A model in which the prognostic field variables are represented as sums of a finite set of spectral modes rather than at gridpoints. The spectral modes may be Fourier modes in the one-dimensional case or double Fourier modes or spherical harmonics in the two-dimensional case. The advantage of a spectral model is that horizontal derivatives can be calculated exactly for the spectral modes represented in the model and thus the model error is confined only to the unrepresented higher spectral modes beyond the model's spectral truncation.