Determining annual cryosphere storage contributions to streamflow using historical hydrometric records

Author: J. Brahney, B. Menounos, X. Wei, P.J. Curtis

Here, we demonstrate the use of a statistical method to isolate the magnitude and change of late summer cryosphere flows that can be used in any region where suitable hydrologic records exist. We apply this method to watersheds with glacierized streams and compare our results to those acquired through alternative methods. Our method identifies changes in the late summer cryosphere contribution to streamflow, which likely includes flows from both glaciers and perennial snowfields. The resulting analyses yields time‐series that provide first‐order estimates of increases or decreases of cryosphere melt contributions to streamflow.

Snow pillow site elevations ranged from 1,595 to 2,090 m above sea
level. We found no significant trends in the snowfall accumulation data
through time at any elevation. A caveat is that existing snow stations
are all at or below treeline, and a significant proportion of the basin
exists above this datum. As such, trends above treeline are difficult
to determine. However, modeling evidence suggests that the higher
elevation snowpack is increasing with respect to lower elevations
(Schnorbus, Bennett, Werner, & Berland, 2011).
The individual CSC to streamflow is correlated to the percent glacier
cover for each catchment with an r2 of 0.86 (p < 0.001). A weaker yet significant relationship also existed between the glacierized area within each catchment (km2), and the mean percent contribution to streamflow r2 of 0.35, p < 0.01. Regressing latitude, maximum elevation, and percent glacier cover against cumulative CSC for a common period (1975–2012) explained 92% of the variance (p < 0.001). Independently, cumulative CSC was correlated to latitude by an r2 of 0.57, p < 0.001, to max elevation with an r2 of 0.23, p = 0.31, and as above to percent glacier area in the catchment. Nineteen of 20 glacierized streams showed declines in CSC through their period of record. On the basis of Spearman rank correlation analyses, eight were significant at p < 0.1 (Table 1); 16 showed significant declines of CSC for August streamflow at p < 0.1 (Table 1). Annual declines through the full period of record ranged from 0 for Canoe Creek to −61% for the Lardeau River. August CSC declines ranged from −1% for Beaver Creek to −62% for Blue River. The largest percent declines were calculated for the streams within median latitudes and with median percent glacier cover (Table 1 and Figure 5). Given the potential influence of varied start/end periods in trend detection, we also evaluate the percent CSC changes through the 1975–2012 period, a time period common to most streams of our study (Figure 5). Time series graphs for all catchment CSC to streamflow are available in Figure S1. We estimated the potential inflation in the CSC to streamflow on the basis of the determined snow water equivalent lapse rate. The inflation factors are presented in Table 1 for each glacierized catchment. The lapse rate was approximately of 65 mm per 100 m, though the regression was not well constrained and the error is approximately ±71 mm per 100 m. The HS‐DMC method compares favorably (Figure 6) to the magnitude and diurnal variability of glacier runoff presented by Hirose and Marshall (2013).TheHS‐DMCwascorrelated to themodeleddata with significant (p < 0.001) Pearson correlation values of 0.84, 0.90, and 0.83, respectively, for hydrologic years 2009, 2010, and 2011. The annual contributions of late summer cryospheric runoff to streamflow for the years 2009, 2010, and 2011 using the HS‐DMS method are 18%, 10.1%, and 8.3% whereas the distributed model yielded 14.4%, 10.6%, and 5.8%. Our HS‐DMC method applied to August flows show moderate‐tostrong correlation (0.33 < r < 0.95, average = 0.67) to the interannual late‐summer flows produced by the Stahl and Moore (2006) method (Figure 7). We found no significant differences between the magnitudes of the z‐scored trends between the two methods. We compared our results to the those from Schiefer et al. (2007) by regressing the glacier wastage volume estimates (m3) against the product of our CSC (mm) and glacier area (km2) multiplied by 1,000 to scale the data to cubic meters. The two datasets were correlated with an r2 of 0.71; however, our estimated volumes are on average 3.7× greater than the estimates by Schiefer et al. (2007). The reason for the discrepancy are potentially due to (a) errors in the Terrain Resource Information Management (TRIM) data used to estimate changes in glacier area in the Schiefer et al. (2007) estimates and (b) a combination of melt from the perennial snow pack and inflation due to strong precipitation lapse rates.

Snow pillow site elevations ranged from 1,595 to 2,090 m above sea
level. We found no significant trends in the snowfall accumulation data
through time at any elevation. A caveat is that existing snow stations
are all at or below treeline, and a significant proportion of the basin
exists above this datum. As such, trends above treeline are difficult
to determine. However, modeling evidence suggests that the higher
elevation snowpack is increasing with respect to lower elevations
(Schnorbus, Bennett, Werner, & Berland, 2011).
The individual CSC to streamflow is correlated to the percent glacier
cover for each catchment with an r2 of 0.86 (p < 0.001). A weaker yet significant relationship also existed between the glacierized area within each catchment (km2), and the mean percent contribution to streamflow r2 of 0.35, p < 0.01. Regressing latitude, maximum elevation, and percent glacier cover against cumulative CSC for a common period (1975–2012) explained 92% of the variance (p < 0.001). Independently, cumulative CSC was correlated to latitude by an r2 of 0.57, p < 0.001, to max elevation with an r2 of 0.23, p = 0.31, and as above to percent glacier area in the catchment. Nineteen of 20 glacierized streams showed declines in CSC through their period of record. On the basis of Spearman rank correlation analyses, eight were significant at p < 0.1 (Table 1); 16 showed significant declines of CSC for August streamflow at p < 0.1 (Table 1). Annual declines through the full period of record ranged from 0 for Canoe Creek to −61% for the Lardeau River. August CSC declines ranged from −1% for Beaver Creek to −62% for Blue River. The largest percent declines were calculated for the streams within median latitudes and with median percent glacier cover (Table 1 and Figure 5). Given the potential influence of varied start/end periods in trend detection, we also evaluate the percent CSC changes through the 1975–2012 period, a time period common to most streams of our study (Figure 5). Time series graphs for all catchment CSC to streamflow are available in Figure S1. We estimated the potential inflation in the CSC to streamflow on the basis of the determined snow water equivalent lapse rate. The inflation factors are presented in Table 1 for each glacierized catchment. The lapse rate was approximately of 65 mm per 100 m, though the regression was not well constrained and the error is approximately ±71 mm per 100 m. The HS‐DMC method compares favorably (Figure 6) to the magnitude and diurnal variability of glacier runoff presented by Hirose and Marshall (2013).TheHS‐DMCwascorrelated to themodeleddata with significant (p < 0.001) Pearson correlation values of 0.84, 0.90, and 0.83, respectively, for hydrologic years 2009, 2010, and 2011. The annual contributions of late summer cryospheric runoff to streamflow for the years 2009, 2010, and 2011 using the HS‐DMS method are 18%, 10.1%, and 8.3% whereas the distributed model yielded 14.4%, 10.6%, and 5.8%. Our HS‐DMC method applied to August flows show moderate‐tostrong correlation (0.33 < r < 0.95, average = 0.67) to the interannual late‐summer flows produced by the Stahl and Moore (2006) method (Figure 7). We found no significant differences between the magnitudes of the z‐scored trends between the two methods. We compared our results to the those from Schiefer et al. (2007) by regressing the glacier wastage volume estimates (m3) against the product of our CSC (mm) and glacier area (km2) multiplied by 1,000 to scale the data to cubic meters. The two datasets were correlated with an r2 of 0.71; however, our estimated volumes are on average 3.7× greater than the estimates by Schiefer et al. (2007). The reason for the discrepancy are potentially due to (a) errors in the Terrain Resource Information Management (TRIM) data used to estimate changes in glacier area in the Schiefer et al. (2007) estimates and (b) a combination of melt from the perennial snow pack and inflation due to strong precipitation lapse rates.