© crown copyright met office breakout 2 how can nonlinear pde work be exploited to improve the...

© Crown copyright Met Office

Breakout 2How can nonlinear PDE work be exploited to improve the long-term accuracy of weather forecast models?

Exeter Workshop 1st April 2009


Topics Discussed

The following topics (amongst others) were discussed:

• Where is the bottleneck?

• Dynamics

• Physics

• Data assimilation

• Hierarchy of models


Where is the bottleneck?

• Model = resolved (dry dynamics) + unresolved (physics) + data assimilation (reality)

• Which is holding us back?


Dynamics


Dynamics

• Discrete conservation properties:Conserve mass, unavailable energy, …Dissipate enstrophy as well?

• Structures as well as TKE spectra:AMR would help.


Dynamics: Use of SG etc

• Theoretical results available:eg. long-range predictability

• SG informed design of UM dynamical core


Physics


Physics: Coupling to Dynamics

• Physics often not expressed as PDEs!Turbulence modelling approach to convection.

• Grid dependence necessitates extensive retuning when changing resolution.Bad news for AMR.

• No-man’s land of intermediate resolution.Incorporate filter scale in well-defined way. No spectral gap: could have several filter scales.

• Believable and unbelievable scales.Do physics at believable scales (Lander & Hoskins).


Physics: Coupling to Dynamics (contd)

• Parametrization serves two roles:Represents subgrid physics and corrects resolved dynamics (BL winds, spurious over-turning)


Physics: Approaches to Parametrization

• Do physics on a finer grid:ECMWF found this beneficial

• Superparametrization: a CRM in each GCM grid-box

• Amalgamate parametrizations for smoother physics:eg. BL+shallow convection

• Automatic parameter estimation?Avoid pitfall of compensating errors.


Physics: Going Stochastic

• Could make deterministic forecast more robust, as well as improving statistics.But forecast error may go up as well as down.

• Mimics physical upscale transfer of energy.Not just a correction for model dissipation.


Physics: Ensembles

• Pay-off to be found between resolution and size of ensemble.Climate people well aware of this!

• What are limits of predictability?Change of resolution affects forcings (eg. orography) as well as truncation – difficult to untangle.

• An optimistic note:Smaller scales could be controlled by larger scales – better predictability.


Assimilation & Models


Data Assimilation

• Puts information into model on pre-determined spatial scale.Could physics be made to do likewise?

• Could physics parameters be determined by data assimilation?Time-dependent physics parameters.Lack of smoothness is a problem!

• All models are wrong:Could use nudging to enforce balance.Use already made of PV inversion: pseudo-obs.


Use of Models

• Hierarchy of models may be used to improve understanding of phenomena (eg. MJO)Beware that phenomena may be complex – not captured by simple ODE models.

• Could better use of observations be made to improve models?Parametrizations are developed with close attention to obs data.

• Are we resolving the important scales?Might just have to wait for bigger computers…


Questions and Comments

© crown copyright met office breakout 2 how can nonlinear pde work be exploited to improve the...

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