Mathematical modelling for environmental applications represents a research area of significant importance. Numerical simulations of geophysical flows are not only an essential tool for ocean and weather forecast, but they could also provide insights on the mechanisms governing climate change. The typical resolution required by a Direct Numerical Simulation (DNS) for mesoscale atmospheric problems is of the order of 0.1 mm. Such a resolution is beyond reach even with modern supercomputers. When a DNS is possible, it is usually expensive in terms of computational time and memory demand due to the large amount of degrees of freedom to be considered for a proper description of the flow system. In addition, often long time intervals have to be simulated. In this work we present two ways to reduce the computational cost associated to the numerical simulations of atmospheric flows. These are: (i) Large Eddy Simulation (LES) models that allow to use a coarser mesh by modeling the effect of the small scales that do not get resolved and (ii) Reduced Order Models (ROMs) that enable fast computations without a significant loss in terms of accuracy.