ISSN 1028-334X, Doklady Earth Sciences, 2017, Vol. 476, Part 1, pp. 1080–1083. © Pleiades Publishing, Ltd., 2017. Original Russian Text © V.V. Klimenko, O.V. Mikushina, D.M. Volkov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 476, No. 2, pp. 224–227.
GEOGRAPHY
An Improved Quasi-Rhythm Method to Forecast the Annual Side Inflow to the Reservoirs of the Volga-Kama Hydropower Plants Cascade Academician V. V. Klimenko*, O. V. Mikushina, and D. M. Volkov Received February 15, 2017
Abstract—It was shown that an improved quasi-rhythm method can make it possible to predict the annual side inflows into the hydrological sections of the Volga-Kama Hydropower Plants (HPP) Cascade with a one-year lead time with high quality and good forecast verification. DOI: 10.1134/S1028334X17090148
The quasi-rhythm method has been used successfully [1–3] to forecast the average annual and seasonal temperature in different areas of Russia. The method is based on distinguishing hidden climatic rhythms, obtained on the basis of characteristics that are similar to the characteristics calculated from the Buijs-Ballot tables [4]. The estimations of the forecast verification based on the quasi-rhythm method [1, 2] showed their advantages compared to the inertial forecasts. The subsequent modifications of the method [3] markedly improved the quality of the forecasts in comparison with the previous results. In our view, the quasirhythm method is of undoubted interest in hydrological studies, especially in study of the long-term fluctuations of the river runoff. The point is that the repeating pattern of the river runoff, i.e., alternating cycles of high-water and low-water years, are likely due to the rhythmic variations of the geophysical (circulational), heliophysical, and tide-generating factors [5]. In the study of the river runoff cycle by the quasi-rhythm method, cycles of various duration and embedded cycles are simultaneously selected in the hydrological data, and the desired forecast is carried out by the superposition of the cycles and their repeating. The improvement in the quasi-rhythm method, proposed by [3], is to find optimum sets of the rhythms among all possible rhythms by minimizing the error functional of the preliminary one-year lead-time forecasts and to average over the ensemble of the optimal forecasts. Our work was focused on the annual side inflow (m3/s) into the Volga–Kama Cascade Reservoirs of the HPP from 1915 to 2015. The side inflow was stud-
National Research University “Moscow Power Engineering Institute,” Moscow, 111250 Russia *e-mail:
[email protected]
ied for two hydrological sections on the Volga River in the area of Rybinsk and Nizhny Novgorod HPPs and for two hydrological sections on the Kama River in the area of the Kama and Nizhnekamsk HPPs (data of Public Joint-Stock Company RusGydro). Successful application of the quasi-rhythm method is dominated by the correct determination of the trends in the initial data. We plotted ten trends for each hydrological series on the variable data moving windows of the same range using the inverse discrete cosine-transform formula [6]. Figure 1 shows the trends of low frequency plotted on the data windows of 1924–2015 and the corresponding data on the water inflow into the hydrological sections of the Volga– Kama Cascade. The trends describe fluctuations with more than 15-year periods. The contribution of such trends to the data variability is 55–65% for the period of 1930–2000. Linear filtering in the interval of the low frequency is carried out by these trends. The residual series (ten series for each hydrological section), which were obtained over the last 50 years of observations, include rhythms of various power with periods of ~14, 11–12, and 7–8 years and irregular fluctuations in the range from 2 to 4 years. Similar rhythms were shown in [7], like the rhythms of the most frequent occurrence in the temperatures recorded by the Russian meteorological stations. Figure 2 shows the actual data on the average annual side inflows into the hydrological sections of the Rybinsk, Nizhny Novgorod, Kama, and Nizhnekamsk HPPs for the period from 2007 to 2015 and the time series, each point of which is the forecast of the proper inflow with a one-year lead time. These forecasts were obtained by the improved quasi-rhythm method with subsequent ensemble averaging of the optimal rhythm sets. To calculate each forecasting value, the data, which were obtained over the preced-
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2.5 2.0 1.5 1.0 0.5 0 −0.5 −1.0 −1.5 −2.0 −2.5 1920 2.5 2.0 1.5 1.0 0.5 0 −0.5 −1.0 −1.5 −2.0 −2.5 1920
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4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 −0.5 −1.0 −1.5 −2.0 2020 1920 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 −0.5 −1.0 −1.5 −2.0 2020 1920
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Fig. 1. Normalized to zero mean and unit variance data series (1) on the side inflow of water into the hydrological sections of the Rybinsk (a), Nizhny Novgorod (b), Kama (c), and Nizhnekamsk (d) HPPs and their trends (2) plotted on the data windows of 1924—2015.
ing 40 years, and the ten-year interval of the optimal rhythms were used. The average values of the inflows over the seven years preceding the forecast year were used as the forecasting values of the trends, which are required for the reverse transition from the residual series to the initial data. It should be noted that the forecasts of the average annual inflows for the Volga River, which were made by the improved quasi-rhythm method (dashed lines in Figs. 2a, 2b), are of high correlation with the actual data; however, in 2014 a significant divergence in the absolute values was registered. The forecasts of the average annual inflows for the Kama River (dashed lines in Figs. 2c, 2d), which were made by the quasirhythm method, are correlated much worse with the actual data. The results can be improved, for example, by addition of the assuming input of the climatic factor, the connection of which with the studied hydrological data is statistically confirmed. This factor has to be taken into account to foresee the occasional extremal climatic episodes, which can provoke significant deviation of the actual hydrological data from the rhythmical fluctuations forecasted. The extremely high temperature in the spring seasons of 2014 and 2015 was DOKLADY EARTH SCIENCES
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one of such episodes. The high temperature was likely related to the specific character of the circulation processes in the atmosphere resulting in the extremal values of the winter indices of the North Atlantic and Arctic fluctuations in 2014–2015. Extreme values of these circulating indices were also registered in 2010. In the model of periodic instability, which was proposed in [7], an extreme climatic episode can be considered as the external disturbance providing for series of the new, forced fluctuations at the given moment in the system of fluctuations of the hydrological data, which had been already evolved due to the previous external effects. However, the moment of the climatic disturbance cannot be predicted only on the basis of the average annual inflow data. Therefore, allowing for the important climatic factors (spring temperatures for the Volga River inflows and the winter index of the Arctic Oscillation for the Kama River inflows), which from time to time dramatically change the natural regime of the inflow fluctuations, markedly improve the forecasts made only on the basis of the quasi-rhythm method. In our work, the input of the climatic factor was estimated by the parameters of its linear relationship with the average annual inflow in 1966–2006.
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m2/s 1600
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Fig. 2. Actual data (1) of the average annual side inflow of water into the hydrological sections of the Rybinsk (a), Nizhny Novgorod (b), Kama (c), and Nizhnekamsk (d) HPPs in 2007–2015 and their forecasts carried out by the improved quasi-rhythm method with allowance (2) and without allowance (3) for the climatic factors.
the inertial forecast by 0 and Q < 1. For our work, the methodological forecasts were initiated in the interval of 2007–2015. The norms of 1996–2006 are used as inertial forecasts. If the actual value or the methodological forecast differ from
It appears that, the forecasts that were corrected allowing for the climatic factors for all studied inflows, are satisfactory in sign and in magnitude of deviation from the actual value (Table 1). It is important to emphasize that even without allowance for the climatic factors, good results can be achieved by the improved quasi-rhythm method. The forecasts of the average annual inflow into the hydrological sections of the Nizhny Novgorod and Nizhnekamsk HPPs were satisfactory in sign and in magnitude. The forecasts of the average annual inflow into the hydrological sections of the Rybinsk and Kama HPPs were satisfactory
Table 1. Estimation of the quality of the forecasts carried out by the improved quasi-rhythm method for 2007–2015 Method Quasi-rhythms Quasi-rhythms allowing for climatic factors
Rybinsk
Nizhny Novgorod
Kama
Nizhnekamsk
ρ
Q
ρ
Q
ρ
Q
ρ
Q
0.25(8) 0.56(9)
1.05 0.85
1.00(9) 1.00(8)
0.59 0.55
0.13(9) 0.56(9)
1.31 0.95
0.71(7) 0.43(8)
0.86 0.93
In brackets a number of forecasts used to calculate ρ is indicated. DOKLADY EARTH SCIENCES
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only in sign. Therefore, it was shown that the improved quasi-rhythm method provides an opportunity to achieve a high quality forecast of the average annual inflow into the hydrological sections of the Volga–Kama Cascade HPP with a one-year lead time with good verification.
3. 4. 5.
ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 14-19-00765, the Ministry of Education and Science of the Russian Federation, project no. 131137.2017/П4 of government task. V. V. Klimenko thanks the Ministry of Education and Science of the Russian Federation for support, project no. 13.4662.2017/ВУ of government task.
6. 7. 8.
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Hydrometeorol. Inform. Int. Data Center, Obninsk, 2008) [in Russian]. O. V. Mikushina and V. V. Klimenko, Vestn. Mosk. Energ. Inst., No. 4, 222–227 (2013). C. H. D. Buijs-Ballot, Les changement periodiques de temperature (Utrecht, 1847). A. Sh. Reznikovskii, A. Yu. Aleksandrovskii, V. V. Aturin, et al., Hydrological Foundations of Hydropower Engineering (Energoatomizdat, Moscow, 1989) [in Russian]. N. Ahmed, T. Natarajan, and K. R. Rao, IEEE Trans. Comput. 23 (1), 90–93 (1974). B. G. Sherstyukov, Arkt. Sev., No. 24, 39–67 (2016). RD (Guiding Document) No. 52.27.284-91: Methodological Instructions. Industrial Tests of New and Improved Methods for Hydrometeorological and Heliogeophysical Forecasts (Com. Hydrometeorol. USSR, Moscow, 1991). A. V. Murav’ev and R. M. Vil’fand, Meteorol. Gidrol., No. 12, 24–34 (2000).
Translated by V. Krutikova
