Sensitivity of the climate system to small perturbations of external forcing

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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
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• The climate system - the system consisting of
  atmosphere, hydrosphere, cryosphere, land and
  biota.

• The climate - the ensemble of states the climate
  system passes through during a sufficiently long
  time interval.

• Characteristics of the climate system as a
  physical object
• quasi-two-dimensionality
• impossibility of purposeful physical experiments

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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?
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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.
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Climate simulations and investigation of the
climate sensitivity to the increase of CO2 with
coupled atmosphere - ocean GCM
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Response to the increasing of CO2
CMIP models (averaged)
INM model
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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.
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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

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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
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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
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Stationary response For covariance matrix we
have and response operator M could be obtained
as
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Response operator for 1st moment (nonlinear
theory)
Nonlinear model for system dynamics (
is the white noise in time) Perturbed
system
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Stationary response Fokker-Plank equation
for the density of invariant measure has unique
stationary solution .
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To the first order in Consequently, In the
case of normal distribution we arrive at
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Numerical experiments
Construction of the approximate response operator
(A.S.Gritsoun,G.Branstator, V.P.Dymnikov,
R.J.Numer.AnalysisM.Model, (2002), v.17,p. 399)
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Reconstruction of the CCM0 response to the
sinusoidal heating anomaly
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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).
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Reconstruction of the low-level heating anomalies
using the inverse response operator
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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
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Procedure for the construction of the approximate
response operator is analogues to (A.S.Gritsoun,
G.Branstator, V.P.Dymnikov, R.J.Numer.
AnalysisM.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)
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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.
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Acknowledgments

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