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arxiv: 2606.08623 · v1 · pith:VX36B33Inew · submitted 2026-06-07 · ⚛️ physics.ao-ph

Climate network characterization of the AMOC edge state

Laure Moinat , Reyk B\"orner , Valerio Lucarini , Maura Brunetti , Henk A. Dijkstra This is my paper

Pith reviewed 2026-06-27 17:45 UTC · model grok-4.3

classification ⚛️ physics.ao-ph
keywords AMOCclimate networksedge stateteleconnectionstipping elementsdegree centralityEarth system models
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0 comments X

The pith

Climate networks detect equatorial teleconnections as the AMOC approaches its edge state

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper treats the AMOC as a tipping element and examines the edge state that marks the boundary of the collapsed state's basin of attraction. Simulations with an EMIC under SSP2-4.5 CO2 forcing produce qualitatively different AMOC behaviors depending on interaction with this edge state. The authors construct climate networks from instantaneous temporal correlations between grid points and apply network measures, especially normalized degree centrality, to these runs. The measure shows the development of teleconnections across the equator precisely when the AMOC nears the edge state. The same pattern appears in an ESM that exhibits either AMOC collapse or recovery, indicating the network signature could mark the onset of tipping in more complex models.

Core claim

The central claim is that network measures, specifically normalized degree centrality, reveal the presence of teleconnections across the equator as the AMOC approaches the edge state in both EMIC and ESM simulations that exhibit collapse or recovery under CO2 forcing.

What carries the argument

Climate networks constructed from instantaneous temporal correlations between geographical locations, using normalized degree centrality to detect teleconnections

If this is right

  • Normalized degree centrality can characterize the edge state during AMOC transitions under intermediate climate change scenarios.
  • The appearance of equatorial teleconnections supplies a detectable signal for proximity to the tipping boundary.
  • The network signature observed in EMIC runs extends to ESM runs that show collapse or recovery.
  • Climate networks supply one route toward estimating the probability of future AMOC transitions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same network construction could be applied to observational reanalysis products to check whether real-world AMOC variability produces comparable teleconnection patterns.
  • The method might transfer to other ocean tipping elements such as Antarctic Bottom Water formation.
  • Combining the network measure with existing early-warning indicators based on variance or autocorrelation could strengthen detection of AMOC proximity to tipping.

Load-bearing premise

Instantaneous temporal correlations between grid-point variables in the model output capture dynamical proximity to the edge state rather than model-specific noise or forcing artifacts.

What would settle it

A simulation in which the AMOC stays far from the edge state yet normalized degree centrality still shows strong cross-equatorial teleconnections would falsify the link between the network measure and approach to the edge state.

Figures

Figures reproduced from arXiv: 2606.08623 by Henk A. Dijkstra, Laure Moinat, Maura Brunetti, Reyk B\"orner, Valerio Lucarini.

Figure 1
Figure 1. Figure 1: FIG. 1. Regions used to compute the connection density in the climate network. They include the [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Region-to-region temperature connections for the ON state at surface, ORA20C at surface, [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Region-to-region connections for the ON (first column), OFF (second column), EDGE [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Overturning streamfunction in the Atlantic basin for the EDGE weak/phase [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Temporal evolution of the 30-years moving average AMOC intensity (first column), global [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Same as Fig. 5 in three GISS simulation ensembles (r1i1p1f2, r7i1p1f2 and r10i1p1f2, [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

The Atlantic Meridional Overturning Circulation (AMOC) has been identified as a tipping element in the Earth system. Under the current climate change scenarios, it is urgent to develop robust methods for determining the probability of future AMOC transitions. Recent studies using an Earth System Model of Intermediate Complexity (EMIC) have revealed the importance of an AMOC edge state, located on the boundary of the attraction basin of the collapsed state, in AMOC transitions. Here, we provide a characterization of this edge state through climate networks, using instantaneous temporal correlations between geographical locations to define the network links. We apply the climate network analysis to a set of EMIC simulations with CO$_2$ forcing according to an intermediate climate change scenario (SSP2-4.5) that exhibit qualitatively different AMOC responses as a result of interaction with the edge state. We show that network measures, specifically the normalized degree centrality, reveal the presence of teleconnections across the equator as the AMOC approaches the edge state. A similar result is obtained for an Earth System Model (ESM) simulating AMOC collapse or recovery, suggesting that climate networks could be used to detect the onset of an AMOC tipping event in ESMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript claims that climate networks constructed from instantaneous temporal correlations between grid points in EMIC simulations under SSP2-4.5 forcing can characterize the AMOC edge state, with normalized degree centrality revealing cross-equatorial teleconnections specifically when trajectories interact with the edge state; analogous behavior is reported in an ESM.

Significance. If the network signature can be shown to isolate edge-state dynamics from external forcing and model noise, the approach would offer a potentially useful diagnostic for proximity to AMOC tipping in intermediate and full-complexity models. The work builds on prior EMIC edge-state studies but does not yet demonstrate robustness against the confounding factors raised in the stress test.

major comments (2)
  1. [Abstract / Results] Abstract and Results: The central claim that normalized degree centrality 'reveals the presence of teleconnections across the equator as the AMOC approaches the edge state' is not supported by any surrogate-data tests, linear detrending, or comparison against non-tipping trajectories under identical SSP2-4.5 forcing. Without these controls, the reported cross-equatorial links cannot be distinguished from artifacts of the external CO2 trend or EMIC-specific variability.
  2. [Methods] Methods: No quantitative thresholds, bootstrap error estimates, or sensitivity tests to correlation-window length are reported for the network measures. This absence makes it impossible to assess whether the observed changes in degree centrality exceed the variability expected from the forcing protocol alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which identify key areas where additional controls would strengthen the manuscript. We respond to each major comment below and outline the planned revisions.

read point-by-point responses

  1. Referee: [Abstract / Results] Abstract and Results: The central claim that normalized degree centrality 'reveals the presence of teleconnections across the equator as the AMOC approaches the edge state' is not supported by any surrogate-data tests, linear detrending, or comparison against non-tipping trajectories under identical SSP2-4.5 forcing. Without these controls, the reported cross-equatorial links cannot be distinguished from artifacts of the external CO2 trend or EMIC-specific variability.

    Authors: We agree that surrogate-data tests, linear detrending, and explicit side-by-side comparisons with non-tipping trajectories are necessary to isolate edge-state effects from the external CO2 trend. Although the simulations already comprise multiple realizations under identical SSP2-4.5 forcing that produce qualitatively different AMOC outcomes due to edge-state interaction, the manuscript does not present these comparisons directly for the network measures. In the revised version we will add (i) direct network comparisons between tipping and non-tipping trajectories, (ii) linear detrending of the time series prior to correlation calculation, and (iii) surrogate-data tests that preserve the forcing trend while destroying temporal correlations. These controls will be reported in the Results section. revision: yes

  2. Referee: [Methods] Methods: No quantitative thresholds, bootstrap error estimates, or sensitivity tests to correlation-window length are reported for the network measures. This absence makes it impossible to assess whether the observed changes in degree centrality exceed the variability expected from the forcing protocol alone.

    Authors: We concur that the absence of these quantitative assessments limits evaluation of robustness. The revised Methods section will specify the correlation threshold used to define links, include bootstrap resampling (with replacement across ensemble members) to obtain error estimates on normalized degree centrality, and report sensitivity tests for correlation-window lengths ranging from 5 to 30 years. These additions will allow readers to judge whether the reported changes exceed forcing-induced variability. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical network metrics computed directly from simulation correlations

full rationale

The paper computes instantaneous temporal correlations between grid-point variables in EMIC output to define network edges, then calculates normalized degree centrality on those networks to observe cross-equator teleconnections in trajectories that interact with the edge state. This is a direct data-driven procedure with no fitted parameters renamed as predictions, no self-definitional equations, and no load-bearing self-citation that reduces the central claim to an unverified prior result by the authors. The edge-state context is referenced from prior work but the network characterization itself is independently applied to the described simulation ensembles and compared across qualitatively different AMOC responses.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard assumption that linear correlation defines meaningful network edges in climate data and that the EMIC ensemble adequately samples the edge-state dynamics.

axioms (1)
  • domain assumption Instantaneous temporal correlations between grid-point variables define network links that reflect dynamical proximity to the edge state.
    Invoked when constructing the climate network from EMIC output.

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