Interaction between Atlantic cyclones and Eurasian atmospheric blocking drives warm extremes in the high Arctic

Abstract. Atmospheric blocking can influence Arctic weather by diverting the mean westerly flow polewards, bringing warm, moist air to high latitudes. Recent studies have shown that diabatic heating processes in the ascending warm conveyor belt branch of extratropical cyclones are relevant to blocking dynamics. This leads to the question of the extent to which diabatic heating associated with midlatitude cyclones may influence high-latitude blocking and drive Arctic warm events. In this study we investigate the dynamics behind 50 extreme warm events of wintertime high Arctic temperature anomalies. Classifying the warm events based on blocking occurrence within three selected sectors, we find that 30 of these events are associated with a block over the Urals, featuring negative upper-level PV anomalies over central Siberia north of the Ural Mountains. Lagrangian back-trajectory calculations show that almost 60 % of the air parcels making up these negative PV anomalies experience lifting and diabatic heating (median 11 K) in the six days prior to the block. Further, almost 70 % of the heated trajectories undergo maximum heating in a compact region of the midlatitude North Atlantic, temporally taking place between six and one days before arriving in the blocking region. We also find anomalously high cyclone activity (on average five cyclones within this five-day heating window) within a sector northwest of the main heating domain. In addition, 10 of the 50 warm events are associated with blocking over Scandinavia; the contribution of diabatic heating to these blocks is again around 60 % for six-day back-trajectories, of which 60 % undergo maximum heating over the North Atlantic but generally closer to the time of arrival in the block and further upstream relative to heated trajectories associated with Ural blocking. This study highlights the role of diabatic heating in high-latitude blocking dynamics and the importance of the interaction between midlatitude cyclones and Eurasian blocking as driver for Arctic warm extremes.



Introduction
The positive trend observed in global-mean surface temperatures is unequally distributed, with greater and more rapid surface 20 warming seen over the Northern Hemisphere high latitude regions. This phenomenon, specifically observed in winter during recent decades, is known as Arctic amplification (e.g., Serreze and Barry, 2011;Cohen et al., 2014). As a result, dramatic VAPV anomaly (shading) overlaid with SLP anomalies (hPa, black contours every 10 hPa, negative values dashed, zero contour not shown), total column water (5 kg m −2 isoline, green solid) and VAPV anomaly (-1.3 pvu, cyan dashed). Dotted areas show the identified blocking regions and the black line and the magenta box indicate the location of the cross-section in (a) and the Ural sector, respectively.
It is worth mentioning that the four most extreme events (January 2006, March 1992, November 2016and January 2000 are well distinguished from the other extremes, obtaining T2m anomalies greater than 10 K. A detailed overview of the 50 warm extreme events is presented in Sect. 4.

Blocking identification
Quasi-stationary atmospheric blocks are identified using a PV-index method, which is based on upper-level (150-500 hPa) 125 negative vertically averaged PV anomalies, following the algorithm by Schwierz et al. (2004). The 6-hourly vertically averaged PV (hereafter VAPV) anomaly fields, computed with respect to the monthly climatology and temporally smoothed using a 2-day running-mean filter, are used as input data for the blocking index calculations. This dynamically-based method cap- tures the core of the PV anomaly located in the upper troposphere, enabling a more comprehensive analysis of its dynamical characteristics, lifetime, maintenance and evolution.

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A temporal and spatial overlapping criterion is used to find each blocking life-cycle. Here, at each time step, blocking masks are determined from the VAPV field where it falls below a threshold value of -1.3 pvu (1 pvu = potential vorticity unit = 10 −6 m 2 s −1 K kg −1 ), which is based on previous studies (e.g., Croci-Maspoli et al., 2007;Pfahl et al., 2015;Steinfeld and Pfahl, 2019;Lenggenhager and Martius, 2020). Then, these masks are connected in time if at two consecutive time steps they overlap by at least 70 %. We then identify a block if the temporally connected masks persist for at least 5 days. Applying the 135 blocking algorithm for the whole study time period results in fields indicating the presence of a block at each grid point and 6-hourly timestep and its unique identification number .
Additionally, the life stage of each individual blocking life cycle is quantified by the D-index. This index attains values between 0 and 1, and is defined as follows: D-index = Time since blocking onset Total blocking duration .
(1) 140 Figure 1 illustrates the blocking identification method applied to event 9, where the black box in Fig. 1a highlights the identified upper-level blocking region in which the above-mentioned criteria are fulfilled. Within this box, the elevated tropopause coincides with positive and negative geopotential height and PV anomalies, respectively. The block north of the Ural mountains in Fig. 1b has a northwestward tilt relative to the region of positive sea-level pressure (SLP) anomalies observed at the surface, and it is accompanied by a northward flow of moist air to the west of the block.

Trajectory calculation
To further quantify the importance of different processes leading up to the identified blocks, we compute 10-day threedimensional kinematic back-trajectories using the Lagrangian Analysis Tool (LAGRANTO; Sprenger and Wernli, 2015). LA-GRANTO calculates trajectories x(t) using three-dimensional wind fields on reanalysis model levels and a 30 minute computational time step. Trajectory starting positions are selected based on the blocking mask, re-gridded to match the same horizontal 150 resolution as the reanalysis data. More specifically, trajectories are initialized at every grid point within the blocking mask, equally at every 80 km × 80 km grid, every 50 hPa from 500 to 150 hPa. Starting times are daily at 12 UTC. For the analysis, however, blocking preceding a warm event is being represented by one specified day within the narrow −3 to −1 day window before each warm event, as will be explained in Sect. 4. Only starting points with < 1 pvu are used in the interest of studying tropospheric air. Additionally, various quantities are traced along each trajectory, such as PV, θ, PV anomaly (here calculated 155 with respect to the 10-d running-mean climatology) and specific humidity (Q).
D e c -0 6 D e c -1 3 D e c -2 0 D e c -2 7 J a n -0 3 J a n -1 0 J a n -1 7 J a n -2 4 J a n -3 1 F e b -0 7 F e b -1 4 to the right of each event-line. The magenta and cyan horizontal thin lines mark the 90 th percentile thresholds of the daily blocking fractions and the lifetime of two blocks are indicated by magenta and cyan shading for Ural and Scandinavian blocks, respectively. The timings of the maximum blocking fraction within three (corresponding to the time of trajectory initialization) and six days prior to each event are shown by hatched and solid circles, respectively, where light blue circles refer to event 28, light purple markers to event 9 and magenta markers to event 1. The x-ticks are shown at 1200 UTC.

Cyclone tracking method
Cyclone tracks are calculated using the algorithm developed by Murray and Simmonds (1991). Tracking is done on mean sea-level pressure data (MSLP) north of 30 • N. Same instruction parameters as listed in Table 1 in the study by Uotila et al. (2009)  and 1, occurring on the 8 th , 17 th and 24 th and attaining a high-Arctic averaged T2m anomaly of 8, 9 and 12 K respectively (see Fig. 2). It is clear that though they are classified as individual events, the three peaks are actually local maxima within a 170 constantly increasing temperature anomaly until reaching the most extreme event. The analysis below suggests that they could also be thought of as sub-events in a single, persistent warm extreme supported by two separate blocking events that manifest in two different sectors, one near the Ural mountains and another over Scandinavia; these sectors are further discussed in Sect. 4.

Synoptic situation
On 3 January (Fig. 3a), a ridge (high θ 2pvu values) extends over the North Atlantic and further eastward. An upper-level block 175 is identified northwest of the United Kingdom (dotted shaded region). Two days later (Fig. 3d), the upper-level block has moved northeastwards and now extends over Scandinavia. Meridional flow in the North Atlantic prevails, bringing warm and moist air northwards driven by the dipole in the SLP field. Two days later (lag = −1 day, Fig. 3g), the block maintains its position over Scandinavia and the moist and warm air continues to penetrate deeper into the Arctic. The peak in blocking fraction in the Scandinavian sector ( Fig. 2) occurs at the same time. At the peak of the warm event (Fig. 3j), the block is still located over 180 Scandinavia and steers the flow northwards, but is then slowly decaying (see Fig. 2) and moving southwards (not shown).
Three days after the first peak, on 12 January, a new event begins (Fig. 3b). The Scandinavian block is replaced by a lowpressure system, the remaining block (dotted region over Poland) directs the flow around the Urals and enters into the Arctic over the Barents and Kara Seas. However, two days later (Fig. 3e) the high over the Urals is strengthened and a low-pressure center is formed east of Greenland. At this time there is no substantial blocking identified (Fig. 2). The meridional flow 185 strengthens as a consequence of the stronger dipole over the North Atlantic, favouring deep penetration of warm and moist air into the high Arctic at lag −1 day (Fig. 3h). Note that a new block is identified over the Arctic Ocean northeast of Scandinavia (dotted area, the Ural sector is shown in magenta). The upper-level block tilts northwestward from the surface high pressure over the Urals and northern Siberia (see also Fig. 1 and discussion in Sect. 2.2). The block expands eastwards, covering large parts of the Ural sector at the day of the warm event ( Fig. 3k and Fig. 2) and the northwestward tilt remains. A strong positive 190 response in the temperature anomaly is also seen to the north/northwest of the block and a negative one to the south/southeast of the block (Fig. 3n), resembling the WACE pattern.
The next event occurs one week after the second temperature anomaly peak, also influenced by the same established Ural block. The peak in the Ural sector fraction reaches its maximum value five days prior to the warmest event (see Fig. 2), after which the Ural sector fraction decreases such that three days prior to event 1 a Eurasian block is no longer detected (Fig. 3f).

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However, the northward advection of warm and moist air continues with the main pathway east of Greenland (Fig. 3c, f, i). After this period of increased blocking activity over Eurasia, the temperature anomaly decreases (see Fig. 2) as the flow becomes more zonal (not shown).
3.2 Linkage between Atlantic cyclones and blocks over Eurasia associated with the three warm events in January

2006
To explore whether there is a link between the identified blocks and cyclones, we present three sets of back-trajectories ( Fig. 4) initialized from the two identified Eurasian blocks: the Scandinavian block one day prior to event 28 (first column), and from 205 the Ural block influencing both of the last two events; one day prior to event 9 (second column) and three days before event 1 (last column), times identical with the synoptic situation presented previously in Fig Only 2 % of all heated trajectories experience their maximum heating (green density contours) already at this stage, mainly in 215 the vicinity of cyclones over the eastern Pacific and southwestern North Atlantic. The air parcels experience maximum heating at various times during their journey into the blocking region, though with a peak (13 % of all heated trajectories) over the North Atlantic 3.5 days prior to arrival in the block (Fig. 4d). A few of the back-trajectories that pass over the Mediterranean get heated and lifted one day later (not shown). After the maximum, all blocking trajectories reside in the upper troposphere for several days before reaching the block (Fig. 4a).

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The remaining panels show back-trajectories from the same short-lived (persisting for only six days) Ural block, initialized at different life-stages of the block with respect to the peak of event 9 and 1. As for the event 28, most of the heated trajectories initialized at the onset stage of the Ural block ( Fig. 4b), eight days prior to event 1, reside around or south of 40 • N in the northern part of the subtropical high over the ocean six-days prior to arrival into the block (Fig. 4h). Also here, a small fraction of the computed trajectories experience their maximum heating at this early stage, mainly over the eastern Pacific. However, 225 the majority of the maximum heating occurs within the North Atlantic at different times from four days before arrival, with a peak (15 % of all heated trajectories) observed 2.5 days prior to arrival into the blocking region (Fig. 4e). The trajectories follow a fairly coherent path and move quickly once they reach the upper troposphere. Again, the lifting occurs primarily in the vicinity of a mid-latitude cyclone, located northwest of the center of maximum heating.
In contrast, capturing only 5 % of heated trajectories initialized from the decaying stage of this Ural block three days prior 230 to event 1 (Fig. 4c), the time window where the maximum heating within the North Atlantic occurs is narrowed to the first two days from the end points of the trajectories. Already 15 % of all trajectories experience heating over the North Atlantic six-days prior to arrival ( Fig. 4i) and 21 % a few days later (maximum peak at lag −4.25 day, Fig. 4f), after which all trajectories again reside in the upper-troposphere for several days before arriving in the block. Again, we observe a cyclone located to the north of the region of maximum heating (Fig. 4f, i), which in fact is the same cyclone contributing to the late lifting in Fig. 4e, though 235 at different times and spatial locations. This suggests that a substantial portion of the lifting for these Ural blocking trajectories is accomplished by just one cyclone in the North Atlantic. The observed negative correlation between blocking life-stage and the timing of maximum heating over the North Atlantic-i.e. younger blocks experience maximum heating at later timeswill be discussed more generally in Sect. 5.
In summary, we showed in this case study that two significant blocks, one over Scandinavia and one over the Urals, con-240 tributed to three close-in-time warm extreme events in January 2006, the latter of which is the most extreme in the entire observational record. Additionally, a large fraction of six-day back-trajectories traced from the blocks experienced heating, in agreement with Pfahl et al. (2015) and Steinfeld and Pfahl (2019). We also saw that the majority of the heating and lifting is accomplished by a small number of cyclones in the North Atlantic. Arctic warm extreme events introduced in Sect. 2.1. We address that question in this section. We start by examining the 50 events collectively and assess whether or not they were preceded by significant blocking, and then proceed to classify the events by the type of blocking observed. Additionally, we discuss events that are temporally close to each other and their relation to 250 blocks. Figure 5a shows composite VAPV anomalies for all 50 events, averaged over the 3 days preceding the peak of the events.
The composite shows a prominent negative anomaly in the Ural sector and a weaker negative anomaly over Scandinavia, suggesting that blocking in these regions is indeed a common feature to many of the events. The corresponding SLP anomalies  Table 1). We then define a blocking index for each sector based on the area fraction of the sector that intersects with a block as identified by the algorithm described in Sect. 2.2.

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Specifically, at each 6-hourly time step we compute the total area of the grid cells within the sector belonging to a block, divide by the total sector area and take a daily mean to yield a daily sector blocking index. We then relate a warm event to a blocking in a specific sector if the corresponding sector index exceeds its 90 th percentile value at some point over the 6 days prior to the warm event. For the Pacific sector, we use the 99 th percentile in order to capture only the strongest blocking in this frequently blocked area. shows patterns very similar to that for composites over all 50 events, though with greater amplitude. In these cases, the max-280 imum negative VAPV anomaly is concentrated in and around the Ural sector, while the SLP anomaly shows a clear dipole straddling the pole and promoting warm advection from the North Atlantic into the high Arctic. The Scandinavian composite ( Fig. 5d) has peak VAPV anomaly over Scandinavia, as expected, while the SLP again shows a dipole structure with a high over Scandinavia, partly extending over to northern Siberia, and a low over Greenland, again promoting advection from the North Atlantic. The Pacific composite shows very strong negative VAPV anomalies over Alaska, and the SLP anomalies show 285 a dipole with a high over Alaska and a low over eastern Siberia. This pattern supports warm advection from the North Pacific, reflected in the structure of the total column water field (green contour) showing intrusion of mid-latitude air into the Arctic from the Pacific. Note that the 30 % blocking frequency contour (light blue) nicely encloses regions of peak negative VAPV anomaly in each of the aforementioned cluster composites. Finally, the 11 residual events show weak VAPV and SLP anomalies with a structure similar to that in the pure Ural composite. This resemblance suggests that many of the residual events 290 are in fact weak Ural events, and might have been classified as such had we used a lower VAPV threshold in the blocking identification algorithm. However, in the remainder of the paper we focus on the higher-amplitude events in the other clusters.
As noted in Sect. 3, our case study shows that two successive warm extremes occurring in rapid succession can in fact be driven by a single blocking event. We find that this occurs 5 times within our top 50 warm extremes. These 5 pairs of warm events (connected by black lines in Fig. 6a) all occur within 13 days of each other, and the second event is always warmer than 295 the first. The criteria used to select the warm extremes (following Messori et al., 2018) arbitrarily stipulate that two consecutive events are considered independent if they are separated by more than 1 week. As also noted in Sect. 3, the more physicallybased blocking perspective taken here suggests that these pairs of events could also be thought of as single, long-lasting warm events driven by a single blocking event.
The previous section showed a strong association between blocks and extreme Arctic warm events. Here, we take a closer look at the dynamics behind these blocking events, focusing on the sources of low-PV air as identified by Lagrangian backtrajectories initialised within the blocks (Sect. 2.3). We are particularly interested in the contribution of diabatic heating within mid-latitude cyclones (Pfahl et al., 2015;Binder et al., 2017).

Ural blocking 305
We focus first on blocking in the Ural sector, combining the 18 pure Ural blocks with the 12 mixed Ural/Scandinavian events ( Fig. 5b). For the latter, the blocking algorithm identifies two disjoint blocking regions-one over the Urals and one over Scandinavia-in 6 cases; in these cases, trajectories are initialised only from the Ural block. In the remaining 6 cases, a single block extending over both sectors is identified. We apply an additional geographical mask in order to initialize trajectories only over the portion of the block residing over the Ural mountains (mainly north of 60 • N). Furthermore, a few of the pure Ural 310 events also obtain scattered blocking regions, for which we apply the same method as described above. The exact masks used for a total of seven Ural events are shown by the footnotes after each event number in Table S1 in the supplemental material (text section S1). Back-trajectories are started at the time of maximum Ural blocking fraction within the interval 3 to 1 days before the peak of each warm event. We compute a total of 97405 trajectories initialized three, two and one day prior to each warm event for 12, 6, and 12 of the 30 Ural events, respectively.

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Following previous work (Pfahl et al., 2015;Steinfeld and Pfahl, 2019), we assess the role of diabatic heating by examining the change in dry potential temperature (∆θ) along trajectories as follows. We identify the absolute maximum θ along the trajectory and find the (positive) difference ∆θ + between this maximum and the previous minimum θ. Similarly, we find the (negative) difference ∆θ − between the absolute minimum and the subsequent maximum. If ∆θ + > 2 K, the trajectory is classed as "heated" and ∆θ = ∆θ + ; otherwise, the trajectory is classed as "not heated" and ∆θ is set equal to either ∆θ + or 320 ∆θ − , whichever has greater absolute value. at 1 day to almost 60 % (59 %, 57323 trajectories) at 6 days but changes little thereafter, implying that 6 days is a reasonable trajectory length when considering diabatic heating effects in Ural blocking. Figure 7c shows the time evolution of θ and pressure for trajectories in the 6-day heated regime. At 6 days before arrival, air parcels are almost entirely below the 500 hPa level (warm colours), with the median trajectory (thick black line) close to 700 hPa and θ around 300 K, typical values for mid-latitude air (Hoskins et al., 1985). In the subsequent days they warm and 330 rise into the upper troposphere. The median trajectory rises by around 300 hPa in 3 days, but the ascent rate for individual trajectories is considerably more rapid: the maximum 2-day pressure drop for these trajectories has a median value around Table 1. Sectors and regions used in the study for the event clustering (right) and cyclone frequencies and the heating domain (right).

Sector coordinates Region coordinates
Ural (Fig. 8e). Further, the median humidity change along these trajectories is a drying of around 4 g kg −1 (Fig. 8i); condensation of this amount of water vapour yields an isobaric warming of around 10 K, comparable to the median heating of about 11 K for 6-day trajectories shown in Fig. 8a. Overall, these results are consistent with the view that diabatic heating 335 occurs principally through latent heat release in the rising branches of cyclones .
Trajectories in the no-heating regime, on the other hand, are almost entirely in the upper troposphere on day −6 (Fig. 7e); they cool diabatically at a median rate of around 1.3 K day −1 (Fig. 8a), consistent with typical radiative cooling rates in the upper troposphere, and subside by around 140 hPa as they travel to the blocking region.
The results above show that diabatic heating plays a major role in the identified Ural blocking events, at least when averaging 340 over all 30 cases. There is considerable variability among cases, but 23 of them (77 %) have a 6-day heated fraction in excess of 40 % (Fig. 9, red markers). Cases 1 and 8 both have a very low heating fraction, less than 10 %. Interestingly, these are both cases in which a single blocking event generates 2 consecutive warm events (see Fig. 6). They are thus examples of long-lived blocks, where low-PV air has been recirculating for several days after diabatic heating (Steinfeld and Pfahl, 2019). Low heating fractions is also consistent with the blocks being in the decaying stage of their life-cycles (e.g., Pfahl et al., 2015;Steinfeld 345 and Pfahl, 2019). Averaging over the per-event defined 6-day heating fractions, we obtain a slightly lower percentage of 54 %, mainly due to the influence of these two events.
We turn now to the question of where geographically the diabatic heating and ascent of air parcels feeding into Ural blocks takes place. For each trajectory in the 6-day heated class, we identify the location of peak diabatic heating rate as the point of maximum θ increase over a six-hour period between 6 to 1 days before arrival at the blocking region. To filter high fre-350 quency noise, we first smooth the one-hourly θ values with a six-hourly running-mean. Fig. 10a presents the resulting spatial distribution of peak heating. The bulk of the trajectories (68 %) undergo peak heating in the Atlantic sector (dashed lines in the figure, see also   Fig. 10a strongly points to a connection between Ural blocking and diabatic heating in cyclones within the main North Atlantic storm track, as we will explore in Sect. 6 below. Figure 11a shows the time evolution of trajectory density for trajectories undergoing maximum heating in the Atlantic sector (note that only 29 of the 30 events are included here, since trajectories initialized from the block associated with event 5 originate from the Pacific and are advected over Siberia). Two days before peak heating, trajectories are concentrated in the lower troposphere over the subtropical to mid-latitude western Atlantic. SLP composites at this time (shading in Fig. 11a) We have now shown that the majority of the Ural blocking trajectories undergo maximum heating and lifting in the Atlantic sector (Fig. 11), mostly in the period between 1 and 6 days prior to arrival into the blocking region (Fig. 7c). Frequency reveal that maximum heating is typically concentrated in one (70 %) or two (20 %) bursts, the former temporally taking place either at early (longer than 3.5 days, 30 %) or late (shorter than 3.5 days, 17 %) lags or around lag −3.5 day (23 %). The remaining events experience maximum heating almost evenly within the 5-day window or lack maximum heating over the Atlantic (one event). Based on the frequency distributions, we then define for each event a time of peak heating, i.e. one lag 380 when majority of the heated trajectories experience maximum heating.
The maximum heating on average occurs at approximately 4 days prior to arrival in the blocking region (median lag of −3.5 days, Fig 12b). We refer the reader to the supplemental material for a discussion of the change in time of maximum heating by applying additional pressure criteria (text section S2 and Fig. S2 in the supplemental material), where we show a shift of maximum heating to later times, closer to the blocking region, when approaching the definition of WCBs.

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We further find a correlation of −0.42 between the time of peak heating and the life stage of the block (D-index, Eq. (1), visualized in Fig. 12a. This implies that trajectories initialized from older blocks (higher D-index) generally experience peak heating in the Atlantic sector at early lags, many days prior to arrival at the block, and vice versa (as also seen for the Ural blocking trajectories presented in the case study in Sect. 3). As the sector blocking fraction partly reflects the size of the block, we observe that blocks at their mature stage (D-index values close to 0.5) usually obtain high sector fractions, as seen by the 390 darker coloring of the markers in Fig. 11a. This is consistent with the climatology of the evolution of blocking size presented by Croci-Maspoli et al. (2007).
Lastly, when considering the time of peak heating for all heated trajectories per each Ural event, not only for those experiencing maximum heating within the Atlantic sector, we find a weaker correlation of −0.33 between the time of peak heating especially when only a minority of the air parcels experience maximum heating in the Atlantic sector. The event-wise defined peak lags for both cases discussed above, as well as the relative fractions of heated trajectories being heated over the Atlantic and the D-index related to each block are listed in the supplemental material (Sect. S1) in Tables S1-S4.

Scandinavian blocking
This section examines the dynamics behind Scandinavian blocking events, following the same approach as for Ural events 400 in the previous section. Back-trajectories are initialized from blocks observed over the Scandinavian sector (Table 1, see also light blue sector in Fig. 5d). In Fig. 6a, markers overlaid with a small black dot denote the ten events included here, namely six pure Scandinavian events and an additional four events from the mixed Ural/Scandinavian cluster which show an isolated blocking region over Scandinavia. To enable comparison with the Ural case and analyse blocking trajectories initialized within lags −3 to −1 days relative to trajectory starting points, events where the block decays more than 3 days prior to the peak 405 warm anomaly are excluded. One of the pure Scandinavian events (event 24) features two separate blocks, which are treated separately here. This leaves us with 10 Scandinavian events consisting of 11 blocks for the Lagrangian analysis performed in this section. One event obtains scattered blocking regions, to which a geographical mask is applied in order to retain only the region of the block located over Scandinavia (see footnote in Table S3 in the supplemental materials, Sect. S1). We compute a total of 32255 trajectories initialized on the day of maximum Scandinavian blocking fraction: three days prior to the Arctic 410 warm event in five cases, and one day prior in six cases.
The frequency distributions of ∆θ for different trajectory lengths (Fig. 7b) resembles the distributions obtained for the Ural events, with a bimodal structure and increased heating and cooling for longer trajectories. However, the fraction of heated trajectories (inset panel in Fig. 7b) increases more rapidly than in the Ural case, reaching 41 % already at 3 days for Scandinavian events compared to 32 % for the Ural case. This rapid increase saturates after 5 days; by 6 days, the heating fraction of 58 % 415 (18595 heated trajectories) is comparable to Ural case. The case-to-case variability of the computed heating fractions at 6 days is much smaller for the Scandinavian than for the Ural events: 10 of 11 Scandinavian blocks obtain fractions over 40 %, with a minimum fraction of 36 % (see Table S3 in the supplemental material, Sect. S1). As a result, the average over the per-event fractions at 6 days is actually 60 %, somewhat higher than the respective value for the Ural events. Thus, diabatic heating plays a major role also for Scandinavian blocking events.

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At 6 days before arrival in the blocking region, about 75 % of trajectories in the heating regime are in the lower troposphere, at pressures >500 hPa (Fig. 7d). As for the Ural cases, the median trajectory is close to 700 hPa but with a higher θ of 308 K.
From here, the air parcels warm and rise into the upper troposphere, obtaining a median heating of 10 K for six-day trajectories (Fig. 8b). The ascent rate within two days and the change in specific humidity along the heated trajectories are slightly smaller in magnitude compared to the Ural ones, obtaining median values of around 300 hPa (Fig. 8f) and a drying of around 3 g kg −1 425 (Fig. 8j), respectively. On the other hand, trajectories in the non-heating regime are almost totally in the upper troposphere on day −6 (Fig. 7f), obtaining similar cooling rates as for the Ural ones (Fig. 8b) and an insignificant change in the specific humidity (Fig. 8j).
Turning to the question of where the diabatic heating of air parcels feeding into Scandinavian blocks takes place, the spatial distribution of peak heating location (Fig. 10b) shows that it is again mostly in the Atlantic sector, but with marked displacement 430 toward the south-west, in closer correspondence with the climatological distribution (Steinfeld and Pfahl, 2019). In addition, a considerable number of trajectories undergo maximum heating over eastern North America and smaller numbers over the eastern Mediterranean and the eastern Pacific. Nonetheless, as seen for the Ural events, the distribution shown in Fig. 10b similarly suggests a connection between Scandinavian blocking and diabatic heating in mid-latitude Atlantic cyclones.
As for the Ural events, the maximum heating of Scandinavian blocking trajectories experiencing maximum heating in the 435 Atlantic sector temporally takes place in one (91 %) or two (9 %) bursts, the former being clearly larger than for the Ural ones. Furthermore, almost half of the events in the former experience peak heating at later lags (shorter than three days, 46 %), whereas earlier lags (longer than three days) or heating around day −3, being favoured by the Ural events, here are less preferred (18 and 27 %, respectively). Most of the heating takes place at later lags, closer to the blocking region, with a median lag of about −2 days (Fig. 12d), which is clearly smaller compared to the median lag of −3.5 days obtained for the 440 Ural events (Fig. 12b). The bulk of the temporal distribution for peak heating defined separately for all individual trajectories experiencing maximum heating in the Atlantic sector is shifted to slightly earlier lags, though with a median lag of −3 days, as seen in Fig. 12d, right. However, Scandinavian blocking trajectories tend to experience maximum heating in the Atlantic sector generally at later lags compared to the Ural events, which is consistent with the fact that about 40 % of the Scandinavian blocking air parcels experience heating already in the first three days after initialization (Fig. 7b). The negative correlation we  Tables S3-S4 in the supplemental material (Sect. S1).

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6 Linkage to mid-latitude cyclones The previous section showed that most diabatically heated trajectories associated with both Ural and Scandinavian blocks undergo heating and lifting in the time period between −6 and −1 days relative to blocking starting points. Figure 13 shows the tracks of all cyclones present during this five-day interval for all Ural (a) and Scandinavian (b) events. In the North Atlantic,  . 10), consistent with the idea that diabatic heating occurs predominantly in the warm sectors to the south-east of the cyclone centres. Each event has at least two (up to seven) cyclones that reside in the yellow box at some time within the relevant fiveday period and 90 % of all these events obtain at least one (up to three) cyclones located within the box at the time of peak 460 heating. For the remaining four events, the yellow dot is located just west or north of the box and the majority of the red-colored cyclones either experience genesis shortly after the time of peak heating or undergo lysis just before it. Nevertheless, the majority of the yellow markers reside within or close to the yellow box, confirming the importance of cyclones for the diabatic heating experienced by the blocking trajectories.
For the 30 Ural cases, an average of five cyclone tracks per event cross the yellow box in Figure 13a during the relevant 465 five-day window preceding blocking (involving values between a minimum of 2 and a maximum of 7 crossings in individual cases). To compare with climatology, we select 30 random winter pentads, compute the mean number of crossings per pentad, and repeat 500 times. This procedure yields a median of only four cyclone crossings per pentad (Figure 14), and shows that the 30 Ural cases constitute a rare sample with exceptionally high mean cyclone activity, well above the 99 th percentile of the climatological distribution. The 10 Scandinavian cases, on the other hand, show an average of only four cyclone crossings per 470 event (interval 3 -6); comparison with climatology using random sampling of 10 pentads shows that this average lies within the interquartile range and cannot be considered exceptional. These results indicate that serial cyclone clustering (Pinto et al., 2013) can be important for generating Arctic warm events, at least in those cases associated with Ural blocking.
Returning to Fig. 13, we note that with the exception of a few cyclones, almost all of the red tracks in the figure experience lysis either within the yellow box or immediately to the north, north-east and west of the box; only a handful continue northward 475 to enter the Arctic. To further quantify whether the majority of Arctic cyclones at the time of peak event undergo genesis in high-latitudes, we select cyclone tracks present during a 3-day period leading up to each of the Ural (Fig. 13c) or Scandinavian and Scandinavian (Fig. 13d) events, respectively. Even though Scandinavian events in general obtain less Arctic cyclones with local genesis around the peak of the event compared to the Ural events, our results presented here support the results of Messori et al. (2018) showing that cyclones present in the high Arctic around the time of peak event are mainly locally generated within 485 the polar cap or in the close vicinity of it. Only a few of the red-colored cyclone tracks undergo genesis in the mid-latitudes (see e.g. the two red dots at 50 • N in Fig. 13c). In fact, these two cyclones are related to event 9, of which one is shown to be responsible for the lifting of the Ural blocking trajectories in the Atlantic sector, as discussed in the case study in Sect. 3.2.
Another interesting difference between these two cases is the location of the selected cyclones at the peak of each event (yellow markers on red tracks), where 60 % of the 30 red cyclones existing at the peak of Ural events (Fig. 13c) reside within the polar 490 cap, whereas already half of the four red cyclones prevailing at the peak of Scandinavian events have exited the polar cap ( Fig. 13d).
As seen by the SLP anomaly composite (shading in Fig. 13c,d) representing the peak of each warm event, the region of negative SLP anomalies in the northwestern Atlantic is displaced northwards, now reaching all the way into the Arctic. On the other hand, the region of positive SLP anomalies over the Urals in Fig. 13c becomes even more pronounced at the peak of the 495 warm events. For the Scandinavian events, there are two distinct centers of positive SLP anomalies; one over Scandinavia and one over Urals, the latter due to the four events from the mixed cluster.

Discussion
Previous studies show that Ural blocking enhances Arctic warming and sea-loss especially over Barents-Kara-Seas (Luo et al., 2016b;Gong and Luo, 2017;Luo et al., 2017Luo et al., , 2019, and that Ural blocks are able to produce stronger sea-ice decline compared 500 to Scandinavian blocking (Luo et al., 2019). This is in agreement with our findings, where 37 of the top-50 wintertime high-Arctic warm extreme events are attributed to blocking over the Urals, Scandinavia or over both regions simultaneously, with a majority of events featuring a strong Ural block preceding peak warming in the high Arctic. Next we discuss the sequence of dynamical processes, based on the 30 warm events associated with Ural blocking, leading to these warm extremes in the high-Arctic (Fig. 15).

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1. The first stage, "Preconditions" (Fig. 15a), comprises days 9 to 6 prior to peak Ural blocking, i.e. the time before the majority of the trajectories experience diabatic heating. This period is characterized by a subtropical high SLP anomaly and significant negative SLP anomalies over Greenland, a pattern resembling the positive phase of NAO (NAO+). The circulation pattern promotes eastward/northeastward advection of warm and moist air towards the central Atlantic. Already at this stage, some events exhibit positive SLP anomalies over the Urals.

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2. The second stage, "Heating", comprises the 5-day period (6 to 1 days preceding the peak in Ural blocking) when most trajectories experience diabatic heating (Fig. 15b). The NAO+ phase continues, with deeper negative SLP anomalies found over Greenland (Fig. 15b) and the positive SLP anomalies over north Siberia strengthen, forming a dipole over the Nordic seas conducive to advection of warm and moist air into the high Arctic.
We find that the majority (68 %) of the six-day heated Ural blocking trajectories experience lifting and maximum diabatic 515 heating in the midlatitude North Atlantic during this 5-day period. The spatial distribution of maximum heating (Fig 10a) differs markedly from the climatological distribution presented in Steinfeld and Pfahl (2019) and regions favoured by ascending WCBs, as showed by Madonna et al. (2014). For the warm events preceded by Scandinavian blocks (Fig. 10b), on the other hand, the distribution better resembles those in the studies cited above.
Additionally, this 5-day period is characterized by anomalously high cyclone activity within a region (yellow box in 520 Fig. 15b), consistent with the region of negative SLP anomalies, located northwest of the region favoured by maximum heating for blocking trajectories. This is consistent with the NAO+, characterized by a higher activity of intense wintertime North Atlantic cyclones (Pinto et al., 2009). The combination of NAO+ pressure pattern and Ural blocking ensures a pathway for moisture transport from North Atlantic into the Arctic and thus promotes Arctic warming and sea-ice decline (Luo et al., , 2019Papritz and Dunn-Sigouin, 2020;Fearon et al., 2020).

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3. The "Event" stage ( Fig. 15c) coincides with the 1-3 day time window between the peak in Ural blocking fraction and the peak of the warm event. The lag between the peak Ural blocking and peak Arctic warming found here is in line with a lag of four days found between Ural blocks and observed warming and sea-ice loss over the Barents-Kara Seas (Gong and Luo, 2017). The formation or strengthening of Ural blocking at this stage, subsequent to the NAO+ event noted in prior stages, is consistent with previous work showing a development of Ural blocks 4-7 days after NAO+ (Luo et al.,530 2016a). The combined effect of a decaying NAO+ pattern and the growing block over the Ural mountains, is to create an SLP anomaly dipole (Fig. 15c) enabling penetration of heat and moisture into the polar cap leading to Arctic warming (Fearon et al., 2020;Papritz and Dunn-Sigouin, 2020). This moisture transport is also seen in Fig. 15c, which shows significant positive moisture anomalies over the Arctic Ocean.
4. The "Post" stage ( Fig. 15d), is represented by a composite over three days after the warm event. Here, the upper-level 535 forcing is diminishing and the dipole in the SLP pattern clearly weakens, concomitant with weaker moisture anomalies over the central Arctic.
As noted by Luo et al. (2016a), the formation and strengthening of the Ural blocking anomaly subsequent to the NAO+, may be the result of wave activity propagation from the decaying NAO+ towards the Ural Mountain. Our findings do not contradict this idea, but rather provide additional insight into the amplification mechanisms of Ural blocks. Specifically, we find that 540 diabatic heating plays a leading role in amplifying Ural blocks, with around 60 % of the air parcels in Ural blocks being subject to diabatic heating over the 6-day period prior to peak blocking. These results hint at a self-amplifying mechanism behind Ural blocks: they are potentially initiated by adiabatic wave propagation and, once established, promote further advection of low-PV diabatically-processed air into the block as it is produced in the ascending branches of North Atlantic cyclones. Further study of this self-amplifying mechanism could be an interesting avenue for future work.

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Given the key role of blocking and its interaction with midlatitude cyclones as a driver for the top-50 Arctic wintertime warm extremes that we find here, another interesting question that arises is whether this is also a common feature in other, less extreme warm events in the high Arctic. Starting from a blocking perspective and applying the methods used in this study could help enhance our understanding of the processes responsible for Arctic warming. A further promising avenue for further investigation would be to study events based on anomalies in the surface energy budget rather than in temperature, as the 550 former directly affects sea ice development and could allow for deeper insights into the dynamical processes responsible for sea ice decline in the Arctic.

Summary and Conclusions
We have investigated the dynamics behind the 50 most extreme wintertime high Arctic warm anomalies, focusing on the importance of Ural and Scandinavian blocking preceding the warm extremes. Furthermore, the dynamical processes responsible for 555 the emergence of these events were assessed, focusing mainly on the contribution of diabatic heating in midlatitude cyclones to the formation and amplification of the blocks. We answer the questions posed in the introduction as following: • What is the role of blocking in driving the extreme warm events?
Blocking plays a central role for the majority of the top-50 warm events: Composites of vertically-averaged uppertropospheric potential vorticity anomalies over the 50 events show a prominent negative anomaly over the Ural and 560 Scandinavian sectors. The surface expression of this pattern is a SLP anomaly dipole between a high over Siberia and a low over Greenland, promoting warm and moist air advection into the high Arctic.
• Are there regional differences in the circulation patterns?
We find regional differences in the circulation patterns among the different warm extremes: 30 events are associated with Ural blocking-18 of which have a block only over Urals and 12 obtaining blocking over both Scandinavia and the 565 Urals-where the peak blocking is preceded by a NAO+ pattern. Furthermore, seven events were found to be preceded by Scandinavian blocking and two by strong blocking over the Pacific, whereas 11 events-resembling the structure of Ural events but with a weaker amplitude-were not associated with any block in the three favoured blocking regions.
• What is the importance of diabatic processes in driving the blocks?
Diabatic heating plays an important role in the dynamics of high-latitude blocking associated with Arctic warm events: 570 analysis of Lagrangian back-trajectories from Ural blocks show that 59 % of the air parcels experience lifting (median ascent of 363 hPa within two days) and diabatic heating (median heating of 11 K) within six days prior to arrival at the block. Almost half of the air parcels making up the negative VAPV anomalies of Scandinavian blocks experience heating already within the 3-day journey into the blocking region, reaching up to 58 % over six days. The strongest heating is found over a region in the North Atlantic, temporally taking place at a median day of 3.5 and 2.75 prior to arrival into 575 the Ural and Scandinavian blocks, respectively.
Furthermore, we find that the time of peak heating within the North Atlantic region, defined per each Ural and Scandinavian event, and the life-stage of the blocks are negatively correlated, indicating that younger blocks experience maximum heating preferably at later times, closer to the blocking region and vice versa.
• How do cyclones and blocks interact during the events? 580 We find a strong interaction between midlatitude cyclones and Eurasian blocks as driver of wintertime Arctic warm extremes: an exceptionally high midlatitude cyclone activity-coinciding both spatially and temporally with the time window of maximum heating for blocking trajectories in the North Atlantic-highlights the importance of latent heat release in cloud-diabatic processes ahead of strong surface cyclones in providing low-PV air into upper-level block, thus enhancing and amplifying the high-latitude block. On the other hand, these cyclones are also guided polewards by the 585 block, further promoting northward transport of heat and moisture and thus helping generate the Arctic warm extremes.
These midlatitude cyclones mostly decay before entering the high Arctic, whereas around the time of each warm event, a peak in locally-generated polar cyclone activity is observed. For Scandinavian events, on the other hand, the cyclone activity is not as exceptional.
This study deepens the understanding of the underlying processes driving the warming seen in the high Arctic, emphasizing 590 the importance of atmospheric blocks and their tight interaction with midlatitude cyclones-as amplifiers of the block or being guided by the block-as well as the combined effect of the prevailing circulation patterns on the appearance of high Arctic extreme warm events. It also highlights processes that need to be well captured in models to be able to represent the Arctic wintertime climate. . Statistical distributions of maximum absolute change in potential temperature (K) (a, b), maximum 6-hourly change in potential temperature (K) (c, d), maximum absolute ascent (hPa) within 48-hours (e, f), maximum pressure (hPa) (g,h) and maximum change in specific humidity (g kg −1 ) (i, j) along the 6-day back-trajectories belonging to the "non-heating" regime (N, blue lines) and "heating" regime  Cyclones observed within lags −1 to −6 days relative to trajectory initialization (blocking region), shown for 30 Ural (a) and 10 Scandinavian (b) events, respectively. Tracks are colored red if the selected cyclone is both in temporal and spatial correspondence with the considered time period in the yellow sector (C, 10 -60 • W, 50 -70 • N). If there is only a temporal match, the cyclones are colored gray. Shading shows the SLP anomaly composite over these events at the case-defined peak of maximum heating within the main heating domain for blocking trajectories (for 29 Ural and 10 Scandinavian events in (a) and (b), respectively, see also Tables S2 and S4 in the supplemental material (Sect. S1). Yellow circles show the location of the red-colored cyclones at this peak of maximum heating. Red or gray solid triangles show the lysis of cyclones that cross or stay outside the chosen sector, respectively. (c, d) Same as in (a, b) but shown for cyclones observed up to three days prior to the peak of each Ural (c) or Scandinavian (d) event, respectively, where the red coloring refers to cyclones that reside in the high Arctic (≥ 80 • N, yellow latitude band at 80 • N) within the time period considered. The SLP anomaly composite field and yellow circles for the red-colored cyclones are shown at the time of each warm event. Red and gray solid circles denote the genesis of cyclones that cross or stay outside the chosen sector, respectively. events 10 Scandinavian events 0 1 2 3 4 5 6 Nr of cyclones Figure 14. Cyclone climatology presented as the average cyclone frequency observed in the chosen sector (C, yellow sector in Fig. 13a,b, 60-10 • W, 50-70 • N) northwest of the main heating region during a 5-day window (lags −1 to −6 day relative to trajectory initialization within the block) for 30 Ural (magenta) and 10 Scandinavian (light blue) events, computed using Monte Carlo re-sampling of 30 or 10 arbitrary "events" within the analysis period with 500 repetitions, respectively. The black horizontal line denotes the median, mean is shown with diamonds, the box refers to the IQR and the whiskers the 1 st -99 th percentile range of the distribution. The magenta and light blue horizontal line at each boxplot denote the cyclone frequency for the 5-day window averaged over the 30 or 10 chosen Ural and Scandinavian events, respectively. (days −9 to −6 relative to trajectory initialization, 3 days per event) (a), at heating (−6 to −1 days with respect to trajectory initialization, 5 days per event) (b), in the close vicinity of the warm events (days between lag −1 day relative to trajectory initialization until the peak of warm event, 2-4 days per event) (c) and at post conditions (up to three days after each warm event, 3 days per event) (d). Significant total column water anomalies shown in shading (kg m −2 , significant when > 67 % of the 30 members obtain the same sign in the anomaly as the composite mean), overlaid with SLP anomalies (hPa, every 5 hPa, significant in bold contours, red for positive, blue for negative anomalies, zero anomaly contour is not shown) and potential temperature on the 2 pvu surface (purple solid isoline for 310 K). The black dashed region in (b) denotes the main heating region, the yellow sector in (b) the cyclone region and the dashed black circle shows the latitude band at 40 • N.