1 / 24

Sensitivity of the climate system to small perturbations of external forcing

Sensitivity of the climate system to small perturbations of external forcing. V.P. Dymnikov , E.M. Volodin, V.Ya. Galin, A.S. Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov. Institute of Numerical Mathematics RAS, Moscow.

taipa
Télécharger la présentation

Sensitivity of the climate system to small perturbations of external forcing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sensitivity of the climate system to small perturbations of external forcing V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S. Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov Institute of Numerical Mathematics RAS, Moscow

  2. The climate system - the system consisting of atmosphere, hydrosphere, cryosphere, land and biota. • The climate -the ensemble of states the climate systempasses through during a sufficiently long time interval. • Characteristics of the climate system as a physical object: • quasi-two-dimensionality • impossibility of purposeful physical experiments

  3. The central direction of the climate sensitivity studies: mathematical modeling Problems: 1. The identification of models by sensitivity. 2. Is it possible to determine the sensitivity of the climate system to small external forcing using single trajectory?

  4. The climate model sensitivity to the increasing of CO2 CMIP - Coupled Model Intercomparison Project http://www-pcmdi.llnl.gov/cmip CMIP collects output from global coupled ocean-atmosphere general circulation models (about 30 coupled GCMs). Among other usage, such models are employed both to detect anthropogenic effects in the climate record of the past century and to project future climatic changes due to human production of greenhouse gases and aerosols.

  5. Climate simulations and investigation of the climate sensitivity to the increase of CO2 with coupled atmosphere - ocean GCM

  6. Response to the increasing of CO2 CMIP models (averaged) INM model

  7. Global warming in CMIP models in CO2 run and parameterization of lower inversion clouds. T - global warming (K), LC - parameterization of lower inversion clouds (+ parameterization was included, - no parameterization, ? - model description is not available). Models are ordered by reduction of global warming.

  8. Mathematical theory of climate • 1. Formulation of model equations • 2. Proof of the existence and uniqueness theorems • 3. Attractor existence theorem, dimension estimate • 4. Stability of the attractor (as set) and measure on it • 5. Finite-dimensional approximations and correspondent convergence theorems

  9. Mathematical theory of climate (sensitivity) 6. Construction of the response operator for measure and its moments (“optimal perturbation”, inverse problems,….) 7. Methods of approximation for 8. Numerical experiments

  10. Response operator for 1st moment (linear theory) Linear model for the low-frequency variability of the original system: ( A is stable, is white noise in time) Perturbed system

  11. Stationary response For covariance matrix we have and response operator M could be obtained as

  12. Response operator for 1st moment (nonlinear theory) Nonlinear model for system dynamics: ( is the white noise in time) Perturbed system

  13. Stationary response Fokker-Plank equation for the density of invariant measure has unique stationary solution .

  14. To the first order in Consequently, In the case ofnormal distribution we arrive at

  15. Numerical experiments Construction of the approximate response operator (A.S.Gritsoun,G.Branstator, V.P.Dymnikov, R.J.Numer.Analysis&M.Model, (2002), v.17,p. 399)

  16. Reconstruction of the CCM0 response to the sinusoidal heating anomaly

  17. Field Field Correlation Correlation Amplitude ratio Amplitude ratio |Nonlin.|/|Lin.| |Nonlin.|/|Lin.| 0.88 1.09 0.13 0.69 1.06 0.21 0.87 1.13 0.10 0.63 1.05 0.17 0.85 1.16 0.17 0.78 0.91 0.27 0.76 0.92 0.15 0.72 0.82 0.17 average 0.84 1.08 0.14 average 0.71 0.96 0.20 Reconstruction of the CCM0 response (continued) Reconstruction of the equatorial sinusoidal heating anomalies. Average values of correlations, amplitude ratios are shown (for 24 different heating positions). Reconstruction of the equatorial low-level heating anomalies. Average values of correlations, amplitude ratios are shown (for 24 different heating positions).

  18. Reconstruction of the low-level heating anomalies using the inverse response operator

  19. Construction of the optimal heating forcing for the excitation of the AO • (using NCEP/NCAR data and output of AGCM of INM RAS) AO (1EOF of surface pressure) calculated using DJF NCEP/NCAR data AO (1EOF of surface pressure) calculated using output of AGCM of INM RAS

  20. Procedure for the construction of the approximate response operator is analogues to(A.S.Gritsoun, G.Branstator, V.P.Dymnikov, R.J.Numer. Analysis&M.Model, (2002), v.17,p. 399) Optimal perturbation for AO (1EOF of PS) calculated using NCEP/NCAR reanalysis data (zonal average) Optimal perturbation for AO (1EOF of PS) calculated using output of AGCM of INM RAS (zonal average)

  21. Global warming in CMIP models in CO2 run and parameterization of lower inversion clouds. T - global warming (K), LC - parameterization of lower inversion clouds (+ parameterization was included, - no parameterization, ? - model description is not available). Models are ordered by reduction of global warming.

  22. Acknowledgments • Our studies are supported by: • Russian Ministry for Industry, Sciences and Technology • Russian Academy of Sciences • Russian Foundation for Basic Research • INTAS

More Related