Reduction of numerical mixing by means of vertically adaptive coordinates in ocean models

1. Reduction of numerical mixing by means of vertically adaptive coordinates in ocean models Hans Burchard1, Ulf Gräwe1, Richard Hofmeister2, Knut Klingbeil1, Inga Hense3 and Jean-Marie Beckers4 1. Leibniz Institute for Baltic Sea Research Warnemünde, Germany 2. Helmholtz-ZentrumGeesthacht, Institute for Coastal Research, Germany 3. ClimaCampus, University of Hamburg, Germany 4. GHER, University of Liege, Belgium

2. Whatismixing ? Reynolds-averagedsalinityequationwithdowngradient turbulent transport(nohorizontal turbulent transport): Salinityvarianceequation: ? Mixing isdissipationoftracervariance. Numericalmixing due totraceradvectioncanbecalculated. Burchard andRennau (2008)

3. 2 approachestoquantifynumericalmixing A: Comparesquareofadvectedtracerwithadvectedtracersquare (Burchard & Rennau 2008) B: Reconstructtracertransportsthrough individual layerinterfaces andquantifythemixing (Maqueda Morales & Holloway 2006; Klingbeil et al. in prep.)

4. „Baltic Slice“ simulation Burchard andRennau (2008)

5. salinity velocity numericalmixing physicalmixing Burchard andRennau (2008)

6. Adaptive vertical gridsin GETM Horizontal direction z hor. filteringof layer heights Vertical zooming of layer interfaces towards: a) Stratification b) Shear c) surface/ bottom hor. filteringof vertical position Lagrangiantendency Vertical direction isopycnaltendency Solution of a verticaldiffusionequation forthecoordinateposition bottom Burchard & Beckers (2004); Hofmeister, Burchard & Beckers (2010a)

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

8. Baltic slice with adaptive verticalcoordinates Fixed coordinates Adaptive coordinates Numericalmixing Physicalmixing Numericalmixing Physicalmixing Hofmeister, Burchard & Beckers (2010)

9. Salinitymixinganalysis in Western Baltic Sea (adaptive coordinates) Klingbeil et al. (almostsubmitted)

10. Grid adaptation in Northern North Sea (additional adaptation to biogeochemistry) Temperature transect [°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.)

11. Grid adaptation in Northern North Sea (additional adaptation to biogeochemistry) [mmol N/m3] Nutrient transect 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.)

12. Conclusions In stratifiedflowsimulations, thenumericallyinducedmixingmay beofthe same order orevenmuch larger thanthephysicalmixing. 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.