On the numerical stability of surface–atmosphere coupling in weather and climate models
Coupling the atmosphere with the underlying surface presents numerical stability challenges in cost-effective model integrations used for operational weather prediction or climate simulations. These are due to the choice of large integration time steps compared to the physical timescale of the probl...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2017-02-01
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| Series: | Geoscientific Model Development |
| Online Access: | http://www.geosci-model-dev.net/10/977/2017/gmd-10-977-2017.pdf |
| Summary: | Coupling the atmosphere with the underlying surface presents numerical
stability challenges in cost-effective model integrations used for
operational weather prediction or climate simulations. These are due to the
choice of large integration time steps compared to the physical timescale of
the problem, aiming at reducing computational burden, and to an explicit flux
coupling formulation, often preferred for its simplicity and modularity.
Atmospheric models therefore use the surface-layer temperatures
(representative of the uppermost soil, snow, ice, water, etc.) at the
previous integration time step in all surface–atmosphere heat-flux
calculations and prescribe fluxes to be used in the surface model
integrations. Although both models may use implicit formulations for the time
steps, the explicit flux coupling can still lead to instabilities.<br><br>In this study, idealized simulations with a fully coupled implicit system are
performed to derive an empirical relation between surface heat flux and
surface temperature at the new time level. Such a relation
mimics the fully implicit formulation by allowing one to estimate
the surface temperature at the new time level without
solving the surface heat diffusion problem. It is based on similarity reasoning and
applies to any medium with constant heat diffusion and heat capacity parameters.
The advantage is that modularity of the code is maintained and that the heat flux
can be computed in the atmospheric model in such a way that instabilities
in the snow or ice code are avoided. Applicability to snow–ice–soil models with
variable density is discussed, and the loss of accuracy turns out to be small.
A formal stability analysis confirms that the parametrized implicit-flux coupling
is unconditionally stable. |
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| ISSN: | 1991-959X 1991-9603 |