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

cooling a t w in ter

in terna lm ixing

perm anent ha locline

uplift

in terleaving

in terna lw ave m ixing

bottomcurrententra inm ent

surface w avem ixing

boundarym ixing

convectiveentra inm ent

shear-inducedentra inm ent

d ifferentia 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 d

irection

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.)

Conclusions

In 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.