1. HIRLAM 3/4D-Var developments Nils Gustafsson, SMHI

2. Parallel data assimilation work along 2 lines in HIRLAM HIRLAM for the synoptic scales: 3D-Var and 4D-Var Further developments during 2008-2009 To be phased out operationally 2010-2012 HARMONIE for the mesoscale: Based on ALADIN (IFS) 3D-Var mid 2008 4D-Var early 2009 To replace the synoptic scale HIRLAM (2010- 2012)

3. HIRLAM 4D-Var components: Tangent linear and adjoint of the semi- Lagrangian (SETTLS) spectral HIRLAM. Simplified physics packages: Buizza vertical diffusion and Meteo France (Janiskova) package(vertical diffusion, large-scale condensation and convection). Multi-incremental minimization (spectral or gridpoint HIRLAM in outer loops). Weak digital filter constraint. Control of lateral boundary conditions.

4. Noise in assimilation cycles with the gridpoint model

5. Comparison tests 3D-Var – 4D-Var SMHI area, HIRLAM 7.1.1, KF/RK, SMHI area, statistical balance background constraint, reference system background error statistics (scaling 0.9), no ”large-scale mix”, LINUX cluster, 4.5 months, operational SMHI observations and boundaries 3D-Var with FGAT, incremental digital filter initialization 4D-Var, 6h assimilation window, weak digital filter constraint, no explicit initialization

6. Summary of forecast scores PeriodSurface pressureUpper air April 2004NeutralPositive impact of 4D-Var Jan 2005Positive impact of 4D-Var June 2005NeutralPositive impact of 4D-Var Jan 2006 (11 days) Positive impact of 4D-Var Small positive impact of 4D-Var Jan 2007Positive impact of 4D-Var Small negative impact of 4D-Var on 300 and 200 hPa heights

9. Operationalization of 4D-Var SMHI tests show positive impact of 4D-Var in comparison with 3D-Var SMHI results need to be confirmed with the reference system (and new NL physics) Improved parallel scaling is needed: (a) openMP within nodes & MPI between nodes; (b) Message passing for SL advection ”on demand” To be included in HIRLAM 7.2 (late 2007)

10. Pre-operational tests of 4D-Var at SMHI Cop - SMHI op. 22 km, Hirlam-6.3.5, KF/RK, 3DVAR FGAT Cnn - Hirlam-7.1.2, KF/RK, 4DVAR

11. Impact of one single surface pressure observation 5 hPa less than the corresponding background equivalent (red: surface pressure, black: winds at lowest mod level) Statistical NMC (36-12)Statistical Ensemble Analytical NMC (48-24) Illustration structure functions

12. Flow dependent background covariances through non-linear balance equations Non-linear balance equation on pressure levels: Tangent-linear version of balance equation on pressure levels: Tangent-linear version of omega equation on pressure levels: where

13. Vertical crossection of T increments Statistical balanceWeak constraints balance eq.

14. A new moisture control variable and a new moisture balance Within the analytical balance formulation we follow Holm and use relative humidity as control variable and the TL RH definition for the balance: In addition, the background error variance depends on the background relative humidity (makes it more Gaussian). Within the statistical balance formulation (with q as control variable), we already have a statistical balance relation:

15. In order to avoid double-counting of the temperature- moisture balance, we could try to improve the statistical balance relation by using coefficients from the analytical balance relation, for example: So far we have tried: In this case, we also used a background error variance depending on the background relative humidity

16. New assimilation control variable for humidity (analytical balance version) Old formulationNew formulation: qq  RH*=  RH/σ b (RH b +0.5  RH)

17. New assimilation control variable for humidity (statistical balance with multivariate humidity) Assimilation increments due 5 simulated specific humidity observations, 10 g/kg smaller than corresponding background equivalent (sigmao: 1 g/kg) q at 850 hPa (g/kg times 10) p s (hPa times 10)

18. SEVIRI data coverage (At SMHI, we don’t store the raw-data for the full SEVIRI disc operationally)

19. Example of impact of SEVIRI data on 3D-Var analysis Difference of analysed 500hPa relative humidity (SEVIRI experiment minus Control) Impact can be seen mainly in the southern part of the domain

20. 3D-Var4D-Var

21. 3D-Var/4D-Var impact study 3D-Var: Positive impact on upper-troposhperic water vapour is found Positive impact on MSLP forecast is found 4D-Var: Positive impact on upper-tropospheric water vapour is found Also Temperature and Geopotential fields show some response (small positive impact) Another impact study for December 2005 shows neutral impact of SEVIRI data in terms of forecast scores. Work is now continuing with a much more difficult problem, assimilation of cloudy SEVIRI radiances!

22. What can we expect to achieve with the HIRLAM data assimilation before it will be phased out? 4D-Var with several outer loops and improved moist physics Control of lateral boundary conditions in 4D-Var A new moisture control variable Large scale mix vi a Jk cost function term Background and large scale error statistics based on EnsAss Tuning of screening and VarQC Use of several new types of observations. (IASI?) Most development efforts should be finished during 2008! A synoptic scale HARMONIE should be comparable!!