Simulation of the dynamics of the Hansbreen tidal glacier (Svalbard) based on the stochastic model

• Published in: Journal of Geophysical Research: Earth Surface
• Main Authors: A. Kislov V., A. Glazovsky F., А. Кислов В., А. Глазовский Ф.
• Other Authors: A.V.Kislov was supported by the RFBR grant № 18-05-60147 and the State funding АААА-А16-116032810086-4. A.F.Glazovsky was supported by the RFBR grant № 18-05-60109 and acknowledge funding from the State Contract 0148-2019-0004 (АААА-А19-119022190172-5)., А.В. Кислов благодарен за поддержку этой работы гранту РФФИ № 18-05-60147 и финансированию госбюджетной темы АААА-А16-116032810086-4. А.Ф. Глазовский благодарен за поддержку этой работы гранту РФФИ № 18-05-60109 и финансированию по Госзаданию 0148-2019-0004 (АААА-А19-119022190172-5).
• Format: Article in Journal/Newspaper
• Language: Russian
• Published: IGRAS 2019
• Subjects: modeling; Svalbard; tidal (tidewater) glacier; the Fokker-Plank equation; the Langevin equation; моделирование; приливный ледник; уравнение Ланжевена; уравнение Фоккера–Планка; Шпицберген; glacier; Polar Research; The Cryosphere; Tidewater
• Online Access: https://ice-snow.igras.ru/jour/article/view/603; https://doi.org/10.15356/2076-6734-2019-4-441

The dynamics of the Hansbreen tidal glacier (Svalbard) is manifested at different time scales. In addition to the long-term trend, there are noticeable inter-annual fluctuations. And the last ones are precisely the subject of this work. Based on general conclusions of the theory of temporal dynamics of the massive inertial objects, the observed inter-annual changes in the length of the glacier can be explained as a result of the accumulation of anomalies of the heat fluxes and water flows. In spite the fact that the initial model of glacier dynamics is deterministically based on the physical law of conservation of ice mass (the so-called the «minimal model» was used), the model of length change is interpreted as stochastic. From this standpoint, it is the Langevin equation, which includes the effect of random temperature anomalies that can be interpreted as a white noise. From a mathematical point of view, this process is analogous to Brownian motion, i.e. the length of the Hansbreen glacier randomly fluctuates in the vicinity of its stable equilibrium position. Based on the Langevin equation, we passed to the Fokker–Planck equation, the solution of which allowed us to obtain the distribution function of the probabilities of interannual fluctuations of glacier length, which is close to the normal law. It was shown that the possible range of the variability covers the observed interval of the length fluctuations. The pdf is close to normal distribution. Для моделирования межгодовой динамики длины ледника Ханса на Шпицбергене использована «минимальная модель», интерпретируемая как стохастическое уравнение Ланжевена с переходом к уравнению Фоккера–Планка. Получена формула, выражающая дисперсию колебаний длины ледника в зависимости от его параметров. Сопоставление расчётов с данными наблюдений позволило получить хорошие результаты.