8. Seasonal-to-Interannual Predictability and Prediction 8.1 Predictability 8.2 Prediction.
Predictability associated with nonlinear regimes in an idealzied atmospheric model
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Predictability associated with nonlinear regimes in an idealzied atmospheric model
Sergey Kravtsov
University of Wisconsin-MilwaukeeDepartment of Mathematical Sciences
Atmospheric Science Group
Collaborators:
N. Schwartz, J. M. Peters, University of Wisconsin-Milwaukee, USA
Presentation at the AGU Fall Meeting 2011, San Francisco, CA, USA
December 7, 2011
http://www.uwm.edu/kravtsov/
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Atmospheric flow regimes
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dx
dt=Lx +N1 (x,x) +N2(x,x') +N3(x',x') +F
x — large-scale, low-frequency flow
x’ — fast transients, F — external forcing
• N3 can be approximated as Gaussian noise
• If N1 and N2 are small or linearly parametrizable, x will also be Gaussian-distributed
• Deviations from gaussianity — REGIMES — can be due to N1, N2 and F
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Two paradigms of regimes
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dx
dt= −dV (x)
dx+ B(x)η
• Regimes are due to deterministic non-linearities (e.g., Legras and Ghil ‘85)
• Regimes are due to multiplicative noise (Sura et al. ’05)
• The first type of regimes is inheren-tly more predictable
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Is there enhanced predictability associated with regimes?
• We address this ques-tion by studying the out-put from a long simula-tion of a three-level QG model (Marshall&Molteni ’93)
• The QG3 model is tuned to observed clima-tology and has a realistic LFV with non-gaussian regimes (Kondrashov et al.)
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Regime Identification• Regimes defined as regions of enhanced probability of persistence relative to a benchmark linear model (cf. Vautard et al. ’88; Kravtsov et al. ‘09), in Uz200 and Psi200 EOF-1–EOF-2 subspaces
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Four Distinct Regimes in QG3 model
1: AO+ 2: AO–
Psi 3: NAO+Uz 3: N-AO+
• AO Regimes 1 and 2 are largely zonally symmetric and stati-stically the same bwn the two metrics
• Non-AO Regimes 3 in Uz and Psi are less zonally sym-metric; they are distinct regimes
• Similar regimes were obtained before
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Regimes and Predictability• “Predictable” R1 and R2 have precursor regions of low RMSD (blue areas in fig.)1
2
3
• Same precursor regions for lead 5 and 10-day fcst
• Initializations in precursor regions end up in regimes
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• Initializations from precursor regions slow down in regime regions and stay there, while maintaining low spread
Predictable regimes:Regime 1 Regime 2
Day 1
Day 5
Day 10
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• Initializations from non-precursor regions spread out faster and quickly decay to climatology
Unpredictable states:Non-regime Regime 3
Day 1
Day 5
Day 10
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Discussion• Regimes are not always associated with enhanced predictability (cf. Sura et al. ‘05)
• In QG3, the predictable regimes arise as a combination of (i) nonlinear slowdown of trajectories’ decay toward climatology (deterministic nonlinearity) and (ii) reduced spread of trajectories in regime regions (multiplicative noise). Unpredictable regimes don’t have (ii).
• Detailed effects of deterministic nonlinearity and multiplicative noise onto predictability are studied by fitting a nonlinear stochastic SDE to the QG3 generated time series (Peters and Kravtsov 2011)