Abstract: In the peper multiple atmospheric equilibria are studied by using a barotropic vorticity equation with thermal forcings and dissipative effects. Different low-spetral models are used to discuss the variations of the equilibrium states,with the results that the multiple features of equilibrium saltes depend heavily on the truncations of the spectra and the low-spectral model has obvious shortcomings in solving non-linear equations,suggesting that one has to be very careful to employ highly truncated low-spectral model in approximating partial differential equations.