Debris properties and mass-balance impacts on adjacent debris-covered glaciers, Mount Rainier, USA

Figures & data

Figure 1. Map of the study area on the north and east slopes of Mount Rainier, showing the approximate extent of continuous debris cover according to the methods outlined in the main text. Background image is the panchromatic band from a Landsat 8 OLI scene captured during the field study.

Figure 2. View across the debris-covered terminus of Emmons Glacier toward the summit of Mount Rainier (right) and Little Tahoma (left). Field measurements in 2014 took place just beyond the triangle-shaped boulder rising above the debris-covered ice in the middle ground.

Table 1. Debris properties and observations at ablation stake sites, Emmons Glacier, August 2014.

Stake	$H$ (cm)	$\dot{m}$ (mm/d)	$\overline{T_s}$ (°C)	Site description
A1	21.5	26.6	19.0	Small boulders, large cobbles, gravel and sand
A2	11.5	26.9	16.4	Small cobbles and pebbles; moist gravel and sand at depth
A3	31	18.1	18.3	Large cobbles, gravel and sand
A4	44	19.4	17.9	Small boulders, large cobbles, gravel and sand
B1	12	30.5	13.2	Moist sand with pebbles and small cobbles
B2	24	26	17.4	Boulders and cobbles; uneven ice surface
B3	20	25.5	18.3	Large cobbles, moist sand and gravel
B4	22.5	13	16.3	Large cobbles and moist sand and gravel
C1	9	32.3	11.7	Small boulders, gravel and sand; site is partly shaded
C2	3	38.7	12.3	Boulders, small cobbles, gravel and sand
C3	10	27.7	14.0	Moist sand and gravel
C4	5.5	32.1	12.8	Large cobbles, moist gravel and sand; site shaded by boulder
D1	31	20.3	20.3	Small boulders and large cobbles, no matrix
D2	18	7.1	14.3	Small cobbles and moist gravel
D3	26.5	27.8	18.5	Small boulders, gravel and moist sand; fully saturated
D4	10	32.3	13.8	Cobbles and moist gravel

Figure 3. Data from the temporary meteorological station and wireless temperature sensors installed on Emmons Glacier during early August 2014. (a) Air temperature 2 m above the glacier surface (left axis) and incoming shortwave radiation (right axis). (b) Debris temperature measured by thermistors (points) and Hobo pendant loggers (lines) at uniform depth intervals throughout a 0.5-m debris layer.

Table 2. Values of variables and constants used in simplified energy balance model (Equation 2) and satellite retrieval of thermal resistance (Equation 6).

Variable, units	Value
$Q_{s0}$, W m^−2	231 (Equation 2); 470 (Equation 6)
$T_a$, K	288 (Equation 2)
$\alpha$, dimensionless	0.3
$F$, dimensionless	0.71
$\sigma$, W m^−2 K^−4	5.39 $\times$ 10^−8
${\epsilon }_a$, dimensionless	0.7 (Hock 2005)
${\epsilon }_r$, dimensionless	0.95
$c_1$, dimensionless	0.384
$c_2$, °C	11.5

Figure 4. Ablation rate, averaged over 8 days of measurement, plotted as a function of debris thickness. Dots are field measurements, while the line represents a numerical solution of the energy balance model of Nicholson and Benn (2006) driven with averaged in situ measurements of solar radiation and estimated thermal conductivity from the Emmons Glacier field site over the measurement interval. Horizontal error bars represent uncertainty in debris thickness determination, estimated as 0.25 times the largest particle diameter adjacent to the stake. Vertical error bars represent one standard deviation of the daily variation in melt rate at each stake.

Table 3. Size and estimated debris extent of study glaciers from remote-sensing analysis.

Glacier	Total area (m^2)	Debris area (m^2)	Debris volume (m^3)	Percent covered	Mean debris H (cm)
Carbon	7,450,732	3,167,698	182,289	43%	5.6
Emmons	11,230,885	1,921,975	177,847	17%	9.0
Winthrop	8,763,390	2,218,931	191,272	25%	8.2

Figure 5. Estimated thermal resistance [°C m² W⁻¹] of the Carbon, Winthrop, and Emmons (from upper left to lower right) debris-covered termini, overlain on a hillshade map. The color scale remains fixed over all three termini, and warmer colors indicate higher thermal resistance.

Figure 6. Normalized discrete (a–c) and cumulative (d) frequency distributions of thermal resistance on each debris-covered glacier terminus. Equivalent debris thickness, according to the best fit function given in the main text, is shown as an upper (nonlinear) horizontal axis for reference. The colors in the bar charts (a–c) match the color of the corresponding cumulative frequency curve (d).

Figure 7. Modeled relationship between thermal resistance and daily ablation rate for average weather conditions observed on Emmons Glacier during 1–10 August 2014, including the apparent increase in effective thermal conductivity on thermal resistance.

Hock, R. 2005. Glacier melt: A review of processes and their modelling. Progress in Physical Geography 29:362–91. doi:10.1191/0309133305pp453ra.

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Nicholson, L. I., and D. I. Benn. 2006. Calculating ice melt beneath a debris layer using meteorological data. Journal of Glaciology 52:463–70. doi:10.3189/172756506781828584.

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