1. About the advantages of vertically adaptive coordinates in numerical models of stratified shelf seas 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

2. The North Sea – Baltic Sea system: A modelling challenge Strong tides Seasonal stratification Permanent stratification Dense inflows

3. North Sea: example for seasonal stratification Scanfish transect from BSH at 58°N (July 2010)

4. Kriegers Flak Sweden 16.11.2005 Umlauf et al. (2007) North Sea: example for dense inflow

5. Transport pathways in the Baltic Sea Reissmann et al. (2009)

6. Pressure gradient problem of sigma coordinates Sigma coordinate problem Inflows

7. Inflow approximation problem of geopotential coordinates Geopotential coordinate problem (bottom) Inflows

8. Geopotential coordinate problem (surface) Additionally, both coordinate types share the problem of numerical mixing. Geopotential coordinates typically have coarse near-surface resolution.

9. What is mixing ? Salinity equation (no horizontal turbulent transport): Salinity variance equation: ? Mixing is dissipation of tracer variance. Numerical mixing due to tracer advection can be calculated. Burchard and Rennau (2008)

10. Sufficient vertical resolution cannot be obtained with fixed coordinates. Fixed coordinate problem (moving isopycnals) Isopycnal coordinates would fix this part, but cause problems in mixed layers.

11. Bleck et al. (2004) Early model with vertically adaptive coordinates: HYCOM

12. 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 Burchard & Beckers (2004); Hofmeister, Burchard & Beckers (2010a)

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

14. Adaptive coordinates in Bornholm Sea

15. 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) Feistel et al., 2004 Observations November 2003

16. 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)

17. 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)

18. Grid adaptation in Central Baltic Sea Holtermann et al. (in prep.)

19. Grid adaptation in Central Baltic Sea Holtermann et al. (in prep.)

20. Grid adaptation in Central Baltic Sea (additional adaptation to injected tracer)

21. Northern North Sea with sigma coordinates Gräwe et al. (in prep.)

22. Northern North Sea with adaptive coordinates Gräwe et al. (in prep.)

23. Physical and numerical T-mixing in Northern North Sea Gräwe et al. (in prep.)

24. Conclusions In stratified flow simulations, the numerically induced mixing may be of the same order or even much larger than the physical mixing. Vertical coordinate adaptation leads to optimised model resolution in a way that its additional computational effort is strongly overcompensated by the gain in accuracy. Vertical coordinate adaptation can also be applied to biogeochemical properties or other tracers (in addition to u & T & S). The vertically adaptive coordinates are so far implemented into GETM, but implementation into any other ocean model using general vertical coordinates should be straight forward. Advantages of vertically adaptive coordinates are substantial for shelf sea simulations, but also large scale simulations should profit from this concept.