Surface Meltwater Impounded by Seasonal Englacial Storage in West Greenland

The delivery of surface meltwater through englacial drainage systems to the bed of the Greenland Ice Sheet modulates ice flow through basal lubrication. Recent studies in Southeast Greenland have identified a perennial firn aquifer; however, there are few observations quantifying the input or residence time of water within the englacial system and it remains unknown whether water can be stored within solid ice. Using hourly stationary radar measurements, we present observations of englacial and episodic subglacial water in the ablation zone of Store Glacier in West Greenland. We find significant storage of meltwater in solid ice damaged by crevasses extending down to 48 m below the ice surface during the summer, which is released or refrozen during winter. This is a significant hydrological component newly observed in the ablation zone of Greenland that could delay the delivery of meltwater to the bed, changing the ice dynamic response to surface meltwater.


Introduction
Meltwater drainage from the surface to the bed along the margin of the Greenland Ice Sheet produces transient ice velocity fluctuations by enhancing basal sliding through hydraulic pressurization (Andrews et al., 2014;Bartholomew et al., 2012;Schoof, 2010;Zwally et al., 2002). However, this effect is not fully understood, with surface velocity measurements often displaying a contrasting relationship with meltwater input. For example, comparable surface meltwater production on the same glacier can lead to notable flow acceleration in 1 year and produce a diminished velocity response in another (Fitzpatrick et al., 2013;Joughin et al., 2013;Moon et al., 2014). This variation across Greenland is likely closely linked to the flow, storage, and distribution of water among and within the englacial and subglacial drainage systems (Andrews et al., 2014;Bartholomew et al., 2012;Sole et al., 2011).
To date, most hydrological studies have focused on either supraglacial or subglacial drainage (Andrews et al., 2014;Bartholomew et al., 2012;Smith et al., 2015). These studies demonstrate that switches in the configuration of subglacial drainage between efficient and inefficient systems are partly responsible for the observed complex velocity response (Bartholomew et et al., 2011). Recent studies in Southeast Greenland have also highlighted the importance of a perennial englacial firn aquifer and its unknown role in modulating ice dynamics (Forster et al., 2013;Koenig et al., 2014;Miège et al., 2016;Miller et al., 2017;Montgomery et al., 2017). Englacial aquifers provide long-term storage of meltwater, potentially reducing the proportion of surface water reaching the bed. Thermal observations have also identified similar meltwater retention in the accumulation area in West Greenland (Humphrey et al., 2012). Despite its importance, observations of englacial storage are mostly limited to firn in high accumulation regions, with only a few observations of storage within the bare ice zones (Cooper et al., 2018). The prevalence of water storage outside the permeable firn regions and the fraction of annual meltwater stored in bare ice remains unknown.
We present simultaneous observations of the englacial and subglacial water systems of Store Glacier, Greenland using a high-resolution, low-power, autonomous phase-sensitive radio-echo sounder (ApRES).
The ApRES system is a ground-based frequency-modulated continuous wave radar that operates across the 200-400 MHz frequency range (Brennan et al., 2014). While similar systems have been previously deployed in Antarctica to quantify rapid variations in vertical strain (Kingslake et al., 2014) and basal melt rates (Nicholls et al., 2015), we present the first study that utilizes the full temporal resolution of ApRES measurements to characterize and quantify englacial water storage.

ApRES Deployment and Data Processing
An ApRES system was deployed at Store Glacier in Western Greenland~15 km downstream of the equilibrium line altitude during two periods from 9 May 2014 to 16 July 2014 and 4 August 2014 to 30 November 2014 and measured simultaneous changes in meltwater storage for both englacial and subglacial drainage systems (Figure 1; Young et al., 2018). At this location, the ice is between 600-650 m thick and the glacier experiences seasonal changes in ice flow velocities ranging from~600 m/a in the winter to~700 m/a during the melt season. We process the ApRES data and generate a set of 2-D cross sections of radar echo power from the top to bottom of the ice sheet every 1 hr (May-July) and 4 hr (August-November; Figure 2). Variation in echo power from identified internal ice layers and the bed provides observational constraints on changes in englacial and subglacial water storage with subdaily temporal resolution. The presence of englacial water within the ice can dramatically increase volumetric scattering and attenuates received  (Joughin et al., 2015). The red line indicates the equilibrium line altitude (ELA). Elevation contours were generated using ArcticDEM release 6. DEM created by the Polar Geospatial Center from DigitalGlobe, Inc., imagery. (b) Schematic of ApRES deployment on Store Glacier. The presence of water within the ice column imaged by ApRES will attenuate the measured echoes from both the internal layers and the bed. Water at the basal interface will modify the basal reflectivity, further modifying the bed echo. radar signals, decreasing the return power of internal layers and bed echoes. We utilize the attenuating properties of englacial water to constrain how englacial water storage changes throughout our study period on Store Glacier.
In order to identify temporal changes in radar attenuation, we track the power of strong reflectors identified in the 2-D ApRES cross sections. These features likely correspond to internal layers beneath the region of both ApRES deployments . We track 22 features as internal layers every hour throughout deployment 1 of the ApRES array from 9 May 2014 to 16 July 2014 and of 21 features every 4 hrs during deployment 2, from 4 August 2014 to 30 November 2014. The ApRES array was relocated approximately 400 m upglacier and rotated by 12°relative to the principal flow direction between deployments 1 and 2 (supporting information Figure S1). We apply a constant correction to calibrate the systematic offsets in radar echo power between the two deployments by performing a linear fit to the average power of the internal layers at the end of deployment 1 and the start of deployment 2. By taking the slope of the mean internal layer power (À0.88 dB/day during deployment 1 and À0.84 dB/day in deployment 2) a constant offset of À38.49 dB was needed to calibrate the echo power values for deployment 2 that began 19 days later.

Modeling Radar Attenuation From Englacial Water Storage
Englacial water storage will increase the observed radar attenuation depending on the amount and electrical conductivity of the water (Schroeder et al., 2015). For centimeter-scale pores, volumetric scattering will also increase radar attenuation by an amount depending on the porosity of the englacial storage and average pore size (Aglyamov et al., 2017;Bohren & Huffman, 1983;Ulaby et al., 2014). To forward model the expected radar attenuation we estimate the two-way attenuation through the region of water storage according to its skin depth, where A is attenuation, T is the thickness of the region of water storage, and δ is the skin depth. The skin depth is given by where f c is the center frequency of the radar, σ ws is the conductivity of the region of water storage, and μ 0 is the permeability of free space (Schroeder et al., 2015). Estimates of cumulative mass loss estimated by the RACMO2.3p2 1-km surface mass balance (SMB) model (Noël et al., 2018) are used to approximate the amount of accumulated liquid water for the ApRES deployment period. We calculate the thickness of the region required to store the estimated accumulated water, T, for a given porosity, φ. Using a mixing model previously designed and applied to estimate the electrical conductivity of sea ice (Geldsetzer et al., 2009), we calculate the conductivity of englacial water storage given by where σ w is the surface water conductivity, φ is the water volume fraction (porosity), φ c is the volume fraction limit below which the connectivity of conductive pores can be ignored, and y is an empirical parameter that controls the increase in conductivity for volume fractions above φ c . Following previous work, we set φ c = 0 and y = 1.67 (Clarke et al., 1978;Geldsetzer et al., 2009).
We use an open source MATLAB Mie scattering solver (Bohren & Huffman, 1983;Mätzler, 2002) for homogeneous spheres to model volume scattering. The calculated scattering efficiency of water-filled pores of a given radius, r, within an ice column is used to estimate the two-way scattering losses (Aglyamov et al., 2017). The index of refraction of ice (Warren & Brandt, 2008) and water (Segelstein, 1981) at a wavelength of 100 cm were used to estimate the scattering efficiency. The minimum (3.4 cm) and maximum (4.3 cm) pore radius were estimated by forward modeling attenuation using mean estimates of conductivity and porosity, 0.175 and 3 μS/cm.
To estimate the thickness of the englacial storage region from the data, we reverse the above equations to forward model radar attenuation and estimate T for a given φ, σ w , and r based on the observed ApRES attenuation ( Figure S2). Since the fraction of attenuation resulting from volume scattering is independent of T, we can quantify the attenuation resulting from water storage. The estimates of water storage required to produce the observed attenuation are then compared with surface melt measured by an automatic weather station (AWS) installed within 1 km of the ApRES deployment and estimates of cumulative mass loss from the RACMO2.3p2 1-km SMB.

ApRES Observations
The observed time series of radar profiles reveals substantial seasonal changes in both the internal layer and bed echo power (Figure 3). Within the ice, the internal layer echo strength decreases by 45 dB from May to December (Figure 3a). This decrease is gradual in the early season with~8 dB of change between May and the end of June. Before significant surface melting occurs, we observe~1 dB diurnal variations in internal layer power likely due to surface temperature variations. Later in the season, the internal layer power reduces bỹ 35 dB between July and September. Notably, the internal layer power remains low until the end of our observational record in December. Across both deployments, the observed layer attenuation signal has no depth dependence (Figure 3a), suggesting the source of the power variation impacts all internal layers equally. This indicates that any possible feature responsible for the decrease in power is located above the identified internal layers in the region of surface inhomogeneity as shown in Figure 2 such that the returned signal from all of the strong reflectors passes through this feature. Over the same period, we also observe periodic fluctuations at 10-15 dB in bed echo power superimposed on the same background attenuation signal as the layers (Figure 3b). These oscillations are well defined before 11 June before becoming more sporadic later in the season.

Evidence of Englacial Water Storage
We interpret the 45 dB decrease in both the internal layers and bed echo power to be a result of the formation of near-surface englacial water storage. Neither instrumental power nor seasonal temperature variations Figure 3. (a) Observed~45-dB reduction in returned power from identified internal layers from 9 May to 7 September overlain with predicted attenuation curves using the observed AWS surface melt record near the ApRES deployment and cumulative mass loss as predicted by RACMO2.3p2 1-km SMB as an estimate of surface melt. Power returned by internal layers are colored according to depth. As the most sensitive parameter, attenuation models are shown for a range of r = 3.4-4.3 cm using a mean, φ = 0.175, and σ = 3 μS/cm. (b) Observed bed power superimposed on the internal layer average. Periodic variations in bed power are observed between May and early June providing evidence of subglacial water. These periodic variations become more sporadic after 11 June possibly indicating a transition from a poorly to well-connected subglacial system. could produce a large enough attenuation signal to explain our observed radar power loss in the internal layers.
Penetration of warm summer air temperatures through the ice sheet could affect the upper ice column temperatures through heat conduction (Cuffey & Paterson, 2010). A warming of 1°C in the ice column would increase the englacial attenuation by~1-5 dB km À1 and would reduce the internal layer power (MacGregor et al., 2015). To estimate a worst-case scenario, we consider a theoretical temperature swing of 40°C between the end of March and mid-July. By applying this value in an energy balance model (Hooke, 2005), we estimate an average ice temperature increase of 2.4°C localized in the top 15 m of an ice column at the ApRES site. We propagate this temperature change through a radar attenuation model (MacGregor et al., 2007, Matsuoka et al., 2010 and calculate an upper-bound estimate of the cumulative change in englacial attenuation of less than 1 dB between May and December through the top 50 m of ice. Variations in the ice column temperature alone cannot explain the substantial 10-to 45-dB reduction in internal layer power. Similarly, a systematic decrease in transmit power is also unlikely to be responsible for the observed reduction in internal layer power. The battery voltage of the ApRES array is stable for both deployments, gradually decreasing by~0.2 V over 3-4 months. Stored englacial water increases scattering losses and englacial attenuation as a function of pore radius, volume, and electrical conductivity. Therefore, we can use the observed attenuation to further constrain the properties and configuration of the englacial storage. For our initial assessment of englacial storage, we use a range of porosities from 0.05 to 0.3 based on previous observations (Cooper et al., 2018;Koenig et al., 2014) and a range of meltwater conductivities of 1.6-4.4 μS/cm from an englacial profile through a borehole adjacent to the ApRES deployment (Doyle et al., 2018). For this range of conductivity and porosity, we estimate water storage in macroporous ice between 3.4 and 4.3 cm in radius is responsible for the observed attenuation in Figure 3a. To place conservative bounds on the minimum and maximum englacial storage fraction and to capture the uncertainty inherent in our model parameters, we estimate water storage for each combination of these parameters (Table S1). Although the specific combination of conductivity, porosity, and water volume that predicts the observed attenuation is nonunique, this model demonstrates that the observed attenuation signal is consistent with storing a significant fraction of the observed surface melt.
We estimate that 1.3-2.6 m of surface meltwater is stored in a macroporous ice layer between 4.6 and 45.0 m thick. Our estimates of a 4.6-to 45.0-m-thick porous layer are comparable to the 7.7-to 37.8-m-thick firn aquifer previously identified at Helheim Glacier in Southeast Greenland (Koenig et al., 2014;Miller et al., 2017). However, unlike the firn aquifer, we found no distinctive bright reflector within the ice column or any loss of radar bed echoes directly beneath the englacial storage at our study site ( Figure S3; Leuschen, 2014). This indicates that englacial storage in the bare ice region of Store Glacier is distinctly different from the perennial firn aquifer observed on the high accumulation region on Helheim Glacier (Forster et al., 2013). Instead, we associate our observed water storage with a porous layer of damaged solid ice, resulting from fast and extensional glacier flow and surface crevasses extending to an estimated depth between 44 and 48 m at the ApRES deployment ( Figure S1; Todd et al., 2018). Our observations suggest more water is stored than is currently plausible in 1-2 m of weathered crust (Cooper et al., 2018), but it could be possible a thick region of weathered ice has accumulated beneath the ApRES deployments. This region of macroporous or damaged ice likely extends laterally over an area of at least 400 m encompassing both deployments 1 and 2 as both locations exhibit the same attenuation signal ( Figure S1).

Comparing Observed Storage to Seasonally Available Local Surface Melt
The englacial storage of 1.3-2.6 m of water between May to December represents a significant portion of the 1.9 m of surface melt production determined from AWS data acquired at the ApRES deployment site and confirmed by ablation stake measurements. These observations are validated by regional climate model (RACMO2.3p2; Noël et al., 2018) estimates of surface water budget that suggests a cumulative SMB loss of 1.9 m, runoff of 2.1 m, and surface melt of 2.4 m. The bulk of mass loss and positive temperature events occur over a 3-month span ranging from 1 June to 9 September ( Figure S4). The cumulative reduction in internal layer power remains past the end of melt season and does not recover by December (Figure 3a). The englacial water did not locally refreeze or drain throughout the observational period since the loss of liquid water would reduce the englacial attenuation signal. Thermal observations and theoretical models support the idea that englacial water can remain liquid for long periods of time up to months or years (Forster et al., 2013;Humphrey et al., 2012;Meyer & Hewitt, 2017). While we do not have data over multiple years to determine how long the liquid water remains stored englacially, the observed echo strengths and seasonal increase in attenuation are inconsistent with many years of accumulated water storage.
To investigate the possibility of multiyear storage, we estimate the maximum amount of melt observable by the ApRES, by analyzing the signal to noise ratio of the radar bed echoes from the processed 2-D radar profiles (Figure 2). We estimate the noise floor is around À70 to À80 dB. Given that the bed power at the start of May is about À28 dB, the maximum power loss possible before the bed echo is lost in noise is roughly 52 dB. This power loss corresponds to a maximum possible amount of storage between 1.4 and 3.5 m of water in a porous layer between 5.1-63.0 m thick, slightly larger than is estimated in this study for 2014. If comparable englacial storage persisted from any previous melt season, it would be unlikely that the ApRES system could have measured the bed echo starting in May of our 2014 deployment. The englacial water system of Store Glacier appears to have a short residence time amounting to a year at the most, with the impounded water likely refreezing or draining to the bed after our observational period between December and early May of the following season.

Evidence of Subglacial Drainage
The 2-D radar profiles collected by ApRES simultaneously capture radar echoes from both englacial layers and the bed. From the bed echoes, we observe an active subglacial water system throughout both deployments directly beneath the region of englacial water storage. Between May and early June, we observe periodic changes in bed echo power of 10-12 dB, lasting between 11 and 17 days, superimposed on the attenuation signal ( Figure 3b). The magnitude of these oscillations is consistent with episodic drainage events through a subglacial water system causing a brighter bed interface as water is routed directly beneath the deployment site (Chu et al., 2016;Peters et al., 2005). From the AWS record, positive temperatures were briefly observed on 8 May while the bulk of melting occurred between 1 June and 9 September. We observe at least two periodic drainage events after 9 May, before the first supraglacial lakes appear in satellite imagery around 1 June (Williamson et al., 2017). Therefore, the initial source of subglacial water appears not to be immediately supraglacial in origin and is either from the drainage of subglacial lakes upstream or from periodic drainage of water stored at the ice-bed interface during the previous winter (Chu et al., 2016;Willis et al., 2015). The transition after 11 June to more sporadic bed power variations and a potentially well-connected subglacial system dependent on surface melt aligns with a sharp increase in surface melting or runoff as suggested by RACMO2.3p2 SMB estimates and persistent AWS temperatures above freezing. Supraglacial lakes are also observed to persist on the ice surface after 10 June (Williamson et al., 2017) and the subglacial drainage of these lakes likely contribute to these sporadic power variations.
No clear local hydraulic connection between the englacial and subglacial systems is observed during our record from May to December. Since all internal layers are equally attenuated, no intermediate features within the ice column linking the englacial water storage to drainage events are apparent in the 2-D ApRES radar profiles. The persistence of the attenuation signal beyond the end of the melt season also suggests water remains stored englacially with no connection to the bed through December. We would expect the drainage of englacial water to be marked by a detectable increase in internal layer power. Given our estimates of maximum water storage in section 4.2 however, it is possible either a subglacial connection develops outside of our observational record or significant refreezing occurs after December.

Conclusions
This radiometric time series of phase-sensitive radar sounding observations offers an unprecedented view of the interaction between the englacial and subglacial water drainage systems of the Greenland Ice Sheet. Our results demonstrate that englacial water storage may be a pervasive, yet overlooked feature of ice sheet hydrology, occurring not only in the thick firn layers (Forster et al., 2013) but also in bare ice regions (Cooper et al., 2018). At Store Glacier, englacial water storage can intercept a significant portion of the surface water budget which persists for likely one melt season. Without the incorporation of regional englacial storage delaying a fraction of the surface melt water from reaching the bead, model-based assessments of the Greenland Ice Sheet will not fully capture the dynamic response to surface melt water input. Our observations also indicate that the englacial water storage at Store Glacier is locally disconnected from the subglacial drainage during the melt season, which contrasts with studies in Southwest Greenland where vertical recharge from englacial storage does reach the bed (Miller et al., 2017;Poinar et al., 2017). If such recharge occurs at Store Glacier, it would have to occur during the late winter, potentially leading to a dampening of seasonal variations in basal lubrication and flow (Schoof, 2010). Therefore, glacial hydrology models that do not include varied and evolving englacial water systems are unlikely to capture the role of surface melt in ice sheet behavior, stability, and sea-level contribution.