Direct test for critical slowing down before Dansgaard-Oeschger events via the volcanic climate response

TL;DR

The paper investigates whether statistical early-warning signals reliably predict past climate tipping points by directly testing critical slowing down ($CSD$) using the climate’s averaged response to hundreds of volcanic eruptions. A multivariate ice-core proxy set is compressed into a single slow-mode observable via diffusion maps, enabling a direct test of $CSD$ in the approach to Dansgaard–Oeschger transitions. The results show $CSD$ evidence prior to DO cooling transitions but not for warming transitions, while many proxies exhibit broad EWS prior to both, highlighting a disconnect between $CSD$ and proxy-based EWS and signaling the need for caution when interpreting EWS in individual observables. Overall, the findings support a nuanced view: some bifurcation precursors align with EWS for cooling events, but the lack of universal $CSD$ signals and proxy variability calls for more data and modeling to robustly forecast future climate tipping points.

Abstract

It is tested whether past abrupt climate changes support the validity of statistical early-warning signals (EWS) as predictor of future climate tipping points. EWS are expected increases in amplitude and correlation of fluctuations driven by noise. This is a symptom of critical slowing down (CSD), where a system's recovery from an external perturbation becomes slower as a tipping point (represented by a bifurcation) is approached. EWS are a simple, indirect measure of CSD, but subject to assumptions on the noise process and measurement stationarity that are hard to verify. In this work the existence of CSD before the Dansgaard-Oeschger (DO) events of the last glacial period is directly tested by inferring the climate's recovery from large volcanic eruptions. By averaging over hundreds of eruptions, a well-defined, stationary perturbation is constructed and the average climate response is measured by eight ice core proxies. As the abrupt DO warming transitions are approached, the climate response to eruptions remains the same, indicating no CSD. For the abrupt DO cooling transitions, however, some key proxies show evidence of larger climate response and slower recovery as the transitions are approached. By comparison, almost all proxies show statistical EWS before cooling and warming transitions, but with only weak confidence for the warming transitions. There is thus qualitative agreement of CSD and EWS, in that the evidence for bifurcation precursors is larger for the cooling transitions. However, the discrepancy that many proxies show EWS but no direct CSD (and vice versa) highlights that statistical EWS in individual observables need to be interpreted with care.

Figures (8)

• Figure 1: Critical slowing down and early-warning signals for a tipping point (TP) caused by a saddle-node bifurcation, illustrated for dynamics in a two-dimensional (quasi-)potential. There are two stable fixed points at local minima of the potential (red and blue dots), as well as one saddle point (green triangle). When far from the TP ( a), both minima are relatively deep. After applying fast perturbations to the system (open circles), it relaxes quickly back to the fixed point. Noise-driven fluctuations are small and relatively isotropic, indicated by the small white ball around the red fixed point. When close to the TP ( b), one minimum is very shallow and the potential around it very flat. The most flat direction is along the slow (center) manifold, which is the line connecting the saddle and the fixed point. Now, relaxation trajectories after a perturbation first quickly approach the manifold and then evolve very slowly back towards the fixed point. This is CSD. Noise-driven fluctuations become much larger, which gives rise to EWS, and evolve in a preferred direction indicated by the white ellipse. If the system is non-gradient, i.e., does not evolve solely in directions defined by the gradient of a potential, large fluctuations do not have to be directed towards the center manifold, as illustrated by the short noisy trajectory in black.
• Figure 2: Two of the ice core proxy records used in this study, as well as the record of volcanic eruptions (crosses above the time series). Shown are the NGRIP $\delta^{18}$O ( a) and $Ca$ ( c) records over the time period 11.7-60 ka, as well as zoom-ins on a shorter period b,d. A separation of the time period into warm and cold phases of DO cycles is given by shadings in grey (GI) and yellow (GS). The vertical dashed and dotted red lines in b,d, as well as the coloring of the crosses marking volcanic eruptions, show the division of each GI and GS into three segments of equal duration. This is used here to analyze how the proxy variability and the climate response after volcanic eruptions changes as the climate progresses from the beginning (first of three segments) towards the end (third of three segments) of a GI or GS period.
• Figure 3: Average anomalies in eight ice core proxies associated with volcanic eruptions in the interval 11.7-60 ka. The eruptions are divided according to whether they occurred during stadial (GS, black solid line) or interstadial (GI, green dashed line) periods. For the impurity records in panels c-h, the quantity shown is $- (\ln C - \ln C_0)$, i.e., minus the logarithm of the concentration $C$ anomalies with respect to the mean $C_0$ in the 50 years prior to an eruption. Thus, a volcanic anomaly value of, say, -0.5 corresponds to an increase in $C$ above the baseline $C_0$ by a factor of $e^{0.5} \approx 1.65$. For $\lambda$, the quantity shown is $(\frac{\lambda}{\lambda_0} - 1)\cdot 100$, i.e., the percentage change anomalies of $\lambda$ with respect to the baseline value $\lambda_0$.
• Figure 4: Average volcanic anomalies in the eight proxies for the eruptions occurring during GS, divided into three subsets according to whether they happen at the beginning of a GS (labelled 'Old'), in the middle of a GS ('Mid') or towards the end of a GS before the abrupt transition ('Young'). For the latter category, the shading shoes the uncertainty in the average signal, given by the standard deviation of the mean signal in the 50 years prior to the eruption.
• Figure 5: Average volcanic anomalies of the proxies $\delta^{18}$O ( a), dust ( b) and $Na$ ( c) for eruptions occurring during the GI periods. The thick solid curve (red) and shading (one standard deviation of the mean signal) is the signal averaged over all eruptions that occur during the youngest third of a GI. The dashed curve is the average signal for the remaining eruptions in the older two thirds of each GI. Also shown in all panels is the average volcanic sulfate signal in the youngest (solid blue curve) and older (blue dotted line) parts of the GIs.