Surface Mass Balance Controlled by Local Surface Slope in Inland Antarctica: Implications for Ice‐Sheet Mass Balance and Oldest Ice Delineation in Dome Fuji

The limited number of surface mass balance (SMB) observations in the Antarctic inland hampers estimates of ice‐sheet contribution to global sea level and locations with million‐year‐old ice. We present finely resolved SMB over the past three centuries in a low‐accumulation region with significant depth hoar formation on Dome Fuji derived from ∼1,100 km of microwave radar stratigraphy dated with a firn core. The regional‐mean SMB over the past 264 years is estimated to ∼22.5 ± 3.3 kg m−2 a−1, but with large local variability of up to 30%. We found that local SMB is negatively correlated with surface slope at scales of a few hundred meters, resulting in anomalous zones of low SMB which represent as much as 8–10% of the total SMB on the inland plateau if the SMB‐slope relationship is more widely valid. This impact should be investigated further to improve estimates of Antarctic mass balance and sea‐level contribution.

• Ultrawide band microwave radar reveals spatially highly variable surface mass balance (SMB) over the past three centuries in inland Antarctica • SMB anomalies resulting from local surface slopes may represent as much as 8-10% of the total SMB on the inland plateau • The new SMB data have direct implications for the search for millionyear-old ice in the Dome Fuji area, East Antarctica

Supporting Information:
Supporting Information may be found in the online version of this article.

Citation:
Van Liefferinge, B., Taylor, D., Tsutaki, S., Fujita, S., Gogineni, P., Kawamura, K., et al. (2021). Surface mass balance controlled by local surface slope in inland Antarctica: Implications for ice-sheet mass balance and Oldest Ice delineation in Dome Fuji. Geophysical Research Letters, 48, e2021GL094966. https://doi. org/10.1029 with larger SMB due to the increased vertical advection of cold snow which lowers the basal temperatures. On the other hand, considering very old ice near the bed, larger SMB increases the depth of the ice at a certain age and correspondingly reduces the age resolution of the ice (Dansgaard & Johnsen, 1969). SMB data sets commonly used in ice-sheet modeling (e.g., Huybrechts et al., 2000;Ritz et al., 2001;Van Liefferinge & Pattyn, 2013) tend to show overestimation in the East Antarctic inland around Dome Fuji (e.g., Fujita et al., 2011;Satow et al., 1999), which can lead to underestimation of basal melting as indicated by a simulation study where observed SMB was partially implemented (Saito & Abe-Ouchi, 2004). Better areal coverage of reliable field-based SMB data for integration into ice-sheet models is thus critical for searching Oldest Ice in the candidate areas.
Here, we present SMB over the last three centuries in the vicinity of Dome Fuji based on microwave radar profiling and shallow firn coring. High local SMB variability at scales of a few hundred meters is quantified and related to local surface slopes. We further discuss the results in context of ice-sheet mass balance and the presence of Oldest Ice.

Dome Fuji Region
As a part of a site survey for future deep ice coring of Oldest Ice (Text S1), we investigated the area (Figure 1) south of Dome Fuji Station where two deep ice cores were drilled earlier (Kawamura et al., 2007(Kawamura et al., , 2017Watanabe et al., 2003). This area includes the current topographic crest, constituting a major continental drainage boundary. Satellite microwave emission data indicate a distinct contrast in SMB across the crest (Fujita et al., 2011). At Dome Fuji Station near the crest, SMB has been estimated to 25.5 ± 0.3 kg m −2 a −1 averaged over 1260-2001 CE (Igarashi et al., 2011), and 28 ± 3 kg m −2 a −1 over the early Holocene (Svensson et al., 2015). For a more recent period between 1995 and 2006, SMB was measured to be 27.3 ± 0.4 kg m −2 a −1 using multiple snow stakes near the station (Fujita et al., 2011;Kameda et al., 2008). Radar data analyzed in this study were collected along the blue segments in three boxes, A, B, and C and between NDFN and Dome Fuji Station. According to the Japanese and German bed topography data, Box A include smoother bed, Box B has relatively thick ice that gives frozen bed if geothermal heat flow is proportionately low, and Box C has elevated bed which may constrain the ice-dome position in the past. Boxes A and C are located on one side of the subglacial massif, and Box B is located on the other side. Contours show surface elevations with 10-m internals (Howat et al., 2019). Yellow dots show locations of the four firn cores drilled in the 2017-2018 and 2018-2019 seasons, and the Dome Fuji Station where deeper cores have been drilled in the past (see Table S2 for coordinates). The black dashed line depicts ice flow divides from the MEaSUREs data set (Mouginot et al., 2017). The inset in A shows the coverage of the main map. (b) Overview of the larger region with the radar survey grid shown together with past surface mass balance (SMB) traverse routes by Japan-Sweden (Fujita et al., 2011) and Norway-US (Müller et al., 2010). The background colors show interpolated large-scale SMB for the last 200-700 years. All maps are in the Antarctic Polar Stereographic projection (EPSG:3031), and panel a was prepared with Quantarctica (Matsuoka et al., 2021).
Larger-scale SMB data in the region have previously been collected from a long-term snow-stake network along the ∼1,000 km traverse route from the coast to Dome Fuji Station (Hoshina et al., 2016), as well as using radar data and firn cores of scientific traverses of Japan-Sweden (Fujita et al., 2011) and Norway-US (Müller et al., 2010) during the 2007-2008 International Polar Year (Figure 1b). Fujita et al. (2011) showed that SMB varies between 24 and 30 kg m −2 a −1 over the past seven centuries along the northwestern divide within 400 km from Dome Fuji Station. Müller et al. (2010) showed that SMB averaged over the past 200 years ranges between 20 and 30 kg m −2 a −1 about 200 km inland of the Dome Fuji Station. Interpolation between these SMB transects indicate a spatial contrast in SMB across the continental divide ( Figure 1b) which is broadly consistent with satellite microwave emission data (Fujita et al., 2011); see also Text S2.
Our new radar data coupled with multiple shallow firn cores give a uniquely dense sample of recent SMB over a large area, useful for assessing the impact of local variability on regional-scale SMB and for delineation of Oldest Ice.

Data and Methods
We surveyed the Dome Fuji region in the 2018-2019 austral summer with a new ultrawide-band FM-CW radar (Taylor et al., 2019) mounted on a platform of a tracked vehicle moving ∼10 km/hr. The radar operates at 2-8-GHz with 6-GHz bandwidth, giving a depth resolution of about 25 mm in snow. After fast Fourier transform, coherent and incoherent averaging were performed to increase the signal-to-noise ratio. The processed data are spaced at ∼1.1-m intervals over ∼1,100 line kilometers in about 500 km 2 ( Figure 1a). The study area was covered by a series of parallel profiles with a nominal separation of 1 km, and with numerous cross-over sites particularly near the survey camp and the firn core sites NDF and NDFN. In the radargram, we tracked the surface and three englacial reflectors, which were selected for their continuity across all profiles ( Figure 2d). We assumed that the reflectors are isochrones that can be dated with depth chronology from firn cores.
Firn density-depth profiles are needed to determine reflector depths and SMB. Although SMB is spatially variable in our study area, the tracked reflectors are all in the shallow part of the firn (density <550 kg m −3 , Figure 2a) where densification is dominated by grain boundary sliding which is to first-order independent of SMB (Herron & Langway, 1980). This was confirmed by the similarity of the measured density-depth profiles in four firn cores drilled in the 2017-2018 and 2018-2019 seasons ( Figure 2a). Density in the top several meters of firn is often underestimated due to the high variability in the near surface which creates irregularity in the sample volume of these fragile core segments (Weinhart et al., 2020). At 20-m depth, the cores are more stable and less error prone. We used a single linear fit between the average density down to ∼1-m depth from multiple snow pit observations (Table S1) and the average density at ∼20-m depth from the stable part of the cores (Table S2). To account for density measurement errors, we developed uncertainty bounds from Monte Carlo simulations (Text S3). The resulting linear function is ρ = (9.11 ± 1.27)d + (331 ± 24.2) where ρ is the density (kg m −3 ) and d is the depth (m). We also attempted various linear and polynomial fits with all core data, but found that it had little impact on the resulting SMB.
We derived a depth-profile of permittivity (ϵ) based on the fitted density profile following Kovacs et al. (1995): ϵ = 0.021d + 1.60. This equation for local permittivity is used to derive depth-variable propagation speed and then accurate depths of the reflectors. Separately, the dielectric permittivity of the NDFN firn core was measured at −30 C at frequencies over 15-20 GHz with a ∼30-mm resolution from the surface to 15.0 m with an open resonator method . This resulted in a consistent permittivity profile of ϵ = 0.020d + 1.64 ( Figure 2c).
The radar reflectors were dated using data from the NDFN firn core that was drilled in the same season. There are nine independent radar profiles with 700 sampling points within 50 m from the NDFN core site. Within this zone, depths of the three tracked reflectors vary by 1.6-3.7% of their mean depths. Dielectric conductivity was measured along the core, revealing six peaks that were identified to be of volcanic origin and tied to sulfate peaks in the WAIS Divide ice core (Sigl et al., 2014), giving six aged depths in the top 20 m (Figure 2b and Table S3). We then constructed a depth-age model (Buizert et al., 2018) that assumes constant SMB between the volcanic tie points and accounts for uncertainties (2σ) due to tie-point matching, age interpolation, and firn density variability (Text S4). This resulted in reflector ages of 78.1 ± 4.5, 95.9 ± 4.1, and 263.7 ± 6.0 years before 2019 (Table S4).
As a consistency check, we similarly derived reflector ages based on the NDF core that was drilled 1 year earlier at a location ∼6 km south of NDFN (Table S5).
The nominal ice thickness of the surveyed region is around 2.5 km , so all tracked reflectors are within 0.6% of the ice thickness from the upper surface. Within this depth range, the depths of reflectors are mainly dependent on SMB. First-order densification processes are also accounted for in our analysis since both density and propagation speed are considered as depth variable. Therefore, SMB can be derived as the integrated mass from the surface to the three reflectors divided by the corresponding number of years, resulting in three reference SMB periods denoted T1 (
In our survey area, SMB is highest in the dome summit area within 20 km from Dome Fuji Station, and then gradually decreases downslope toward NDFN (Figure 3). SMB within the grid areas is more variable over short distances than the two segments to the Dome Fuji Station. We attribute this difference to surface slope (Figure 3).  Figure 1a. A depthdensity relationship (green line) was fitted to the spatially averaged densities down to ∼1-m depth from snow pits and at ∼20-m depth from firn cores (orange circles, Tables S1 and S2). The black curve shows density derived from permittivity (c) using Kovacs et al. (1995).  Figure S1 for tracking procedures. The radargram shows returned power in dB relative to the mean value of the presented domain. See Figure 1a for profile location.
We derived absolute magnitudes of surface slope for 200 m × 200 m grid cells using the Reference Elevation Model of Antarctica (REMA, Howat et al., 2019). The region between Dome Fuji Station and NDFN has small surface slopes (< 0.03 • ) and there are no strong slope patterns. In contrast, the grid areas have more variable slopes, up to > 0.12 • , and distinct alternations of steeper slopes and flatter slopes. We observe larger SMB over flatter slopes and smaller SMB over steeper slopes. This relationship is robust even if slopes are calculated over shorter or longer distances. However, the correlation weakens when slopes are calculated over distances shorter than ∼100 m or distances longer than ∼2 km. Potential directional dependencies cannot be easily addressed as almost all observations are in southerly aspects.
We validated the gridded REMA slopes with independent surface slopes derived from ICESat-2 laser altimetry data. We used the ATL06 product  which has a surface elevation precision better than 9 cm on the Antarctic plateau . Surface slopes are provided at a scale of 40 m along-track and 90 m across-track, and we further applied a running mean filter over 200-m distances along each laser beam before calculating absolute slopes comparable to REMA. The REMA and ICESat-2 slope patterns match very well (Figure S4b), and their mean and third quartile differences in slope magnitudes are 0.019° and 0.027°. Most larger discrepancies are associated with a few ICESat-2 ground tracks ( Figure S5).
We quantified the observed SMB dependency on surface slopes derived from REMA using all ∼1 million data points (Figure 3 inset). We approximated this relationship linearly, y = ax + b, where x is the surface slope in degrees and y is measured SMB (kg m −2 a −1 ), and obtained (a, b, R 2 ) = (−11.4, 26.1, 0.22) for T1, = (−14.6, 26.0, 0.32) for T2, and = (−12.4, 23.6, 0.35) for T3. The results are consistent when using ICESat-2 data for surface slopes ( Figure S5) or when calculating surface slopes at different length scales from ∼100 m to ∼2 km.  . Firn core sites are shown with yellow circles. Similar plots for the periods T1 and T3 are provided in Figures S2 and S3, respectively. The inset shows the relationship between SMB and REMA surface slopes for ∼1 million locations for the same period. The number of data points is shown using contours. The dashed red line shows the linear fit to the data.

Discussion
Microwave radar layering has been used to measure recent SMB at various locations in Antarctica. However, most of earlier work has been done in West Antarctica, which has an order of magnitude larger SMB than the inland East Antarctica (Medley et al., 2013(Medley et al., , 2015. The inland East Antarctic plateau has very low SMB and strong vertical vapor transportation near the surface resulting in depth hoar formation (Gallet et al., 2014;Scambos et al., 2012) which can be a challenge for SMB applications of microwave radar. Our study demonstrates that microwave radar can be used to determine spatial patterns of SMB in a low-accumulation region with abundant depth hoar.
Shallow radar reflectors are widely considered as isochrones in Greenland and West Antarctica (e.g., Spikes et al., 2004), but not yet well validated in the inland East Antarctic plateau. The separately analyzed NDF core is used for this validation and to examine our age uncertainties (2σ) derived from the NDFN core. The NDF core location is ∼6 km south of NDFN and 330 m away from one radar profile. There are 663 data points within 350 m from the core site. After correcting for the 1 year difference between the radar survey and the NDF coring, averaged depths of L1, L2, and L3 reflectors within 330-350 m from the core site are 80.0 ± 3.6, 98.7 ± 3.3, and 256.7 ± 3.4 years before 2019, respectively. These age estimates are all within 3% of the reference ones derived from the NDFN core, and the associated uncertainties are overlapping (Tables S4 and S5).
This dense radar survey grid combined with multiple firn cores ( Figure 1) give us an opportunity to estimate area-averaged SMB with high confidence over the past three centuries. The regional-mean SMB for each of the three periods appears to slightly increase with time from 22.5 to 25.1 kg m −2 a −1 which is consistent with many other locations on the Antarctic plateau (Fujita et al., 2011); however, given the estimated SMB uncertainty this trend is not statistically robust. As inferred from past radar traverse data (Figure 1b), larger-scale SMB shows a slight decrease from Dome Fuji Station toward the southern end of our study area ( Figure S6). Our regional-mean SMB values are within the range of the estimates from two commonly used regional climate models: 22.5 kg m −2 a −1 (van Wessem et al., 2018) and 31 kg m −2 a −1 (Agosta et al., 2019). We observed the lowest SMB in a wind scour zone (Figure 3), a steep eroded surface feature formed by wind acceleration and probably related to the bed topography . Topographically induced snow redistribution and sublimation by downslope wind is a likely mechanism to explain the observed SMB variability in our study area.
Previous studies have also pointed out correspondences between SMB and surface slope, as well as between surface and bed slopes (Black & Budd, 1964;Cavitte et al., 2018;Frezzotti et al., 2004Frezzotti et al., , 2005Frezzotti et al., , 2007Fujita et al., 2002Fujita et al., , 2011Furukawa et al., 1996;Le Meur et al., 2018;Minghu et al., 2011;Wang et al., 2015). However, these studies relied on along-track slopes derived using GPS data along the radar transect or digital elevation models (DEM) with spatial resolutions at kilometer scales. The surface elevation products of REMA with a native 8-m horizontal resolution allows us to derive precise slopes at higher resolutions (Figure 4), which we have validated with independent analysis of ICESat-2 altimetry data ( Figure S5). Our analysis shows that SMB can differ by 30% within ∼500 km 2 in the vicinity of an inland dome where wind is particularly weak, and where SMB is typically assumed to be nearly uniform.
We used the new SMB data to re-evaluate promising Oldest Ice locations proposed earlier Van Liefferinge et al., 2018). Their studies assumed regional-mean SMB values (van de Berg et al., 2006) that are 15-60% larger than our new estimate south of Dome Fuji, which is consistent with the previous observation at Dome Fuji Station. The first guiding principle to search for Oldest Ice is frozen bed conditions (Fischer et al., 2013). The threshold (maximum) geothermal heat flow to maintain a frozen bed over the last 1.5 million years becomes ∼10 mW m −2 lower when the new SMB data are applied. Van Liefferinge et al. (2018) diagnosed ∼25% of the Dome Fuji region (Figure 3 domain) as promising Oldest Ice sites. However, if SMB is assumed uniform at the regional-mean SMB from our observations, then the areal fraction of the promising sites would be 5-18% of Figure 3 domain, depending on the data set used for geothermal heat flow. This areal fraction is also sensitive to ice thickness, and the estimate above was made using a regional ice thickness data set . The results confirm the importance of using observational SMB for investigating the thermal condition and age of the deep ice (Saito & Abe-Ouchi, 2004).
We explored possible impacts of the SMB-slope relationship on estimating large-scale SMB over inland East Antarctica using our simple parametrization of SMB with local slopes ( Figure S6), though SMB depends on many other factors including the curvature of the surface. Regional climate models typically have grid-cell sizes of a few tens of kilometers, and thus slopes over these cells are very low (10 −2 -10 −5 degrees) compared to surface slopes at the scale of a few hundred meters (up to 10 −1 -10 −2 degrees, Figure S4a). For a relative estimate of 7 of 10 topographic SMB impacts, we first derived surface slopes using REMA at 200-m resolution for the entire East Antarctic plateau. Second, REMA was downsampled to generate a coarser DEM with 25-km resolution, which is comparable to those used in regional climate models. Third, slopes derived from the coarse DEM were subtracted from the slopes derived from REMA at 200-m resolution to determine the residual slope variability. By applying the SMB-slope parametrization for the T2 period for the residual slopes across the plateau, we infer a widespread occurrence of low-SMB zones related to local slope variability ( Figure S6). If the slope-induced residual SMB is integrated over the ice-sheet interior, we obtain total numbers of 13.0 Gt a −1 for areas higher than 3 km a.s.l. and 3.6 Gt a −1 for areas higher than 3.5 km a.s.l. This corresponds to 8-10% of the integrated SMB of regional climate models over the same areas (e.g., van Wessem et al., 2018). This could imply an overestimation of icesheet SMB in larger-scale SMB products, or it could be balanced by an opposite offset over flatter slopes. Our parameterization is only based on the observed SMB conditions near the inland dome, and effects of wind on SMB can be stronger over katabatic wind regions, which may cause an even larger slope dependency on SMB.
More extensive SMB measurements are needed to accurately quantify SMB over large areas, and ultrawide-band microwave radar is the most practical method for such missions.

Conclusions
SMB over the past three centuries was mapped using microwave radar reflectors in the top 15 m of the firn over a 500 km 2 area near Dome Fuji in East Antarctica. Our dense survey grid enabled us to precisely evaluate regional-mean SMB and document small-scale SMB variations. The regional-mean SMB for the past 264 ± 6 years was quantified to 22.5 ± 3.3 kg m −2 a −1 , which is considerably lower than what was used to delineate promising Oldest Ice in earlier studies. With an updated SMB, the areal fraction of promising sites in the Dome Fuji region is reduced significantly, and a further refined estimate using the spatial SMB, ice thickness, and geothermal heat flow is needed. Our SMB observations reveal a ∼30% local variability and a strong negative correlation with surface slope at length scales from ∼100 m to ∼2 km. Using the high-resolution REMA product, we quantified for the first time the SMB-slope relationship at scales of a few hundred meters. If this relationship is generally valid in inland East Antarctica at elevations higher than 3 and 3.5 km a.s.l., then the local SMB anomalies associated with small-scale steeper slopes represent as much as 8-10% of the integrated SMB over the whole region. This is significant for assessments of Antarctica's overall mass balance and contribution to sea-level change.

Data Availability Statement
There are three data sets generated in this study: (a) Ice core data are archived at Arctic Data Archive System at National Institute of Polar