Modern digital elevation models (DEMs) of Sperry Glacier and adjacent terrain were derived from national technical means imagery collected in 2005 and DigitalGlobe WorldView imagery collected in 2014. These DEMs were generated by Fahey (2014) and are the same data as used by Clark et al. (2017). Both images were collected in September, when glacier mass is at an assumed annual minimum, specifically on 2 September 2005 and 7 September 2014. The DEMs were generated with SOCET SET^® software, which uses photogrammetric methods to extract terrain data from imagery (Zhang, 2006). Grid cell resolution was 5 m. The absolute accuracy of the DEM with respect to an independent vertical datum was 3.05 m in the horizontal and 7.54 m in the vertical. The precision of the DEM was 0.44 and 0.47 m in the horizontal and vertical, respectively.

U.S. Geological Survey (USGS) topographic maps at 6.1 m (20 ft) contour resolution were available for Sperry Glacier for 1950 and 1960 (Johnson, 1980). These maps were originally created using aerial photography and Kelsh plotter techniques, guided by 13 plane table benchmarks. Both maps document elevation near the assumed September glacier mass minimum, on 1 September 1950 and 8 September 1960. We digitized these historic elevation data by first manually tracing scanned maps to produce digitized contours and then interpolating digitized contours using a natural neighbor interpolation tool (ESRI, 2014; Sibson, 1981). Grid cell resolution was 5 m. We found that the historic elevation data from the original Johnson maps from 1950 and 1960 were 56 m lower than the modern vertical datum due to the authors' sea level datum assumption. We remedied this error by adding 56 m to the 1950 and 1960 DEMs.

The 1950 and 1960 DEMs did not require co-registration because they were originally mapped using a common vertical datum and spatial reference frame. We co-registered the 2005 and 2014, and the 1960 and 2005, DEMs following universal co-registration methods outlined by Nuth and Kääb (2011). The method used a statistical approach that minimized vertical differences over stable (i.e., not prone to landslide/rockfall), vegetation-free, snow-free, and low-sloping (< 30∘) bedrock (Fig. S1 in Supplement). After co-registration, the root mean squared error of elevation differences over stable bedrock improved from 8.43 to 6.91 m for the 1960 and 2005 DEMs, and from 2.48 to 2.01 m for the 2005 and 2014 DEMs. The mean of bedrock elevation differences after co-registration was effectively zero, i.e., < 10-15 m, but differences over individual pixels still ranged from -42 to +83 m for the 1960 and 2005 DEMs and -15 to +14 m for the 2005 and 2014 DEMs (Fig. S2). These large differences tended to occur over steep terrain and are included in our elevation error estimate.

Glacier margin data for 2005 and 2014, used to clip DEMs to glacier extent, were derived from aerial and satellite imagery (i.e., Fig. 1b) and ground-based GPS surveys of the glacier terminus. We defined 1950 and 1960 glacier margin data by digitally tracing the glacier from the same historic topographic maps by Johnson (1980).

We generated a record of geodetic mass balance for Sperry Glacier, given by Ba=ΔVAρiρw, where Ba is the specific surface mass balance expressed in meters water equivalent, ΔV is the change in glacier volume (determined from DEM data described in Sect. 3.1), ρi is the density of ice, ρw is the density of water (1000 kg m-3), and A is the average of initial and final glacier area. To convert volume to mass, we adopted the approximation outlined by Huss (2013) and assigned ice density as ρi=850±60 kg m-3.

There are three main sources of uncertainty in our geodetic mass balance calculation: elevation errors that affect the volume calculation, density errors which affect the volume to density conversion, and map coverage errors that affect the historic geodetic mass balance.

Sperry Glacier has been the focus of a USGS intensive glacier mass balance monitoring program since 2005. Therefore, glaciological mass balance measurements of seasonal mass gains and losses at Sperry Glacier are available from the year 2005 onward (Clark et al., 2017). We used these data, measured in the field according to standard mass balance protocols (Kaser et al., 2003; Østrem and Brugman, 1991), to define specific, conventional (Cogley et al., 2011) winter and summer glacier mass balance from 2005 to 2014. We also analyzed point balance data collected along a longitudinal transect (stakes in Fig. 1; data from Clark et al., 2017) to inspect mass balance gradients at Sperry Glacier. To correct for bias in the raw, specific glaciological balances reported by Clark et al. (2017), we performed calibration as outlined by Zemp et al. (2013). The results of this calibration, which utilized the 2005–2014 geodetic mass balance calculated in this study to correct the absolute magnitude of annual and summer glaciological balances without losing seasonal/annual variability (Zemp et al., 2013), are reported in Table 1. Such calibration ensures that systematic errors in the glaciological method are rectified and that englacial and subglacial mass changes not measured at surface stakes are accounted for. Details on this calibration are provided in the Supplement.

Employing annual glaciological measurements (Clark et al., 2017), we defined a functional relationship (i.e., linear regression) between 2005–2014 specific surface mass balance and regional climate. Regional climate was defined by data on winter peak snow water equivalent (SWE) and summer positive degree days (PDDs). Climate data from 2005 to 2014 were used to define the regressions, and climate data from 1950 to 2005 were used to apply the regressions back in time.

Attributing the hypothesized change in the glacier–climate relationship to the increasing influence of local topographic effects requires inspection of topographically influenced processes at Sperry Glacier. To assess topographic shading, we used the Solar Area Radiation tool (ESRI, 2014) to calculate cumulative insolation received across Sperry Glacier during the melt season months of July, August, and September in 2014 – when the glacier was smaller, steeper, and more shaded – versus 1950, when the glacier was larger, flatter, and less shaded. This hemispherical viewshed algorithm (Fu and Rich, 2002) calculated radiation based on an upward-looking sky map for every grid cell within our 2014 DEM, the seasonal progression of the position of the sun relative to Earth, a fixed atmospheric transmissivity, topographic shading, latitude, elevation, slope, and aspect. To qualitatively assess avalanching and wind-drifting snow processes, we examined field observations, historic photographs, and field-measured mass balance data collected by Clark et al. (2017).

Sperry Glacier has decreased from 1.30 km2 in 1950, to 1.23 km2 in 1960, to 0.86 km2 in 2005, to 0.80 km2 in 2014 (Table 2). During the mid-20th century the glacier extended onto relatively flat (< 15∘ slope) bedrock terrain; therefore the lower portion of the glacier was relatively low angle. As a result, between 1950 and 2014, despite nearly 0.5 km of retreat, the glacier terminus only receded upward by 56 m in elevation. The loss of this northwest-oriented, low-sloping terminus resulted in a steepening of the glacier's median slope by 9∘ and a rotation of the glacier's median aspect toward the north by 11∘.

Elevation change across the glacier surface is generally similar in its spatial pattern, but not magnitude, during 1950–1960, 1960–2005, and 2005–2014 (Fig. 3a, c, e). Thinning occurred across the lower portion but was most pronounced at the terminus. The upper elevations of the glacier thickened from 1960 to 2005 and from 2005 to 2014, but at rates less than +1 m yr-1 (Fig. 3). The magnitude of thinning near the terminus is distinct for each period. Terminus thinning rates from 1950 to 1960 were up to -2.5 m yr-1 (Fig. 3b), whereas terminus thinning rates from 1960 to 2005 (Fig. 3d) and from 2005 to 2014 (Fig. 3f) were smaller than -1.5 m yr-1. No development of debris cover at the glacier terminus that might explain this decreased thinning rate is evident. The magnitude of thickening was likewise distinct between periods, with 1950–1960 showing a bulge near the glacier's middle (approximately 2500 m), growing at nearly +1 m yr-1 (Fig. 3b).

Despite differences in the magnitude of elevation change, the hypsometry of the glacier remained similar in 1950, 1960, 2005, and 2014. Sperry Glacier lost 50 m of ice at the glacier terminus during the 1960–2005 interval, which agrees with the average amount of thinning (52.4 m) reported for glaciers in the Canadian Rockies for the same period (Clarke et al., 2017). Commensurate with its area loss and thinning, the glacier also lost volume. Geodetic mass balance results show Sperry Glacier shrank by -3.33 ×106 m3 from 1950 to 1960, -11.3 ×106 m3 from 1960 to 2005, and -0.90 ×106 m3 from 2005 to 2014 (Table 3). It lost -2.83 ×109 kg of mass from 1950 to 1960, -9.68 ×109 kg from 1960 to 2005, and -0.76 ×109 kg from 2005 to 2014 (Table 1). The rate of mass change at Sperry Glacier was -0.22 ± 0.12 m w.e. yr-1 from 1950 to 1960, -0.18 ± 0.05 m w.e. yr-1 from 1960 to 2005, and -0.10 ± 0.03 m w.e. yr-1 from 2005 to 2014 (Table 3). The glacier is near balance but slightly losing mass.

Linear regressions show strong (r2>0.97), statistically significant (p<0.03) correlation between climate and glaciological data (Fig. 4). The model therefore effectively defines a functional relationship between glacier mass balance and regional climate for 2005–2014. The regressions correlate warmer summers with more negative summer mass balance (r2=0.978), and snowier winters with more positive winter mass balance (r2=0.973). From the regression results, the proportionality factor for winter (mw), which scales snow course data on peak SWE to winter glaciological measurements, is 2.99. The proportionality factor for summer (ms), which scales meteorological data on PDDs to summer glaciological measurements, is -0.004 m w.e. ∘C-1 day-1.

We used climate data to apply the linear regression back in time to 1950 (Fig. 5). Average PDD during 1950–1960 was 709±53 ∘C day, which was virtually the same as average PDD during 1960–2005 (717±86 ∘C day). Summer PDD then showed a 41 ∘C day increase to an average of 758±75 ∘C day during 2005–2014, although this increase was well within interannual variability. Snow data show that, on average, SWE decreased from 1.31±0.26 m w.e. in 1950–1960, to 1.08±0.32 m w.e. in 1960–2005, to 0.95±0.25 m w.e. in 2005–2014, although these step decreases are likewise within the range of interannual variability. The step change in peak SWE during the mid-1970s is consistent with other regional SWE records (Fig. S3b) and has been interpreted as a result of a modal change in the Pacific decadal oscillation, a pattern of ocean climate variability which is closely tied to peak SWE in this region (McCabe and Dettinger, 2002; Pederson et al., 2011; Selkowitz et al., 2002). Generally, PDD and SWE in 1950–1960 compared to 2005–2014 seem to differ. To quantitatively assess the difference, we performed simple t tests. T test results showed that the lower (higher) average SWE (PDD) during 2005–2014 differed statistically from 1950–1960 SWE (PDD) at p<0.01, α=0.99 (p<0.15, α=0.85). This evidence supports the notion that 2005–2014 had relatively dry winters and warm summers compared to 1950–1960.

Nevertheless, geodetic results show that average mass change rates at Sperry Glacier for 2005–2014 (-0.10 ± 0.03 m w.e. yr-1) and 1950–1960 (-0.22 ± 0.12 m w.e. yr-1) were comparable, i.e., within error bounds. This differs drastically from mass balance results derived from the regression, which include many years of net mass gain during the mid-20th century (Fig. 5). Sufficient individual years are positive during the mid-20th century to yield positive averages from 1950 to 1960 and from 1960 to 2005, at +0.98 ± 0.83 and +0.34 ± 0.75 m w.e. yr-1, respectively. However, confidence intervals from the linear regression model suggest the possibility of a negative average during 1960–2005. Conversely, error on the 1950–1960 mass balance include only positive averages, i.e., glacier thickening and mass gain. The 1950–1960 mass gain predicted by the regression (+0.98 ± 0.83 m w.e. yr-1) is distinctly at odds with the 1950–1960 geodetic mass balance of -0.22 ± 0.12 m w.e. yr-1.

The amount of potential clear-sky radiation available for specific summer melt at Sperry Glacier decreased by 118 605 kJ m-2 (approximately 15 W m-2) from 1950 to 2014, likely due to steepening of the glacier surface and a greater proportion of the glacier becoming shaded. Given the heat of fusion for ice (334 J g-1), this energy deficit translates to 0.36 m w.e. less potential melt for the summer melt season averaged over the entire glacier, driven only by changes in the relative influence of local effects (i.e., shading, steepening), independent of climate. Field observations show that the rock headwall extending above Sperry Glacier (Fig. 2) contributes high-frequency, low-volume, loose avalanches (Fig. 6b), and that the cornice above the bergschrund often breaks in the spring, subsequently triggering localized slab avalanches that extend 500 m down from the crest of the ridge to an elevation of 2460 m. (Fig. 6c). Historic aerial photographs show that a prominent ridge of wind-drifted snow consistently develops at lower elevations in the basin (Fig. 6a). Field-measured mass balance data showing highly variable snow accumulation provide evidence of wind effects. Accumulation ranges from 0.00 m w.e. in wind-scoured areas, where seasonal snowpack had been stripped down to bare ice, up to more than 5 m w.e. in wind-loaded areas (Clark et al., 2017).

Field-measured point data (n=551), taken along stakes from the terminus toward the headwall of the glacier (Clark et al., 2017), show the impact of these local effects (shading, avalanching, wind drifting) on the mass balance elevation gradient (Fig. 7c). Toward the glacier terminus, at elevations lower than 2475 m, the mass balance gradient of winter accumulation is 10×10-4 m w.e. (m)-1. Toward the glacier head, at elevations above 2475 m, the mass balance gradient of winter accumulation is an order of magnitude higher at 150×10-4 m w.e. (m)-1. The elevation gradients shown by summer ablation measurements show a similar inflection (Fig. 7c). At elevations higher than 2475 m, where the glacier is steeper and more shaded, the melt gradient rate increases 8-fold from 6.6×10-4 to 53×10-4 m w.e. (m)-1.