Internal Stochastic Structure of Annual Discharge Time Series of Serbia’s Large Rivers - page 5

Contrary to the standard approach that assesses the trend over an entire time series, the alternative multi-temporal approach addresses the time series trend through a combination of subseries. This trend analysis requires that subseries be combined not only from the beginning of the time series, but also from the beginning of the segments. Figure 3a shows the results of trend analysis of annual time series, following the multi-temporal approach. The analysis indicated that trend intensity and direction varied, depending on the selected time interval. The method demonstrated that the length of the time segment, within which the trend was assessed, represented an important parameter in the trend analysis. Such variable trend behavior was attributable to multiple-year macro cycles in the annual discharge time series.

A significant downward trend at a confidence level of 95% was noted in the last decades on the Danube, Sava and Velika Morava (Fig. 3b). In contrast, a significant upward trend in the last decades was registered on the Tisa. No significant trend was noted if the entire time series were analyzed, but there were significant trends in certain time segments. The downward trends in the past several decades were attributed to reduced annual precipitation totals in southern Europe, resulting in negative trends of the Danube, Sava and Velika Morava. Similarly, precipitation levels increased in the north and resulted in upward trends of the Tisa.

The changing precipitation distribution in Europe is associated with the North Atlantic Oscillation, expressed by the NAO index. The NAO index is based on the atmospheric pressure gradient between the northern and southern parts of the northern hemisphere. This gradient is an indicator of the direction, frequency and location of rain clouds in the atmosphere above Europe. When the pressure gradient is low, rain clouds reach the Mediterranean and increase precipitation there.


 This period represents the positive phase of the NAO index. In the negative phase, when the pressure gradient is high, rain clouds move towards Scandinavia and increase precipitation in northern Europe (Bower et al., 2008). Protracted negative circulation leads to reduced evapotranspiration as a result of increased cloudiness and air humidity. This phenomenon potentially leads to increased average annual river discharges. The winter discharges in Europe, when negative circulation is pronounced, amount to between 23% and 43% of overall annual discharges (Bower et al., 2006).

The periodicity of atmospheric parameters is an important contributor to annual and decadal periodicity of river discharges. Many studies show that discharge variability is a result of atmospheric circulation above the oceans, which affects precipitation distributions on Earth (Hurrell, 1995; Rodriquez-Puebla et al., 1996; Rimbu et al., 2002; Danilovich et al., 2007). In contrast, Zang and associates (Zang et al., 2007) claim that precipitation variations on Earth cannot be attributed solely to atmospheric circulation; anthropogenic impacts over the past century have contributed to significantly increased precipitation levels in the northern hemisphere, reduced precipitation in the tropics and elevated air humidity in the southern hemisphere.

Prior to proceeding with the determination of the periodicity of the time series of annual discharges, the Hurst coefficient was assessed applying the (R/S) analysis. The following values were obtained at the studied stations: Orsova (h=0.622), Bogojevo (h=0.682), Sremska Mitrovica (h=0.657), Senta (h=0.738) and Ljubičevski Most (h=0.697). The conclusion was that the time series of annual discharges had a long memory. The periodicity of the annual discharges was determined using the continuous spectrum according to the B-T method (Eq. 8), where the adopted covariance function truncation length was M=25 (Fig. 4).


Fig03Figure 3: Multi-temporal trend analysis: Mann-Kendall trend test (a) and trend significance (b)


Figure 4: Annual discharge spectra according to the B-T method, 95% confidence intervals.


Analysis in the frequency domain demonstrated that the time series of annual discharges exhibited a distinct periodic component at low and high frequencies. Table 3 shows the first five most influential periods, T, for the studied time series, along with influential frequencies f and spectral intensity S.


Table 3: Most influential periods of annual river discharges according to the B-T method


The results show that the assessed time series of annual river discharges exhibited significant periods in the low frequency domain, of 3.6 and 4.9 years. These periods characterized secondary macro periodicity. The periodicity in the domain of low frequencies or large periods is extremely important in time series assessments. Multiple-year macroperiods represented the primary periodicity, which could be classified in terms of period length into the following groups: Group I (8.5–10.5 years), Group II (12.5–14.5 years), Group III (20.5–24.5 years), and Group IV (27.5–35.5 years). The determined periodicity of annual discharges was consistent with the results released to date by Pekarova et al. (2003), Labat (2006), Stojković et al. (2012a) and Stojković et al. (2012b).