Consistency of resilience indicators in terrestrial vegetation models

Terrestrial ecosystems are affected by climate change, deforestation and other human influences. There is concern that the resilience of these ecosystems, i.e. their ability to recover from perturbations, is thereby decreased and that their sensitivity to environmental change is increased. In the extreme case, this sensitivity could diverge at a “tipping point”, and propel systems into alternative states. A prominent example is the potential dieback of the Amazon rainforest and the transition to a savanna-like state.

The notion of resilience is a highly complex and multi-faceted concept. Ecological resilience theory and the mathematical properties of dynamical systems suggest that a number of different resilience quantifiers are related to each other, or even equivalent, which would allow improved “resilience monitoring” from space. For instance, indicators based on the phenomenon of “critical slowing down” (CSD) like variance and autocorrelation, and related indicators have been used to detect changes over time. In contrast to empirical recovery rates, these indicators do not require one to directly observe the recovery from rare extreme disturbances. Also, they do not rely on the observation or attribution of the responsible environmental drivers.

Based on the assumption that fluctuations in remotely sensed proxies of vegetation properties (like biomass or vegetation greenness) behave like iconic one-dimensional stochastic models (most importantly, the Ornstein-Uhlenbeck process), CSD-based indicators should be related to empirical recovery rates after perturbations, to the more general Kramers-Moyal coefficients rooted in statistical mechanics, and to the sensitivity of a dynamical equilibrium state to environmental change. It has been shown that in observations, the theoretically expected relationships between some of these measures roughly hold. At the same time, process-based models, as well as observations, can deviate from such simple stochastic models, e.g. when multiple plant types affect the resilience of an ecosystem but not its sensitivity to environmental change.

In our contribution, we show and discuss examples for such deviations in a global vegetation model LPJ. In addition, we compare resilience indicators across a number of state-of-the-art models from CMIP6 and compare the results to an assessment of observations, in order to separate limitations that are related to the practical measurement process (e.g. uncertainties related to retrieval algorithms) from limitations that are associated with unjustified theoretical assumptions. Our results are meant to guide resilience monitoring toward meaningful indicators and to focus on regions and observable properties that can warn of future loss of ecosystem services.