The transitional seasons (spring and autumn) between winter and summer are typically short in duration and associated with abrupt change in general circulation over the Northern Hemisphere (Yeh et al., 1959; Bordoni and Schneider, 2008; Yao et al., 2026). As such, the extended-range prediction (or subseasonal-to-seasonal, S2S prediction) during the transitional seasons is particularly difficult due to the volatile background of large-scale circulation (Breeden et al., 2022). However, weather conditions during the transitional seasons can be disastrous, as evidenced by extreme events that swept the Northern Hemisphere during May–June 2023, such as the wildfires in Canada (Jain et al., 2024; Byrne et al., 2024; Fig. 1a and b), floods in Italy (https://www.eumetsat.int/european-state-climate-2023, last access: 8 September 2026; Fig. 1b), persistent precipitation in East Asia in late May (Gao and Gao, 2023; Fig. 1d), and heatwave in Northwest Europe in June (Berthou et al., 2024; Fig. 1e and f).

Previous studies have shown that these extreme events were associated with regional persistent anticyclones or blocking in the troposphere (contours in Fig. 1). Specifically, the Canadian blocking is suggested to enhance surface temperature and vapor pressure deficit while suppressing precipitation and soil moisture, thereby promoting severe Canadian wildfires (Barnes et al., 2025; Luo et al., 2025). The Ural ridge and associated East Asian trough are widely considered to lead southward cold-air transport, thereby favoring anomalous precipitation in East Asia (Tao, 1980; Diao et al., 2023). The European blocking contributed to the Northwest Europe heatwave via sustained subsidence and clear skies, further amplified by marine heatwave feedbacks (Berthou et al., 2024). Beyond these specific events, the dynamical linkages between blocking and heatwaves (Black et al., 2004; Bartusek et al., 2022; White et al., 2023), cold surges (Ding et al., 2008; Yao et al., 2023), and floods (Lau and Kim, 2012; Martius et al., 2013; Xu et al., 2023) have been revealed, but research has focused on specific regions and solstice seasons (for reviews, see Woollings et al., 2018; Lupo et al., 2021; Kautz et al., 2022; Wang et al., 2026). Therefore, understanding the dynamics and predictability of the persistent circulation anomalies during transitional seasons is not only scientifically challenging, but also societally pivotal. To address this issue, we present a study on the dynamical mechanisms and subseasonal predictability of three successive high-impact blocking events in May–June 2023, with special attention to their potential dynamical interconnections from a global perspective.

Atmospheric blocking represents one of the most prominent modes of low-frequency variability in the extratropical troposphere. Several theories have been proposed for the dynamical mechanisms of blocking. For example, Pelly and Hoskins (2003a) developed a wave-breaking theory, Luo et al. (2014) proposed a nonlinear multiscale interaction theory, and Nakamura and Huang (2018) introduced a local finite-amplitude wave activity framework. Comparative discussions of these theories can be found in Woollings et al. (2018) and Lupo (2021). From the perspective of wave propagation, blocking formation can be understood as the process by which a high-pressure ridge becomes quasi-stationary (Yeh et al., 1962). Using the nonlinear multiscale interaction model, Luo et al. (2019) and Zhang et al. (2025) investigated the movement features of high-pressure ridges throughout the life cycle of blocking. They found that when blocking is strong and the meridional potential vorticity gradient is weak, the system exhibits westward movement and slower decay. Furthermore, owing to the planetary-scale nature of blocking circulation (Cheung et al., 2013; Luo et al., 2014), the spatial scale of blocking has also been suggested as a potential impact factor of phase speed changes (Yeh et al., 1962). More recently, van Mourik et al. (2025) found that westward-moving blocks have larger size compared to eastward-moving blocks. The scale effect, which means that a larger spatial scale leads to enhanced westward propagation relative to the eastward zonal mean flow for a given disturbance amplitude (Hoskins et al., 1985), provides an intuitive explanation. Therefore, it is worthwhile to analyze the relationship between the day-to-day evolution of blocking amplitude and wavenumber and the associated changes in phase speed.

Another important aspect of the wave propagation perspective is its close connection to weather extremes. Using Fourier decomposition to derive the mid-latitude average Rossby wave phase speed, previous studies have revealed the linkage between low phase speeds and both extreme surface temperatures (Coumou et al., 2014; Kornhuber et al., 2019) and the occurrence of blocking (Riboldi et al., 2020). However, because blocking and most weather extremes are spatiotemporally localized phenomena, this inevitably raises the need for diagnostic methods capable of quantifying wave amplitudes and phase speeds with high spatiotemporal resolution. Recently, a Hilbert transform-based method has been developed to quantitatively diagnose local Rossby wave parameters (Fragkoulidis and Wirth, 2020; Li et al., 2025). This approach enables direct calculation of the time-mean as well as the day-to-day evolution of local phase speed, amplitude, and wavenumber throughout the life cycle of blocking, thereby unraveling the wave propagation characteristics and their links to surface extreme weather. In addition, the stationary wavenumber Ks provides a reference for the zonal scale at which Rossby waves tend to become quasi-stationary under a given background flow (Hoskins and Ambrizzi, 1993) and has recently been used in the studies of quasi-stationary waves (Fei and White, 2025; White and Mareshet Admasu, 2025). Therefore, comparing Ks with our diagnosed wavenumber could provide an additional perspective for understanding the propagating behavior of blocking system.

The subseasonal predictability of blocking remains a major challenge, with potential predictability typically within 2 weeks (Pelly and Hoskins, 2003b; Kautz et al., 2022). It is therefore of interest to evaluate the subseasonal forecast of the ECMWF S2S model for the blocking anticyclones during the transitional season of 2023, and to investigate how subseasonal forecast errors in blocking anticyclones are linked to errors in Rossby wave dynamics. In short, we aim in this study to investigate the dynamical linkages, Rossby wave parameters, and subseasonal predictability of three successive atmospheric blocking episodes in May–June 2023. The remainder of this study is organized as follows. Section 2 describes the data and methods. Section 3 presents observed phenomena from ERA5 Reanalysis and Rossby wave diagnostics, while Sect. 4 investigates the dynamic source of predictability in ECMWF S2S ensemble forecasts. Section 5 provides a summary and discussion.

It is interesting to check the capability of ensemble forecasts by ECMWF model in forecasting the blocking circulation in these three episodes. Figure 6a–c shows the forecasted temporal mean Z500 during each episode based on the 50 members. The subseasonal forecast results for these three episodes exhibit notable similar features. First, for each episode we note that very few members (usually less than 2) predict a negative anomaly (less than -1σ) with almost all of initialization dates (blue lines in Fig. 6d–f). Remarkably, for the forecasts initialized 15–19 d ahead of each episode, i.e. initialized at 13 April for episode 1 (Fig. 6d), initialized at 1 and 4 May for episode 2 (Fig. 6e), and initialized from 15 to 22 May for episode 3 (Fig. 6f), there are usually 40 %–65 % of the total 50 members (20–32 members) predicting a significant positive Z500 anomaly (larger than +1σ, red lines in Fig. 6d–f), and more than 80 % of the total member predicting a temporal mean Z500 above the climate mean (gray lines in Fig. 6d–f). The predictability drops for the forecasts made during the following week, but the number of correct-forecast members increases markedly and becomes dominant for initializations made 2–5 d ahead of each episode. In the following sections we try to understand the sources of predictability 2 weeks in advance for these three episodes, and examine how forecast errors relate to errors in Rossby wave dynamics.

Figure 7 compares the day-to-day evolutions in Z500, wave amplitude, and zonal wavenumber between the good-forecast and bad-forecast ensemble members' forecasts initialized approximately two weeks ahead for each episode. In each episode, the good members and bad members are defined as the 10 members with the strongest and weakest time- and spatially averaged Z500 over the blocking region, respectively. The initialization dates are 17 April (14 d lead) for episode 1, 4 May (16 d lead) for episode 2, and 22 May (15 d lead) for episode 3. For episode 1 (the blocking over Canada), even the good ensemble members predict a Z500 intensity of only about half the observed value (red line in Fig. 7a), with weaker growth in wave amplitude and scale (Fig. 7d and g). Among the three episodes, episode 2 (the quasi-stationary ridge over the Ural Mountains) shows the best forecast skill. The good ensemble members successfully capture both the intensity and duration of the Z500 anomaly seen in ERA5, and the amplification of wave amplitude and spatial scale after 18 May (Fig. 7e and h). In episode 3 (the blocking over Europe), although the good ensemble members predict the prolonged positive Z500 anomaly after 6 May, the forecasted peak of Z500 occurs noticeably earlier than in ERA5 (Fig. 7c). Similarly, forecasts of wave parameters in episode 3 show weaker amplification. Overall, forecasts of wave amplitude and scale perform more poorly than those of Z500, particularly in episodes 1 and 3. Interestingly, for the bad ensemble members, the forecasts of Z500 and wave parameters show a tendency to return toward their climatology (blue lines in Fig. 7), as also noted in Pelly and Hoskins (2003b).

To further elucidate the sources of subseasonal predictability for these three episodes beyond 2 weeks, we examine the ensemble-mean Z500 differences between the good and bad ensembles in the Hovmöller diagrams (Fig. 8). The three episodes display similar pattern, with pronounced differences emerging after approximately 10 d after initialization and showing a clear connection to upstream quasi-stationary troughs. For episode 1, the good ensemble not only predicts the quasi-stationary ridge over Canada but also capture the quasi-stationary trough over the North Pacific (Fig. 8a). For episodes 2 and 3, in addition to the quasi-stationary ridges over the Ural region and Europe, respectively, the good ensemble consistently predicts the presence of an upstream trough over the North Atlantic (60° W–0° E) (Fig. 8b and c). Moreover, the successful prediction of a strong trough downstream of the Ural blocking (Fig. 8b) explains why the prediction of the wave amplitudes and the spatial scales are better in episode 2. Across all three episodes, the troughs and ridges exhibit a clear downstream development, indicating that better prediction of the upstream wave precursors (i.e., quasi-stationary trough here) plays a crucial role. This is in line with the findings of Maddison et al. (2019), who showed that upstream cyclones are important for the predictability of blocking onset.

We further find from the WAF diagnostic (Fig. 9) that the good ensemble successfully forecasts planetary-scale Z500 anomalies and the associated WAF (Fig. 9a, c, and e) that closely resemble those in ERA5 (Fig. 3a, d, and g). For episode 2 and 3, the good ensemble also captures the downstream dispersion of wave energy following the collapse of the Canadian blocking, as well as the subsequent formation of planetary-scale trough-ridge patterns (Fig. 9c and e; also Fig. 8b and c). In contrast, the Rossby waves in the bad ensemble primarily propagated as synoptic-scale waves along the subtropical or mid-latitude jet, showing limited amplification into blocking pattern (Fig. 9b, d, and f). The bad ensemble even predicts an erroneous intensification of the Canadian ridge in episode 3.

These results indicate that the collapse of the exceptionally strong Canadian blocking and the subsequent shift to North Atlantic Oscillation-like regime (as shown in Fig. 9c and e) provide a window of opportunity for the longer than 2-week predictability of the Ural and European blockings. Indeed, in forecasts initialized on 17 April, ensemble members with a strong Canadian ridge in episode 1 (good ensemble) predict a stronger Ural ridge in late May after the collapse of the Canadian ridge, with a lead time exceeding 33 d (Fig. 10a). In contrast, ensemble members that miss the Canadian ridge (bad ensemble) also fail to predict the Ural ridge in episode 2 (Fig. 10b). Overall, we show that predictability beyond 2 weeks does exist for these three blocking episodes, and it depends on the better prediction of the upstream wave precursors and associated quasi-stationary Rossby wave energy propagation.

This study investigates the subseasonal dynamical processes and predictability associated with three consecutive large-scale blocking episodes over Canada and Eurasia during May–June 2023, using ERA5 reanalysis data, ECMWF S2S ensemble forecasts, and local wave parameter diagnostics. The main conclusions are as follows: 1.

The three blocking events are dynamically linked through the energy propagation of quasi-stationary Rossby waves. During episode 1 (1–19 May), wave activity flux originating from the North Pacific favors the maintenance of the Canadian blocking. Following the collapse of the Canadian blocking, the wave energy propagates downstream toward Europe and the Ural region, promoting the establishment and persistence of the ridges in episode 2 (20 May–5 June). In episode 3 (6–20 June), the quasi-stationary wave energy propagation over the North America–North Atlantic sector splits into branches that converge over Europe, thereby favoring the formation and maintenance of the European blocking.

The transition from small-amplitude transient synoptic-scale waves to large-amplitude quasi-stationary planetary-scale waves during blocking onset aligns with previous studies (Luo et al., 2014; Woollings et al., 2018). What distinguishes this work from prior research is the application of the Hilbert transform to quantitatively diagnose the local phase speed, amplitude, and wavenumber throughout the life cycle of blocking, thereby enabling a detailed analysis of the evolution of these wave parameters. Furthermore, we find that the evolution of wavenumber is also important for blocking movement (Yeh et al., 1962; van Mourik et al., 2025). Comparisons between k and Ks in these cases suggest that blocking generally moves westward during its onset with k < Ks, moves rapidly eastward after collapse with k > Ks, and maintains quasi-stationary or slow movement when k approaches Ks. However, cases with k < Ks but eastward movement can also occur after the collapse of blocking. In the future, this method could be extended to statistical analyses of the links between blocking-related wave parameters and surface weather extremes, as well as to quantitative evaluations of model performance.

While this study elucidates the dynamical linkages among the successive blocking events and their subseasonal predictability through the horizontal propagation of Rossby waves, the potential roles of vertical planetary wave propagation, stratospheric processes, and lower-boundary forcing remain unclear. Future research should also extend the analysis to a larger sample of blocking events across different seasons and regions to clarify whether and why wave amplitude and spatial scale fail to amplify sufficiently in blocking forecasts, thereby providing insight into the sources of model errors and pathways for improving prediction skill. While the subseasonal predictability beyond 2 weeks and the links between different blockings demonstrated in this study is encouraging, we also note that the predictability of ensemble forecasts may oscillate between leading-time of 15 and 5 d (Fig. 6d–f), which highlights the importance of supplementary diagnostic methods in understanding this phenomenon and in sorting out the better ensemble members (Mu and Duan, 2025).