Application of wavelet analysis to investigate precipitation variability at western region of Iran

Wavelet analysis is a major development in the methods of data analysis in the last twenty years, in both research and applications. With concern over current climate changes and their attribution, the analysis of natural climate variability on relatively long timescales has attracted much attention in recent years. While the short instrumental record provides only a tentative estimate of multi-decadal variability, in a long paleo-climatologic series the multi-decadal oscillation appears as a statistically significant mode of climatic variability with a heterogeneous spatial pattern (Datsenko et al., 2001). A powerful method for analyzing the localized intermittent oscillations is the wavelet transform, which is known as one of the best-suited tools for tracing a given oscillation through a time series (Holschneider, 1995). The application of wavelet analysis in analyzing timebased data, particularly those with non-stationary characteristics, has been found to be very successful. The wavelet transform of time series is a convolution with the local base functions or wavelets, which can be stretched and translated with a flexible resolution in both frequency and time. The wavelet transform decomposes a series into time-frequency space, enabling the identification of both the dominant modes of variability and the manner in which those modes vary with time. One of the wavelets which has both real and imaginary parts is the Morlet wavelet. This wavelet is the most commonly used complex wavelet in climate studies. As with its Fourier counterpart, there is an inverse wavelet transform that allows the original signal to be recovered from its wavelet transform by integrating all scales and locations, a and b. If we limit the integration over a range of a scale rather than all of scale a, we can perform a basic filtering of the original signal. In this study, time-frequency spectral decomposition has been conducted to investigate the precipitation variability in a western region of Iran, including Kermanshah, Sanandaj, Hamadan, and Khoram Abad, and to compare these stations with each other over a 43- year period from 1966 to 2009. The wavelet transform spectra were computed for the monthly total precipitation of each record. Results show that all stations had annual return periods with a confidence interval above 90 percent, and that in some years it became strong and in some years becomes weak, showing as well as the occurrence of wet and drought period in these regions. Moreover, at all stations there are some inter-annual components and a similar 128- to 256-month-long returning period with a high statistical confidence level. Precipitation behavior in various frequency bands showed that the local and large scale behaviors of the stations are very similar to each other, although in some scales the difference is significant. Additionally, the trend of variability in the 32-64 frequency band, unlike other bands, shows increased variability of precipitation.