Computational mathematics of Arctic processes

The Arctic is a vast and complex environment which influences planet-scale budgets of water and energy fluxes. The project will develop robust computational models and their mathematical analyses for coupled phenomena in the Arctic including thermal, hydrological, and mechanical processes in permafrost soils as well as selected biosphere processes. Beside their connections to large scale climate, these processes have significant local impact on humans and infrastructure.

The models developed in this project and their use for predictive simulations of realistic scenarios will contribute to the knowledge supporting the plans to mitigate the effects, e.g., of permafrost thaw. Graduate and undergraduate students will be involved and trained in computational mathematics as well as in an ability to contribute meaningfully and critically to the interdisciplinary efforts within and outside the project, with efforts towards an effective mentoring support structure for underrepresented groups. Training both undergraduate and graduate students on the topics of the project is expected.

The project will develop algorithms for approximations of solutions to the models of coupled processes in the Arctic including the thermal, hydrological, mechanical, and biosphere processes. The main challenges are the nonlinearity and complexity of the underlying partial differential equations and the sparsity of data which is not easy to collect in the vast Arctic environment.

These challenges are exacerbated for coupled systems across the many relevant temporal and spatial scales. The investigators will focus on the cross-cutting theme of multiple scales connecting the microscopic Pore scale of x-ray images of permafrost soil to the Darcy scale of experiments to the Landscape scale of kilometers common in observations. These efforts will support the development of efficient prototype and surrogate models along with new metrics for the quality of the approximations, and these tools can be used for simulations of realistic scenarios of climate events associated with Arctic permafrost.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.