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.

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 al., 2012 ; Chu et al., 2016 ; Schoof, 2010 ; Sole 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.

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 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.

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.

Englacial water storage will increase the observed radar attenuation depending on the amount and electrical conductivity of the water (Schroeder et al.,). 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.,; Bohren & Huffman,; Ulaby et al.,). To forward model the expected radar attenuation we estimate the two‐way attenuation through the region of water storage according to its skin depth,whereis attenuation,is the thickness of the region of water storage, andis the skin depth. The skin depth is given bywhereis the center frequency of the radar,is the conductivity of the region of water storage, andis the permeability of free space (Schroeder et al.,). Estimates of cumulative mass loss estimated by the RACMO2.3p2 1‐km surface mass balance (SMB) model (Noël et al.,) 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,, for a given porosity,. Using a mixing model previously designed and applied to estimate the electrical conductivity of sea ice (Geldsetzer et al.,), we calculate the conductivity of englacial water storage given bywhereis the surface water conductivity,is the water volume fraction (porosity),is the volume fraction limit below which the connectivity of conductive pores can be ignored, andis an empirical parameter that controls the increase in conductivity for volume fractions aboveFollowing previous work, we setand(Clarke et al.,; Geldsetzer et al.,).

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 (Young et al., 2018 ). 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 (−0.88 dB/day during deployment 1 and −0.84 dB/day in deployment 2) a constant offset of −38.49 dB was needed to calibrate the echo power values for deployment 2 that began 19 days later.

Example 2‐D ApRES cross section from 9 May 2014 showing the location of the identified internal layers (blue circles) tracked from May to July 2014. The internal layers were identified as the strong reflectors present in the upper 300 m of ice (Young et al., 2018). Below 300 m, little internal structure is visible before the strong bed echo at about 617 m. Similar features were identified as internal layers and tracked during deployment 2 from August to November 2014.

(a) Landsat‐8 image of Store Glacier from 1 July 2014 showing the location of the ApRES deployment and the position of the deployment relative to Greenland, overlain by winter MEaSUREs ice flow velocity for 2014–2015 derived from InSAR data (Joughin et al.,). 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.

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 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.

(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.

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 3 a). 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 by ~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 3 a), 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 3 b). These oscillations are well defined before 11 June before becoming more sporadic later in the season.

4 Discussion

4.1 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 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−1 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, 2015, Matsuoka et al., 2010, 2012) 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).

4.2 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 −70 to −80 dB. Given that the bed power at the start of May is about −28 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.