Using Stochastic Physics to represent Model Uncertainty

1. Using Stochastic Physics to represent Model Uncertainty Judith Berner ECMWF

2. Outline • Model error in weather forecasting and climate models • A new stochastic kinetic energy backscatter scheme (SPBS) • Impact of SPBS on probabilistic weather forecasting (medium-range) • Impact of SPBS on systematic model error (seasonal to climatic time-scales)

3. Sensitivity to initial perturbations Edward Lorenz “… one flap of a sea-gull’s wing may forever change the future course of the weather” (Lorenz, 1963)

4. Ensemble Forecast for Thurs 15th 2007

5. Representing initial state uncertainty by an ensemble of states RMS error • Represent initial uncertainty by ensemble of states • Flow-dependence: • Predictable states should have small ensemble spread • Unpredictable states should have large ensemble spread • Ensemble spread should grow like RMS error spread ensemble mean analysis

6. Underdispersion of the ensemble system Systems • The RMS error grows faster than the spread • Ensemble isunderdispersive • Ensemble forecast is overconfident -------spread around ensemble mean RMS error of ensemble mean • Underdispersion is a form of model error • Forecast error = initial error + model error Buizza et al., 2004

7. Manifestations of model error In medium-range: • Underdispersion of ensemble system (Overconfidence) • Can extreme weather events be captured? On seasonal to climatic scales: • Not enough internal variability • To which degree do detection and attribution studies for climate change depend on a correct estimate of internal variability? • Underestimation of the frequency of blocking • Tropical variability, e.g. MJO, wave propagation • Systematic error in T, Precip, …

8. y Causes of Model Error: Conventional parameterization schemes • Existing bulk-parameterizations assume that subgrid-scale is in equilibrium with the resolved state. • Not always true! • Remedy: Pick a realization from subgrid-scale PDF (Buizza et al, 1999)

9. Nastrom and Gage, 1985 Causes of Model Errors: Unrepresented processes in weather and climate models Kinetic energy spectra drop off too steeply Flow over mountains is modelled by drag (sink of kinetic energy) but flow accelerates in certain areas (source of kinetic energy) Palmer, 2001

10. within conventional parameterization schemes Stochastic parameterizations (Buizza et al, 1999, Lin and Neelin, 2000) Multi-parameterizations approaches (Houtekamer, 1996) Multi-parameter approaches (e.g. Murphy et al,, 2004; Stainforth et al, 2004) Multi-models (e.g. DEMETER, ENSEMBLES, TIGGE, Krishnamurti) outside conventional parameterisation schemes Nonlocal parameterizations, e.g., cellular automata pattern generator (Palmer, 1997, 2001) Stochastic kinetic energy backscatter (Shutts and Palmer 2004, Shutts 2005) Representing Uncertainty

11. Stochastic parameterizations or multi-parameter, multi-parameterization, multi-model parameterizations? Multi-model ensemble members do not have the same climate …

12. Stochastic parameterizations in weather and climate models Edward Lorenz “I believe the ultimate climatemodels…will be stochastic, i.e. random numbers will appear somewhere in the time derivatives.”(Lorenz, 1975)

13. Stochastic parameterizations have the potential to reduce model error Potential • Stochastic parameterizations can change the mean and variance of a PDF • Impacts variability of model (e.g. internal variability of the atmosphere) • Impacts systematic error (e.g. blocking, precipitation error) Weak noise Strong noise PDF Unimodal Multi-modal

14. Model error in weather forecasting and climate models A new stochastic kinetic energy backscatter scheme: SPectral Backscatter Scheme Impact of SPBS on probabilistic weather forecasting (medium-range) Impact of SPBS on systematic model error

15. Rationale: A fraction of the dissipated energy is scattered upscale and acts as streamfunction forcing for the resolved-scale flow (LES, CASBS: Shutts and Palmer 2004, Shutts 2005); New: spectral pattern generator Spectral Backscatter Scheme Total Dissipation rate from numerical dissipation, convection, gravity/mountain wave drag. Spectral Markov chain: temporal and spatial correlations prescribed

16. Contribution to Total Dissipation Rate

17. with Spectral Backscatter scheme Assume a streamfunction perturbation in spherical harmonics representation Assume furthermore that each coefficient evolves according to the spectral Markov process Find the wavenumber dependent noise amplitudes so that prescribed kinetic energy dE is injected into the flow

18. Stochastic Spatial and temporal correlations Control over wavenumber forcing allows scale selection Flow-dependent (weighting with dissipation rates) Spectral (consistent with spectral dynamical core); isotropic pattern in sphere; Injects energy in regions of large dissipation, which are the regions of large model errors Characteristics of Spectral Backscatter Scheme

19. Model error in weather forecasting and climate models A new stochastic kinetic energy backscatter scheme (SPBS) Impact of SPBS on probabilistic weather forecasting (medium-range) Impact of SPBS on systematic model error

20. Experiment setup • 50 member ensemble with and without SPBS • 46 cases between May 2004 and April 2005 • Resolution T255L40 • Focus on Northern Hemispheric midlatitudes (35-60N) and tropics (20S to 20N) • NB: Effective generation of spread by stochastic backscatter scheme allows the reduction of the initial perturbations by 15%

21. ------- spread around ensemble mean RMS error of ensemble mean Overdispersion of ensemble in NH is reduced No Stochastic Backscatter Stochastic Backscatter SPBS Overdispersion of z500 in NH for short forecast ranges is reduced!

22. ------- spread around ensemble mean RMS error of ensemble mean RMS error in tropics is reduced No Stochastic Backscatter Stochastic Backscatter • Underdispersion of u850 in tropics for all forecast ranges is reduced! • RMS error is reduced!

23. x Analysis Ensemblemean x x Ensemble members Ensemble mean error Decrease in ensemble mean error

24. Tropical skillscores (ROC area) u850 T850 • Large ROC means more skillful ensemble • Skill of u850 and T850 in tropics improved

25. Skill scores summary

26. Forecast error growth n-3 n-5/3 • For perfect ensemble system: • the analysis should be indistinguishable from a perturbed ensemble member • forecast error and model uncertainty (=spread) should be the same --- Forecast error --- Model uncertainty See also: Tribbia and Baumhefner, 2004

27. Forecast error growth in ensemble with SPBS and reduced Initial Perturbations (IP) n-3 n-5/3 • Since IPs are reduced, forecast error is reduced for small forecast times • More kinetic energy in small scales --- Forecast error --- Model uncertainty

28. Kinetic energy spectra in 500hPa(rotational component) n-3 Kinetic energy spectrum is closer to that of T799 analysis ! n-5/3

29. Model error in weather forecasting and climate models A new stochastic kinetic energy backscatter scheme (SPBS) Impact of SPBS on probabilistic weather forecasting (medium-range) Impact of SPBS on systematic model error

30. Experimental Setup for Seasonal Runs “Seasonal runs: Atmosphere only” • Atmosphere only, observed SSTs • 40 start dates between 1962 – 2001 (Nov 1) • 5-month integrations • One set of integrations with stochastic backscatter, one without • Model runs are compared to ERA40 reanalysis (“truth”)

31. Reduction of systematic error of z500 over North Pacific and North Atlantic No StochasticBackscatter Stochastic Backscatter

32. Increase in occurrence of Atlantic and Pacific blocking ERA40 + confidence interval Stochastic Backscatter No StochasticBackscatter

33. Increase of systematic error of z500 over Southern Hemisphere No Stochastic Backscatter Stochastic Backscatter

34. Empirical Orthogonal Functions 1 & 2 in the Tropics ERA40 No Stochastic Backscatter • EOF1 has different pattern and too much explained variance (too zonal?)

35. Empirical Orthogonal Functions 1 & 2 in the Tropics improve in pattern and explained variance ERA40 Stochastic Backscatter

36. Wavenumber-Frequency SpectrumSymmetric part, background removed (after Wheeler and Kiladis, 1999) Observations (NOAA) No Stochastic Backscatter

37. Improvement in Wavenumber-Frequency Spectrum Observations (NOAA) Stochastic Backscatter • Backscatter scheme reduces erroneous westward propagating modes

38. Improvement of error in tropical precipitation No Stochastic Backscatter Stochastic Backscatter • ITCZ not locked, more variability • Nudges system into the right direction, but systematic error still present

39. ENSEMBLES project Stoch Phys No Stoch Phys Courteousy of Antje Weisheimer and Paco Doblas-Reyes

41. Summary and conclusion • Stochastic parameterization have the potential to reduce model error by changing the mean state and internal variability. • It was shown that the new stochastic kinetic energy backscatter scheme (SPBS) produced a more skilful ensemble and reduced systematic model error • But: Stochastic parameterizations are not the answer to all model error problems, they can only be as good as the understanding of the underlying physical processes they are aimed at representing

42. Future Work/Open questions • It would be desirable to use coarse-grained high-resolution models (e.g. CRMs) to inform stochastic schemes • How do stochastic parameterizations compare to multi-parameter and multi-parameterization approaches? • Can we use the same stochastic parameterizations for climate and NWP model?