This study presents a new way to model how Earth’s surface changes over time as the deep interior moves. The method tracks the surface directly, allowing clearer and more detailed results worldwide while using less computing power. It improves accuracy compared to existing approaches and makes it easier to connect deep Earth processes with oceans, climate, landscapes, and life through time.

Vegetation plays a fundamental role in regulating Earth’s climate on time scales ranging from seconds to millions of years. Here, we develop and test a new vegetation model that uses evolutionary principles to predict vegetation structure, functioning, and diversity under environmental conditions fundamentally different from the present. Using the model in combination with fossil data from Earth's past may help to better understand the response of vegetation systems to environmental change.

This study introduces a new way to track Earth’s surface and other boundaries in computer models of the planet’s interior. It replaces noisy, tracer-based methods with a technique that cleanly follows surfaces while conserving volume. The approach produces smoother, more accurate results in both 2D and 3D, reduces dependence on large numbers of tracers, and supports future links between deep Earth processes, oceans, and surface environments.

Tracers are commonly used in geodynamical models to track various quantities as material moves around. However, methods used to advect them typically do not respect the mass conservation equation, resulting in gaps and bunches in the tracer distribution. Here a method to correct this, based on nudging tracer positions in order to respect mass conservation, is presented. Tests show that it is effective and has a low computational cost.

Large density jumps in numerical simulations of solid Earth dynamics can cause numerical oscillations. An effective method to prevent these at a free surface already exists. Here this is tested for compositional layers deeper in the mantle. The stabilisation method works effectively if density gradients due purely to compositional gradients are used but produces severe artefacts if total density is used.