  Geophysical flow simulations using hyperbolic shallow water moment equations
require an efficient discretization of a potentially large system of PDEs, the
so-called moment system. This calls for tailored model order reduction
techniques that allow for efficient and accurate simulations while guaranteeing
physical properties like mass conservation. In this paper, we develop the first
model reduction for the hyperbolic shallow water moment equations and achieve
mass conservation. This is accomplished using a macro-micro decomposition of
the model into a macroscopic (conservative) part and a microscopic
(non-conservative) part with subsequent model reduction using either
POD-Galerkin or dynamical low-rank approximation only on the microscopic
(non-conservative) part. Numerical experiments showcase the performance of the
new model reduction methods including high accuracy and fast computation times
together with guaranteed conservation and consistency properties.
