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Informations for Ph.D. students:
Scientific Executive Summary: ``Hamiltonian-based numerical
methods for forced-dissipative climate prediction''
The advective and thermodynamic nonlinearities of atmospheric and
oceanographic climate models remain present in the conservative
limit, that is, in the absence of forcing and frictional mechanisms
such as solar heating, radiation and viscosity. Most "good"
numerical climate models conserve some of the conservation laws,
such as mass and energy, which characterise the system in this
conservative limit. In contrast, the Hamiltonian particle mesh
numerical method not only preserves most of the conservation laws,
but also the Hamiltonian phase-space structure which the system
carries in the conservative limit. It is generally considered
desirable to preserve conservation laws in the numerical
discretization in the frictionless and forcing-free limit. In
accordance with this belief and based on promising symplectic
integrations of weakly dissipative low-order models, we hypothesize
that preservation of the limiting Hamiltonian structure provides
superior climate predictions.
Hence, the objective of the research proposed is to assess how
important the numerical preservation of the limiting Hamiltonian
structure actually is in (idealized) climate models in which
climatological forcing and dissipation mechanisms are present. This
main objective is investigated in three ways:
- The difference in performance between Hamiltonian and
non-Hamiltonian based numerical discretizations will first be
investigated for low-order models.
- Symplectic Hamiltonian particle mesh methods with many degrees
of freedom will be constructed for hydrostatic stratified models
on the sphere using isentropic or mixed vertical and isentropic
coordinates.
- The performance of the Hamiltonian particle mesh models will
be tested by simulating one of the two following atmospheric
applications: the dynamics of stratospheric chemical species
such as ozone; and the coupling between the troposphere and the
stratosphere for the benchmark calculation proposed by Held and
Suarez.
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