Equilibrium states of the Charney-DeVore quasi-geostrophic equation in mid-latitude atmosphere

On the predictability of atmospheric blocking in the mid-latitude atmosphere, a quasi-geostrophic beta-plane channel model equation was introduced in a pioneering work by Charney and DeVore in 1979 based on the understanding of quasi-stationary weather patterns. The equation is driven by a zonal thermal flow representing a mid-latitude westerly jet and a wave function representing an ocean land topography. They truncated the equation into a three spectral mode model, which gives rise to the existence of multiple equilibrium states showing a blocking mechanism profile. Moreover, they predicted numerically the absence of the multiple equilibrium states with respect to the flat topography situation. In the present paper, this absence observation is discussed from rigorous analysis and the coexistence of two stable equilibrium states, similarly to the three mode model equilibrium states accounting for atmospheric blocking, is investigated numerically with the increment of topographic amplitude.