1. Parameterization of the Planetary Boundary Layer -NWP guidance Thor Erik Nordeng and Morten Køltzow NOMEK 2010 Oslo 19. – 23. April 2010

2. Outline Short description of the fundamental problem and how it is parameterized Examples from operational NWP Ways to circumvent the problems Summary

3. The primitive equations

4. Decomposition of each variable into a mean part and a fluctuating (turbulent) part

5. Quasi-static approximation Neglecting viscous effects Hydrostatic approximation (here: Boussinesq approx.) similar equations for temperature and moisture

6. Reynholds stresses (turbulent fluxes of heat, moisture and momentum) - viscous diffusion analogy

7. Exchange coefficients depend on the flow itself ( l=kz and Ri is Richardson number, )

8. from and

9. Integration at neutral conditions z 0 = z 0 (unresolved terrain, local surface etc.) probably very different from local (real) roughness.

11. Model roughness is different from local roughness - resolution (z 0 in the model is an average over a grid square) - model roughness compensates for unresolved motion (e.g. orographically induced drag). This is often implemented as an effective roughness which is computed from the non-resolved orography variance making the roughness length in mountainous areas of the order of meters O(1m) while the local (vegetation) roughness should be two orders of magnitude smaller, i.e. O(0.01m).

12. Oslo from the air

13. Urban fraction for Oslo in the UM1-model (blue) and high resolution data set (green)

14. roughness length used in Hirlam12 for southern Norway. exceeding 1m (black), in the range 0.25m to 1m (blue), less than 0.25m (red).

15. It may have a large effect z 0 =0.01m => U 10 =0.75U 100 z 0 =1.00m => U 10 =0.50U 100

16. To obtain a corrected surface wind, we may assume that there is a reference height (Z ref ) where the wind is not too much dependent on local roughness At the reference height (assuming neutral conditions) So by integrating downwards (ECMWF uses Z ref = 75 m)

17. Resolution -resolving the terrain Wind speed will in general increase with height Temperature will in general decrease with height (but not always…..) Model orography is smooth; peaks are flattened and valleys filled in

18. Topography at 500m horizontal resolution

19. Topography at 1km horizontal resolution

20. Topography at 4km horizontal resolution

21. Topography at 8km horizontal resolution

22. Topographic height at horizontal resolution 500m Topography, H(500m) – H(8km)

23. Height corrections of T2m is necessary! BIAS Model topography – real topography HIRLAM8 T2m

24. Variations in time and space Nov.Dec.Jan.Feb. Full black – mean Dashed – stdev Progs; T+0->T+48

25. ALNA BLINDERN TRYVANN BJØRNHOLT HAKADAL KJELLER

26. Elevation correction of temperature: “Traditional” adiabatic correction by 0.6°/100m will on the average give good results. But an adiabatic correction fails during inversions. A dynamical height correction based on T2m and vertical temperature profile from HIRLAM8 has been developed (500m horizontal resolution terrain information).

27. Green, T2m, model output from HIRLAM8. Red, T2m from HIRLAM8 height corrected with 0.6/100m. Yellow, temperature 300m above the surface in HIRLAM.

28. “A typical winter example” Red contours = adiabatic height correction Dashed blue contours = dynamical height correction

29. Summer 2009

30. Winter (2008/9): Station height > model height

31. A method for elevation correction of wind speed

32. topography used in Hirlam12.

34. Table 1. Observed and modeled wind speed with fine scale NWP models for Fokstua for the first two weeks of May 2009. The ECMWF model is included for reference.

35. From the corrected 10m wind speed due to local roughness length; not the value used in the model is then

36. Integration from 10m above model topography z m upwards gives, u 10 ’ is 10m wind speed already corrected for local roughness. If we instead integrate from 10m above the real topographic height z real, we similarly get,

38. An example Z real =500m; Z m =200m; z 0real =0.03 Then U 10 ’’=1.15 U 10 ’ (i.e. 15% increase in wind speed)

39. Wind Norway, autumn 2008:

40. Wind, mountain stations, autumn 2008:

41. Correcting wind speed for difference between model height and real height?

42. Summary - guidelines for users Due to a number of reasons modeled “surface” temperature and wind will NOT be representative with what’s observed (wrong roughness, wrong altitude, not resolved local flow, inadequate physics, wrong large scale forcing) There exist methods however to minimize some of these (but not all) Users will have to use common sense based on their meteorological knowledge to compensate for model weaknesses

43. Thank you for your attention