Using Discrete Wavelet Transform for Trend Analysis and Oscillatory Patterns Identification of Temperature (Case Study: Mashhad Synoptic Station)

Studying long-term trend changes of meteorological parameters is one of the routine methods in atmospheric studies, especially in the climate change subject. Among the meteorological parameters, temperature is always considered as one of the most atmospheric elements and studying it in order to gain a better understanding of the climate change phenomenon, has been effective. In addition to identifying trends, extraction of oscillatory patterns in the atmospheric phenomena and parameters occurrence can be an applicable and reliable method to explore the complex relations between atmospheric-oceanic cycles and short term or long term consequences of meteorological parameters. In this paper, monthly average temperature time series in Mashhad synoptic station in 55 years period (from 1956 to 2010) in monthly, seasonal, annual and seasons separately (winter, spring, summer and autumn) have been analyzed. Discrete wavelet transform and Mann-Kendall trend test were the main methods for performing this research. Wavelet transform is a powerful method in signal processing and it is an advanced version of short time Fourier transforms. Moreover, it has many improvements and more capabilities compared with Fourier transform. In the first step, temperature time series in various time scales (which was mentioned above) have been decomposed via discrete wavelet transforms into approximation (A) and detail (D) components. For the second step, Mann-Kendall trend test was applied to the various combinations of these decomposed components. For detecting the most dominant periodic component for each of the time scales datasets, results of Mann-Kendall test for the original time series and the decomposed components were compared to each other. The nearest value indicated the most dominant periodicity based on the D component’s level. To detect the similarity between results of the Mann-Kendall test, relative error method was employed. Additionally, it must be noted that before applying Mann-Kendall test, time series has to be assessed for its autocorrelation status. If there are seasonality patterns in the studied time series or lag-1 autocorrelation coefficient of data is significant, then some modified versions of the Mann Kendall test have to be employed. Results of this study showed that the temperature trend at every time scaled dataset (monthly, seasonal, annual and seasons separately) is positive and significant. Autocorrelation coefficients indicated that only seasonal time series and winter datasets did not have significant ACFs. On the other hand, monthly and seasonal datasets had seasonality pattern. Based on these results, Hirsch and Slack’s modified version of Mann-Kendall test was employed for monthly and seasonal time series and for the winter temperature data, the original version of the Mann-Kendall test was applied. For the remaining time series, the Hamed and Rao’s modified version of the Mann-Kendall trend test was employed. Dominant periodicities in monthly, seasonal and annual, confirmed the oscillatory behavior of each other. However, in the seasons, it seems that periodic patterns with the same temperature ranges are more similar. On the other hand, due to the greater similarity between the results of the Mann-Kendall test in the warmer seasons and the data with monthly, seasonal and annual time scale, it seems that yearly warm period has more noticeable impacts on the positive and significant trend of temperature in the study area. It must be noted that in any of the studied time series, results of the Mann-Kendall test for detail (D) component was not significant and after adding approximation (A) component, Mann-Kendall statistics turned to a significant value. This happens because the long term variations or trends appear in approximation components in most of the time series. In this study, a powerful signal processing method called wavelet transform was employed to detect the most dominant periodic components in temperature time series in various time scales, in Mashhad synoptic station. Results showed that using frequency-time analysis methods has more benefits compared with the use of only classic statistical methods, since one can explore any time series with more accuracy. Because most of the meteorological variables have periodic structures, it seems that using advanced signal processing methods like wavelet for analysis of these variables can have many advantages compared with linear-based methods. It can be suggested for future studies to use and employ signal processing methods for exploring the large scaled phenomena (e.g. ENSO, NAO, etc.) and discovering the relationship between these phenomena and climate change in recent decades.