Complexity

Volume 2018 (2018), Article ID 3140915, 8 pages

https://doi.org/10.1155/2018/3140915

## Recent Trends in the Recurrence of North Atlantic Atmospheric Circulation Patterns

^{1}Laboratoire des Sciences du Climat et de l’Environnement, UMR 8212 CEA-CNRS-UVSQ, IPSL & U Paris-Saclay, CE l’Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France^{2}Centre National de Recherches Météorologiques, UMR 3589 CNRS-Météo-France, 42 avenue G. Coriolis, 31057 Toulouse, France

Correspondence should be addressed to Pascal Yiou

Received 8 August 2017; Revised 7 December 2017; Accepted 11 January 2018; Published 12 February 2018

Academic Editor: Daniela Paolotti

Copyright © 2018 Pascal Yiou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A few types of extreme climate events in the North Atlantic region, such as heatwaves, cold spells, or high cumulated precipitation, are connected to the recurrence of atmospheric circulation patterns. Understanding those extreme events requires assessing long-term trends of the atmospheric circulation. This paper presents a set of diagnostics of the intra- and interannual recurrence of atmospheric patterns. Those diagnostics are devised to detect trends in the stability of the circulation and the return period of atmospheric patterns. We detect significant emerging trends in the winter circulation, pointing towards a potential increased predictability. No such signal seems to emerge in the summer. We find that the winter trends in the dominating atmospheric patterns and their recurrences do not depend of the patterns themselves.

#### 1. Introduction

Recent North Atlantic winter and summer extremes have been associated with persistent patterns of atmospheric circulation. Those patterns have been rather contrasted from one year to another. Cold spells of January 2010, December 2010, and February 2012 in Europe resulted from persisting blocking situations over Scandinavia [1, 2]. Warm winter 2006/2007 [3, 4] and stormy winter 2013/14 [5, 6] were dominated by persistent high-pressure systems over the Azores and the Mediterranean Sea, respectively. The warm summers of 2003 and 2015 in Europe were associated with either a persisting blocking pattern over Scandinavia or Atlantic low conveying warm air into Europe from North Africa. Therefore it is difficult to claim that a given atmospheric pattern has dominated during recent years to create such climate extremes. However it has been speculated that the amplitude of atmospheric patterns is changing, in particular through a connection between Arctic sea-ice cover and meanders of the jet stream [7, 8]. The statistical significance of such a trend as well as the relevance of the evoked mechanisms has been debated [9–11].

The midlatitude atmospheric variability is characterized by a baroclinic instability of the zonal flow [12]. This instability grows into Rossby waves. It has been argued that the excitation conditions of those Rossby waves have increased in the past decades [8, 13].

Faranda et al. [14] studied how unstable fixed points of the extratropical atmospheric circulation correspond to blocking patterns of the circulation. Faranda et al. [15] investigated the local dimension of North Atlantic atmospheric circulation and examined the implications for predictability in the winter season. The local dimension is linked to the recurrence properties of a complex system [16–18].

In this paper, we analyze recently observed trends in the surface North Atlantic circulation in winter and summer. We focus on recurrences of patterns of the atmospheric circulation [16, 19]. We examine trends in the intraseasonal recurrence of flow patterns by using the notion of recurrence networks within a season, as introduced by Donner et al. [20]. The trend in interannual pattern recurrence is examined through the probability of detecting good analogues of circulation. Those intra- and interannual diagnostics allow detecting emerging properties of the atmospheric circulation.

#### 2. Data and Methods

##### 2.1. Data

We use the reanalysis data of the National Centers for Environmental Prediction (NCEP) [21] between January 1948 and March 2017. We consider the sea-level pressure (SLP) over the North Atlantic (80W–30E; 30–70N). One of the caveats of this reanalysis dataset is the lack of homogeneity of assimilated data, in particular before the satellite era. This can lead to breaks in pressure related variables, although such breaks are mostly detected in the southern hemisphere and the Arctic regions [22]. A multiple breakpoint detection algorithm [23] was applied to the time series we generate, in order to determine whether our results depend on the assimilated data of the reanalysis. No breakpoint was detected at or near the years of introduction of satellite data in the reanalysis (not shown).

The SLP field structure contains a seasonal cycle that needs to be removed. We computed seasonal anomalies of SLP. For each grid point of the reanalysis, a daily seasonal cycle is computed with a smoothing spline of daily averages, with a differentiability constraint at December 31 and January 1. The mean seasonal cycles obtained at each gridpoint are subtracted to the time series of SLP in order to produce anomalies of SLP.

##### 2.2. Intraseasonal Recurrence

The first concept we develop is the intraseasonal recurrence of atmospheric patterns for the winter and summer seasons (December-January-February (DJF) and June-July-August (JJA)). The temporal autocorrelation (number of days with an autocorrelation significantly above 0) of SLP around the North Atlantic is close to 5 days on average [24]. If the atmospheric circulation fluctuates around a given state on time scales that are longer than 5 days, this might not be reflected by the sample autocorrelation. Beyond the* persistence* defined by “remaining in a pattern during consecutive times,” we are interested in the fact that the atmosphere could come back to a given pattern, after a significant disturbance. This identifies a recurrent—although unstable—state of the atmosphere, potentially corresponding to a wave excitation. This state does not need to be the same from one year to another. In this subsection we adopt two ways of measuring the intraseasonal recurrence of patterns within a season.

The first one is based on the analysis of weather regimes of the atmospheric circulation. For each season, the SLP anomalies (with respect to the seasonal cycle) are classified onto four weather regimes. This number corresponds to what is usually found in the literature [25–27]. We compute the principal components (PCs, [28]) of the NCEP reanalysis SLP anomaly data. SLP data is weighed by the cosine of latitude for the computation of PCs/EOFs. The weather regimes (WR) are determined by a -means clustering of the first 10 PCs, between 1970 and 2000 [27, 29].

For each year and each season (winter and summer, between 1948 and 2017), the daily SLP anomaly patterns are attributed to the closest WR pattern (in terms of Euclidean distance to the cluster mean). The annual* frequency* of WR is the ratio of number of occurrences of the WR to the length of the season. For each year and each season, the dominant WR is the one with the highest frequency, and we report the frequency of the dominant weather regime.

The second approach to that concept of intraseasonal recurrence is based on the similarity of intraseasonal daily SLP anomaly patterns. For each reference day within a season, we determine all the days of the same season that yield a spatial rank correlation that exceeds a threshold . Here, we take , which corresponds to the 60th percentile of all intraseasonal sample correlation values. We construct a* network* of analogue days , for all days in years by

The days in fall in the same season (DJF or JJA). The so-called “dominating” network is the one that yields the largest number of analogue patterns. This network definition is similar to the recurrence network of Donner et al. [20]. We consider the number of days in the dominating analogue network and the frequency (percentage of days) within a season. We call this percentage of days the* frequency* of the analogue network (or for short).

This approach is akin to the dominating WR analysis, but it does not constrain the geographical location of the predefined weather patterns. The fluctuations of the frequencies of the dominating WR or the network help us assess how the persistence of atmospheric patterns varies through time. Those two intraseasonal quantities (frequencies of dominating weather regime and dominating network) allow investigating recurrent but potentially unstable patterns of the atmospheric circulation. Those patterns do not need to be visited in spates of consecutive days.

Those two approaches are meant to determine the trend of intraseasonal pattern recurrence. The choice of is justified a posteriori by comparing the values of the frequency of the network and the frequency of the dominating WR. If the threshold correlation increases, the size of decreases. A value of divides size of by 2 and gives a range of variations that is much smaller than the average value of the dominating WR frequency, which leads to a more difficult physical interpretation.

We emphasize that this concept of intra-annual network recurrence is distinct from the clustering index examined by Faranda et al. [15], which focuses on the local persistence of the system. But the concept is complementary to the analyses of Faranda et al. [14] because we identify regions in the phase space of the atmospheric circulation to which trajectories “try” to come back close to.

##### 2.3. Interannual Recurrence

The second concept we use is the interannual recurrence of SLP patterns. In contrast with the previous definitions, the* interannual* recurrence in atmospheric sciences [e.g., [16]] based on events that occur in* different* years but the same season, in order to ensure statistical independence. The time evolution of the (interannual) recurrence properties (e.g., in terms of closeness or return time) provides information on trends in the dynamics of the system [18, 30]. Such trends suggest the emergence of patterns.

In this paper, the long-term emergence (or disappearance) of patterns is estimated from interannual analogues of circulation [4, 16]. For each day, we determine the best 20 analogues of circulation by minimizing a Euclidean distance to all days occurring in a different year, but at most 30 calendar days apart. Good analogues have a distance that is smaller than a threshold corresponding to the 25th percentile of distance, and a spatial correlation that is higher than a threshold corresponding to the 75th percentile of spatial correlations of all 20 best analogues. In practice, the number of good analogues for a given day is always lower than 10 for such data. Therefore retaining more than the 20 best analogues would not change the results.

The distributions of correlations for interannual analogues (i.e., picked in another year) and intraseasonal analogues are different, which explains that the value corresponds to different quantiles in the two cases. The seasonal average number of good analogues is a proxy for the probability of observing a circulation pattern and gives access to the usual character of a season. If this number decreases, then one can conclude that the circulation during that season becomes less typical, leading to the appearance of new patterns with no past analogues.

The intraseasonal and interannual analogues (or recurrences) are illustrated in Figure 1. They are linked through recurrence diagrams [19]. The intraseasonal analogue networks are related to thickness of the diagonal lines of recurrence diagrams, when one considers short-term recurrences. The interannual analogues are related to off-diagonal properties of recurrence diagrams, when one considers longer term recurrences. The distinction we make simplifies the visualization of the analyses, as the two timescales (intra-annual versus interannual) refer to two timescales of a complex system that pertain to different types of behavior.