Kolmogorov-Zurbenko Filter Research Articles

Analysis of maximum and minimum daily temperatures recorded at Fabra Observatory (Barcelona, NE Spain) in the period 1917–1998

AbstractDaily maximum and minimum temperatures recorded without interruption at Fabra Observatory (Barcelona) from 1917 to 1998 are analysed studying their homogeneity, randomness, possible trends and their statistical significance, and time irregularities detected by means of concepts of entropy and spectral power analysis. The homogeneity of the series is tested on a monthly scale using the adaptive Kolmogorov–Zurbenko filter. With respect to the randomness of the time series, the von Neumann ratio test is applied to standardized values of extreme temperatures in four different time‐scales (daily, monthly, seasonal and annual). The statistical significance of trends is quantified by applying the Spearman and Mann–Kendall tests to daily, monthly and seasonal data. The Mann–Kendall sequential test also leads to the detection of sharp changes in the time series when monthly data is analysed. The quantification of irregularities through entropy is investigated for standardized temperatures on daily, monthly and seasonal scales, based on the concept of mathematical information theory. Periodicities derived from spectral power analyses are checked with the hypothesis of white‐noise and Markov red‐noise stochastic processes. The most notable features, common to maximum and minimum temperatures, are the lack of randomness of the series for all the time‐scales considered and the different trends obtained for the periods 1917–1980 and 1917–1998, which are confirmed by the Spearman and sequential Mann–Kendall tests. Nevertheless, the maximum and minimum temperature series show quite a different behaviour from the point of view of results concerning time irregularities in terms of entropy and periodicities. The main features of the results are discussed by comparing them with those obtained for other areas of the Mediterranean domain. Copyright © 2001 Royal Meteorological Society

Separating Different Scales of Motion in Time Series of Meteorological Variables

The removal of synoptic and seasonal signals from time series of meteorological variables leaves datasets amenable to the study of trends, climate change, and the reasons for such trends and changes. In this paper, four techniques for separating different scales of motion are examined and their effectiveness compared. These techniques are PEST, anomalies, wavelet transform, and the Kolmogorov–Zurbenko (KZ) filter. It is shown that PEST and anomalies do not cleanly separate the synoptic and seasonal signals from the data as well as the other two methods. The KZ filter method is shown to have the same level of accuracy as the wavelet transform method. However, the KZ filter method can be applied to datasets with missing observations and is much easier to use than the wavelet transform method.

Determining Temporal and Spatial Variations in Ozone Air Quality

Unless the change in emissions is substantial, the resulting improvement in ozone air quality can be easily masked by the meteorological variability. Therefore, the meteorological and chemical signals must be separated in examining ozone trends. In this paper, we discuss the use of the Kolmogorov-Zurbenko filter in evaluating the temporal and spatial variations in ozone air quality utilizing ozone concentration data from several monitoring locations in the northeastern United States. The results indicate a downward trend in the ozone concentrations during the period 1983-1992 at most locations in the northeastern United States. The results also reveal that ozone is a regional-scale problem in the Northeast.