On Robust Estimation of Low-Frequency Variability Trends in Discrete Markovian Sequences of Atmospheric Circulation Patterns

Abstract Identification and analysis of temporal trends and low-frequency variability in discrete time series is an important practical topic in the understanding and prediction of many atmospheric processes, for example, in analysis of climate change. Widely used numerical techniques of trend identification (like local Gaussian kernel smoothing) impose some strong mathematical assumptions on the analyzed data and are not robust to model sensitivity. The latter issue becomes crucial when analyzing historical observation data with a short record. Two global robust numerical methods for the trend estimation in discrete nonstationary Markovian data based on different sets of implicit mathematical assumptions are introduced and compared here. The methods are first compared on a simple model example; then the importance of mathematical assumptions on the data is explained and numerical problems of local Gaussian kernel smoothing are demonstrated. Presented methods are applied to analysis of the historical sequence of atmospheric circulation patterns over the United Kingdom between 1946 and 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 the differences 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 than in the case of the local Gaussian kernel smoothing algorithm. Analysis results are investigated with respect to model sensitivity and compared to a 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.