High-resolution 3D modelling

of oceanic fine structures using vertically adaptive coordinatesHans 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

hans.burchard@io-warnemuende.de

Representation of thin layers in numerical models

Patch of materialCurrent shear Thin layer of material

Numerical grid

Thin layer of material?

Motivated by Stacey et al. (2007)

Zooplankton migration in Central Baltic Sea

There is certainly a numerical problem to be solved before we predict thin layers in 3D models.

What is mixing ?

Salinity equation (no horizontal mixing):

Salinity variance equation:

?

Mixing is dissipation of tracer variance.

Principle of numerical mixing diagnostics:First-order upstream (FOU) for s:

FOU for s is equivalent to FOU for s² with variance decay :

numerical diffusivitySalinity gradient squared

See Maqueda Morales and Holloway (2006)

1D advection equation for S:

1D advection equation for s2:

Generalisation by Burchard & Rennau (2008):

( advected tracer square minus square of advected tracer ) / Dt

Numerical variance decay is …

„Baltic Slice“ simulation

Burchard and Rennau (2008)

salinity velocity

numerical mixing physical mixing

Burchard and Rennau (2008)

Burchard and Rennau (2008)

Vertically integrated salinity variance decay

Numerical mixing erodes structures which are numerically not well

resolved, including thin layers vertically moving with internal waves.

Neither high resolution nor non-diffusive advection schemes do

efficiently solve the problem.

What can be done?

Here is the problem:

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

isopycnaltendencySolution of a

vertical diffusion equation for the coordinate position

Hofmeister, Burchard & Beckers (2010a)

Baltic slice with adaptive vertical coordinates

Fixed coordinates Adaptive coordinates

Hofmeister, Burchard & Beckers (2010)

Hofmeister, Burchard & Beckers (2010)

Baltic slice with adaptive vertical coordinates

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)

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)

Holtermann et al. (in prep.)

Gotland Sea tracer release study

thermocline

halocline

Holtermann et al. (in prep.)

Gotland Sea tracer release study

Holtermann et al. (in prep.)

Gotland Sea tracer release study

Grid adaptation to tracer concentration:

Annual North Sea simulation using adaptive coordinates• 6 nm resolution • 30-50 vertical layers with a minimum thickness of 10 cm

• adaptation towards stratification

• adaptation towards nutrients

and phytoplankton • production run 2005-2006 • NPZD included via FABM

• NPZD starts 2005 from uniform values

• open boundaries for FABM are

taken from a 1D simulation of GOTM

• hydrographic boundary conditions and atmospheric forcing are taken from the global NCEP CFSR runs (1/3o resolution

FABM = Framework of Aquatic Biogeochamical Models (made by Jorn Bruggeman)

AdaTemperature in S1

[°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.)

Layer thickness in S1

[m]

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.)

Physical mixing in S1

log10[Dphy/(K2/s)]

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.)

Numerical mixing in S1

log10[Dnum/(K2/s)]

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.)

Additionally to physical properties (shear and stratification)

diffusivities for grid layer position equation are now also composed

of inverse values of bgc gradients such as nutrient and

phytoplankton concentration gradients.

How strong the impact of bgc gradients is depends on the

individual weighting of the components.

Adaptation to biogeochemical properties:

phys & bio adaptive with 50 layers

phys & bio adaptive with 30 layers

phys adaptive with 30 layers

non-adaptive with 30 layers

Nutrients at S1 [mmol N/m3]

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

Phytoplankton at S1

[mmol N/m3]

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

Phytoplankton at S1

log10[P/(mmol N/m3)]

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

Zooplankton at S1 [mmol N/m3]

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

Detritus at S1 [mmol N/m3]

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 along T1

[°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

Physical mixing along T1

log10[Dphy/(K2/s)]

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

Nutrients along T1 [mmol N/m3]

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

Phytoplankton along T1

[mmol N/m3]

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

[mmol N/m3]

Zooplankton along T1

Gräwe et al. (in prep.)

Conclusions

Thin layers are difficult to represent in fixed vertical grids … … unless the thin layers are thick or the number of layers is extremely high.Numerical mixing due to advection of bgc properties tends to erode thin layers, due to internal waves and tides.Neither high resolution nor high-order advection schemes can prevent this.Adaptation of vertical layer thickness and position to locations of high shearand stratification may significantly improve the situation.The real solution would be vertical coordinates adapting to bgc properties. The next step would be to realistically simulated a typical thin layer formationand maintenance scenario in 3D, using this new method.