The analyses presented in this study are based on the ERA5 reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF) and covers the period 1 January 1979–31 December 2021 . We use 3-hourly model level data provided by ECMWF for a high-resolution computation of PV anomalies in the upper troposphere (see Sect. 2.3) on a 0.5°×0.5° latitude-longitude grid, and a coarser dataset (1°×1°) for the PV inversion on 17 pressure levels (1000, 950, 925, 900, 850, 800, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, and 50 hPa).

The quasi-Lagrangian PV framework, developed by and further refined in , identifies and tracks patches of negative PV anomalies in the upper troposphere and quantifies the contribution of different processes to their amplitude evolution. This approach builds on the θ-PV framework for midlatitude Rossby wave packets by . The central variable is Ertel PV, defined by : q=-g(ζθ+f)∂θ∂p, where g is the gravitational acceleration, ζθ the isentropic relative vorticity, f the Coriolis parameter, θ the potential temperature, and p the pressure. The full framework is documented in detail in ; here, we briefly summarize the key steps only to avoid redundancy.

Upper-tropospheric PV anomalies are defined as the difference between the vertically averaged PV (VAPV) between 150–500 hPa and its 30 d centred running-mean climatology (1979–2021). We identify the PVAs- as contiguous regions of negative PV anomalies that fall below a seasonally varying threshold cf.their Fig. A1c, with higher thresholds in winter than in summer. All PVAs- are tracked using an overlap-based tracking algorithm that also accounts for feature splitting and merging. When a merge occurs, instead of assigning a new tracking ID, which would fragment a single life cycle into a disjointed “puzzle” of multiple IDs, the algorithm retains the tracking ID of the larger feature and archives the metadata of the smaller merging feature. A similar strategy is applied when features split. This approach enables the reconstruction of complete life cycles of PVAs-. The dataset of tracked PVAs- within the chosen ERA5 period (1979–2021) is available for the entire Northern Hemisphere in .

To investigate the amplitude evolution of PVAs-, we employ the piecewise PV tendency framework, which is based on the PV tendency equation. This equation states that the local change in PV (q) is governed by PV advection and non-conservative PV modification: ∂q∂t=-v⋅∇θq+N1=-(v0+vdiv′+vup′+vlow′+vres′)⋅∇θq+N. Here, v is the horizontal wind field; v=(u,v,0), ∇θ the gradient operator along an isentropic surface, and N the non-conservative PV modification. The full wind field v is decomposed using PV inversion and Helmholtz Partitioning, which results in the divergent wind field vdiv′, the wind fields vlow′ and vup′ associated with upper-tropospheric and lower-tropospheric PV anomalies (non-divergent), the residual wind field vres′, and the background wind field v0, defined as the 30 d running mean climatology of v (1980–2019). The PV inversion yields three-dimensional wind fields defined on pressure levels, which are subsequently interpolated onto isentropic surfaces for the analysis. Equation () is further transformed into an equation for the amplitude evolution of enclosed PV anomalies – analogously to . As a result, the integrated amplitude evolution over the area A(t) of a PV anomaly feature reads as 2ddt∫A(t)q′dA=∑i-∫A(t)vi′⋅∇q0dA-∫A(t)-vi′⋅∇q0dA︸i+∫A(t)q′(∇⋅vdiv′)dA-∫A(t)q′(∇⋅vdiv′)dA︸DIVdiv+∫A(t)NdA-∫A(t)N0dA︸NONCONS+∮S(t)q′(vs-v)dS︸Bnd, with i referring to div, up, low and res wind fields (cf. Eq. 1), S(t) as the boundary of A(t), vs the motion of the boundary S(t) and the climatological background PV q0 which is constructed the same way as v0. The terms enclosed by the mean operator 〈〉 refer to 30 d centred averages of a given term between 1980–2019 for each calendar day. Taking into account these terms, we can quantify the contributions of different processes to the change in background PV their Appendix A. Equations () and () are evaluated on isentropic surfaces ranging from 315 to 355 K in steps of 5 K. Following the approach of and , we compute an isentropic average by including the surfaces ±5 K around the central level. For the year-round analysis of PVAs-, the selection of the representative isentropic level is crucial. Therefore, we adopt the seasonally varying levels recommended by : 320 K for December–March, 325 K for April and November, 330 K for May and October, 335 K for June and September, and 340 K for July and August.

The physical meaning of each term in Eq. () is explained below and schematically shown in Fig. b. The term UP refers to upper-tropospheric (quasi-)barotropic dynamics and describes the advection of upper-level background PV by the wind field associated with upper-tropospheric PV anomalies e.g.Sect. 6a. This describes the intrinsic propagation mechanism of Rossby waves and amplitude changes due to group propagation (blue arrows in Fig. b). The term LOW captures baroclinic interaction, namely the amplitude modification of upper-level PV anomalies by the wind field associated with low-level PV anomalies (gold arrows in Fig. b), thereby contributing to baroclinic growth when the upper- and lower-level anomalies are suitably phased e.g.Sect. 6b. Moist processes may strengthen the low-level PV anomaly, but LOW represents the quasi-adiabatic, balanced response to that anomaly rather than its diabatic generation. Numerical and inherent inaccuracies in piecewise PV inversion lead to a residual wind field, which is usually small. The advection of background PV by this residual flow is captured by the term RES. While it lacks physical interpretability , it is included for budget closure in the PV tendency equation. Two terms describe the impact of divergent winds (dark red arrows in Fig. b) on the amplitude evolution of PV anomalies: (1) DIV_adv represents the advection of background PV by the divergent wind field and (2) DIV_div accounts for divergence or convergence within the PV anomaly itself, which leads to its growth or decay, respectively. Upper-level divergence can arise from both dry dynamical forcing and latent heat release below. In particular, strong divergence is frequently associated with diabatic outflow near the tropopause, such as from WCBs e.g.. A detailed sensitivity analysis by their Sect. 5.3 demonstrates, however, that upper-tropospheric divergence is more sensitive to proxies of latent heat release than to proxies of dry dynamics, supporting the interpretation that these terms predominantly reflect indirect moist contributions, while acknowledging that dry dynamical forcing may still contribute and cannot be quantitatively disentangled with the present diagnostics. The term NONCONS represents direct diabatic modification of PV by non-conservative processes such as latent heating (grey cloud in Fig. b), radiative effects, friction, and turbulent mixing e.g.. While diabatic PV tendencies can be locally strong – particularly in association with deep convection – their spatially localized nature implies that their contribution to the area-integrated PV budget is typically small cf.their Figs. 9 and 10. In principle, this small net contribution could also arise from cancellation between opposing non-conservative processes; however, available process-based budget analyses for upper-level PV anomalies, based on Year of Tropical Convection (YOTC) data e.g., do not indicate such cancellation to be dominant . Radiative PV tendencies, although more spatially coherent, exhibit little spatio-temporal variability over the life cycle of upper-level PV anomalies . Diabatically generated PV anomalies may nonetheless influence the large-scale flow indirectly through rapid upscale interactions, for example via divergent circulations, which are represented by other terms in the PV budget. NONCONS processes are therefore not expected to substantially affect the integrated amplitude of PVAs- considered here. Because the available reanalysis data do not permit a further separation of individual non-conservative processes beyond the bulk NONCONS term, and given its small magnitude, NONCONS is not analysed explicitly in the present study, following previous studies e.g..

The final term on the right-hand side of Eq. () is the boundary term Bnd, that is estimated as follows: Bnd=-∫A(t)∇⋅(vq′)dA3-∫A(t)〈-∇⋅(vq′)〉dA+q‾′⋅ΔA with q‾ as the average of q′ along the boundary S(t) and ΔA as the observed area change of the PV anomaly. The first two terms of Bnd describe the contribution to amplitude change caused by eddy flux divergence or convergence within the anomaly area. The last term estimates the change in amplitude by the change in anomaly area between two consecutive time steps and can reach high values in case of splitting and merging of different anomaly features. For more details on Bnd, the reader is referred to Appendix B of .

We denote to the diagnosed amplitude change (DIAG) as the sum of all terms in Eq. (): DIAG=UP+LOW+DIVdiv+DIVadv+RES+Bnd. DIAG is compared to the observed amplitude change (OBS), which is defined as the forward difference in the area-integrated PV anomaly amplitude between two time steps. Following , we exclude time steps where the deviation between DIAG and OBS is large, as this indicates that the PV budget fails to accurately capture the observed evolution. Such large DIAG–OBS deviations primarily occur during non-linear evolution phases, such as large-scale splitting or merging events, or during periods when the VAPV anomaly contour does not fully capture isentropic-level PV anomalies. In line with , the sign convention for the PV tendency terms is such that a positive value indicates an amplification of PVAs-, while a negative value indicates a weakening.

In this study, we use the year-round weather regime definition for the North Atlantic–European region developed by and apply it to ERA5 reanalysis data to distinguish between different blocking configurations in this region. A detailed technical documentation of the regime definition is given in and we briefly repeat the essence in the following. To define the regimes, 6-hourly geopotential height anomalies at 500 hPa (Z500) are calculated using a 90 d centred running-mean climatology (1979–2019) and then filtered with a 10 d low-pass Lanczos filter . After normalizing the anomalies, we perform an empirical orthogonal function (EOF) analysis over the North Atlantic–European domain (80° W–40° E, 30–90° N). The seven leading EOFs, which describe 74.4 % of the total variance, are retained to construct an expanded phase space. A k-means clustering is then applied in this phase space, yielding an optimal number of seven clusters, which correspond to seven distinct weather regimes: Three cyclonic regimes (Zonal regime – ZO, Scandinavian trough – ScTr, Atlantic trough – AT) and four anticyclonic regimes (Atlantic ridge – AR, European blocking – EuBL, Scandinavian blocking – ScBL, Greenland blocking – GL). To assign individual time steps to these regimes, we use the weather regime index (IWR) proposed by and , which quantifies the similarity between a given instantaneous Z500 field at time t and each of the seven weather regimes (WR): 4IWR(t)=PWR(t)-PWR‾1NT∑t=1NT[PWR(t)-PWR‾]2 with 5PWR(t)=∑(λ,φ)∈EOFΦL(t,λ,φ)ΦWRL(λ,φ)cos⁡φ∑(λ,φ)∈EOFcos⁡φ. PWR(t) describes the projection of the filtered anomaly ΦL(t,λ,φ) to the EOF cluster mean ΦWRL(λ,φ) within the EOF domain. NT is the total number of time steps within the climatological sample (1979–2019) and the respective longitude/latitude within the EOF domain is noted as (λ,φ). PWR‾ describes the climatological mean of the projection PWR. As a result, IWR is computed as the deviation of PWR(t) from PWR‾, normalized by the standard deviation. This index, IWR, can also be computed beyond the climatological sample – i.e., for each of the seven regimes and every 3-hourly time step throughout the full ERA5 period considered (1979–2021). Following , we derive objective regime life cycles, associated life cycle stages (onset, mature stage, decay) and regime transitions – all based on the IWR. A detailed description on the algorithms used to determine those characteristics is given in and .

From January 1979 to December 2021, we identified a total of 177 life cycles for AR, 183 for EuBL, 192 for ScBL, and 177 for GL. Figure  presents the four blocked regime patterns as year-round mean composites based on upper-tropospheric PV anomalies and calculated over all time steps within the respective life cycles of each blocked regime. All four regimes are characterized by a dominant negative PV anomaly that defines the block; however, the location of this anomaly varies across regimes. For AR, the negative PV anomaly spans the largest area and is centred south of Iceland (Fig. a). A comparison between EuBL and ScBL highlights the need to refine the classical four-regime blocking framework e.g. by distinguishing these two as separate sub-regimes due to their markedly different spatial structures. EuBL exhibits a pronounced positive PV anomaly over Greenland and displays features indicative of anticyclonic Rossby wave breaking over Europe (Fig. b). In contrast, ScBL is associated with a high-latitude block flanked by a strong positive PV anomaly over the eastern North Atlantic, and shows signs of cyclonic Rossby wave breaking extending toward Greenland (Fig. c). For GL, the block is associated with a more isolated negative PV anomaly centred over the Labrador Sea (Fig. d).

This work utilizes the EuLerian Identification of ascending AirStreams (ELIAS 2.0) data set of . ELIAS 2.0 uses convolutional neural networks (CNNs) to identify the footprints of three WCB stages, which have been defined from a Lagrangian perspective based on the location of air parcels that classify as WCB Δp>600 hPa for Δt≤48 h;: (i) inflow (p≥800 hPa), (2) ascent (800 hPa ≤p≤400 hPa), and (3) outflow (p≤400 hPa). A step-wise forward selection approach has been applied to identify the five most important meteorological predictors . The training has been performed on 6-hourly ERA-Interim data and applied to 3-hourly ERA5 data. The CNN gives conditional probabilities of WCB stage occurrences as output. This is transformed into a binary WCB occurrence given a seasonal-dependent and grid-point-dependent decision threshold, optimized to minimize the climatological bias and maximize the correlation coefficient in the midlatitude storm-track regions, where WCBs occur most frequently .

The negative upper-level PV anomaly linked to blocked regime onset over Greenland does not develop in-situ but propagate via different pathways towards Greenland . Consistent with these results, we distinguish two pathways based on whether the anomaly emerges upstream or downstream of the blocking region and examine if these pathways also exist in the other three blocked regimes. First, we define the area where to expect the anticyclonic anomaly during the blocked regimes by the -0.3 PVU-contour in the year-round composite (Fig. ). Using the traced PVAs- (details in Sect. 2.2), for every blocked regime life cycle, we determine a so-called onset PVA⁻ that exhibits the highest spatial overlap with the respective regime mask around blocked regime onset. To quantify the two pathways, each onset PVA⁻ is assessed for its dominant position relative to the centre of mass longitude of the regime mask (0.5° E for EuBL, 13.0° E for ScBL, 24.0° W for AR, and 51.5° W for GL) in the 3 d before onset.

When split into the two pathways, the majority of onset PVAs- follow the upstream pathway: 76.5 % for EuBL, 65.6 % for ScBL, and 57.1 % for AR. This deviates from the dominant retrogression pathway for GL, where upstream onset PVAs- account for only 42.4 %. These findings are consistent with the climatological storm-track position, characterized by reduced storm-track activity downstream of Europe and upstream of Greenland. Investigating the seasonal occurrence of the pathways reveals more differences between the blocked regimes (Fig. ). First, the more continental blocked regime types east of the North Atlantic (EuBL, ScBL) show a dominance of the upstream pathway mostly independent of the month (Fig. b and c). The differences in pathway frequency are less pronounced for AR with a more frequent retrogression pathway in April, May, and December (Fig. a). The seasonality of the pathways for GL is more complex with the dominant retrogression pathway only being prevalent in winter and late spring/early summer (Fig. a).

Figure  provides more insights into the position of onset PVAs- before blocked regime onset (grey contour lines). Apart from AR, onset PVAs- are located in the mean outside or at the edge of the blocking region 3 d before blocked regime onset, in particular in the southwest quadrant of the regime mask-centred composite (grey contour lines). This highlights the non-stationary development of PVAs- for multiple blocked regimes and extends the previous result found for GL by . Although most GL life cycles are assigned to the retrogression pathway, the maximum in onset PVA⁻ frequency is located southwest of the blocking domain (Fig. d), suggesting a more confined pathway of upstream onset PVAs- compared to retrograding onset PVAs-.

The location of onset PVAs- in the days preceding blocked regime onset depends on the regime type. For North Atlantic–centred blocked regimes (Fig. a and d), both pathways are predominantly oceanic. In contrast, for blocked regimes over Europe and Scandinavia (EuBL and ScBL), retrogression pathways (orange shading) remain confined to continental regions, while upstream pathways (violet shading) extend over the ocean (Fig. b and c).

Onset PVAs- along the upstream pathways peak outside the regime mask for all blocked regime types, providing clear evidence that they do not evolve in situ. In contrast, the location of onset PVAs- along the retrogression pathway in the days before blocked regime onset – whether inside, outside, or partially covering the regime mask – depends on the blocked regime type. For AR, retrograding onset PVAs- already reside very centrally in the regime mask 3 d before onset (Fig. a). The signal of retrograding onset PVAs- of EuBL is mixed given the low sample size (cf. Fig. 3b), but reveals that PVAs- are distributed both within and outside of the regime mask to its northeast (Fig. b). For ScBL, most retrograding onset PVAs⁻ are located at the eastern edge of the regime mask; for GL, they lie further east, entirely outside the mask (Fig. c and d). This means that, despite sharing the same temporal reference point (blocked regime onset), the timing at which onset PVAs- enter the blocking region differs not only between individual life cycles but also systematically between blocked regime types. To avoid conflating these differences in timing and evolution in an Eulerian composite framework, a quasi-Lagrangian perspective is particularly well suited here.

About 3 d before blocked regime onset, certain regions with high onset PVA⁻ frequency coincide with the location of the regime mask associated with another blocked regime type (Fig. ). This raises the broader question of whether the pathways of onset PVAs- are linked to preferred regime transitions. Figure a shows the climatological frequency of regime transitions for each of the four blocked regimes. All four blocked regimes can arise from any regime type, except for GL, which never transitions from ZO during 1979–2021. The no-regime state is the most frequent origin, accounting for 30 %–42 % of transitions to blocked regimes. When the seven regime types are grouped into cyclonic and blocked regime types, GL and AR most often evolve from other blocked regimes, with transition frequencies of 58 % and 47 %, respectively. After the no-regime state, the most common transitions are ScBL to GL and EuBL to AR. Interestingly, the second most frequent transition into EuBL originates from ZO, showing that cyclonic-to-blocked transitions, while not dominant, occur regularly.

Figure b and c show deviations in transition frequencies from the climatological mean for the upstream and retrogression pathways, respectively (positive values indicate higher-than-average frequency). A comparison of regime transitions between the pathways shows that the upstream pathway dominates for blocked regime life cycles that develop from none of the seven regimes. This suggests that blocked regimes forming during periods of more transient large-scale flow are primarily associated with upstream PVAs-. A clear relationship emerges between the pathways and specific regime transitions when considering transitions between blocked regimes. Transitions from blocked regimes whose regime mask is located downstream of the current regime are predominantly linked to the retrogression pathway. Conversely, when the regime mask of the previous blocked regime is located upstream, onset PVAs- tend to follow the upstream pathway. This relationship holds for all blocked-to-blocked transitions, except for the climatologically frequent ScBL-to-GL transition, for which both pathways occur with similar frequency. However, it has been shown that both pathways can occur at the same time, as multiple PVAs- propagate and trigger GL onset, with the onset PVA⁻ merging with another PVA⁻ along the alternative pathway .

Given the connection between pathways and regime transitions, we analyse whether the onset PVA⁻ of a blocked regime was inherited from the block of the preceding regime. Focusing specifically on blocked-to-blocked regime transitions (40.2 % of all cases), for each time step of an active blocked regime, we identified the PVA⁻ with the largest overlap with the regime mask as the “dominant” PVA⁻. If the onset PVA⁻ of a blocked-to-blocked transition coincided with the dominant PVA⁻ of the preceding regime, the two regimes could be connected. We find that 57 % of blocked regime onsets are linked to the dominant PVA⁻ from the previous block, whenever the onset follows a blocked regime. This indicates that PVAs- do not necessarily form independently of the previous blocked regime but are instead displaced or reorganized remnants of the earlier blocking configuration. Along the retrogression pathway, notable continuity was found for transitions from ScBL to GL (60 %), EuBL to AR (76 %), and AR to GL (92 %). For the upstream pathway, strong linkages of PVA⁻ were observed for EuBL-to-ScBL (77 %) and AR-to-EuBL (88 %) transitions. However, not all transitions exhibit such continuity. During GL-to-ScBL transitions, the PVA⁻ dominating the onset is unconnected to the preceding GL block in 72 % of cases, which implies that the ScBL block forms in situ rather than as a continuation of the GL anomaly.

In this section, we first take a regime-centred perspective and consider the amplitude evolution of onset PVAs- relative to regime onset, consistent with previous studies of weather regime dynamics e.g.. Subsequently, we switch to an anomaly-centred perspective and consider the evolution relative to the maximum amplitude of onset PVAs-.

A major result of this study is the dominance of moist processes during the amplification phase of onset PVAs- prior to blocked regime onsets, as presented in Sect. 3.3. Here, we investigate the spatial distribution of amplifying DIVdiv tendencies and WCB activity within the onset PVAs-, and analyse whether the contribution of moist processes depends on the geographic position of the PVAs- relative to the storm track. Given the maximum in DIVdiv during the 2 d preceding blocked regime onsets (cf. Fig. a) and to be consistent with Fig. , we present onset PVA⁻-centred composites of WCB activity and DIVdiv tendencies for the period from -3 d to onset (corresponding to period II in Fig. ), shown separately for the four blocked regimes and pathways.

Onset PVAs- of most regimes and pathways reveal amplifying DIVdiv tendencies to the northwest of the PVA⁻ centre, with a distinct WCB structure before regime onset: WCB inflow in the southwestern, WCB ascent in the western, and WCB outflow in the northern part of the anomaly (Fig. ). This composite structure of the full WCB corresponds well with many case study-based findings of WCB activity along the western edge of a ridge or block e.g.. There is a strong spatial overlap of WCB outflow, negative DIVdiv tendencies, and areas of pronounced upper-tropospheric divergence (wind vectors in Fig. ), all located to the northwestern part of the anomaly. Consistent with this spatial linkage, we find a modest, significant positive correlation between the anomaly-integrated DIVdiv tendencies and WCB area size within the onset PVAs-, with r=0.32 for WCB ascent and r=0.34 for WCB outflow. demonstrated this relationship for a single case, but here we show that the relationship holds systematically in a climatological sense, i.e. in the average over many cases. This result is consistent with the notion that tropopause modification by upper-tropospheric divergent flow is enhanced by latent heat release in WCBs and suggests a link between WCBs and the divergent PV tendencies that reinforce negative PV anomalies. Upper-level convergence, in contrast, occurs in the eastern part of the onset PVAs-, where it contributes to a local increase in PV. However, when considered in an integrated sense, the anomaly-amplifying tendencies of DIVdiv dominate, resulting in a net amplifying effect of DIVdiv (cf. Fig. ).

High variations are found in the activity and co-occurrence of WCBs with onset PVAs- before onset, showing a strong dependency on the blocked regime type and, in particular, on the pathway (Fig. ). WCB activity and associated DIVdiv tendencies are overall more pronounced for onset PVAs- following the upstream pathway compared to the retrogression pathway (Fig. , upper vs. lower panels). The strongest and most coherent WCB outflow is present for upstream pathway cases of AR, EuBL, and GL, and is characterized by widespread outflow covering the northern part of the onset PVAs- and contributing to anticyclonic anomaly amplification. In contrast, WCB activity is generally weaker and less spatially coherent for PVAs- following the retrogression pathway, particularly for EuBL and ScBL, where no robust composite WCB signal is evident. While DIVdiv makes a substantial net contribution to the PVA⁻ amplification along the retrogression pathway (Fig. a), this signal is weak in the mean spatial composites (Fig. b and c). This is likely due to several factors, including changes in anomaly size and shape that smear the signal, as well as contributions from upper-tropospheric processes not directly related to WCB outflow, such as jet-related ageostrophic (dynamically forced dry) secondary circulations and balanced Rossby-wave dynamics.

As previously noted for GL , WCB-related diabatic outflow can contribute to ridge amplification and may in some cases support the westward extension of PVAs-. Generalized for all four blocked regimes considered here, the upstream WCB activity and DIVdiv-related amplification play distinct roles depending on the pathway. Along the upstream pathway, WCBs primarily act as an amplification mechanism, strengthening PVAs- and favouring downstream development and progressive evolution. Along the retrogression pathway, the weaker and less spatially coherent WCB activity may in some cases contribute to the deformation of PVAs- and thereby aid anomaly retrogression by locally extending PVAs- westward, which is consistent with reduced ridge propagation e.g.. This suggests that while WCBs dominate anticyclonic amplification in PVAs- following the upstream pathway, their influence during retrogression is secondary and more heterogeneous, acting as an additional aid rather than a primary driver of the evolution, consistent with .

The partly large differences in WCB activity between the blocked regime types and pathways in the 3 d before blocked regime onset raise the question of whether the location and pathway of onset PVAs- determine the extent to which they are amplified by moist processes. To address this question, Fig.  presents the spatial distribution of the mean WCB outflow area within onset PVAs- in the 6 d prior to blocked regime onset. The results reveal a clear spatial dependence: the largest mean WCB outflow areas within PVAs- are found over the western North Atlantic across all regimes, while moderate outflow areas occur over the eastern North Atlantic and only small outflow areas are found for onset PVAs- located over North America, Europe, and over western parts of Asia. This pattern closely follows the climatological distribution of WCB activity e.g., indicating that PVAs- located in storm-track regions are more strongly exposed to moist processes. When considering the blocked regime types separately and accounting for their respective pathway orientations, these spatial patterns also help explain the differences in diabatic contributions to PVAs- amplification, as indicated by DIVdiv (Fig. ). For AR and EuBL, the upstream pathways intersect regions of frequent WCB activity (Fig. a and b), consistent with stronger moist amplification. For ScBL, the retrograding pathway remains largely outside these regions, showing comparatively weak WCB outflow within the corresponding onset PVAs-. Overall, Fig.  shows that the differences in PVA⁻-centred WCB activity and associated DIVdiv composites (Fig. ) arise from the distinct geographical positioning of the PVAs- relative to the North Atlantic storm track (Fig. ; black contours), and thus to regions where WCB frequency climatologically peaks.

To conclude, the close link between WCB activity and amplifying DIVdiv tendencies underscores the importance of moist processes along the pathways of onset PVAs-. Onset PVAs- crossing the North Atlantic storm-track region are more likely to be amplified by moist processes than those propagating through more continental areas, such as the retrogression pathways of EuBL and ScBL.

Considering 729 blocked regime life cycles over the North Atlantic–European region, this study provides a quasi-Lagrangian view on the origin and propagation of onset PVAs-. These anomalies do not develop in-situ but rather propagate into the target region within the blocked regime pattern. Based on their location in the days before blocked regime onset, most onset PVAs- approach their blocked regime location from upstream, i.e. from the west of or within the North Atlantic–European sector, consistent with previous findings that identify the western North Atlantic as a typical genesis region for atmospheric blocks . For EuBL, more than 75 % of onset PVAs- follow the upstream pathway, supporting earlier results linking blocking over Europe to Rossby wave trains from the subtropical western Atlantic .

Retrogression of blocks has received less attention, although early work already highlighted this behaviour, particularly in spring. GL is the only blocked regime with a consistently more frequent retrogression pathway (58 %) than an upstream one. Previous studies have suggested that processes on the western flank of a block can lead to westward expansion or displacement , and that divergent outflow may decelerate the eastward propagation of ridges or blocks . In agreement with , our results suggest that barotropic dynamics primarily contribute to the westward propagation of PVAs-, while moist-process-related divergent outflow may additionally support their westward extension by amplifying anomalies on the western flank prior to blocking onset. When viewed alongside and , these results suggest that moisture can modulate block retrogression, as dry simulations typically exhibit a more zonal flow and less pronounced westward displacement.

Propagation of blocks has also been studied in the context of weather regime transitions e.g.. linked the propagation and dissipation of blocking highs to regime transitions over the North Atlantic–European region. We find that a single PVA⁻ can contribute to multiple blocked regimes during such transitions, explained by overlapping pathways and formation regions between successive regimes. The AR–GL transition, characterized by northwestward-propagating PVAs- from the central North Atlantic, was already described by . Using our quasi-Lagrangian PV perspective, we confirm that 92 % of AR–GL transitions involve retrogression of the PVA⁻ from the eastern North Atlantic toward Greenland. Likewise, the upstream propagation of anticyclones associated with EuBL–AR transitions is confirmed in 76 % of cases where onset PVAs- of AR followed the retrogression pathway.

Using the quasi-Lagrangian PV framework, we reveal that onset PVAs- strongly amplify in the days before the actual blocked regime onset, independent of pathway and blocked regime type. Thereby, the amplitude evolution shows greater similarity across all blocked regimes than between the two pathways: The timing of maximum amplification poses the major disparity with a later amplification of upstream PVAs- and a much earlier amplification of retrograding PVAs-. Anomaly-amplifying divergent PV tendencies (DIVdiv) contribute dominantly to this amplification and we confirm their link to latent heat release in WCBs. Previous climatological studies have highlighted the importance of moist contributions to blocking onset e.g., using a purely Lagrangian perspective based on air-parcel trajectory diagnostics. Baroclinic interaction (LOW) and the general growth in PVA⁻ area are of secondary importance and further strengthen the PVA⁻ amplitude. The role of quasi-barotropic wave dynamics (UP) depends on the pathway and can contribute either to the weakening or strengthening of a PVA⁻.

A closer look at the DIVdiv-WCB activity link revealed that the contribution of moist processes depends on the location of onset PVAs- relative to the storm-track region – consistent with , who reported stronger latent-heating effects for Atlantic than for continental blocks. Overall, the moist contribution is stronger for the upstream pathway, as these onset PVAs- typically reside within or near the midlatitude storm track where WCB activity is frequent and promotes amplification of onset PVAs-. For the retrogression pathway, moist processes are weaker and more heterogeneous but can still provide an additional aid to the evolution of onset PVAs- when they intersect the storm-track region over the North Atlantic during their westward propagation. This occurs, for example, by contributing locally to their westward extension. Our results also align with regarding the timing of moist amplification. They showed that extending backward trajectories from 3 to 7 d substantially increases the share of heated trajectories, indicating that moist processes can act well before blocking onset. This timing dependence is consistent with our finding that moist amplification occurs earlier for retrogressing onset PVAs-, whereas upstream PVAs- intensify closer to the onset. Extending the analysis period therefore captures the moisture contribution of all PVAs-, including those that experienced earlier, weaker amplification phases.

Using an anomaly-centred perspective, a clearer picture emerged on the life cycle dynamics of onset PVAs- for different blocked regimes and pathways. DIV_div still dominates the amplification, but the contribution of UP is more distinct and consistently acts to strengthen the PVA⁻, in comparison to the onset-centred perspective. This indicates that the relative importance of UP is highly sensitive to the choice of reference time, i.e. whether it is aligned with the onset of the blocked regime or with the maximum amplitude of PVAs-. Comparing the evolution of onset PVAs- to the amplitude evolution of negative PV anomalies linked to ridges as part of RWPs suggests that the underlying tendency patterns are similar: Onset PVAs- grow by downstream development (UP), followed by enhanced LOW tendencies, and, in particular, DIVdiv. This sequence is consistent with what has been termed downstream moist-baroclinic development .

The fact that the maximum amplitude of onset PVAs- does not coincide with the blocked regime onset suggests that the transition into a blocked regime is less directly linked to the in-situ amplification of individual anomalies, and more consistent with a reorganization of pre-existing PVAs- into the large-scale blocked pattern. This interpretation is rooted in the definition of blocking used here within a weather-regime framework. While specific blocking indices often emphasize the intensity of a block e.g., the weather regime perspective primarily focuses on the similarity of the large-scale flow pattern, with a secondary emphasis on amplitude. This allows for more transience, such that the onset of a blocked regime does not necessarily coincide with a peak in PVA⁻ intensity. Moreover, the PVAs- contributing to the onset of a blocked regime are not always identical to those dominating at the regime maximum cf.their Fig. 9a, highlighting the role of transient eddy contribution in shaping the blocking structure . Together, these results suggest that the transition to a blocked regime is associated with a structural reorganisation of the flow rather than sustained local growth of a single PV anomaly.

analysed the same types of blocked regimes during the same time period as in the current study from an Eulerian PV perspective. In that study, very similar PV tendency terms were projected onto the regime patterns to assess the relative importance of different processes in building the regime pattern. In contrast to our focus on the negative PV anomaly, the results published in pertain to the full regime pattern, including the area of the patterns' positive PV anomaly. When computing the projections only for the region of the positive and negative PV anomaly, respectively, the results look very similar on average, as documented for a single case in .

For all blocked regime life types, found that linear quasi-barotropic dynamics and non-linear eddy flux convergence dominate regime development, while baroclinic and divergent PV tendencies contribute only marginally. That study also identified two clusters resembling the pathways found here. In comparison, our results suggest that divergent PV tendencies can appear more pronounced when diagnosed from the perspective of PV anomaly evolution, consistently across all pathways and blocked regime types.

Building on , who reconciled results from Eulerian, Lagrangian, and quasi-Lagrangian perspectives for a single case study, we here generalize these findings across the onset phases of multiple blocked-regime types in the North Atlantic–European region and reconcile conclusions from previous Eulerian- and Lagrangian-based studies on blocking dynamics. The Eulerian perspective emphasizes the reorganisation of anomalies within the regime mask, rather than their initial amplification, highlighting a key distinction from the quasi-Lagrangian approach. Onset PVAs- mostly amplify in the days before blocked regime onset, when they are located outside of the regime mask. Hence, their moist-dynamical contributions occurs remotely and the Eulerian perspective largely misses this formation and amplification stage. Instead, it captures the propagation of onset PVAs- into the regime mask as a form of anomaly reorganization within the dominant barotropic PV tendency term. Thus, the Eulerian signature of anomaly reorganisation is reconciled with the quasi-Lagrangian evidence of remote, moist-driven PVA⁻ amplification.

In conclusion, our quasi-Lagrangian PV analysis revealed two distinct PVA⁻ onset pathways to blocked regimes, showing that pathway-dependent dynamics exceed differences between regime types, and underscoring the importance of moist processes in their amplification. These results reconcile previous inconsistencies regarding the roles of dry and moist processes, showing that both are essential but act at different stages and locations. By linking remote moist amplification of PVAs- with local, dry barotropic pattern formation, we gain a more unified understanding of how different blocked regimes and pathways emerge. The analyses using the quasi-Lagrangian PV framework also highlight the importance of capturing dry and moist processes in models, especially the interactions across scales and the role of moist-baroclinic eddies, to improve the prediction and conceptual understanding of blocked regimes. Notably, these findings directly address multiple key challenges and knowledge gaps in understanding the physical processes linked to atmospheric blocking, which were recently identified in the perspective review by .

While the quasi-Lagrangian PV approach provides novel insights into the evolution and amplification of PVAs- linked to blocked regime onsets, several limitations remain. The sample size of blocked regime life cycles becomes limited when separating blocked regime types and pathways, which may affect the robustness of detailed, pathway-specific conclusions and further stratification, e.g. to examine seasonal variability. Our diagnostic tracks only negative PV anomalies, whereas the Eulerian framework considers both positive and negative anomalies in a joint framework, making it difficult to compare in more detail the quasi-Lagrangian insights with the full-pattern Eulerian results. Finally, the study focuses on (pre-)onset dynamics and does not address the full blocked regime life cycle or the factors determining regime duration, which is important for understanding how initial anomaly development translates into the persistence and decay of blocked regimes.

Our findings highlight distinct contributions of moist- and dry-related processes, while also reflecting that their separation is not always clear for individual terms, for example for divergent PV tendencies, as discussed above. However, beyond the attribution of individual processes, a key open question remains regarding the transition into blocked regimes. In particular, why only some diabatically enhanced, slowly propagating PVAs-–whose amplification closely resembles ridge growth in RWPs and largely samples the climatological distribution of WCB activity – ultimately develop into blocked regimes is not yet understood. Recent work by finds little evidence that these PVAs- have systematically distinct moist characteristics, suggesting that the key question is not the moist processes themselves, but the conditions under which remotely amplified anomalies develop into a block. Thus, the central challenge for future research is to understand the coupling between remote moist-dynamical amplification and local dry anomaly rearrangement, and what factors determine whether this coupling leads to blocking.