Introduction to surface ocean modelling SOPRAN GOTM School Warnemünde: 10.-11.09.07 Hans Burchard Baltic Sea Research Institute Warnemünde, Germany.
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Introduction to surface ocean modelling
SOPRAN GOTM SchoolWarnemünde: 10.-11.09.07
Hans BurchardBaltic Sea Research Institute Warnemünde,
Germany
Surface ocean processes
Surface ocean physical processes (Thorpe, 1995)
How to model all this ?
Basic physical principles:
•conservation of volume (incompressibility)•conservation of mass (water, salt, …) •conservation of momentum (velocity)•conservation of angular momentum•conservation of total energy (mechanical & thermodynamic)
plus
material laws for water (viscosity, …)
gives
Dynamic equations for momentum, heat, salt, …
These dynamic equation are valid on all scales, and all these scale are relevant.
Problem: in numerical models, we cannot resolve from millimeter to kilometer.
Therefore, equations are statistically separated intomean (expected) and fluctuating part (Reynolds decomposition):
The Reynolds decomposition allows to derive dynamic equations for mean-flow quantaties, but …
… new (unknown) terms are introduced, the turbulent fluxes: Reynolds stresses
Turbulent heat fluxTurbulent salt flux
Eddy viscosity
Eddy diffusivity
The TKE equation
Reynolds stresses cause loss of kinetic energy from mean flow, which is a source of turbulent kinetic energy (TKE, k).
TKE may is produced as large eddy sizes andis dissipated into heat by small eddy sizes at rate (dissipation rate).
At stable stratification, TKE is converted intopotential energy (vertical mixing, depening of mixedlayer).
Unstable stratification converts potential energy into TKE (convective mixing).
Spectral Considerations
From Schatzmann
How to calculate the eddy viscosity / eddy diffusivity ?
Turbulent macro length scale
The well-known k- model uses dynamic equations for the TKE and its dissipation rate.
There are however many other models in use …
Tree of turbulence closure models (extention of Haidvogel & Beckmann, 1999)
Bulk models Differential models
Kraus-Turnertype models
KPP Empirical models
Statisticalmodels
Ri number depending
models
Flowdepending
models
Algebraic stressmodels
Full Reynoldsstress models
Treatment of TKEand length scale
Treatment of algebraic stresses
Non-equilibrium models
Quasi-equilibriummodelsOne-equation
modelsZero-equation
modelsTwo-equation
models
MY
k-k-
Generic lengthscale
Mixing lengthformulations Blackadar-type
length scaleGaspar et al.(1990) type
models
Convenient approximations:
•Hydrostatic approximation (vertical velocity dynamically irrelevant)
•One-dimensional approximation (horizontal homogeneity, far away from coasts and fronts)
The dynamic equations for momentum, temperature, etc.,are PDEs (Partial Differential Equations), andtherefore need initial and boundary conditions.
Initial conditions are either from observations, idealised, or simply set todummy values (because they may be forgotten after a while).
Surface boundary conditions for physical properties come from atmosphericconditions:
Wind stress vector
Latent heat flux
Sensitive heat flux
Simulated short-wave radiation profile in water, I(z)
Surface radiation Attenuation lengths
Bio-shadingWeighting
Short-wave radiation in water
The local heating depends on the vertical gradient of I(z).
Have we modelled all this ?
Example: Station P in Northern Pacific
Example: Station P in Northern Pacific
Example: Station P in Northern Pacific
Time series of SST (observed and simulated)
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