the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Feb 2026
An Information-Based World-Earth System Resilience Index
Abstract. In order to address the emerging global polycrisis, it is essential to develop quantitative indicators for estimating resilience of essential bio-geophysical and social drivers of change. Such indicators are required to navigate the Anthropocene and to assess which actions increase the likelihood of achieving a safe and just operating space (SAJOS). In this paper, we propose a novel information-based resilience metric. We define it as the conditional probability of a system reaching a desired system state, e.g. a SAJOS, given initial conditions and an information set. This information set reflects knowledge about relevant ranges of bio-physical and socio-cultural system dynamics, boundaries and perturbations. The resulting resilience index is highly dependent on the available information about the system and its intrinsic action capacities. An increase in epistemic knowledge about the system does not necessarily result in enhanced resilience. It is still possible to envisage scenarios in which one could find oneself in a world that is capable of attaining a SAJOS in only a limited number of circumstances. Our proposed approach facilitates the operationalization and quantification of resilience in complex World-Earth system (WES) models. Resilience should be understood as being constrained by available information about the system, its internal processes, boundaries, and the capacity of the system to act in an uncertain future. This further implies the importance of making informed investment decisions that balance improving system understanding (i.e. gaining information), increasing (anticipatory) capacities of action, and taking common-sense action to enhance resilience. Our information-based index can be applied to any kind of system. Since it answers the classical question of "resilience of what, to what" on a meta level, it allows moving beyond a highly specified and static notion of resilience, allowing for a wide range of application cases.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Earth System Dynamics.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-6345', Anonymous Referee #1, 10 Mar 2026
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RC2: 'Comment on egusphere-2025-6345', Anonymous Referee #2, 18 May 2026
General Commemnts:
The authors propose a novel approach to reslience metrics that accounts for the dynamics of the World-Earth system (WES) and is potentially useful in policy considerations. They consider the WES as a stochastic dynamical system accounting for biological, physical and social drivers and define an index of resilience as a probabalistic metric for the system being in a region that is "desired". They argue that the metric can take account of different information sets chosen by different stakeholders as well as different policy sets. Their approach is rather general and they illustrate the application to a particular WES that is well described in the literature for human population dynamics, capital fluxes and ec onomic production.Technical Comments:
1. They define their index as a conditional probability of a system reaching a desired system state, given initial conditions and an information set. This implies that there is an underlying stochastic process, likely a random field as the index set is inherently spatio-temporal (e.g. time and n-regions). However there is no formal description of the properties of the underlying stochastic process, which is problematic since essentially all drivers of the WES are non-autonomous implying non-stationarity of any process and, due to history dependence a Markov assumption is not reasonable. The examples they choose are either a stochastic differential equation (Ito form) which gives a diffusion process, or else an Ornmstein-Uhlenbeck process with jumps. What is not clear is how their general model or the particular examples they give deal with non-stationarity. This is problematic because the entire approach outlined in Equations (7)-(10) in Figure 2 to calculate the index assumes some ergodicity of the process (so the sample averages actually converge, which is not at all guaranteed for non-stationary processes).
2. The index is defined as a conditional probability of a system reaching a desired system state, but it is only later that they specify that this is the probability the system is in the desired state at a fixed time, T. This implies that they have specified in advance a fixed time scale for the index but they do not discuss how this time scale relates to that of the underlying stochastic process. In the WES examples they assume fixed parameters affecting the population and production states but clearly these have their own dynamics and the time scales of these may well not match with the time horizon T (e.g. they may operate on very much faster or slower time scales. It would be helpful in making this approach readily applicable to policy to discuss in more detail the underlying assumptions about the dynamics of drivers and the fixed time T.
3. Another problematic aspect of the index as they describe it (e.g. in equation (11)) is the fact that what the state of the process is at a particular fixed time doesn't necessarily say much of anything about the state of the process prior to that fixed time T. So the conditional probability that the process is in the desired rigion might be quite high at T but the stochastic sample paths may have wandered outside this region for much of the time interval. A more reasonable and useful index would account for this, by incorporating the properties of the sample path so that the index measures what fraction of the time T the process is in the desired region.
4. A key assumption they mention in point 1 in section 2 of the paper is that the WES actually has attractors. This is the classic dynamical systems perspective but it is far from clear that it makes any sense at all in WES framework, given non-autonomy of the earth system (ENSO being just one example) as well as that of the social system (as just one example the current and sudden shift in production due to the Iraq war). If they wish to take this perspective, I encourage the authors to carerfully describe the assumptions about filtering needed for any attractors to be considered. Alternatively, why mention attractors at all in this? Is it a necessary assumption? For what they are trying to do all that matters is whether the WES process enters and remains in a particular region - why does it matter that there are or are not attractors? Context dependency is a property of many biological and social processes in the world, which is one reason why it is so challenging to for example determine what species will become invasive or where and when the next major conflicts will arise. Stu Kauffman calls this the "adjacent possible" and it isn't at all clear how the proposed index deals with such context dependency.
5. Point 2 in section 2 implies that there is a feasible means to separate out actionable processes from those that are not. For a major production system, agrculture, essentially every process is actionable - it isn't at all clear wat is not actionable for land cropping and forest resourse systems, though marine systems may be more separable in this. This is another example of the lack of attractors - agricultural systems are maintained in certain states only through regular actions and the underlying system crashes out of these "temporary transient states" without the maintenance of the control systems.
Specific comments:
1. The authors wish to have an information-based index as a tool to translate what policy actors think they know (e.g., their priors) into a single number using conditional probability. So this is an explicitly Bayesian aopproach but there is little said about choosing priors in the information sets. It might be helpful to have an example with different priors (for example in the two regions) to illustrate the impacts on the index.
2. The authors make an argument in line 405 regarding the benefits of their approach of using a fixed time point to ascertain a single metric of resilience over the IPCC model comparison activity (which has time trajectories with uncertainty envelopes). This argument could be strengthened if they did indeed have an index defined that accounted for the time course of the WES - it is exactly the time dependence that is missing from their index approach at a fixed time point, and some would conbsider this a weakness in comparison to the IPCC model comnparisons.
3. The argument in line 68 that a resilience index is most useful if it can inform a recursive decision-making process in driving the dyanmical system as well as teasing out additional information (e.g. updating the priors) is very reminiscent of the ideas of active adaptive management. Perhaps somne discussion of this would be helpful.
Citation: https://doi.org/10.5194/egusphere-2025-6345-RC2
Data sets
An Information-Based World Earth System Index; Data Max Bechthold and John M. Anderies https://doi.org/10.5281/zenodo.17098743
Model code and software
An-Information-Based-World-Earth-System-Resilience-Index Max Bechthold and John M. Anderies https://doi.org/10.5281/zenodo.17100929
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This article presents a novel, integrative, and widely applicable framework for quantifying social-ecological resilience by infusing stochasticity and agency into classic topological resilience. The dynamic nature of the IBRI allows for updated information and agency alongside physical uncertainties, making it especially appropriate for modeling iterative policy-making. The main results, that only about 30% of cases lead to existence in the safe operating space, along with the finding that the largest “leverage point” in the system is the timing of decarbonization, are sobering and represent the need for urgent decarbonization. The authors also find the counterintuitive result that gaining more specific knowledge can decrease IBRI. This is an important social dynamic and should be investigated in subsequent literature. The explicit math formulation of the IBRI is sound and well-supported, and accepts a wide range of systems, access to information, and stochasticity, adding realism to resilience metrics that implicitly assume objective characterization.
Specific comments:
TECHNICAL CORRECTIONS