Predictability associated with nonlinear regimes in an idealzied atmospheric model Sergey Kravtsov University of Wisconsin-Milwaukee Department 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,

Atmospheric flow regimes x — large-scale, low-frequency flow x’ — fast transients, F — external forcing N 3 can be approximated as Gaussian noise If N 1 and N 2 are small or linearly parametrizable, x will also be Gaussian-distributed Deviations from gaussianity — REGIMES — can be due to N 1, N 2 and F

Two paradigms of regimes 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.) 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 1Regime 2 Day 1 Day 5 Day 10

Initializations from non- precursor regions spread out faster and quickly decay to climatology Unpredictable states: Non-regimeRegime 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)