领域：学术论文 · 自然科学

The Atlantic meridional overturning circulation (AMOC) is a major tipping element in the climate system and a future collapse would have severe impacts on the climate in the North Atlantic region. In recent years weakening in circulation has been reported, but assessments by the Intergovernmental Panel on Climate Change (IPCC), based on the Climate Model Intercomparison Project (CMIP) model simulations suggest that a full collapse is unlikely within the 21st century. Tipping to an undesired state in the climate is, however, a growing concern with increasing greenhouse gas concentrations. Predictions based on observations rely on detecting early-warning signals, primarily an increase in variance (loss of resilience) and increased autocorrelation (critical slowing down), which have recently been reported for the AMOC. Here we provide statistical significance and data-driven estimators for the time of tipping. We estimate a collapse of the AMOC to occur around mid-century under the current scenario of future emissions.
A forthcoming collapse of the Atlantic meridional overturning circulation (AMOC) is a major concern as it is one of the most important tipping elements in Earth’s climate system1–3. In recent years, model studies and paleoclimatic reconstructions indicate that the strongest abrupt climate fluctuations, the Dansgaard-Oeschger events4, are connected to the bimodal nature of the AMOC5,6. Numerous climate model studies show a hysteresis behavior, where changing a control parameter, typically the freshwater input into the Northern Atlantic, makes the AMOC bifurcate through a set of co-dimension one saddlenode bifurcations7–9. State-of-the-art Earth-system models can reproduce such a scenario, but the inter-model spread is large and the critical threshold is poorly constrained10,11. Based on the CMIP5 generation of models, the AR6 IPCC report quotes a collapse in the 21st century to be very unlikely (medium confidence)12. Among CMIP6 models, there is a larger spread in the AMOC response to warming scenarios, thus an increased uncertainty in the assessment of a future collapse13. There are, however, model biases toward overestimated stability of the AMOC, both from tuning to the historic climate record14, poor representation of the deep water formation15, salinity and glacial runoff16. When complex systems, such as the overturning circulation, undergo critical transitions by changing a control parameter λ through  a critical value λc, a structural change in the dynamics happens. The previously statistically stable state ceases to exist and the system moves to a different statistically stable state. The system undergoes a bifurcation, which for λ sufficiently close to λc can happen in a limited number of ways rather independent from the details in the governing dynamics17. Besides a decline of the AMOC before the critical transition, there are early-warning signals (EWSs), statistical quantities, which also change before the tipping happens. These are critical slowing down (increased autocorrelation) and, from the FluctuationDissipation Theorem, increased variance in the signal18–20. The latter is also termed “loss of resilience”, especially in the context of ecological collapse21. The two EWSs are statistical equilibrium concepts. Thus, using them as actual predictors of a forthcoming transition relies on the assumption of quasi-stationary dynamics. The AMOC has only been monitored continuously since 2004 through combined measurements from moored instruments, induced electrical currents in submarine cables and satellite surface measurements22. Over the period 2004–2012, a decline in the AMOC has been observed, but longer records are necessary to assess the significance. For that, careful fingerprinting techniques have been applied to longer records of sea surface temperature (SST), which, backed by a survey of a large ensemble of climate model simulations,have found the SST in the Subpolar gyre (SG) region of the North Atlantic (area marked with a black contour in Fig. 1a) to contain an optimal fingerprint of the strength of the AMOC23–25. Figure 1b shows the SG and the GM SSTs obtained from the Hadley Centre Sea Ice and Sea Surface Temperature data set (HadISST)26. Figure 1c shows the SG anomaly, and Fig. 1d shows the GM anomaly with a clear global warming trend in the last half of the record. The AMOC fingerprint for the period 1870–2020 is shown in Fig. 1e. This is the basis for the analysis. It has been reported11,27 that this and similar AMOC indices show significant trends in the mean, the variance and the autocorrelation, indicating early warning of a shutdown of the AMOC. However, a trend in the EWSs within a limited period of observation could be a random fluctuation within steady-state statistics. Thus, for a robust assessment of the shutdown, it is necessary to establish a statistical confidence level for the change above the natural fluctuations. This is not easily done given only one, the observed realization of the approach to the transition. Here we establish such a measure of the confidence for the variance and autocorrelation and demonstrate that variance is the more reliable of the two. A further contribution is an estimator of not only whether a transition is approaching but also the time when the critical transition is expected to occur. The strategy is to infer the evolution of the AMOC solely on observed changes in mean, variance and autocorrelation. The typical choice of control parameter is the flux of freshwater into the North Atlantic. River runoff, Greenland ice melt and export from the Arctic Ocean are not well constrained28; thus, we do not assume the control parameter known. Boers27 assumes the global mean temperature T to represent the control parameter. Although T has increased since ~1920 (Fig. 1d), the increase is not quite linear with time. All we assume here is that the AMOC is in an equilibrium state prior to a change toward the transition. The simplest uninformed assumption is that the change is sufficiently slow and that the control parameter approaches the (unknown) critical value linearly with time. This assumption is confirmed by a close fit of the estimated model to the observed AMOC fingerprint. Although we make no explicit assumptions, the primary driver of climate change, the logarithm of the atmospheric CO2 concentration, does, in fact, increase close to linearly with time in the industrial period29. Our results are robust without making specific assumptions regarding the driver of the AMOC. In this work, we show that a transition of the AMOC is most likely to occur around 2025-2095 (95% confidence interval).
Modeling and detecting the critical transition  Denote the observed AMOC fingerprint by x(t) (Fig. 1e). We model it by a stochastic process Xt, which, depending on a control parameter λ < 0, is at risk of undergoing a critical transition through a saddle-node bifurcation for λ = λc = 0. The system is initially in a statistically stable state, i.e., it follows some stationary distribution with constant λ = λ0. We are uninformed about the dynamics governing the evolution of Xt but can assume effective dynamics, which, with λ sufficiently close to the critical value λc = 0, can be described by the stochastic differential equation (SDE):dX t = ðAðX t mÞ2 + λÞdt + σdBt , ð1Þ  where m = μ ∣λ∣=A  p and μ is the stable fixed point of the drift, A is a time scale parameter, Bt is a Brownian motion and σ2 scales the variance. Disregarding the noise, this is the normal form of the codimension one saddle-node bifurcation17 (see “Methods”). The squareroot dependence of the stable state: μ m ∼  λc λ  p is the main signature of a saddle-node bifurcation. It is observed for the AMOC shutdown in ocean-only models as well as in coupled models, see Fig. 2, in strong support of Eq. (1) for the AMOC.At time t0, λ(t) begins to change linearly toward λc = λ(tc) = 0:  λðtÞ = λ0ð1 Θ1⁄2t t0 ðt t0Þ=τr Þ, ð2Þ  where Θ[t] is the Heaviside function and τr = tc − t0 > 0 is the ramping time up to time tc, where the transition eventually will occur. Time tc is denoted the tipping time; however, an actual tipping can happen earlier than tc due to a noise-induced tipping. As the transition is approached, the risk of noise-induced tipping (n-tipping) prior to tc is increasing and, at some point, making the EWSs irrelevant for predicting the tipping. The probability for n-tipping can, in the small noise limit, be calculated in closed form, Pðt,λÞ = 1 expð t=τnðλÞÞ, with mean waiting time  τnðλÞ = ðπ= ffi∣ffiλffiffi∣ffi  p Þ expð8∣λ∣3=2=3σ2Þ (see “Methods”). The mean and variance are calculated from the observations as the control parameter λ(t) is possibly changing. These EWSs are inherently equilibrium concepts and statistical; thus, a time window, Tw, of a certain size is required for a reliable estimate. As the transition is approached, the differences between the EWSs and the preramping values of the variance and autocorrelation (baseline) increase; thus, a shorter window Tw is required for detecting a difference. Conversely, close to the transition critical slowing down decreases the number of independent points within a window, thus calling for a larger window for reliable detection. Within a short enough window, [t − Tw/2, t + Tw/2], we may assume λ(t) to be constant and the noise small enough so that the process (1) for given λ is well approximated by a linear SDE, the Ornstein–Uhlenbeck process30. A Taylor expansion around the fixed point μ(λ) yields the approximation ... where ... and ... is the inverse correlation time. For fixed λ, the process is stationary, with mean μ, variance γ2 = σ2/2α and one-lag autocorrelation ρ = expð αΔtÞ with step size Δt = 1 month. As λ(t) increases, α decreases, and thus variance and autocorrelation increase. From μ, γ2 and ρ the parameters of Eq. (1) are determined: α = log ρ=Δt, σ2 = 2αγ2, A = α/2(μ − m) and  λ = ðσ2=4γ2Þ2=A. Closed form estimators for μ, γ2 and ρ are obtained from the observed time series within a running window by maximum likelihood estimation (MLE) (Supplementary text S1, see also ref. 31). The uncertainty is expressed through the variances of the estimators γ^2 and ^ρ obtained from the observations within a time window Tw. The hats indicate that they are estimators and thus stochastic variables with variances around the true values. Detection of an EWS at some chosen confidence level q (such as 95 or 99%) requires one of the estimates γ^2 or ^ρ for a given window to be statistically different from the baseline values γ^2  0 or ^ρ0, which depend on the window size as well as how different the EWSs are from their baseline values.

翻译考点：
考点1：“Climate Model Intercomparison Project (CMIP)”推荐译为“气候模式对比计划”
考点2：“tipping”推荐译为“颠覆”，而不应该翻译成专有名词中常见表述“临界的”
考点3：“co-dimension one saddle node bifurcations”推荐译为“共维一鞍节点分叉点”
考点4：“resilience”推荐译为“恢复力”
考点5：“quasi-stationary”推荐译为“准稳态/平稳”
考点6：“Heaviside function”推荐译为“赫维赛德函数”