Data-Driven Transition Path Analysis Yields a Statistical Understanding of Sudden Stratospheric Warming Events in an Idealized Model

Justin Finkel aDepartment of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts

Search for other papers by Justin Finkel in
Current site
Google Scholar
PubMed
Close
https://orcid.org/0000-0002-5670-9890
,
Robert J. Webber bDepartment of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California

Search for other papers by Robert J. Webber in
Current site
Google Scholar
PubMed
Close
,
Edwin P. Gerber cCourant Institute of Mathematical Sciences, New York University, New York, New York

Search for other papers by Edwin P. Gerber in
Current site
Google Scholar
PubMed
Close
,
Dorian S. Abbot dDepartment of the Geophysical Sciences, University of Chicago, Chicago, Illinois

Search for other papers by Dorian S. Abbot in
Current site
Google Scholar
PubMed
Close
, and
Jonathan Weare cCourant Institute of Mathematical Sciences, New York University, New York, New York

Search for other papers by Jonathan Weare in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting) and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective “average event.” We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT’s capacities on a wave–mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass, which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article () studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also backward in time to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the reactive current. The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Justin Finkel, ju26596@mit.edu

Abstract

Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting) and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective “average event.” We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT’s capacities on a wave–mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass, which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article () studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also backward in time to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the reactive current. The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Justin Finkel, ju26596@mit.edu

Supplementary Materials

    • Supplemental Materials (PDF 467 KB)
Save
  • Andrews, D. G., and M. E. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration. J. Atmos. Sci., 33, 20312048, https://doi.org/10.1175/1520-0469(1976)033<2031:PWIHAV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Antoszewski, A., C. Lorpaiboon, J. Strahan, and A. R. Dinner, 2021: Kinetics of phenol escape from the insulin R6 hexamer. J. Phys. Chem., 125B, 11 63711 649, https://doi.org/10.1021/acs.jpcb.1c06544.

    • Search Google Scholar
    • Export Citation
  • Birner, T., and P. D. Williams, 2008: Sudden stratospheric warmings as noise-induced transitions. J. Atmos. Sci., 65, 33373343, https://doi.org/10.1175/2008JAS2770.1.

    • Search Google Scholar
    • Export Citation
  • Bolhuis, P. G., D. Chandler, C. Dellago, and P. L. Geissler, 2002: Transition path sampling: Throwing ropes over mountain passes in the dark. Annu. Rev. Phys. Chem., 53, 291318, https://doi.org/10.1146/annurev.physchem.53.082301.113146.

    • Search Google Scholar
    • Export Citation
  • Charlton, A. J., and L. M. Polvani, 2007: A new look at stratospheric sudden warmings. Part I: Climatology and modeling benchmarks. J. Climate, 20, 449469, https://doi.org/10.1175/JCLI3996.1.

    • Search Google Scholar
    • Export Citation
  • Charlton, A. J., and Coauthors, 2007: A new look at stratospheric sudden warmings. Part II: Evaluation of numerical model simulations. J. Climate, 20, 470488, https://doi.org/10.1175/JCLI3994.1.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., and P. G. Drazin, 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83109, https://doi.org/10.1029/JZ066i001p00083.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., and J. G. DeVore, 1979: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci., 36, 12051216, https://doi.org/10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Christiansen, B., 2000: Chaos, quasiperiodicity, and interannual variability: Studies of a stratospheric vacillation model. J. Atmos. Sci., 57, 31613173, https://doi.org/10.1175/1520-0469(2000)057<3161:CQAIVS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Crommelin, D. T., 2003: Regime transitions and heteroclinic connections in a barotropic atmosphere. J. Atmos. Sci., 60, 229246, https://doi.org/10.1175/1520-0469(2003)060<0229:RTAHCI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Crommelin, D. T., J. D. Opsteegh, and F. Verhulst, 2004: A mechanism for atmospheric regime behavior. J. Atmos. Sci., 61, 14061419, https://doi.org/10.1175/1520-0469(2004)061<1406:AMFARB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Du, R., V. S. Pande, A. Y. Grosberg, T. Tanaka, and E. S. Shakhnovich, 1998: On the transition coordinate for protein folding. J. Chem. Phys., 108, 334, https://doi.org/10.1063/1.475393.

    • Search Google Scholar
    • Export Citation
  • E, W., and E. Vanden-Eijnden, 2006: Towards a theory of transition paths. J. Stat. Phys., 123, 503523, https://doi.org/10.1007/s10955-005-9003-9.

    • Search Google Scholar
    • Export Citation
  • E, W., W. Ren, and E. Vanden-Eijnden, 2004: Minimum action method for the study of rare events. Commun. Pure Appl. Math., 57, 637656, https://doi.org/10.1002/cpa.20005.

    • Search Google Scholar
    • Export Citation
  • Esler, J. G., and M. Mester, 2019: Noise-induced vortex-splitting stratospheric sudden warmings. Quart. J. Roy. Meteor. Soc., 145, 476494, https://doi.org/10.1002/qj.3443.

    • Search Google Scholar
    • Export Citation
  • Finkel, J., D. S. Abbot, and J. Weare, 2020: Path properties of atmospheric transitions: Illustration with a low-order sudden stratospheric warming model. J. Atmos. Sci., 77, 23272347, https://doi.org/10.1175/JAS-D-19-0278.1.

    • Search Google Scholar
    • Export Citation
  • Finkel, J., R. J. Webber, E. P. Gerber, D. S. Abbot, and J. Weare, 2021: Learning forecasts of rare stratospheric transitions from short simulations. Mon. Wea. Rev., 149, 36473669, https://doi.org/10.1175/MWR-D-21-0024.1.

    • Search Google Scholar
    • Export Citation
  • Finkel, J., E. P. Gerber, D. S. Abbot, and J. Weare, 2022: Revealing the statistics of extreme events hidden in short weather forecast data. arXiv, 2206.05363v1, https://doi.org/10.48550/arXiv.2206.05363.

    • Search Google Scholar
    • Export Citation
  • Forgoston, E., and R. O. Moore, 2018: A primer on noise-induced transitions in applied dynamical systems. SIAM Rev., 60, 9691009, https://doi.org/10.1137/17M1142028.

    • Search Google Scholar
    • Export Citation
  • Frame, D. J., S. M. Rosier, I. Noy, L. J. Harrington, T. Carey-Smith, S. N. Sparrow, D. A. Stone, and S. M. Dean, 2020: Climate change attribution and the economic costs of extreme weather events: A study on damages from extreme rainfall and drought. Climatic Change, 162, 781797, https://doi.org/10.1007/s10584-020-02729-y.

    • Search Google Scholar
    • Export Citation
  • Freidlin, M. I., and A. D. Wentzell, 1970: Random Perturbations of Dynamical Systems. Springer, 460 pp.

  • Helfmann, L., E. Ribera Borrell, C. Schütte, and P. Koltai, 2020: Extending transition path theory: Periodically driven and finite-time dynamics. J. Nonlinear Sci., 30, 33213366, https://doi.org/10.1007/s00332-020-09652-7.

    • Search Google Scholar
    • Export Citation
  • Helfmann, L., J. Heitzig, P. Koltai, J. Kurths, and C. Schütte, 2021: Statistical analysis of tipping pathways in agent-based models. Eur. Phys. J. Spec. Top., 230, 32493271, https://doi.org/10.1140/epjs/s11734-021-00191-0.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R., and C. Mass, 1976: Stratospheric vacillation cycles. J. Atmos. Sci., 33, 22182225, https://doi.org/10.1175/1520-0469(1976)033<2218:SVC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kron, W., P. Löw, and Z. W. Kundzewicz, 2019: Changes in risk of extreme weather events in Europe. Environ. Sci. Policy, 100, 7483, https://doi.org/10.1016/j.envsci.2019.06.007.

    • Search Google Scholar
    • Export Citation
  • Lee, C.-Y., M. K. Tippett, A. H. Sobel, and S. J. Camargo, 2018: An environmentally forced tropical cyclone hazard model. J. Adv. Model. Earth Syst., 10, 223241, https://doi.org/10.1002/2017MS001186.

    • Search Google Scholar
    • Export Citation
  • Lengaigne, M., and G. A. Vecchi, 2010: Contrasting the termination of moderate and extreme El Niño events in coupled general circulation models. Climate Dyn., 35, 299313, https://doi.org/10.1007/s00382-009-0562-3.

    • Search Google Scholar
    • Export Citation
  • Lesk, C., P. Rowhani, and N. Ramankutty, 2016: Influence of extreme weather disasters on global crop production. Nature, 529, 8487, https://doi.org/10.1038/nature16467.

    • Search Google Scholar
    • Export Citation
  • Lubis, S. W., C. S. Y. Huang, and N. Nakamura, 2018: Role of finite-amplitude eddies and mixing in the life cycle of stratospheric sudden warmings. J. Atmos. Sci., 75, 39874003, https://doi.org/10.1175/JAS-D-18-0138.1.

    • Search Google Scholar
    • Export Citation
  • Lucente, D., J. Rolland, C. Herbert, and F. Bouchet, 2021: Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain. arXiv, 2110.05050v3, https://doi.org/10.48550/arXiv.2110.05050.

    • Search Google Scholar
    • Export Citation
  • Lucente, D., C. Herbert, and F. Bouchet, 2022: Committor functions for climate phenomena at the predictability margin: The example of El Niño–Southern Oscillation in the Jin and Timmermann model. J. Atmos. Sci., 79, 23872400, https://doi.org/10.1175/JAS-D-22-0038.1.

    • Search Google Scholar
    • Export Citation
  • Mann, M. E., S. Rahmstorf, K. Kornhuber, B. A. Steinman, S. K. Miller, and D. Coumou, 2017: Influence of anthropogenic climate change on planetary wave resonance and extreme weather events. Sci. Rep., 7, 45242, https://doi.org/10.1038/srep45242.

    • Search Google Scholar
    • Export Citation
  • Miloshevich, G., B. Cozian, P. Abry, P. Borgnat, and F. Bouchet, 2022: Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data. arXiv, 2208.00971v1, https://doi.org/10.48550/ARXIV.2208.00971.

    • Search Google Scholar
    • Export Citation
  • Miron, P., F. J. Beron-Vera, L. Helfmann, and P. Koltai, 2021: Transition paths of marine debris and the stability of the garbage patches. Chaos, 31, 033101, https://doi.org/10.1063/5.0030535.

    • Search Google Scholar
    • Export Citation
  • Miron, P., F. J. Beron-Vera, and M. J. Olascoaga, 2022: Transition paths of North Atlantic deep water. J. Atmos. Oceanic Technol., 39, 959971, https://doi.org/10.1175/JTECH-D-22-0022.1.

    • Search Google Scholar
    • Export Citation
  • Mohamad, M. A., and T. P. Sapsis, 2018: Sequential sampling strategy for extreme event statistics in nonlinear dynamical systems. Proc. Nat. Acad. Sci. USA, 115, 11 13811 143, https://doi.org/10.1073/pnas.1813263115.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., and A. Solomon, 2010: Finite-amplitude wave activity and mean flow adjustments in the atmospheric general circulation. Part I: Quasigeostrophic theory and analysis. J. Atmos. Sci., 67, 39673983, https://doi.org/10.1175/2010JAS3503.1.

    • Search Google Scholar
    • Export Citation
  • Oksendal, B., 2003: Stochastic Differential Equations: An Introduction with Applications. Springer, 379 pp.

  • Pavliotis, G. A., 2014: Stochastic Processes and Applications. Springer, 339 pp.

  • Ragone, F., and F. Bouchet, 2020: Computation of extreme values of time averaged observables in climate models with large deviation techniques. J. Stat. Phys., 179, 16371665, https://doi.org/10.1007/s10955-019-02429-7.

    • Search Google Scholar
    • Export Citation
  • Ragone, F., J. Wouters, and F. Bouchet, 2018: Computation of extreme heat waves in climate models using a large deviation algorithm. Proc. Natl. Acad. Sci. USA, 115, 2429, https://doi.org/10.1073/pnas.1712645115.

    • Search Google Scholar
    • Export Citation
  • Ruzmaikin, A., J. Lawrence, and C. Cadavid, 2003: A simple model of stratospheric dynamics including solar variability. J. Climate, 16, 15931600, https://doi.org/10.1175/1520-0442(2003)016<1593:ASMOSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Stephenson, D. B., B. Casati, C. A. T. Ferro, and C. A. Wilson, 2008: The extreme dependency score: A non-vanishing measure for forecasts of rare events. Meteor. Appl., 15, 4150, https://doi.org/10.1002/met.53.

    • Search Google Scholar
    • Export Citation
  • Strahan, J., A. Antoszewski, C. Lorpaiboon, B. P. Vani, J. Weare, and A. R. Dinner, 2021: Long-time-scale predictions from short-trajectory data: A benchmark analysis of the trp-cage miniprotein. J. Chem. Theory Comput., 17, 29482963, https://doi.org/10.1021/acs.jctc.0c00933.

    • Search Google Scholar
    • Export Citation
  • Strahan, J., J. Finkel, A. R. Dinner, and J. Weare, 2022: Forecasting using neural networks and short-trajectory data. arXiv, 2208.01717v1, https://doi.org/10.48550/ARXIV.2208.01717.

    • Search Google Scholar
    • Export Citation
  • Tantet, A., F. R. van der Burgt, and H. A. Dijkstra, 2015: An early warning indicator for atmospheric blocking events using transfer operators. Chaos, 25, 036406, https://doi.org/10.1063/1.4908174.

    • Search Google Scholar
    • Export Citation
  • Thiede, E., D. Giannakis, A. R. Dinner, and J. Weare, 2019: Approximation of dynamical quantities using trajectory data. arXiv, 1810.01841v2, https://doi.org/10.48550/arXiv.1810.01841.

    • Search Google Scholar
    • Export Citation
  • Thual, S., A. J. Majda, N. Chen, and S. N. Stechmann, 2016: Simple stochastic model for El Niño with westerly wind bursts. Proc. Natl. Acad. Sci. USA, 113, 10 24510 250, https://doi.org/10.1073/pnas.1612002113.

    • Search Google Scholar
    • Export Citation
  • Timmermann, A., F.-F. Jin, and J. Abshagen, 2003: A nonlinear theory for El Niño bursting. J. Atmos. Sci., 60, 152165, https://doi.org/10.1175/1520-0469(2003)060<0152:ANTFEN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Vanden-Eijnden, E., 2006: Transition path theory. Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, Springer, 453–493, https://doi.org/10.1007/3-540-35273-2_13.

  • Vitart, F., and A. W. Robertson, 2018: The Sub-Seasonal To Seasonal Prediction project (S2S) and the prediction of extreme events. npj Climate Atmos. Sci., 1, 3, https://doi.org/10.1038/s41612-018-0013-0.

    • Search Google Scholar
    • Export Citation
  • Webber, R. J., D. A. Plotkin, M. E. O’Neill, D. S. Abbot, and J. Weare, 2019: Practical rare event sampling for extreme mesoscale weather. Chaos, 29, 053109, https://doi.org/10.1063/1.5081461.

    • Search Google Scholar
    • Export Citation
  • Yoden, S., 1987a: Bifurcation properties of a stratospheric vacillation model. J. Atmos. Sci., 44, 17231733, https://doi.org/10.1175/1520-0469(1987)044<1723:BPOASV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yoden, S., 1987b: Dynamical aspects of stratospheric vacillations in a highly truncated model. J. Atmos. Sci., 44, 36833695, https://doi.org/10.1175/1520-0469(1987)044<3683:DAOSVI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 581 547 35
Full Text Views 136 129 8
PDF Downloads 190 184 11