1. Reduction of numerical mixing by means of vertically adaptive coordinates in ocean models Hans Burchard 1, Ulf Gräwe 1, Richard Hofmeister 2, Knut Klingbeil 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. What is mixing ? Reynolds-averaged salinity equation with downgradient turbulent transport (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)

3. 2 approaches to quantify numerical mixing A: Compare square of advected tracer with advected tracer square (Burchard & Rennau 2008) B: Reconstruct tracer transports through individual layer interfaces and quantify the mixing (Maqueda Morales & Holloway 2006; Klingbeil et al. in prep.)

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

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

6. 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)

7. Burchard & Beckers (2004); Example for grid adaptation for wind entrainment experiment

8. Baltic slice with adaptive vertical coordinates Fixed coordinatesAdaptive coordinates Hofmeister, Burchard & Beckers (2010) Numerical mixing Physical mixing

9. Salinity mixing analysis in Western Baltic Sea (adaptive coordinates) Klingbeil et al. (almost submitted)

10. [°C] Gräwe et al. (in prep.) phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Temperature transect Grid adaptation in Northern North Sea (additional adaptation to biogeochemistry)

11. phys & bio adaptive with 50 layers phys & bio adaptive with 30 layers phys adaptive with 30 layers non-adaptive with 30 layers Nutrient transect [mmol N/m 3 ] Gräwe et al. (in prep.) Grid adaptation in Northern North Sea (additional adaptation to biogeochemistry)

12. 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). Advantages of vertically adaptive coordinates are substantial for shelf sea simulations, but also large scale simulations should profit from this concept.