1. Introduction
Mass loss from the Greenland Ice Sheet is predicted to accelerate during the twenty-first century, further contributing to sea level rise and with downstream consequences on ocean circulation and ecosystems (Bamber et al. 2019; Goelzer et al. 2020; Böning et al. 2016; Frajka-Williams et al. 2016; Arrigo et al. 2017; Oksman et al. 2022). Freshwater fluxes from the ice sheet are discharged in the form of both solid and liquid forms contributing cumulatively 7700 ± 460 and 8400 ± 1680 km3 of freshwater, respectively, from 2000 to 2016 (Bamber et al. 2018). The freshwater and its dissolved and particulate chemical content are released into long and narrow fjords before being routed onto the continental shelves where they can affect regional circulation, salinity, biogeochemistry, and potentially large-scale deep convection, although recent evidence suggests Greenland’s freshwater might remain close to the coast (Straneo and Cenedese 2015; Böning et al. 2016; Frajka-Williams et al. 2016; Thornalley et al. 2018; Hendry et al. 2021; Le Bras et al. 2021). The freshwater from glaciers also impacts regional ecosystems through both the direct injection of nutrients and the upwelling of ambient deep nutrients leading to highly productive fjords and fisheries (Cape et al. 2019; Meire et al. 2016a,b, 2017; Hopwood et al. 2020) that are, therefore, sensitive to future changes in freshwater fluxes (Hopwood et al. 2018; Oliver et al. 2020). The impact of freshwater will vary depending on how, when, and where it mixes with seawater. This mixing is in turn affected by fjord circulation and stratification (Mortensen et al. 2011, 2020). Therefore, determining how fjord dynamics alter the distribution and export of freshwater is crucial to understanding the impact of the Greenland Ice Sheet on the ocean and ecosystems.
The liquid component of freshwater enters fjords in three forms: (i) through direct melting of ice by the ocean (submarine meltwater; SMW), (ii) meltwater from the ice sheet surface that has drained to the ice sheet base and enters the fjord from beneath a glacier (subglacial meltwater discharge; SGD), and (iii) meltwater from the ice sheet surface that has not drained to the base and enters the fjord at the surface (meltwater runoff). Since it is expected that the majority of surface meltwater does drain to the ice sheet base in this system, and since this study excludes the surface layers of the fjord, we here make no further mention of meltwater runoff. SMW fluxes are sensitive to ocean heat and released at various depths along the face of the terminus. Additionally, SMW is produced by melting icebergs as they transit through the fjord. Meltwater drained as SGD is buoyant and produces turbulent plumes which entrain ambient water and drive a strong overturning circulation within the fjord (Straneo and Cenedese 2015; Carroll et al. 2017). This overturning circulation, along with tidal flows and shelf-forced fluctuations, drives horizontal and vertical mixing within the fjord and determines the exchange of freshwater with the shelf (Zhao et al. 2021). However, the transport and outflow depth of the SGD plume is sensitive to fjord stratification, resulting in a complex feedback between fjord circulation and freshwater content (De Andrés et al. 2020).
Glacial fjords are often described as being in one of two states, a winter state with decreased stratification and a shelf-influenced circulation, and a summer state with increased stratification and a strong plume-driven circulation (Jackson and Straneo 2016; Gladish et al. 2015; Mortensen et al. 2014). These dramatic differences in circulation and stratification can lead to a seasonal description of glacial fjords that overlooks the dynamic evolution of fjords within a season. Additionally, the challenges of obtaining measurements in ice-congested fjords often limit field campaigns to short-duration summer surveys (Stevens et al. 2016; Beaird et al. 2015, 2017; Cape et al. 2019; Motyka et al. 2011; Wood et al. 2018; Moon et al. 2018; Inall et al. 2014; Bendtsen et al. 2015, 2021; Muilwijk et al. 2022). While these surveys provide invaluable snapshots of heat, nutrient, and meltwater fluxes, it is often assumed that the data are representative of the whole summer and some heat budgets explicitly assume the fjord is in a “steady state” or use a single summer average (Inall et al. 2014; Jackson and Straneo 2016).
However, a limited number of observations have shown significant subseasonal variability of hydrographic properties in fjords (Stuart-Lee et al. 2021; Carroll et al. 2018; Mortensen et al. 2014, 2013, 2018; Meire et al. 2016b; Mernild et al. 2015). For example, Mortensen et al. (2011, 2014, 2018) show that Godthåbsfjord freshens and the isopycnals deepen throughout the summer, suggesting that fjord processes modulate the timing and vertical distribution of freshwater export. This is in contrast to the approach of large-scale ocean models, which often input freshwater from glacial freshwater at the surface and assume the transit time of meltwater through fjords is negligible (Arrigo et al. 2017; Dukhovskoy et al. 2019). To further understand the subseasonal evolution of glacial fjords and their impact on freshwater export, we use a dataset of high-frequency hydrographic and velocity observations collected over 10 days during each of the summers of 2012 and 2013 in Saqqarleq (previously known as Sarqardleq Fjord), a midsize fjord in west Greenland associated with Saqqarliup Sermia glacier. The data revealed a rapid freshening trend of −0.05 and −0.04 g kg−1 day−1 in 2012 and 2013, respectively, within the intermediate layer of the fjord less than 2.5 km from the glacier. These freshening trends were of similar magnitude despite the fact that 2012 was a year of record surface melt and 2013 was an average melt year. The freshening indicates that SMW and SGD from the glacier are stored within the fjord leading to a transformation of fjord waters and a delay in the net export of freshwater. A box model is developed to elucidate the storage and release dynamics of the glacial fjord. The box model is formulated for Saqqarleq, but is generic and can be applied to other systems. Our results suggest that Greenland’s glacial fjords are nonsteady and respond rapidly to the input of ice sheet meltwater. The freshwater storage results in a lag of peak freshwater export from the glacier to the ocean that needs to be accounted for in any regional or global ocean model that does not resolve fjords and fjord processes.
2. Setting, data, and methods
a. Setting and background
We investigate changes within Saqqarleq (SQ), a midsized glacial fjord in west Greenland associated with the glacier Saqqarliup Sermia, during a period of sustained SGD. SQ is the southern arm of the Ilulissat Isfjord system which connects Sermeq Kujalleq (commonly referred to as Jakobshavn Isbrae) with Disko Bay (Fig. 1a). SQ has a broad sill (S1) about 500 m from the grounding line isolating the glacier from the deepest SQ waters. This sill varies in depth from 50 m at its southwest end to 100 m at its deepest point. The fjord varies in width from about 6 km at the head of the fjord, to 2.2 km in the main channel of the fjord before it connects to Tasiusaq (TQ) and then Ilulissat Isfjord. SQ and TQ are separated by an 80-m-deep sill (S2) that is 16 km downfjord of Saqqarliup Sermia, and TQ is separated from Ilulissat Isfjord by a 125-m-deep sill (S3). The sill between TQ and Ilulissat prevents the deeper relatively warm basin waters of Ilulissat from reaching SQ.
(a) A regional map of Saqqarleq (SQ), Tasiusaq (TQ), and Ilulissat Isfjord showing sill locations and nearby glaciers Saqqarliup Sermia (SS) and Sermeq Kujalleq (SK). The inset map shows the location of SQ within the Greenland continent. The yellow dashed line is the bathymetry slice shown in (d) and (e). (b) Map of SQ with the locations of CTDs in 2012 (red), 2013 (blue), and a 2013 XCTD (black). (c) Near-terminus bathymetry and a schematic of the circulation. Locations of the primary plume (red star) and secondary plume (black star) based on Stevens et al. (2016) and location of moored ADCP (Fig. 7). (d) Along-track bathymetry profile created using BedMachinev3 (Morlighem et al. 2017). Cross hatching fills the region where data are unreliable. A circle marks the single depth point available (2013 XCTD). (e) A close-up of SQ, with overturning schematic.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
SQ lacks a thick ice mélange, unlike major glacial fjords such as Ilulissat Isfjord and Sermilik, which enables measurements to be made within 200 m of the terminus and makes SQ ideal for field studies of ice–ocean interactions (Stevens et al. 2016; Mankoff et al. 2016; Slater et al. 2018; Wagner et al. 2019; De Andrés et al. 2020). SGD enters the fjord from below the glacier at two locations, a primary plume located 2.3 km along the terminus from the southwest corner and a secondary plume 4.5 km along the terminus (Fig. 1c; Stevens et al. 2016). The secondary plume is associated with substantially weaker SGD resulting in a deeper neutral buoyancy depth (Stevens et al. 2016; De Andrés et al. 2020). A remote-control kayak equipped with a depth-varying CTD sampled within the surface expression of the primary plume in 2013, finding that the plume was composed of 90% entrained ambient water, 10% SGD and less than 0.1% SMW (Mankoff et al. 2016). Along-fjord transects of temperature and velocity revealed that after surfacing, the plume submerged and flowed out as a subsurface jet (Mankoff et al. 2016). A high-resolution simulation of SQ, constrained with observations from 2013, found that the plume-turned-jet impinged on the fjord wall and generated a vigorous terminus-scale wide recirculation generating widespread melting of the glacier terminus (Fig. 1c; Slater et al. 2018).
Previously, De Andrés et al. (2020) used parts of this dataset to explore differences in the surface emergence of a subglacial plume across two consecutive years, including one in a year with record SGD (2012). They found that greater cumulative SGD was associated with increased fjord stratification which, in turn, exerted a dominant influence on plume height. They did not investigate, however, the physical mechanisms controlling the stratification and the potential impacts this stratification has on the export of freshwater.
b. Data
An upward-looking moored Teledyne RDI 300-kHz acoustic Doppler current profiler (ADCP) was deployed 1.6 km from the terminus (Fig. 1c) and collected velocity data from July 2012 to April 2013. The ADCP was deployed on the seafloor at 114 m and recorded velocity in 4-m bins from 10 to 106 m, after removing the top two bins for side-lobe effects. The barotropic tide was estimated from a pressure sensor or the Arctic Ocean Inverse Tide Model (Padman and Erofeeva 2004; Erofeeva and Egbert 2020) when data were unavailable, and subtracted from the ADCP data (Fig. S1 in the online supplemental material). The estimates of SGD entering the fjord are taken from the Modele Atmospherique Regional (MAR; Fettweis et al. 2017; Delhasse et al. 2020) with the dataset provided by Mankoff et al. (2020). We also use salinity values collected from seals as reported in Mernild et al. (2015) and calibrate them against our CTD data (Fig. S2).
3. Analysis of observational data
a. Background hydrography
The hydrography of SQ has been investigated by De Andrés et al. (2020) and Stevens et al. (2016), but a brief description is necessary here to provide context for our analysis. During summer, the fjord can be approximated as a three-layer system with a surface layer approximately 10–15 m deep, an intermediate layer between 15 and 100 m deep, and a homogeneous layer deeper than 100 m (BW, Fig. 2). Temperature profiles (Fig. 2a) reveal a warm surface layer, presumably from solar heating, and a colder layer extending from 15 m to the bottom. There is little difference in temperature between the second and third layer. Interannual differences between 2012 and 2013 are small with mean temperatures below the surface layer of 0.9° and 1°C, respectively. Salinity profiles (Fig. 2b), show that the intermediate layer of the fjord is substantially fresher in 2012 (mean salinity 31.9 g kg−1) than in 2013 (32.9 g kg−1). The interannual differences in salinity are consistent with 2012 being a year of record ice sheet surface melt (Nghiem et al. 2012; Tedesco et al. 2013). Below 100 m in the basin layer, the salinity between the two years is similar. This evidence suggests that S1 blocks the majority of glacial water from reaching the basin layer and that BW is primarily composed of waters unmodified by SS and imported from outside of the fjord, similar to the deep basin waters of some shallow-silled glacial fjords (Hager et al. 2022). This basin water has characteristics of diluted Baffin Bay Polar Water, one of the two water masses found in Greenland north of Davis Strait (Gladish et al. 2015; Stevens et al. 2016; Rysgaard et al. 2020; Mortensen et al. 2022).
(a) Conservative Temperature vs depth (red 2012, blue 2013). (b) Absolute Salinity. (c) Stratification (N2) over the top 150 m. In all profiles the mean profile is given in bold. The stratification profiles are low-pass filtered over a window of 10 m to remove noise. The x axis in (c) is logarithmic.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
The density in SQ is dominated by salinity, and the stratification profiles reveal that decreased salinity above 100 m is associated with increased vertical density gradients (Fig. 2). In both years, the stratification exhibits peaks around the surface layer but decreases with depth. Above 40 m, the mean stratification was approximately double in 2012 (2 × 10−3 s−2) compared to 2013 (1 × 10−3 s−2). The mean stratification between 40 and 100 m is about 4 times higher in 2012 (2.7 × 10−4 s−2) compared to 2013 (0.07 × 10−4 s−2). The profiles in 2012 also exhibit a peak in stratification just above the homogeneous layer (100 m) before converging to the 2013 properties reflecting the presence of sill S2.
b. Continuous fjord freshening
We find that SQ gets fresher during the summer field campaign in both years indicating it is not in steady state. We analyze freshwater storage by examining temporal trends in salinity within layers of the fjord. We focus on the intermediate layer (15–100-m depth) because the surface layer shows a high degree of variability, presumably, imparted by processes that are not the focus of this study, such as runoff (meltwater, land, and precipitation) and solar insolation (Fig. S4). While these surface processes are important, strong stratification (N2 ≈ 10−2 s−2) likely limits their impact at depth in this system. In both 2012 and 2013, the mean salinity over the intermediate layer continuously decreased over the course of each field campaign (Fig. 3). The mean salinity also exhibited an along-fjord trend with fresher waters closer to the glacier, but the temporal trend is greater than the longitudinal trend. We can thus rule out that the freshening is due to the advection of freshwater from Ilulissat Isfjord as otherwise the salinity gradient would be reversed. The freshening trend in 2012 is −0.05 ± 0.01 g kg−1 day−1 (r2 = 0.77) and in 2013 is −0.04 ± 0.01 g kg−1 day−1 (r2 = 0.74), with uncertainty defined using a bootstrapping method. This trend is consistent with a moored CTD at 70 m that recorded salinity continuously over this time period (Fig. S3). The CTD data are concentrated near the head of SQ where mixing is likely to be most intense (Bendtsen et al. 2021), and therefore it is unclear how close to the shelf the freshening trend persists. The jet from the glacier outflows at around 20-m depth, but the freshening occurs at all depths (Fig. S4) suggesting that either the outflowing freshwater is being vertically mixed downward or strong submarine melting is freshening waters at all depths.
(a) Mean Absolute Salinity of 2012 CTD profiles from 15 to 100 m (from the surface layer to S2 depth) with a best fit trend. Colors indicate distance from terminus. The x axis is the Julian day. (b) As in (a), but for 2013.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
c. Subglacial meltwater discharge is the dominant freshwater source
Next, we show that the freshening trend is due to an increase in SGD content in the water column. We can visually identify which freshwater source is responsible using a temperature and salinity (TS) diagram with the depths 25, 40, 80, and 100 m highlighted in Fig. 4. The profiles shown are representative of the start, middle and end of the field campaign and were all collected from approximately the same distance from the glacier. By looking at the change in temperature associated with freshening we can determine the source of freshwater. For example, we expect freshening driven by SMW to be associated with a substantial cooling of water while freshening due to SGD is associated with a much smaller change in temperature. In 2012, the change in properties at each depth are roughly parallel to the subglacial meltwater discharge–mixing line indicating that the freshening is due to an increase in SGD at depth rather than SMW. However, in 2013, only the properties at 25 m appear parallel to the subglacial meltwater discharge–mixing lines while deeper water appears to be on a slope between the subglacial meltwater discharge–mixing line and the submarine melt line. Following the procedure of Mankoff et al. (2016) and Mortensen et al. (2020) (see supplemental material), we use a water-mass analysis to quantify changes in the relative concentration of SGD and SMW (Table 1). The fraction of SGD significantly increased by around 1% in both years (p < 10−4 for all cases). Changes in the fraction of SMW were mostly significant (p < 10−4 for all cases except 2013 at 25 m), but varied with decreases (2012) or increases (2013) around 0.1%. In both years the increase in SGD is an order of magnitude higher than changes in SMW. Thus, while SMW is present, we conclude that the freshening trend is being driven primarily by the accumulation of SGD. This process must occur from the top down as SGD is exported in the jet which outflows around 20-m depth (Mankoff et al. 2016; Slater et al. 2018).
(a) TS diagram of days 1, 4, and 10 in 2012 with the depths of 25 (triangles), 40 (stars), 80 (circles), and 100 m (diamond) highlighted with symbols. (b) As in (a), but for 2013; the final point is from day 8 rather than day 10. On top of the TS diagram, we plot a subglacial meltwater discharge–mixing line (red) that represents the mixing between SGD (S = 0 g kg−1, Θ = 0°C) and water at 100 m. There are also submarine melt lines (gray lines), or Gade slopes, which represent a hypothetical mixture of BW and SMW (SA = 0, Θ = −87°C).
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
Change in freshwater concentration of SGD and SMW from day 1 to day 10 in 2012 and from day 1 to day 8 in 2013.
d. Interannual subglacial meltwater discharge differences
Comparison of SGD time series from MAR highlights that SGD flux into the fjord was substantially higher in 2012 than in 2013 (Fig. 5). In 2012, the SGD flux into the fjord started about 10 days earlier and the mean flux during the period of sustained SGD (DOY 160–215) was 138 m3 s−1 compared to 111 m3 s−1 in 2013 (Fig. 5a). This increased SGD flux resulted in cumulative freshwater input that was 40% higher in 2012 by the end of summer (Fig. 5b). The difference in cumulative SGD grew throughout the summer, such that by the end of the respective field seasons, 0.3 Gt more freshwater had entered in the fjord in 2012 than 2013 (Fig. 5c).
(a) MAR SGD flux (Qsg) into SQ in 2012 and 2013. (b) The cumulative SGD (Gt). Windows are overlaid during the period of the field campaign in 2012 (red) and 2013 (blue). (c) The cumulative difference in SGD between 2012 and 2013.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
e. Density differences across the outer sill (S2)
Comparison of CTD profiles from inside and outside of SQ shows how the increase in stratification in the inner fjord driven by SGD leads to greater interaction with topography (Fig. 6). In 2012, a density difference arose between the fjord interior and exterior near the depth of S2 (80 m), which separates SQ from TQ. Below this sill depth, the outside profile was less stratified and denser than profiles within the fjord (Fig. 6a). This feature is not evident in 2013 (Fig. 6b). Note that all profiles have had the linear temporal trend in salinity (Fig. 3) removed so that we can compare profiles taken on different days. Only a single cast was available from outside of the fjord in 2012 and only two profiles in 2013; however, the density is outside the range of variability observed within the fjord, so the feature is less likely to be transient. The density difference which is centered at the sill depth suggests that as freshening progresses within the inner fjord, the sill can block the export of deep, relatively fresh waters. In 2013, when there was no visible difference between interior and exterior casts, the influence of SGD likely did not extend below S2. The density differences at depth between 2012 and 2013 further support the hypothesis that freshwater is being mixed from the surface downward, as the fjord had both a larger SGD flux and a longer time to accumulate freshwater at depth in 2012.
(a) Detrended potential density anomaly for CTD casts in 2012 where the black cast was taken past S2 in Tasiusaq. The dashed line is the depth of S2. (b) As in (a), but for 2013; note that the black cast was calculated using an XCTD.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
f. Seasonal change in circulation
A moored upward-looking ADCP observed fjord circulation for 9 months starting in July 2012, and the changes in circulation were consistent with a seasonal response to freshwater input (Fig. 7). Since the ADCP is located at a single point in an area of recirculation (Fig. 1c; Fig. S6), it provides an incomplete description of the full circulation. However, it remains the best data available to characterize the seasonal variation in velocity. Additionally, the depth structure of velocity recorded by the ADCP in July is consistent with the snapshot of overturning recorded by across-fjord transects (Figs. S7–S12), indicating that the ADCP measurements are correlated with the large-scale fjord circulation. Therefore, we separate the ADCP velocity into three phases: the plume-driven overturning circulation during the summer, an adjustment period in September, and a weaker phase of circulation after October (Fig. 7a). In July, the outflowing layer was about 30 m thick and centered around 25 m, while the inflowing layer was 40 m thick and centered around the depth of S2, and the basin layer below 100 m had relatively weak velocities (Fig. 7c). During this time period, the plume-driven overturning is clear with the upper layer (25 m) flowing straight out toward the mouth and the middle layer (80 m) flowing in toward the glacier (Fig. 7b). In late August, the estimated SGD flux dropped below 15 m3 s−1 (10% of peak; Fig. 5) and the upper layer was no longer consistently directed oceanward and there was intermittent flow reversal. In the middle layer however, the flow remained directed toward the glacier, although it was weaker in magnitude and eventually dropped below 0.005 m s−1 in October. During this transition period in September, the along-fjord velocity can be described as weak, but steady inflow below 20 m (Fig. 7c). The rapid change in the upper-layer velocity direction suggests that the plume-driven overturning is quickly shut down after SGD weakens, but that a weaker inflow is still present at depth. This weaker exchange flow could be driven by the density gradient between the fjord and S2 (Fig. 6a) that was previously maintained by the plume and recirculation. After October, the lower circulation is weak (<0.005 m s−1) and no longer directed toward the glacier. The time interval between the plume shut down (Qsg < 15 m3 s−1) and the shift in circulation to weak velocity is approximately 45 days. Although we lack CTD observations in the fall, Mernild et al. (2015) show a rapid salinity increase in SQ coincident with the shift away from the overturning circulation observed by the ADCP in September.
(a) Time series of (2-day running mean) along-fjord velocity from moored ADCP. Negative velocities are directed out of the fjord. The time period when SGD is substantial (>10% of peak) is outlined in black. (b) Directional plot of the (5-day running mean) along-fjord velocity at the depths 25 m (top) and 80 m (bottom). Arrows pointing directly up show flow toward the glacier. West is to the right and the along-fjord velocity is defined positive at 170° from north at this location. (c) Vertical profile of along-fjord velocity averaged over the months of July (green) and September (purple).
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
4. Box model of freshwater storage and export
We develop a box model to better understand the seasonal variability of fjord circulation and estimate storage of freshwater. The observations imply that under sustained SGD the fjord freshens (Fig. 3) and that freshwater is mixed downward throughout the summer (Fig. 6) before eventually being exported in the fall (Fig. 7). However, we lack measurements to capture this process continuously and instead rely on observations collected from different years as proxies of different points in the melt season. A box model enables us to explore the dynamics controlling the seasonal cycle and quantify time scales for both freshwater storage and export.
The model is similar in style to previous minimal fjord models in that layer thicknesses and properties evolve according to parameterized exchange with the SGD plume (Zhao et al. 2021) and the external fjord basin (Tasiusaq; Babson et al. 2006; Gillibrand et al. 2013). The model is kept as simple as possible intending to resolve only the first-order dynamics controlling the salinity of the fjord.
a. Box model setup
1) Model layout
We assume the fjord can be described as a three-layer system where the top layer is composed of outflowing glacially modified water, the middle layer has inflowing water above sill height, and the basin layer has water that is isolated in the deep basin by the sills (Fig. 8). These layers roughly correspond to the observed salinity layers (Fig. 2) and are meant to represent the overturning circulation within the fjord (Fig. 7c). The boxes are forced by a plume at the glacier end and can exchange water in and out of the fjord at the sill 2 (Fig. 8). The fjord has a total depth H and surface area A that is constant with depth. The bottom box represents the waters below sill depth at all times, and therefore we set and hold fixed H3. Since water is entrained into the plume from this layer, this necessitates the inclusion of an overflow term QO that represents a flux from the middle layer to the bottom layer. The fjord exterior is assumed to be composed of water with an average salinity Sext.
Schematic of the box model comprising an outflowing upper layer, an inflowing middle layer, and a deep passive layer. Layer thickness and salinity are Hj and Sj, respectively, where j denotes the layer. Volume flux exchange occurs at the fjord head due to the plume (red) which entrains from the boxes (QPj) and at the outer edge due to fjord–shelf density gradients (QEXj). Sill 1 limits the depth of H1 and overflow term QO is necessary to keep the basin layer volume constant. Sill 2 sets the height of the outflowing layer.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
Temperature is dynamically passive since density gradients are dominated by salinity, and because temperature is relatively homogeneous below 15 m, we neglect it from the box model. Submarine melting of the glacier is not included as a freshwater source because it is an order of magnitude smaller than the SGD flux (Table 1) and its omission simplifies the model equations. However, in fjords that have large concentrations of icebergs such as Ilulissat Isfjord or Sermilik, SMW would have to be included as a freshening term (e.g., Moon et al. 2018; Beaird et al. 2018). Furthermore, inclusion of submarine melting in the box model was found to have little impact on freshwater storage (Fig. S11). We wish to keep the model as simple as possible to understand the effects of the primary freshwater source (SGD), so we neglect the effects of sea ice, winds, icebergs, and surface forcing. Last, the model does not include mixing between layers explicitly, instead mixing is represented through changes in the layer thicknesses which are controlled by the balance between the SGD plume and exchange at the mouth.
2) Plume to fjord exchange
3) External fjord exchange
4) Conservation equations
5) Initial conditions and forcing
The model is forced with SGD taken from the regional climate model MAR (Fig. 5; Mankoff et al. 2020) and we assume a 15% uncertainty (Mankoff et al. 2020). The model is solved by stepping through the conservation equations with a backward implicit Euler scheme using a 0.1-day time step. The model is run from day 70 to day 365 in each of 2012 and 2013.
b. Model results
We start with the box model’s seasonal evolution and then compare the predicted salinity and salinity trends with observations. As SGD enters the fjord, the exchange out of the fjord is initially weak and so the top layer thickens (Fig. 9a). The H1 thickens earlier in 2012 than 2013 since SGD enters the fjord earlier, but both reach a maximum thickness of about 70 m. The salinity in the upper layer decreases (Fig. 9b) as freshwater is not sufficiently exported. The freshening of the upper layer starts earlier in 2012, but both years reach a minimum in salinity near day 218. As Qsg weakens at the end of summer then the average salinity in the plume grows [Eq. (6)] and S1 starts to level off. Since the reduction in Qsg occurs at a similar time in 2012 and 2013, salinity minimums in S1 occur at similar times in both years.
(a) Box model H1 for 2012 (red) and 2013 (blue) as a function of Julian day. (b) As in (a), but for S1. (c) Volume fluxes in and out of the top box with dashed lines for the plume fluxes in and solid lines for exchange flow fluxes out.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
As the upper layer gets thicker, the plume has less distance to rise and so less volume is entrained by the plume, decreasing QP1 (Fig. 9c). At the same time, the changes in H1 and S1 increase the density gradient between the fjord and external fjord basin resulting in a higher exchange flow QEX1. H1 increases until the exchange flow is greater than the inflow from the plume. Ultimately however, QEX1 overtakes QP1 only when Qsg decreases and the plume shuts down. Since the crossing point is tied to Qsg, it also occurs at a similar time in both years.
The box model results compare reasonably well with the
(a) Comparison of the observed vertically averaged salinity (
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
c. Freshwater export
(a) The volume of freshwater (Vfw) stored in the box model for 2012 (red) and 2013 (blue) as a function of Julian day. (b) Freshwater export (Qfw) from Eq. (22) and SGD (Qsg) in the box model. A 10-day running mean has been applied to smooth the signal. (c) The fraction of SGD that was stored in the fjord during the time period when the plume was active.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
d. Scaling for freshwater storage
We can evaluate how Vfw compares across fjord systems under steady state. Initially, the stored freshwater will start out small and all glacial fjords should be in a position where Rstor < 1. However, as Vfw increases, a steady state regime will be reached when Rstor = 1. Using representative values (Table 2): we set Rstor = 1 and get a Vfw of 1.9, 0.20, and 2.5 (109 m3) for SM, SQ, and IL, respectively, indicating IL will store the most freshwater before exchange is efficient at removing it. However, as a proportion of fjord volume these are 0.004, 0.03, and 0.008 for SM, SQ, and IL which indicates we should expect the greatest changes in mean salinity to occur in SQ. Based on Eq. (26), we see that SQ might be uniquely placed to observe large freshening because it is relatively small and has a moderate sill height compared to grounding line depth. For other systems, such as SM, the combination of a deep sill and large fjord volume may limit the observed freshening. With a known rate of freshwater input (e.g., Qsmw or Qsg), this threshold Vfw could be turned into a residence time. However, these results are based on the assumption that fjord circulation can be described as a gravitational circulation. The exchange of other glacial fjord systems might be primarily wind-driven, geostrophic, or hydraulically controlled (e.g., Jackson et al. 2014; Schaffer et al. 2020; Zhao et al. 2021) and so care should be taken in choice of the exchange flow parameterization. Last, for systems with significant iceberg cover, we expect iceberg melt to significantly impact the freshwater budget such that it should be accounted for in the box model (Moon et al. 2018; Davison et al. 2020).
Table of values used in the exchange flow scaling for three fjord systems; Qsg is the average SGD in July in 2012 and 2013 (Mankoff et al. 2020). For Sermilik and Ilulissat we assume L = Ls because these systems connect directly with the shelf.
5. Discussion
a. Mechanisms driving freshwater storage
We observe that the mean salinity of SQ decreases during the melt season due to the net accumulation of freshwater. We propose that this process occurs primarily through vertical mixing of SGD. Initially, the density-driven exchange out of the fjord is insufficient at removing freshwater stored near the head, but as the fjord freshens, the exchange flow increases until either the plume shuts off or the fjord reaches steady state. In this section, we discuss these steps in more detail and discuss the possible physical processes contributing to freshwater storage.
The hydrographic observations indicate that the region close to the glacier (<6 km from the terminus) was accumulating freshwater during the field seasons (Fig. 3) and that the freshening occurred from the surface downward. While submarine melting of glaciers, especially in larger fjords, provides a freshening source at depth, we identify SGD as the primary freshwater being stored. This finding is consistent with independent estimates of freshwater flux into the fjord as Wagner et al. (2019) estimated a combined calving and SMW flux of 0.5 Gt yr−1 during summer compared to our MAR-estimated SGD flux of 3.5–4.4 Gt yr−1 during summer.
Using our box model we explored the balance between plume-driven freshwater storage and density-driven freshwater export between fjord basins. Early in the melt season, the exchange out of the fjord is weak and freshwater from the jet is mixed vertically (Fig. 12a). This process deepens the pycnocline within the fjord, akin to H1 increasing in the model, and is consistent with observed stratification and density profiles of the fjord (Figs. 2 and 6). As the pycnocline deepens, the along-fjord density gradient between the fjord and the shelf increases until a crossing point is reached between the tendency for storage and export (Fig. 12b). After the plume shuts down, freshwater is no longer accumulated, and the fjord adjusts through exchange with the external fjord basin over the next 45 days (Fig. 12c). In reality, the along-fjord density gradient is nonlinear in space with the majority of the isopycnal gradients occurring close to the glacier (Mankoff et al. 2016), and mixing in the rest of the fjord likely relatively weak, but not negligible (Bendtsen et al. 2021).
Schematic of the freshwater storage process. (a) The start of the melt season with mixing near the head of the fjord deepening the pycnocline and relatively weak exchange flow. (b) A potential steady state that could be reached during the melt season between exchange and mixing within the fjord. (c) The end of the melt season or when mixing tied to the buoyancy-driven circulation weakens and exchange is strong.
Citation: Journal of Physical Oceanography 53, 5; 10.1175/JPO-D-22-0137.1
In our box model, the mixing of freshwater between layers is not represented explicitly and instead is included in the exchange parameterization through the frictional time scale 1/r. Although the friction appears physically consistent with shear-driven mixing from the jet (see supplemental material), other possible sources of mixing which could be represented include dissipation along the walls of the fjord or in the lee of a sill. These mixing processes are common in nonglacial fjords (Klymak and Gregg 2004; Staalstrøm et al. 2015) and along sinuous submarine canyons (Wain et al. 2013), and will be intensified in the presence of recirculation. Additionally, small-scale mixing from the submarine melting of ice outside of the plume would enhance the background diffusivity, and future field campaigns should be designed to estimate the energy budgets of these systems.
The parameterization could further be improved by representing recirculation which likely acts to increase the residence time of freshwater in the fjord. Recirculation gyres driven by plumes are found in both observations and models to exist near termini in fjord (Carroll et al. 2017; Slater et al. 2018; Zhao et al. 2021) and large-scale recirculations in glacial fjords are connected to glacial melt rates and overturning strength (Zhao et al. 2022). The strong recirculation cell in SQ can potentially contribute to freshwater storage by redirecting SGD away from the export and back into the plume. Although only a snapshot, ADCP transects across the fjord indicate the volume flux in the recirculation gyre was substantially higher than in the main channel and approximately 50% of the main outflow was redirected back toward the plume in 2013.
We propose the stratification of the fjord increased during the summer, in part due to vertical mixing of freshwater. Glacial fjord plumes are energetic and turbulent (Podolskiy et al. 2021), and shear-driven mixing from buoyant jets can take freshwater at the surface (or within the plume itself) and mix it down below the primary export depth. Recently Bendtsen et al. (2021) found that turbulent mixing rates close to the terminus of Store Gletscher were 100 times higher than mixing rates in the rest of the fjord. Additionally, De Andrés et al. (2020) showed that in 2012 the hydrographic properties of the plume-turned-jet were significantly diluted within a few hundred meters of the terminus indicating that there was additional entrainment and mixing by the jet outflow. Velocity transects across SQ (Figs. S8–S12), show that the Froude number is greater than 1 in the core of the outflowing jet indicating that the jet was an inertial-driven flow susceptible to strong shear-driven mixing.
Freshwater storage has also been observed in a glacial fjord in LeConte, Alaska, due to the outflow plume impinging on the sill and being redirected back toward the glacier (Hager et al. 2022). In that study, a reflux coefficient (Cokelet and Stewart 1985; MacCready et al. 2021) is calculated which quantifies the amount of export that is mixed vertically back toward the glacier. In a more generic box model than the one we have presented, a reflux coefficient that is a function of Qsg could be added to the fjord-exchange parameterization. Tidal flow over the sill is responsible for the intense mixing, which leads to the observed freshwater storage in Godthåbsfjord (Mortensen et al. 2011, 2014). Another potential source of mixing includes internal waves which can be generated by the plume when it impinges on the pycnocline or from tidal flow over the sill (Ezhova et al. 2016, 2017; Mortensen et al. 2014; Stuart-Lee et al. 2021). Therefore, sills and regions close to the terminus are likely mixing “hotspots” that are elevated by SGD plumes and buoyancy-driven circulation (Bendtsen et al. 2021). Last, the interior stratification of the fjord could increase due to the compression of isopycnals with no significant interior mixing taking place. In this scenario, the isopycnal layer corresponding to the neutral buoyancy depth of the plume thickens and the isopycnals below and on top of the neutral buoyancy depth get closer together. However, if this was the dominant mechanism of observed freshening, then the profiles would overlap in TS space in contrast to our observations, which indicate mixing with SGD and SMW (Fig. 4).
b. Delayed freshwater export
In ocean circulation models that include Greenland Ice Sheet freshwater forcing, the effects of freshwater storage within glacial fjords should be included as the potential lag can be significant. The lag in peak freshwater export, or freshwater residence time, determined from the box model in SQ is about a month. Our estimated time scale of stored freshwater export is faster than in nearby Ameralik fjord (Stuart-Lee et al. 2021) and Godthåbsfjord (Mortensen et al. 2018), but these glacial fjords have strong tidal mixing and are primarily renewed by dense coastal overflows in the winter. However, our time scale of stored freshwater export is similar to the time scale of destratification that occurs in the fall in LeConte, Alaska (Hager et al. 2022).
It is clear that the lag in freshwater export will be determined by the relationship between exchange at the mouth Qex and the volume flux from the plume Qp as our scaling showed [Eq. (26)]. In a system where Qex is primarily driven by shelf forcing (e.g., alongshore winds, eddies, coastal trapped waves) then Qex will be independent of Qp and freshwater storage will be set by whether the shelf forcing acts to enhance or reverse the buoyancy-driven flow (Giddings and MacCready 2017). If however, Qex is driven by buoyancy forcing from the glacier, then its value at the mouth will be sensitive to the amount of reflux or recirculation which occurs within the fjord both of which can act to increase freshwater storage. These volume fluxes will also be influenced by fjord geometry. For example, fjords that are narrow and have shallow sills will limit Qex resulting in a larger delay of freshwater export (Zhao et al. 2021). Given the sensitivity of fjord–shelf exchange to a number of parameters (e.g., tides, winds, iceberg presence, fjord geometry), continental-wide estimates of freshwater export delay will need to be informed by observations of both hydrography and bathymetry from within a large number of Greenland’s glacial fjords (Straneo et al. 2019).
c. Applicability to other fjord systems
Due to several factors such as fjord size and the presence of a single oceanic water mass, it is easier to detect freshwater storage in SQ than in other glacial fjords. As shown with Eq. (26), the volumes of larger glacial fjords such as Sermilik or Ilulissat Icefjord reduce the magnitude of observable salinity trends despite greater freshwater fluxes. However, Stuart-Lee et al. (2021) observed freshwater storage and delayed export occurring in Ameralik, a land-terminating glacial fjord in west Greenland. In that study they attributed the freshwater storage to intense tidal mixing at the sill which drew down freshwater from the surface and increased fjord stratification during the summer and into the fall. This process could also be occurring in SQ and future work should aim to quantify the contribution of tidal mixing at the sill versus mixing induced by the plume/jet. We attribute the mixing primarily to physical processes linked with the jet because we observe freshening first near the terminus and then at S2. However, the two mixing processes are likely working together to increase the fraction of freshwater that is stored.
The processes that led to rapid freshening in SQ, including turbulent plumes and glacier-wide recirculation, will be active in all of Greenland’s major glacial fjords since they are driven by SGD. Making equivalent observations to those in SQ at large glacier–fjord systems is extremely challenging due to mobile and thick ice mélange, but the downsloping isopycnals observed near the heads of some glacial fjords (Gladish et al. 2015; Jackson and Straneo 2016; Beaird et al. 2015) could be evidence of a vigorous near-terminous circulation. Experiments with additional endmembers, such as noble gases or oxygen, which can be used as meltwater tracers, are needed to confirm the late departure of freshwater in other systems (Beaird et al. 2015, 2017, 2018).
6. Conclusions
Glacial fjord circulation and properties are often described as bimodal with plume-driven circulation and strong stratification in the summer and a shelf-driven circulation and weak stratification in the winter. This viewpoint overlooks the potentially significant subseasonal variability within fjords and the potential for transient storage of ice sheet freshwater. We find evidence that during the summer, freshwater is stored within Saqqarleq, a midsized glacial fjord in west Greenland, resulting in nonsteady mean salinity during the melt season. Specifically, observations of salinity collected in SQ show a freshening trend of −0.05 and −0.04 g kg−1 day−1 in 2012 and 2013, respectively. The observations suggest that vertical mixing of SGD increases stratification and freshwater content within the fjord when the plume is active. We developed a box model that is forced by SGD at its glacial boundary and a density-driven exchange with at its sill boundary. Competition between these boundary conditions determines whether freshwater is being stored or removed from the fjord. The box model indicates that glacial fjords with intense mixing are inefficient at removing freshwater, resulting in a lag of 25–30 days between the peak SGD entering the fjord and the freshwater export from the fjord. Future work should aim to identify this process in larger glacial fjords and quantify the interior mixing that redistributes freshwater. Our results provide evidence that fjords modulate the timing and magnitude of ice sheet freshwater entering the wider ocean; processes that should be represented in large-scale climate models if we are to better predict the impact of ice sheet meltwater on the ocean.
Acknowledgments.
We would like to acknowledge Margaret Lindeman for helpful discussion and suggestions. We acknowledge Clark Richards, Rebecca Jackson, Sarah Das, Jeff Pietro, and others for help in collection of the data. RS and FS acknowledge funding from the NSF OCE 1948482 and funding from the Heising Simons Foundation. DAS acknowledges support from NERC Independent Research Fellowship NE/T011920/1. We would also like to acknowledge the comments of two anonymous reviewers who greatly improved the manuscript.
Data availability statement.
Data for 2013 are available through the NSF Arctic Data Center at the following DOIs: 2013 Ship-based ADCP measurements (doi:10.18739/A2P843W9W); 2013 CTD profiles (doi:10.18739/A2B853H78); moored ADCP (doi:10.18739/A2G73753N); pressure data (doi:10.18739/A2M03XZ70). The 2012 ship-based ADCP and CTD measurements are available through the NOAA National Centers for Environmental Information (NCEI) using NCEI Accession Number 0210572. The subglacial meltwater discharge data are available from Mankoff et al. (2020). Python notebooks to run the box model are available upon request.
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