## 1. Introduction

Analysing hydrological signals such as precipitation and runoff can give significant information about the past and future variability of hydrological and climatic regimes. This is very important for planning and management of water resources. Therefore, there is increasing interest in the analysis of past hydrological and climatic variables.

Statistical methods such as spectral analysis and Fourier transform (FT) assume that the signal is stationary and its statistic does not change with time (Drago and Boxall, 2002). They cannot take into account temporal evolution of a signal. However, hydro-meteorological time series are natural and generally change their statistical characteristics in time. The wavelet transform is a mathematical tool that provides a time-scale representation of a signal in the time domain (Daubechies, 1990; Polikar, 1999). It is a useful tool for non-stationary processes such as hydrological time series (Pisoft *et al.*, 2004).

Recently, there has been growing interest in wavelet analysis in water resources and meteorology. Wavelet transforms were employed for streamflow characterization (Smith *et al.*, 1998), for defining the relationship between the southern oscillation index (SOI) and the Indian Summer Monsoon (Kulkarni, 2000), for founding relationship between the North Atlantic oscillation (NAO) and sea level changes (Yan *et al.*, 2004), for studying El-Nino southern oscillation (Torrence and Compo, 1998) and for defining inter-decadal and inter-annual characteristics of rainfall and precipitations (Lu, 2002; Xingang *et al.*, 2003; Penalba and Vargas, 2004). Wavelet transforms are useful tools especially for defining connections between hydro-meteorological variables. Wavelet analysis of precipitation and runoff series can give meaningful information regarding the temporal variability of the rainfall–runoff relationship. Labat *et al.* (2000) researched rainfall–runoff relations by using wavelet and multi-resolution analyses. In their study, the proposed methods were applied to weekly, daily and half-hourly data. They carried out useful investigations regarding the relationship of rainfall–runoff in France. Nakken (1999) studied continuous wavelet transform (CWT) for exploring the temporal variability of rainfall and runoff. He used the rainfall and runoff records from South Wales. He also researched the influence of SOI on the rainfall–runoff records. His study showed a strong relationship between the SOI and the rainfall with a dominant frequency of SOI at 27 months. Drago and Boxall (2002) researched the relationship between sea level variability and meteorological parameters of Malta. Atmosphere parameters (wind speed, direction, air pressure, temperature, relative humidity and solar radiation) and hourly averaged sea levels were decomposed by discrete wavelet transform (DWT). The decomposed series at different levels were compared with other one. Their wavelet analysis results present significant evidences between sea level variability and meteorological parameter variability.

The wavelet analysis was used to determine the non-stationary trends and periodicals in some studies (Jung *et al.*, 2002; Taleb and Druyan, 2003; Pisoft *et al.*, 2004). Taleb and Druyan (2003) determined a positive linear trend for two periodic bands. These bands include 3–5 day-periods and 5.5–9-day periods in rainfall series. Partal and Kucuk (2006) researched non-parametric trends on wavelet coefficients of measured precipitation series at distinct scales. These studies showed that wavelet transform is a useful tool to determine the linear or non-linear trend. Some statistical non-parametric tests, such as the Mann–Kendall test, were applied to detect the trend in Turkey's precipitation and streamflow records. Partal and Kahya (2006) showed that some decreasing trends were observed in Western Turkey (especially in the Aegean region). Kahya and Kalayci (2003) investigated downward trends in the records of rivers located in western Turkey. Similarly, Cıdızodlu *et al.* (2005) found decreasing trends in the annual mean and low flows in Turkey. Türkeş (1996) studied the Turkish annual rainfall data by using statistical tests for long-term trends and changes in runs of dry and wet years. He determined some significant trends with a downward direction. These studies show that trends detected in the flow and precipitation data of Turkey are generally found to be parallel to each other. Kalayci and Kahya (2005) researched streamflow variability and relationships between the streamflow and precipitation of Turkey by using principal component (PC) analysis. Significance correlations were determined between the first PCs of precipitation and streamflow. The wavelet technique was applied on the Turkey hydrological data in only a few studies but for different purposes except in the study by Partal and Kucuk (2006). This technique was used to simulate streamflow (Bayazıt *et al.*, 2001; Bayazıt and Aksoy, 2001), to simulate rainfall (Ünal *et al.*, 2004) and to forecast daily precipitation (Partal and Kisi, 2007).

This study aims to explore the periodical fluctuations and the relationship between precipitation and runoff in the Aegean region of Turkey. The CWTs and the DWTs were used to expose time-scale characteristics of the measured series. Furthermore, some statistical interpretation of the wavelet components was presented. In this study, the Aegean precipitation and runoff records were analysed for investigating their characteristics in long-term drought and inter-decadal changes. The Aegean hydrological data had showed strong decreasing trends in the past trend studies. Therefore, we selected the Aegean hydrologic data. Decreasing trends found in previous studies of Aegean precipitation and runoff data were also clarified by using wavelet transforms. The continuous wavelet analysis on Turkey hydro-meteorological data is a new research for studying periodicities and long-term variability.