  The series of mean daily temperature of air recorded over a period of 215
years is used for analysing the dimensionality and the predictability of the
atmospheric system. The total number of data points of the series is 78527.
Other 37 versions of the original series are generated, including ``seasonally
adjusted'' data, a smoothed series, series without annual course, etc. Modified
methods of Grassberger and Procaccia are applied. A procedure for selection of
the ``meaningful'' scaling region is proposed. Several scaling regions are
revealed in the ln C(r) versus ln r diagram. The first one in the range of
larger ln r has a gradual slope and the second one in the range of intermediate
ln r has a fast slope. Other two regions are settled in the range of small ln
r. The results lead us to claim that the series arises from the activity of at
least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it
possesses the potential predictability of several weeks. We suggest that this
subsystem is connected with seasonal variability of weather. The second
subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7
days. It is found that the predictability differs in dependence on season. The
predictability time for summer, winter and the entire year (T_2 approx. 4.7
days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring,
T_2 approx. 3.6 days for autumn). The role of random noise and the number of
data points are discussed. It is shown that a 15-year-long daily temperature
series is not sufficient for reliable estimations based on Grassberger and
Procaccia algorithms.
