The reduced-order modelling problem was addressed by considering a nonlinear shallow-water equations model with limited-area region in rotating atmosphere. The proper orthogonal decomposition method (POD) and the discrete empirical interpolation method (DEIM) were used to establish the reduced-order model (ROM), and then to obtain the numerical solutions, to evaluate the capability and efficiency of simulating large-scale atmospheric motion. The study shows that the ROM fundamentally improves the computational efficiency and reduces the computation cost. The computational efficiency of the ROM based on POD/DEIM is significantly higher than that based on POD and the full-order model. The ROM based on POD/DEIM can capture more than 99.8% energy of the full-order model. It consumes very little CPU time, especially when the quantity of spatial grids obviously increases. However, the simulation quality of the ROM based on POD/DEIM relies on the choices of the dimension of snapshots and DEIM interpolation points. As the dimension of the DEIM interpolation points is decreased, the CPU time cost of the reduced-order model based on POD/DEIM will be reduced obviously.