Abstract: The DYNAMO model is a meteorological primitive system capable of simulating several phenomena of importance in atmospheric dynamics. In particular, it can be used for testing initialization schemes as well as for the incorporation of effects such as orographic forcing. Since the given equations are non-linear, the continum model is usually discretized on time over a spatial grid and the resulting system is then solved numerically. If we introduce spatial matrix differentation and we take into account the nature cyclic boundary conditions for limited area, we can formulate the discretization as a non-linear matrix differential equation for the vorticity and divergence fields an the geopotential. The linear part being a block matrix circulant. A primite approach, would lead us a singular non-linear matrix differential equation for the velocity field and geopotential. This model will be discussed by using singular matrix decompositions for field reconstructions, an unmodal representation for the transistion matrix and block circulant techniques.