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Geophysical flow simulations using hyperbolic shallow water moment equationsrequire an efficient discretization of a potentially large system of PDEs, theso-called moment system. This calls for tailored model order reductiontechniques that allow for efficient and accurate simulations while guaranteeingphysical properties like mass conservation.  In this paper, we develop the first model reduction for the hyperbolicshallow water moment equations and achieve mass conservation. This isaccomplished using a macro-micro decomposition of the model into a macroscopic(conservative) part and a microscopic (non-conservative) part with subsequentmodel reduction using either POD-Galerkin or dynamical low-rank approximationonly on the microscopic (non-conservative) part. Numerical experiments showcasethe performance of the new model reduction methods including high accuracy andfast computation times together with guaranteed conservation and consistencyproperties.

Macro-micro decomposition for consistent and conservative model order  reduction of hyperbolic shallow water moment equations: A study using  POD-Galerkin and dynamical low rank approximation