| 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: 1.The difference in performance between Hamiltonian and non-Hamiltonian based numerical discretizations will first be investigated for low-order models. 2.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. 3.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. |
