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| Titel |
A framework for evaluating model error using asymptotic convergence in the Eady model |
| VerfasserIn |
Abeed Visram, Colin Cotter, Mike Cullen |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250073485
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| Zusammenfassung |
| Operational weather forecasting requires the accurate simulation of atmospheric motions on
scales ranging from the synoptic down to tens of kilometers. Weather fronts, ubiquitous of
mid-latitude weather systems, are generated through baroclinic instability on the large scale
but are characteristically “sharp” features in which temperature and winds can vary rapidly on
the short scale.
The Eady model of baroclinic instability, Eady (1949), captures the important aspects of
the frontogenesis process in an idealised system. Discontinuous solutions arise in finite time
from an initially smooth, large scale flow. Long term solutions have been shown using the
semigeostrophic equations and a fully Lagrangian model, Cullen (2007), which
exhibit multiple lifecycles after the initial frontogenesis. Previous Eulerian solutions
have relied on the addition of explicit viscosity to continue past the point at which
the front collapses down to the scale of the grid spacing, e.g. Snyder et al. (1993),
Nakamura (1994), but the artificial diffusion renders the subsequent lifecycles much less
pronounced.
We present a framework for evaluating model error in terms of asymptotic convergence
using the Eady model; by rescaling in one spatial dimension we are able to approach
solutions of a balanced model, given by the semigeostrophic equations, using the
non-hydrostatic, incompressible Euler-Boussinesq Eady equations. Using this approach we
are able to validate the numerical implementation and assess the long term performance in
terms of solution lifecycles.
We present results using a finite difference method with semi-implicit time-stepping and
semi-Lagrangian transport, and show that without any explicit viscosity we are able to
proceed past the point of frontal collapse and recover the theoretical convergence rate. We
propose that artificial diffusion of potential vorticity after collapse is detrimental to the long
term evolution of the solution. |
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