1. High-resolution 3D modelling of oceanic fine structures using vertically adaptive coordinates Hans Burchard 1, Ulf Gräwe 1, Richard Hofmeister 2, Peter Holtermann 1, Inga Hense 3 and Jean-Marie Beckers 4 1. Leibniz Institute for Baltic Sea Research Warnemünde, Germany 2. Helmholtz-Zentrum Geesthacht, Institute for Coastal Research, Germany 3. ClimaCampus, University of Hamburg, Germany 4. GHER, University of Liege, Belgium hans.burchard@io-warnemuende.de

2. Representation of thin layers in numerical models Patch of material Current shear Thin layer of material Numerical grid Thin layer of material? Motivated by Stacey et al. (2007)

3. Zooplankton migration in Central Baltic Sea There is certainly a numerical problem to be solved before we predict thin layers in 3D models.

4. What is mixing ? Salinity equation (no horizontal mixing): Salinity variance equation: ? Mixing is dissipation of tracer variance.

5. Principle of numerical mixing diagnostics: First-order upstream (FOU) for s: FOU for s is equivalent to FOU for s² with variance decay : numerical diffusivity Salinity gradient squared See Maqueda Morales and Holloway (2006) 1D advection equation for S: 1D advection equation for s 2 :

6. Generalisation by Burchard & Rennau (2008): ( advected tracer square minus square of advected tracer ) /  t Numerical variance decay is …

7. „Baltic Slice“ simulation Burchard and Rennau (2008)

8. salinityvelocity numerical mixingphysical mixing Burchard and Rennau (2008)

9. Vertically integrated salinity variance decay

10. Numerical mixing erodes structures which are numerically not well resolved, including thin layers vertically moving with internal waves. Neither high resolution nor non-diffusive advection schemes do efficiently solve the problem. What can be done? Here is the problem:

11. Adaptive vertical grids in GETM hor. filtering of layer heights Vertical zooming of layer interfaces towards: a) Stratification b) Shear c) surface/ bottom z bottom Vertical direction Horizontal direction hor. filtering of vertical position Lagrangian tendency isopycnal tendency Solution of a vertical diffusion equation for the coordinate position Hofmeister, Burchard & Beckers (2010a)

12. Baltic slice with adaptive vertical coordinates Fixed coordinatesAdaptive coordinates Hofmeister, Burchard & Beckers (2010)

13. Baltic slice with adaptive vertical coordinates

14. Adaptive vertical coordinates along transect in 600 m Western Baltic Sea model Gräwe et al. (in prep.)

15. Adaptive coordinates in Bornholm Sea

16. 1 nm Baltic Sea model with adaptive coordinates - refinement partially towards isopycnal coordinates - reduced numerical mixing - reduced pressure gradient errors - still allowing flow along the bottom salinity temperature km Hofmeister, Beckers & Burchard (2011)

17. Channelled gravity current in Bornholm Channel sigma-coordinates adaptive coordinates - stronger stratification with adaptive coordinates - larger core of g.c. - salinity transport increased by 25% - interface jet along the coordinates Hofmeister, Beckers & Burchard (2011)

18. Gotland Sea time series 3d baroclinic simulation 50 adaptive layers vs. 50 sigma layers num. : turb. mixing 80% : 20% num. : turb. mixing 50% : 50% Hofmeister, Beckers & Burchard (2011)

19. Holtermann et al. (in prep.) Gotland Sea tracer release study thermocline halocline

20. Holtermann et al. (in prep.) Gotland Sea tracer release study

21. Holtermann et al. (in prep.) Gotland Sea tracer release study Grid adaptation to tracer concentration:

22. Annual North Sea simulation using adaptive coordinates 6 nm resolution 30-50 vertical layers with a minimum thickness of 10 cm adaptation towards stratification adaptation towards nutrients and phytoplankton production run 2005-2006 NPZD included via FABM NPZD starts 2005 from uniform values open boundaries for FABM are taken from a 1D simulation of GOTM hydrographic boundary conditions and atmospheric forcing are taken from the global NCEP CFSR runs (1/3 o resolution FABM = Framework of Aquatic Biogeochamical Models (made by Jorn Bruggeman)

23. Ada Temperature in S1 [°C] phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Gräwe et al. (in prep.)

24. Layer thickness in S1 [m] phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Gräwe et al. (in prep.)

25. Physical mixing in S1 log 10 [D phy /(K 2 /s)] phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Gräwe et al. (in prep.)

26. Numerical mixing in S1 log 10 [D num /(K 2 /s)] phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Gräwe et al. (in prep.)

27. Additionally to physical properties (shear and stratification) diffusivities for grid layer position equation are now also composed of inverse values of bgc gradients such as nutrient and phytoplankton concentration gradients. How strong the impact of bgc gradients is depends on the individual weighting of the components. Adaptation to biogeochemical properties:

28. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Nutrients at S1 [mmol N/m 3 ] Gräwe et al. (in prep.)

29. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Phytoplankton at S1 [mmol N/m 3 ] Gräwe et al. (in prep.)

30. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Phytoplankton at S1 log 10 [P/(mmol N/m 3) ] Gräwe et al. (in prep.)

31. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Zooplankton at S1 [mmol N/m 3 ] Gräwe et al. (in prep.)

32. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Detritus at S1 [mmol N/m 3 ] Gräwe et al. (in prep.)

33. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Temperature along T1 [°C] Gräwe et al. (in prep.)

34. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Physical mixing along T1 log 10 [D phy /(K 2 /s)] Gräwe et al. (in prep.)

35. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Nutrients along T1 [mmol N/m 3 ] Gräwe et al. (in prep.)

36. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Phytoplankton along T1 [mmol N/m 3 ] Gräwe et al. (in prep.)

37. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers [mmol N/m 3 ] Zooplankton along T1 Gräwe et al. (in prep.)

38. Conclusions Thin layers are difficult to represent in fixed vertical grids … … unless the thin layers are thick or the number of layers is extremely high. Numerical mixing due to advection of bgc properties tends to erode thin layers, due to internal waves and tides. Neither high resolution nor high-order advection schemes can prevent this. Adaptation of vertical layer thickness and position to locations of high shear and stratification may significantly improve the situation. The real solution would be vertical coordinates adapting to bgc properties. The next step would be to realistically simulated a typical thin layer formation and maintenance scenario in 3D, using this new method.