In this chapter, the historical records of annual surface air temperature, pressure, and precipitation with the longest observational time series will be studied. The analysis of the statistically significant systematic variations, as well as random fluctuations of such records, provides important empirical information for climate change studies or for statistical modeling and long-range climate forecasting. Of course, compared with the possible temporal scales of climatic variations, the interval of instrumental observations of meteorological elements proves to be very small. For this reason, in spite of the great value of such records, they basically characterize the climatic features of a particular interval of instrumental observations, and only some statistics, obtained with their aid, can have more general meaning. Because each annual or monthly value of such records is obtained by averaging a large number of daily observations, the corresponding central limit theorem of the probability theory can guarantee their approximate normality. In spite of this, we computed the sample distribution functions for each time series analyzed below and evaluated their closeness to the normal distribution by the Kolmogorov- Smirnov criterion. As expected, the probability of the hypothesis that each of the climatic time series (annual or monthly) has a normal distribution is equal to one with three or four zeros after the decimal point. As seen in this section, the straight line least squares approximation of the climatic time series enables us to obtain very simple and easy-to-interpret information about the power of the long period climate variability. Carrying out such an approximation, we assume that the fluctuation with a period several times greater than the observational interval will become apparent as a gradual increase or decrease of the observed values. Using only a small sample, it is impossible to determine accurately the amplitude and frequency of such long-period climate fluctuation. Consequently, the straight-line model is the simplest approach in this case. Let us begin with an analysis of the annual surface air temperature time series, the observations of which are published in Bider et al., (1959), Bider and Schiiepp, (1961), Lebrijn (1954), Manlcy (1974), and in the World Weather Records (1975).
Keywords: atmospheric pressure, climate change, historical records, statistics and climate change, surface air temperature spectra and autocorrelation functions, univariate modeling of historical records
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