Sinusoidal regression model for assessment of mudflows dynamics

A sinusoidal model of the dynamics of mudflow series, temperature and precipitation in the warm seasons in the high-mountain zone of Kabardino-Balkaria complements the previously obtained statisti­cal analysis of the average characteristics of the series, results of a comparative analysis of their average values for two subperiods (base 1953-1983 and modern 1984-2015), improves the quality of the unidirectional regression model of the number of mudflows and meteorological parameters over the past 60 years. The article shows that the use of the sinusoidal regression function makes it possible to identify the cyclicity of time series, which will help in assessing the dynamics of mudflows taking into account long-term changes in climate variables. The increased efficiency of the models is confirmed by the criteria. The coefficient of determination R², determined for lin­ear regression models, increases in sinusoidal regression models: for series with the number of mudflows from R² = 0.067 to R² = 0.645, for precipitation from R² = 0.028 to R² = 0.653, for temperatures from R² = 0.012 to R² = 0.829. In the sinusoidal regression model, using eight harmonics, short-period ripples are added against the back­ground of slow changes. In the series with mudflows, these are short periods from T = 2.4 years to T = 10.7 years against the background of the main period T = 62 years. In the series of temperatures there are short periods from T = 1.9 years to T = 5.2 years to a long period T = 63 years. In the series with precipitation, a long period T = 20.1 years is added to the short periods from T = 2.2 years to T = 8.7 years. The identified long-period fluctuations in mudflows and temperatures (T = 62 years, 63 years) are associated with significant and nonlin­ear changes in the elements of these series during the period under study. In contrast to these series, the precipitation series is dominated by short-period changes (T = 4 years) against a background of slow fluctuations with a period of T = 20.1 years.

1. Dokukin MD, Bekkiev MYu, Kalov RKh, Shagin SI. Zones affected by mudflows in 1967 in the Baksan River valley (Central Caucasus). Nature Management. 2023;(1):102-107. (In Russ.).

2. Malneva IV, Dokukin MD, Kalov RKh, Akaev AR. Mudflow in the Djily-Su tract (Northern Elbrus region) October 4, 2022: causes and factors. Study of hazardous natural processes and geotechnical monitoring during engineering surveys. In Materials of the All-Russian Scientific and Practical Conference. M.: Geomarketing LLC; 2023. P. 111–118. (In Russ.).

3. Malneva IV, Kononova NK. The activity of mudflow processes in mountains of Russia and adjacent countries in 20 century. In International Symposium on Latest Natural Disasters (September 5–8, 2005. Sofia, Bulgaria). CD. Topic VI. Case studies. Conclusions and recommendations. Sofia; 2005. P. 787-800.

4. Kul EV, Gedueva MM, Ataev ZV. Mudflow activity in the Samur River basin (Eastern Caucasus) based on monitoring results in 2020. News of the DSPU. 2021;15(1):73-88. (In Russ.).

5. Bekkiev MYu, Dokukin MD, Kalov RKh, Tashilova AA. Modern degradation of valley glaciers of the Central Caucasus. Fundamental and applied climatology. 2021;8(3):57-80. (In Russ.).

6. Tashilova AA, Fedchenko LM, Zalikhanov MCh, Kondratyeva NV. Analysis of the dynamics of mudflows against the background of climate change in the high-mountain zone of Kabardino-Balkaria. Science. Innovations. Technologies. 2024;(1):71-90. (In Russ.). https://doi.org/10.37493/2308-4758.2024.1.4

7. Dvoretskaya IV, Kruchenitsky GM, Matvienko GG, Stanevich  II. Astronomical factors in the long-term evolution of the Earth’s climate. Optics of the atmosphere and ocean. 2014;27(2):139-149. (In Russ.).

8. Statnikov KA, Kruchenitsky GM. Statistical modeling of global tectonic activity and some physical consequences of its results. Space and time. 2015;1-2(19-20): 314-317. (In Russ.).

9. Ashabokov BA, Kesheva LA, Kruchenitsky GM, Tashilova AA, Shokuev RA. Modeling of seasonal and long-term variability of snow cover in the Southern Federal District of Russia. In Proceedings of the A.F. Military Space Academy Mozhaisky. 2018;(662):22-25. (In Russ.).

10. Malneva IV, Kononova NK. Mudflow activity in Russia and neighboring countries in the 21st century. Georisk. 2012;(4):48-56. (In Russ.).

11. Kondratyeva NV. Distribution and features of mudflow processes on the northern and southwestern slopes of the Greater Caucasus. Dis. dr. geogr. sciences: 25.00.23. Kondratyeva Nataliya Vladimirovna. Nalchik; 2018. 402 p. (In Russ.).

12. Hammer Ø, Harper DAT, Ryan PD. PAST: Paleontological Statistics Software Package for Education and Data Analysis. Palaeontologic Electronica. 2014;4(1):9.

13. Handbook ofApplied Statistics. Ed. By E. Lloyd, W. Lederman, YuN Tyurin. M.: Finance and Statistics; 1989. Vol. 1. 51  p.

14. Hirotugu A. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 1974;19(6):716-723.