1. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting 1. 1.What is model error and how can we distinguish it from initial condition error? 2. 2.The parameterisation problem and shortcomings of conventional parameterisations 3. 3.Stochastic parameterisations

2. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting What is model error?  Examples and reasons

3. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting What is model error?  Examples for model error  Wrong representation of clouds  Not enough blocking  Not enough variability in the tropics  Not enough spread in the ensemble prediction system …   Reasons   Numerical truncation of continuous process to finite resolution   Limitations of parameterizations to subscribe physics (e.g. locality)   Missing processes   …

4. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Model error “True attractor” “Model attractor”   Dynamical systems view: model and atmosphere do not have the same attractor   not enough degrees of freedom   Atmosphere might evolve in a direction not part of model attractor

5. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Model error?

6. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Ensemble Forecast for Wed 24 th 2006 Model uncertainty = Initial condition error + Model error

7. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Initial Condition Error: Model error: Truth Model Physics Model error at time will lead to initial condition error at time Disentangling model and initial condition error It is difficult to disentangel model error from initial condition error !

8. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Representing model uncertainty by running ensemble forecasts   Represent model uncertainty by ensemble of states   Ensemble spread should grow like RMS error analysis spread RMS error ensemble mean

9. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Buizza et al., 2004 Systems Not enough spread Spread-skill for medium-range ensemble forecasts RMS error of ensemble mean Ensemble spread

10. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Under-dispersion of ensemble Example: same ensemble mean, but not enough spread   one form of model error

11. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Model error at different timescales  Medium-range: Ensemble is under-dispersive  Model uncertainty is not captured by ensemble  Long-range: Systematic model error  Climatological PDF of model and atmosphere differ

12. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting   Multi-model (eg., DEMETER)   Multi-parameterization (eg., Houtekamer, 1996)   Multi-parameter (eg.,Murphy et al, 2004; Stainforth et al 2004) The multi-model multi-parameterization approach Sample over different:   Parameterizations/parameter values   account for shortcomings in any given bulk- parameterization   Models   account for further model error (different numerical schemes, boundary conditions, methods to generate uncertainty in initial condition)

13. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Palmer, 2001 Palmer et al., 2005 Nastrom and Gage, 1985 Unrepresented and insufficiently represented processes

14. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting The parameterization problem

15. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting The parameterization problem Coupled system of grid-scale and subgrid-scale processes (Lorenz, 1996) Equation for grid-scale process with parameterized subgrid-scale processes : Classical bulk-parameterization: Local and deterministic: each large scale state is in equilibrium with ensemble of subgrid-states

16. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Shortcomings of local parameterizations There are several realizations of the subgrid-state for a given large-scale state After Wilks, 2005 y

17. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Sample distribution of subgrid-scale states Draw at each time t a realization of the subgrid-state: Model uncertainty is represented in stochastic manner   Accounting for the known unknown t y For Lorenz ‘96: Reduces systematic-error and improves forecast skill (Wilks, 2005)

18. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Increase of spread: better representation of model uncertainty Reduction of systematic error (noise-induced drift and transition) Potential benefits of stochastic parameterizations

19. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Initial Perturbation: Initial Perturbation and Stochastic Physic: Stochastic Physic: Physics Increase in spread

20. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Initial perturbations & stoch. Phys. Initial perturbations only Stoch. Phys. only => Interaction is nonlinear Initial perturbations vs stochastic physics Error E_m

21. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Reduction of systematic error: Noise-induced transitions (white noise sufficient) No noise delta-function Weak noise Multi-modal PDF Strong noise Unimodal PDF

22. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Noise PDF State/flow-dependent noise Noise-induced drifts (state-dependent noise)

23. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Summary   Model uncertainty is not only caused by initial condition error, but also model error (under-dispersion of ensemble)   Multi-models, multi-parameters ensembles have the potential to improve model error, but still rely on conventional parameterizations   Representation of sub-grid scales by stochastic or stochastic-dynamic parameterizations have the potential to reduce model error by increasing the spread while at the same time reducing the systematic error

24. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting  Introduces tendency perturbations P to u, v, T, q (Buizza et al., 1999)  nonlocal: constant over 10x10 lat/long  memory: constant over 6h intervals  flow-dependent, multiplicative noise ECMWF stochastic physics scheme Operational stochastic scheme

25. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting CASBS: A cellular-automaton stochastic backscatter scheme

26. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Cellular Automaton Stochastic Backscatter Scheme (CASBS) smooth scale Non-local, quasi-random, state-dependent Rationale: A fraction of the dissipated energy is scattered upscale and acts as streamfunction forcing for the resolved-scale flow (LES) (Shutts and Palmer 2004, Shutts 2005) Dissipation rate Pattern with spatial and temporal correlations

27. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Dissipation rate (numerical sources, mountain/gravity wave drag and deep convection) Cellular Automaton Backscatter Scheme (CABS) backscatter fraction smooth scale Idea: A fraction of the dissipated energy is scattered back (i.e., upscale) and acts as streamfunction forcing for the resolved- scale flow (LES) CA structure function (smoothed, coarse- grained) Streamfunction forcing Shutts, 2005

28. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Total Dissipation (annual average over 46 dates)

29. Contributions to Dissipation rate DJF

30. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Experimental setup  An ensemble of 10 members has been run at T255L40 for 46 dates in 2005/2006  Experiments differ in  the included contributions (shallow convection, deep convection, numerical dissipation, gravity mountain wave drag)  magnitude of combined stochastic forcing (related to backscatter ratio)  parameters for evaluating the various dissipation rates (e.g., assumed cloud-fraction for mass-flux formulation of dissipation from deep-convection; factor associated with semi- Lagrangian dissipation )

31. Spread around ensemble mean No Stoch Phys CABS NH SH

32. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Skill No Stoch Phys CABS Impact close to neutral

33. Change of spread: CABS – initial perturbations only CABS has at d7 more spread over NH, but less over SH Z500 u850 day 7

34. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting No Windgust problem T755 Control stoch CABS

35. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Energy spectrum in T799 No stochastic physicsWith CASBS backscatter Shutts, 2005; Palmer et. al (2005) E(n) missing energy E(n)

36. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Reduction of systematic error in North Pacific CABS-er40 Ctrl-er40 Experimetal setup: 40 year climate runs

37. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Increase in occurrence of blocking er40 CABS Control Experimental setup: 40 year climate runs

38. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Summary  Medium Range  CASBS creates spread efficiently in NH  Impact on probabilistic skill is close to neutral  Decreases spread in the SH for reasonable backscatter ratios  Has no windgust problem  Caveat: May be sensitive to changes in physical parameterizations  Too early to draw definite conclusions  Earlier positive results of Shutts (2005) may be due to lower resolution and different model cycle  Climate and Systematic errors  Improves blocking, systematic error of Z500 in North Pacific (Jung et al. 2005)  In coupled runs: Improves tropical precipitation and ocean variability  Future work  Currently alternative ways of generating random fields based on an spectral autoregressive model are under development

39. ECMWF Meteorological Training Course: Predictability, Diagnostics and Seasonal Forecasting Area under ROC curve. E: precip>40mm/day. Winter- top curves. Summer – bottom curves Stoch phys No stoch phys Buizza et al., 1999 Impact of stochastic physics on medium-range prediction