The spectra of linearized barotropic quasigeostrophic model is one of classical but not yet completelysolved problems in dynamic meteorology. This paper is devoted to a detailed investigation of this problem.It is obtained that in the case of zonal basic flow μ(y), there exist two types of spectra, the discrete andcontinuous. Each discrete spectrum (eigenvalue) gives an eigenfunction (normal mode); and the real num-bers in the interval [μ_(min), μ_(max)] are the continuous spectra; every point c ? [μ_(min), μ_(max)] gives a spectralfunction which is bounded and whose derivative is unbounded but integrable. Every disturbance can berepresented as a linear combination of two parts, ψ’(x, y, t) and ψ’(x, y, t), the former is expressed bythe discrete spectra, and the latter by the continuum. ψ’_d can be easily derived from the initial conditionby the use of the generalized “weighted orthogonality” of normal modes. It is also proved that ψ’_c as wellas its energy E’_c and mean y-direction scale l_c a The spectra of linearized barotropic quasigeostrophic model is one of classical but not yet completelysolved problems in dynamic meteorology. This paper is devoted to a detailed investigation of this problem. It is obtained that in the case of zonal basic flow μ (y), there exist Each discrete spectrum (eigenvalue) gives an eigenfunction (normal mode); and the real num-bers in the interval [μ_ (min), μ_ (max)] are the continuous spectra; every point μ [min], μ_max] gives a spectral function which is bounded and whose derivative is unbounded but integrable. Each disturbance can be represented as a linear combination of two parts, ψ ’(x, y, t) and ψ ’(x, y, t), the former is expressed by the discrete spectra, and the latter by the continuum. ψ’_d can be easily derived from the initial condition by the use of the generalized “weighted orthogonality ” of normal modes. It is also proved that ψ’_c as wellas its energy E’_c and mean yd irection scale l_c a