The change of the attractor dimension (Kaplan-Yorke dimension) with an increase in the number of modes included in the Fourier expansion is investigated for a quasi-geostrophic two-layer system with topographic forcing. A particular case has been chosen such that the attractor is represented by a single “weather regime”, consisting of weak fluctuations around a fixed flow pattern. In this respect, the large-scale flow structure isleast“chaotic”. Anticipation is that this kind of organized flow may be described by a low dimensional attractor. No convergence of the dimension is found by increasing the total number of Fourier modes up to 210. The result suggests that the quasi-geostrophic system cannot be reduced to a low-dimensional dynamical system in general. The crucial importance of a large number of small scale modes to predict the planetary scale dynamics, is suggested.