1. © Crown copyright Met Office Mismatching Perturbations at the Lateral Boundaries in Limited-Area Ensemble Forecasting Jean-François Caron … or why limited-area ensemble forecasting can be more difficult than global ensemble forecasting

2. © Crown copyright Met Office Perturbations Downscaling interpolation & IC perturbations derived from LAM Forecasts Ensemble method & From interpolation Limited-Area EPS: 3 approaches FullFields Downscaling interpolation & ProsCons No small-scales in the ensemble mean No small-scales in the IC perturbations Simple Ensemble Coherence: No mismatch between the IC from the two ensembles Not appropriate for short-term forecasting Small-scales in the ensemble meanNo small-scales in the IC perturbations Perturbation Coherence: No mismatch between the ensemble perturbations Small-scales in the ensemble mean Small-scales in the ensemble perturbations Risk of generating mismatches in the ensemble perturbations at the LBCs Complex Appropriate for short-term forecasting and for ensemble DA

3. © Crown copyright Met Office Description of a 1.5 km ETKF-based limited-area EPS for research purposes An example of spurious perturbations triggered by mismatches between IC and LBC perturbations To alleviate mismatches: A perturbation blending approach called ‘the scale-selective ETKF’ Outline Impact of the new method on Forecast performance Ensemble-derived background error covariances

4. © Crown copyright Met Office Introduction Examine 1-h forecast error covariances for the benefit of a NWP-based nowcasting system in development (Bannister et al., 2011,Tellus) Predictability studies of very short-term weather events (Migliorini et al., 2011, Tellus) Test hybrid VAR DA at convective scale Purpose of this convective- permitting EPS MOGREPS-G (60 km) – operational MOGREPS-R (18 km) - operational ETKF-1.5 km - research 540 km 432 km

5. © Crown copyright Met Office ETKF 1.5km: The setup

6. © Crown copyright Met Office ETKF 1.5km: The setup Control analysis from 3DVAR SUK 1.5km 1-h cycle with cloud and latent heat nudging and UK 4km LBC 23 IC perturbations are produced by the ETKF using +1h forecast perturbations and the locations and the estimated errors of the assimilated observations. Surface obs, Aircrafts Radio-sondes GPS, radiances No localizations Variable multiplicative inflation factor derived from surface obs (u, v, T) and aircraft data (u,v, T) No representation of model errors LBC taken from MOGREPS-R

7. © Crown copyright Met Office ETKF 1.5km - Case study #3 00Z 05/12/2009 21Z 04/12/2009 00Z 05/12/2009 03Z 05/12/2009

8. © Crown copyright Met Office Comparison of p surf spread fields valid at 06z 05/12/2009 MOGREPS-R : 12h fcstETKF 1.5km : 1-h fcst +53% -20% Relative difference (%) Domain average = +9.9% 600-60-3025500-50-2525 % hPa

9. © Crown copyright Met Office The time-evolution of surface pressure perturbation in ensemble member #8 Overestimation of p surf spread hPa + 1 min+ 5 min+ 15 min+ 30 min+ 60 min+ 90 min The Horror Movie

10. © Crown copyright Met Office The Incremental Analysis Update (IAU, i.e., how we add the IC perturbations) XaXa Pert. LBC t-30m tt+30m Sources of discontinuities at the LB (1) CTRL X a 1-h IAU t-30m tt+30m Pert. X a Initial Conditions Lateral Boundary Conditions 1-h Incremental LBC Update (ILBCU) CTRL LBC Pert. LBC

11. © Crown copyright Met Office Relative difference in p surf spread : 1.5km ETKF vs. MOGREPS-R IAU only Sources of discontinuities at the LB (1) +41% Domain average = +9.95% IAU + ILBCU 1h forecast valid at 06z 05/12/2009 Other sources of discontinuities between IC and the LBC must be present +53% -20% Domain average = +9.90% 600-60-3025500-50-2525 % 600-60-3025500-50-2525 %

12. © Crown copyright Met Office Relative difference in p surf spread : 1.5km ETKF vs. MOGREPS-R Perturbations Downscaling Domain average = -0.15% Perturbation Downscaling 1h forecast valid at 06z 05/12/2009 600-60-3025500-50-2525 % ETKF with ILBCU +41% Domain average = +9.95% 600-60-3025500-50-2525 %

13. © Crown copyright Met Office The construction of the IC perturbations Sources of discontinuities at the LB (2) Comparison of the ensemble perturbations from MOGREPS-R and the 1.5km-ETKF (at low resolution)

14. © Crown copyright Met Office The construction of the IC perturbations Sources of discontinuities at the LB (2) Comparison of the ensemble perturbations from MOGREPS-R and the 1.5km-ETKF (at low resolution)

15. © Crown copyright Met Office The Scale-Selective ETKF (SSETKF) Driving-EPS forecast perturbations on LAM domain LAM 1h forecast perturbations 1h small-scale forecast perturbations High- Pass Filtering step ETKF small-scale IC perturbations ETKF step Full IC perturbations Low- Pass Filtering step Large-scale IC perturbations Large-scale perturbation downscaling Small-scale IC perturbations derived from LAM Forecasts

16. © Crown copyright Met Office Three flavours of SSETKF SSETKF-F48-96 SSETKF-F96-192 SSETKF-F192-384

17. © Crown copyright Met Office Relative difference in p surf spread : 1.5km ETKF vs. MOGREPS-R SSETKF: Impact on p surf spread Perturbation Downscaling ETKF-ILBCU 600-60-3025500-50-2525 % SSETKF-F48-96 SSETKF-F96-192SSETKF-F192-384

18. © Crown copyright Met Office Verification of 1-h precipitation rate (Brier Score) relative to the ETKF Positive (Negative) means a better (worse) forecasts than the ETKF SSETKF: Impact on precipitation

19. © Crown copyright Met Office The Met Office VAR control variable transform SSETKF: Impact on B auto covariances only Global and LAM Parameter transform Vertical transform Horizontal transform 1 2 3 4 LAM Global

20. © Crown copyright Met Office Degree of linear balance between mass and rotational wind SSETKF: Impact on B Degree of balance

21. © Crown copyright Met Office Horizontal correlation lenghtscales based on a SOAR function SSETKF: Impact on B

22. © Crown copyright Met Office Vertical auto-correlations with model level 30 (~700 hPa) SSETKF: Impact on B

23. © Crown copyright Met Office Summary and discussion As expected, applying the ETKF approach in a limited-area EPS generates mismatches between IC and LBC perturbations This is likely to be true for all current limited-area EnDA approach In our small domain, discontinuities were found to introduce significant spurious perturbations in the pressure field. This is likely to be less important in larger domains. Results from the scale-selective ETKF showed that mismatches at low wave numbers were responsible for the spurious perturbations. The scale-selective ETKF has also improved slightly some other variables compared to both the ETKF and perturbation downscaling. In terms of background error covariances, perturbation mismatches at the LBCs tend to: Significantly reduce the degree of balance between mass and rotational wind Reduce horizontal and vertical correlation lengths

24. © Crown copyright Met Office Summary and discussion Pros and Cons of the scale-selective (or blending) approach The small scale IC perturbations are constructed without the knowledge of the large scale perturbations The small scale IC perturbations could potentially be incoherent with the large scale component. Ensures that an a priory specified component of the IC perturbations is coherent with the driving EPS Scale-selection is potentially better than traditional methods but is not the optimal approach. What’s the optimal approach?

25. © Crown copyright Met Office Questions