Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System*

Yang, Shun; Baker, Debra; Li, Hong; Cordes, Katy; Huff, Morgan; Nagpal, Geetika; Okereke, Ena; Villafañe, Josue; Kalnay, Eugenia; Duane, Gregory S.

doi:10.1175/jas3739.1

Cited by 79 publications

(90 citation statements)

References 36 publications

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“…Alternatively, we propose to connect linear combinations of these model variables. Yang et al (2006) already showed the potential of this approach by using bred and singular vectors. In this study we use empirical orthogonal functions (EOF) (Preisendorfer and Mobley, 1988).…”

Section: P H Hiemstra Et Al: Complete Synchronization By Connectinmentioning

confidence: 99%

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Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Hiemstra

Fujiwara

Selten

et al. 2012

Nonlin. Processes Geophys.

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Abstract. Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5-12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.

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Section: P H Hiemstra Et Al: Complete Synchronization By Connectinmentioning

confidence: 99%

“…Nudging these directions could be an efficient means of obtaining CS. This approach shares some similarities with the work of Yang et al (2006) The matrix V is constructed by…”

Section: Connecting Using Eofsmentioning

confidence: 99%

Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Hiemstra

Fujiwara

Selten

et al. 2012

Nonlin. Processes Geophys.

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“…It has been suggested Yang et al, 2006;Carrassi et al, 2008;and Abarbanel et al, 2010) that synchronization may be a useful mechanism to explore for applications to data assimilation. NWP represents a relatively general class of synchronization problem, and we suggest that studying its successes in the prediction of geophysical systems may benefit the general nonlinear dynamics community.…”

Section: Introductionmentioning

confidence: 99%

Mathematical foundations of hybrid data assimilation from a synchronization perspective

Penny

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The state-of-the-art data assimilation methods used today in operational weather prediction centers around the world can be classified as generalized one-way coupled impulsive synchronization. This classification permits the investigation of hybrid data assimilation methods, which combine dynamic error estimates of the system state with long time-averaged (climatological) error estimates, from a synchronization perspective. Illustrative results show how dynamically informed formulations of the coupling matrix (via an Ensemble Kalman Filter, EnKF) can lead to synchronization when observing networks are sparse and how hybrid methods can lead to synchronization when those dynamic formulations are inadequate (due to small ensemble sizes). A large-scale application with a global ocean general circulation model is also presented. Results indicate that the hybrid methods also have useful applications in generalized synchronization, in particular, for correcting systematic model errors. Data assimilation is a mathematical discipline that arose out of the development of numerical weather prediction (NWP), which required initialization of numerical models based on a set of relatively sparse observations. In recent years, popular solution approaches for this state estimation problem have evolved into two main categories: variational methods and ensemble-based Kalman filters. As each approach has its own unique benefits, researchers began creating hybrid combinations of these methods to take advantage of the strengths of both. We describe how data assimilation can be interpreted as a type of synchronization problem in which a modeled system is driven by observations of a natural system and extend this formalism to include the aforementioned hybrid data assimilation techniques.

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“…Meteorological data assimilation, in which observations are introduced into a numerical simulation of the atmosphere or oceans, has also been reinterpreted in terms of the synchronization of chaotic systems through weak coupling of a subset of simulated flow components with sequences of observations (e.g., Duane et al, 2006;Yang et al, 2006;and Abarbanel et al, 2009). This approach has been further developed most recently in the context of multi-model ensembles of climate simulations as a means of accounting for systematic errors between different models through mutual assimilation of model variables, forming the socalled "super-model" (van den Berge et al, 2011;Duane, 2015;and Shen et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

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Morice-Atkinson

Allen

et al. 2017

Chaos

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A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to timedependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction d of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and d was varied over the range 0:1 d 1. Reducing d was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at d ¼ 0:1. Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles. Synchronization is commonly discussed in the context of discrete, coupled oscillators which may be periodic or chaotic. But under some circumstances, extended nonlinear systems which are formally infinite-dimensional, such as fluid flows, may exhibit discrete oscillations and behave as if they consisted of discrete oscillating components. We study such an example in the laboratory, consisting of amplitude-modulated, azimuthally travelling baroclinic waves in a thermally driven, rotating annulus experiment. Earlier experiments showed that, under conditions in which the unperturbed travelling waves are spontaneously (either periodically or weakly chaotically) modulated in time, the amplitude modulation of the waves can be phase-locked and synchronized with periodic perturbations of the applied (axisymmetric) temperature difference between the inner and outer cylinders of the experiment. We use this potentially synchronized system to explore what happens if the periodic perturbations are applied for only a given fraction of each cycle-i.e., for a duty cycle <100%. Our systematic exploration of variations in both the duty cycle and detuning (difference in period between the natural oscillation period and that of the imposed boundary temperature variations) shows that the duty cycle acts in the same way as a variable coupling coefficient, demonstrating a narrowing of the frequency interval over which complete phase synchronization is observed as ...

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Data Assimilation as Synchronization of Truth and Model: Experiments with the Three-Variable Lorenz System*

Cited by 79 publications

References 36 publications

Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

Mathematical foundations of hybrid data assimilation from a synchronization perspective

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

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