Stochastic modelling of thermokarst lake distributions

Thermokarst lakes are among the most common and dynamic landscape features in ice-rich permafrost regions. They form due to melting of ground ice and subsequent ground subsidence. Their presence and dynamic behavior do not only influence the carbon exchange with the atmosphere by accelerating permafrost thaw and facilitating the production of methane, but also have an impact on soil hydrology as well as biophysical fluxes between atmosphere and land surface, such as energy and water transfer. These feedbacks have implications for both the regional and global climate and are therefore highly relevant when investigating the climate response to changes in permafrost systems under different future carbon emission and warming scenarios. Despite their significant role in the climate system, thermokarst lakes are only rudimentarily or not at all represented in Earth system models. Because the involved hydrological processes are complex and depend on small-scale sub-surface heterogeneities that are difficult to measure, we treat them as probabilistic and use a stochastic approach to create a model of thermokarst lake dynamics (formation, expansion and drainage). More specifically, we utilize common stochastic approaches, such as the Poisson process and Brownian motion, as tools to simulate changes in lake density, size distributions and fractions of water and drained area. Recent advancements in remote sensing offer an opportunity to use high-resolution satellite data products for model calibration and the parameterization of inherent and/or climate-induced thermokarst lake dynamics. We expect our approach and the results of our simulations to contribute to a more accurate representation of permafrost dynamics in Earth system models.