Abstract. Data regarding 25 lakes (9 Belarusian and 16 Polish) provided the basis for spectral analysis of water level fluctuations. The obtained output data concerned a 55-year observation sequence covering the years 1956-2010. The selection of lakes was determined by two factors, i.e. data continuity and inconsiderable anthropogenic impact. The lakes were divided into three groups depending on the course of the water level spectrum. The first group included the highest number of lakes (14) which were distinguished by smooth curves with no significant peaks (e.g. Lake Wygonoszczańskie). The second group shows a four-year variability (e.g. Lake Łukomskie). The third group is distinguished by an even peak of three-year water fluctuation (e.g. Lake Łebsko). The location of the lakes categorised into those three groups suggests a certain regionalisation. The first group is represented by lakes of central and northern Belarus, and eastern Poland. The second group includes lakes of eastern Belarus, and the third group -lakes of central and northern Poland. This suggests that alongside local factors, the location of the distinguished groups of lakes may also be determined by regional factors. Presumably, continentalism of climate increasing in an eastwards direction is one of the key factors responsible for the detected regional diversity of lake water level fluctuations.
as a result of the conducted investigations of the level fl uctuations in lake naroch the initial data are divided into 3 components: a polynomial regression that makes it possible to fi nd out an independent on time law of trajectory, a periodic component of sinusoidal type and a residual sequence of independent random quantities. Modeling of the trajectory fl uctuations is based on the deterministic part, consisting of the regression of the 8th order and periodic component, and also the random part, consisting of independent equally distributed quantities. Using this model it can be modeled the trajectory of the level fl uctuations in lake naroch. The modeled trajectory by 200 years long demonstrated the probability of exceeding of maximum annual level, equal 1 per cent.
On the basis of the mean volume of annual water levels of 25 lakes (9 Belarusian and 16 Polish) over a period of 55 years (1956-2010) spectral time analysis of water fluctuations has been executed. The choice of the lakes was based on two factors, i.e. the continuous period of observation and insignificant anthropogenic influence. The complex analysis of water level fluctuation cycles has shown that for Belarus the cycles observed most often were 3, 5 and 10-year cycles. Polish lakes also have three cycles, but in the majority of them they amount to 5 and 10-years. It can be assumed that this is impacted by the continental climate growing to the east. Most probably it is one of the key factors defining the diversity of water fluctuations in all the analyzed lakes.
The research results of runoff changes in the River Viliya at 3 stations (Steshitsy Village, Vileyka Town and Mihalishki village) during the period 1946–2014 for the average annual, maximum, minimum summer-autumn and winter runoff are presented. It has been concluded that heterogeneity in the time series of the river runoff is caused by natural-climatic and anthropogenic factors. At Mihalishki Village the average annual runoff is about 59.7 m3 s–1, the maximum 1570 m3 s–1, minimum summer–autumn is 22.0 m3 s–1, the minimum winter runoff is 17.3 m3 s–1, and the environmental runoff is 21.1 m3 s–1. A forecast of runoff changes for the River Viliya, depending on forecasted climate change using the “Atlas of Global and Regional Climate Projections” was made on the basis of four scenarios RCP8.5, RCP6.0, RCP4.5, RCP2.6. The results of research indicate that significant changes in runoff will not occur as the forecasted climatic parameters did not change significantly. A forecasted decrease in spring runoff was investigated, thus reducing the minimum runoff is not essential. In the event of possible low water periods the Vileyka reservoir resources, involving the Olkhovskoye and the Snigyanskoye water reservoirs, can be used for compensation measures, which may be considered as the most reliable backup source of industrial water supply for the Belarusian Nuclear Power Plant.
The article investigates the problem of mathematical description of long-term fluctuations of river runoff, which is relevant for solving problems of modeling and forecasting in engineering hydrology. The description of the process of runoff fluctuations is based on the stochastic differential equations of Orshtein-Uhlenbeck and Fokker-Planck-Kolmogorov. A technique that makes it possible to apply low-parameter nonlinear dynamic models of river runoff has been developed. Mechanisms of the cyclicity of long-term fluctuations the Pripyat, Neman, West Dvina, Dnieper, and Berezina rivers are described. Comparison of the forecasting results according to the methodology developed by us showed better results than the modeling method using a simple Markov chain. The nonlinear model makes it possible to predict a series that has a correlation function similar to the original series with a shift of 4 or more years, and the Markov model gives good results only for an autocorrelation function with a shift of one year. The simulated series of annual runoff have statistical parameters that differ from the parameters of the original series within ±5-10%.
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