Stochastic modelling of thermokarst lakes: size distributions and dynamic regimes

Thermokarst lakes are among the most common and dynamic landscape features in ice-rich lowland permafrost regions. They influence carbon, water and energy fluxes between atmosphere and land surface, and are an important component of Arctic lowland hydrology. Despite their significant role in the climate system, thermokarst lakes are only rudimentarily or not at all represented in Earth system models (ESMs). Attempts at stand-alone modelling of their dynamics have mostly been limited to the scale of individual lakes. Because lake formation, expansion, and drainage depend on small-scale surface and sub-surface heterogeneities that are difficult to measure, a deterministic modelling-approach would be a challenge at the regional or pan-Arctic scale. We therefore treat these processes as probabilistic across a landscape and create a model of thermokarst lake dynamics using stochastic approaches. With the inclusion of stochasticity and volatility, our method allows us to account for the diversity of individual lake behaviour that results from the small-scale differences in environmental conditions. We present idealized simulations and, additionally, test novel high-resolution remote sensing data products that capture annual lake areas for model initialization and the calibration of inherent or climate-induced lake dynamics. Our model is able to capture three plausible regimes by incorporating the main processes behind thermokarst lake dynamics and represents a new step towards stochastic representation of permafrost landscapes in ESMs. Furthermore, our findings emphasize the importance of continuing the retrieval of remote sensing data for model parameterization and acquiring additional data products containing information on past thermokarst lake behaviour.