A topological computation method (called the Morse graph method for stochastic time-series date, or the MGSTD method) is applied to noisy time-series data obtained from meteorological measurement. This method is based on the idea of the Morse decomposition, which is a decomposition of the dynamics into invariant sets, called the Morse sets, and their gradient-like connections. A Morse decomposition of a dissipative dynamical system can be obtained by dividing the phase space into grids and constructing a combinatorial multivalued map over the grids [Z. Arai et al., SIAM J. Appl. Dyn. Syst., 8 (2009), pp. 757-789; J. Bush et al., Chaos, 22 (2012), 047508]. In the case of time-series data generated by a dynamical system, a combinatorial multivalued map over the grids can be similarly constructed. However, time-series data obtained from real measurements (e.g., meteorological data) are often highly stochastic due to the presence of noise. A multivalued map is then determined statistically by preferable transitions between the grids. We consider time-series data taken from the first two principal components of the pressure patterns in the troposphere and the stratosphere in the northern hemisphere, measured over 31 years, 90 days in each year × every 6 hours per day. The application of the MGSTD method to the troposphere data yields some particular transitions between the Morse sets, corresponding to specific motions in the phase space spanned by the principal components. The motions detected by our analysis are consistent with changes between characteristic pressure patterns that have been previously recognized in meteorological studies. A similar result is also obtained with the stratosphere data.