Identification and analysis of temporal trends and low-frequency variability in
discrete time series is an important practical topic in understanding and predic-
tion of many atmospheric processes, for example, in analysis of climate change.
Widely used numerical techniques of trend identification (like local Gaussian ker-
nel smoothing) impose some strong mathematical assumptions on the analyzed
data and are not robust to model sensitivity. The latter becomes crucial when
analyzing historical observation data with a short record. Two global robust nu-
merical methods for the trend estimation in discrete non-stationary Markovian
data based on different sets of implicit mathematical assumptions are introduced
and compared here. The methods are first compared on a simple model exam-
ple, the importance of mathematical assumptions on the data is explained and
numerical problems of local Gaussian kernel smoothing are demonstrated. Pre-
sented methods are applied to analysis of the historical sequence of atmospheric
circulation patterns over UK between 1946-2007. It is demonstrated that the
influence of the seasonal pattern variability on transition processes is dominated
by the long-term effects revealed by the introduced methods. Despite of the dif-
ferences in the mathematical assumptions implied by both presented methods,
almost identical symmetrical changes of the cyclonic and anticyclonic pattern
probabilities are identified in the analyzed data, with the confidence intervals
being smaller then in the case of the local Gaussian kernel smoothing algorithm.
Analysis results are investigated with respect to model sensitivity and compared
to standard analysis technique based on a local Gaussian kernel smoothing. Finally, the implications of the discussed strategies on long-range predictability of
the data-fitted Markovian models are discussed
