History and Current State of Numerical Weather Prediction

1. Weather forecasting by computer Michael Revell NIWA m.revell@niwa.co.nz

2. Introduction • History • Operational NWP system • Forecast model • Data assimilation • Verification • Interpretation and limitations of output

3. NWP History • Wilhelm Bjerknes (1904) • Suggested integrating differential equations that describe atmosphere • Lewis Fry Richardson (1922) • First attempt (WW1) • Dismal failure, but wrote method down • Estimated 64,000 people needed to do calculation • Courant, Friedrichs, Lewy (1928) • Time and space steps can’t be chosen independently • Radiosonde invented (1930) • Upper air data

4. NWP History (cont) • Rossby (1930+) • Simplified version of vorticity equation • Von Neuman + ENIAC (1945) • Electronic Numerical Integrator and Computer • First electronic computer • Charney (1950) • First successful numerical forecast based on vorticity equation • Satellite technology (1970+) • Much improved data coverage over sea (SH) • Faster computers + global models + improved use of initial data ECMWF (1980+)

5. Numerical Weather Prediction Aim: To predict future state of atmospheric circulation from knowledge of present state by using numerical approximations to the dynamical equations

6. Operational NWP system Requirements: • Closed set of appropriate physical laws • Expressed in mathematical form • Accurate numerical method to integrate these equations forward in time • Suitable initial and boundary conditions • (on the globe no lateral boundaries)

7. Closed set of appropriate physical laws • Conservation of momentum (u,v,w) • Conservation of energy (T) • Conservation of mass (p) • Conservation of water substance (r) • 6 equations – 6 unknowns

8. Expressed in mathematical form • Example: • With c a specified speed • q(x,0) a known initial condition

9. Accurate numerical method to integrate these equations forward in time • Approximate with centred differences • Giving

10. Initial and boundary values

11. An NWP cycle • Get first guess at current situation • Usually 3 or 6 hr forecast • Make new observations • (Generally not at model grid points) • Interpolate these to model grid points • Filter out information the model can’t resolve • Step the model forward (3 or 6 hrs) • Use this forecast to repeat from step 1.

12. Time (hours) 0 3 6 9 12 A 48 h forecast bkg bkg 3 h forecast A A obs obs obs 3 h forecast… bkg 48 h forecast A NZLAM-VAR: Forecast-Analysis Cycle

13. Simple! So why are forecasts not perfect? Over recent years there have been dramatic improvements, but there remains • Model error • Models now solve the conservation laws quite accurately down to the scale of the grid • Still have to represent the effect of scales that the model doesn’t resolve (parameterize) • Cumulus clouds • Mixing / diffusion • Surface friction • Surface energy balance • Radiation (dependent on moisture) • chemistry These are predominantly the sources and sinks for our conservation laws

14. Model error • Specifying the initial and boundary conditions is still a problem – lack of good data • This is being improved by remotely sensed satellite data • Better methods to utilise it • This has improved SH forecasts by ~ 2-3 days

15. Brisbane Invercargill Conventional Data • TEMP: 12 & 24 h • PILOT: 12 & 24 h • Ships : 3 h • Buoys: ~6 h • SYNOPS: 3 h • AMDAR & AIREP

16. Satellite Data • TOVS / ATOVS: • NOAA14 • HIRS 2, 3, 4, 5 • MSU 2, 3, 4 • NOAA15 • AMSU 4, 5, 6, 7, 8, 9, 10, 11 • SSM/I • 1D-VAR retrievals of surface wind speed • SATWINDS • GMS atmospheric motion vectors

17. Forecasts • What does the output from a weather prediction model look like?

18. ECMWF MSLP + RH predictions

19. 5D Visualisation – Vis5D

20. 12 km NZLAM: Model Domains Uses UK Met Office Unified Model and 3DVAR Data Assimilation: • 12 km resolution domain • 324 × 324 × 38 • 4 km resolution domain • 600 × 600 × 38

21. 4 km NZLAM: Model Domains Uses UK Met Office Unified Model and 3DVAR Data Assimilation: • 12 km resolution domain • 324 × 324 × 38 • 4 km resolution domain • 600 × 600 × 38 • 2 km resolution domain • 800 × 800 × 38 (Largest UM run to date – 360 Processors on Cray T3E)

22. NZLAM 10m Wind Forecast:22-Jun-05:06 UTC • NZLAM 10m Winds: • 24 h forecast Verifying QuikSCAT 10 m winds

23. Microphysics: Cloud Predictions NZLAM-VAR 12 hour forecast: low, low + mid, low + mid + high “Verifying” GMS 11m image for 16 Dec 1999, 1640 UTC

24. Microphysics: Rain rates

25. Example NZLAM Simulations

26. Verification • How good are our models at predicting weather variables?

27. Temperature

28. Wind

29. Surface forecasts

30. Observations “Truth” Low res. model High res. model Issues & Challenges • Right feature, wrong place?

31. Future • Improve data coverage • Increase grid resolution • Improve model representation of sub grid processes • How do we cope with imperfect models? • There is useful information there • How do we get at it? • Ensemble methods (probabilities) • Model output statistics (correct statistically for model biases)

32. Ensemble methods

33. Ensemble methods (cont)

34. Questions?