The Search for a Low-Dimensional Characterization of a Local Climate System

Along with the computation of attractor dimension via the Grassberger-Procaccia method and the nearest neighbour algorithm, a variety of phase space tests are used to search for low-dimensional characterization of daily maximum and minimum atmospheric temperature data (ca. 25 000 points each, spanning about a 70-year period). These tests include global and local singular value decompositions, as well as others for uncovering nonlinear correlations among amplitudes of the global singular vectors and for recognizing determinism in a time series. The results show that a low-dimensional characterization of the temperature data is unlikely.