2.1. Regional Climate
The North Cascades have had a temperate maritime climate with mild year-round temperatures, abundant winter precipitation, and dry summers. The two key climate variables for the glaciers have been the accumulation-season precipitation (November–April) and ablation-season temperature (May–September) [7
]. A warming of 0.8 °C in the mean annual temperature from 1900 to 2012 was observed from in the North Cascades [10
]. The warming was accelerated to +0.20 C per decade, for the 1980–2012 period. Every season, except spring, had experienced warming, particularly during the 1980–2012 period [10
Approximately 70% of the region’s precipitation occurred during the wet season (October–April) when the North Cascades were on the receiving end of the Pacific storm track [11
]. From late spring to early fall, high pressure to the west kept the Pacific Northwest comparatively dry. Occasionally in the winter, warm fronts elevated temperatures and freezing levels, which resulted in rainfall at the glacier elevations. Rain on snow events had increased in frequency, this led to an increase in the ratio of the winter precipitation falling as rain versus it falling as snow. Mote [11
] noted a decline in the snowpack storage efficiency in the Pacific Northwest, with the ratio between the total accumulation season precipitation and April 1 having retained snowpack SWE (snow water equivalent). Pelto [8
] used the Diablo Dam and concrete weather stations for the total accumulation season precipitation for November–March—the period of accumulating the snowpack at the six SNOTEL sites, with long term records in the North Cascades—in order to determine the snowpack storage efficiency (Fish Lake, Lyman Lake, Park Creek, Rainy Pass, Stampede Pass, and Stevens Pass). For these six USDA (United States Department of Agriculture) SNOTEL stations that were utilized in this study, the mean April 1 SWE declined by 29% from 1946 to 2014. During the same period, the winter precipitation had increased slightly. The change in SWE was comparable with the change in the snowpack storage efficiency, which indicated that this was the primary cause of the reduced April 1 SWE at the North Cascade SNOTEL stations. The freezing level was a key factor in determining the snowpack storage efficiency, and an online application the North American Freezing Level Tracker was developed by Abatzoglou [12
] that was utilized for the comparison of the freezing level during the winter season for Mount Baker.
The other key factor in glacier mass balance is the magnitude of ablation, which is primarily controlled by air temperature [13
]. That air temperature is the key is indicated by the success of degree day factors (DDF) for assessing glacier ablation on glaciers in this region [13
]. Nearly all of the ablation occurred during the May–September period, with the majority of the ablation having occurred from June–September. The most reliable weather station in the region was Diablo Dam, which was used for DDF derivation on the South Cascade Glacier [13
]. An examination of trends in the melt season temperature at this station indicated a nearly identical pattern for May–September and June–September, which indicated that either period could be used to identify the melt season climate change. We utilized June–September, in this study, as the melt season. Six of the ten warmest melt seasons during the 1946–2014 period occurred since 2003. The long term melt season warming was 0.7 °C at Diablo Dam. The average June–September temperature from 2003 to 2014 was 0.6 °C above the mean of that for the 1946–2002 period.
The Pacific Decadal Oscillation Index (PDO) has been the leading principal component of North Pacific monthly sea surface temperature variability, poleward of 20 N [15
]. During the positive PDO phase, warm weather was favored in the Pacific along the Northwest Coast and over the Pacific Northwest. During the negative phase, cool ocean water was found off the Northwest Coast and cooler temperatures were found across the Pacific Northwest [15
]. In the past century, “cool” PDO regimes prevailed from 1890 to 1924 and again from 1947 to 1976, while “warm” PDO regimes dominated from 1925 to 1946 and again from 1977 to 1998 [15
The El Niño/Southern Oscillation (ENSO) phenomenon was the most observable of the atmospheric circulation indices that led to year-to-year climate variability. ENSO positive events (El Nino) heralded abnormally warm sea surface temperatures (SST) over the eastern half of the equatorial Pacific. La Niña, was the opposite phenomenon, which was indicative of abnormally cold SST in the eastern half of the equatorial Pacific [16
]. ENSO was an east–west atmospheric pressure seesaw that directly affected the tropical weather around the globe and indirectly impacted a much larger area [16
]. The ENSO multivariate index (MEI-ENSO) that was used was based on the principal observed climate variables over the tropical Pacific. The index was a weighted average of the main ENSO features that were contained in the following six variables, namely: the sea-level pressure, east–west and north–south components of the surface wind, SST, surface air temperature, and total amount of cloudiness [16
]. Positive MEI-ENSO values were usually accompanied by a sustained warming of the central and eastern tropical Pacific Ocean. Negative values of the MEI-ENSO index were associated with stronger Pacific trade winds and warmer sea temperatures in the Western Pacific to the north of Australia [16
Bitz and Battisti [17
] noted the importance of PDO and MEI-ENSO to glaciers in the region and observed that PDO had a greater influence during the 1960–1995 period. Josberger et al. [8
] indicated that the importance of PDO had declined recently. They used three time periods, 1966–2004, 1966 to 1988, and 1989–2004, and found a significant change in the relationship between the PDO and the winter balances of the Wolverine Glacier, however less so for the South Cascade Glacier. Pelto [18
] utilized the indices during the accumulation season as a first order forecast for the annual glacier mass balance, and found that the impact was the strongest when PDO and ENSO were either both positive or both negative.
2.2. Surface Mass Balance
Annual surface mass balance (Ba) was the difference between the annual accumulation of snow/ice and the loss of snow/ice by ablation. It was typically measured on a water year basis, beginning approximately October 1 and ending September 30, in the Northern Hemisphere.
Since 1984, NCGCP monitored the Ba of 9–10 glaciers every year [18
]. Seven glaciers had a 32-year record, namely, the Columbia, Daniels, Ice Worm, Lower Curtis, Lynch, Rainbow, and Yawning glaciers. The Foss Glacier had a 30 year record (1984–2013) and was discontinued because of the glacier separating into several individual bodies. Sholes and Easton Glacier had a 26-year record (1990–2015). The glaciers represented a range of geographic characteristics and spanned the North Cascade Range (Table 1
and Figure 1
). The key geographic variables were the glacier orientation, elevation, accumulation sources and distance to the mountain range watershed, and climate divide. The Columbia Glacier and the Rainbow Glacier were part of the 42 reference glaciers of the WGMS data set.
NCGCP measured the conditions on a glacier near the time of minimal mass balance, at the end of the water year, using a fixed date method. NCGCP methods emphasized the surface mass balance measurements with a relatively high density of sites on each glacier (>100 sites km−2
), consistent measurement methods that were applied on fixed dates and at fixed measurement locations with consistent supervision [18
]. The use of a high measurement density and consistent methods generated errors, which resulted from an imperfectly representative measurement network that was largely consistent and correctable; the error range had been observed at ±0.10–0.15 ma−1
]. Fischer [22
] examined the mass balance errors and observed that the error had declined with increased density of measurements from 0.33 ma−1
, with a lower density to 0.10 ma−1
on a glacier that had a high density.
Any additional ablation that occurred after the last visit to a glacier was measured during the subsequent hydrologic year. The methods were reviewed in detail by Pelto [18
2.3. Accumulation Area Ratio
At regional scales and on specific glaciers there were two common proxies for assessing mass balance without detailed observations. They were the AAR and equilibrium line altitude (ELA), both of which could be derived from satellite imagery or photographs [23
]. The AAR was the ratio of a glacier that was in the accumulation zone. The ELA was the elevation at which the ablation equaled accumulation, on temperate alpine glaciers this was coincidental with the transient snow line (TSL) at the end of the melt season. The ELA was not typically an easily discernible line or elevation on the North Cascades glaciers, because of the variability of the snow accumulation from the impacts of wind and avalanche redistribution. The ELA could be calculated from the balance gradient, but in such cases it was not an independent variable. The AAR was a more accurately determined parameter and a better proxy in this case [20
]. The accumulation zone was a patchwork of the retained snowpack and ablation areas. Each patch of the retained snowpack was mapped and included in the AAR determination. The AAR in the North Cascades was determined from either photographs or direct surface mapping, by measuring the GPS along the TSL around each patch of the retained snowpack. The AAR–Ba method was proven to be reliable for the annual balance estimates [20
]. A comparison of the annual AAR and Ba observations in WGMS [26
] indicated correlation coefficients (Pearson’s r in all cases in the paper) ranging from 0.70 to 0.92 for fifteen glaciers, with at least 10 years of records. The World Glacier Monitoring Service (WGMS) had adopted the reporting of AAR with mass balance values [26
] and was plotting the relationship for each glacier. A combination of the AAR observations and Ba measurements from 1984 to 2015 on the North Cascade glaciers provided an opportunity to assess the relationship for each glacier and the variability between glaciers.
The AAR0 value was the AAR for a glacier with an equilibrium mass balance [28
]. Braithwaite and Muller [29
] noted that the AAR0 for an alpine glacier with an equilibrium balance had averaged 0.67. The mean AAR0 that was reported for 89 temperate alpine glaciers to the WGMS was 0.57, the AAR0 value was determined from a regression of the observed Ba and AAR [26