A Lagrangian Analysis of the Dynamical and Thermodynamic Drivers of Greenland Melt Events during 1979–2017

In this study, we systematically investigate the dynamical and thermodynamic processes that lead to 77 Greenland melt events affecting high-elevated regions of the Greenland Ice Sheet (GrIS) in June–August (JJA) 1979–2017. For that purpose, we compute 8-day kinematic backward trajectories from the lowermost ∼500 m above the GrIS during these events. The key synoptic feature accompanying the melt events is an upper-tropospheric ridge southeast of the GrIS associated with a surface 5 high pressure system. This circulation pattern is favourable to induce rapid poleward transport (up to 40◦ latitude) of warm (∼15 K warmer than climatological air masses arriving on the GrIS) and moist air masses from the lower troposphere to the western GrIS and subsequently to distribute them in the anticyclonic flow over North and East Greenland. During transport to the GrIS, the melt event air masses cool by ∼15 K due to ascent and radiation, which keeps them just above the critical threshold to induce melting. The thermodynamic analyses reveal that the final warm anomaly of the air masses is primarily 10 owed to anomalous horizontal transport from a climatologically warm region of origin. However, before being transported to the GrIS, i.e., in their region of origin, these air masses were not anomalously warm. Latent heating from condensation of water vapour, occurring as the airstreams are forced to ascend orographically or dynamically, is of secondary importance. These characteristics were particularly pronounced during the most extensive melt event in early July 2012, where, importantly, the warm anomaly was not preserved from anomalously warm source regions such as North America experiencing a record 15 heat wave. The mechanisms identified here are in contrast to melt events in the low-elevation high Arctic and to midlatitude heat waves, where adiabatic warming by large-scale subsidence is essential. Considering the impact of moisture on the surface energy balance, we find that radiative effects are closely linked to the air mass trajectories and enhance melt over the entire GrIS due to (i) enhanced downward longwave radiation related to poleward moisture transport and a shift in the cloud phase from ice to liquid primarily west of the ice divide, and (ii) increased shortwave radiation in clear-sky regions east of the ice divide. 20 Given the identified mechanisms that cause extensive melt over the GrIS, the understanding of upper-tropospheric ridges over the North Atlantic, i.e., also Greenland blocking, and its representation in climate models is crucial in determining future GrIS melt and so global sea-level rise. 1 https://doi.org/10.5194/wcd-2020-16 Preprint. Discussion started: 28 April 2020 c © Author(s) 2020. CC BY 4.0 License.

Q4) Does the answer to Q2 and Q3 differ for subregions of the GrIS?
2 Data and Methods

ERA-Interim data
This study is based on ERA-Interim reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF; 95 Dee et al., 2011). The data is available every 6 h from 1979 to 2017, on 60 vertical levels and interpolated to a grid with a horizontal grid spacing of 1 • . The reanalysis data serves as best estimate of the past atmospheric state on the synoptic scale, which is why we implicitly refer to it as the actual state of the atmosphere. As climatologies of the variables used for Eulerian analyses (Table 1), we compute 10 d-averages of the 6-hourly data centered on the respective calendar day over the entire period 1979-2017 (i.e., the long-term average of 39 x 41 time steps). Note that for radiation, we use fields with the same time 100 of day only to account for the daily cycle (i.e., 39 x 11 time steps). We use the ice outline after Zwally et al. (2012) to separate ice from land grid cells in Greenland. Only grid cells with a center inside the ice outline are classified as ice grid cells, which leads to 519 ice grid points in ERA-Interim, corresponding to a GrIS area of 1.73 million km 2 , which is slightly larger (+0.7%) than observed (Zwally et al., 2012).

Melt event definition 105
As previous studies focused on single Greenland melt events, such as in July 2012 (e.g., Nghiem et al., 2012;Bennartz et al., 2013;Tedesco et al., 2013;Neff et al., 2014;Bonne et al., 2015), there is yet no generally accepted definition of a melt event for climatological studies. We define them as follows: The occurrence of surface melt is approximated by a skin temperature (SKT) greater or equal to −1 • C, as in earlier studies (e.g., Nghiem et al., 2012). A time step is interpreted as part of a melt event if at least 5% of the total GrIS surface area is melting and including grid points above 2000 m elevation ("melt time 110  Table 2. Average (Avg.), standard deviation (σ), minimum (Min.) and maximum (Max.) of melt event duration, maximum elevation experiencing surface melt (ME) and maximum two-meter temperature (T2M) at this highest grid point, respectively, as well as minimum and maximum melt extent during the melt event. For T2M@ME, the elevation at which it was observed is indicated in brackets. The total number of melt events is N = 77. step"), to distinguish melt events from the typical summer melt in the GrIS ablation area. In order to avoid splitting of a -from a dynamical point of view -coherent melt event due to the pronounced diurnal temperature cycle, we include non-melt time steps when identifying coherent melt events. This is done as follows: intermediate non-melt and melt time steps are connected in time to yield melt events with the starting (end) date defined as the first (last) time step when melt was detected, but not preceded (followed) by melt for more than 24 hours. The thresholds of 5% and 2000 m were chosen with hindsight, such that 115 a reasonable maximum melt event duration of around two weeks and a sufficiently large sample size of 77 melt events results.
Events shorter than 24 hours are neglected.

Trajectories
In addition to the classical way of depicting atmospheric phenomena from the Eulerian perspective, we use the Lagrangian framework to investigate air mass modifications, the underlying physical processes and general flow structures. The Lagrangian analysis tool LAGRANTO (Wernli and Davies, 1997;Sprenger and Wernli, 2015) basically solves the trajectory equation where x is the position of an individual air parcel and u the 3D wind vector. We use 3D ERA-Interim wind fields to calculate kinematic backward trajectories from pre-defined starting locations and trace a set of variables along the trajectories (Table 3). One application of the trajectories is to perform so-called Lagrangian forward projections (LFP; Liniger and Davies, 2003;Sodemann et al., 2008), i.e., certain properties of the air mass, such as for example the total 8-day adiabatic warming, are projected onto the trajectory starting point above Greenland.

Lagrangian evaluation of thermodynamic energy equation
We evaluate the thermodynamic energy equation in order to get insight into the warming mechanisms along trajectories.

DT Dt
According to Holton and Hakim (2012) and Bieli et al. (2015), the relationship between temperature, vertical motion, and diabatic processes (Eq. 2) follows from the thermodynamic energy equation and the material derivative of potential temperature Adiabatic warming/cooling is a consequence of adiabatic compression/expansion due to vertical motion (ω). We expect diabatic heating (H) to be dominated by radiative clear-sky cooling at ∼1 K d −1 (Cavallo and Hakim, 2013;Papritz and 155 Spengler, 2017) and latent heating/cooling by condensation of water vapor or evaporation/sublimation of hydrometeors in and below clouds. Oceanic surface sensible heat fluxes in the midlatitudes are typically reduced in summer compared to winter and can only affect the few airstreams travelling in the surface layer.

Detailed analysis of melt event EV69
In order to illustrate our methodology and the processes at play, we start with a detailed case study of the EV69 melt event. It 160 lasted from 18 UTC 2 July to 18 UTC 17 July 2012 and included the most extreme period of surface melt in terms of elevation (up to the highest grid cell at 3175 m) and maximum coverage (94.8%) on 12 July.

Synoptic situation
The synoptic flow configuration during EV69 was characterized by an exceptionally strong 500 hPa geopotential height anomaly, Z500 , over and near Greenland (Figs. 1a,c), and can be divided in two distinct periods of about one week each.

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The first period was initiated by the deepening of a slowly propagating low pressure system near Newfoundland (not shown) and an amplifying upper-level ridge over the Central North Atlantic. During the subsequent eight days, from 18 UTC 2 July to 12 UTC 10 July, the North Atlantic circulation pattern resembled a typical Omega-blocking (e.g. Woollings et al., 2018), as evident from the shape of the Z500 contours ( Fig. 1a). High values of Z500 located southeast of Greenland, with an anomaly vastly above the 90th percentile, were sustained and stabilized by an upstream trough over Newfoundland and a downstream 170 trough over the UK. Another strong ridge was present further downstream over Russia (Fig. 1a). In the lower troposphere, the southerly flow between the upstream low and the Greenland ridge advected exceptionally warm air to southern and western Greenland, causing near-surface potential temperature anomalies, θ 10m , of more than 5 K, as well as to neighbouring regions such as Newfoundland, the Labrador Sea and Baffin Bay (Fig. 1b). Another striking feature is the exceptional heat wave of similar anomaly magnitude over the Great Plains of North America (Hoerling et al., 2014;Neff et al., 2014).

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By the end of the first period, the positive Z500 migrated poleward. Thus, the circulation during the second half of EV69, the 7.25-day period from 18 UTC 10 July to 18 UTC 17 July, was characterized by a less meridional flow south of Greenland and a cut-off anticyclone centered over the GrIS, while a deep trough dominated over northern Europe (Fig. 1c). The median Z500 over Greenland during this period was around +150 m (>90th percentile), except for the southern tip of the GrIS. It went 180 along with an equally exceptional θ 10m over the GrIS and the northeastern North Atlantic, peaking in northern Greenland with values of >+7 K (Fig. 1d).
The combination of the cyclone over Newfoundland and the anticyclone over the GrIS favoured northward transport of low-level air masses from the subtropical North Atlantic towards the southern tip of Greenland and the Labrador Sea. Figure  Figure 1. The median fields of 500 hPa geopotential height (Z500; contours) for the two periods during EV69 (a, b) 18 UTC 2 July to 12 UTC 10 July (8 days) and (c, d) 18 UTC 10 July to 18 UTC 17 July (7.25 days). Median anomalies of the synoptic fields in the respective periods are shown in colors (a, c) Z500 and (b, d) near-surface potential temperature (θ10m). Hatching (stippling) indicates an anomaly outside the 25-75 (10-90) percentile range of equally long periods in JJA 1979-2017. The yellow box indicates the location of the GrIS.
2 shows air masses arriving over the GrIS during melt time steps -hereafter referred to as "melt air masses". Several distinct streams of melt air masses can be identified: Two airstreams originating close to the east coast of North America ascended over the southern tip of Greenland into the mid-troposphere and descended anticyclonically onto the central and eastern GrIS (labels C, E). Another important contribution stemmed from the subtropical North Atlantic. These airstreams followed a northward trajectory also towards southern Greenland, where the higher air masses ascended slightly to reach Southdome in a straight 190 trajectory (S), whereas those in the marine boundary layer moved into the Labrador Sea and from there -remaining at low altitudes -further northward to reach the northern GrIS in a final rapid ascent (N1). It is interesting to note that the bulk of N1 air parcels did not ascend along Greenland's west coast but instead remained at low levels until they approached Northwest Greenland. An additional airstream reached the North at lower altitudes from neighbouring regions and approached the GrIS from the Northwest (N2) or descended in the dry intrusion of the low near Newfoundland. Hereafter, we refer by C, E, N, S, or 195 W air masses to air masses arriving in the specific region, irrespective of whether they follow a similar trajectory as shown in the previsouly discussed example (Fig. 2).

Lagrangian forward projection
The Lagrangian analysis is split in two parts in which we identify (i) sources of air masses (Sect. 3.2.1) and (ii) mechanisms (Sect. 3.2.2) that contributed to surface ice melt over the GrIS prior to or during EV69; specifically, we consider the character-200 istics of the air mass origin and the following transport focusing on thermodynamic temperature changes along the trajectories.

Air mass origin
By comparing with the climatological characteristics of air masses arriving over the GrIS, we pinpoint the anomalous nature of the EV69 melt trajectories in terms of latitude, altitude and temperature anomaly. For each melt trajectory we define the relative minimum latitude and relative minimum pressure as the differences between the respective values of latitude and pressure at  Generally speaking, the median melt air mass moved poleward by about 20 • latitude in region S and up to 40 • latitude in region N (Fig. 3a). Thus, it originated from a region in the atmosphere located around 20 • latitude further south wrt. climatology (Fig. 3b). In addition, it descended by about 50 hPa less than the climatological air parcels, which applies, in 215 particular, to Southdome and the region N ( Fig. 3d). In fact, many melt air masses arriving in these regions show a relative minimum pressure of less than 20 hPa, meaning that they had never reached far above their final elevation and hence ascended from the lowermost parts of the troposphere (Fig. 3c). Further, most air parcels show initially, at t = 192 h, a small potential temperature anomaly wrt. the local climatology, θ cl , of ∼0.5-2.5 K, which is highly unusual compared to the average air mass, which shows an approximately 0 K initial anomaly (Fig. S1c). The origin of these initial warm anomalies is related to the 220 North American heat wave (Hoerling et al., 2014) and other anomalously warm source regions, predominantly in the Canadian Arctic. An interesting exception concerns melt air masses reaching region N, which did not come from regions with a positive temperature anomaly. They, however, show the largest relative minimum latitude, i.e., strongest meridional transport, of more than 40 • latitude (Fig. 3a). Other exceptional melt air masses arrived over regions C and E, showing slightly increased descent compared to the climatological air masses (Fig. 3d).

Air mass evolution
In order to assess the relative importance of adiabatic and diabatic temperature changes for the final temperature anomalies of EV69 melt air masses, we first consider the typical temperature evolution of all air parcels that arrive over the GrIS during JJA 1979-2017. The initial temperature is very uniform for all trajectories with a median of T = −3.8 • C at t = −192 h ( Fig. 4a). While in the following all air parcels experience diabatic cooling of about 0.5-1 K day −1 (Fig. 4c), mostly due to 230 longwave radiative fluxes, the adiabatic temperature changes exhibit a strong elevation dependence. Specifically, C air masses cool adiabatically, indicating ascent prior to arrival over the GrIS (Fig. 4b). Air masses arriving in the coastal areas, in contrast, experience overall adiabatic warming. This descent is likely the result of katabatic drainage flows prevalent over the GrIS (cf. Heinemann and Klein, 2002). Consequently, cooling dominates the temperature evolution of most air masses arriving over the elevated regions of the GrIS, whereas at lower elevations adiabatic warming compensates for much of the radiative cooling 235 such that these air masses experience little to slightly positive overall temperature changes (Fig. 4d). Except for some of the latter, summertime air parcels arrive with negative temperatures within the lowermost 60 hPa (∼500 m) aloft the GrIS, because of T < 0 • C at t = 192 h (Fig. 4a) and cooling during the transport to Greenland (Fig. 4d).
The adiabatic and diabatic temperature modifications of EV69 melt air masses deviated from the typical summer air mass as 240 shown in Fig. 4. At the start of their trajectory (t = −192 h), melt air masses were about 10-16 K warmer than climatological air masses (Fig. 5a). Melt air masses arriving closer to the coast of Greenland showed a smaller initial temperature anomaly (T'<+10 K) than those arriving in region C (T'>+16 K). From the evolution during the subsequent eight days, we again refer to representative melt airstreams with different characteristics (see Fig. 2): a melt airstream arriving over (i) the central plateau and East Greenland ("C" and "E"), (ii) North Greenland ("N1", "N2"), and (iii) South Greenland (including Southdome; "S"), 245 respectively. Figures 5b-d and f-h show the adiabatic and diabatic temperature changes during days 0-4, 5-6, and the last two days of the transport to Greenland. N air masses exhibited a thermodynamic evolution in the beginning that was close to that of the climatological air masses (Figs. 5b, f) and an orographically induced final ascent reflected in enhanced adiabatic cooling (Figs. 5c,d). In close proximity to the GrIS, N air parcels ascended from the South (N1 in Fig. 2) or the West (N2 in Fig. 2) to the northern GrIS. Airstream S showed a similar pathway as N1 but with initially exceptional adiabatic cooling before reaching 250 Greenland (Fig. 5b) and subsequently orographic ascent from the South (Fig. 5d). The associated adiabatic cooling and diabatic warming were less pronounced and occurred later in S compared to N (Figs. 5c,d,g,h).  Airstreams C and E experienced much stronger than usual adiabatic cooling during most of the 8-day period, especially between t = −144 h and −48 h, which indicates enhanced ascent (Figs. 5b,c). This ascent either stemmed from dynamical lifting 255 at the polar front, i.e., by the trough over Newfoundland (C in Fig. 2), and/or orographic lifting at the southern tip of Greenland (E in Fig. 2; cf. Stohl, 2006). Interestingly, during the final 48 h, these airstreams experienced strong adiabatic warming due to descent onto the GrIS. Over eight days, the total adiabatic warming anomaly is typically below −10 K and diabatic heating in melt air masses is anomalous by +5 K -both signals especially distinct in airstreams C and E. The total temperature change was uniform over the GrIS and its GrIS-wide median equaled −6.2 K (Fig. 5e), with the initially warmest air masses (Fig. 5a) 260 cooling more than the rest. Nevertheless, 40-80% of the initial warm temperature anomaly of the melt air masses wrt. the climatological air masses (Fig. 5a) was sustained and not compensated by stronger cooling than along the climatological trajectories.
Previous studies (Neff et al., 2014;Bonne et al., 2015) have shown that anomalously warm and humid air masses associated with the heat wave over North America contributed to EV69. To quantify this contribution, we extend our set of backward 265 trajectories to ten days and define heat wave trajectories as those melt trajectories that (i) pass the North American Great Plains at some point, and (ii) at the same time have a potential temperature anomaly wrt. θ cl in excess of 3 K. The fraction of these trajectories among all melt trajectories is shown in Figs. 6a, b. The highest contributions of heat wave air masses are found for airstreams C and E (up to 70% near Summit; C and E in Fig. 2). The heat wave trajectories ending at locations with more than 60% U.S. heat wave contribution were initially anomalously warm (also constrained by the selection criteria) and had a high 270 specific humidity of ∼8 g kg −1 (Fig. 6c). During their way from the American continent to the western North Atlantic (until 13 https://doi.org/10.5194/wcd-2020-16 Preprint. Discussion started: 28 April 2020 c Author(s) 2020. CC BY 4.0 License. t = −120 h), however, these air masses lost most of their warm anomaly. This is in contrast to the idea that they carried the original temperature anomaly from North America to Greenland. At the same time, they conserved their moisture to a large degree, with the driest ones picking up additional moisture once they reached the open ocean. It is only between t = −120 h to −48 h when the air masses rapidly moved poleward into a climatologically much colder region that their warm anomaly 275 increased from around +1 K to almost +10 K. The concurrent reduction of specific humidity confirms the condensation of water vapour and aforementioned diabatic warming during that period (Figs. 5f, g), which was linked to ascent along the sloping isentropes as the air mass moved poleward. Indeed, air masses came from the U.S. heat wave but the temperature anomaly near the origin of their trajectories was not directly responsible for the warm anomaly upon arrival in Greenland.

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In summary, we conclude that exceptional poleward transport and ascent of relatively moist and climatologically warm air masses contributed substantially to EV69 by advection towards the climatologically much colder GrIS region. Nevertheless, air masses leading to this Greenland melt event were cooled stronger than usual during their transport to the GrIS. In these warm, moist and poleward ascending airstreams, cloud formation and latent heating compensated some of the adiabtic cooling and contributed to the warm anomaly over the GrIS.  arriving on the GrIS. The ascending airstreams S, N1, and N2 were associated with strong anomalies of TCLW and rainfall in southern and north-western Greenland, respectively (Figs. 7a, b, e, f). In particular, airstream N1 carried moisture far northward 295 and, as it ascended onto the GrIS north of Summit, the air parcels reached saturation. Consequently, TCLW and RR exceeded their climatologies in the entire region N. Similarly, also region S experienced strong TCLW and RR anomalies due to the ascending airstream S. Interestingly, in region W, TCLW and RR were below average. This is related to the fact that the humid air masses associated with airstream N1 remained in the boundary layer and did not ascend until they reached northwestern Greenland. Consequently, the air masses arriving in region W were transported at higher levels than airstream N1 and did not 300 ascend or may even have experienced slight descent, thus leading to cloud-free conditions. Regions with precipitation experienced an additional heat flux into the ice from rain, while snowfall and total column ice water were widely reduced (Fig. S2b), as was previously highlighted by Doyle et al. (2015) and Fausto et al. (2016). In direct relation to increased TCLW, SSRD was strongly reduced, especially in region N (Figs. 7c, g). In contrast in regions E and W, clear-sky conditions with hardly any precipitation prevailed (Fig. 7a), as evident from extremely low TCLW (Fig. 7b), as well as substantially increased SSRD (Fig. 7g).  Southeast of the plateau, this relates to the branch of the descending airstreams C and E that stretched anticyclonically from west to east across the central portion of the GrIS.
Despite the reduction in downwelling shortwave radiation in the regions with above average TCLW, the sum of net shortand longwave radiation was positive across the entire GrIS (Fig. 7d) and almost everywhere in excess of climatological val-310 ues (Fig. 7h). This is in part explained by enhanced downwelling longwave radiation in the cloudy regions. There and also at and north of Summit, the shift of the cloud phase to the liquid regime was found to be decisive for the observed melt (Bennartz et al., 2013;Solomon et al., 2017). In addition, also total column water vapour was above the long-term summer climatology over all of the GrIS (area-weighted average anomaly of +3.3 kg m −2 ; Fig. S2f). The area-weighted GrIS-wide average anomaly of SSR+STR (Fig. 7h) amounted to +9.4 W m −2 and provided additional energy corresponding to a melting 315 15 https://doi.org/10.5194/wcd-2020-16 Preprint. Discussion started: 28 April 2020 c Author(s) 2020. CC BY 4.0 License.

Climatological analysis for melt events in 1979-2017
In this section we generalize the results from the EV69 case study by considering all 77 Greenland melt events. We present the synoptic situation during Greenland melt events (Sect. 4.1), the air masses associated with these events and their temperature 320 modifications (Sect. 4.2), and finally precipitation, moisture, and radiation patterns over the GrIS and its subregions (Sect. 4.3).

Synoptic situation
We illustrate the synoptic situation related to all Greenland melt events in 1979-2017 by compositing Z500 and its anomaly field, Z500 , relative to climatology (Fig. 8). The composites are calculated five and two days prior to the melt time steps, at the melt time steps, and five days later. It is important to note that some of the time steps entering lagged composites were 325 themselves part of the respective melt event if the melt criterion is satisfied also at the lagged time. As for EV69, melt events are characterized by a dipole pattern of Z500 with a positive anomaly centered over southeastern Greenland and a pronounced negative anomaly over northern Europe. A positive Z500 of +50-70 m is typically present already 120 h before melt occurs, accompanied by troughs both upstream and downstream. This initial pattern is, thus, akin to the geopotential height anomalies associated with cyclonic Rossby wave breaking and omega-type blocking ( Fig. 8a; Liu and Barnes, 2015). Towards lag = 0 h, 330 the anomalies transition into the dipole pattern with a strong ridge or cut-off anticyclone over Greenland and a pronounced trough over the British Isles and Scandinavia (Figs. 8b, c). Z500 near Greenland peak at >+90 m around 24 h before melt occurs. Five days after a melt event, the positive Z500 has shifted towards northwestern Greenland and the high Arctic (Fig. 8d).
The dipole pattern is characteristic of the Greenland blocking regime (e.g., Grams et al., 2017), which projects negatively onto the NAO index and positively onto the GBI.

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This synoptic configuration provides favourable conditions for the poleward advection of warm and moist air masses from lower latitudes towards Greenland (Liu and Barnes, 2015), as reflected in the enhanced total column horizontal water vapour transport (TCVHT) especially along the southwestern GrIS (Fig. 9). The anomalous TCVHT starts over the Labrador Sea several days before the melt event (not shown) and the anomaly increases up to >+60 kg m −1 s −1 at lag = −48 h while at the 340 same time reaching the northern and central GrIS (Fig. 9a). The anomaly then gradually fades and vanishes completely in line with the weakening Z500 after melt events (Figs. 9b, c). The centering of the positive geopotential height anomaly between southeastern Greenland and Iceland instead of over Greenland is a particularly important ingredient for the transport of moistwarm air parcels towards western Greenland and in an arc-shaped anticyclonic flow pattern across northwestern and northern Greenland, as discussed already for EV69.

Lagrangian forward projection
The analyses presented in the following are analogous to those for EV69 (Sect. 3.2), but now for all Greenland melt events in JJA 1979-2017. Note, however, that melt at the most elevated parts of the GrIS is very rare, which is why the results near Summit strongly resemble those in EV69.

Air mass origin 350
Except for some arriving high on the GrIS, at t = −192 h melt air masses are not anomalously warm compared to the local climatology θ cl (Fig. S1a). They are, however, located much further south than usual, i.e., in a climatologically warmer region -more so for air masses arriving in region C and N and near Southdome (Fig. 10b). Coastal air masses previously move further poleward by 10 • latitude and inland air masses by up to 26 • latitude than normal summertime backward trajectories from these location (Fig. 10a). At the same time, the melt trajectories reach less high levels prior to arriving on the GrIS and, therefore, 355 experience less subsidence than climatological air masses (Fig. 10d). Comparing spatial patterns in Fig. 10, we find that, as during EV69, air masses ending in regions C, E, N, and S (subfigure in Fig. 2) share very similar transport characteristics (Sect. 3.2). N and S air masses reach the maximum elevation of their entire 8-day trajectory once they reach the GrIS (Fig. 10c).
The only melt air masses influenced by anomalously strong descent arrive in region E after -embedded in the anticyclonic flow -crossing the GrIS in an arc-like fashion (Fig. 10d).

Air mass evolution
Due to a climatologically warmer origin (lower elevation and/or lower latitude), all melt air masses are at t = −192 h warmer wrt. the climatological summertime air mass arriving at the same location (Fig. 11a). There are no substantial local temperature anomalies at t = −192 h (Fig. S1a). Thus, the positive anomalies of 10-20 K in Fig. 11a can be attributed to the unusual origin of air masses. The time series of adiabatic (Figs. 11b-d) and diabatic temperature change anomalies (Figs. 11f-h) along the 365 trajectories during all melt events look very much alike the ones for EV69 (Sect. 3.2). C air masses ascend and cool adiabatically by a larger amount than the climatological air masses between t = −144 h to −48 h (Figs. 11b, c), while at the same time experiencing more diabatic heating (Figs. 11f, g). Furthermore, C and E air masses both show a stronger final descent reflected in enhanced adiabatic warming in the last two days (Fig. 11d). Finally, air masses ending in regions N and S ascend more wrt. the climatological summertime air masses within the last two days due to their advection towards sloping orography, that is 370 19 https://doi.org/10.5194/wcd-2020-16 Preprint. Discussion started: 28 April 2020 c Author(s) 2020. CC BY 4.0 License. south-to northwesterly advection towards region N or southerly advection towards region S (Fig. 11d).
Overall, the anomalies are slightly weaker than for EV69 and show a stronger elevation dependency. Air masses at lower elevation have a thermodynamic history close to that of climatological air masses with slightly enhanced cooling for S, and enhanced warming for E and N air masses, respectively (Fig. 11e). In contrast, air masses ending in region C and near Southdome 375 are more strongly cooled adiabatically, which is in part compensated by enhanced diabatic heating during the above-normal ascent. In total, however, most melt air masses experience stronger anomalous cooling during the eight-day period prior to arrival over the GrIS. As a consequence, only about 50-90 % of the higher initial temperature as seen in Fig. 11a remains when the air masses arrive on the GrIS.

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In line with the characteristic regions shown in Fig. 2 and the spatial patterns identified in Figs. 10 and 11, we select several trajectory starting points between 2000-2500 m altitude representative of air masses ending in regions E, S, and N (see Fig. 12e). Furthermore, for region C, we consider melt trajectories arriving above 2500 m altitude. In the following we will consider the evolution of T , θ, and θ cl for trajectories arriving in each region. The air masses' evolution in θ−T space (Figs. 12a, c) gives insight into the contributions of adiabatic temperature changes associated with vertical motion (changes along horizontal 385 axis) and diabatic processes (changes along vertical axis). Furthermore, the evolution in θ − θ cl space (Figs. 12b, d) indicates when the final potential temperature anomalies emerge and it reveals the relative importance of transport from climatologically warmer regions towards Greenland (changes along horizontal axis) and diabatic processes (changes along vertical axis). For a more detailed discussion of this type of diagrams we refer to Papritz (2020).

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The commonalities of all climatological air masses arriving over the GrIS include diabatic (radiative) cooling, as well as weak subsidence on the order of 25-50 hPa with associated adiabatic warming during the 8-2 d prior to arrival on the GrIS. This leads to a nearly isothermal temperature evolution in this period (Fig. 12a). Subsidence and poleward motion are both associated with transport from potentially warmer to a colder regions. Since this transport occurs at a rate exceeding that of diabatic cooling, the trajectories acquire a weak potential temperature anomaly of +1-2 K until two days before arrival on the 395 GrIS (Fig. 12b). Within the last one to two days, air masses ascend nearly adiabatically to the GrIS and those arriving in region E additionally descend during the final 12 h (Fig. 12a). During this final period, the potential temperature anomaly fades away and the climatological air mass arrives on the diagonal in the θ − θ cl space (Fig. 12b). Now considering melt air masses, we see that they are initially around 5 K (E) to 18 K (C) warmer and evolve in a distinct 400 way from the climatological summertime air masses (compare Figs. 12a, c). The differences are most striking for C air masses.
During the first four days, these air masses remain at around 800 hPa (Fig. 12c) with no substantial local potential temperature anomaly (Fig. 12d). Then, within two to three days, they experience diabatic heating of around 6 K while ascending by nearly 250 hPa (Fig. 12c) and a potential temperature anomaly of more than 7 K forms (Fig. 12d). Note that the formation of the potential temperature anomaly is about equally due to diabatic heating and transport into a climatologically colder region at the beginning and end of the backward trajectories. Overall, C melt air masses experience a strong cooling of 15 K in eight days, while their potential temperature slightly increases.
In contrast, E, N, and S air masses have an evolution in θ−T space that is more similar to climatological air masses (Fig. 12c).
Notable differences include reduced diabatic cooling and larger ascent and an associated decrease of temperature during the 410 final two to three days, which is consistent with an origin at lower altitudes. Furthermore, the descent of air masses arriving 21 https://doi.org/10.5194/wcd-2020-16 Preprint. Discussion started: 28 April 2020 c Author(s) 2020. CC BY 4.0 License.
in region E is more pronounced. The decisive difference between melt event air masses and their climatological reference is, therefore, the much higher T and θ values at t = −192 h. E, N, and S air masses show a similar evolution in θ − θ cl space as climatological air parcels, but with a stronger effect of transport that results in final potential temperature anomalies of about +3-5 K (Fig. 12d). The gradual increase of the potential temperature anomalies along with the similar temporal evolution 415 as climatological air masses highlights the importance of the anomalous origin and the enhanced poleward transport for the anomalous nature of melt event air masses.
In summary, we note that air masses associated with melt over the GrIS have no initial potential temperature anomaly but they originate from climatologically warmer regions further to the South. The atmospheric circulation, characterized by a large 420 positive geopotential anomaly over Southeast Greenland, then induces strong poleward transport towards the western GrIS, ascent, and latent heat release. Combined with the warmer origin of air masses, these diabatic temperature modifications are altogether responsible for the anomalously warm nature of the air masses when arriving over the GrIS. The importance of diabatic temperature modifications depends strongly on the altitude of the trajectory arrival position and are most important for air masses arriving near Summit.

Linkage to clouds and radiative effects
As in Section 3.3 for EV69, we analyze here the distribution of rainfall, total cloud liquid water, and surface radiation (Fig. 13), which are key quantities modulating the surface energy balance during the 77 observed melt events. As for EV69, there is a clear distinction between the regions west of the ice divide (including large parts of regions C, N, and S), which are exposed to the moist-warm anticyclonic inflow, and the eastern GrIS, which is located on the lee side of the of the ice divide and thus is 430 affected to a much smaller degree by the increased total column horizontal water vapour transport (Fig. 9).
On average, more rain falls in regions NW,S,and W (Figs. 13a,e), especially around Southdome, where a strong shift of precipitation from snow to rain occurs (not shown). Everywhere except region E, there is less incoming solar radiation during melt events compared to climatology (Fig. 13g). In fact, in the higher elevated regions this roots in a shift towards higher 435 TCLW, i.e., a phase shift to the liquid regime and potentially also more cloud cover (Fig. 13f). Even though TCLW is reduced at lower elevations along region W, there is sufficient cloud cover to reduce the incoming shortwave radiation. In contrast, in region E, related to descending air masses, little rain and reduced TCLW are a sign of clear-sky conditions, enabling SSRD to be very close to its maximum for this latitude and time of the year (Figs. 13a, f, g). Furthermore, the median total column water vapour anomaly is positive over the entire GrIS with an area-weighted average of +2.8 kg m −2 (Fig. S3f). Despite the reduction  In light of the disputed sign of the cloud radiative effect over the GrIS, we find that the warm-moist conditions during 445 melt events as such increase the sum of incident short-and longwave radiation, even though contributions vary regionally as described above. The downward longwave radiation is on average increased by +35.6 W m −2 and even more at high elevations, where the cloud water phase shifts, peaking at Southdome with an anomaly of +99.6 W m −2 (Fig. S3h). The results here confirm the importance of moisture transport by the prevailing anticyclonic weather regime for Greenland melt events (Fig. 9) via the longwave radiative effects of water vapour and clouds as previously highlighted by Mattingly et al. (2016), Van Tricht et al.

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(2016), Ding et al. (2017) and Hofer et al. (2019). We conclude that during melt events: 1. moistening of the atmospheric column increases the incoming longwave radiation over the entire GrIS; 2. liquid clouds that were most prominent regions S, NW, and W go along with less incident shortwave radiation and thus reduce melt especially in the ablation area by preventing the strong shortwave ice albedo feedback (Box et al., 2012;Wang et al., 2019), but are highly dependent on the interplay of albedo and optical cloud properties (Van den Broeke 3. rain, mostly affecting the same regions as (2), enhances melt (i) directly by its positive temperature, (ii) indirectly through the albedo feedback by darkening the surface (Fausto et al., 2016), and (iii) by thereby precondition the ice surface for following melt; 4. clouds in the high albedo accumulation region C have a net warming effect at the surface, especially with the observed 460 higher liquid water content and if their optical thickness lies in the optimal intermediate range as during EV69 (Bennartz et al., 2013;Solomon et al., 2017).
Thus, our results indicate that during melt events, the synoptic circulation and transport patterns favour a distribution of cloud (and moisture) radiative effects that potentially enhance melt all over the GrIS because processes (1), (3), and (4) overcompensate the competing shortwave cooling effect (2).

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The JJA near-surface potential temperature (θ 10m ) correlates well (r = 0.66) with the cumulative melt extent (CME) obtained from accumulating melt extent over all melt event time steps (see Section 2.2) in a given summer (Fig. 14a). This is especially noteworthy considering the asymmetry of the CME timeseries, which only varies in the presence of melt events but not when they are absent (i.e., CME ≥ 0). Despite the higher correlation of CME with climate warming (r = 0.57; Fig. 14b), 480 there is a clear relationship between the seasonal circulation-induced θ 10m anomaly and CME (r = 0.41; Fig. 14c). Circulation can amplify warming by a factor of two, e.g., in summers 2010 and 2012, which belonged to the series of summers with persistent NAO-/GBI+ summer circulation anomalies Hanna et al., 2018). Likewise, circulation can also offset climate warming such as in summers 2009 and 2015. The exceptional melt event EV69, discussed here as a case study, was part of -and contributing to -the warmest summer on record (2012; θ 10m = +2.6 ± 0.6 K). EV69 is a textbook example 485 of a Greenland melt event as most of the general dynamical and thermodynamic characteristics of melt events were strongly pronounced. The most prominent synoptic characteristic of Greenland melt events is a upper-level ridge or tropospheric cut-off with its center located southeast of Greenland (Q2, Sect. 1). Despite the anomalously strong final descent of air masses arriving in 490 central and eastern Greenland during these events, large-scale subsidence and adiabatic warming within the anticyclonic flow anomaly is of very little importance for Greenland melt events. This is opposed to lower tropospheric warm extremes in the central Arctic Papritz, 2020) and in mid-latitude heat waves (Bieli et al., 2015;Zschenderlein et al., 2019). The location of the geopotential height anomaly southeast of Greenland is favourable for inducing a southerly flow and enhanced total column horizontal water vapour transport to the West and towards the southern tip of Greenland. As these air masses 495 impinge on Greenland's orography, they are forced to ascend, accompanied by cloud formation and precipitation, subsequently followed by anticyclonic transport across the GrIS and eventually descent along the eastern slope of the ice sheet.
The two most important processes contributing to the warm anomaly of air masses of Greenland melt events are (Q3, Sect. 1): 1. Transport: Melt event air masses originate from a region that is 15 K warmer than climatological air masses. At their 500 origin eight days prior to arrival in Greenland, melt event air masses are, however, not generally anomalously warm.
Hence, it is their origin at lower latitude and/or lower altitude and the subsequent rapid meridional transport of up to 40 • latitude that are decisive for their final temperature anomaly. During transport to the GrIS, the melt air masses cool more than usual, i.e., by ∼15 K, which keeps the trajectories arriving closest to the surface just above the critical threshold to induce melt. As we found, the warm anomaly associated with air masses that arrived near Summit during EV69 arose 505 due to strong meridional transport to Greenland and did not result from a pre-existing warm anomaly such as associated with a heat wave in the Great Plains of North America (Hoerling et al., 2014;Neff et al., 2014;Bonne et al., 2015).
2. Latent heat release: As the GrIS has an average elevation of more than 2000 m, airstreams ascend either dynamically or orographically along their 8-day trajectory. This ascent occurs at the poleward edge of a band of prominent horizontal moisture transport. Latent heat release during ascent and, consequently, cloud formation is contributing substantially to 510 the final warm anomaly of air masses arriving over the plateau region. Both processes, meridional transport and latent heating, are most pronounced for the high-elevation, central regions of the GrIS. Air masses causing melt higher on the GrIS come from warmer and more southerly regions and experience diabatic warming and adiabatic cooling that deviates more from the climatological summertime air parcel (Q4, Sect. 1). Melt air masses of the northern and southern GrIS undergo ascent later along their 8-day trajectory and have an origin at lower levels than air masses of the central GrIS. 515 We further find that the melt events go along with increased total column water vapour (everywhere), related to the enhanced poleward moisture transport, and a phase change of cloud water and precipitation from ice to liquid forming where airstreams ascend over the southern tip of Greenland, along the west coast, as well as in the North of the GrIS (Q3, Sect. 1). The resulting net radiative anomaly contributes positively to surface melt during Greenland melt events (GrIS-wide area-weighted average melting potential of 2.1 cm ice day −1 ), especially in high-elevated regions and the Northwest of the GrIS. Clear-sky conditions prevail over the eastern GrIS, resulting in reduced total column water and enhanced incoming shortwave radiation. In contrast, the enhanced liquid water content in the elevated regions in the South, West and North of the GrIS lead to a reduction of incident shortwave radiation. Yet, the net radiation anomaly is positive due to enhanced longwave radiation. Generally, downward longwave radiation is a key element in triggering surface melt in Greenland and the remaining Arctic (Mortin et al., 2016;Lee et al., 2017), and enhanced poleward moisture transport improves the simulation of Arctic clouds and near-surface tempera-525 ture (Baek et al., 2020). The dynamical and thermodynamic characteristics of melt event air masses found here, confirm the importance of moisture transport as a result of the long-range transport of air masses from the South towards Greenland for (i) inducing latent heating along the trajectory, and (ii) causing a positive cloud radiative effect over the GrIS.
ridges and blocks and their development and lifespan is highly relevant to Greenland's climate, GrIS mass loss (Hanna et al., 2014;Van den Broeke et al., 2017), and global sea-level rise (Van den Box et al., 2018). The dynamical understanding of blocks Steinfeld and Pfahl, 2019) and heat extreme-related upper-tropospheric ridges (Zschenderlein et al., 2020) now includes the important role of upstream latent heating for establishing and maintaining the negative potential vorticity anomalies in the upper troposphere. The representation of those processes in climate models is 535 yet uncertain. More generally, global climate models are yet not able to capture the strong and persistent NAO-circulation anomalies of recent years . If these changes are the result of natural variability, long-term trends predicted by the models could still be trustworthy, as the model performance may mainly be limited by the internal variability of the climate system (Fischer et al., 2013;Knutti and Sedláček, 2013). In the long run, Greenland blocking is not predicted to change significantly towards the end of this century (e.g., Gillett and Fyfe, 2013). If, however, the current decrease in summer 540 NAO is a manifestation of systematic circulation changes associated with global warming, the ability of today's climate models to simulate future trends in the North Atlantic circulation is questionable, and GrIS mass loss at the end of this century could be underestimated by a factor of two (Delhasse et al., 2018). Given the importance of upper-tropospheric ridges and blocks, and associated transport of moist-warm air for Greenland melt events, future work should, therefore, focus on their representation, life-cycle and trends in climate models.

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Code and data availability. All results are based on ERA-Interim data, which can be downloaded from ECMWF (https://apps.ecmwf.int/ datasets/data/interim-full-daily/levtype=sfc/), and analyzed with two additional tools: LAGRANTO (Wernli and Davies, 1997;Sprenger and Wernli, 2015) and clim-ei (Sprenger et al., 2017). Scripts used for the analyses and plotting, mostly written in Python 3.7, are available on request from the authors.
Author contributions. MH performed most of the analyses, supported by LP, and wrote a first version of the manuscript based on his MSc 550 thesis (Hermann, 2019). All authors contributed to the design of the study, the interpretation of the results and the writing.
Competing interests. The authors declare that they have no conflict of interest.