1. The status and development of the ECMWF forecast model M. Hortal, M. Miller, C. Temperton, A. Untch, N. Wedi ECMWF

2. Layout of the talk Continuous form of the equations Horizontal resolutions and spectral method Vertical resolution and vertical discretization Semi-Lagrangian scheme Efficiency Mass conservation and noise reduction Coupling with physics Future plans

3. Continuous equations Horizontal momentum equation Thermodynamic equation Humidity equation Ozone equation

4. From continuity equation => Hydrostatic equation: where

5. Horizontal resolutions in use at ECMWF T L 511 for the deterministic forecast and outer loop of 4D-Var with a time step T L 255 for EPS T L 159 for inner loop of 4D-Var T L 95 for seasonal forecast T L 42 for error minimization computation T L 799 used in some tests

6. D+3 rainfall from a T L 799 experiment T L 799T L 511

7. Full and reduced Gaussian grids

8. The quadratic and linear Gaussian grids quadratic grid at T63 linear grid at T L 95 Spectrally fitted orography linear grid at T L 95 with smoothing

9. Cost of various parts of the model at different horizontal resolutions T L 319T L 511 T L 799

10. Vertical resolutions used at ECMWF 60 levels for deterministic forecasts & 4D-Var (top at 0.1 hPa) 40 levels for EPS and seasonal forecasts ( top at 10 hPa ) 90 levels under test (top at 0.1 hPa)

11. Vertical discretization In the semi-Lagrangian framework no vertical derivatives are needed Vertical integrals are computed with a finite-element method based on cubic B-splines Main benefits of finite-element scheme: –no staggering of variables is required (advantage for semi- Lagrangian) –reduction in vertical noise in the stratosphere –significant reduction of a persistent cold bias in the lower stratosphere –improved vertical transport ( => better conservation of ozone) –smallest eigenvalues of the vertical modes are 10x larger than with the finite-difference method using the Lorenz staggering (facilitates use of PV as control variable in 4D-Var)

12. Eigenvalues of the vertical structure matrix for several vertical discretization schemes

14. Two-time-level semi-Lagrangian (SETTLS scheme) Generic forecast equation: Trajectory equation: where X is a generic field, L are the linear terms and N the non-linear terms

15. Efficiency of algorithms Operational scheme s-L ~ 4rGg+2tl ~ 3lGg+L50 ~ 6

16. D+10 from 0.59 hPa to 0.02 hPa at T106L31 Reduces mass loss: Continuity & thermodynamic equations Continuity equation with Reduces noise over orography. Thermodynamic equation

17. Coupling of the dynamics with the physical parameterizations where P denotes the contribution of the physical parameterizations and N AV is evaluated according to the SETTLS scheme. Reduces noise and improves mass conservation.

18. Validity of the present setup of the model Experience so far indicates that hydrostatic models give very similar results to non-hydrostatic ones at horizontal resolutions down to about 10 km The spectral transform method will remain affordable and competitive down to about 15 km Latitude-longitude grids allow easy coding of semi-Lagrangian advection schemes and communications in MPP’s

19. Plans for the future Higher horizontal resolution –T L 1280 (~15 km) Higher vertical resolution –L90 by 2003, L120 Reduction in cost of spectral transforms –spherical harmonics double Fourier series Improvements to semi-Lagrangian scheme: –improve interpolation (cubic spline for the vertical) –add formal conservation properties Improve interfacing between dynamics and physics Should be achievable with the present dynamical core

20. Plans for the future (cont.) Non-hydrostatic when the horizontal resolution approaches 10 km Relax the shallow-atmosphere approximation (coded for the IFS already by Meteo-France) Increase the degree of implicitness –tests have been performed with a predictor-corrector method –re-computation of the semi-Lagrangian trajectory in the corrector step improves the forecast skill scores, mainly at high horizontal resolution