Supplemental Online Material
S1. Mass Balance methods
Seasonal and annual glacier mass balance is determined through combination of the glaciological, or direct, method and the geodetic method (Cox and March 2004; Cuffey and Paterson 2010). At three sites on each glacier, stake and snowpit measurements occur twice yearly, during spring and fall (close to annual mass extrema). Point estimates of seasonal and annual mass balance result at each site. Point balances are adjusted for accumulation and ablation that occurs over the short interval between the observation and mass extrema. Post-observation ablation is usually measured directly the following spring, a temperature-index model is applied to estimate accumulation, as described in van Beusekom et al. (2010). Glacier-wide mass balance is calculated by dividing the glacier into three elevation-defined bins (with boundaries at the midpoints between stakes), and then summing the product of each point mass balance and its representative glacier area (van Beusekom et al. 2010).
Direct measurements are supplemented with photogrammetric analysis of opportunistically acquired stereo imagery. Construction of digital elevation models (DEMs) from the imagery allows us to evolve the area altitude distribution (AAD) used to estimate direct mass balance. AADs are updated annually between DEMs using linear interpolation. The rate of area change is held constant from the last available interval to extrapolate geometric evolution from the last DEM to the present. Thus, our estimates represent conventional balances related to water mass, not reference-surface balances related more to climate (Elsberg et al. 2001). Additionally, these DEMs are differenced to produce a time series of cumulative volume change. Before differencing, all DEMs are co-registered in ice-free areas (Nuth and Kääb 2011). Mass change is estimated via an assumption of material density (900 g/cm3) gained or lost.
The direct and geodetic methods are essentially independent of each other, which allows us to perform a weighted least-squares adjustment between the cumulative balance time series resulting from each method (Huss et al. 2009). Weights are assigned based on DEM quality. The adjustment (-0.02 m/yr for Gulkana Glacier and -0.43 m/yr for Wolverine Glacier) minimizes the global misfit between the two datasets such that the adjusted time series exhibits short-term variability guided by field observations and long-term trends guided by geodetic observations. This procedure corrects for systematic errors in the direct glacier-wide balance estimate (estimated at 0.2 m/yr; van Beusekom et al. 2010), thereby increasing confidence in interannual variability. The adjustment primarily affects the cumulative balance series; relative differences between individual balance estimates are unaffected by the adjustment. It does, however, result in small discrepancies between seasonal sums and annual balances. No constraints exist to further adjust seasonal balances as others have done (e.g. Huss et al. 2009).
The 46-year record used here (1966–2011) is a direct extension of the re-analyzed data set compiled by van Beusekom et al. (2010), which produced significant changes from earlier published versions (Hodge et al. 1998; Josberger et al. 2007; Harrison et al. 2009). Our analysis introduces additional field data through 2011, as well as updates to the geometry of both glaciers. Two DEMs (2008, 2011) were produced for Wolverine Glacier, and one DEM for Gulkana Glacier (2009). The new geometries affect the direct mass balance history between the new and previous DEMs (1999 Gulkana, 2000 Wolverine), but resulting changes to recent balance estimates were small (<10%). This analysis departs from van Beusekom et al. (2010) by performing a single weighted least-squares adjustment to the geodetically-determined mass change with no adjustments to point data.
S2. Details of statistical methods
Two methods were used to detect long-term changes or trends in the data. First, we tested for a change in median value over the study interval, assuming steady spread and shape of each distribution using the Rank-sum Test (Helsel and Hirsch 1992). We applied this test to evaluate the null hypothesis of constant median between the first and last decades of the study (1966–76 and 2001–2011). Time periods were selected to form two continuously sampled, equal length intervals, with the maximum possible time between them. Neither interval spans a major climate regime shift, although the first interval terminates at the widely accepted North Pacific climate regime shift of 1976 (Hare and Mantua 2000). Although this sampling methodology is subject to short-term aliasing, the 10–year samples provide enough data for reliable statistics minimally affected by interannual variability, and may indicate where long-lived single-direction shifts occurred, especially when the results agree with alternate tests.
A second method, the Mann-Kendall Test, was employed to identify long-term monotonic trends. This rank-based test has no theoretical or empirical sensitivity to missing values (Hirsch and Slack 1984). The null hypothesis of no trend was rejected when test confidence exceeded 90% (a = 0.1). To reduce bias from long-term persistence, testing was performed on “standardized deviates”, which are the nonparametric equivalent to standard normal deviates (Hodgkins 2009). The standardized deviate of a time series is calculated by subtracting the median then dividing by the scaled interquartile range (STD = IQR/1.35) for each value.
Both Walters and Meier (1989) and Hodge et al. (1998) were early to establish that Wolverine Glacier is modulated primarily by winter precipitation, while Gulkana Glacier demonstrates control from summer melt. Comparing the updated record to a re-analysis of the 1966–95 Hodge et al. (1998) interval reveals that the glacier–climate interactions established by 1995 appear to continue today. The primary exception is that the updated data set reveals a significant correlation between annual and summer balance at Wolverine Glacier existed in the first interval, likely an oversight in the early publication. The reanalyzed data also strengthens the inter-glacier correlation for summer balance, suggesting summer temperatures have always been more in phase than original publications described.
Supplemental Figures
Figure S1. Location of the mass balance measurement sites and weather stations for both USGS benchmark glaciers, which are shown in the regional map (Figure 1) for context. Glacier outlines are from 2009 at Gulkana Glacier and 2011 at Wolverine Glacier. Watershed basin outlines are given as dashed lines.
Figure S2. Standardized summer streamflow and mass balance deviates at Gulkana and Wolverine glaciers. Blue bars are annual values, and red lines are smoothed using a nonparametric kernel-smoothing filter with a 3–year bandwidth. Units are in approximated standard deviations (see text). Panels a and b are summer discharge, c and d are annual balance, e and f are summer balance, g and h are winter balance. Panels with red labels indicate time series that exhibit statistically significant trends (1966–2011) as evaluated by the Mann-Kendall test with a = 0.1. Results of hypothesis tests are also shown in Table S4.
Supplemental Tables
Basin Characteristics:
Basin Area (km2) / Glacier Area (km2) / Initial coverage (%) / Area Change (%)1967 / 2011
Gulkana / 31.5 / 22.1 / 16.7 / 70 / -17
Wolverine / 24.6 / 17.0 / 16.1 / 69 / -4
Table S1. Basin characteristics of the USGS benchmark glaciers. Glacier areas are given for the initial 1967 geometry as well as the final 2011 state. The fractional basin glacierization is listed as well as the area change over the interval, expressed as a percent of the original.
Gulkana / WolverineMean / Change / Mean / Change
Ta / -3.2 / 0.59 / -0.4 / 0.37
Ts / 4.6 / 0.44 / 5.7 / 0.70
Tw / -7.4 / 0.59 / -3.9 / 0.32
TableS2. Seasonal and annual mean temperatures and cumulative changes (°C) at Gulkana and Wolverine glaciers (1966–2010). Summer is defined as May through September and winter the remainder of the year. Cumulative changes were estimated by multiplying the linearly determined rate of change by the length of the study interval.
Gulkana / WolverineBa / Bs / Bw / Qs / Ba / Bs / Bw / Qs
Gulkana / Ba / 0.86
(0.83) / 0.36
(0.26) / -0.65 / 0.53
(0.48)
Bs / -0.16
(-0.32) / -0.65 / 0.71
(0.66)
Bw / -0.15 / 0.02
(-)
Qs / -0.66 / -0.67 / -0.11 / 0.53
Wolverine / Ba / 0.53
(0.51) / 0.64
(0.59) / 0.85
(0.89) / -0.37
Bs / 0.71
(0.63) / 0.17
(-) / -0.56
Bw / 0.02
(-) / -0.13
Qs / 0.53 / -0.37 / -0.56 / -0.12
Table S3. Inter- and intra-glacier mass balance correlations (r) over the interval 1967–2011. Bold indicates the presence of a strong correlation, italics a marginal correlation. Recomputed values over the 1966–1995 interval, but estimated with the updated data set are given in parentheses, and where they differ markedly from Hodge et al. (1998) values (not shown) are shaded yellow.
References
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