scholarly journals Network-based study of Lagrangian transport and mixing

2017 ◽  
Vol 24 (4) ◽  
pp. 661-671 ◽  
Author(s):  
Kathrin Padberg-Gehle ◽  
Christiane Schneide

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.

2017 ◽  
Author(s):  
Kathrin Padberg-Gehle ◽  
Christiane Schneide

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.


Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 49
Author(s):  
Moussa Ndour ◽  
Kathrin Padberg-Gehle ◽  
Martin Rasmussen

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.


2017 ◽  
Author(s):  
Jezabel Curbelo ◽  
Victor J. García-Garrido ◽  
Carlos R. Mechoso ◽  
Ana M. Mancho ◽  
Stephen Wiggins ◽  
...  

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.


2016 ◽  
Author(s):  
Victor José García-Garrido ◽  
Jezabel Curbelo ◽  
Carlos Roberto Mechoso ◽  
Ana María Mancho ◽  
Stephen Wiggins

Abstract. In this work we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the Sudden Stratospheric Warming event that took place during September 2002. The Lagrangian analysis of the transport and mixing processes is carried out in the framework of dynamical systems theory, by means of a Lagrangian descriptor. We seek to describe the Lagrangian skeleton of geometrical structures that lead to filamentation phenomena and the breakdown of the polar vortex, and establish its relation with how planetary waves interact. Our approach is based on the construction of a simple kinematic model, inspired by the Fourier decomposition of the geopotential field. We show that this model is capable of reproducing the key Lagrangian features present on the reanalysis data such as the formation of filaments eroding the stratospheric polar vortex and the breakdown of the vortex.


2017 ◽  
Vol 24 (3) ◽  
pp. 379-392 ◽  
Author(s):  
Jezabel Curbelo ◽  
Víctor José García-Garrido ◽  
Carlos Roberto Mechoso ◽  
Ana Maria Mancho ◽  
Stephen Wiggins ◽  
...  

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.


2021 ◽  
Author(s):  
Alice Portal ◽  
Paolo Ruggieri ◽  
Froila M. Palmeiro ◽  
Javier García-Serrano ◽  
Daniela I. V. Domeisen ◽  
...  

AbstractThe predictability of the Northern Hemisphere stratosphere and its underlying dynamics are investigated in five state-of-the-art seasonal prediction systems from the Copernicus Climate Change Service (C3S) multi-model database. Special attention is devoted to the connection between the stratospheric polar vortex (SPV) and lower-stratosphere wave activity (LSWA). We find that in winter (December to February) dynamical forecasts initialised on the first of November are considerably more skilful than empirical forecasts based on October anomalies. Moreover, the coupling of the SPV with mid-latitude LSWA (i.e., meridional eddy heat flux) is generally well reproduced by the forecast systems, allowing for the identification of a robust link between the predictability of wave activity above the tropopause and the SPV skill. Our results highlight the importance of November-to-February LSWA, in particular in the Eurasian sector, for forecasts of the winter stratosphere. Finally, the role of potential sources of seasonal stratospheric predictability is considered: we find that the C3S multi-model overestimates the stratospheric response to El Niño–Southern Oscillation (ENSO) and underestimates the influence of the Quasi–Biennial Oscillation (QBO).


2009 ◽  
Vol 66 (2) ◽  
pp. 495-507 ◽  
Author(s):  
Lawrence Coy ◽  
Stephen Eckermann ◽  
Karl Hoppel

Abstract The major stratospheric sudden warming (SSW) of January 2006 is examined using meteorological fields from Goddard Earth Observing System version 4 (GEOS-4) analyses and forecast fields from the Navy Operational Global Atmospheric Prediction System–Advanced Level Physics, High Altitude (NOGAPS-ALPHA). The study focuses on the upper tropospheric forcing that led to the major SSW and the vertical structure of the subtropic wave breaking near 10 hPa that moved low tropical values of potential vorticity (PV) to the pole. Results show that an eastward-propagating upper tropospheric ridge over the North Atlantic with its associated cold temperature perturbations (as manifested by high 360-K potential temperature surface perturbations) and large positive local values of meridional heat flux directly forced a change in the stratospheric polar vortex, leading to the stratospheric subtropical wave breaking and warming. Results also show that the anticyclonic development, initiated by the subtropical wave breaking and associated with the poleward advection of the low PV values, occurred over a limited altitude range of approximately 6–10 km. The authors also show that the poleward advection of this localized low-PV anomaly was associated with changes in the Eliassen–Palm (EP) flux from equatorward to poleward, suggesting an important role for Rossby wave reflection in the SSW of January 2006. Similar upper tropospheric forcing and subtropical wave breaking were found to occur prior to the major SSW of January 2003.


2022 ◽  
pp. 1-63

Abstract Motivated by the strong Antarctic sudden stratospheric warming (SSW) in 2019, a survey on the similar Antarctic weak polar events (WPV) is presented, including their life cycle, dynamics, seasonality, and climatic impacts. The Antarctic WPVs have a frequency of about four events per decade, with the 2002 event being the only major SSW. They show a similar life cycle to the SSWs in the Northern Hemisphere but have a longer duration. They are primarily driven by enhanced upward-propagating wavenumber 1 in the presence of a preconditioned polar stratosphere, i.e., a weaker and more contracted Antarctic stratospheric polar vortex. Antarctic WPVs occur mainly in the austral spring. Their early occurrence is preceded by an easterly anomaly in the middle and upper equatorial stratosphere besides the preconditioned polar stratosphere. The Antarctic WPVs increase the ozone concentration in the polar region and are associated with an advanced seasonal transition of the stratospheric polar vortex by about one week. Their frequency doubles after 2000 and is closely related to the advanced Antarctic stratospheric final warming in recent decades. The WPV-resultant negative phase of the southern annular mode descends to the troposphere and persists for about three months, leading to persistent hemispheric scale temperature and precipitation anomalies.


2018 ◽  
Vol 18 (18) ◽  
pp. 13547-13579 ◽  
Author(s):  
Zachary D. Lawrence ◽  
Gloria L. Manney ◽  
Krzysztof Wargan

Abstract. We compare herein polar processing diagnostics derived from the four most recent “full-input” reanalysis datasets: the National Centers for Environmental Prediction Climate Forecast System Reanalysis/Climate Forecast System, version 2 (CFSR/CFSv2), the European Centre for Medium-Range Weather Forecasts Interim (ERA-Interim) reanalysis, the Japanese Meteorological Agency's 55-year (JRA-55) reanalysis, and the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2). We focus on diagnostics based on temperatures and potential vorticity (PV) in the lower-to-middle stratosphere that are related to formation of polar stratospheric clouds (PSCs), chlorine activation, and the strength, size, and longevity of the stratospheric polar vortex. Polar minimum temperatures (Tmin) and the area of regions having temperatures below PSC formation thresholds (APSC) show large persistent differences between the reanalyses, especially in the Southern Hemisphere (SH), for years prior to 1999. Average absolute differences of the reanalyses from the reanalysis ensemble mean (REM) in Tmin are as large as 3 K at some levels in the SH (1.5 K in the Northern Hemisphere – NH), and absolute differences of reanalysis APSC from the REM up to 1.5 % of a hemisphere (0.75 % of a hemisphere in the NH). After 1999, the reanalyses converge toward better agreement in both hemispheres, dramatically so in the SH: average Tmin differences from the REM are generally less than 1 K in both hemispheres, and average APSC differences less than 0.3 % of a hemisphere. The comparisons of diagnostics based on isentropic PV for assessing polar vortex characteristics, including maximum PV gradients (MPVGs) and the area of the vortex in sunlight (or sunlit vortex area, SVA), show more complex behavior: SH MPVGs showed convergence toward better agreement with the REM after 1999, while NH MPVGs differences remained largely constant over time; differences in SVA remained relatively constant in both hemispheres. While the average differences from the REM are generally small for these vortex diagnostics, understanding such differences among the reanalyses is complicated by the need to use different methods to obtain vertically resolved PV for the different reanalyses. We also evaluated other winter season summary diagnostics, including the winter mean volume of air below PSC thresholds, and vortex decay dates. For the volume of air below PSC thresholds, the reanalyses generally agree best in the SH, where relatively small interannual variability has led to many winter seasons with similar polar processing potential and duration, and thus low sensitivity to differences in meteorological conditions among the reanalyses. In contrast, the large interannual variability of NH winters has given rise to many seasons with marginal conditions that are more sensitive to reanalysis differences. For vortex decay dates, larger differences are seen in the SH than in the NH; in general, the differences in decay dates among the reanalyses follow from persistent differences in their vortex areas. Our results indicate that the transition from the reanalyses assimilating Tiros Operational Vertical Sounder (TOVS) data to advanced TOVS and other data around 1998–2000 resulted in a profound improvement in the agreement of the temperature diagnostics presented (especially in the SH) and to a lesser extent the agreement of the vortex diagnostics. We present several recommendations for using reanalyses in polar processing studies, particularly related to the sensitivity to changes in data inputs and assimilation. Because of these sensitivities, we urge great caution for studies aiming to assess trends derived from reanalysis temperatures. We also argue that one of the best ways to assess the sensitivity of scientific results on polar processing is to use multiple reanalysis datasets.


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