Soil and vegetation water content identify the main terrestrial ecosystem changes.

Environmental change is a consequence of many interrelated factors. How vegetation responds to natural and human activity still needs to be well established, quantified and understood. Recent satellite missions providing hydrologic and ecological indicators enable better monitoring of Earth system changes, yet there is no automatic way to address this issue directly from observations. Here, we develop an observation-based methodology to capture evidence of changes in global terrestrial ecosystems and attribute these changes to natural or anthropogenic activity. We use the longest time record of global microwave L-band soil moisture and vegetation optical depth as satellite data and build spatially explicit maps of change in soil and vegetation water content and biomass reflecting large ecosystem changes during the last decade, 2010-20. Regions of prominent trends (from [Formula: see text] to 9% per year) are observed, especially in humid and semi-arid climates. We further combine such trends with land cover change maps, vegetation greenness and precipitation variability to assess their relationship with major documented ecosystem changes. Several regions emerge from our results. They cluster changes according to human activity drivers, including deforestation (Amazon, Central Africa) and wildfires (East Australia), artificial reforestation (South-East China), abandonment of farm fields (Central Russia) and climate shifts related to changes in precipitation variability (East Africa, North America and Central Argentina). Using the high sensitivity of soil and vegetation water content to ecosystem changes, microwave satellite observations enable us to quantify and attribute global vegetation responses to climate or anthropogenic activities as a direct measure of environmental changes and the mechanisms driving them.

Explicit Granger causality in kernel Hilbert spaces.

Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables' cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled Rössler systems, and it is exploited to disclose the El Niño-Southern Oscillation phenomenon footprints on soil moisture globally.