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, Germany2. Helmholtz-Zentrum Geesthacht, Institute for Coastal Research,

Germany3. ClimaCampus, University of Hamburg, Germany

4. GHER, University of Liege, Belgium

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)

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.)

„Baltic Slice“ simulation

Burchard and Rennau (2008)

salinity velocity

numerical mixing physical mixing

Burchard and Rennau (2008)

Adaptive vertical grids in GETM

hor. filteringof layer heightsVertical zooming

of layer interfaces towards:

a) Stratification

b) Shear

c) surface/ bottom

z

bottom

Vertical direction

Horizontal direction

hor. filteringof vertical position

Lagrangiantendency

isopycnaltendency

Solution of a vertical diffusion equation for the coordinate position

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

Burchard & Beckers (2004);

Example for grid adaptation for wind entrainment experiment

Baltic slice with adaptive vertical coordinates

Fixed coordinates Adaptive coordinates

Hofmeister, Burchard & Beckers (2010)

Numerical mixing Numerical mixingPhysical mixing Physical mixing

Salinity mixing analysis in Western Baltic Sea(adaptive coordinates)

Klingbeil et al. (almost submitted)

[°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)

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/m3]

Gräwe et al. (in prep.)

Grid adaptation in Northern North Sea(additional adaptation to

biogeochemistry)

ConclusionsIn stratified flow simulations, the numerically induced mixing maybe of the same order or even much larger than the physical mixing.

Vertical coordinate adaptation leads to optimised model resolution in a waythat 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 seasimulations, but also large scale simulations should profit from this concept.