Changes in the River’s Ice Regime Characteristics of the Votkinskoe Reservoir Catchment for 1936–2018

The paper is devoted to the study of long-term variability of the stable dates of ice formation and the duration of the freeze-up period at 12 gauges on the rivers of the Votkinskoe Reservoir catchment for 1936–2018. It turns out which of the statistical models is more consistent with the series of observations: the resampling model, the linear regression model, or the model of the change in the mean value starting from a certain point in time. The study was carried out in two stages. At the first stage the stable dates of ice formation and the duration of the freeze-up data were analyzed separately for each gauge. There were tested: the hypotheses of randomness, normality of the series of observations, hypotheses about the absence of a linear trend and autocorrelations in the data; hypotheses of homogeneity of series of observations. At the second stage the stable dates of ice formation and the duration of the freeze-up data were analyzed jointly using a two-dimensional normal distribution model for each gauge. There were tested: the hypotheses on two-dimensional normality and equality of data covariance matrices; the hypothesis of homogeneity of two-dimensional data. Using the methods of difference-integral curves and t-test revealed statistically significant changes in the behavior of the characteristics under consideration with the change point in 1997. Within each of the periods 1936–1997 and 1998–2017 for all gauges, the initial data allow describing the behavior of the characteristics under study using a resampling model, the elements of which have the same normal distribution law. There are no autocorrelations in the observation series. At the same time, statistically significant shifts in the dates of ice formation to the late side by 7–14 days and a reduction in the duration of the freeze-up period by 6–18 days were established. The transition from a separate analysis of the dates of ice formation and the duration of the freeze-up period to their joint analysis did not affect the nature of the results obtained. The results make it possible to improve the forecasting of the ice-thermal regime of rivers and improve the planning and organization of the work of water transport and hydraulic structures.