Optimale pådriv for endringer i hyppigheten av atmosfæriske strømningsmønstre, spesielt COWL

Optimale pådriv for endringer i hyppigheten av atmosfæriske strømningsmønstre, spesielt COWL Trond Iversen, Jørn Kristiansen, Thomas Jung* and Jan Barkmeijer** * ECMWF ** KNMI

Innhold Litt teori (med noen resultater) Motivasjon for studien Kort om metoden Flere resultater

Værvarslene er kritisk avhengig av selve initial-tilstanden/strømningsbildet; for gitt analysefeil - noen ganger stor usikkerhet i varslene, andre ganger er varslene sikre flere dager frem i tid sommerfugleffekten

Scientific basis Sensitive and non-sensitive trajectories; nonlinearity! Likely initial states or uncertainty in the analysis; SMALL perturbations 1 Pattern A Pattern B Predictable and non-sensitive to perturbations; small spread/uncertainty in the forecast 2 Transition from non-sensitive (1) to sensitive (2); some spread/uncertainty in the forecast (cf. the forecast ending in pattern A or B from about the same initial state) Unpredictable and sensitive; no skill (compared to climatology) at the end of the forecast (throwing a dart arrow at the attractor is about as useful as the (modeled) forecast)

D+4 In the real atmosphere: the COWL index is less (more) predictable for sensitive (non-sensitive) cases (as expected) COWL Index one parameter describing the atmospheric state D+4 Perfect forecast r - correlation coefficient (forecast, analysis) s - st.dev. of the forecast error The differences are substantial; 99.9% significance level (for s) analysis

Sensitiviteten avhenger av posisjonen på attraktoren, eks. 4 dagers trajektorie

Eksterne pådriv kan, på samme måte som perturbasjoner av initial-tilstanden, endre strømningsmønsteret etter en tid Sensitive områder endret hyppighet eggekartong z f = 4.5 ( e x + e y ) x

COWL: Cold Ocean Warm Land Tsurface Z500 Corti et al. (1999): Monthly mean anomalies during NH winter 4 hemispheric regimes identified 1971-94 COWL (AO) frequency increased (decreased) compared to 1949-71 An increase in COWL frequency is consistent with an increase in mean surface temperature (and a lesser increase in the atmosphere above) changes in regime frequency will be sensitive to forcing perturbations which may have little spatial correlation with the regimes themselves (non-normality) Basis for our study: investigate the structure of these sensitive patterns ( optimal forcing fields)

Tool: ECMWF IFS model Atmospheric component 60 vertical levels Sensitivity suite T63 Global NWP Diabatic adjoint model Full physics complexity TE norm (dry) Cycle 29r2 Initial conditions from ERA40

Governing Equation(s) The prognostic and deterministic equation describing the evolution of the atmospheric state is given by: x is the atmospheric dx = G (x) (1) state vector dt G is a nonlinear function The solution to (1) is the nonlinear control (or basic state) trajectory. Adding forcing perturbations we get: dx = G ( x) + f dt (2)

Forced transition to a predefined pattern (COWL), γ t = T(= 4d) xt xct = γ dεt G L εt + f dt ~ ε = M(0,T)f t =0 dxct c = G(xt) dt dxt = G(xt)+ f dt T εt = xt x c t "Choose"f such that εt γ f is the optimal perturbation or sensitivity pattern

Initial state (only) perturbation xt xct = γ dεt G Lεt dt ε0 t =0 t = T(= 4d) εt = M(0,T)ε0 εt γ

Sensitivity Cost function: 1 J = P(εT γ),p(εt γ) TE 2 Minimize J, i.e. maximize δ J : δj i,f J,f where TE ~ * P * Pγ i,f J = M Sensitivity Index: i,f J γ

Experimental design 22 winter seasons from 1957 to 2002 Prolonged Winter (15 Oct 15 Apr) 5 day forecast interval 4 days linear integration (i.e. local perturbations) 6 iterations Focus is the region northward of 30 degrees North

Metoden fungerer; COWL trer frem i de ikke-lineært utviklede perturbasjonene Z500 Forcing Initial Average St.dev.

PDF with respect to COWL 20 Frequency 15 10 5 0-11 -10-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 8 COWL index The results are consistent with the ones in Corti et al. (1999) (but obvioulsy overestimates the number of transitions ) So how often is the atmosphere susceptible to (external) forcing perturbations or how many of our transitions are likely to occur? sensitivity

Sensitivity

The external forcing needs to project positively onto the sensitivity patterns below (5% most sensitive!)

The sensitivity patterns are case dependent (ex. 10 most sens. cases)

Temperature is the parameter to perturb (especially for forcing!)

Sensitivity studies results from 22 winter seasons Perturbing the initial state is distinctively different from perturbing the forcing (as for SVs). Not shown, but it is! High sensitivity cases are rare and of short duration Temperature is the important forcing parameter and mid-atmospheric perturbations are dominant Evidence of changes in the occurrence of low-frequency atmospheric modes There are two fairly distinct paths in phase space associated with predictable and unpredictable transitions Individual perturbations are highly localized