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Air Sea fluxes and Ocean Models

- Driving the Ocean
- Ocean forcing formulation
- Various ways to apply the forcing
- Strait flux application
- Relaxation
- Feedback (correction)
- Bulk

- State estimation
- Parameter estimation
- Air-sea fluxes as parameters

Air Sea fluxes driving the Ocean

- Why some sort of flux correction is required

Air Sea flux estimates

or are necessary at each time step to drive the model

Bulk formula and their

input parameters

T and S equations

Penetrating Solar Radiation

Observed values

Ways to apply the forcing

Strait flux application

The model meridonal heat transport is fully constrained

- Model will have no predictive skill on MHT

- It usually results in inconsistent model SST (over 40°C in

the tropics) ...

... because feedback to the atmosphere is not accounted for

Ways to apply the forcing

Relaxation or nudging to observed values

source term

is diagnosed

Heat flux

is zero when observed and model SST agree

Flux values and SST are inconsistent

Ways to apply the forcing

Feedback (flux correction)

Sensitivity of the Heat Flux to changes in SST (space-time dependent).

It is a crude representation of the local effect of the air-sea coupling on the fluxes (feedback term).

Obtained from a Taylor expansion of bulk formulas

The model meridonal heat transport is prognostic

- Model have some predictive skill on MHT

- Model SST are realistic

Ways to apply the forcing

Bulk - fluxes are applied strait but:

are calculated during model integration with observed atmospheric variables and model prognostic SST.

The model meridonal heat transport is prognostic

- Model have some predictive skill on MHT

- Model SST are realistic

Ways to apply the forcing

The flux correction or the bulk formula are first approaches to coupled A/O GCMs.

More sophisticated feedback formulation (non local atmospheric transport) have been formulated.

Full GCM coupling is now common for climatye change studies. The coupling between the Oceanic and the Atmospheric model is made through bulk formulas

AGCM

Surface variables (air temp, humidity, etc..+ radiation

boundary conditions

Bulk formulas

SST, surface currents, ...

OGCM

Most used formulations require

Bulk formulaFlux correction

Flux estimates (radiation)?Flux estimates

SST

Accurate bulk formulas Accurate bulk formula

Atmospheric surface variablesAtmospheric surface variables

sea state characteristics

Aimed accuracy?

A few Wm-2 at interannual time scale to detect climate changes

Air Sea fluxes and Ocean Models

- Ocean state estimation
- Parameter estimation
- Air-sea fluxes as parameters

Q(ti)

Initial conditions

model solution 1

- 4DVAR modelling system
- DM: non linear direct model
- TL: tangent linear direct model
- AM: adjoin model

observations

Objective

Build a solution of the model which is the closest of the observations

Define a cost function J adapted to your problem to be minimised

initial condition model solution at ti

Background initial condition

flux fields

Background flux fields

Observations at time ti

Project of model solution at time ti at observation point

Minimising J means ....

Q(ti)

observations

model solution 2

Initial conditions

model solution 1

- 4DVAR modelling system
- DM: non linear direct model
- TL: tangent linear direct model
- AM: adjoin model

Define a cost function J adapted to your problem

1 - Compute TL(or DM) and save full model solution. Input: X0 initial conditions, Q(ti) forcing

Output : X(ti) model solution 1

2 - Use AM to bring the gradients of cost function J to zero.

Input: X(ti) model solution 1

Output: direction and amplitude of correction applied to selected parameters dX0, dQ(ti)

3 - Use TL to calculate a new solution. Input: X0+ dX0 initial conditions, Q(ti)+dQ(ti) forcing

Output : X(ti) model solution 2

Iterate loops 1-2-3 until increment dX dQ < e

Q(ti)

observations

model solution 2

Initial conditions

model solution 1

4DVAR modelling system

OUTPUT:

A description of the state of the ocean over the assimilation period which is close to consistent to observations.

Corrected initial conditions and air-sea fluxes which are consistent with ocean observations over the assimilation period.

BUT:

Model errors and biases may yields large errors in the increments

Many parameters to control simplifications additional errors

Do we have the data sets required for the aimed accuracy? (GODDAE)

Air Sea fluxes and Ocean Models

- Other data assimilation systems for,ocean state estimation
- Optimal interpolation, Kalman filters/smoother/ensemble
- Operational system Mecator
- European IP Mersea
- Not as well suited for parameter estimation but ...
- Operational centers produce ocean re-analyses
- They have flux requirements for forcing
- as for ocean models
- need forecast
- Assimilation of SST and forcing the model with fluxes ... does it provide a consistent flux correction?

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