Achieving the paradoxical goals of modeling

Numerical models used to predict weather and climate have two competing goals: stability, which comes from a dissipation term, and energy conservation, which determines the physical fidelity.

Brecht et al. address these conflicting aspirations with a modeling scheme that follows the continuous decay framework, conserving the total energy while allowing dissipation of an otherwise conserved quantity. They combined this framework with the variational discretization framework to obtain a discrete selective decay framework.

The authors applied the discrete selective decay framework to shallow water equations. This approach conserved energy while dissipating the potential enstrophy, a quantity corresponding to dissipation effects in a fluid.

This scheme improves the model stability. The authors simulated a flow over a mountain and found this framework increases resolution of small-scale features, resulting in a simulation more like the reference solution computed at a higher resolution. The results suggest the scheme improves the quality of approximate solutions, making it a viable framework for long-term climate simulation.

“Climate and weather simulations are essentially always resolution limited. They run the highest-resolution simulations possible for a given computational budget,” said author Rüdiger Brecht. “The selective decay framework offers a chance to improve fidelity in these simulations by better resolving small scales often neglected or diffused by existing methods.”

The shallow water equations used in this study are a simplified approximation. Next, the authors will apply their discrete selective decay framework to more realistic geophysical models, such as the primitive equations used in accurate simulations of climate dynamics.

Source: “Selective decay for the rotating shallow-water equations with a structure-preserving discretization,” by Rüdiger Brecht, Werner Bauer, Alexander Bihlo, François Gay-Balmaz, and Scott MacLachlan, Physics of Fluids (2021). The article can be accessed at https://aip.scitation.org/doi/full/10.1063/5.0062573 .