Drivers for Atlantic-origin waters abutting Greenland

The oceanic heat available in Greenland’s troughs is dependent on the location of the trough, the warm water origin, and how the water is impacted by local processes. This study investigates the mechanisms that bring warm water to the shelf and into the troughs abutting the Greenland Ice Sheet (GrIS). Warm water that is exchanged from the trough into the fjord may influence the melt on the marine terminating glaciers. Regional ocean model experiments showed that Melville Bay troughs experienced 5 warming following 2009. An increase in ocean heat in these troughs may drive a retreat of the GrIS. In 2004 to 2006, model experiments captured an increase in onshore heat flux in the Disko Bay trough, coinciding with the timing of the disintegration of Jakobshavn Isbrae’s floating tongue and observed ocean heat increase in Disko Bay. Warm Irminger water can extend far north into Baffin Bay, reaching as north as Melville Bay troughs. However, it diminishes north of 67N on the east coast. Seasonality of the maximum onshore heat flux differs due to distance away from the original source. The north-west coast 10 and south-east coast respond differently to changes in meltwater from Greenland and high frequency atmospheric phenomena. With a doubling of the GrIS meltwater, Baffin Bay troughs brought ∼ 40 % more heat. The lack of presence of storms resulted in an increase in heat flux ( ∼ 20 %) through Helheim glacier’s trough. These results demonstrate the importance of onshore heat transport through troughs and its potential implications to the GrIS.

buoyancy, which impacts convection, a balance between heat loss and freshwater input; the former drives deep convection and the latter lowers the density of the surface waters, slowing down convection (Aagaard and Carmack, 1989;Straneo, 2006;Weijer et al., 2012). Thus, an increase of the accumulation of meltwaters in the Labrador Sea may affect and slow down deep convection, the process that forms deep ocean waters by mixing surface waters down the water column (Boning et al., 2016;Weijer et al., 2012). A weakening of the deep water formation may impact the Atlantic Meridional Overturning Circulation 5 (AMOC), influencing how the earth distributes heat, impacting sea ice production and dissolved gases such as oxygen and carbon dioxide, and altering ecosystems. (Boning et al., 2016;Weijer et al., 2012;Swingedouw et al., 2014;Arrigo et al., 2017).
Numerous studies have focused on the causation for the increase in mass loss from the GrIS, such as atmospheric warming (Box et al., 2009) and synoptic wind patterns (Christoffersen et al., 2011). The mass balance of the GrIS has been persistently 10 negative since the rapid retreat of marine terminating glaciers began in 1995 (van den Broeke et al., 2016). There are approximately 900 marine terminating glaciers on the GrIS (Rastner et al., 2012) which drain ∼ 88 % of the ice sheet (Rignot and Mouginot, 2012). Therefore, it is this type of glacier that has the greatest control over the fate of the ice sheet. Past studies have concluded that the influences affecting marine terminating glaciers include glacier surface thinning (Csatho et al., 2014), glacier fjord and geometry (Porter et al., 2014;Fenty et al., 2016;Rignot et al., 2016a;Williams et al., 2017;Felikson et al., 15 2017), state of the ice melange (Moon et al., 2015), subglacial discharge (Bartholomaus et al., 2016;Jenkins, 2011), ocean warming (Holland et al., 2008;Myers and Ribergaard, 2013;Straneo and Heimbach, 2013), and ocean induced melting (Cai et al., 2017;Rignot et al., 2016b;Wood et al., 2018). Wood et al. (2018) showed that ocean warming at intermediate depths, below 200 m, has the potential to increase ocean induced undercutting, which has initialized the retreat of the majority of marine terminating glaciers. 20 The fluctuation of heat content in the North Atlantic Subpolar Gyre (NASPG) may have been the cause of ocean warming in fjords of marine terminating glaciers (Holland et al., 2008;Myers and Ribergaard, 2013;Straneo and Heimbach, 2013). The NASPG contains a southern branch that travels northward across the North Atlantic Ocean to the West European Basins (Fig.   1). This branch then can travel westward, forming the Irminger Current circulating along Reykjanes Ridge. The Atlantic water that remains in the Irminger Current carries relatively warm and saline waters along the south-east coast of Greenland, while 25 waters from the Arctic Ocean and Greenland meltwaters from the East Greenland Current (EGC) and East Greenland Coastal Current merge to create a mixed and modified current (Bacon et al., 2014). This current forms the West Greenland Current (WGC) near Cape Farewell. The WGC separates into two branches: one travels northward along the west coast of Greenland into Baffin Bay bringing with it both less saline, cold Polar water and relatively warm, saline, modified Atlantic water, and the second, warmer and more saline branch joins the southward flowing Baffin Island Current at Davis Strait (Fratantoni and 30 Pickart, 2007;Myers et al., 2009). A portion of the NASPG can branch off northward through the Iceland-Scotland ridge, which separates the Norwegian Sea from the North Atlantic Ocean, as the Norwegian Atlantic Current (NwAC) (Beszczynska-Möller et al., 2012). Instead of recirculating in the Fram Strait, a part of the NwAC can enter Barents Sea, south of Spitzbergen or north through Fram Strait (Beszczynska-Möller et al., 2012). A large volume of water that travels through Fram Strait may recirculate directly in the strait and return south to the Nordic Seas (Karcher et al., 2011;Beszczynska-Möller et al., 2012).
to the mouths of fjords. Then, depending on the height of the fjord's sills, it can allow waters access to or block waters from reaching the marine terminating glaciers and accelerating their mass loss (Cai et al., 2017;Rignot et al., 2016b;Wood et al., 2018;Straneo et al., 2012). If the warm waters from the NASPG can reach these transverse troughs, changes in heat content of the NASPG may influence the state of marine terminating glaciers on the GrIS.
This study investigates the following questions: What are the processes that drive the warm water to the coast of Greenland? 10 What is the significance of the deep troughs along Greenland's shelf to the supply of warm water to the fjords with marine terminating glaciers? How does an increase in horizontal resolution benefit an ocean model's representation of this? What is the mean state and variation of the onshore heat flux through the troughs around Greenland? How does the enhanced GrIS meltwater impact the renewal of ambient waters into the troughs? And what is the impact of high frequency atmospheric events on bringing warm waters to the coast?

Model description
A high resolution coupled ocean-sea ice model is utilized in this study. The fundamental modelling framework used is the Nucleus for European Modelling of the Ocean (NEMO) version 3.4 (Madec, 2008). The ocean component is based on Ocean Parallelise (OPA) and is used for the ocean dynamics and thermodynamics. For sea ice dynamics and thermodynamics, Louvain 20 la Neuve Ice Model (LIM2) is used (Fichefet and Morales Maqueda, 1997). The regional domain for the coupled ocean-sea ice model covered the Arctic and Northern Hemisphere Atlantic Oceans (ANHA), with two open boundaries: one at the Bering Strait and the other at the latitude of 20 • S. All simulations start from January 2002, and are integrated to December 2016.
Initial and monthly open boundary conditions (temperature, salinity, horizontal velocities, and sea surface height) are derived from the 1 / 4 • Global Ocean Reanalyses and Simulations (GLORYS2V3) product (Ferry et al., 2008). The surface atmospheric 25 forcing fields (10 m surface wind, two metre air temperature and humidity, downward shortwave and longwave radiation, and total precipitation) with a temporal resolution of one hour and spatial resolution of 33 km, are from the Canadian Meteoro- The ANHA horizontal mesh grid is extracted from a global tripolar grid, ORCA (Barnier et al., 2007), with two different horizontal resolutions. One is at a 1 / 4 • (hereafter referred to as LowRes for low resolution) with a resolution ranging from ∼ 11 km to ∼ 15 km around Greenland, and the other one at a 1 / 12 • (hereafter referred to as HighRes for high resolution) 5 with a resolution ranging from ∼ 3.5 km to ∼ 5 km around Greenland. In the vertical, the ANHA configurations use the geopotential or z-level coordinate with a total of 50 levels. The layer thickness increases smoothly from 1.05 m at the surface level to 453.1 m in the last level (at a depth of 5727.92 m). High resolution is applied to the upper ocean, i.e., 22 levels for the top 100 m. Partial step (Bernard et al., 2006) is also enabled to better represent the sea floor. Bathymetry in LowRes is taken from the existing global ORCA025 bathymetry (MEOM, 2013), which is based on a global relief model (ETOPO1) (Amante 10 and Eakins, 2009) and a gridded bathymetric data set (GEBCO1) (BODC, 2008) with modifications (Barnier et al., 2007).
For HighRes, the bathymetry is generated by using ETOPO1 (Amante and Eakins, 2009) for the polar region, and the Global Predicted Bathymetry (Smith and Sandwell, 1997) from satellite altimetry and ship depth soundings for the rest of the domain.
The HighRes configuration provides model fields at a finer scale that is not always visible in LowRes. This provides the potential for a better simulation of warm ocean currents travelling towards the GrIS via a better representation of deep troughs. 15 In addition, model resolution also plays a role in simulating ocean mixing and mesoscale features, such as eddies, that bring warm water towards the shelf through the trough along the GrIS. Note that, even the 1 / 12 • resolution referred to as HighRes in this study, the small scale interactions of plume dynamics and glacier ice-ocean interactions within the fjord is still not resolved. Therefore, this study will focus on the relatively large scale processes outside of the fjords with an assumption that the meltwater will reach the ocean surface once out of the fjord (Fig. 2). This is also consistent with how Greenland discharge 20 is added in the model, injected at the surface level then mixed into a 10 m thick layer. This approach is common in the present generation of ocean models at this horizontal scale, such as in Castro de la Guardia et al. (2015) and Dukhovskoy et al. (2016).

Enhanced Greenland discharge experiment
LowRes and HighRes simulations use two interannual monthly runoff sources. Greenland's freshwater flux (tundra and river runoff) is provided by Bamber et al. (2012). Runoff in the rest of the model domain is provided by Dai et al. (2009) Previous studies (Holdsworth and Myers, 2015;Garcia Quintana et al., 2019), have shown that high frequency atmospheric phenomena, such as storms, barrier winds, fronts, and topographic jets, plays an important role in the ocean processes (e.g., deep convection in the Labrador Sea) in the study area. Do they also influence warm water brought towards the GrIS? Until this study, this has not yet been studied. With the use of the Kolmogorov-Zurbenko (KZ) filter (Zurbenko et al., 1996), the removal of atmospheric variability (such as temperature and wind speeds) that persisted for a length of 10 days or less from 10 the atmospheric forcing was done to drive a sensitivity simulation, called LowResNoStorms. For more information regarding the methodology of the KZ filtering, please see Garcia Quintana et al. (2019). A complete list of simulations used in this study is given in Table 1.

Mean flow and its fluctuation
To evaluate the ocean's heat that reaches onto the shelf and into the troughs, heat fluxes are calculated at six sections along the 15 coast of Greenland (across one trough per section, as shown in purple and tan, respectively, in Fig. 1). Section names and their associated trough names are seen in Fig. 1. To calculate the fluctuation of the heat flux, the five day averaged model output of both temperature and velocity normal to the section are treated as the full current. A moving averaged was applied by taking the average of five model outputs (25 days) centered on a particular output by taking outputs from two previous, the centered, and two future. Therefore the mean of the temperature and velocity can be taken over a longer period (25 days). The mean 20 values were then subtracted from the full current to get the fluctuation component of the heat flux. Given Eq. (1), ρ 0 is the reference density, Cp is the specific heat capacity of sea water, n is the length of the section, H(z) is the water depth along the section, T (t, z, n) is the temperature, and U (t, z, n) is the velocity normal to the section.
To understand the importance of the fluctuation component of the flow around Greenland, the eddy kinetic energy (EKE) 25 was calculated using the five day average model outputs of velocity in the zonal (u) and the meridional (v) components. To see the annual average of EKE the EKE was calculated first using Eq.
(2). The monthly EKE averages for each month was calculated, and the yearly EKE averages for each year over the period of 2004 to 2016 were calculated.

Backward Lagrangian tracking of warm water reaching marine terminating glaciers
To find the source of the warm waters (i.e. waters of temperature > 0 • C) found near marine terminating glaciers, virtual particles were released at six locations close to the model coastline (cyan lines in Fig. 1). An offline Lagrangian tool, ARIANE, was used to integrate the trajectories of warm water back to five years (Blanke and Raynaud, 1997;Blanke et al., 1999). The This study focuses on six sections around Greenland ( Fig. 1) with marine terminating glaciers and deep bathymetric features.
To examine the sensitivity to different resolution, an examination of the EKE takes place. Figure 3 shows the comparison of EKE in regions along west, south-east and north-east coast of Greenland from the HighRes and LowResControl. In Fig. 4, the six sections are drawn (seen in light purple on the map inset 1). HighRes model bathymetry is in grey and each section runs north to south on the x-axis starting at the left hand side of the figure indicated by the zero kilometre marker. The rest of this 15 section will compare the six sections and discuss how observed bathymetry from other studies compares to the HighRes model bathymetry (Fig. 4) as well as discuss the regions EKE (Fig. 3).

West coast
In north-west Greenland, Kong Oscar is the fastest marine terminating glacier, terminating into Melville Bay (Rignot and Kanagaratnam, 2006;Rignot and Mouginot, 2012). Twenty percent of the GrIS drainage volume is directed along glaciers that 20 feed into Melville Bay, amounting to a discharge of ∼ 80 km 3 yr −1 (Rignot and Kanagaratnam, 2006). Located in north-east Baffin Bay ( to 320 km long, 45 to 120 km wide and reach depths between 740 m to 1100 m with shallow banks (around 100 m below sea level) called inter-trough banks (Slabon et al., 2016;Morlighem et al., 2017). The HighRes bathymetry (seen in Fig. 4a) 25 is relatively shallow compared to the observations discussed. MVBNT is located at the kilometre markers 10 km to 120 km, The maximum depth is reached at kilometre marker 120 km with a depth slightly greater than 500 m.
79NG has a floating ice tongue that abuts Hovgaard Ø, which divides the tongue into two sections (Wilson and Straneo, 2015). The most rapid melting occurs at the grounded (pinned) front, south of Hovgaard Ø, where the ice tongue is thickest 10 and is exposed to deeper and warmer waters (Seroussi et al., 2011;Wilson and Straneo, 2015). Atlantic Intermediate Water flows via bathymetric channels to the south of Hovgaard Ø at a pinned ice front, where there is a shorter pathway between the shelf and cavity, exposing more shelf driven processes such as intermediary flows (Jackson et al., 2014). The warm water is supplied from the warm water that resides in Norske Trough (NT) east of Hovgaard Ø ( Fig. 1) (Wilson and Straneo, 2015).
Some of the relatively fresh glacially modified water is exported to the continental shelf via Dijmphna Sund, north of the glacier In the north-east region (Fig. 3g, Fig. 3h, and Fig. 3i), EKE increases along the troughs at the 250 m and 500 m isobaths.
The differences of the EKE hover around − 0.5 × 10 −3 m 2 s −2 to 0.5 × 10 −3 m 2 s −2 . This region is unique because it is the 20 only region that does not show as significant changes in EKE due to resolution, though HighRes captures stronger EKE over all. Turbulent mixing is highest along shelf breaks and changes of bathymetry, but predominately strongest in the south-east region (Fig. 3). Weak EKE off the north-west and north-east coast of Greenland may be due to the semi-permanent sea ice cover.
What is the significance of the deep troughs along Greenland's shelf to the supply of warm water to the fjords with marine 25 terminating glaciers? A look at the onshore heat flux through these troughs will be shown using HighRes, as the benefits of a higher horizontal resolution have been shown. However, given the numerical costs of the HighRes, LowRes is utilized for the sensitivity experiments that will be discussed later in this paper.
3.2 Onshore heat flux through coastal troughs 3.2.1 West coast: mean state 30 The section drawn for Melville Bay (Fig. 4a) The section drawn for Disko Bay (Fig. 4b), located on the west coast of Greenland, shows two deep troughs: UT and DBT.
Both troughs experience an onshore heat flux at the south edge (kilometre marker about 180 km and 480 km, for UT and DBT, respectively) and an offshore heat flux at the north edge (kilometre marker 100 km to 120 km and 400 km to 420 km, for UT 15 and DBT, respectively). In addition to modified Atlantic water travelling northward via the WGC, along the coast, this study shows that the warm waters are influenced by the bathymetry and are steered eastward into the trough towards the coast.  (Holland et al., 2008).

West coast: seasonal and interannual variation 25
The seasonality of the average onshore heat flux is shown in MVBCT (Fig. 5a). Late fall and early winter shows the maximum onshore heat flux with a peak in November. Through late winter to spring onshore heat flux is weakest, with the minimum (hovering close to 0 TW). This peak in 2004 to 2006 is shown in DBT (Fig. 4b).
In 2011 there is a spike of onshore heat flux in December, reaching over 10 TW, then decreased in January (Fig. 5b). For UT, in 2011, there was also a peak onshore heat flux (Fig. 4b).
Observations at Davis Strait see a temperature maximum in August through to November . The results show DBT received onshore heat flux earlier in the season in the period of 2004 to 2006, around June and July. As the years 5 progressed in the model the timing of the maximum heat flux becomes later in the season, from September to January (Fig.   5b). These results show an early arrival in warm waters occurs at the time when JI melted rapidly (Holland et al., 2008). This may therefore have been due to not only increase in ocean heat but perhaps an arrival of warm waters earlier in the melt season.

South-east coast: mean state
The section drawn for Helheim (Fig. 4c)

South-east coast: seasonal and interannual variation
For HGT2 (Fig. 5c), the period of August through to May has the weakest onshore heat flux. However, offshore heat flux occurs all year round making this location unique compared to all other regions. Observations from a fjord in south-east Greenland showed that in the winter months the layer of Atlantic water is warmer than the summer (Straneo et al., 2011). Looking at 25 HGT2 (Fig. 5c), from October to March there was large variability in the magnitude and direction of the heat flux. At KT (Fig.   5d), a peak of onshore heat flux occurs after August for most years. Summer onshore heat peaks occur in 2004, 2005, 2015, and 2016.

North-east coast: mean state
The section drawn for Scoresby Sund (Fig. 4e), shows Scoresby Sund Trough (SBST). It is again on the north edge of the 30 maximum depth, at kilometre marker 110 km that there is a consistent signal for onshore heat flux of more than 0.025 TW. On the north edge of the kilometre marker 20 km to 30 km, there is variability in the offshore heat flux. The middle of the section is where the heat is coming towards the coast.
The section drawn for 79NG (Fig. 4f), located north-east of Greenland, is drawn from north to south. On the north side of the trough, at around 400 km there is a pattern for onshore heat flux at different periods within the time series, and also similar for 1000 km and 1100 km. This area's bathymetry is quite complex and the deeper regions such as kilometre marker, 40 km, 5 and from 1000 km to 1100 km, has heat flux onshore. The onshore heat flux has a much smaller magnitude than any of the other sections, reaching its maximum value at about 0.04 TW.

North-east coast: seasonal and interannual variation
At SBST ( Further north, a later arrival occurs at MVBCT (September through December). On the north-east coast of Greenland, warm water is received from the NwAC. The transport through the three troughs peak in onshore heat flux thusly: KT from August to November, followed by SBST from November to April and the NT peaked from September to January. Therefore, HGT2 could receive warm water first from the Irminger Sea, then the WGC reaches DBT then MVBCT and the NwAC reaches KT, identify what processes drives the heat flux through the troughs (Fig. 6). This section will compare LowResControl, LowRes-DoubleMelt and HighRes.
For the west coast of Greenland, MVBCT and DBT show that the mean flow is crucial for bringing heat on the shelf (Fig. 6a and Fig. 6c). For MVBCT (Fig. 6b)  The south-east Greenland trough, HGT2, shows that the fluctuation component has transports between 0 TW to ∼ 4 TW of onshore heat flux (Fig. 6f). The fluctuation is crucial for bringing heat onto the shelf especially for HighRes, as there is a large mean offshore heat flux through the study period (Fig. 6e). It is due to the mean velocity, normal to the section, that is TW, whereas the LowRes experiments reaches about 7 TW and 7 TW in those years. It is interesting to note the differences between HGT2 and KT, in HighRes, since they are located in close proximity to each other.
In the north-east at SBST (Fig. 6i) varying the meltwater or the resolution does not impact the mean onshore heat flux. The  Further north at NT (Fig. 6k), the mean component dominates over the fluctuation component for onshore heat flux. The mean component carries heat offshore as well with values reaching over − 3 TW compared to ∼ 0.5 TW onshore. The fluctuation component also contributes to carrying heat towards the shelf, with values reaching ∼ 0.2 TW (Fig. 6l).
To see what is happening further off shelf, a section was drawn called NToff (Fig. 1). Now there exists stronger onshore pulses of the mean heat flux (values reach 2 TW or up to as high at 4 TW) (Fig. 6m). Most onshore mean heat flux pulses  (Fig. 6n).
The percent difference of the annual summation of the onshore heat through NToff verus NT is 5.3 %, 6.5 %, and 6.3 % for HighRes, LowResDoubleMelt, and LowResControl, respectively. Therefore, NToff has more heat travelling through the 5 section than NT. This may be to do the deepening off shelf allowing for warm waters to enter this region, and not closer to the shelf where the bathymetry shallows.

Impact of enhanced Greenland meltwater
Through each section, the annual average onshore heat flux and the total onshore heat flux was calculated for the study period (2004 to 2016). A comparison between the experiments were made for each sector (west includes Melville Bay, Disko Bay, 10 south-east includes Helheim and Kangerdlussuaq, north-east includes Scoresby Sund, 79NG sections) ( Table 2). With double the meltwater, the west sector had a 37 % increase in onshore heat flux. It appears that this mechanism (increase of heat flux with an increase in meltwater) is not as strong or reproduced in any other sector (−5 % and 9 % for south-east and north-east sectors).
For Melville Bay in LowResControl (Fig. 7a), a warm core of water exists at depths 100 m to 400 m, with a maximum (kilo-15 metre marker 500 km) in MVBST reaching almost 2 • C. In LowResDoubleMelt (Fig. 7b), the warm water core temperature to melt, Baffin Bay's ocean heat may increase the most compared to other regions around Greenland. Thus increasing the potential for glaciers to continue to melt, impacting climate, SLR, and ecosystems.

Impact of high frequency atmospheric events
A question of how the atmospheric variability may impact the region of HG for renewing heat from the shelf has been discussed in previous observational studies (Straneo et al., 2010;Christoffersen et al., 2011). Section 3.1 showed that regions with   LowResNoStorms. LowResNoStorms has a total of 2260.2 TW, and the LowResControl is ∼ 18 % less, with a total of 1914.5 TW. This extra 345.7 TW could have the potential to melt 1037.1 kilotons of ice per second. Therefore this increase in total onshore heat flux might be due to less heat being transferred off the shelf due to high variability atmospheric forcing.
3.6 Source of warm water reaching the marine terminating glaciers West coast 25 As described in Sect. 3.1, the west coast of Greenland has fast marine terminating glaciers, such as Kong Oscar and JI. This study shows that the Irminger water's influence on the GrIS can extend far north into Baffin Bay, reaching Melville Bay and its subsequent troughs. In Fig. 9a and Fig. 9b, Lagrangian trajectories show that warm waters (T>0 • C, modified Atlantic water), sourced from the Irminger Sea, supplies heat to the west coast of Greenland. In both figures the highest probability (values greater than 0.1 %) of warm waters come directly from the troughs. Warm water in Melville Bay (Fig. 9a), was found south-west Greenland, following the bathymetric features with the boundary currents to then reach the north-west coast of Greenland. There is a small likelihood that warm water found near Melville Bay would come from Fram Strait or the CAA.
Further south on the north-west coast, near Disko Bay, Fig. 9b, warm water travelled a similar route as it did to reach Melville Bay. Warm water found north of Iceland has a higher probability to enter Disko Bay than it did to enter Melville Bay. This could be due to the timing of the five year trajectories, as the warm water reaching further north (to Melville Bay) will have 5 a longer distance to travel and endure more modification and cooling. It is evident that the Irminger Sea plays a vital role in sourcing heat to the west coast of Greenland, even in the far north of Baffin Bay (Straneo and Heimbach, 2013). Water mass changes and temperature fluctuations in the Iceland Sea may thus have more impact on glaciers that terminate into the fjord systems that reach Disko Bay and not further north into Melville Bay. Beyond the scope of this study would be to look how how the glaciers have been changing in the CAA and if warm water can be seen in the troughs or fjords in this region.

South-east coast
As described in Sect. 3.1, in the south-east region there are two large glaciers of interest HG and KG. The south-east coast of Greenland, where HG and KG are located, receives warm water differently than Baffin Bay. In Fig. 9c and Fig. 9e, it is shown that the Irminger Sea plays a more indirect role in supplying heat to these regions. HG (Fig. 9c) receives its warm water from the Iceland Sea with a higher probability of waters sourced through the Fram Strait. This warm water from Fram Strait 15 has travelled via the NwAC along the shelf break into the Iceland Sea, then along the east coast along the shelf via the EGC, feeding into the troughs. There does exist a low percentage of warm water travelling north from the Irminger Sea towards the shelf, directly feeding into the troughs towards Sermilik Fjord. Further north at KG, warm water has a very low likelihood that it will be supplied from south of Iceland. This is consistent with Azetsu-Scott and Tan (1997); Jiskoot et al. (2012), that Irminger Current's influence diminishes north of 67 • N due to Denmark Strait. HG is located ∼ 65 • N , and KG at ∼ 67 • N .

20
Warm waters that KG (Fig. 9d) receives are sourced similarly as explained for HG, from the Fram Strait. Figure 9d shows more clearly that the Fram Strait water is most likely recirculated Atlantic water that has travelled across the Iceland-Scotland Ridge and continued as the NwAC. The recirculated Atlantic water travelled south, shoaling and travelling onto the shelf to KG, and reaches the trough, KT, supplying the coast with warm water.
North-east coast 25 As described in Sect. 3.1, in the north-east, Daugaard-Jensen Glacier terminates into Scoresby Sund and 79NG terminates into the sound of Jøkelbugten, north-east of Greenland. Scoresby Sund differs from the previously mentioned KG paths, as it is more defined (Fig. 9e). This warm water has either been recirculated via NwAC and travelled through the Fram Strait, or is water from the Arctic which has travelled along the coast of Canada, another possible route of Pacific Water as seen in Hu and Myers (2013). If the warm water has been recirculated via NwAC it has travelled along the shelf break at a depth of ∼ 300 m, 30 and if it has travelled from the Arctic, this water travelled east, at a depth of ∼ 550 m along the Canadian Shelf and into the Fram Strait. Warm water that travels to 79NG (seen in Fig. 9f) follows the shallow bathymetry of the north-east Greenland shelf. Warm waters which have been fed through the Fram Strait are most likely to be received south through NT, as seen in Wilson and Straneo (2015); Schaffer et al. (2017). It appears that this location has the highest chance of receiving warm waters from the Arctic. It is possible that these warm waters may be sourced from the Arctic, being modified Atlantic waters or potentially the Pacific Water, by travelling through the Arctic via the transpolar route (Hu and Myers, 2013;Dmitrenko et al., 2019). 5 This highlights the importance of ocean properties in the Fram Strait and how they may impact marine terminating glaciers on the north-east coast. Therefore, a change in water mass at this location may impact the marine terminating glaciers on the north-east and east coast of Greenland.

Conclusions
The oceanic heat available in Greenland's troughs is dependent on both the location of the trough, variability of the warm 10 water origin, how the water is transformed as it travels to the troughs, as well as local processes occurring, such as heat loss to the atmosphere. It is important to understand the processes that bring this warm water to the shelf and into the troughs, as this water can be then exchanged into the fjords. Warm water that exists in fjords create an oceanic heat forcing on the marine terminating glaciers (Cai et al., 2017;Rignot et al., 2016b;Wood et al., 2018). To our knowledge this is the first look at changes in heat flux in troughs that are connected to fjords with marine terminating glaciers. 15 The study's model experiments showed that Melville Bay troughs experienced a warming following 2009. Therefore an increase in ocean heat presence in these troughs may have driven more heat to glaciers that terminate here. In 2004 to 2006, model experiments captured an increase in onshore heat flux in DBT, coinciding with the timing of the disintegration of JI floating tounge and observed ocean heat increase in Disko Bay (Holland et al., 2008).
This study showed that the Irminger water can extend far north into Baffin Bay, reaching as north as Melville Bay and its  (Dodd et al., 2012;Hu and Myers, 2013;Dmitrenko et al., 2019).
Seasonality of the maximum onshore heat flux through troughs around the GrIS differs due to distance away from the 25 original warm water source. The seasonality of the maximum onshore heat flux through all six regions were presented. For the Irminger Current influence the peaks begin: June for HGT2, July for DBT and September for MVBCT. Then for the areas receiving warm water from the NwAC: August for KT, November for SBS, and September to January for NT.
The EKE was shown to have the highest values along shelf breaks and changes in bathymetry. This study found that the south-east region has the highest values of EKE. Weak EKE off the north-west and north-east coast may be due to semi- The south-east region has the highest EKE as well as stronger sensitivity with changes in atmospheric conditions than all other regions. Therefore the south-east coast of Greenland is impacted the most by the atmospheric filter (i.e. no storms). No storms resulted in a reduction of EKE (∼ 50 %) and less offshore heat transport and therefore more heat flux ( ∼ 20 %) through 5 the Helheim glacier trough (HGT2).
It is imperative to try to understand how sensitive the ocean is to additional meltwater from Greenland. Baffin Bay is Since global or regional ocean models do not have the capability to resolve small scale processes such as fjord circulation, the exchange between fjords and troughs cannot be looked into. Instead, there is an assumption in place, that the water characteristics that exist in the troughs will match those in the fjords due to dynamics of cross shelf exchanges (Jackson et al., 15 2014;Sutherland et al., 2014). A warming of ocean heat in troughs may lead to a warming of ocean heat to fjords. Due to the model bathymetry under representing the depth of these troughs, this study may be underestimating the amount of ocean heat available to enter these troughs. Ocean models should take advantage of recent bathymetric data sets to improve their models bathymetry such as BedMachineV3 (Morlighem et al., 2017). Beyond the scope of this study would be to look how the glaciers have been changing in the CAA and if warm water can be seen in the troughs or fjords in that region. Additionally, the study       Values here correspond to the percentage out of all particles and grid cells that virtual particles can be found in a given grid cell.  Bamber et al. (2012). All simulations use the same atmospheric forcing, CGRF (Smith et al., 2014), but with the winds and temperature filtered in the LowResNoStorms.