Introduction to data assimilation in meteorology Pierre Brousseau, Ludovic Auger

1. Introduction to data assimilation in meteorology Pierre Brousseau, Ludovic Auger ATMO 08,Alghero, 15-18 september 2008

2. Initial state at t0 Model integration Introduction • Numerical weather-prediction systems provide informative forecast of atmospheric variables. • The accuracy of these forecasts depend on, among other things, the initial conditions used. state at t0+t

3. Introduction The main goal of a meteorological data assimilation system is to produce an accurate image of the true state of the atmosphere at a given time, called analysis. This analysis could also be used as a comprehensive and self-consistent diagnostic of the atmosphere ( re-analysis).

4. Outlines • General ideas on data assimilation • Some kinds of observation • A new meso-scale data assimilation system • Assimilation experiments

5. Assimilated information : observations Observation : a measurement of an atmospheric physical parameter. Exemple : Surface pressure measurements, 10 september 2008, 00 UTC

6. Assimilated information : background Problems : Lack of observation in some part of the atmosphere. Observation number smaller than the numerical state dimension (for AROME 104 VS 107)‏. Need of an other information source : a previous forecast of the atmospheric state. Background xb Analysis at t0 Observationsyo

7. General ideas : assimilation cycle Background xb Numerical model integration Analysis xa 6 hr forecast Observations yo TIME 6 hr assimilation window

8. A simple case : estimation of the room temperature information : 2 measurements T1 et T2 Best Linear Unbiased Estimate Minimise the objective function 8

9. Generalisation in meteorology The Best Linear Unbiased Estimate : xa = xb + x = xb + BHT (HBHT+R)-1 (yo – H(xb ))‏ , d : difference between observations and background optimal weighting • With : B and Rrespectively background errors and observations errors covariance matrices H : observation operator and H linear observation operator • Variational formulation : minimisation of the cost function J(x) =Jb(x) + Jo(x) = xT B-1x + (d-Hx)T R-1(d-H x)‏ ,

10. Background error statistics • Background-error statistics determine how observations modify the background to produce the analysis, filtering and propagating innovations. • B should contain some information about the uncertainty of the guess, which depends on : • the model • the domain • the meteorological situation of the day (flow and initial conditions). • To determinate this uncertainty is a major problem in data assimilation

11. Outlines • General ideas on data assimilation • Some kinds of observation • A new meso-scale data assimilation system • Assimilation experiments

12. Radiosonde observations • Vertical profile of temperature, wind and humidity : • very accurate • but only twice a day with an irregular spatial coverage

13. Satellite observations • Instruments on : • geostationnary satellite. • polar satellite. • Radiance measurements providing vertical profile of temperature and/or humidity (stratosphere and high-troposphere). AMSU-A, 11 september 2008, 00 UTC (six hour assimilation window)

14. Satellite observations • Observations not always available on limited domain AMSUB intrument, 11 september 2008 12 UTC : measurements from 2 satellites 00 UTC : no measurement

15. Surface observations • Surface pressure, 2m temperature and humidity and 10m wind • Very usefull to provide information on the low atmospheric layers 10 september 2008, 00 UTC

16. Radar observations • Doppler-wind and reflectivity observations 10 september 2008, 00 UTC

17. Different kinds of observation • Lots of observations which differ in : • Measured parameter • spatial and temporal coverage • resolution • Observations informative for • large-scale model : ex : AMSU-A (Atmospheric sounder) : resolution of 48 km. • Meso-scale model : ex : Doppler-wind measurement

18. Outlines • General ideas on data assimilation • Different kinds of observation • A new meso-scale data assimilation system • Assimilation experiments

19. The AROME project • AROME model will complete the french NWP system in 2008 : • ARPEGE : global model (15 km over Europe) • ALADIN-France : regional model (10km) • AROME : mesoscale model (2.5km) • Aim : to improve local meteorological forecasts of potentially dangerous convective events (storms, unexpected floods, wind bursts...) and lower tropospheric phenomena (wind, temperature, turbulence, visibility...). ARPEGE stretched grid and ALADIN-FRANCE domain AROME France domain

20. Initial and lateral boundary conditions • Lateral boundary conditions for Limited Area Model provided during the forecast by : • a global model • a larger LAM • Initial conditions could be provided by : • a larger model (dynamical adaptation) • A local data assimilation system. • Local data assimilation systems for ALADIN and AROME

21. AROME data assimilation system • Use a variational assimilation scheme • 2 wind components, temperature, specific humidity and surface pressure are analysed at the model resolution (2.5 km). • Use of a Rapid Update Cycle • Forecasts initialized with more recent observations will be more accurate • Using high temporal and spatial frequency observations (RADAR measurements for example) to the best possible advantage

22. Objective scores : analysis compared to radiosonde at 00 UTC • Analysis from the AROME RUC compared to ALADIN analysis show an important reduction of Root Mean Square Error and Bias for all parameters all over the troposphere except for the humidity field around 200 hPa ---------- Bias --x---x-- rmse Temperature wind specific humidity

23. Objective scores : forecast compared to surface observations • Improvement in the first hours of the forecast Surface pressure assimilation Dynamical adaptation 2m temperature ---------- Bias --x---x-- rms

24. First results objective scores show that the general benefit of the AROME analysis appears during the first 12-h forecast ranges, then lateral conditions mostly take over the model solution. Subjective evaluation confirms many forecast improvement during the first 12-h forecast ranges. In some particular cases, this benefit can also be observed after this range.

25. Outlines • General ideas on data assimilation • Different kinds of observation • A new meso-scale data assimilation system • Assimilation experiments

26. Precipitating event, 5 october 2007 24-h cumulative rainfalls Better location of the maximum of precipitation RADAR MEASUREMENT AROME with assimilation AROME in dynamical adaptation ALADIN 80 mm

27. Fog event, 7 february 2008 AROME low cloud cover at 9-h UTC Fog is not simulated in spin-up mode assimilation Dynamical adaptation

28. An observation influence study : ground-based GPS • Experiment in order to evaluate the influence of additional Ground-based GPS observations in AROME data assimilation system. • Use of 194 stations (blue star) + 84 additional stations (green circle). • Give information on integrated humidity profile

29. Cumulative rainfall, 18 July 2007 03-15 UTC 194 stations Raingauges measurements 194 + 84 stations

30. Conclusion on data assimilation • Data assimilation provide an accurate image of the true state of the atmosphere at a given time in order to initialize numerical weather forecast using : • Observations • A previous forecast of the state of the atmosphere • Observations used are various and numerous and provide large and small scale information. • The use of a meso-scale data assimilation system improve Limited Area Model forecast accuracy up to 18 hours. • This system has been tested for one year and will be put into operation next month

31. Thank you for your attention…