Research
Research Statement
The consensus in the scientific community is that Earth's climate is undergoing critical changes. Understanding critical phenomena in the Earth's system stands out as one of the most urgent challenges in science today. Many issues arising in the study of the climate system possess a significant theoretical dimension. The range of critical phenomena, including equilibrium and non-equilibrium transitions, bifurcation, and tipping points, is traditionally studied in simpler physical systems.
The implementation of mathematical modeling, incorporating the theory of dynamical systems, bifurcation theory, statistical mechanics, stochastic theory, and statistical methods, among others, in investigations of critical phenomena, represents a new approach. This approach can help uncover the fundamental physics underlying climate change and conserve computational resources by improving calculations in traditional climate models.
My current research and educational training primarily focus on the mathematical contributions that can enhance our understanding of the mechanisms of critical phenomena in the climate system and ecosystems.
Stochastic Processes
In most cases critical phenomena in the climate system and its sub-systems induced by random (stochastic) processes. For example, the random changing of the states of natural landscape patterns (e.g., melt ponds, tundra lakes etc.) could lead to the changing of states of the climate system. The stochastic theory offers an approach to climate and environmental modeling that could dramatically reduce the time and brute-force computing that current climate simulation techniques require.
Projects:
Permafrost: Thawing, Dynamics and Transitions. In a changing climate, thawing permafrost and the resulting decomposition of previously frozen organic carbon to methane is potentially one of the most significant feedbacks from terrestrial ecosystems to the atmosphere. As a result of tundra permafrost thawing, lake patterns have randomly formed, and methane has entered the atmosphere. Here we discuss how to apply stochastic theory and statistical methods for the description of the evolution of tundra lakes.
Melt Ponds: Fractals, Metastability and Ising Model. During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow-covered ice to beautiful mosaics of ice and melt ponds (that develop on the surface of sea ice floes). Small, disconnected ponds on the ice surface grow and coalesce to form much larger connected structures with complex boundaries. Thus, melt pond geometry has a complex fractal structure. Here, we ask if the evolution of melt pond geometry exhibits universal characteristics that do not necessarily depend on the details of the driving mechanisms in melt pond formation.
Applied Dynamical Systems
Modeling of physical processes in climate and environmental systems leads to complicated problems, involving the Navier-Stokes equations, and complicated systems of differential equations for biological and chemical processes. However, it is difficult to estimate the reliability of our computations, since it is connected with a difficult mathematical problem on the structural stability. Possibly, an adequate approach is to build models of dynamical systems to investigate critical processes in these systems.
Projects:
Greenhouse Gases: Emission, Convection and Tipping Points. In this project, we use the radiative-convective atmospheric model taking into account effects connected with greenhouse gas production, a chemical degradation of the greenhouse gas molecules, and greenhouse gas diffusion and convection. Our analytical approach makes the problem of a greenhouse gases climate catastrophe more mathematically tractable and allows us to describe catastrophic tipping points in the atmosphere induced by soil greenhouse gas sources.
Large Ecosystems in Transition: Interactions, Feedback and Mass Extinction. The development of a realistic dynamical system model for ecosystems using different factors of environmental forcing (temperature, albedo, greenhouse gas emissions etc.) as a control parameter would allow for the investigation of long-term behaviors of ecosystems. In this project we develop a few models of a species population to investigate its dynamics (including the case of mass extinction) under climate-ecosystem feedback as well as under minor fluctuations of environmental parameters.