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
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.