  The simulation of atmospheric flows by means of traditional discretization
methods remains computationally intensive, hindering the achievement of high
forecasting accuracy in short time frames. In this paper, we apply three
reduced order models that have successfully reduced the computational time for
different applications in computational fluid dynamics while preserving
accuracy: Dynamic Mode Decomposition (DMD), Hankel Dynamic Mode Decomposition
(HDMD), and Proper Orthogonal Decomposition with Interpolation (PODI). The
three methods are compared in terms of computational time and accuracy in the
simulation of two well-known benchmarks for mesoscale flow. The accuracy of the
DMD and HDMD solutions deteriorates rather quickly as the forecast time window
expands, although these methods are designed to predict the dynamics of a
system. The reason is likely the strong nonlinearity in the benchmark flows.
The PODI solution is accurate for the entire duration of the time interval of
interest thanks to the use of interpolation with radial basis functions. This
holds true also when the model features a physical parameter expected to vary
in a given range, as is typically the case in weather prediction.
