The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined.

In Part I of this study, the impact of Ural blocking (UB) on the warm Arctic–cold Eurasian (WACE) pattern associated with the winter (DJF) arctic sea ice loss during 1979–2013 is examined by dividing the arctic sea ice reduction region into two dominant subregions: the Barents and Kara Seas (BKS) and the North American high-latitude (NAH) region (Baffin and Hudson Bay, Davis Strait, and Labrador Sea). It is found that atmospheric response to arctic sea ice loss resembles a negative Arctic response oscillation with a dominant positive height anomaly over the Eurasian subarctic region. Regression analyses of the two subregions further show that the sea ice loss over the BKS corresponds to the UB pattern together with a positive North Atlantic Oscillation (NAO⁺) and is followed by a WACE anomaly, while the sea ice reduction in the NAH region corresponds to a negative NAO (NAO⁻) pattern with a cold anomaly over northern Eurasia.Further analyses reveal that the UB pattern is more persistent during the period 2000–13 (P2) than 1979–99 (P1) because of the reduced middle-to-high-latitude mean westerly winds over Eurasia associated with the intense BKS warming. During P2 the establishment of the UB becomes a slow process because of the role of the BKS warming, while its decay is slightly rapid. In the presence of the long-lived UB that often occurs with the NAO⁺, the BKS-warming-induced DJF-mean anticyclonic anomaly is intensified and widened and then expands southward during P2 to amplify the WACE pattern and induce the southward displacement of its cold anomaly and the further loss of the BKS sea ice. Thus, midlatitude Eurasian cold events should be more frequent as the sea ice loss continues over the BKS.

The extratropical atmosphere is characterized by robust circulations which have time scales longer than that associated with developing baroclinic systems but shorter than a season. Such low‐frequency variability is governed to a large extent by nonlinear dynamics and, hence, is chaotic. A useful aspect of this low‐frequency circulation is that it can often be described by just a few quasi‐stationary regime states, broadly defined as recurrent or persistent large‐scale structures, that exert a significant impact on the probability of experiencing extreme surface weather conditions. We review a variety of techniques for identifying circulation regimes from reanalysis and numerical model output. While various techniques often yield similar regime circulation patterns, they offer different perspectives on the regimes. The regimes themselves are manifest in planetary scale patterns. They affect the structure of synoptic scale patterns. Extratropical flow regimes have been identified in simplified atmospheric models and comprehensive coupled climate models and in reanalysis data sets. It is an ongoing challenge to accurately model these regime states, and high horizontal resolutions are often needed to accurately reproduce them. The regime paradigm helps to understand the response to external forcing on a variety of time scales, has been helpful in categorizing a large number of weather types and their effect on local conditions, and is useful in downscaling. Despite their usefulness, there is a debate on the “nonequivocal” and systematic existence of these nonlinear circulation regimes. We review our current understanding of the nonlinear and regime paradigms and suggest future research.

This study investigates the significance of trends of four temperature time series—Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

Given the recent observational evidence that the positive (negative) phase of the North Atlantic Oscillation (NAO) is the remnant of anticyclonic (cyclonic) wave breaking, this study uses a multilevel primitive equation model to investigate important dynamical attributes of the above wave breaking behavior. For this purpose, a hierarchy of different basic states (two- and three-dimensional) and initial perturbations are used. With the three-dimensional climatological flow as the basic state, it is found that initial perturbations located equatorward (poleward) and upstream of the climatological Atlantic jet lead to wave breaking similar to that of the positive (negative) NAO phase. Consistently, analysis of observational data indeed shows that the Pacific storm track is displaced equatorward (poleward) prior the onset of the positive (negative) NAO phase. This result suggests that the latitudinal position of the Pacific storm track plays an important role for determining the phase of the NAO. Sen... Abstract Given the recent observational evidence that the positive (negative) phase of the North Atlantic Oscillation (NAO) is the remnant of anticyclonic (cyclonic) wave breaking, this study uses a multilevel primitive equation model to investigate important dynamical attributes of the above wave breaking behavior. For this purpose, a hierarchy of different basic states (two- and three-dimensional) and initial perturbations are used. With the three-dimensional climatological flow as the basic state, it is found that initial perturbations located equatorward (poleward) and upstream of the climatological Atlantic jet lead to wave breaking similar to that of the positive (negative) NAO phase. Consistently, analysis of observational data indeed shows that the Pacific storm track is displaced equatorward (poleward) prior the onset of the positive (negative) NAO phase. This result suggests that the latitudinal position of the Pacific storm track plays an important role for determining the phase of the NAO. Sen...