Combining measurements and models in atmospheric physics

1. Combining measurements and models in atmospheric physics Saroja Polavarapu Data Assimilation and Satellite Meteorology Division Meteorological Research Division Environment Canada U Toronto Physics Colloquium, 10 Jan. 2008

2. OUTLINE • What is data assimilation? • Recent advances in DA • A new application: data assimilation with a climate model

3. 1. What is data assimilation?

4. Atmospheric Data Analysis An analysis is a regular, physically consistent, representation of the state of the atmosphere Instruments sample imperfectly and irregularly in space and time. analysis

5. Why do people want analyses? • To obtain an initial state for launching weather forecasts • To make consistent estimates of the atmospheric state for diagnostic studies. • For an increasingly wide range of applications (e.g. atmospheric chemistry) • To challenge models with data and vice versa

6. The Global Observing System http://www.wmo.ch/web/www/OSY/GOS.html

7. Data coverage examples Some data used by CMC on Jan. 6, 2008 12 UT

8. Underdeterminacy X = state vector Z = observation vector • Cannot do X=f(Z), must do Z=f(X) • Problem is underdetermined • Need more information!

9. NxM NxN MxM Analysis vector Background or model forecast Observation vector Observation operator Can’t invert! Optimal Interpolation N×1 N×1 N×M M×1 M×N N×1 Weight matrix

10. Analysis increments (xa – xb) must lie in the subspace spanned by the columns of B Properties of B determine filtering properties of assimilation scheme!

11. The fundamental issues in atmospheric data assimilation • Problem is under-determined: not enough observations to define the state • Forecast error covariances cannot be determined from observations. They must be stat. modelled using only a few parameters. • Forecast error covariances cannot be known exactly yet analysis increments are composed of linear combination of columns of this matrix • Very large scale problem. State ~ O(108) • Nonlinear chaotic dynamics

12. Analysis step assimil. scheme model forecast step Data assimilation cycle

13. 2. Recent advances in data assimilation at operational weather forecasting centres

14. 3D-Variational assimilation Instead of solving this: Optimal Interpolation Minimize this: • Obs and models can be nonlinearly related. To assimilate radiances directly, H includes an instrument-specific radiative transfer model. • Matrix inverses can be avoided

15. 4D-Variational assimilation Analysis trajectory Background trajectory

16. Differences between 4D-Var and 3D-Var RMS errors for day-1 forecasts 500 hPa GZ (dam), avg. over Jan 1998 Dark areas: 4D-Var beats 3D-Var 4D-Var beats 3D-Var over storm track areas 4D-Var is better at picking up unstable initial conditions Klinker et al. (2000)

17. Popular assimilation techniques in weather forecasting centres • 1980’s – Optimal interpolation • 1990’s – 3D variational assimilation • 2000’s – 4D variational assimilation • Future – ? Advances are being driven by improvements in computational power and increase in amount of observations.

18. Why are the lids of operational weather forecast models moving up into the mesosphere (>80 km)?

19. 1mb 10mb 100mb 1000mb • By raising forecast model lid, satellite radiances are better analysed • Satellite radiances sense deep layers of atmosphere so analyses are improved in troposphere as well as stratosphere • Improved analyses give improved forecasts • ECMWF, GMAO (NASA), UK Met Office have lids ~80 km • CMC system with model lid at 65 km to be operational in 2008

20. Winter Polar vortex • Westerly wind increasing with height • Dominant feature of stratosphere in winter • Occasional disruption of polar vortex by sudden warming events (in Arctic) http://www.nasa.gov/images/content/113260main_arctic-vortex-447.jpg

21. Time delay Long timescale The stratosphere and troposphere are dynamically coupled. Low model lids compromise this coupling. Baldwin and Dunkerton (2001)

22. 3. A new application: Data assimilation with a climate model

23. Middle Atmosphere Dynamics Ozone from OSIRIS for March 2004 • Brewer-Dobson circulation • wave driven, thermally indirect • affects temperature, transport of species • Gravity waves also important • Helps drive meridional circulation • But normally seen as “noise” in assimilation process Shaw and Shepherd (2008)

24. Approximate mass-wind balance in mid-troposphere extra-tropics Lars Isaksen (2007) http://www.ecmwf.int/newsevents/training/meteorological_presentations/MET_DA.html

25. Balance in data assimilation Time evolution of surface pressure over 24 hours • Because of obs errors, integrating a model from an analysis leads to motion on fast scales • Noisy forecasts, e.g. precipitation • 6-h forecasts are used to quality check obs • Extra-tropical troposphere is largely balanced • Historically, after the analysis step, a separate “initialization” step was done to remove fast motions Initialized forecast Raw forecast Williamson and Temperton (1981)

26. Gravity waves may be a nuisance in the troposphere, but they are prevalent in the mesosphere and are part of the signal! T profiles over one night from lidar R.J. Sica (U Western Ontario) http://pcl.physics.uwo.ca/science/temperature/

27. No obs obs CMAM + 3DVar CMAM = Canadian Middle Atmosphere Model How does information propagate into the mesosphere? AMSU 10-13 conventional obs + sat.

28. Global mean temperature profiles at SABER locations for various filtering options SABER DF12 DF6 IAUC IAU6 IAU4 Jan. 25, 2002 Sponge layer No obs obs Sankey et al. (2007)

29. More waves --> more damping --> more heating There are more resolved waves in the upper mesosphere with less filtering Sankey et al. (2007)

30. Changing the assimilation scheme in the stratosphere and troposphere has huge impacts on the mesosphere! • Waves (real or spurious) in the lower atmosphere propagate up to the mesosphere • Small errors lower down can look big in the mesosphere

31. Information from below propagates to the mesosphere. Is the mesosphere improved?

32. Stratopause is above 0.01 hPa! 70ºN zonal mean temperatures during 2006 SSW ECMWF too low too cold GEOS-5 too low too warm Gloria Manney, JPL

33. Low lids of operations models deterrent to study of stratopause region • Research models with higher lids show improvement relative to operational systems, in this region • CMAM-DAS with no mesospheric DA • NOGAPS-ALPHA with MLS, SABER data • Compared to independent data, CMAM-DAS looks reasonable

34. Climate models are extensively validated statistically against observations. Data assimilation with a climate model allows one to compare to measurements on a specific day.

35. Stratospheric Sudden Warming (SSW) • Dramatic event: T increases near pole of 40-60 K in 1 week at 10 hPa • Every couple of years in NH (+2002 SH) • Major SSW (1+2), Minor SSW (1 only) • Poleward increase of zonal-mean temperature between 60° and pole at 10 hPa • Zonal mean zonal wind reverses • Waves propagate up from troposphere, interacts with mean flow (Matsuno 1971).

36. Total column ozone from Earth Probe Total Ozone Mapping Spectrometer (EPTOMS) August 15 – September 26, 2002 http://www.gsfc.nasa.gov/topstory/20020926ozonehole.html

37. C W C Mesospheric Coolings schematic diagram NH winter 2005/06 Courtesy of Kirstin Krüger (Labitzke 1972)

38. South Pole temperature in 2002 during stratospheric warming 10 hPa (30km) 0.1 hPa (65 km) hits 1995-2005 Met Office analyses misses Ren et al. (2008)

39. No obs obs <“hits”> - <“misses”> Zonal mean temperature difference (K) “hits” are colder in the mesosphere “hits” are warmer in the stratosphere Ren et al. (2008)

40. Resolved waves GWD GWD misses hits All waves Waves 1-5 Averages over Sept. 25 – Oct. 1, 2002 Ren et al. (2008)

41. 2002 Stratospheric Warming study • Assimilation with a climate model allowed us to understand what caused the mesospheric cooling above the stratospheric warming in our simulations • Planetary waves responsible for mesospheric cooling below 60 km • Mesospheric cooling is mainly due to parameterized GWs above 75 km • Observations inserted in stratosphere and troposphere indirectly impact the mesosphere through a GWD scheme!

42. Summary • The atmospheric data assimilation problem is characterized by huge, nonlinear systems and insufficient observations. • Because the math is well known, the key to progress is using atm physics to make the right approximations • Information from below propagates to the mesosphere (through both resolved and parameterized waves) during 6-h forecasts

43. Other areas of current research in data assimilation • Chemical weather forecasting • Ensemble Kalman filtering • Inferring winds from tracer measurements • Improving climate models by determining uncertain parameters • Evolving 4D-Var covariances from one cycle to the next • Improving tropical analyses

44. The End