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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 - PowerPoint PPT Presentation
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About the advantages of
vertically adaptive coordinates in numerical models of stratified shelf seas
Hans Burchard1, Ulf Gräwe1, Richard Hofmeister2, Peter Holtermann1, 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
The North Sea – Baltic Sea system: A modelling challenge
Strong tides
Seasonal stratificationPermanent stratification
Dense inflows
North Sea: example for seasonal stratification
Scanfish transect from BSH at 58°N (July 2010)
Kriegers Flak
Sweden
16.11.2005
Umlauf et al. (2007)
North Sea: example for dense inflow
Transport pathways in the Baltic Sea
heating a t sum m er
overflow s
outflow s
seasonal therm ocline
coo ling a t w inte r
in ternalm ix ing
perm anent ha locline
uplift
in terleaving
in terna lw ave m ixing
bottomcurrenten tra inm ent
surface w avem ixing
boundarym ix ing
convectiveentra inm ent
shear-inducedentra inm ent
d ifferen tia ladvection
riverrunoff
w ind stresscoasta lupw elling
sun
Reissmann et al. (2009)
Pressure gradient problem of sigma coordinates
Sigma coordinate problem
Inflows
Inflow approximation problem of geopotential coordinates
Geopotential coordinate problem (bottom)
Inflows
Geopotential coordinate problem (surface)
Additionally, both coordinate types share the problem of numerical mixing.
Geopotential coordinates typically have coarse near-surface resolution.
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)
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.
Bleck et al. (2004)
Early model with vertically adaptive coordinates: HYCOM
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)
Adaptive vertical coordinates
along transect in 600 m Western Baltic Sea model
Gräwe et al. (in prep.)
Adaptive coordinates in Bornholm Sea
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
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)
Gotland Sea time series
3d baroclinic simulation 50 adaptive layers vs. 50 sigma layers
num. : turb. mixing80% : 20%
num. : turb. mixing50% : 50%
Hofmeister, Beckers & Burchard (2011)
Grid adaptation in Central Baltic Sea
Holtermann et al. (in prep.)
Grid adaptation in Central Baltic Sea
Holtermann et al. (in prep.)
Holtermann et al. (in prep.)
Grid adaptation in Central Baltic Sea(additional adaptation to injected tracer)
Northern North Sea with sigma coordinates
Gräwe et al. (in prep.)
Northern North Sea with adaptive coordinates
Gräwe et al. (in prep.)
Physical and numerical T-mixing in Northern North Sea
Gräwe et al. (in prep.)
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).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 seasimulations, but also large scale simulations should profit from this concept.