Time Series Analysis: A New Methodology for Comparing the Temporal Variability of Air Temperature

Temporal variability of three different temperature time series was compared by the use of statistical modeling of time series. The three temperature time series represent the same physical process, but are at different levels of spatial averaging: temperatures from point measurements, from regional Baltan65+, and from global ERA-40 reanalyses. The first order integrated average model IMA(0, 1, 1) is used to compare the temporal variability of the time series. The applied IMA(0, 1, 1) model is divisible into a sum of random walk and white noise component, where the variances for both white noises (one of them serving as a generator of the random walk) are computable from the parameters of the fitted model. This approach enables us to compare the models fitted independently to the original and restored series using two new parameters. This operation adds a certain new method to the analysis of nonstationary series. 1. Introduction Atmospheric reanalyses are widely used in meteorological and climatological research, as it makes available long time series of gridded meteorological variables, to explore climatic trends and low-frequency variations. Traditional analysis of air temperature time series, focused on trend detection and fitting of statistical models, has shown itself a useful tool (e.g., [1, 2] and references wherein). A use of structural time series models (i.e., linear trend plus red noise) has been popular in recent years (e.g., [3, 4]). Our paper differs from cited above approach because no a priori model structure is supposed. We use the structure and correlation functions of temperature time series to select an applicable model type according to the scheme introduced by [5] inside the family of autoregressive integrated moving average (ARIMA) models. The scheme has been tested by means of various daily series before by [6, 7], and the earlier analysis shows that the first order integrated moving average model IMA(0, 1, 1) is applicable for daily temperature anomaly time series. Nonstationary nature of the fitted IMA(0, 1, 1) model indicates that the traditional characterization of temperature variability on the basis of sample moments is unjustified. Due to nonstationarity, the moments do not converge if the sample size increases. This means that in order to compare temporal variability of air temperatures from different sources (e.g., measured and reanalysed), some other characteristic parameters are needed. A nonstationary IMA(0, 1, 1) model is divisible into a sum of white noise (WN) and random walk (RW) component [5]. The variances for