Wavelet analysis and multi-scale characteristics of the runoff and precipitation series of the Aegean region (Turkey)

Authors

  • Turgay Partal

    Corresponding author
    1. Dumlupınar University, Engineering Faculty, Civil Engineering Department, Kutahya, Turkey
    • Dumlupınar University, Engineering Faculty, Civil Engineering Department, Kutahya, Turkey.
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Abstract

This study focuses on the variability of precipitation and runoff over time and the relationship between precipitation and runoff at the Aegean region of Turkey. The wavelet transform technique, which has been widely used for the analysis of hydrological data in the last years, provides detailed information regarding time-frequency representation of the data. According to the continuous wavelet transform (CWT), the main periodic events are seen at the scale levels of 1–4 and 16 years. This study shows that variability of both the runoff and the precipitation over time is generally similar, with noticeable decrease in the runoff in all the stations. The dominant inter-decadal periodic events are seen approximately at the 16-year scale level. This periodicity is dominant between 1962 and 1985 for the runoff data. The power of the 16-year periodicity becomes less apparent after 1985. In addition, the global wavelet spectrum (GWS) and the decomposed series of the hydrological data were studied to investigate the effective periodic characteristic of the observed data. In this study, the period of investigation is 39 years extending from 1962 to 2000. The validity of the decreasing trend founded by previous studies for the Aegean hydrological data is verified by the wavelet analysis. Copyright © 2010 Royal Meteorological Society

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.

2. Case study

The monthly precipitation and runoff data that belong to stations located in the Aegean region were employed in this study (Figure 1). The period of investigation is 39 years extending from 1962 to 2000. As seen in Figure 1, the precipitation and streamflow stations are located near the Aegean Sea. The Aegean region, which is one of the highly populated and industrialized regions of Turkey, is generally associated with Mediterranean climatic regime (a sub-tropical climatic regime with a cool and rainy winter and a hot and dry summer). Heavy and intense rainfall has sometimes caused hazards that have led to flooding along the Aegean cities such as Yzmir. The topography may cause strong variations in the climate. In the Aegean region, the mountains are not parallel to the coast. Therefore, the mountains led the air mass to move into the central Aegean (Tatlı et al., 2004). Local orographic precipitations can heavily affect the inner parts of the Aegean. The streamflow stations are located on different river catchments. The Manisa and Kayalıodlu (Akhisar) gauging stations are located on the Gediz stream in Gediz catchment. The catchment of this stream is approximately 15.6 × 103 km2, and it has a mean elevation of 23 m. The other station (Aydın) is located on the Big Menderes stream in the Big Menderes catchment. The precipitation area of this stream is approximately 19.5 × 103 km2, and it has a mean elevation of 25 m. The annual mean of the monthly runoff and annual total of the monthly precipitations were subjected to wavelet transforms. The average annual runoff at Manisa station was 42.44 m3/s, whereas the average annual total precipitation at this station was 730 mm (Table I). The maximum annual mean at the Manisa station was 123 s/m3, whereas the maximum of annual precipitations is 1165 mm. The cross correlations between annual mean runoff and annual total precipitation at Manisa station are 0.72 (Table II).

Figure 1.

Location of gauging stations used in this study

Table I. Related information for runoff and precipitation stations used in this study
Station noStation nameVariableAnnual mean runoff/annual total precipitationMaximum of annual runoff/maximum of annual total precipitation
518ManisaRunoff42.44 (m3/s)123 (m3/s)
706AydınRunoff59.58 (m3/s)136 (m3/s)
509Kayalıoǧlu (Akhisar)Runoff2.97 (m3/s)9.6(m3/s)
17186ManisaPrecipitation730 (mm/year)1165 (mm/year)
17234AydınPrecipitation614 (mm/year)932 (mm/year)
17184AkhisarPrecipitation573 (mm/year)902 (mm/year)
Table II. Cross-correlation coefficients between runoff and precipitation records
Stations (rainfall–precipitation)Correlation
Manisa-Manisa0.72
Aydın-Aydın0.53
Kayalıoǧlu-Akhisar0.73

The Aegean hydrological data have been subjected to trend research in past studies. The precipitation data collected from Aydın, Akhisar and Manisa were studied by Partal and Kahya (2006) for a long-term trend analysis, and the annual precipitations in the study of Aydın and Akhisar have shown a statistically significant decreasing trend. A downward trend was found to exist on the streamflow stations (Aydın, Akhisar and Manisa) in the study by Kahya and Kalayci (2004).

3. Wavelet analysis

3.1. Continuous wavelet transform

The wavelet transform is a useful mathematical tool that presents non-stationary variance analysis at many different scales (periods) in a time series (Daubechies, 1990; Smith et al., 1998). The wavelet transform, which has been developed in the past few decades, appears to be a more effective tool than the FT, which does not provide an accurate time-frequency analysis for non-stationary signals (Coulibaly and Burn, 2004). Wavelet analysis detects periodicities in the time series and also shows their time dependences (Taleb and Druyan, 2003). CWT provides an ideal opportunity to examine the process of energy variations in terms of where and when hydrological events occur (Kucuk and Agiralioglu, 2006).

If a continuous time series x(t), t ∈ [∞, − ∞], wavelet function ψ(η) that depends on a non-dimensional time parameter η can be acquired as follows

equation image(1)

where t stands for time, s for wavelet scale, and τ for the time step in which the window function is iterated. ψ(η) must have zero mean and must be localized in both time and Fourier space (Meyer, 1993). The successive wavelet transform of x(t) is defined as

equation image(2)

where (*) indicates the conjugate complex function. By smoothly varying both s and τ, one can construct a two-dimensional picture of wavelet power, |W(τ, ,s)|2 showing the frequency (or scale) of peaks in the spectrum of x(t), and how these peaks change with time (Drago and Boxall, 2002).

The lower scales refer to a compressed wavelet, and help in tracing abrupt changes or high-frequency components of a signal. However, the higher scales composed of the stretched version of a wavelet and the corresponding coefficients represent slowly progressing occurrences or low-frequency components of the signal. The continuous wavelet spectrum of the data was calculated using the Morlet wavelet. The advantage of the Morlet wavelet function is that it gives a good definition of the signal in the spectral-space (Coulibaly and Burn, 2004).

The significance of the wavelet spectra can be determined with a significance testing based on the background (or noise) spectrum (Coulibaly and Burn, 2004). The noise spectrum depends on the nature of the data (Lafreniere and Sharp, 2003). If the lag-1 autocorrelation coefficient (ρ) (lag-1 autoregressive parameter) is positive (ρ> 0), then the process is red noise (increasing variance with increasing scale), and, if the lag-1 autocorrelation coefficient is zero, then the process is white noise (constant variance across all scales) (Torrence and Compo, 1998; Lafreniere and Sharp, 2003). The continuous wavelet spectra of the time series are compared with the spectrum of the background process at the 95% confidence level (Lafreniere and Sharp, 2003). For the noise process, a more detailed description is presented by Torrence and Compo (1998) and Lafreniere and Sharp (2003).

3.2. Global wavelet spectrum

Assuming a vertical slice through a wavelet plot to be a measure of the local spectrum, the time-averaged wavelet spectrum over certain periods, or all the local wavelet spectra, is then explained as

equation image(3)

where T is the number of points in the time series. The time-averaged wavelet spectrum is generally called the global wavelet spectrum (GWS) (Torrence and Compo, 1998). The smoothed Fourier spectrum approaches towards the GWS when the amount of necessary smoothing decreases with increasing scale. Therefore, the GWS provides an unbiased and consistent estimation of the true power spectrum, which is a useful tool for the analysis of non-stationary time series analysis. Spectral components are defined as the frequency in a power spectrum, and periodic components are ordered according to period scales in a GWS. A global spectrum is calculated via the continuous spectrum; therefore, the initial and final time of the periodic components can also be determined.

The significance of the GWS can be evaluated by a background spectrum. The GWS of time series is compared with the spectrum of the background function at a determined confidence limit (Lafreniere and Sharp, 2003). A peak in the GWS is significant if it is above this background spectrum. The corresponding distribution for the local wavelet spectrum is

equation image(4)

at each time t and scale s. The value of Pk is the mean spectrum at the Fourier frequency k that corresponds to the wavelet scale s (Torrence and Compo, 1998). equation image is the chi-square value for the chosen confidence limit. For the red noise spectrum, the Fourier power Pk is

equation image(5)

where α is the assumed lag-1 autocorrelation coefficient for the time series.

3.3. Discrete wavelet transform

Computing the wavelet coefficients at every possible scale (resolution level) generates substantial data. If wavelet coefficients are only obtained at defined scales, the wavelet analysis will be much more efficient and useful. Most common wavelet scales are dyadic scales. This transform is called DWT and is described as follows

equation image(6)

where m and n are integers that control the scale and time respectively, s0 is a specified fixed dilation step greater than 1 and t0 is the location parameter and that must be greater than zero. The most general choice for the parameters s0 and τ0 is 2 and 1 (time steps), respectively.

DWTs, which present power of two logarithmic scaling of the translations, is the most efficient solution for practical purposes (Mallat, 1989). For a discrete time series xi, where xi occurs at discrete time i (i.e. here integer time steps are used), the DWT becomes

equation image(7)

In this equation, Wm, n is the wavelet coefficient for the discrete wavelet of scale s = 2m and location τ = 2mn.

The DWT provides for obtaining one or more detailed series and an approximation at different scales.

4. Results

4.1. The wavelet analysis results

In this section, the wavelet transforms were applied to the observed runoff and precipitation series. Figure 2(b) and (c) shows the results of the CWT analysis of the annual mean runoff and the annual total precipitation at Manisa station. Effective periodic events are seen as the light region on the CWT figure. The dashed white line curve is the cone of influence of the wavelet analysis, which depends on the red noise process (Coulibaly and Burn, 2004). Therefore, the white line curve presents periodic events, which are statistically significant at the 95% confidence level for a red noise process with a determined lag-1 autocorrelation coefficient (ρ = 0.23 for Manisa runoff). Figure 2(a) clearly shows that there is a strong downward tendency in the runoff records. It is estimated from Figure 2(a) that this tendency is because of a decrease in the runoff value after 1985. The average annual runoff through time series is shown by respective solid lines. The dashed lines show the linear tendency. Similarly, the downward tendency can be seen for the precipitation data.

Figure 2.

Plot (a) and continuous wavelet spectrum (b) of runoff time series; continuous wavelet spectrum (c) and plot (d) of the precipitation time series at the Manisa station. The dashed white line curve (the cone of influence) in wavelet spectra is considered to determine statistically significant areas (at the 95% confidence level for a red noise process with ρ = 0.23 for Manisa runoff, ρ = 0.23 for Manisa precipitation)

In the Figure 2(b) and (c), the inter-annual periodicities (light region) located between the 1- and 4-year scale levels are seen between 1962 and 1985 for the runoff data, and between 1962 and 1968 for the precipitation data. After this time period, clear periodical events are not seen between the 1- and 4-year scale levels for both the CWT figures. Approximately, the 16-year periodicity is the most significant inter-decadal event. The inter-decadal periodicity (the central periodicity is at a 16-year scale level) is seen approximately between 1962 and 1985, but it is statistically significant after 1972 (Figure 2(b) and (c)). After 1985, the 16-year periodicity is not statistically significant and becomes less apparent for the runoff data. This may be assumed to be caused by a long-term decrease in the streamflow data. The probability of long-term drought has been demonstrated in the runoff wavelet spectrum. The inter-decadal periodic event (16 years) is seen to be continuous but weak for the precipitation data. Also, a weak inter-decadal periodicity is seen at the 32-year scale level for both the figures, but it is never statistically significant in terms of the red noise process. In the continuous wavelet spectrum figures of the runoff data, the variability over time of the major inter-annual and inter-decadal periodicities changes evidently at around 1985.

The dominant periodic components in the runoff and the precipitation series can be seen clearly from the GWS. The 95% confidence limit shown as a dashed line is based on the red-noise background spectrum with a lag-1 coefficient α, and indicates peaks above this background spectrum that are statistically significant. As seen in Figure 3, dominant inter-annual and decadal periodic events in the runoff and the precipitation records are presented by the GWS. It shows spectrum peaks at 1–4-, 16- and also 32-year periods for both data. The GWS of the runoff data shows that a major decadal periodic event occurs at the 16-year scale level and it is statistically significant. For the GWS of the precipitation records, two statistically significant peaks can be seen clearly at the 16- and 32-year scale levels.

Figure 3.

GWS of (a) Manisa runoff records and (b) Manisa precipitation records. The dashed line is the 95% confidence limit for the GWS, assuming α = 0.23

CWT was also applied to the monthly mean runoff and the monthly total precipitation records from Manisa station. CWT figures for the monthly data explain the variability of low periodic structures (annual and inter-annual) over time. As seen in Figure 4, the 12-monthly periodicity (1 year) is the major event for both variables. However, this event became less apparent in time for the runoff records as shown in Figure 2(b). Also, the vertical light lines are seen in this figure. Some of these lines are lighter than the others. These lines show the probability of seasonal oscillation being high runoffs [as seen in Figure 2(a)]. Events of stronger fluctuations in the runoff records are shown by lighter vertical lines. After 1985, vertical lines become less apparent. As seen in the figure, there is only one strong periodical event (light vertical line) at low scale after 1985. The mentioned signal appears in 1999. For the precipitation, the annual variability is continuous through the time, whereas its weakest period is approximately in the 1970s and 1990s.

Figure 4.

Continuous wavelet spectrum (a) of Manisa monthly average runoff time series, (b) Manisa monthly total precipitation time series

Figures 5 and 7 show the wavelet maps of the runoff and the precipitation records at Akhisar and Aydın stations. At the Akhisar station, the inter-annual periodicities located between the 1- and 4-year scale level are seen in two distinct periods of 1962–1969 and 1977–1985, but it is weaker for the precipitation. For example, the periodicities at low scales become invisible in time for both the variables. For the two variables, inter-decadal periodicities (16 yearly) are seen continuous through the time, but it is seen to be statistically significant only between 1977 and 1985. For Aydın runoff records, inter-decadal periodicities (highlighted in the 16-year scale level) are very intensive for the years extending from 1962 to 1985, but it is statistically significant only from 1977 to 1985. They also become less apparent after 1985. The inter-annual periodicities are not statistically significant. These periodicities are clear for the years extending from 1962 to 1969, but they are not seen after 1969. Figure 6(b) (for the precipitation data) shows that the inter-decadal variability (16 years) is fairly recognizable through the time. Figures 6 and 8 show the GWS of the time records of the Akhisar and Aydın stations. Figures show that the dominant component for the runoff and the precipitation records is the 16-year periodicity, and it is statistically significant. Moreover, the inter-annual periodic events in the runoff and precipitation records are seen at the 32-year scale level, but they are never statistically significant except for the GWS of the precipitation records of Akhisar. As a result, the 16-year periodicity is the main inter-annual event and it is statistically significant.

Figure 5.

Continuous wavelet figures (a) for annual runoff time series at Kayalıodlu (Akhisar); (b) for annual precipitation time series at Akhisar. The dashed white line curve is considered to determine statistically significant areas (at the 95% confidence level for a red-noise process with ρ = 0.21 for Akhisar runoff, ρ = 0.13 for Akhisar precipitation)

Figure 6.

GWS of (a) Akhisar runoff records and (b) Akhisar precipitation records. The dashed line is the 95% confidence limit for the GWS, assuming α = 0.23

Figure 7.

Continuous wavelet figures (a) for annual runoff time series at Aydın and (b) for annual precipitation time series at Aydın. The dashed white line curve is considered to determine statistically significant areas (at the 95% confidence level for a red-noise process with ρ = 0.70 for Aydın runoff, ρ = 0.28 for Aydın precipitation)

Figure 8.

GWS of (a) Aydın runoff records and (b) Aydın precipitation records. The dashed line is the 95% confidence limit for the GWS, assuming (a) α = 0.70 and (b) α = 0.28

Figure 9(a) and (b) shows the dominant periodical components for the standardized runoff and precipitation records. Similarities for strong periodicities between the GWS of the runoff and precipitation are clear in Figure 9(a). This figure shows that the 16-year periodicity has high magnitudes and major components for both the data. In addition, it shows spectrum peaks at 2–4-year periods for precipitation data and also at 32-year periods for both the data. However, the 32-year period is not statistically significant with respect to the red-noise process at 95% significant levels on continuous wavelet spectra. The dominant periodicities in the runoff and precipitation records of Aydın are at 2–4-, 16- and also 32-year periods. The relationship between the runoff and the precipitation periodical structures was evaluated by the three-dimensional wavelet spectra and the GWS. The GWS of the standardized runoff and precipitation can be explained by Figure 10(a) and (b), respectively. For the runoff data, the strong periodic is common at the 16-year period. Two- to four-year periods are strong for the Akhisar station, but weak for the Aydın station. For the precipitation data, the strong events at 2–4- and 16-year periods are nearly the same. Namely, the general behaviour of the precipitation data is the same.

Figure 9.

GWS of (– – – –) standardized runoff time series and (————) standardized precipitation time series for (a) Akhisar and (b) Aydın

Figure 10.

GWS for (a) runoff series and (b) precipitation series of each station

4.2. Multi-scale components and decomposed series

The hydrological data were decomposed into details and approximation series by the DWT. Daubechies wavelet is the basis function to be decomposed into different parts on different scales. The time series of the discrete wavelet coefficient (D) shows variations at the inter-annual and decadal scales. The hydrological time series were decomposed into wavelet components at five levels on 2-year (D1), 4-year (D2), 8-year (D3), 16-year (D4) and 32-year (D5) scales. The decomposed wavelet components of the runoff and the precipitation data for the Manisa station can be seen in Figure 11. The solid lines show the decomposed wavelet series of the runoff records, whereas the dashed lines show the decomposed wavelet series of the precipitation records. The variability of inter-annual and decadal periodic components is very similar and is observed in detail. The first-level detailed wavelet coefficients series (D1) indicates strong seasonal events [light vertical lines in Figure 4(a)] found in the CWT figure of the monthly runoff and can be detected as fluctuations from 1962 to 1970 and from 1980 to 1990 (Figure 11). Moreover, the powerful seasonal event in 1998, which is seen in the continuous wavelet spectra figures of the monthly runoff, can be seen as a strong fluctuation in the D1 series of both runoff and precipitation.

Figure 11.

The time series of standardized wavelet coefficients obtained by DWT (– – – –) for precipitation data and (————) runoff data of the Manisa station

Figure 12(a) presents total energies of the wavelet components at each scale. The total energies can be computed as follows:

equation image(8)
Figure 12.

(a) Total energy of runoff wavelet components and (b) correlation coefficients between measured runoff series and each decomposed wavelet component of measured runoff series

Total energies were standardized by dividing them with their highest value for comparison with components. The stations show similar energy magnitudes as seen in Figure 12(a). The energies of the D4 and the D1 components are generally higher than energies of the other components. The correlation between the observed runoff data and its wavelet components is shown in Figure 10(b). This figure shows that the correspondence between the D4 components and the runoff data (correlation coefficient is 0.68) is highest for Manisa data. The D4 decomposed series show the highest correlation (equal to 0.76) for the Aydın station. The correlation for D1 and D4 is relatively higher than that for the other components, as seen in Figure 12(b). At all the stations, the D4 component has a slightly higher correlation. The results show that the Aegean runoff and precipitation is characterized by the 2-year and, especially, the 16-year periodicities. As a result, all wavelet analyses (continuous wavelet analysis, GWS and discrete wavelet components) show that decadal events, such as 16-year periodicity, are the major phase for the hydrological records.

Figure 11 shows how decadal periodic variations affect linear trend (best linear fit) of the observed time series. The linear relationship corresponding to the regression line of y with respect to x can be described as follows:

equation image(9)

where a and b are regression coefficients. These coefficients are determined in such a way that the sum of the squares of the differences between the values of y are to be estimated from Equation (9) and the observed values of y must be minimum (the least square method) (Bayazıt, 2001). Here, the coefficient of b presents the change per unit time of y (runoff) with respect to x (time as year) in a time series having a linear trend. For Manisa runoff data, the regression equation is y = − 1.82x + 78.9 (b = − 1.82). Namely, the observed runoff records show a linear decreasing trend at a rate of 1.8 m3/s/year in the past 39 years [Figure 11(a)]. The 16-year component (D4) and the 32-year component of Manisa runoff show a linear downward trend as seen in Figure 13(b) and (c). The original time series can be reconstructed by using each of the wavelet components (decomposed and approximate series). The reconstructed time series are the sum of the wavelet coefficients at all scales. Figure 13(d) shows the reconstructed runoff signal, but 16–32-year scale (D4 and D5) was removed from the runoff signal. As seen in Figure 13(d), the reconstructed runoff series present a weak linear decreasing tendency at a rate of 0.14 m3/s/year in the past four decades. Similarly, Figure 14 shows the reconstructed precipitation series. Here, the D4 and D5 components were not included in the reconstructed series. The time series of the observed precipitation records [Figure 2(d)] show a linear decreasing trend (at a rate of 6.5 mm/year in the past 39 years) at the Manisa station, while the reconstructed series (Figure 14) do not show a clear linear trend. These approaches explain that these decreases in the hydrological series are principally due to variations of the time series at the decadal scale.

Figure 13.

Plot of (a) the runoff time series (b) D4 and (c) D5 components (Manisa station) and (d) plot of the reconstructed runoff series is the removed inter-decadal part at the fourth level (D4) and fifth level (D5), linear trend is displayed as dashed line

Figure 14.

Reconstructed precipitation series (Manisa station) is the removed inter-decadal part at the fourth level (D4) and fifth level (D5), linear trend is displayed as dashed line

4.3. Tele-connections with SOI and interpretation of the results

In this section, the wavelet components of the streamflow patterns were first analysed in association with both the SOI and the NAO. Kahya and Karabork (2001) researched evidences of SOI in streamflow of Turkey by using a comprehensive empirical method. They showed that monthly streamflow data of some regions in Turkey (such as Northwest Anatolia and Eastern Anatolia) have relationships with the extreme phases (El-Nino or La-Nina) of SOI. Tele-connections with Turkey climatic data on NAO and SOI were studied by Karaborks et al. (2005). These researches indicated potential relationships for both precipitation and streamflow variables in connection with the NAO. The SOI showed weaker relationships in comparison with those for the NAO. Besides, they showed that the influences of the SOI on Turkish temperature data are negligible. Besides, Karabork and Kahya (2003) researched the effects of El-Nino and La-Nina events on precipitation data of Turkey.

The SOI for the 1962–2000 period is illustrated in Figure 15. The short-term periodicities, such as 2–16-month scales, in the streamflow and precipitation data of Manisa station can be related with the strong El-Nino or La-Nina events (Figure 4(a) and (b), b). The marks of 1962 and 1999 La-Nina events can be seen (as strong vertical light lines) in the wavelet spectrum of streamflow in Figure 4(a). Besides, the strong periodicities in 1977 and 1983 in the streamflow data may be explained by the 1982 El-Nino event, which is one of the strongest El-Nino on record and by the 1977 and 1978 relatively strong El-Nino conditions. Similarly, the traces of 1965, 1969 and 1982 strong El-Nino events can be seen in the wavelet spectrum of precipitation data as strong vertical light lines [Figure 4(b)]. Also, the signs of El-Nino or La-Nina conditions can be connected with periodicities in 2–4-yearly scales of streamflow data, which is seen between 1962 and 1969 and also between 1977 and 1985 (Figures 2, 5 and 6).

Figure 15.

The SOI anomaly for the 1962–2000 period

The correlations between D components of the hydrological data and the SOI anomaly were researched in an annual mode for the period 1962–2000 (Table III). The observed data showed correlation in association with the SOI at 0.10 or lower value (Table III). However, as seen in Table III, the periodic wavelet components have significantly high correlations in comparison with the observed data. While the D5 (32-yearly mode) shows the highest positive correlations, the D3 (8-yearly mode) shows the highest negative correlations. Similarly, 32-yearly modes of the precipitation data indicate the significant correlations in association with the SOI. The correlation magnitude of the long-term periodicities (such as 32-yearly modes) is fairly more noticeable when compared with the short-term periodicities. It can be said that the influence of SOI on 8- and 32-year periodicities should be considered on Aegean hydrological data. However, traces of this influence on the continuous wavelet spectrum of the hydrological data cannot be seen clearly.

Table III. The correlations between D components of the hydrologic data and the SOI (anomaly), period 1962–2000
 StreamflowPrecipitation
 AkhisarAydınManisaAkhisarAydınManisa
D1− 0.05− 0.06− 0.040.050.130.01
D2− 0.150.110.00− 0.080.05− 0.07
D3− 0.24− 0.39− 0.34− 0.07− 0.23− 0.12
D40.000.000.000.02− 0.030.04
D50.360.350.350.360.280.35
Approx.0.110.090.100.12− 0.030.19
Observed data− 0.010.040.030.070.050.10

5. Conclusion and discussion

The results of the wavelet analysis have exhibited the characteristics and multi-variability of the runoff regime and precipitation of the Aegean region. The CWT figures of the annual runoff records show dominant inter-annual periodicities (1–4 year) between 1962 and 1985. The runoff and precipitation data show similar dominant inter-decadal periodicities at the 16-year scale level. Major inter-decadal periodic events are seen approximately at the 16-year scale level, but they are statistically significant between 1977 and 1985 based on the background process with the lag-1 autocorrelation coefficient. This periodicity is evident between 1962 and 1985 for the runoff data. But, after 1985, the 16-year periodicity becomes less apparent. This suggests that the probability of long-term decrease in the runoff records has been demonstrated in the runoff wavelet spectrum. The GWS of the hydrological data shows that the major inter-decadal periodicities are at 16- and also 32-year scale levels. However, the 16-year periodicity is statistically significant and has an influence on rainfall–runoff events. However, the wavelet figure of the monthly runoff data shows that some seasonal fluctuations are stronger. Probably the stronger events refer to years with higher seasonal runoff. This is evident from the plot of the runoff time series for Manisa. However, especially after 1985, these events appear to lose their powers over time. A decrease in the frequency of strong periodic events is clear. This distinct decrease cannot be seen in monthly precipitation series.

It is noted that the results of this study are parallel to the results found by previous trend analysis studies on precipitation data by Partal and Küçük (2006) and streamflow data by Kahya and Kalayci (2004). They found that there are decreasing trends in the precipitation records (Akhisar and Aydın) and in the streamflow records (Manisa, Akhisar and Aydın). The wavelet analysis showed the main factors of the long-term decreasing trends in Aegean hydrological data. The decrease in streamflow measured can be seen from their wavelet transforms. DWT of the measured hydrological data shows dominant periodic components and variability of the components through time. The results show that decadal periodicities are generally main periodic components and may be responsible for producing real downward trends determined from the data. These results are fairly harmonious with previous trend analysis studies on the Aegean Region basin. The validity of decreasing trends in the hydrological data is verified by its wavelet figures and the variability of its decomposed series. However, the wavelet spectra indicate some evidences of SOI in streamflow and precipitation of Aegean. For instance, the signs of 1962 and 1999 La-Nina conditions with 1977 and 1982 El-Nino conditions can be seen in the wavelet spectrum of the Manisa streamflow.

The wavelet transforms have been very useful tools to study phenomena such as industrialization effects, periodicities, trends and climate changes in hydrological and meteorological time series during recent decades. This study presents the wavelet analysis of Aegean hydrological time series. However, it is difficult to say only from this study that the recent variations in Aegean hydrological time series are related to global warming or climate change.

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