An Empirically Grounded Data-Driven Methodology for Setting Planetary Boundaries thresholds with A Case Study on Biosphere Integrity

The planetary boundaries framework is a cornerstone for assessing Earth's resilience and stability, with significant traction in academia and policy-making. However, despite its relevance, many boundaries remain provisional and require rigorous refinement. This study introduces a comprehensive, data-driven methodology to determine planetary boundaries for locally variable Earth system processes. By integrating empirical approaches with advanced analytical techniques, we aim to improve the framework’s precision and applicability. Our approach utilizes spatially explicit binary outcome indicators—such as ecosystem degradation—to identify grid-level thresholds for control variables like Human Appropriation of Net Primary Production (HANPP).

Thresholds are optimized using Receiver Operating Characteristic (ROC) curves for each indicator, and the final local threshold is defined as the median of these values. Widely used in engineering and other disciplines to evaluate model performance and decision thresholds, ROC analysis provides a robust statistical framework for identifying optimal boundaries. Aggregating grid cells exceeding local thresholds enables the derivation of robust global boundaries. We demonstrate this methodology by refining the functional biosphere integrity boundary and propose its application to other locally variable boundaries, including biogeochemical flows, freshwater change, and land-use change.

Additionally, the ROC-based approach allows for the systematic comparison of control variables by quantifying their predictive strength using the Area Under the Curve (AUC). Like ROC analysis, AUC is extensively applied in engineering, data science, and other fields to evaluate the accuracy and performance of predictive models. The AUC is particularly valuable for expanding the planetary boundaries framework to new frontiers, such as the current endeavor to incorporate ocean processes. By providing a robust and empirical means of assessing the compatibility of different proposed control variables, AUC helps ensure that the framework remains both scientifically rigorous and adaptable. This approach also facilitates the evaluation of how well various control variables encompass the breadth of the processes they represent, guiding their selection and potential refinement.

Building on this foundation, we leverage AI algorithms to explicitly predict outcome indicators using one or multiple control variables. This enables a deeper analysis of different regimes of the control variable, as well as spatial variations in behavior, by examining how prediction statistics vary across values. Furthermore, these predictive models offer an opportunity to reframe planetary boundaries, directly based on empirical outcome indicators. Such a reframing allows for clearer, outcome-oriented definitions of boundaries while retaining the ability to simulate and assess their behavior under various scenarios using the original control variables.

Our findings provide a robust, empirically validated methodology for determining planetary boundaries and offer new tools for understanding thresholds and spatial dynamics in Earth system processes. By integrating advanced analytical techniques and predictive models, this approach supports the development of a more precise framework for assessing resilience and stability in a rapidly changing Earth system.