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)