1. Introduction to parametrization Introduction to Parametrization of Sub-grid Processes Anton Beljaars (anton.beljaars@ecmwf.int room 114) What is parametrization? Processes, importance and impact. Testing, validation, diagnostics Parametrization development strategy

2. Introduction to parametrization Why parametrization Small scale processes are not resolved by large scale models, because they are sub-grid. The effect of the sub-grid process on the large scale can only be represented statistically. The procedure of expressing the effect of sub-grid process is called parametrization.

3. Introduction to parametrization The standard Reynolds decomposition and averaging, leads to co-variances that need closure or parametrization Radiation absorbed, scattered and emitted by molecules, aerosols and cloud droplets play an important role in the atmosphere and need parametrization. Cloud microphysical processes need parametrization Parametrization schemes express the effect of sub-grid processes in resolved variables. Model variables are U,V,T,q, (l,a) What is parametrization and why is it needed

4. Introduction to parametrization Reynolds decomposition e.g. equation for potential temperature: advectionsourcemolecular diffusion Reynolds decomposition: Averaged (e.g. over grid box): : source term (e.g. radiation absorption/emission or condensation) : subgrid (Reynolds) transport term (e.g. due to turbulence, convection)

5. Introduction to parametrization Space and time scales

6. Introduction to parametrization Space and time scales 1 hour100 hours0.01 hour

7. Introduction to parametrization Climate models 200 km 500 m100 years Global weather prediction 20 km200 m10 days Limited area weather pred. 10 km 200 m2 days Cloud resolving models 500 m500 m1 day Large eddy models 50 m50 m5 hours Hor. scales Vert. Scalestime range Different models need different level of parametrization Numerical models of the atmosphere

8. Introduction to parametrization Parametrized processes in the ECMWF model

9. Introduction to parametrization Applications and requirements Applications of the ECMWF model –Data assimilation T1279L91-outer and T95/T159/T255-inner loops: 12-hour 4DVAR. –Medium range forecasts at T1279/L91 (16 km): 10 days from 00 and 12 UTC. –Ensemble prediction system at T639L62 (32 km) for 10 days, and T319 (65 km) up to day 15; 2x(50+1) members. –Short range at T1279L91 (15 km): 3 days, 4 times per day for LAMs. –Seasonal forecasting at T95L40 (200 km): 200 days ensembles coupled to ocean model. –Monthly forecasts (ocean coupled) at T159L61: Every week, 50+1 members. –Fully coupled ocean wave model. –Interim reanalysis (1989-current) is under way (T255L60, 4DVAR). Basic requirements –Accommodate different applications. –Parametrization needs to work over a wide range of spatial resolutions. –Time steps are long (from 10 to 60 minutes); Numerics needs to be efficient and robust. –Interactions between processes are important and should be considered in the design of the schemes.

10. Introduction to parametrization Importance of physical processes General Tendencies from sub-grid processes are substantial and contribute to the evolution of the atmosphere even in the short range. Diabatic processes drive the general circulation. Synoptic development Diabatic heating and friction influence synoptic development. Weather parameters Diurnal cycle Clouds, precipitation, fog Wind, gusts T and q at 2m level. Data assimilation Forward operators are needed for observations.

11. Introduction to parametrization Global energy and moisture budgets EnergyMoisture 5 mm/day =P-E Hartman, 1994. Academic Press. Fig 6.1 and 5.2

12. Introduction to parametrization Sensitivity of cyclo-genesis to surface drag controlP centre =918 hPa analysisP centre =925 hPa difference P centre =923 hPa

13. Introduction to parametrization T-tendencies

14. Introduction to parametrization T-Tendencies

15. Introduction to parametrization T-Tendencies

16. Introduction to parametrization T-Tendencies

17. Introduction to parametrization T-tendencies

18. Introduction to parametrization T-Tendencies Imbalance (physics – dynamics) due to: (a) Fast adjustment to initial state (data assimilation problem); (b) Parametrization deficiencies

19. Introduction to parametrization Validation and diagnostics Compare with analysis daily verification systematic errors e.g. from monthly averages Compare with operational data SYNOPs radio sondes satellite Climatological data CERES, ISCCP ocean fluxes Field experiments TOGA/COARE, PYREX, ARM, FIFE,...

20. Introduction to parametrization Day-5, T850 errors Viterbo and Betts, 1999. JGR, 104D, 27,803-27,810

21. Introduction to parametrization Diurnal cycle over land

22. Introduction to parametrization History of 2m T-errors over Europe in the ECMWF model (step60/72) Model temperature errors are influenced by many processes. Observations at process level are needed to disentangle their effect Bias (day/night) RMS (day/night) LESS STABLE BL DIFFUSION

23. Introduction to parametrization TSR: JJA 24 hour forecasts (CY31R1/23R4 - CERES) CY31R1 - CERES CY23R4 - CERES

24. Introduction to parametrization Lat. Heat Flux-DJF (ERA_40_Step_0_6 vs. DaSilva climatology) ERA40 model

25. Introduction to parametrization PYREX experiment

26. Introduction to parametrization PYREX mountain drag (Oct/Nov 1990) Lott and Miller, 1995. QJRMS, 121, 1323-1348

27. Introduction to parametrization Latent heat flux: ERA-40 vs. IMET buoy

28. Introduction to parametrization Cloud fraction (LITE/ECMWF model) Model LITE Cross section over Pacific 45N/120E – 45S/160W (16-09-1994)

29. Introduction to parametrization Parametrization development strategy -Invent empirical relations (e.g. based on theory, similarity arguments or physical insight) To find parameters use: –Theory (e.g. radiation) –Field data (e.g. GATE for convection; PYREX for orographic drag; HAPEX for land surface; Kansas for turbulence; ASTEX for clouds; BOREAS for forest albedo) –Cloud resolving models (e.g. for clouds and convection) –Meso scale models (e.g. for subgrid orography) –Large eddy simulation (turbulence) –Test in stand alone or single column mode –Test in 3D mode with short range forecasts –Test in long integrations (model climate) –Consider interactions

30. Introduction to parametrization Measure diffusion coefficients stableunstable

31. Introduction to parametrization Convert to empirical function Diffusion coefficients based on Monin Obukhov similarity: Operational CY30R2 MO-scheme (less diffusive) Operational CY30R2 MO-scheme (less diffusive)

32. Introduction to parametrization Column test Cabauw: July 1987, 3-day time series Observations versus model (T159, 12-36 hr forecasts)

33. Introduction to parametrization T2-difference DJF (ensemble of 6 integrations) Contours at 1, 3, 5, … K Effect of MO-stability functions instead of LTG

34. Introduction to parametrization Test in 3D model: Data assimilation + daily forecasts over 32 days March 2004 Effect of MO-stability functions

35. Introduction to parametrization Concluding remark Enjoy the course and Dont hesitate to ask questions