领域：学术论文 · 自然科学

Representativeness of measurements for underlying dynamics The above modeling uncertainties arise when one assumes that the time series used are a direct representation of the climate system in question. In practice, that is rarely the case. Tipping elements in the climate are complex, spatially extended systems with many degrees of freedom, and it is always a crude simplification to describe their dynamics by a 1D observational time series. Moreover, it is often unclear whether the relevant dynamical properties of the system in question are captured well by the available measurements. For example, the Amazon rainforest is observed using different remotely sensed vegetation indices, but it remains hard to tell which one is appropriate for understanding its stability (11, 23). The problem is further complicated by the relatively short time span of many climate observations. Tipping elements such as the polar ice sheets or the AMOC evolve over long timescales, and so, time series of a hundred years or more would be necessary to understand and predict their dynamics. When there are no direct measurements on such long timescales, studies use different proxies (“fingerprints”) for the systems. These fingerprints are climate variables that have some physical connection to the system of interest and are thus, to some extent, correlated with the changes of the system. For example, ice core–derived Greenland melt rates have been used as a fingerprint for ice sheet height and SST patterns as a fingerprint for the AMOC streamfunction strength (9, 24). Similarly, satellite-derived vegetation indices should be interpreted as—uncertain and potentially biased—fingerprints of the actual vegetation dynamics (11, 23). Fingerprints that are useful for understanding the evolution of the mean trend are not necessarily useful for predicting tipping times. 
In conclusion, there are often no fingerprints available with the precision required for predicting tipping times, as we will discuss for the AMOC in the next section.  Effect of dataset preprocessing and underlying uncertainties / nonstationary coverage  In addition to the uncertainties arising from the modeling approach and the choice of fingerprint, there are also substantial uncertainties in CSD indicators that originate from the dataset preprocessing steps and the nonstationarity of observational data coverage (23, 25, 26). The number of available climate observations has grown exponentially since 1850 (27, 28), especially with the increase of remote sensing measurements since the 1970s. In earlier years, these measurements are often concentrated in a small number of areas on the globe, resulting in uneven and sparse global coverage until at least the mid-20th century (28). Therefore, to produce globally complete datasets, researchers often merge a number of different instrumental records and fill in the gaps in data using a processing procedure. The bias correction for the different measurements and the infilling methods often prioritize the accuracy of the mean trend over the accuracy of the higher-order statistics [see, for example, (23, 29–32)]. This can cause problems for the detection of CSD (23, 25, 26, 33) and especially for the calculation of the future tipping time. Any calculation of the future tipping time is strongly reliant on the time evolution of the data’s higher-order statistics, and the dataset preprocessing can induce artificial trends in these statistics. To this point, we show the effect of adding white measurement noise of a decreasing amplitude to the synthetic model data of the fold normal form and estimate tipping times using the introduced methods. Figure 2D shows how a small amount of observational uncertainty can incur substantial changes in the estimations. One real-world example of such an effect is the merging of multiple satellite signals. The change in signal-tonoise ratio from one satellite to the next can cause an artificial increase in autocorrelation (23). 
Another issue emerges when missing data are infilled with some sort of principal components analysis, in which case there will be more artificial smoothing in earlier times due to the lack of data, and so quantities like the variance could increase artificially (26, 29). In the next section, we will discuss such dataset uncertainties in detail for the AMOC SST fingerprints.  Uncertainties in predicting the AMOC tipping time  We now address these uncertainties for the specific case of predicting the tipping time of a system by applying DD23’s MLE-based method to SST-based fingerprints of the AMOC (14). We choose to use DD23’s methodology because among the three discussed methods, it performs best for a fold normal form with white noise (Fig. 2A) and was designed for AMOC tipping time prediction. Modeling assumptions  There has long been a discussion about whether the AMOC, when investigated as a complex system under external forcing of, e.g., GMT (or better, regional freshwater forcing), exhibits multiple stable states (34–36). Transitions between such stable states could be bifurcation induced and thus abrupt and irreversible. The so-called fold bifurcation constitutes a minimal example of such behavior. For instance, the conceptual Stommel model of the AMOC features a fold bifurcation (34). Taking this reasoning another step further, the application of the MLE method assumes that the 1D observable of AMOC strength is well represented by the following normal form model  where Xt is the system state at time t, α is the external control parameter, b is a timescale parameter, m is a translation parameter, and the white noise term σdWt represents noisy perturbations within the system. A similar simplification has been applied to more complex AMOC models in multiple studies (37, 38) and is justified by arguing that all fold bifurcations are topologically equivalent to this model. This, however, is only true locally, in potentially very close proximity to the bifurcation point, while the proposed estimation method banks on the assumption that it would hold in arbitrary distance to the bifurcation point. On the basis of the arguments brought forth, we do not see a direct constraint on the dynamics away from the tipping point. When applying the MLE method to data of the closely related 2D Stommel-Cessi AMOC model (39), one obtains a considerable bias in tipping time estimates toward earlier times (Fig. 3A). 
This should be seen as an indication that even models with an underlying fold bifurcation structure, yet not following the very specific normal form model equation above, produce time series which, when applying the MLE method, yield biased tipping time estimates. The AMOC exhibits pronounced decadal variability (40). Before the commencing of the destabilisation at time t0, the AMOC is assumed to resemble paths of a stationary stochastic process X defined by  When applying their MLE method to the AMOC, DD23 estimates  a value of 2b√α ≈ 3.1 [year−1], corresponding to a characteristic correlation time of 0.32 [year]. In contrast, frequency spectra of AMOC evolutions in general circulation models show strongest variability between 5 and 100 years [e.g., figure 6 in (41)]. Such pronounced additional variability on long timescales is not captured by the above Ornstein-Uhlenbeck model. Internal variability independent of the  model noise will thus cause large excursions from the transient mean. The proposed method is not equipped to incorporate the impact of these excursions on the estimated tipping time, since they may be misinterpreted as trends toward a tipping point. This exposes the estimation method to risks of false alarms of a similar nature as in Fig. 1. In addition, recent application of DD23’s MLE method to AMOC tipping in a complex climate model (42) has shown that the tipping time prediction is very sensitive to the time interval analyzed due to the decadal variability of the AMOC, and most 150-year windows cannot accurately estimate the tipping time. Moreover, for quantitative extrapolations of tipping time, any simplifying assumptions on the driving noise would need to be carefully checked. Since disturbances to the equilibrium state are themselves of atmospheric and oceanic origin, time correlation of the noise should be taken into consideration, e.g., via a red noise model (8). Nonstationary red noise present in the system can incur substantial biases in the estimation of the tipping time and even result in false alarms of an approaching bifurcation (as seen in Figs. 1 and 2B).
Assumptions on future AMOC forcing  Previously, we discussed the fact that not only can we not assume the future evolution of the forcing of climate tipping elements to be known, we also cannot assume that the forcing evolved linearly in the past. This is also true for the AMOC: Several studies show that radiative anomalies due to aerosol pollution likely attenuated the AMOC weakening of the past decades (43, 44), and such changes cannot be modeled with a linearly changing control parameter. Moreover, the GMT forcing itself influences the AMOC due to many different nonlinear mechanisms, e.g., via thermal expansion, a strengthening hydrological cycle, as well as sea ice and ice sheet melt (with the influence of the latter in the historical period still under debate) (45, 46). The effective freshwater flux might serve as a better forcing parameter (35, 47), but we do not have long-term measurements of this parameter, and there is evidence that it does not linearly depend on GMT; e.g., Greenland runoff increases nonlinearly over time (48, 49).

翻译考点：
考点1：“Tipping elements”必须译为“临界要素”，避免“临界点要素”等不一致表达。
考点2：“CSD”必须译为“临界减速”，临界减速是指接近临界点时系统动态的减缓。
考点3：“a minimal example”建议译为“最简化例子”，避免翻译为“基本例子”，准确传达“minimal”的含义。
考点4：“white measurement noise”必须译为“测量的白噪声”，避免遗漏“measurement”一词，确保精确性。
考点5：“tipping times”必须译为“临界时间”，确保对“tipping time”术语的标准化翻译。
考点6：“Fingerprint”推荐译为“指纹 / 代理指标”，避免在科学语境中误用“指纹”单独的译法，需附加说明。
考点7：“decadal variability”建议译为“年代际变率”，避免使用“年代际变化”等不准确的翻译。
考点8：“GMT”必须译为“全球平均气温”，避免使用“全球平均温度”或其他混淆表达。确保气候学术语准确传达，避免模糊。
考点9：“underlying dynamics”必须译为“潜在动力学”，避免误用“潜在动态”，保持术语一致性。
考点10：“SST patterns”建议译为“海表温度（SST）模式”，并在首次出现时明确解释“SST”的含义。
考点11：“nonstationary coverage”建议译为“非平稳覆盖范围”，避免遗漏“覆盖范围”的表达。
考点12：“higher-order statistics”建议译为“高阶统计量”，保持术语一致性。
考点13：“autocorrelation”建议译为“自相关”，避免误译为“自相关性”。自相关用于描述数据序列间的相似性，需精确翻译。
考点14：“topologically equivalent”统一译为“拓扑等价的”，避免使用其他含糊的翻译。拓扑等价是数学和物理中常用术语，需确保精准传达。
考点15：“spatially extended systems”建议译为“空间延展系统”，保持准确的术语翻译。确保译文精准传递了系统在空间上的广泛扩展特性。
考点16：“Stommel–Cessi AMOC model”建议译为“斯托梅尔—切西大西洋经向翻转环流模型”，确保音译一致。确认模型的全名和背景，以免误导读者。
考点17：“hydrological cycle”推荐译为“水文循环”，保持正式且准确的翻译。水文循环在气候系统中是核心概念，需确保译文清晰。
考点18：“Greenland runoff”统一译为“格陵兰径流”，避免翻译为“格陵兰的径流量”或其他不标准翻译。