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/

Atmospheric flow regimes

€

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

Two paradigms of regimes

€

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

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.)

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

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

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

• 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

• 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

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)