Comparison between ensembles generated with atmospheric and with oceanic perturbations, using the MPI-ESM model

Transcription

1 Comparison between ensembles generated with atmospheric and with oceanic perturbations, using the MPI-ESM model C. Marini 1. A. Köhl 1. D. Stammer 1 Vanya Romanova 2. Jürgen Kröger 3 1 Institut für Meereskunde - Universität Hamburg 2 Universität Bonn 3 Max Plank Institut für Meteorologie International workshop on seasonal to decadal prediction, May 213 Decadal Climate Prediction

2 Ensemble generation for decadal predictions? Our GOAL: representation of errors on OCEANIC initial conditions WHY? Memory of the ocean = key hypothesis for predictability at decadal time scales Large errors on the oceanic state, especially at depth

3 Ensemble generation for decadal predictions? Our GOAL: representation of errors on OCEANIC initial conditions WHY? Memory of the ocean = key hypothesis for predictability at decadal time scales Large errors on the oceanic state, especially at depth Zanna et al 211, 212 Deep density perturbations in the Atlantic Faster (7.5 vs 18.5 yr) and larger AMOC amplications than with upper oceanic perturbations Overestimation of oceanic predictability in decadal predictions exp where only the atmospheric state is perturbed

4 A need to create more relevant ensembles for decadal predictions? For now, ensemble generation : rather pragmatic Perturbing the atmospheric horizontal diusion coecient (e.g. Matei et al Sci 212) Lagged initialization : shifting by a few days the atmospheric initial conditions the oceanic initial conditions (e.g Smith et al Sci 27, Msadek et al GRL 21, Müller et al GRL 212) Use of ensemble of ocean reanalyses/assimilation runs - obtained by using dierent initial conditial conditions of the historical run - obtained by perturbing the wind stress (+ SST perturbations at the hindcast's start) in Weisheimer et al GRL 29, von Oldenborgh CD 212 Get inspired from weather forecast and seasonal predictions : Singular vectors (Hawkins and Sutton JCLI 29) Anomaly Transform Breeding vectors

5 A need to create more relevant ensembles for decadal predictions? Comparison between : Lagged initialization : shifting by a few days the atmospheric initial conditions Singular vectors... A cheap version of oceanic singular vectors...

6 An attempt to generate climatic relevant perturbations Goal : Finding perturbations growing the most rapidly with a time scale relevant for decadal predictions scaled to represent the uncertainties contained in the initial conditions Singular vectors (SVs) of the tangent propagator of the dynamical system representing the evolution of the ocean (Molteni 1996 for the atmosphere, Palmer and Zanna submitted for a review about SVs)

7 An attempt to generate climatic relevant perturbations Goal : Finding perturbations growing the most rapidly with a time scale relevant for decadal predictions scaled to represent the uncertainties contained in the initial conditions Singular vectors (SVs) of the tangent propagator of the dynamical system representing the evolution of the ocean (Molteni 1996 for the atmosphere, Palmer and Zanna submitted for a review about SVs) TOO EXPENSIVE : requires the tangent propagator and its adjoint of the oceanic model...

8 An attempt to generate climatic relevant perturbations Goal : Finding perturbations growing the most rapidly with a time scale relevant for decadal predictions scaled to represent the uncertainties contained in the initial conditions Singular vectors (SVs) of the tangent propagator of the dynamical system representing the evolution of the ocean (Molteni 1996 for the atmosphere, Palmer and Zanna submitted for a review about SVs) TOO EXPENSIVE : requires the tangent propagator and its adjoint of the oceanic model... dx = Bx + F dt Simplication of the evolution of the oceanic state based on Linear Inverse Modeling (LIM) - x : 3d EOFs of T and S from the 156-yr long historical run of the MPI-ESM model 68.4% of the total variance - B : Deterministic matrix, F : White noise Tzipermann and Zanna JCLI 28 : 3d EOFs of T and S annual anomalies in the Atlantic Hawkins and Sutton JCLI 29 : idem but only from the upper 2km of the Atlantic

9 Linear Inverse Modeling (LIM) Evolution of a perturbation of the system : x(t + τ) = e τb x(t) = G(τ)x(t) Amplication over a time τ under the L2 norm : µ(τ) = x(τ) 2 x() 2 = x(τ)t x(τ) x() T x() = x()t G(τ) T G(τ)x() x() T x() Singular vectors = eigenvectors of G(τ) T G(τ) - τ = 5 yr - Selection of the rst 4 SVs 1 a posteriori errors

10 Linear Inverse Modeling (LIM) Evolution of a perturbation of the system : x(t + τ) = e τb x(t) = G(τ)x(t) Amplication over a time τ under the L2 norm : µ(τ) = x(τ) 2 x() 2 = x(τ)t x(τ) x() T x() = x()t G(τ) T G(τ)x() x() T x() Singular vectors = eigenvectors of G(τ) T G(τ) - τ = 5 yr - Selection of the rst 4 SVs + Rotation and Scaling of the SVs similar to Molteni et al 1996 More uniform spatial distribution Match on average the estimates of the rms error 1 of the oceanic reanalysis used to create the oceanic initial conditions (GECCO2) 1 a posteriori errors

11 Introduction Poor man's oceanic SVs Oceanic vs Atmospheric perturb Comparison with other methods Pattern of the rotated and scaled SVs. Temperature at 15m. SV1 T at 15m SV3 T at 15m C. Marini. A. Köhl. D. Stammer SV2 T at 15m SV4 T at 15m Oceanic perturbations - decadal predictions Conclusion

12 Introduction Poor man's oceanic SVs Oceanic vs Atmospheric perturb Comparison with other methods Pattern of the rotated and scaled SVs. Salinity at 15m. SV1 S at 15m SV2 S at 15m SV3 S at 15m SV4 S at 15m C. Marini. A. Köhl. D. Stammer Oceanic perturbations - decadal predictions Conclusion

13 Introduction Poor man's oceanic SVs Oceanic vs Atmospheric perturb Comparison with other methods Conclusion Rms of the rotated and scaled SVs and rms error of GECCO2 at 15m. rms of the SVs C. Marini. A. Köhl. D. Stammer rms errors Oceanic perturbations - decadal predictions

14 Introduction Poor man's oceanic SVs Oceanic vs Atmospheric perturb Comparison with other methods Conclusion Rms of the rotated and scaled SVs and rms error of GECCO2 at 122m. rms of the SVs C. Marini. A. Köhl. D. Stammer rms errors Oceanic perturbations - decadal predictions

15 Hindcasts with the MPI-ESM model Initial condition from an "assimilation run" : Nudging of T and S towards T and S anomalies from GECCO2 put on the MPI-ESM climatology 1-yr long hindcasts starting every 1st January from 1991 to 26 Two types of ensembles : Atmospheric Perturbations = Atm ICs shifted by 1 to 8 days 1 ensemble = 1 unperturbed member + 8 perturbed members Oceanic Perturbations = Oce ICs +SV1, +SV2, +SV3, +SV4, -SV1, -SV2, -SV3, -SV ensembles = 16 ( ) 1yr = 272 yr

16 A validation of the ensemble spread : Talagrand diagram 9 ensemble members sorted in ascending order 1 bins for each time step : At each time step the observation is located in one bin Histogram : n shape : overestimated spread U shape : lack of spread Associated scores (Keller and Hense 211) : beta score (bs) bs= at histogram bs> too large spread bs< too narrow spread beta bias (bb) bb> bias towards higher values bb< bias towards lower values L shape : bias Flat : relevant spread Mean bias removed following the recommendation of the CMIP-WGCM-WGSIP Decadal Climate Prediction Panel

17 Atlantic meridional overturning circulation around 26.5N Monthly values, Verication values : assimilation run Total Overturning The Ekman component has been removed Oceanic perturbations Atmospheric perturbations 5 bs=-.16, bb=.11 5 bs=-.45, bb=.9 Lag1 4 4 Oceanic perturbations Atmospheric perturbations Lag1 6 bs=-.35, bb=.15 bs=-.95, bb= Lag bs=-.23, bb= bs=-.35, bb=.8 Lag bs=-.43, bb= bs=-.98, bb= Lag bs=-.7, bb= bs=-.28, bb=.1 Lag bs=-.19, bb= bs=-.63, bb= Lag bs=-.22, bb= bs=-.38, bb=.8 Lag bs=-.27, bb= bs=-.81, bb=

18 Atlantic meridional overturning circulation around 47.5N Monthly values, Verication values : assimilation run Oceanic perturbationsatmospheric perturbations Lag1 bs=.17, bb=.17 bs=-.59, bb= Lag bs=-.15, bb= bs=-.6, bb= Lag bs=-.17, bb= bs=-.51, bb= Lag bs=-.29, bb= bs=-.35, bb=

19 Oceanic heat content upper 7m and SST in the Atlantic (yearly values) Atlantic basin Verication values : NODC dataset (Levitus et al 29) x 1⁴ 2.5 Lag Oceanic perturbations Atmospheric perturbations 1 bs=.14, bb=.21 x 1⁴ bs=-1.76, bb=.5 North Atlantic (8W-, -6N) Verication values : HadISST dataset (Rayner et al 23) Oceanic perturbations Atmospheric perturbations bs=.39, bs=.34 bs=.23, bs=.15 Lag x 1⁴ 2 Lag bs=.15, bb=.21 x 1⁴ bs=-.91, bb=.7 8 Lag bs=.43, bs= bs=.2, bs= Lag bs=.22, bb= bs=-.57, bb=.9 8 Lag bs=.38, bs= bs=.9, bs= Lag bs=.25, bb= bs=-.43, bb=.1 8 Lag bs=.38, bs= bs=.17, bs=

20 Ensemble spread of SST averaged in the North Atlantic Ensemble spread from every starting date oceanic perturbations years 1.25 atmospheric perturbations Ensemble spread of SST averaged in the North Atlantic decreases with time for oceanic perturbations Idem for temperature averaged in the upper 2m of the Atlantic basin years 1 Why? Perturbations averaged over these areas are larger than the std of the signal The model gets back to its climatology Trade-o between : strong perturbations that actually represent the errors on initial conditions when too strong perturbations, model gets back to its climatology

21 Does the amplication predicted by the LIM occur in the hindcasts with oceanic perturbation? Amplication over a time τ = 5 yr under the L 2 norm : µ(τ) = x(τ) 2 x() = x(τ)t x(τ) 2 x() T x() = x()t G(τ) T G(τ)x() with x = x() T x() ( T unpert T pert S unpert S pert ) Ampli Ampli SV1 SV year SV2 SV year Red : Amplication predicted by the LIM - Mean of amplication over the hindcasts : Black : +SV Blue : -SV Solid thin line : contribution of temperature Dashed thin line : contribution of salinity Amplications of the perturbations do occur under the L2 norm BUT the average over a given area of the perturbations decreases

22 Comparison with other methods Comparison between ensemble generated with: Cheap Oceanic Singular vectors Atmospheric laggged initialization Atmospheric and Oceanic laggged initialization Jürgen Kröger Ensemble of assimilation runs obtained by using dierent initial conditions of the historical run Jürgen Kröger Anomaly Transform Poster 31 of Vanya Romanova Set up : Initial condition from the "assimilation run" towards GECCO2 anomalies 1-yr long hindcasts starting the 1st January 1996

23 Atlantic Meridional Overturning Circulation at 26.5N Atmospheric lagged initialization Oceanic lagged initialization From ensemble of assimilation run Ensemble std and std of the reference run Anomaly transform Cheap oceanic Singular Vectors Ensemble Mean (dashed), +/-ensemble std (solid), and reference run (red) assimilation run atmospheric lagged initialization anomaly transform cheap oceanic singular vectors from ensemble of assimilation run

24 Temperature averaged in the upper 2m North Atlantic basin Pacic basin Ensemble Mean (dashed), +/-ensemble std (solid), and reference run (red) Ensemble std Ensemble Mean (dashed), +/-ensemble std (solid), and reference run (red) Ensemble std assimilation run atmospheric lagged initialization anomaly transform cheap oceanic singular vectors from ensemble of assimilation run assimilation run atmospheric lagged initialization anomaly transform cheap oceanic singular vectors from ensemble of assimilation run WORK IN PROGRESS part of Miklip... Hard to evaluate the benets of one method with only one starting date...

25 Conclusion Comparison between a cheap version of oceanic singular vectors and atmospheric lagged initialisation Oceanic perturbations globally better spread, at least not worse Too large perturbations model gets back to its climatology? How to improve the cheap oceanic singular vectors? Get rid of the linear approximation Choice of a better norm to compute the singular vectors