Geosciences, edited by Anastasios Tsonis. Springer, 2018. Publisher's Version Abstract

We present and apply a novel method of describing and modeling complex multivariate datasets in the geosciences and elsewhere. Data-adaptive harmonic (DAH) decomposition identifies narrow-banded, spatio-temporal modes (DAHMs) whose frequencies are not necessarily integer multiples of each other. The evolution in time of the DAH coefficients (DAHCs) of these modes can be modeled using a set of coupled Stuart-Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time and space. This methodology is applied first to a challenging synthetic dataset and then to Arctic sea ice concentration (SIC) data from the US National Snow and Ice Data Center (NSIDC). The 36-year (1979–2014) dataset is parsimoniously and accurately described by our DAHMs. Preliminary results indicate that simulations using our multilayer Stuart-Landau model (MSLM) of SICs are stable for much longer time intervals, beyond the end of the twenty-first century, and exhibit interdecadal variability consistent with past historical records. Preliminary results indicate that this MSLM is quite skillful in predicting September sea ice extent.

Kondrashov, Dmitri, and Mickaël D Chekroun. “Data-adaptive harmonic analysis and modeling of solar wind-magnetosphere coupling.” Journal of Atmospheric and Solar-Terrestrial Physics, 177 (2018): 179-189. Publisher's Version Abstract

The solar wind-magnetosphere coupling is studied by new data-adaptive harmonic decomposition (DAHD) approach for the spectral analysis and inverse modeling of multivariate time observations of complex nonlinear dynamical systems. DAHD identifies frequency-based modes of interactions in the combined dataset of Auroral Electrojet (AE) index and solar wind forcing. The time evolution of these modes can be very efficiently simulated by using systems of stochastic differential equations (SDEs) that are stacked per frequency and formed by coupled Stuart-Landau oscillators. These systems of SDEs capture the modes' frequencies as well as their amplitude modulations, and yield, in turn, an accurate modeling of the AE index' statistical properties.

Kondrashov, Dmitri, Mickaël D. Chekroun, and Michael Ghil. “Data-adaptive harmonic decomposition and prediction of Arctic sea ice extent.” Dynamics and Statistics of the Climate System 3, no. 1 (2018): dzy001. Publisher's Version Abstract

Decline in the Arctic sea ice extent (SIE) is an area of active scientific research with profound socio-economic implications. Of particular interest are reliable methods for SIE forecasting on subseasonal time scales, in particular from early summer into fall, when sea ice coverage in the Arctic reaches its minimum. Here, we apply the recent data-adaptive harmonic (DAH) technique of Chekroun and Kondrashov, (2017), Chaos, **27** for the description, modeling and prediction of the Multisensor Analyzed Sea Ice Extent (MASIE, 2006–2016) data set. The DAH decomposition of MASIE identifies narrowband, spatio-temporal data-adaptive modes over four key Arctic regions. The time evolution of the DAH coefficients of these modes can be modelled and predicted by using a set of coupled Stuart–Landau stochastic differential equations that capture the modes’ frequencies and amplitude modulation in time. Retrospective forecasts show that our resulting multilayer Stuart–Landau model (MSLM) is quite skilful in predicting September SIE compared to year-to-year persistence; moreover, the DAH–MSLM approach provided accurate real-time prediction that was highly competitive for the 2016–2017 Sea Ice Outlook.

Kondrashov, Dmitri, Mickaël D. Chekroun, and Pavel Berloff. “Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres.” Fluids 3, no. 1 (2018): 21. Publisher's Version Abstract

The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence.

Ghil, Michael, Andreas Groth, Dmitri Kondrashov, and Andrew W. Robertson. “Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view.” In The Gap between Weather and Climate Forecasting: Sub-Seasonal to Seasonal Prediction, edited by Andrew W. Robertson and Frederic Vitart, 119-142. 1st ed. Elsevier, 2018. Publisher's Version Abstract

This chapter considers the sub-seasonal–to–seasonal (S2S) prediction problem as intrinsically more difficult than either short-range weather prediction or interannual–to–multidecadal climate prediction. The difficulty arises from the comparable importance of atmospheric initial states and of parameter values in determining the atmospheric evolution on the S2S time scale. The chapter relies on the theoretical framework of dynamical systems and the practical tools this framework helps provide to low-order modeling and prediction of S2S variability. The emphasis is on mid-latitude variability and the complementarity of the nonlinear-waves vs. multiple-regime points of view in understanding this variability. Empirical model reduction and the forecast skill of the models thus produced in real-time prediction are reviewed.

2017

Chekroun, Mickaël D., and Dmitri Kondrashov. “Data-adaptive harmonic spectra and multilayer Stuart-Landau models.” Chaos 27 (2017): 093110. Publisher's Version Abstract

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure.

The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum.

The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coe cients stacked by Fourier frequency which can be e ciently modeled—provided the decay of temporal correlations is su ciently well-resolved—within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators.

Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.

Kondrashov, Dmitri. “Data-adaptive Harmonic Decomposition and Real-time Prediction of 2016 September Arctic Sea Ice Extent.” 4th Polar Prediction Workshop, 27-30 March 2017, Bremerhaven, Germany, 2017. Workshop Website Abstract

Decline in the Arctic sea ice extent (SIE) has profound socio-economic implications and is a focus of active scientific research. Of particular interest is prediction of SIE on subseasonal time scales, i.e.~from early summer into fall, when sea ice coverage in Arctic reaches its minimum. However, subseasonal forecasting of SIE is very challenging due to the high variability of ocean and atmosphere over Arctic in summer, as well as shortness of observational data and inadequacies of the physics-based models to simulate sea-ice dynamics. The Sea Ice Outlook (SIO) by Sea Ice Prediction Network (SIPN, http://www.arcus.org/sipn) is a collaborative effort to facilitate and improve subseasonal prediction of September SIE by physics-based and data-driven statistical models.

Data-adaptive Harmonic Decomposition (DAH) and Multilayer Stuart-Landau Models (MSLM) techniques [Chekroun and Kondrashov, 2017], have been successfully applied to the nonlinear stochastic modeling, as well as retrospective and real-time forecasting of Multisensor Analyzed Sea Ice Extent (MASIE) dataset in key four Arctic regions. In particular, the real-time DAH-MSLM predictions outperformed most statistical models and physics-based models in 2016 SIO submissions. The key success factors are associated with DAH ability to disentangle complex regional dynamics of MASIE by data-adaptive harmonic spatio-temporal patterns that reduce the data-driven modeling effort to elemental MSLMs stacked per frequency with fixed and small number of model coefficients to estimate.

This is a joint work with Mickael Chekroun (UCLA) and Michael Ghil (UCLA,ENS).

Groth, Andreas, Yizhak Feliks, Dmitri Kondrashov, and Michael Ghil. “Interannual variability in the North Atlantic ocean’s temperature field and its association with the wind stress forcing.” Journal of Climate 30, no. 7 (2017): 2655-2678. Abstract

Spectral analyses of the North Atlantic temperature field in the Simple Ocean Data Analysis (SODA) reanalysis identify prominent and statistically significant interannual oscillations along the Gulf Stream front and in large regions of the North Atlantic. A 7–8-yr oscillatory mode is characterized by a basin-wide southwest-to-northeast–oriented propagation pattern in the sea surface temperature (SST) field. This pattern is found to be linked to a seesaw in the meridional-dipole structure of the zonal wind stress forcing (TAUX). In the subpolar gyre, the SST and TAUX fields of this mode are shown to be in phase opposition, which suggests a cooling effect of the wind stress on the upper ocean layer. Over all, this mode’s temperature field is characterized by a strong equivalent-barotropic component, as shown by covariations in SSTs and sea surface heights, and by phase-coherent behavior of temperature layers at depth with the SST field. Recent improvements of multivariate singular spectrum analysis (M-SSA) help separate spatio-temporal patterns. This methodology is developed further and applied to studying the ocean’s response to variability in the atmospheric forcing. Statistical evidence is shown to exist for other mechanisms generating oceanic variability of similar 7–8-yr periodicity in the Gulf Stream region; the latter variability is likewise characterized by a strongly equivalent-barotropic component. Two other modes of biennial variability in the Gulf Stream region are also identified, and it is shown that interannual variability in this region cannot be explained by the ocean’s response to similar variability in the atmospheric forcing alone.

2016

Kondrashov, Dmitri, Mickaël D. Chekroun, and Michael Ghil. “Comment on ``Nonparametric forecasting of low-dimensional dynamical systems''.” Phys. Rev. E 93 (2016): 036201. Publisher's Version

Merkin, V. G., Dmitri Kondrashov, Michael Ghil, and B. J. Anderson. “Data assimilation of low-altitude magnetic perturbations into a global magnetosphere model.” Space Weather 14, no. 2 (2016): 165–184. Publisher's Version

Greco, G, Dmitri Kondrashov, S Kobayashi, Michael Ghil, M Branchesi, C Guidorzi, G Stratta, M Ciszak, F Marino, and A Ortolan. “Singular Spectrum Analysis for astronomical time series: constructing a parsimonious hypothesis test.” In The Universe of Digital Sky Surveys, 105–107. Springer, 2016. Publisher's Version

Chen, C., M. A. Cane, N. Henderson, D. Eun Lee, D. Chapman, Dmitri Kondrashov, and Mickaël D. Chekroun. “Diversity, nonlinearity, seasonality and memory effect in ENSO simulation and prediction using empirical model reduction.” Journal of Climate 29, no. 5 (2016): 1809-1830. Abstract

A suite of empirical model experiments under the empirical model reduction framework are conducted to advance the understanding of ENSO diversity, nonlinearity, seasonality, and the memory effect in the simulation and prediction of tropical Pacific sea surface temperature (SST) anomalies. The model training and evaluation are carried out using 4000-yr preindustrial control simulation data from the coupled model GFDL CM2.1. The results show that multivariate models with tropical Pacific subsurface information and multilevel models with SST history information both improve the prediction skill dramatically. These two types of models represent the ENSO memory effect based on either the recharge oscillator or the time-delayed oscillator viewpoint. Multilevel SST models are a bit more efficient, requiring fewer model coefficients. Nonlinearity is found necessary to reproduce the ENSO diversity feature for extreme events. The nonlinear models reconstruct the skewed probability density function of SST anomalies and improve the prediction of the skewed amplitude, though the role of nonlinearity may be slightly overestimated given the strong nonlinear ENSO in GFDL CM2.1. The models with periodic terms reproduce the SST seasonal phase locking but do not improve the prediction appreciably. The models with multiple ingredients capture several ENSO characteristics simultaneously and exhibit overall better prediction skill for more diverse target patterns. In particular, they alleviate the spring/autumn prediction barrier and reduce the tendency for predicted values to lag the target month value.

2015

Mukhin, Dmitry, Dmitri Kondrashov, Evgeny Loskutov, Andrey Gavrilov, Alexander Feigin, and Michael Ghil. “Predicting critical transitions in ENSO models. Part II: Spatially dependent models.” Journal of Climate 28, no. 5 (2015): 1962–1976. Abstract

The present paper is the second part of a two-part study on empirical modeling and prediction of climate variability. This paper deals with spatially distributed data, as opposed to the univariate data of Part I. The choice of a basis for effective data compression becomes of the essence. In many applications, it is the set of spatial empirical orthogonal functions that provides the uncorrelated time series of principal components (PCs) used in the learning set. In this paper, the basis of the learning set is obtained instead by applying multichannel singular-spectrum analysis to climatic time series and using the leading spatiotemporal PCs to construct a reduced stochastic model. The effectiveness of this approach is illustrated by predicting the behavior of the Jin–Neelin–Ghil (JNG) hybrid seasonally forced coupled ocean–atmosphere model of El Niño–Southern Oscillation. The JNG model produces spatially distributed and weakly nonstationary time series to which the model reduction and prediction methodology is applied. Critical transitions in the hybrid periodically forced coupled model are successfully predicted on time scales that are substantially longer than the duration of the learning sample.

Kondrashov, Dmitri, Mickaël D. Chekroun, and Michael Ghil. “Data-driven non-Markovian closure models.” Physica D: Nonlinear Phenomena 297 (2015): 33–55. Abstract

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 broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR–MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lotka–Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model’s parameter space and the existence of multiple attractor basins with fractal boundaries. The positivity constraint on the solutions’ components replaces here the quadratic-energy–preserving constraint of fluid-flow problems and it successfully prevents blow-up.

Kondrashov, Dmitri, and Pavel S. Berloff. “Stochastic modeling of decadal variability in ocean gyres.” Geophysical Research Letters 42 (2015): 1543–1553.

2014

Podladchikova, T. V., Y. Y. Shprits, Dmitri Kondrashov, and A. C. Kellerman. “Noise statistics identification for Kalman filtering of the electron radiation belt observations I: Model errors.” Journal of Geophysical Research: Space Physics 119, no. 7 (2014): 5700–5724. Publisher's Version

Podladchikova, T. V., Y. Y. Shprits, A. C. Kellerman, and Dmitri Kondrashov. “Noise statistics identification for Kalman filtering of the electron radiation belt observations: 2. Filtration and smoothing.” Journal of Geophysical Research: Space Physics 119, no. 7 (2014): 5725–5743. Publisher's Version

Kondrashov, Dmitri, R. Denton, Y. Y. Shprits, and H. J. Singer. “Reconstruction of gaps in the past history of solar wind parameters.” Geophysical Research Letters 41, no. 8 (2014): 2702–2707. Publisher's Version

Kellerman, A. C., Y. Y. Shprits, Dmitri Kondrashov, D. Subbotin, R. A. Makarevich, E. Donovan, and T. Nagai. “Three-dimensional data assimilation and reanalysis of radiation belt electrons: Observations of a four-zone structure using five spacecraft and the VERB code.” Journal of Geophysical Research: Space Physics 119, no. 11 (2014): 8764–8783. Publisher's Version

Chekroun, Mickaël D., J. David Neelin, Dmitri Kondrashov, James C. McWilliams, and Michael Ghil. “Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances.” Proceedings of the National Academy of Sciences 111, no. 5 (2014): 1684-1690. Abstract

Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them—as filtered through an observable of the system—is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap—defined as the distance between the subdominant RP resonance and the unit circle—plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño–Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.

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