Abstract
Reduced order modeling (ROM) provides a way to decrease the degrees of freedom of large-scale ocean models (such as MPAS-O) using a reduced, data-driven basis. This can be useful to reduce the time-to-solution in simulations and has applications in data assimilation and uncertainty quantification. The computational effort in ROM is split between a costly offline phase, which identifies the globally orthogonal basis functions corresponding to the dominant modes of the system and constructs the reduced model, and the much cheaper online phase, which evolves the reduced model in time. The online phase can potentially be reused for multiple parameter sets, leading to efficient simulations. Another benefit of ROM is that the reduced model, which excludes the highest frequency modes, typically eases the time-step restriction existing for explicit methods. The long time-horizons required in climate modeling make the long-term stability of the reduced model critical. For this reason, a Hamiltonian structure preserving ROM (HSP-ROM) method has been developed for the rotating shallow water equations (discretized in space with the TRiSK scheme), leading to a more stable reduced model than conventional ROM methods. In particular, the mass and energy conserving properties of the full order model are inherited by the reduced model. Additionally, if the original model is augmented by additional dissipation terms such as drag or diffusion, the reduced model is dissipative as well. Moreover, the HSP-ROM is constructed in an approximate energy norm which increases the accuracy of the method. Special attention is paid to the efficient numerical treatment of the nonlinear terms appearing in the reduced model, which requires additional approximation steps. Results are presented for different simulations of a single-layer ocean model, which is set up to be either energy conserving, energy dissipating, or includes additional wind forcing terms. The latter setup is inspired by the SOMA testcase. The reduced model will be compared to the original model to assess its potential viability.