Spectral Early-Warning Signals for Sudden Changes in Time-Dependent Flow Patterns

Lagrangian coherent sets are known to crucially determine transport and mixing processes in non-autonomous flows. Prominent examples include vortices and jets in geophysical fluid flows. Coherent sets can be identified computationally by a probabilistic transfer-operator-based approach within a set-oriented numerical framework. Here, we study sudden changes in flow patterns that correspond to bifurcations of coherent sets. Significant changes in the spectral properties of a numerical transfer operator are heuristically related to critical events in the phase space of a time-dependent system. The transfer operator approach is applied to different example systems of increasing complexity. In particular, we study the 2002 splitting event of the Antarctic polar vortex.

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Network-based study of Lagrangian transport and mixing

10.5194/npg-2017-4 ◽

2017 ◽

Author(s):

Kathrin Padberg-Gehle ◽

Christiane Schneide

Keyword(s):

Clustering Algorithms ◽

Transfer Operator ◽

Polar Vortex ◽

Local Network ◽

Node Degree ◽

Trajectory Data ◽

Mixing Processes ◽

Stratospheric Polar Vortex ◽

Spatio Temporal ◽

Transport And Mixing

Abstract. Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational or transfer operator based schemes require full knowledge of the flow field or at least high resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows – the Bickley jet as well as the antarctic stratospheric polar vortex.

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Network-based study of Lagrangian transport and mixing

Nonlinear Processes in Geophysics ◽

10.5194/npg-24-661-2017 ◽

2017 ◽

Vol 24 (4) ◽

pp. 661-671 ◽

Cited By ~ 19

Author(s):

Kathrin Padberg-Gehle ◽

Christiane Schneide

Keyword(s):

Clustering Algorithms ◽

Transfer Operator ◽

Polar Vortex ◽

Clustering Coefficient ◽

Local Network ◽

Node Degree ◽

Trajectory Data ◽

Mixing Processes ◽

Stratospheric Polar Vortex ◽

Transport And Mixing

Abstract. Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operator-based schemes require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, that is, numerical or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows – the Bickley jet as well as the Antarctic stratospheric polar vortex.

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Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

Nonlinear Processes in Geophysics ◽

10.5194/npg-24-379-2017 ◽

2017 ◽

Vol 24 (3) ◽

pp. 379-392 ◽

Cited By ~ 9

Author(s):

Jezabel Curbelo ◽

Víctor José García-Garrido ◽

Carlos Roberto Mechoso ◽

Ana Maria Mancho ◽

Stephen Wiggins ◽

...

Keyword(s):

Three Dimensional ◽

Polar Vortex ◽

Reanalysis Data ◽

Strong Mixing ◽

Mixing Processes ◽

Stratospheric Polar Vortex ◽

Vertical Extension ◽

Antarctic Polar Vortex ◽

The Antarctic ◽

Lagrangian Geometry

Abstract. In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.

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Insights on the three-dimensional Lagrangian geometry of the Antarctic Polar Vortex

10.5194/npg-2017-8 ◽

2017 ◽

Author(s):

Jezabel Curbelo ◽

Victor J. García-Garrido ◽

Carlos R. Mechoso ◽

Ana M. Mancho ◽

Stephen Wiggins ◽

...

Keyword(s):

Three Dimensional ◽

Polar Vortex ◽

Reanalysis Data ◽

Late Winter ◽

Mixing Processes ◽

Stratospheric Polar Vortex ◽

Atmospheric Flows ◽

Vertical Barriers ◽

Antarctic Polar Vortex ◽

Transport And Mixing

Abstract. The present paper introduces an algorithm for the visualization, analysis and verification of transport and mixing processes in three-dimensional atmospheric flows. This algorithm is based on the methodology of Lagrangian descriptors (LDs), a technique from Dynamical Systems Theory. The algorithm is applied to reanalysis data in order to illustrate the evolution of the flow above Antarctica during a period of rapid changes in the southern spring of 1979. The evolution of Lagrangian coherent structures is discussed and connections with the stratosphere is examined. The results suggest that the cyclonic stratospheric polar vortex during late winter appears to extend down to the troposphere. The results are also indicative of features related to invariante manifolds that can act as deep vertical barriers to transport between vortices.

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Energetic particle induced intra-seasonal variability of ozone inside the Antarctic polar vortex observed in satellite data

Atmospheric Chemistry and Physics ◽

10.5194/acp-15-3327-2015 ◽

2015 ◽

Vol 15 (6) ◽

pp. 3327-3338 ◽

Cited By ~ 19

Author(s):

T. Fytterer ◽

M. G. Mlynczak ◽

H. Nieder ◽

K. Pérot ◽

M. Sinnhuber ◽

...

Keyword(s):

Geomagnetic Activity ◽

Seasonal Variability ◽

Transport Model ◽

Three Dimensional ◽

Polar Vortex ◽

Quiet Time ◽

Significance Level ◽

Antarctic Polar Vortex ◽

Ap Index ◽

The Antarctic

Abstract. Measurements from 2002 to 2011 by three independent satellite instruments, namely MIPAS, SABER, and SMR on board the ENVISAT, TIMED, and Odin satellites are used to investigate the intra-seasonal variability of stratospheric and mesospheric O3 volume mixing ratio (vmr) inside the Antarctic polar vortex due to solar and geomagnetic activity. In this study, we individually analysed the relative O3 vmr variations between maximum and minimum conditions of a number of solar and geomagnetic indices (F10.7 cm solar radio flux, Ap index, ≥ 2 MeV electron flux). The indices are 26-day averages centred at 1 April, 1 May, and 1 June while O3 is based on 26-day running means from 1 April to 1 November at altitudes from 20 to 70 km. During solar quiet time from 2005 to 2010, the composite of all three instruments reveals an apparent negative O3 signal associated to the geomagnetic activity (Ap index) around 1 April, on average reaching amplitudes between −5 and −10% of the respective O3 background. The O3 response exceeds the significance level of 95% and propagates downwards throughout the polar winter from the stratopause down to ~ 25 km. These observed results are in good qualitative agreement with the O3 vmr pattern simulated with a three-dimensional chemistry-transport model, which includes particle impact ionisation.

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A quasi-Lagrangian coordinate system based on high resolution tracer observations: implementation for the Antarctic polar vortex

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-8-16123-2008 ◽

2008 ◽

Vol 8 (4) ◽

pp. 16123-16173 ◽

Cited By ~ 3

Author(s):

E. V. Ivanova ◽

C. M. Volk ◽

O. Riediger ◽

H. Klein ◽

N. M. Sitnikov ◽

...

Keyword(s):

High Resolution ◽

Coordinate System ◽

Vortex Core ◽

Polar Vortex ◽

Mixing Ratio ◽

Lagrangian Coordinate ◽

Antarctic Polar Vortex ◽

The Antarctic ◽

Lagrangian Coordinate System

Abstract. In order to quantitatively analyse the chemical and dynamical evolution of the polar vortex it has proven extremely useful to work with coordinate systems that follow the vortex flow. We propose here a two-dimensional quasi-Lagrangian coordinate system {χi, Δχi}, based on the mixing ratio of a long-lived stratospheric trace gas i, and its systematic use with i = N2O, in order to describe the structure of a well-developed Antarctic polar vortex. In the coordinate system {χi, Δχi} the mixing ratio χi is the vertical coordinate and Δχi = χi(Θ)−χivort(Θ) is the meridional coordinate (χivort(Θ) being a vertical reference profile in the vortex core). The quasi-Lagrangian coordinates {χi, Δχi} persist for much longer time than standard isentropic coordinates, potential temperature Θ and equivalent latitude φe, do not require explicit reference to geographic space, and can be derived directly from high-resolution in situ measurements. They are therefore well-suited for studying the evolution of the Antarctic polar vortex throughout the polar winter with respect to the relevant chemical and microphysical processes. By using the introduced coordinate system {χN2O, ΔχN2O} we analyze the well-developed Antarctic vortex investigated during the APE-GAIA (Airborne Polar Experiment – Geophysica Aircraft in Antarctica – 1999) campaign (Carli et al., 2000). A criterion, which uses the local in-situ measurements of χi=χi(Θ) and attributes the inner vortex edge to a rapid change (δ-step) in the meridional profile of the mixing ratio χi, is developed to determine the (Antarctic) inner vortex edge. In turn, we suggest that the outer vortex edge of a well-developed Antarctic vortex can be attributed to the position of a local minimum of the χH2O gradient in the polar vortex area. For a well-developed Antarctic vortex, the ΔχN2O-parametrization of tracer-tracer relationships allows to distinguish the tracer inter-relationships in the vortex core, vortex boundary region and surf zone and to examine their meridional variation throughout these regions. This is illustrated by analyzing the tracer-tracer relationships χi : χN2O obtained from the in-situ data of the APE-GAIA campaign for i = CFC-11, CFC-12, H-1211 and SF6. A number of solitary anomalous points in the CFC-11 : N2O correlation, observed in the Antarctic vortex core, are interpreted in terms of small-scale cross-isentropic dispersion.

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