Permafrost: Thawing, Dynamics and Transitions

Melting processes in the climate system can be investigated through stochastic models, while the nonlinear behavior of the climate system caused by phase transitions can be described with help of standard nonlinear dynamics tools. For example, it was shown that permafrost contains a ‘methane bomb’, namely, about 1015 kg of carbon in a frozen state. As a result of tundra permafrost thawing, a number of small lakes have formed and extended, and methane has entered the atmosphere. In turn, atmospheric methane can reinforce warming, and there appears to be a positive feedback loop that can lead to a climate catastrophe. We model tundra lakes thawing based on the phase transition theory with the Ginzburg–Landau formalism . As a result, we obtain a deterministic equation that serves as a simplified model for lake size growth. To take into account stochastic effects, we derive a Fokker–Planck equation corresponding to the deterministic model. Next, we use this model to compute the methane emission generated by lakes in the Arctic zone and to evaluate possible bifurcations in the climate system. 

Also, we analyze the geometry of the patterns formed by tundra lakes in the Russian high Arctic. Using statistical machine learning, we developed an image-processing algorithm to segment historical topographical maps of permafrost and current satellite images, measure the area and perimeter of each lake, and compute the fractal dimension of the lakes in the images we have studied. Our results indicate that as lake size increases their fractal dimension bifurcates.

More information: 

• I. Sudakov, A. Essa, L. Mander, M. Gong and T. Kariyawasam. The geometry of large tundra lakes observed in historical maps and satellite images, Remote Sens. 2017, 9(10), 1072; doi:10.3390/rs9101072.

• I. Sudakov and S. Vakulenko. A mathematical model for a positive permafrost carbon-climate feedback. IMA Journal of Applied Mathematics, 80(3): 811-824, 2015.

• I. A. Sudakov and T.G. Sukacheva. Issues of Patankar's numerical scheme stability. Computing research and Modeling. Vol. 4, no. 4, 827–835, 2012 (in Russian).

• I.A.Sudakov, Bobylev, L.P., and Beresnev, S.A. Permafrost thermal regime simulation in response to modern climate change. Vestnik of Saint-Petersburg University, Series 7. Geology. Geography, 2011 (7), pp. 81-88 (in Russian).