Dynamic Global Vegetation Models (DGVMs) are important tools for studying how climate and land-use change affect vegetation, carbon, water and nutrient cycles. As these models incorporate more detailed processes, their computational complexity increases substantially. One of these models, the Lund Potsdam Jena managed Land model (LPJmL), is steadily improved by the Potsdam Institute for Climate research (PIK) by including new processes modelling the real world dynamics. Two of these dynamics led to two collaborative projects of the Industrial Mathematics Institute at JKU Linz, RICAM of the Austrian Academy of Sciences, PIK and the University of Zurich:
First, the Computational Sustainability project at the Industrial Mathematics Institute at JKU Linz addresses the challenge of increasing computations complexity. This can be done by developing mathematical and algorithmic methods, in particular for the recently developed methane oxygen module of LPJmL. Second, the ARTECO project, funded by FWF and partner institutions in Germany and Switzerland, aims to develop a new module to model the effects in the Arctic tundra arising from expanding shrub cover, wildfires and thawing of the frozen ground beneath.
The model considered in the Computational Sustainability project represents methane- and oxygen-dynamics in several soil layers and includes processes such as methane production, oxidation and vertical gas transport. Our main goal is to investigate whether these processes can be simulated more accurately and efficiently without changing the underlying physical model.
To this end, we analyze the existing numerical implementation and compare it with alternative methods for reaction, diffusion and operator splitting. Particular attention is paid to the balance between accuracy, stability and computational cost. A central tool is convergence analysis. It allows us to identify which parts of the model actually limit numerical accuracy and whether a more advanced method provides a real benefit. One result of the project is that higher-order methods do not automatically lead to higher-order solutions. In the methane model, a concentration threshold that activates methane oxidation introduces a non-smooth event. We found that this event can reduce the observed convergence order even when the underlying reaction-diffusion solver is formally second order.
This insight is important for the next stage of the project. Instead of simply using some complex time integrator, we can now develop methods that better reflect the mathematical structure of the model, for example through event-aware or adaptive time stepping. The broader aim is therefore to make LPJmL simulations not only faster, but also numerically more reliable and computationally efficient. This illustrates how applied mathematics can contribute directly to the development of next-generation environmental and climate models.
Within the ARTECO project, the focus is on the dramatic changes occurring in the Artic tundra due to the rise of global temperature by approximately 1.2°C above pre-industrial level in 2023. This fragile ecosystem, traditionally stabilized by permafrost, is now undergoing rapid transformation due to expanding shrub cover and increasingly frequent, intense wildfires—altering how heat penetrates and thaws the frozen ground beneath.
This project explores the dynamic interplay between Arctic vegetation and permafrost under a warming climate. While taller, denser plants can act as natural insulation, preserving permafrost, they also provide fuel for fires that can strip away this protective layer in hours, potentially pushing the tundra past irreversible tipping points. By identifying critical thresholds in fire frequency and severity, the project maps out future pathways for Arctic ecosystems and the vast carbon stores they hold.
Views of the forest tundra on the Tazovsky Peninsula (Siberia, Russia) without fire (left) and 28 years after fire (right), credits: Daniel Rieker (TU Dresden):
Combining hands-on field measurements, cutting-edge satellite and drone imagery, and advanced modeling, the project enhances a robust heat conduction model to explicitly include dynamic vegetation as an insulating layer. Inverse techniques refine key parameters, while upgrades to the LPJmL global vegetation model improve simulations of shrub expansion, fire regimes, and permafrost evolution. This integrated approach not only predicts change but also provides actionable insights for scientists, policymakers, and communities to assess risks, protect Arctic resilience, and shape global climate strategies.
Measurement site in the Tussock Tundra at Anaktuvuk in Alaska (USA), credits: Gabriela Schaepman (University of Zurich):
