The relationship between precipitation and temperature of IRAN with the sunspot cycle using wavelet filtering

The sun is the primary source of energy for Earth's atomosphere. Changes in the output energy of the sun and its surface temperature fluctuations can create fluctuations and changes in the Earth's atmosphere. Sunspot activity can affect the Earth's climate system at different time scales and ultimately causing fluctuations and climate change.
The main feature of sunspots is that those have fairly regular variability in 11-year cycle. When 11 year cycle of solar is maximum, there is intense solar activity. Therefore, total solar irradiance increased and the sun transforms energetic particle to space by the solar wind (Lean, 2001).
Much research on the relationship between annual and monthly precipitation and sunspot cycle is done (Fleer 1982; Seleshi et al. 1994; Pérez-Peraza et al.1999; Hiremath & Mandi. 2004; Bhattacharyya & Narasimha. 2004; Zhao et al. 2004; Souza Echer et al. 2008; Selvaraj et al. 2009; Ma et al. 2010; Roy & Haigh. 2012; and in IRAN: Jahanbakhsh & edalatdoost. 2008).
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. 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 have 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 (Addison. 2002).
In this study, was performed Spectral analysis of time series of temperature and precipitation using wavelet theory, to determine the effect of sunspots on the spectral behavior of temperature and precipitation in Iran, in a period of 43 years (1966-2009) in 41synoptic stations. The spectral separation of precipitation and temperature time series in the frequency band from 9 to 12 years using the inverse wavelet transform is done and compare it with time series of sunspots in different years. Then we calculate the correlations of these fluctuations at different stations.
The results show that the 11-year cycle of temperature and precipitation variability and its relation to sunspots, in any station is different. Fluctuations in temperature and precipitation with respect to solar cycle, in some of stations are inverse behavior and have similar behavior on others. In relation to rainfall, whatever move from lower latitudes to higher latitudes, the correlation between the sunspot cycle and the cycle of rainfall variability, changes from large negative values to positive values, therefore, at low latitudes the 11-year variability of precipitation and the number of sunspots has inverse behavior and has similar behavior at high latitudes. In relation to temperature, solar cycle in the South East, East and parts of central and southern coasts have more impact and from South East to the North West of the country, decrease the relationship between temperature and sunspot cycle.
Therefore, Wavelet analysis show different cycles with different intensity at climate time series such as temperature and precipitation. When the cycle is shorter, that is suggested a regional scale forcing and when that is longer, is related to a larger-scale atmospheric forcing.