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.

In early 2018, Cape Town (population ~3.7 million) was at risk of being one of the first major metropolitan areas in the world to run out of water. This was due to a severe multi-year drought that led to the levels of supply dams falling to an unprecedented low. Here we analyze rainfall data from the city catchment areas, including rare centennial records from the surrounding region, to assess the severity of the 2015–2017 drought. We find that there has been a long-term decline in the number of winter rainfall days, but this trend has been generally masked by fluctuations in rainfall intensity. The recent drought is unprecedented in the centennial record and represents a combination of the long-term decline in rainfall days and a more recent decline in rainfall intensity. Cold fronts during the winter months are responsible for most of the rainfall reaching Cape Town and our analysis shows no robust regional trend in the number of fronts over the last 40 years. Rather, the observed multidecadal decline in rainfall days, which threatens to increase the occurrence of severe drought, appears to be linked to a decrease in the duration of rainfall events associated with cold fronts. This change in rainfall characteristics associated with fronts appears to be linked to Hadley Cell expansion seen across the Southern Hemisphere and an increasing trend in post-frontal high-pressure conditions that suppress orographically enhanced rainfall.

Fast and slow Madden–Julian oscillation (MJO) episodes have been identified from 850- and 200-hPa zonal wind and outgoing longwave radiation (OLR) for 32 winters (16 October–17 March) 1980/81–2011/12. For 26 fast cases the OLR took no more than 10 days to propagate from phase 3 (convection over the Indian Ocean) to phase 6 (convection over the western Pacific). For 8 slow cases the propagation took at least 20 days. Fast episode composite anomalies of 500-hPa height (Z500) show a developing Rossby wave in the mid-Pacific with downstream propagation through MJO phases 2–4. Changes in the frequency of occurrence of the NAO+ weather regime are modest. This Rossby wave is forced by anomalous cooling over the Maritime Continent during phases 2 and 3 (seen in phase-independent wave activity flux). The upper-level anticyclonic response to phase-3 heating is a secondary source of wave activity. The Z500 slow episode composite response to MJO phases 1 and 2 is an enhanced Aleutian low followed by a North American continental high. Following phase 4 the development of an NAO+ like pattern is seen over the Atlantic, transitioning to a strong NAO− pattern by phase 8. A dramatic increase in frequency of the NAO+ weather regime follows phases 4 and 5, while a strong increase in NAO− regime follows phases 6 and 7. The responses to MJO-related heating and cooling over the Indian and western Pacific Oceans in phases 1–4 provide a source for wave activity propagating to North America, augmented by storm-track anomalies.

Recurrent atmospheric flow patterns are those that occur more often than expected by chance, and their identification has been an underlying theme in atmospheric science on time scales ranging from weather forecasting to inter-annual fluctuations. This chapter focuses on identifying recurrent, and also persistent flow patterns on intra-seasonal time scales. Recurrent blocking structures seen in five-day means of the 500 hPa geopotential height (Z500) field motivate the use of a new scalar planetary wave index, whose probability distribution function (pdf) is very non-Gaussian, and hints at bi-modality. The search for maxima in pdfs in higher dimensions is best done in the reduced dimensional coordinates defined by principal component analysis, with pdf density maxima assessed as significant against a multi-dimensional Gaussian null hypothesis. Using these ideas, we apply the k-means method of cluster analysis to recover wellknown preferred structures (known as weather regimes) occurring in the Euro-Atlantic region on time scales of 10 to 90 days during boreal winter. Synthetic time series of statistically independent principal components are generated to assess statistical confidence of the analysis. We give a detailed discussion of both the generation of the synthetic time series, and the expected signal-to-noise ratio for multi-modal pdfs in higher dimensions. A layered application of cluster analysis to weather forecasts of the European Centre for Medium-Range Weather Forecasts utilizes forecast scenarios (clusters of the 51-member ensemble evolution of Z500 within a short time window) in order to synthesis information about large-scale structures from the ensemble. Verification is done against the previously defined weather regimes. For application beyond the very robust Euro-Atlantic regimes, more sophisticated tools are needed. The mixture model approach to modeling the full pdf with a multiple Gaussian components is presented. The use of dynamical information (in the form of the time evolution of fields), as well as explicit criteria for persistence, is a feature of the Hidden Markov Method. Using the foundation provided in the earlier sections, readers will be prepared to study these and other statistical/dynamical tools.