This study is based on ERA5 reanalysis data from the European Centre of Medium-Range Weather Forecasts (ECMWF) for the period January 1979–December 2021. The data set is remapped from the original T639 spectral resolution to a regular latitude–longitude grid. For the identification of negative upper-tropospheric PV anomalies, model level data are used with a spatial resolution in the horizontal of 0.5° and a temporal resolution of 3 h. Spatially coarser data in the horizontal (1°) are selected, as the piecewise PV inversion was optimized for a 1° resolution see.

In this study we define periods of Greenland blocking from the perspective of weather regimes. developed a year-round weather regime classification in the North Atlantic–European region (80° W–40° E, 30–90° N) originally based on the former ERA-Interim reanalysis of ECMWF and here applied to ERA5 . Weather regimes are identified in the period 1979–2019, and we repeat key steps of the regime identification in the following. First, 6-hourly anomalies of geopotential height at 500 hPa (based on a 90 d centered running mean climatology, 1979–2019) are filtered by a 10 d low-pass filter Lanczos filter; . Note that all centered n-day running mean climatologies in this study are obtained by calculating the mean for each calendar time over the specified years and subsequently performing a mean centered on each calendar time taking into account the ±n/2 surrounding days. Anomalies are normalized to aim for a year-round definition, and k-means clustering is performed for the expanded phase space of the leading seven empirical orthogonal functions (EOFs) that explain 74.4 % of the variability. This definition yields in total seven weather regimes, with three cyclonic (zonal regime – ZO, Scandinavian trough – ScTr, Atlantic trough – AT) and four anticyclonic regime types (Atlantic ridge – AR, European blocking – EuBL, Scandinavian blocking – ScBL, Greenland blocking – GL).

Following and , a weather regime index IWR is computed to make a quantitative statement about the similarity of an instantaneous geopotential height field to one of the seven weather regimes. It is defined as 1IWR(t)=PWR(t)-PWR‾1NT∑t=1NTPWR(t)-PWR‾2withPWR(t)=∑(λ,φ)∈EOFΦL(t,λ,φ)ΦWRL(λ,φ)cos⁡φ∑(λ,φ)∈EOFcos⁡φ, where NT is the total number of time steps within a climatological sample (all times in 1979–2019) and (λ,φ) is the respective longitude and latitude within the EOF domain. PWR(t) is a scalar measure that describes the projection of the filtered anomaly ΦL(t,λ,φ) to the EOF cluster mean ΦWRL(λ,φ) within the EOF domain. PWR‾ is the climatological mean of the projection PWR such that IWR is computed as the deviation of PWR(t) from PWR‾ normalized by the standard deviation. Even though the weather regimes are defined based on the 1979–2019 data period, IWR can also be computed beyond this data period for each of the seven regime and each 3-hourly time step in the ERA5 period considered (1979–2021).

Based on IWR, objective weather regime life cycles and associated life cycle stages are obtained following . Local maxima of IWR with IWR≥1.0 are determined as preliminary maximum stage of possible weather regime life cycles. Second, preliminary onset and decay dates are defined as first and last time steps around all maximum stages, where IWR≥1.0. Finally, regime life cycles are defined as periods bounded by an onset and a decay time if the difference Δt=tdecay-tonset amounts to at least 5 d in order to ensure sufficient persistence of the regime. In case two local maximum stages of the same regime share the same onset or decay time, two regime life cycles are combined if the additional following conditions apply: (i) the mean IWR between the two maximum stages is ≥1.0 and (ii) the time difference between the two maxima Δtmax=tmax1-tmax2≤100 d. The combined regime life cycle is then characterized by the earliest onset and latest decay time. The maximum stage corresponds to the time, when IWR is highest during the new life cycle period. This definition of weather regime life cycles allows more than one regime to be active at the same time, where “active” here means that the IWR for more than one regime exceeds 1.0 for at least 5 d. For strong and meaningful regime life cycles, it applies that the regime must have the highest IWR out of all seven regimes for at least one time step in the active regime life cycle such that an in-depth analysis of life cycle stages (onset, maximum, decay) is possible.

A total of 177 GL life cycles are identified during 1979–2021: 31 in December–February (DJF), 58 in March–May (MAM), 52 in June–August (JJA), and 36 in September–November (SON). Despite the differences in numbers, the share of days within a season linked to an active GL life cycle is nearly constant (not shown) due to strongly variable length ranging from 5 d to more than a month (Fig. a). Figure a shows the year-round 500 hPa geopotential height (Z500) pattern during GL. Positive Z500 anomalies and northward-bulging isohypses (black lines) indicate the location of the ridge over Greenland, which is flanked to the south by negative Z500 anomalies as the result of the southward shift in the storm track see. The GL pattern resembles the negative phase of the NAO , and, in accordance with , there is a high negative correlation between the IWR of GL and the NAO index (Fig. ). We find a high level of consistency of our regime-based GL definition with other blocking detection methods. Despite differences in persistence criteria, there is a positive correlation of 0.545 between the IWR and the Greenland Blocking Index (GBI) of . In addition, our method classifies 566 d of blocking over Greenland in summer during 1979–2019 which agrees well with the 623 d identified by .

The quasi-Lagrangian PV framework has been introduced in for a single regime life cycle case study and is here further developed for the systematic investigation of year-round GL regime life cycles.

As the identification of WCBs with Lagrangian air parcel trajectories is associated with rather expensive computations for the long ERA5 period, we use the novel EuLerian Identification of ascending AirStreams (ELIAS 2.0) data set, which has been developed by . ELIAS 2.0 uses convolutional neural networks (CNNs) fed with instantaneous gridded fields to predict footprints of different WCB stages: WCB inflow in the lower troposphere, WCB ascent in the mid-troposphere, and WCB outflow in the upper troposphere. For each WCB stage, the four most important predictors identified from a step-wise forward selection approach are used as input data. For a year-round WCB identification, the 30 d running mean Lagrangian-based WCB climatology serves as the fifth predictor. After training the CNNs based on 12-hourly ERA-Interim data from 1980–1999, the CNNs are applied to 3-hourly ERA5 data and provide a conditional probability for WCBs (ranging from 0 to 1). A grid-point-dependent decision threshold decides if a certain probability is associated with any of the three WCB stages. This threshold is determined for each day of the year and for each WCB stage such that the bias between the Lagrangian-based and the CNN-based WCB climatology is minimal.

First we explore the formation of the year-round GL pattern from an Eulerian PV perspective. Figure  (upper row) shows the development of GL regime life cycles centered on all GL onset dates between 1979–2021 based on the field of upper-tropospheric PV anomalies, mean sea level pressure (MSLP), and Z500.

The onset of GL is characterized by a rapid emergence of a blocked situation out of a very zonally oriented circulation pattern over the western North Atlantic within about 6 d (Fig. , upper-row panels). A weak and broad trough prevails over the western North Atlantic 6 d before the onset (Fig. a). No clear upstream wave-train signal is present, which matches the observation of that the negative NAO phase often develops in situ. Low MSLP over the western North Atlantic indicates the presence of extratropical cyclones downstream of the trough close to Greenland in the days before the onset (blue contours in Fig. a and b), which suggests an involvement of synoptic moist-baroclinic activity over the central North Atlantic to the development of GL. The circulation pattern over the western North Atlantic hardly changes in the days before the onset (Fig. a–c). In contrast, the circulation pattern downstream of Greenland indicates a ridge building over Europe in the days before the onset. Previous studies highlight Scandinavian blocking or Atlantic ridge as precursor regime patterns to blocking over Greenland or to negative phases of the NAO e.g.,, which is consistent with high IWR values of Atlantic ridge, European blocking, and Scandinavian blocking in the days before GL onset (see Fig. ). The most rapid development of the large-scale pattern over Greenland takes place in the 4 d around regime onset (Fig. c–e), characterized by a fast amplification of the ridge that establishes over Greenland and is associated with strong negative PV anomalies in the upper troposphere. In accordance with , a split flow is visible from the onset on (Fig. d and e), pointing to the typical southward shift in the midlatitude storm track during GL (see Fig. b). Strong negative PV anomalies prevail over Greenland, and high MSLP values show that the anticyclonic circulation in the upper troposphere over Greenland has manifested as a high-pressure anticyclone near the surface (high MSLP, red contours). A separate consideration of the development depending on the season indicates no fundamental, qualitative difference in the GL pattern development around onset and that seasonal differences are dominated by the increased jet waviness and stronger anomalies in winter compared to summer (see Fig. S1 in the Supplement).

Two separate regions of negative PV anomalies, namely over the northeastern United States and over northern Europe, stand out in the days before GL onset (Fig. b and c), suggesting a propagation of anomalies rather than a rapid in situ development of anomalies over Greenland. found that the circulation anomaly linked to the ridge over Europe propagated westward to build up a block over Greenland. pointed out different pathways to blocking over Greenland in summer. More recently, found two modes of year-round variability in the dynamics of GL by applying EOF analysis and k-means clustering to low-pass-filtered upper-tropospheric PV anomalies in the days before GL onset, linked to the occurrence of negative PV anomalies upstream and downstream of Greenland.

Using the quasi-Lagrangian PV perspective, we identify the negative PV anomalies (PVAs-) linked to blocking over Greenland and investigate their propagation and origin. This allows us to quantify if there exists a direct link between the PV anomalies upstream and downstream and blocking over Greenland. For each GL regime life cycle, we define the PVA- that exhibits the highest spatial overlap with the GL regime mask (see Fig. b, white contour) in the period ±1 d around GL onset as the “onset PVA-”. The frequency of onset PVAs- reveals that PVAs- linked to blocking over Greenland originate from both upstream and downstream of Greenland and thus indicate two pathways of PVAs- to Greenland (gray shading in lower row of Fig. ). For the classification of the two pathways, an objective partitioning of the onset PVAs- is performed by defining two areas around Greenland east and west of 52.5° W (center of mass longitude in year-round upper-tropospheric PV-anomaly-weighted composite; Fig. b) and by determining in which of the two areas the center of mass location of an onset PVA- is more frequently found in the 3 d before GL onset. Eastern ones are assigned to the “retrogression pathway” and western ones to the “upstream pathway”. For the subsequent discussion of the pathways, Fig.  shows the frequency of onset PVAs- for the two pathways separately for selected time steps around the onset, and Fig.  reveals the mean track of PVAs- for the pathways.

Upstream PVAs- are located over northeastern North America 6 d before the onset (Fig. f) and propagate northeastward towards Greenland (Fig. g–j). Thereby, the PVAs- exhibit a quick northward movement once they reach the east coast of the United States (Fig. b). In contrast, PVAs- belonging to the retrogression pathway are characterized by a northwestward propagation against the mean flow from northern Europe towards Greenland in the 4 d before GL onset (Fig. f–j). However, if the PVAs- are traced further back in time, we find their origin in the storm track over the central North Atlantic (Fig. a). Even 9 d before the onset, the anomalies are located upstream of the Greenland blocking region, revealing an eastward propagation of PVAs- assigned to the retrogression pathway before they become stationary for a short time over Europe. Because of the initial eastward movement of PVAs- linked to the retrogression pathway, the assignment to the pathways depends on the chosen time period (Fig. ). The longer the selected period before the onset, the more onset PVAs- are assigned to the upstream pathway. However, the differences in the assignments vary slowly, and the chosen period of 3 d before the onset is sufficient, as this is the time period with the largest differences in the propagation of onset PVAs- (see white crosses in Fig. ).

From a year-round perspective, more GL life cycles are assigned to the retrogression pathway (58 %) than to the upstream pathway (42 %). This matches well with previous studies that point to blocking over northern Europe (and in particular Scandinavia) as a precursor pattern of GL . Interestingly, in fewer life cycles are accounted to their retrograde cluster (50 %) and more to their upstream cluster (50 %), which can be explained by the different classification techniques between and our study, i.e., low-pass filtering, time-averaged EOF analysis, and k-means clustering vs. instantaneous PV fields for quasi-Lagrangian tracking. The seasonal stratification (Table ) reveals differences between seasons, with a dominance of the retrogression pathway in winter (77 %) but slightly more onset PVAs- following the upstream pathway in autumn (53 %).

The large-scale flow evolution around GL onset separated for the two pathways reflects the marked differences between the two pathways (Fig. S2): except for the amplitude the evolution of the pattern differs more between the pathways (Fig. S2) than between seasons (Fig. S1).

We apply the PV anomaly amplitude metric introduced in Sect.  to all GL onset PVAs-. The following PV tendencies in Eq. () are integrated on selected isentropic surfaces over the area of onset PVAs-: UP, LOW, DIVadv, DIVdiv, RES, and Bnd. This reveals the contributions of different processes to the amplitude evolution and, more importantly, sheds light on the importance of dry and moist processes. Note that in our study focusing on the Northern Hemisphere, an amplification (weakening) of a block mathematically goes along with a negative PV anomaly becoming more negative (positive). In line with , all PV tendency terms are multiplied with -1 so that positive (negative) values always indicate amplification (weakening) of the onset PVAs-.

The previous section highlighted the dominant contribution of DIVdiv to the amplification of onset PVAs- for both pathways. Interestingly, the timing of moist contributions to amplification markedly differs between the pathways. Many studies have linked divergent outflow close to the tropopause to moist processes below and in particular to the presence of WCBs. Hence, DIVdiv has often been referred to as an indirect moist contribution. We here investigate in detail the link of the evolution of DIVdiv (Fig. f) and the occurrence of WCBs in the immediate vicinity of the onset PVAs- (Fig. ) for the two pathways.

Onset PVAs- linked to GL onset are often strongly amplified by DIVdiv once they are located over the North Atlantic (Figs. f and ). This suggests a link to WCB activity, as the climatological WCB activity exhibits a local frequency maximum over the storm track region in the North Atlantic see. Retrograding PVAs- experience the maximum contribution of DIVdiv to the amplification around 4 d before the onset over the eastern North Atlantic (Figs. f and a). In comparison, onset PVAs- following the upstream pathway experience a decreasing contribution of DIVdiv to the amplification once they reach the east coast of the United States. The different timing in reaching the North Atlantic thus provides explanations for the variability in the DIVdiv contribution to the onset PVA- amplitude evolution.

Centered composites of upper-tropospheric PV anomalies and WCB activity on the onset PVAs- (Fig. ) highlight WCB activity in the upstream flank of the PVAs-, which is in good agreement with the theoretical understanding that WCBs amplify a downstream ridge in the upper troposphere (; see Fig. 1 of ). WCB inflow in the lower troposphere is located to the southwest of the upper-tropospheric PVA-, WCB ascent is slightly shifted to the north of WCB inflow and in the southwestern corner of the PVA-, and WCB outflow resides in the northwestern or even northern part of the PVA-.

A good spatial agreement is found for WCB outflow frequency and the occurrence of amplifying DIVdiv contributions for both onset PVA- pathways (Fig. ). Following the retrogression pathway, WCB outflow occurs consistently before and even shortly after onset (Fig. , upper-row panels). Although the contribution of DIVdiv decreases in the 4 d before the GL onset in an integrated sense, it still strengthens the onset PVA- amplitude around the onset (Fig. f). The strongest WCB activity in the retrogression pathway occurs early before the onset (Fig. a) and is most likely linked to synoptic-scale cyclone activity upstream (see Fig. , low MSLP in blue). The ongoing WCB activity on the upstream flank of retrograding onset PVA- suggests that moist processes on the northwestern flank of the onset PVAs- importantly aid the retrograding propagation by continuously rebuilding a negative PVA- on its upstream flank. The spatial extent of onset PVAs- measured by the extent of PV anomalies (dashed contours) indicates that retrograding PVAs- exhibit a larger and in particular more zonally elongated area than the more compact upstream PVAs- – a requirement for circulation anomalies to retrograde in the typical thinking of barotropic wave propagation. However, the high frequency of WCB outflow identified here potentially extends the area of the onset PVAs- on its western flank which might critically support the westward propagation of the onset PVAs-. This highlights that the retrogression of blocks might not be purely barotropic and therefore linked to dry dynamics but also involve an important moist-diabatic component.

In comparison to the retrograding onset PVAs-, an increase in WCB outflow frequency towards the onset is found for PVAs- that reach Greenland from upstream (Fig. , lower-row panels). This points to a more important role of moist processes in the few days before the onset compared to earlier times for the onset PVAs- following the upstream pathway and is in line with the higher contribution of DIVdiv to the amplification (Fig. f). In particular 1 d before GL onset, the structure of the WCB is well represented, and we find a very accurate agreement between amplifying tendencies of DIVdiv and high WCB outflow frequencies (Fig. g). The seasonal stratification of WCB activity around GL onset (Fig. S4) highlights the known marked differences in WCB detection in winter compared to summer see. Still the qualitative picture is similar independent of the season with enhanced WCB activity on the upstream flank of the incipient block prior to and maximized just before onset.

Overall, the agreement between WCB outflow and the contribution of DIVdiv to the amplification of the onset PVA- amplitude matches well and therefore supports the close link between amplitude-strengthening DIVdiv tendencies and moist processes in WCBs.

A complex behavior of PV anomalies during a blocking episode was previously noted in passing by and indicated by for another blocking episode. To here demonstrate this complex behavior more explicitly, we briefly look at a long-lived GL regime life cycle in winter 2009/2010, which led to cold temperatures over western and northern Europe e.g.,.

The IWR of GL exhibits two maxima during the life cycle from 11 December 2009 to 10 January 2010 (Fig. a), which is in contrast to the unimodal course of the IWR for the EuBL regime life cycle see Fig. 3 of. This suggests phases of re-intensification of a blocked pattern for longer-lasting regime life cycles and enables a novel angle on blocking from a regime perspective, which allows for more transient behavior than classical blocking detection algorithms e.g.,with their strict overlap criterion. The temporal overlap of PVAs- with the regime mask over Greenland closely reveals the same evolution as the IWR of GL (Fig. b, black and blue lines). Several individual and independent PVAs- dominate the anticyclonic circulation over Greenland intermittently, pointing to a transient behavior of PVAs- close to Greenland during an active GL life cycle (Fig. b, colored lines). One PVA- exhibits a large spatial overlap with the regime mask and determines the onset of the GL life cycle (onset PVA-, blue line in Fig. b). However, within the regime life cycle, another PVA- propagates towards Greenland (not shown) and merges with the onset PVA- (green line). This PVA- solely describes the block over Greenland for the period 13–26 December. After the regime maximum, the IWR of GL decreases temporarily, followed by another increase around 27 December (Fig. a). The overlap of the PVA- around the maximum stage with the regime mask decreases towards this local minimum in IWR (green line, Fig. b) but then merges with a new PVA- (red line) around 26 December, which propagates towards Greenland. This new PVA- is linked to the second peak in IWR on 3 January 2010 (Fig. a), which constitutes a reinforcement of the GL regime life cycle. Although it undergoes splitting and merging events (red to violet to brown lines, Fig. b), this PVA- remains over Greenland in the period from the second IWR peak to the end of the life cycle (9 January) and even beyond.

This illustrative case highlights that different PVAs- represent the block over Greenland at different life cycle days, complicating a systematic investigation of blocking life cycles. An analysis was conducted on how many PVAs- contribute to a single GL life cycle, where only PVAs- were counted that exhibit a spatial overlap with the regime mask of at least 10 % for a minimum duration of 12 h. Around 20 % of the GL life cycles were associated with a single PVA-. Two PVAs- are linked to a regime life cycle in 22 % of all regime life cycles, three PVAs- for 20 %, and four PVAs- for 18 %, and more than four PVAs- were found in 20 % of all GL regime life cycles. The differences in the number of contributing PVAs- motivates the definition of a single maximum PVA- for each regime life cycle. Equivalent to the onset PVA-, we define the maximum PVA- as the PVA- which has the largest spatial overlap with the GL regime mask in the period ±1 d around the GL maximum stage. We further refer to this PVA- as “max PVA-”. In the case of the GL regime life cycle in winter 2009/2010 (Fig. b), the PVA- represented by the green line would be identified as the max PVA-. In 103 out of 177 GL life cycles (58.2 %), the max PVA- is the same PVA- as the onset PVA-.

From a traditional blocking perspective, the blocking anticyclone exhibits a slower propagation and is nearly stationary during its maximum manifestation e.g.,. Such a behavior is also expected from the regime life cycle perspective around the maximum stage. However, the strengthening (weakening) of the IWR before (after) the maximum stage can be associated with either a strengthening (weakening) of a quasi-stationary PVA- within the regime mask or the migration of a PVA- into (away from) the regime mask. Figures  and  present snapshots of the large-scale PV pattern around the maximum stage, PV tendency composites centered on max PVAs-, and the amplitude evolution of max PVAs- including the different contributions. Note again that the sign of the integrated PV tendencies is defined such that positive (negative) values always indicate amplification (weakening) of the max PVAs-.

The length of GL regime life cycles is subject to high variability and can range from 5 to more than 21 d (Fig. a and b). This limits the analysis in Sect.  that is performed for lagged days around the maximum stage. Therefore, in a last step, we want to account for the full life cycle from the onset to the decay stage. Figure  displays the mean net PV tendencies integrated over the max PVAs- in the period from onset to decay for times when the max PVA- existed. Weighted by the total days between onset and maximum and maximum and decay, this allows for an investigation of the full life cycle, independent of life cycle length.

A positive net amplification of max PVAs- occurs in the first part of the GL life cycle from onset to the maximum stage (Fig. , left-side panel). DIVdiv is the key net contribution to the amplification, revealing a dominant importance of moist processes. The net contributions of LOW and UP are of secondary importance. Bnd dampens the amplification, although the net effects of the sub-terms of Bnd (Eq. ) are of different sign, with a dominant dampening of the amplitude by the eddy flux convergence term but a slight strengthening as the result of a net growth in max PVA- area. The net contributions of DIVadv and RES are negligibly small.

In contrast, max PVAs- experience a net decrease in amplitude from the maximum to the decay stage of GL life cycles (Fig. , right side panel). The leading contributions to the decay arise from UP and Bnd. This time, both sub-terms in Bnd weaken the amplitude, which points to a decrease in max PVA- area (not shown). The net effect of LOW is strongly positive and highlights the baroclinic-coupling after the maximum stage. The strongly decreased contribution of DIVdiv to the amplification of max PVAs- compared to the period before the maximum stage indicates the lack of moist processes, which would act as a maintenance mechanism for blocking over Greenland.

The insights obtained from the analysis of the full life cycle from onset to maximum and maximum to decay agree well with the analyses in Sect. , indicating that the investigation of the few days around the maximum stage could already be sufficient to disentangle the dynamics of the maximum stage. Furthermore, together with Fig. , we can conclude that the amplitude maximum of max PVAs- is somehow connected to the maximum in the blocking regime life cycle.