1. Introduction
Atmospheric blocking is characterized by a quasistationary circulation that disrupts the usual eastward flow in mid- and high latitudes for a duration ranging from days to weeks. This disruption results in prolonged periods of anomalous regional weather patterns in precipitation and temperature (Rex 1950). It often leads to extreme weather phenomena which include prolonged heatwaves in summer (Pfahl and Wernli 2012) or cold and dry spells in winter (Buehler et al. 2011). As a blocking deviates the position of the storm tracks, it may also lead to unusual heavy precipitation and wind extremes in specific regions (Kautz et al. 2022). Overall, blocking has strong social and economic impacts, the severity of the extreme being often correlated with the persistence and recurrence of blocking events over a given period (Buehler et al. 2011; Woollings et al. 2018; Kautz et al. 2022).
Despite substantial improvements in numerical weather prediction (NWP) models since the 1990s, current forecast models still struggle to adequately predict blocking events at medium range (Matsueda et al. 2009) and subseasonal time scales (Quinting and Vitart 2019). The main difficulty relies more on predicting blocking onsets and decays rather than their maintenance (Hamill and Kiladis 2014; Ferranti et al. 2015; Quandt et al. 2017). Climate models also struggle to represent present-day blocking statistics accurately (Davini and D’Andrea 2016, 2020). Increasing the horizontal resolution improves the blocking forecast skills of NWP models (Quinting and Vitart 2019) as well as the blocking statistics in climate models (Matsueda 2009; Davini et al. 2017). However, the adequate representation of blocking events in the Euro-Atlantic sector remains a challenge; their predictability is weaker than in other regions (Hamill and Kiladis 2014), and their frequencies are still underestimated in high-resolution climate models (Davini and D’Andrea 2020). Reasons for these difficulties in representing blocking events in models may come from the misrepresented diabatic processes upstream of the blocks (Pfahl et al. 2015), which are probably partly related to misrepresented air–sea interactions over the western oceanic currents (Scaife et al. 2011; Athanasiadis et al. 2022). It also may come from misrepresented orographic drag (Pithan et al. 2016) or tropical convection, as underlined in the review paper of Kautz et al. (2022).
The existing research has highlighted two fundamental processes—dry and moist—that are important for blocking. There is a plethora of dry theories and mechanisms that have been proposed since the pioneering work of Charney and Devore (1979). Two types of waves are usually involved in those dry mechanisms: planetary and synoptic waves. Charney and Devore (1979) showed that the interaction between planetary-scale wave disturbances triggered by orography and the zonal-mean flow may lead to multiple stable equilibria, a zonal flow state, and a blocked state. However, such a theory does not take into account synoptic waves, which Reinhold and Pierrehumbert (1982) later demonstrated to be dynamically important by searching equilibria in a simple model including both planetary and synoptic, baroclinically unstable, waves.
One way to understand the effect of synoptic eddies is the eddy straining mechanism of Shutts (1983): Eddies traveling in a split jet stream, as found in some blocking situations, are stretched and feedback onto the blocking flow in such a way as to maintain it. In the 1980s and 1990s, many studies emphasized the maintenance of blocking systems by transient synoptic eddies (Trenberth 1986; Vautard et al. 1988). Another way of interpreting this positive synoptic eddy feedback onto the blocking is through the successive occurrence of synoptic wave breaking (Pelly and Hoskins 2003; Michel and Rivière 2011; Masato et al. 2012). More recently, synoptic eddy feedback has been interpreted in terms of vortex–vortex interactions between the blocking systems and transient eddies (Yamazaki and Itoh 2013). However, the role of transient eddies is not limited to a positive feedback mechanism and they may also participate in the transition between a blocking regime and other weather regimes (Reinhold and Pierrehumbert 1982; Reinhold and Yang 1993; Michel et al. 2012).
Finally, blocking formation can be seen as resulting from two types of dynamical precursors: one of which is planetary-scale low frequency (periods greater than a week) and may originate from the tropics (Renwick and Revell 1999; Parker et al. 2018) and the other being synoptic-scale high frequency (periods less than a week) and often associated with an upstream cyclone (Nakamura et al. 1997; Michel and Rivière 2011). The relative role of these two precursors varies from block to block, and one precursor may dominate over the other depending on the regions or seasons. In some cases, explosive synoptic-scale cyclogenesis is enough to trigger a blocking onset (Colucci 1985; Maddison et al. 2019).
More recently, Huang and Nakamura (2016) developed a new theoretical framework based on a local wave activity budget to study blocking. This framework is appealing as it provides a close budget for finite-amplitude waves in which blocking formation follows the same behavior as the traffic jam theory (Nakamura and Huang 2018). This is relevant to anticipate blocking statistics in various climates (Paradise et al. 2019) and to better understand blocking life cycles in reanalysis (Wang et al. 2021) and forecast ensembles (Polster and Wirth 2023).
While dry theories and mechanisms of atmospheric blocking are numerous, the literature on moist processes is more recent (Tilly et al. 2008; Croci-Maspoli and Davies 2009) and more limited. The main idea brought by several studies (Croci-Maspoli and Davies 2009; Pfahl et al. 2015; Steinfeld and Pfahl 2019; Maddison et al. 2020; Hauser et al. 2023) is that warm conveyor belts (WCBs), which correspond to air masses gaining moisture and heat in the boundary layer before being elevated downstream of surface cyclones in a region of strong latent heat release, play a key role in the formation of many blocking events. There are usually two arguments about how the diabatic heating affects the formation of the upper-level ridge in the WCB outflow: Not only strong latent heat release in WCBs allows an efficient cross-isentropic transport of low-potential vorticity (PV) air from low to upper levels but also the negative PV tendency produced above the heating maximum may help to reinforce the ridge building. In many situations, such a ridge building creates a large-scale persistent anticyclonic anomaly that forms a blocking anticyclone. Also, the heating may have an indirect effect on the ridge building as it reinforces the divergent flow at upper levels that helps to enlarge the blocking on its northwestern side (Grams et al. 2011; Steinfeld and Pfahl 2019; Hauser et al. 2023).
Pfahl et al. (2015) showed that the cross-isentropic transport of ascending air masses from the lower troposphere is as important as the isentropic advection of air masses from lower latitudes to bring low-PV air in the blocking anticyclonic anomalies. In the same vein, Steinfeld and Pfahl (2019) provided a more detailed climatology of blocking anticyclones and their relationship with the two origins of low-PV air. They revealed how moisture-driven processes, especially in oceanic areas, strongly impact blocking occurrences all year-round, while those over land change with the seasons and are notably reduced during winter in the Eurasian continent. Moreover, the study underlines that moist-diabatic processes are more important during blocking onsets and for higher-intensity and larger blocking systems. Then, Steinfeld et al. (2020) made sensitivity numerical experiments over several blocking cases using the Integrated Forecast System global weather prediction model. By turning off the temperature tendency associated with parameterized cloud and convection schemes in the WCBs upstream of the forming blocking anticyclones, the authors showed that the blocking anticyclones are less intense, smaller in size, and less persistent.
Following the previously cited studies, latent heating exerts an influence on all the characteristics of the blocking. However, the existing literature does not provide all the answers to the questions of the role of moist processes. For instance, can a model that includes only dry processes reproduce the life cycles of observed blocks? To answer that question, rather than artificially turning off the temperature tendency associated with latent heating, our strategy is to run a long-term simulation of a dry general circulation model by including an artificial forcing in such a way that the mean flow is close to the observations and the eddies are as energetic as in the observations. The objective will be then to compare the blocking statistics and characteristics in the long-term dry simulation with those in reanalysis data. One hypothesis could be that moisture is just a source of energy for the eddies, and as long as we get the right amplitude for the eddies, we get the right blocking characteristics. This leads us to refine the core question of the present paper: “Do moist processes induce unique characteristics of blocking life cycles, or do they simply inject extra energy into the waves?”
The same mixed Eulerian–Lagrangian tools as in Steinfeld and Pfahl (2019) will be used. First, the blocking detection algorithm of Schwierz et al. (2004) based on the detection and tracking of negative PV anomalies will provide a comprehensive view of the blocking life cycles. Second, backward Lagrangian trajectories from the blocking anticyclones will be computed to analyze the origins of the air masses in both reanalysis and dry simulation. The paper is structured as follows. Section 2 outlines the numerical model setup, the ERA5 reanalysis datasets, and the tools utilized. Section 3 is dedicated to the main results where a systematic comparison is made between the long-term model simulation and the ERA5. Section 3a presents the climatologies of the mean flow as well as high- and low-frequency eddy kinetic energies in the model and ERA5. An analysis of blocking frequencies in both datasets is made in section 3b. Then, the different blocking characteristics are analyzed: frequencies and persistence in section 3c, spatial structure and size in section 3d, and intensity in section 3e. Finally, conclusions are provided in section 4.
2. Data and methodology
a. Dry model
DYNAMICO is an icosahedral dynamical core model developed at Institut Pierre Simon Laplace (Dubos et al. 2015). It is hereafter used at a uniform horizontal resolution of about 200 km with 20 evenly spaced sigma vertical levels. Land–sea contrasts and orography are included. The friction is parameterized with a Rayleigh drag of 2 days over the oceans and 0.5 days over land as in Chang (2009). Small-scale dissipation is handled using Laplacian operators iterated twice for the divergent and rotational components of the wind and potential temperature. The associated damping time scales are set to 5000 s for all variables.
b. Reanalysis data
ERA5 reanalysis (Hersbach et al. 2020) of all winter months (December–February) from 1979 to 2020 at a 6-hourly time step is used. It corresponds to 3791 days and 15 164 time steps. ERA5 datasets are interpolated on the same horizontal and vertical grids as the model outputs: 1.268° × 2.5° in the horizontal and every 50 hPa in the vertical.
c. Tools
1) Blocking detection
The identification of blocking events is based on the algorithm of Schwierz et al. (2004) which looks for anticyclonic circulations in the upper troposphere. More precisely, it detects and tracks distinct and coherent upper-tropospheric negative PV anomalies satisfying the following criteria: (i) The PV anomaly is defined as a deviation from climatology, computed using monthly mean, and then temporally smoothed using a 2-day running mean filter; (ii) a vertical average of the PV anomaly is made between 500 and 150 hPa; (iii) an intensity threshold is applied to get significant anomalies [here a threshold of −1.3 potential vorticity units (PVU) (1 PVU = 10−6 K kg−1 m2 s−1) is retained]; (iv) a spatial overlap of the PV anomalies between two consecutive time steps is required (50% for 6-hourly datasets); and (v) only PV anomalies persisting more than 5 days are retained. The detected PV anomaly contours that meet all criteria are called persistent negative overlapping PV anomalies (OPVAs) and are referred to as blocking events in the present study as in Steinfeld and Pfahl (2019). Contours identified when the temporal persistence is set to 0 days, that is, when criterion v is suppressed, belong to a category called “all negative OPVAs.”
Different quantities characterizing the detected contours throughout its life cycle are also detected by the algorithm: The size (km2) is defined as the average area covered by the contour, the intensity (PVU) is measured by the spatial average of the PV anomaly within the detected contour, and the duration (days) is calculated as the number of time steps a unique contour is detected.
2) Lagrangian trajectories
Lagrangian trajectories are generated using the tool described in Rivière et al. (2021) and Wimmer et al. (2022). It uses the three wind components on the same grids for the dry model and ERA5. Three-day backward trajectories are initiated in the blocking region, i.e., at each grid point where the persistent negative PV anomaly is less than −1.3 PVU and from all upper levels ranging from 150 to 500 hPa. The computation of the trajectories is based on 6-hourly datasets, but the trajectory model uses a 30-min time step.
3. Results
a. Mean flow and eddy variance climatology
This section presents various climatologies in the simulation of the dry model and ERA5 reanalysis. Figures 1a and 1b first show the 500-hPa zonal wind climatologies of both datasets. The mean positions and spatial structures of the North Pacific, North Atlantic, and subtropical Asian jets are very similar in the dry model and ERA5. As shown by the black contours in Fig. 1b, there are some differences in their peak intensities. The North Pacific jet is more intense by 15%–20% in the dry model than in the ERA5. This is the opposite for the North Atlantic jet, which is stronger by about 10% in the ERA5 than in the dry model. Given that the dry model mean temperatures are close to the ERA5 winter temperatures by construction, this good agreement between the two datasets for the zonal wind climatologies is a consequence of thermal wind balance.
Winter climatologies (December–February) of (a),(b) 500-hPa zonal wind (shadings; m s−1) and (c),(d) standard deviations of high-frequency (shadings; m s−1) and low-frequency anomalies (red contours; interval: 1 m s−1 for values greater than 8 m s−1). (a),(c) ERA5 and (b),(d) dry model. The overlaying black contour in (b) is the zonal wind anomaly (dry model − ERA5; interval: 2 m s−1 for absolute values greater than 3 m s−1).
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
High- and low-frequency 500-hPa meridional wind variances, with periods less and more than 10 days, respectively, are shown in Figs. 1c and 1d. The separation between high and low frequencies is made by applying a 7-point Welch window with a 10-day cutoff period as in Rivière and Drouard (2015). High-frequency eddy variability represents storm-track eddy activity (Blackmon et al. 1977), which is important for low-frequency variability and for blocking events in particular, as discussed in the introduction. The location and intensity of the storm track in the dry model are comparable to the ERA5 in almost all regions. A noticeable difference appears, however, in the North Atlantic basin with a less intense storm track in the model of about 20% for the peak intensity. The low-frequency variance amplitudes are very similar in both datasets. Their peak locations are found downstream of the North Pacific and North Atlantic jets and their associated storm tracks. Some differences can be noticed like a more northward extension over Alaska and a more eastward extension over central Europe in ERA5.
To conclude, the mean flow and eddy variance characteristics are quite similar between the dry model and the ERA5. The dry model, which is forced and tuned to resemble the ERA5, is as good as state-of-the-art climate model simulations with full physics like CMIP6 simulations at representing the winter atmospheric circulation [cf. with Fig. 1 of Harvey et al. (2020) or Fig. S4 of Davini and D’Andrea (2020)].
b. Blocking climatology
Building upon the dry model’s capacity to reproduce the mean flow and eddy variances seen in the observations, we shift our focus on the climatology of blocking frequency as illustrated in Fig. 2. The ERA5 climatology map closely aligns with previous research on the climatology of winter blocking occurrences, in particular with Steinfeld and Pfahl (2019) who used the same algorithm (see Fig. 1a). Two distinct regions of high blocking frequency are observed, each of them displaying blocked day percentages over 10% over large areas. One is situated in the North Atlantic southeast of Greenland and another in the North Pacific southwest of Alaska (Fig. 2a). They both correspond to the exit regions of the climatological jet streams (black contours in Fig. 2a). Blocking events more likely form in the exit regions of the jet streams and the storm tracks because they are often triggered by high-amplitude synoptic waves and their breaking (Pelly and Hoskins 2003; Michel and Rivière 2011; Masato et al. 2012).
Climatology of blocking frequency (shadings; %) and the 500-hPa zonal wind (black contours; interval: 10 m s−1) for (a) ERA5 and (b) dry model. (c) Difference in blocking frequency (dry model − ERA5). Each grid cell on the map corresponds to the number of times it experiences blocking throughout the life cycle of the detected blocks, normalized by the total number of days of the dataset. The dashed orange boxes in (c) correspond to the NA and NP domains used for further analysis.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
Regions of most frequent blocking occurrence in the model are also located downstream of the Pacific and Atlantic storm tracks as in the ERA5 (Fig. 2b). Although the peak frequencies of the two datasets are collocated, the model consistently underestimates the occurrence of observed blocking events (Fig. 2c). These biases are larger in the Pacific than in the Atlantic. South of Alaska, about 6% of the days are blocked in the model, but this number rises to about 10% in the ERA5, which represents an underestimation of about 40% in that region. South of Greenland, the peak frequencies are about 8%–9% in the model and 12% in the ERA5, representing an underestimation of roughly 30%. This negative global bias of blocking frequency is also found when using an alternative blocking index, as the one based on the reversal of the geopotential height gradient (Davini and D’Andrea 2020) as shown in Fig. S1 in the online supplemental material.
Figure 3 presents four metrics comparing the dry model and ERA5 data, which helps to describe the main properties of blocking events. In Fig. 3a, the number of blocks is normalized by the length of each dataset and relative to the total number of blocks detected in ERA5. This comparison is made for the Northern Hemisphere (NH), North Atlantic (NA), and North Pacific (NP) regions, as defined in Fig. 2c. This is complementary to Fig. 2 which shows how often a specific location experiences blocking events over a period of time, while Fig. 3 provides an overview by counting each blocking event only once, regardless of its duration or recurrence. Overall, the comparison reveals that the dry model exhibits a reduction of 28%, 21%, and 36% in the number of blocks compared to the ERA5 in the NH, NA, and NP regions, respectively. These numbers are similar to those deduced from Fig. 2. This is because the mean blocking durations are similar, of order 8–9 days, in the dry model and in the ERA5 (Fig. 3b). Despite this overall similarity, we note a small difference in the NP, where the blocks are less persistent in the dry model than in the ERA5, a point that will be more deeply investigated in the following section.
Normalized bar charts of blocking mean characteristics in ERA5 (no hatching) and dry model (hatching): (a) blocking frequencies as calculated from the percentage of number of blocks relative to the number of days in each dataset (normalized by 17.8%), (b) intensity (normalized by −1.86 PVU), (c) duration (normalized by 9.6 days), and (d) size (normalized by 4 × 106 km2).
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
As is the case of blocking duration, the mean blocking intensity is roughly the same in the model and ERA5. It fluctuates around −1.7 and −1.8 PVU and does not display any obvious regional variation (Fig. 3c). The blocking size in the model is equal to 3.8 × 106 km2 which is only slightly larger than in the ERA5 (3.5 × 106 km2), but no obvious major differences appear.
To conclude, while the blocking frequencies are significantly reduced in the model, the mean blocking characteristics (duration, intensity, size) are surprisingly similar. Following Steinfeld et al. (2020), we were indeed expecting a reduction in the lifetime, intensity, and size of blocking events because of the absence of moisture processes in the dry model. It does not appear to be the case. The reasons for the differences in frequency while the other blocking characteristics remain similar at the same time are investigated hereafter.
c. Blocking frequency and persistence
To understand the smaller blocking frequency in the model, the persistent OPVA properties are compared with those of all OPVAs, i.e., including those that do not satisfy the persistence criterion (see section 2c). The removal of the persistence criterion leads to an increase in at least an order of magnitude in the number of detected negative OPVAs, both in the dry model and in the ERA5. However, since some of them have very small spatial scales, which are not associated with blocking dynamics, spatial filtering is applied (size greater than 5 × 105 km2) after the blocking detection. This spatial filter has a negligible effect on the persistent OPVAs or blocking frequency (cf. Figs. 3a and 4a). While the number of persistent OPVAs is smaller in the dry model than in the ERA5, it is the opposite for all negative OPVAs: Their frequency is larger in the model than in the ERA5 (Fig. 4b). This positive bias with respect to ERA5 is more pronounced in the North Pacific (43%) than in the North Atlantic (13%). Of course, by construction, the mean duration of all negative OPVAs is shorter than for blocking events. However, contrasting with the case of blocking events, there are larger differences between the dry model and the ERA5: Over the entire Northern Hemisphere, the mean duration of negative OPVAs in the dry model (0.9 days) is almost half that in the ERA5 (1.6 days). The difference is smaller in the North Atlantic (1.7 days in the ERA5 and 1.3 days in the dry model) but is larger in the North Pacific (1.9 days in the ERA5 and 1.0 days in the dry model).
(a) Same normalized bar chart of blocking frequency as in Fig. 3a but for negative OPVA with spatial size greater than 5 × 105 km2; (b) as in (a), but for all negative OPVA (persistence set to zero). Values are normalized to the maximum in each category: 17.2% for persistent negative OPVAs and 271% for all negative OPVAs. The percentage corresponds to the average number of negative OPVAs (persistent or all) per day.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
The spatial distribution of all negative OPVAs and persistent negative OPVAs at the time they reach their mature stage is provided in Fig. 5. For the persistent negative OPVAs, the peak frequencies align closely with those shown when including the blocking entire life cycle, albeit with a slight westward shift (cf. Fig. 2a with Fig. 5a and Fig. 2b with Fig. 5b). All negative OPVAs display a larger spatial coverage than the persistent negative OPVAs (cf. Fig. 5c with Fig. 5a and Fig. 5d with Fig. 5b). While persistent negative OPVAs are typically localized in the exit regions of the mean jets, negative OPVAs in general tend to be closer to the jet cores and more longitudinally distributed from the entrance to the exit regions of the jets. Since all negative OPVAs include both persistent and nonpersistent anomalies, these differences support the idea that nonpersistent negative OPVAs exist in more intense westerly flows than persistent ones.
Frequency of negative OPVAs at mature time step: (a),(b) with 5-day persistence and (c),(d) without temporal persistence. (a),(c) ERA5 and (b),(d) dry model.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
There are also interesting lessons to learn by comparing the amplitudes of spatial distributions of all negative OPVAs between the dry model and the ERA5. In the North Pacific, there is clearly an excess of short-lived negative OPVAs (see the discussion above) on the northern flank of the jet. This is likely due to the positive zonal wind biases shown in Fig. 1b. Indeed, a stronger background westerly flow advects the waves faster and prevents them from satisfying the overlapping criterion for a long duration. Such negative PV anomalies are less persistent as a result. Therefore, the smaller blocking frequency in the model in the North Pacific is likely due to the background flow being too strong in that region. In the North Atlantic, there is a strong negative bias of all negative OPVAs on the northern flank of the jet in the dry model compared to the ERA5. The zonal wind biases are small in that region (see Fig. 1b), but the high-frequency eddies are less intense (Figs. 1c,d), which is in agreement with the smaller frequencies of North Atlantic negative OPVAs in the dry model compared to the ERA5. As discussed in the introduction, synoptic eddies are known to be a key driver of blocking events. Such a bias in high-frequency eddy energy could thus explain why blocks are less frequent in that region in the dry model.
To conclude, differences in blocking frequency between the dry model and the ERA5 exist, but they tend to correlate with local biases of the background flow or synoptic eddy energy, which provide a simple and appealing explanation for the differences between the two datasets. In the North Pacific, negative PV anomalies are not persistent enough due to the positive bias of the zonal jet. In the North Atlantic, the storm track is too weak in the model to seed negative PV anomalies frequently enough.
d. Blocking structure and size
The blocking size is larger in the model than in the ERA5 by 10%–15% (Fig. 3d). This result holds over the whole life cycle, from the onset to decay phases (Fig. 6b). This moderate difference in blocking size could come from eddies being larger in the model than in the ERA5, as suggested by a simple spectral analysis (not shown). However, there is a large overlap between the block size distributions in the model and in the ERA5 and a large case-to-case variability in the evolution of blocking sizes. The normalized time tMax at which the maximum mean size is reached ranges between 0.3 and 0.4 for both datasets. Despite that similarity, there is a tail in the probability density function (PDF) up to tMax ∼ 0.8–0.9, which indicates that blocks tend to reach their maximum size later in their life cycle in the dry model than in the ERA5 (yellow curve in Fig. 6a).
(a) PDF of the normalized time at which the maximum size is reached and (b) mean evolution of block size as a function of normalized time: ERA5 (blue) and dry model (orange). The shaded regions correspond to the 20–80 percentiles.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
To further investigate the blocking spatial structures, centered composite maps are shown in Fig. 7 for the different phases of the blocking life cycle. These maps provide an Eulerian viewpoint of blocking structures in a 40° domain around the block’s center (see black star at 0°) for all the blocking events detected in the Northern Hemisphere and for each dataset. The spatial extent of the PV anomaly in the model is slightly bigger than in the ERA5, which confirms the earlier findings on size statistics.
Blocking-centered composite maps of upper-level (150–500 hPa) PV anomaly (shading; PVU), upper-level (500–150 hPa) PV (green contours; interval: 0.3 PVU), and mean SLP (brown contours; interval: 5 hPa) during (left) onset, (center) mature, and (right) decay phases. (top) The ERA5 and (bottom) the dry model.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
In both datasets, the intensity of the upstream surface cyclonic circulation peaks during blocking onset and diminishes during the mature and decay stages. At the onset stage, the upper-level positive PV anomaly is a bit stronger in the ERA5 than in the model, while the surface cyclone is slightly deeper in the model. The positions of the surface cyclones relative to the negative PV anomalies are similar in the two datasets: At the onset stage, they are located to the west, while at the mature stage, they are located more to the northwest. At the mature stage, the surface anticyclone is stronger in the model than in the ERA5, which might be due to the deeper and larger negative PV anomaly at upper levels. Interestingly, the structures of the blocks are slightly different between the two datasets: ERA5 blocks are more Ω shaped, while those in the model are more dipolar and southwest–northeast (i.e., anticyclonically) tilted (cf., for instance, the 2.1 PVU contour in Figs. 7b and 7e). This is consistent with Steinfeld and Pfahl (2019) who showed that blocks with the strongest latent heat contribution are more characterized by an Ω-shaped structure, while those with the weakest latent heat contribution are more characterized by a dipolar configuration and an anticyclonic tilt. This difference in the blocking structure between the ERA5 and the dry model could be related to the effect of moisture in wave breaking. Orlanski (2003) and Rivière and Orlanski (2007) showed that the presence of moisture reinforces cyclonic wave breaking to the detriment of anticyclonic wave breaking. This could help to understand why the cyclonic and anticyclonic tilts on the western and eastern sides of ERA5 blocks, respectively, are more symmetric, while those in the dry model have a more pronounced anticyclonic tilt on the eastern side.
As emphasized by Steinfeld and Pfahl (2019) and recalled in the introduction, latent heating processes have a direct and indirect effect on blocking. The direct effect is the net cross-isentropic transport of low-PV air mass from the lower troposphere to the upper troposphere. The indirect effect is associated with the stronger divergent winds on the western flank of the blocking ridge, due to the stronger ascending motion in the presence of latent heating, which tends to expand the blocking ridge further to the west. Such an effect is expected to be small in the dry model because latent heating is absent in the dry model and the Newtonian cooling forcing [Eq. (1)] does not compensate for this absence. This has been checked by decomposing the quasigeostrophic omega equation into dynamical and diabatic components. The diabatic component in the dry model due to the Newtonian cooling forcing is small upstream of the blocks compared to the dynamical component (Fig. S2), and the block onsets can be considered as quasiadiabatic. In ERA5, both components are equally important (Fig. S3).
To understand this relationship between the divergent wind and the blocking ridge, centered composite maps of PV advection by the divergent and rotational winds are shown in Fig. 8 and denoted as −υχ ⋅ ∇PV and −υψ ⋅ ∇PV, where υχ and υψ stand for the divergent and rotational winds, respectively. As expected from the absence of latent heating in the model, less intense upper-level divergent winds and negative PV advection are observed on the westward flanks of the blocks in the dry model than in the ERA5. The peak values of the PV advection by the divergent winds in the ERA5 are twice as large as in the model when all blocks in the Northern Hemisphere are taken into account (Figs. 8b,e). This difference is more pronounced in the North Atlantic than in the North Pacific (Fig. S4).
Blocking-centered composite maps of upper-level (150–500 hPa) PV advection by (a),(d) the total wind, (b),(e) the divergent wind, and (c),(f) the rotational wind (shadings; PVU day−1) during blocking onset. In (b) and (e), the arrows represent the divergent wind vectors (black arrows). In (c) and (f), the arrows represent the rotational wind vectors. The upper-level PV is shown in green contours (interval: 0.3 PVU). (top) The ERA5 and (bottom) the dry model.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
Since the dry model features weaker westward low-PV air advection by divergent winds on the western flanks of the blocks, we would expect them to move faster eastward and be less persistent in the dry model than in the ERA5. It is not what happens because the eastward PV advection by the rotational component of the wind is also smaller in the model (Figs. 8c,f) and compensates for the smaller westward PV advection by the divergent wind. The total PV advection is weaker in the dry model than in the ERA5 (Figs. 8a,d) because of the weaker eastward advection by the rotational component. To better compare the eastward propagation of the anomalies between the two datasets, it is worth dividing the PV advection terms by the zonal PV gradient as done in the supplemental material (Fig. S5). The conclusion is that the eastward propagation of the anomalies is comparable in the two datasets, but the contributions of the divergent and rotational winds are different. The approximate zonal phase speeds of block-centered composites are estimated at about 10 and 15 m s−1 for the ERA5, and about 10 and 17 m s−1 for the dry model, on the western and eastern sides of the block center, respectively (see Fig. S5). The PV advection analysis supports the findings of section 3c on blocking frequencies: An episode of slower eastward background flow is required to initiate a persistent blocking circulation in the dry model. This is particularly rare in the North Pacific where the climatological zonal flow was shown to be positively biased (Fig. 1b). In other words, to compensate for the weaker divergent winds, episodes of weak eastward flows are needed to initiate a block in the model which makes them less frequent compared to the ERA5.
e. Blocking intensity
As already noted above, the mean blocking intensity is larger by only a few percent in the model than in the ERA5 (Fig. 3c). Such a similarity holds over the entire blocking life cycle, which is very similar in the model and ERA5 (Fig. 9b). In both datasets (ERA5 and dry model), the intensification phase is faster than the decay phase and the peak intensity is reached slightly before the middle of the blocking life cycle. We note that some blocks reach their maximum intensity a bit later in the model than in the ERA5 like for the maximum size (Fig. 9a).
As in Fig. 6, but for the block intensity.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
However, despite these relatively small differences, the similarities of the blocking intensities and life cycles in the two datasets are both striking and surprising. Since the warm conveyor belts are more active in the ERA5 than in the model, we would expect more low-PV air transport from the low levels in the ERA5 and hence larger negative PV anomalies. To better understand the reasons for the similar intensities, backward Lagrangian trajectories were computed from the blocking regions at the onset stage and a Lagrangian PV budget was performed. In total, trajectories originating from 125 blocks in the North Atlantic and 125 blocks in the North Pacific were calculated, resulting in a total of about 1.5 × 105 trajectories for each dataset. Such a number of blocks has been chosen for computational cost reasons and because the results were found not very sensitive to that number.
Figure 10 shows the distribution of the potential temperature change Δθ along the 3-day trajectories. It is obtained by subtracting the potential temperature θ at the time of blocking onset (t = 0) from its value 3 days before (t = −3 days). In ERA5, the distribution exhibits a positively skewed pattern, indicating a prevalence of diabatically heated trajectories during blocking onset. This positive skew disappears when looking at the equivalent potential temperature distribution, which confirms the primary role of latent heating in such a skew. Conversely, the distribution of Δθ in the dry model is symmetrically centered around zero. The difference with Fig. 3 of Steinfeld and Pfahl (2019) is that they show the maximum change in θ while we show the mean change. However, similar to Pfahl et al. (2015) and Steinfeld and Pfahl (2019), we define heated trajectories as those having Δθ greater than 2 K. According to that definition, about 63% (34%) of all the trajectories are classified as heated trajectories in the ERA5 (the dry model). The sole existence of such heated trajectories in the dry model might seem surprising at first glance because of the absence of moist processes in that case. They are due to the presence of the forcing term on the rhs term of Eq. (1). Because of that term, air parcels may undergo rapid changes in potential temperature if the temperature is far from the restoration temperature, which explains the existence of a significant amount of heated trajectories in the dry model.
PDF of the change in potential temperature θ and equivalent potential temperature θe (K) between t = −3 days and t = 0 day along backward trajectories reaching the blocking onset region at t = 0: θ and θe in the ERA5 are shown in blue and dark blue lines, respectively, and θ in the model is in orange.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
Figure 11 shows the spatial distribution of the trajectories 3 days before blocking onset to better understand the origins of the air masses entering the blocking regions. Many ERA5 air parcels originate from levels lower than 800 hPa, while such trajectories barely exist in the dry model. More quantitatively, 68% of the trajectories originate from the atmospheric upper levels (pressure smaller than 500 hPa) and only 32% originate from the lower levels (pressure larger than 500 hPa) in the model. These starting points are more evenly distributed over the atmosphere vertical extent in the ERA5 (54% from the upper levels and 46% from the lower levels). The upper-level trajectories’ starting points are located over continental regions. Lower-level trajectories essentially originate from the atmospheric boundary layer over the western oceanic currents (see Figs. 11a,b where contours and shadings overlap). This is in agreement with the well-established influence of ocean–atmosphere heat exchange processes in this area on synoptic systems (Aemisegger and Papritz 2018; Wernli and Schwierz 2006) and on the formation of blocking further downstream (Scaife et al. 2011; Athanasiadis et al. 2022). By contrast, in the dry model, there is a minority of trajectories coming from the lower troposphere over the oceans. Most of the air parcels originate from the upper troposphere over the continental regions (see Figs. 11c,d). Finally, there is an interesting difference between North Atlantic and North Pacific blocking events that is common to both datasets. Some of the air parcels entering North Atlantic blocking areas originate from the lower levels in the North Pacific. They may thus have undergone diabatic ascents associated with the North Pacific storm track before traveling over North America toward North Atlantic blocks. Similar trajectories (i.e., originating from the North Atlantic) do not exist for North Pacific blocks.
Origin of air parcels 3 days before the blocking onset that ends up in the negative OPVA at the blocking onset for (a),(b) the ERA5 and (c),(d) the dry model. Two domains are considered (see dashed orange boxes): (a),(c) NA and (b),(d) NP. The pressure values averaged over all trajectories located at the same grid point are shown in shadings. Contour lines mark regions inside which 50% and 25% of the trajectories are located 3 days before the blocking onset.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
To better illustrate the characteristics of the different air parcels entering the blocking region, the time evolutions of the potential temperature and latitude are shown in Fig. 12. The mean potential temperature evolution of all ERA5 trajectories shows an increase of about 5–6 K (solid black line in Fig. 12a), which mainly occurs during the final day preceding the blocking onset, i.e., between t = −1 day and t = 0 day. This increase is due to trajectories originating from lower levels, likely experiencing strong latent heat release within WCBs, and resulting in a mean increase in potential temperature of about +10 K (solid red line). ERA5 trajectories coming from upper levels undergo a slight decrease in the potential temperature of a few kelvins, probably due to radiative cooling (solid blue line). In sharp contrast, the potential temperature evolution is relatively flat in the dry model, regardless of the pressure levels the trajectories originate from (dashed lines). In both datasets, air parcels originating from lower levels are coming from low latitudes of about 35°N at t = −3 days, while those coming from upper levels are already embedded in the midlatitude waveguide disturbances and originate from 45°N. Some slight differences between the ERA5 and the dry model can be noticed, with the lower (upper) trajectories originating further south (north) in the ERA5 than in the model.
Temporal evolution of (a) mean potential temperature and (b) mean latitude for 3-day backward trajectories initiated within the blocking region at the time of blocking onset. The black line represents the mean backward evolution (solid) and dry model (dashed). The blue lines represent mean values for trajectories originating from upper levels, and the red lines represent mean values for trajectories originating from lower levels.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
This analysis highlights the distinctive characteristics of the air parcels involved in the genesis of blocking anticyclones between the ERA5 and the dry model. Trajectories originate from not only different geographical locations but also distinct pressure levels and feature very different time evolutions of their potential temperature. These differences can be linked to the different processes at play in the ERA5 and dry model but also challenge our understanding of the similarity in blocking intensities in the two datasets discussed above. The reasons for such a similarity are further investigated below by performing a Lagrangian PV anomaly budget.
Temporal evolution of (a) mean PV anomaly PV and (b) PV climatology PVC and total PV for all the backward trajectories initiated within the blocking region at the time of blocking onset. Temporal evolution of (c) differences between the dry model and the ERA5 in PV anomaly δPVA, PV δPV, and PV climatology δPVC averaged over all trajectories. (d) As in (a), but separating the trajectories into those originating from upper levels (blue) and those originating from lower levels (red) at t = −3 days.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
At t = −3 days, δPVA is slightly negative (near −0.1 PVU; Fig. 13c) as more trajectories in the dry model than in the ERA5 are located in regions featuring negative PV anomalies (Fig. 13a). The term δPVA stays constant until t = −2 days before decreasing down to −0.2 PVU at t = −1 day. This decrease is mainly due to a change in δPVC over the same time interval (see the dotted curve in Fig. 13c or the change in the relative distance between the brown curves in Fig. 13b). The separation between upper and lower trajectories shows that it mainly comes from upper trajectories (blue dotted curve in Fig. 13d). It corresponds to a more efficient air transport from low latitudes in the dry model between t = −2 days and t = −1 day as seen from the more rapid poleward displacement of the upper-level trajectories in the dry model (blue curves in Fig. 12b). As a result, the dry model upper-level trajectories cross more climatological PV isosurfaces.
Between t = −1 day and t = 0 day, δPVA abruptly increases from −0.2 to +0.2 PVU. This is due to both an increase in δPV and a decrease in δPVC (Fig. 13c). The separation between upper- and lower-level trajectories shows that the increase in δPV can be attributed to upper-level trajectories (blue dashed curve in Fig. 13d), while the decrease in δPVC is due to lower-level trajectories (red dotted curve in Fig. 13d). The increase in δPV for the upper trajectories is associated with a rapid decrease in PV in the ERA5, while it is much less in the dry model (Fig. 13b). In ERA5, upper-level trajectories undergo a rapid decrease in PV when they travel between the strong latent heat release of the WCBs and radiative cooling aloft. This is a direct effect of the presence of moisture in ERA5 that is visible in the upper-level trajectories and not in the lower trajectories, an aspect that has not been emphasized by previous studies. The decrease in δPVC for the lower-level trajectories is due to more efficient crossing of the PV climatology isosurfaces by ERA5 trajectories as they strongly ascend within the WCB outflow region.
To conclude, the trajectories in the dry model and ERA5 exhibit distinct airmass evolution processes. In addition to Fig. 13, these differences can also be illustrated by the mean lower- and upper-level trajectories in both samples (see Fig. 14). Upper-level trajectories of the dry model more efficiently transport low climatological PV air from lower to higher latitudes than those of ERA5, and such upper-level trajectories are more numerous in the dry model than in the ERA5 (see the longer latitudinal displacement of the upper-level trajectories in the dry model than in the ERA5 in Fig. 14, in particular between t = −2 days and t = −1 day). Such a more efficient and more important low-PV air transport from lower latitudes at upper levels in the dry model compensates for two diabatic effects in the ERA5: One is the diabatic decrease in PV undergone by upper-level trajectories as they travel above the WCB outflow region, and the other is the stronger ascending motion of the lower-level trajectories which more efficiently and more importantly transport low-PV air from lower levels (see the longer upward displacement of the lower-level trajectories in the ERA5 than in the dry model in Fig. 14, in particular between t = −1 day and t = 0 day). While the stronger ascending motion effect has been emphasized by Pfahl et al. (2015) and Steinfeld and Pfahl (2019), the diabatic decrease in PV undergone by upper-level air masses constitutes an original aspect of our results that contributes to a more detailed understanding of the physical processes at work in the genesis of blocking events in the ERA5.1
Mean time evolution of trajectories coming from upper (blue) and lower (red) levels at t = −3 days across pressure and latitude for (a) the ERA5 and (b) the dry model. Markers indicate means of the trajectories at specific time steps with circles at −1 day, triangles at −2 days, and squares at −3 days. The green contours represent the PV climatology (PVU).
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
4. Conclusions
The study presents a comprehensive comparison of climatological characteristics and processes of Northern Hemisphere winter blocking events between ERA5 reanalysis and a dry GCM configured to closely match the background mean flow and wave energy of ERA5.
The dry model forcing is built following the iterative procedure of Chang (2006, 2009) which leads to a good agreement between the model and the reanalysis dataset in terms of their mean flow and eddy energy. The main conclusion is not only that the model shows a moderate underestimation of blocking frequencies of about one-third compared to the ERA5 over the entire Northern Hemisphere, but also that the mean characteristics of the blocks, such as duration, intensity, and size, remain similar to those of ERA5 blocks. More detailed conclusions are hereafter provided.
Despite the generally good agreement between the dry model and the ERA5 in terms of mean flow and eddy energy, the underestimation of blocking frequencies is partly related to regional biases in those two quantities. In the North Pacific, the westerly flow is positively biased, and the negative PV anomalies are less persistent than in the ERA5 and less likely to form a blocking event. At the entrance of the North Atlantic, the storm track is weaker than in the ERA5 and could explain the slight underestimation of blocking frequencies in the North Atlantic. However, there is an additional argument to explain the less frequent blocks in the model. Since the divergent flow is weaker in the warm conveyor belt outflow region of the dry model because of the absence of heat release, the westward PV advection by divergent winds that counteracts the eastward advection by the mean westerly flow as emphasized in Steinfeld and Pfahl (2019) is weaker in the dry model. To compensate for the lack of westward expansion due to weaker divergent winds, blocking events in the dry model are formed during episodes of weaker westerly flow compared to the ERA5. This results in less frequent favorable conditions for the formation of blocking events in the dry model, particularly in the North Pacific region where the westerly flow is positively biased.
The mean blocking size in the dry model is slightly larger than those in the ERA5 over the whole blocking life cycle, but a large variability in the blocking sizes exists in both datasets. Interesting differences appear between the two datasets in the blocking spatial structures. Blocks in the ERA5 are more Ω shaped, while those in the dry model are more dipole shaped and more marked by an anticyclonic wave breaking. Such a difference is schematically represented in Fig. 15 (see magenta PV isolines). This difference can be explained by the fact that cyclonic wave breaking is favored in the presence of moisture (Orlanski 2003; Rivière and Orlanski 2007).
Three-dimensional schematic representing the main air masses entering the blocking ridge at the blocking onset for (a) reanalysis and (b) dry model. Air parcels originating from upper and lower levels are in blue and red arrows, respectively. The width of the arrows is proportional to the percentage represented by the corresponding air parcels. The block is represented by one PV isoline in the upper troposphere (gray), the surface cyclone in magenta, and the cold and warm fronts by the blue and red lines in the lower troposphere. The mean temperature in the lower troposphere is represented with orange, green, and blue shadings. A zonal-mean perspective is provided on the right side of each panel where it shows the climatological PV (solid contours) and isentropes (dashed contours) in addition to the two air masses.
Citation: Journal of the Atmospheric Sciences 82, 2; 10.1175/JAS-D-24-0048.1
Blocking intensities in the ERA5 and dry model are almost equal regardless of the stage of the blocking life cycle that is being considered. Since the intensity is defined as the strength of the PV anomalies, a Lagrangian approach was found suitable to investigate the blocking intensities. Large differences between the two datasets appear in the origins of the air parcels entering the blocking anticyclones during their formation. In ERA5, there are two preferential areas of origin of air parcels with equal importance: air parcels coming from the boundary layer above the western oceanic currents which ascend in warm conveyor belts and air parcels coming from the continental regions and the upper troposphere (see blue and red arrows of similar width in Fig. 15a). In the dry model, a majority of the trajectories come from upper levels and the continental regions 3 days before the blocking onset, while a minority come from lower levels and mainly above the boundary layer (see the thick blue and thin red arrows in Fig. 15b). Despite these large differences, the strengths of the PV anomalies at the blocking onset are similar. The dry model is slightly more efficient in transporting low-PV air from lower to upper latitudes than the ERA5. Additionally, its poleward transport of low-PV air being more intense than its upward transport, the dry model tends to favor air masses coming from upper levels. This more important and more efficient poleward transport is enough to compensate for the stronger cross-isentropic transport of low-PV air from lower altitudes and the diabatic decrease in PV undergone by upper-level trajectories in the ERA5 when they travel in the WCB outflow region.
What lessons can we learn from the above results? First, it confirms that blocking statistics are largely dependent on mean flow and synoptic eddy properties and that blocking frequency biases in climate models are closely related to biases in mean flow and synoptic eddy energy as underlined in previous studies (Scaife et al. 2010; Vial and Osborn 2012; Davini et al. 2017). Second, despite the different processes at play in the ERA5 and dry model, there are no major blocking characteristics or subcategories of blocks that cannot be reproduced by dry processes, except maybe the slight structural differences underlined in the centered composite maps (i.e., more Ω shape with moist processes and more dipolar shape with dry processes). These results do not contradict the recent studies of Steinfeld and Pfahl (2019) and Steinfeld et al. (2020) who showed that the presence of moisture increases the intensity, size, and duration of the blocks. The numerical strategy of Steinfeld et al. (2020) was to artificially turn off the temperature tendency associated with latent heating upstream of the blocking anticyclones and as such suppress a source of energy for the upstream eddies. In the present case, an artificial source of energy for the eddies is provided via the forcing of the dry model. These are the main reasons why the two numerical strategies are not directly comparable and should be thought of as complementary to better understand moisture effects on blocking. Our main conclusion is that, once eddies are artificially set to a realistic amplitude, and the mean flow is realistic too, blocks are largely similar to the observations, even with the sole effects of dry processes.
Differences between the ERA5 and the dry model may have various origins (horizontal resolution, air–sea interactions, orographic drag) in addition to the moisture effects discussed in the present paper. Despite the effort made to compensate for such differences by making the large-scale flow and eddy properties similar, it would be appropriate in future studies to compare long-term dry and moist simulations using the same dynamical core and the same resolution to better separate the differences.
Acknowledgments.
This project is part of EDIPI, which has received funding from the European Union’s Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant 956396. This work was granted access to the HPC resources of IDRIS under the allocation 2023-AD010113024R2 made by GENCI.
Data availability statement.
The ConTrack blocking detection algorithm used in the present study is made available at https://github.com/steidani/ConTrack. The Lagrangian trajectory algorithm was further developed and modified by us and is now available at https://github.com/Vinita-D/LagranTraj.
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