1. Using Observations and Theory to Evaluate Model Convergence at Fronts Ben Harvey Thanks to: Chloe Eagle, Humphrey Lean (Met Office @ Reading) John Methven (Uni Reading)

2. T-NAWDEX pilot flight 3 FAAM BAe146 24th November 2009 Trailing cold front approaching UK Aircraft performed low level (300m) circuit around front Comparison of observations with model runs at a range of resolutions 00Z 25-11-2009 Knippertz et al., Weather (2010)

3. T-NAWDEX pilot flight 3

4. Science Questions 1.Does the resolved flow near the front converge towards the observations with model resolution? 2.Do the near-surface turbulent fluxes converge towards the observations with model resolution? 3.A strong pre-frontal gravity wave was observed. Is this present in the model? Can its generation be understood using the theory of Shakespeare & Taylor (2014)?

5. Science Questions 1.Does the resolved flow near the front converge towards the observations with model resolution? 2.Do the near-surface turbulent fluxes converge towards the observations with model resolution? 3.A strong pre-frontal gravity wave was observed. Is this present in the model? Can its generation be understood using the theory of Shakespeare & Taylor (2014)?

6. Observations Timing of circuit: 1456-1604 Altitude: 300m Route designed with the aim of forming a closed circuit in a system-relative sense For comparison with model data at fixed time (15Z), shift track points by Vf*(t-t0) where Vf is the estimated velocity of the front v: 15Z, 300m

7. Observations B C D E F Lots. Here use u and v at 1 Hz (≈100m) Also have momentum, heat and moisture fluxes and TKE calculated from 16 Hz data (used later) v: 15Z, 300m

8. Observations B C D E F Lots. Here use u and v at 1 Hz (≈100m) Also have momentum, heat and moisture fluxes and TKE calculated from 16 Hz data (used later) Frontal width ≈ 600m Double front structure on return leg v: 15Z, 300m

9. Model Runs Thanks to: Chloe Eagle UM8.4 (New Dynamics) 5 nested regional simulations: – 12km – 2.2km – 1.5km – 500m – 200m Initialised respectively at 06Z, 12Z, 15Z and 18Z on the previous day, and 12Z on the same day (200m) lsrain: 18Z 12km2.2km1.5km 500m 200m

10. How to compare model runs with observations? – Circuit integrals: utilise having a closed circuit to compute area-average quantities – Local values: width of front, magnitude of frontal shear Model Comparison v: 15Z, 300m n s

11. Circuit Integrals – Results 1 Divergence values vary widely between model runs Vorticity values converge with resolution, but are larger than the observations

12. Circuit Integrals – Results 1 Two complications: `Sampling error’ due to front roll-up Non-frontal contributions from convection behind the front

13. Vorticity and Divergence fields 12km2.2km 1.5km500m

14. Circuit Integrals – Results 2 v: 15Z, 300m Explore possible sampling error by repeating calculation at multiple locations along the front

15. Circuit Integrals – Results 2 Explore possible sampling error by repeating calculation at multiple locations along the front Circuit integral vorticity and convergence have converged to within the sampling error by 2.2km Divergence values are consistent with the observed value, but the vorticity values are not

16. Width of front estimate 12km2.2km 1.5km500m Grey = obs (two transects) Colours = models (11 sample transects) Along-front wind component (Upara)

17. Width of front estimate 500m Simple frontal width measure: distance between Upara=15m/s and Upara=25m/s

18. Aside: Overshoots and Interpolation Semi-Lagrangian scheme requires interpolation This causes implicit numerical (hyper-)diffusion The order of the interpolation scheme determines the order of the diffusion – Linear interpolation – Cubic interpolation 500m linear cubic Simple illustration: front in strain s

19. Has the resolved flow converged? Net shear and convergence across front – Circuit integrals are converged by 2.2 km – However, the vorticity values are inconsistent with the observations. Why? The width of the front – Only 200m model reproduced observed frontal width

20. Has the resolved flow converged? The structure of the frontal roll-up – What resolution is needed for convergence? – Cannot expect to match the locations of rolls between runs, but can expect same spatial scale? – Is the required resolution the same as for convergence of the frontal width? – Candidate: physical processes need to limit the frontal width rather than numerical diffusion?  turbulent fluxes

21. Science Questions 1.Does the resolved flow near the front converge towards the observations with model resolution? 2.Do the near-surface turbulent fluxes converge towards the observations with model resolution? 3.A strong pre-frontal gravity wave was observed. Is this present in the model? Can its generation be understood using the theory of Shakespeare & Taylor (2014)?

22. Turbulent Flux Observations B C D E F v: 15Z, 300m Calculated from covariances of 16Hz data over de- trended 2 minute runs (approx. 10km) Aircraft altitude: 300m Calculated by Cook and Renfrew (2014)

23. Model Comparison B C D E F v: 15Z, 300m From model runs: parameterised fluxes (solid lines) and resolved fluxes (circles) Resolved fluxes calculated similarly to obs: covariances of model variables over 2 minute runs

24. Ahead of front (E to F average) B C D E F v: 15Z, 300m Resolved components are all small Sensible heat, wind stress and latent heat fluxes: reasonable values, but not converged by 200m TKE: values too small except 200m which is anomalous

25. Behind front (C to D average) B C D E F v: 15Z, 300m Most transition from no resolved component at 12km to about 80% of total due to resolved component at 200m, with a roughly constant total Sensible heat flux is exception: intermediate resolutions have resolved and parameterised components of opposing signs

26. Comments B C D E F v: 15Z, 300m Further work will: – Explore further the division between the resolved and parameterised components – Produce error bars on average flux estimates – Look at fluxes in the vicinity of the front itself