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Understanding the relationship between probabilistic and deterministic predictabilities is important for climate predictability studies. Focusing on the actual skill of dynamical seasonal prediction, we previously found that the probabilistic skills of resolution and relative operating characteristic (ROC)/discrimination, but not reliability, have functional relationships with deterministic anomaly correlation (AC). Herein, we further investigate the relationship between probabilistic and deterministic seasonal potential predictabilities. The potential predictabilities are characterized by the potential skills of the AC, resolution, and ROC evaluated using the perfect-model framework, under which reliability is ideal and not considered. A theoretical argument demonstrates that similar theoretical relationships to those for actual skills exist between probabilistic and deterministic potential predictabilities, regardless of how different the potential predictabilities are from the corresponding actual skills. These theoretical relationships are strictly monotonic and characterized by symmetrical probabilistic predictabilities for the below- and above-normal categories, and lower predictability for the near-normal category corresponding to deterministic predictability. A subsequent diagnostic analysis reveals that while the probabilistic and deterministic potential predictabilities in current dynamical climate models differ noticeably from the corresponding actual skills, they exhibit quasi-monotonic relationships as expected theoretically, which effectively and quantitatively validates the theoretical argument. This work, combined with our previous findings, establishes a solid equivalence of the resolution and discrimination aspects of probabilistic predictability to deterministic predictability in seasonal prediction, which can have beneficial implications for further studying probabilistic predictability.

In June 2021, Western North America experienced an intense heat wave with unprecedented temperatures and far‐reaching socio‐economic consequences. Anomalous rainfall in the West Pacific triggers a cascade of weather events across the Pacific, which build up a high‐amplitude ridge over Canada and ultimately lead to the heat wave. We show that the response of the jet stream to diabatically enhanced ascending motion in extratropical cyclones represents a predictability barrier with regard to the heat wave magnitude. Therefore, probabilistic weather forecasts are only able to predict the extremity of the heat wave once the complex cascade of weather events is captured. Our results highlight the key role of the sequence of individual weather events in limiting the predictability of this extreme event. We therefore conclude that it is not sufficient to consider such rare events in isolation but it is essential to account for the whole cascade over different spatiotemporal scales. Plain Language Summary In June 2021, Western North America experienced an intense heat wave with unprecedented temperatures and far‐reaching socio‐economic consequences. We show that the forecast of the extreme temperature anomalies was limited due to a complex sequence of weather events across the Pacific. Thus, state‐of‐the‐art weather forecasts were only able to predict the magnitude of the heat wave once the cascade of weather events was captured in the forecast. Key Points Intense 2021 North American heat wave is associated with extremely amplified upper‐level ridge Magnitude of record‐high temperatures was not predicted beyond 7 days Chain of synoptic‐scale precipitation events constitutes predictability barrier

The organization of real networks usually embodies both regularities and irregularities, and, in principle, the former can be modeled. The extent to which the formation of a network can be explained coincides with our ability to predict missing links. To understand network organization, we should be able to estimate link predictability. We assume that the regularity of a network is reflected in the consistency of structural features before and after a random removal of a small set of links. Based on the perturbation of the adjacency matrix, we propose a universal structural consistency index that is free of prior knowledge of network organization. Extensive experiments on disparate real-world networks demonstrate that ( i ) structural consistency is a good estimation of link predictability and ( ii ) a derivative algorithm outperforms state-of-the-art link prediction methods in both accuracy and robustness. This analysis has further applications in evaluating link prediction algorithms and monitoring sudden changes in evolving network mechanisms. It will provide unique fundamental insights into the above-mentioned academic research fields, and will foster the development of advanced information filtering technologies of interest to information technology practitioners. Significance Quantifying a network's link predictability allows us to ( i ) evaluate predictive algorithms associated with the network, ( ii ) estimate the extent to which the organization of the network is explicable, and ( iii ) monitor sudden mechanistic changes during the network's evolution. The hypothesis of this paper is that a group of links is predictable if removing them has only a small effect on the network's structural features. We introduce a quantitative index for measuring link predictability and an algorithm that outperforms state-of-the-art link prediction methods in both accuracy and universality. This study provides fundamental insights into important scientific problems and will aid in the development of information filtering technologies.

Purpose of Review Recent Atlantic climate prediction studies are an exciting new contribution to an extensive body of research on Atlantic decadal variability and predictability that has long emphasized the unique role of the Atlantic Ocean in modulating the surface climate. We present a survey of the foundations and frontiers in our understanding of Atlantic variability mechanisms, the role of the Atlantic Meridional Overturning Circulation (AMOC), and our present capacity for putting that understanding into practice in actual climate prediction systems. Recent Findings The AMOC—or more precisely, the buoyancy-forced thermohaline circulation (THC) that encompasses both overturning and gyre circulations—appears to underpin decadal timescale prediction skill in the subpolar North Atlantic in retrospective forecasts. Skill in predicting more wide-ranging climate variations, including those over land, is more limited, but there are indications this could improve with more advanced models. Summary Preliminary successes in the field of initialized Atlantic climate prediction confirm the climate relevance of low-frequency Atlantic Ocean dynamics and suggest that useful decadal climate prediction is a realizable goal.

Recent empirical evidence suggests that the variance risk premium predicts aggregate stock market returns. We demonstrate that statistical finite sample biases cannot “explain” this apparent predictability. Further corroborating the existing evidence of the United States, we show that country-specific regressions for France, Germany, Japan, Switzerland, the Netherlands, Belgium, and the United Kingdom result in quite similar patterns. Defining a “global” variance risk premium, we uncover even stronger predictability and almost identical cross-country patterns through the use of panel regressions.

Driven by the variety of available measures intended to estimate predictability of diverse objects such as time series and network links, this paper presents a comprehensive overview of the existing literature in this domain. Our overview delves into predictability from two distinct perspectives: the intrinsic predictability, which represents a data property independent of the chosen forecasting model and serves as the highest achievable forecasting quality level, and the realized predictability, which represents a chosen quality metric for a specific pair of data and model. The reviewed measures are used to assess predictability across different objects, starting from time series (univariate, multivariate, and categorical) to network links. Through experiments, we establish a noticeable relationship between measures of realized and intrinsic predictability in both generated and real-world time series data (with the correlation coefficient being statistically significant at a 5% significance level). The discovered correlation in this research holds significant value for tasks related to evaluating time series complexity and their potential to be accurately predicted.

Roughly one‐third of sudden stratospheric warming (SSW) events lack a strong canonical surface response, and this can lead to a forecast bust if a strong response was predicted. Hence, it is desirable to predict before SSW onset if an event will propagate downward. The predictability of the downward response of SSWs is considered in seven subseasonal‐to‐seasonal forecast models for 16 major SSWs between 1998 and 2022, a larger sample size than considered by previous works. The models successfully predict before SSW onset which SSWs have a stronger downward response to 100 hPa, however they struggle to predict which have a stronger tropospheric response. The downward response is stronger if the magnitude of the deceleration of the 10 hPa winds is more accurately predicted. Downward response is stronger for split and absorbing SSWs. In contrast, there is little relationship between SSWs whose onset can be predicted at earlier leads and the downward response. Plain Language Summary The wintertime stratosphere typically features circumpolar strong westerly winds, but on occasion these strong winds can reverse and temperatures over the pole can rise by tens of degrees in an event known as a sudden stratospheric warming (SSW). Such an event increases the likelihood of extreme cold over Northern Eurasia and wet conditions in Southern Europe, however roughly a third of events do not feature such downward propagation. Sixteen SSW events have occurred in the Northern Hemisphere over the period 1998 to 2022, and this study considers whether the models that have contributed to the subseasonal to seasonal (S2S) database are able to distinguish which are downward propagating and which are not. We also explore the factors that govern downward propagation of the SSW signal in these models. Key Points Downward versus non‐downward response of SSWs to 100 hPa is predicted by subseasonal prediction models ∼20 days before SSW onset In contrast, models struggle to predict the presence/absence of a tropospheric response before SSW onset Downward response and predictability of SSWs unrelated; split and absorbing SSWs show stronger downward response in models and reanalysis

Composing sentence meaning is easier for predictable words than for unpredictable words. Are predictable words genuinely predicted, or simply more plausible and therefore easier to integrate with sentence context? We addressed this persistent and fundamental question using data from a recent, large-scale ( n = 334) replication study, by investigating the effects of word predictability and sentence plausibility on the N400, the brain's electrophysiological index of semantic processing. A spatio-temporally fine-grained mixed-effect multiple regression analysis revealed overlapping effects of predictability and plausibility on the N400, albeit with distinct spatio-temporal profiles. Our results challenge the view that the predictability-dependent N400 reflects the effects of either prediction or integration, and suggest that semantic facilitation of predictable words arises from a cascade of processes that activate and integrate word meaning with context into a sentence-level meaning. This article is part of the theme issue ‘Towards mechanistic models of meaning composition’.

The funders had no role in study design, data collection and analysis, decicion to publish, or preparation of the manuscript. 1. Birkeland MS, Nielsen MB, Knardahl S, Heir T (2015) Associations between Work Environment and Psychological Distress after a Workplace Terror Attack: The Importance of Role Expectations, Predictability and Leader Support.

To determine whether (or not) the intrinsic predictability limit of the atmosphere is two weeks and whether (or not) Lorenz’s approaches support this limit, this entry discusses the following topics: (A). The Lorenz 1963 model qualitatively revealed the essence of a finite predictability within a chaotic system such as the atmosphere. However, the Lorenz 1963 model did not determine a precise limit for atmospheric predictability. (B). In the 1960s, using real-world models, the two-week predictability limit was originally estimated based on a doubling time of five days. The finding was documented by Charney et al. in 1966 and has become a consensus. Throughout this entry, Major Point A and B are used as respective references for these topics. A literature review and an analysis suggested that the Lorenz 1963 model qualitatively revealed a finite predictability, and that findings of the Lorenz 1969 model with a saturation assumption supported the idea of the two-week predictability limit, which, in the 1960s, was estimated based on a doubling time of five days obtained using real-world models. However, the theoretical Lorenz 1963 and 1969 models have limitations, such as a lack of certain processes and assumptions, and, therefore, cannot represent an intrinsic predictability limit of the atmosphere. This entry suggests an optimistic view for searching for a predictability limit using different approaches and is supported by recent promising simulations that go beyond two weeks.