## 2 Study Area  
Columbia Glacier (61.14\({}^{\circ}\)N, 147.10\({}^{\circ}\)W) is a large marine-terminating glacier located in Southcentral Alaska. The glacier extends from sea level to about 3050 m a.s.l. Due to its location in the Alaskan coastal range, the glacier experiences a maritime climate with mean annual precipitation of about 3080 mm yr\({}^{-1}\) as measured at Cannery Creek Weather Station (61.01\({}^{\circ}\)N, 147.51\({}^{\circ}\)W, 26 m a.s.l.) during 1980-2015. Daily mean air temperatures at sea level rarely fall below \(-20\)\({}^{\circ}\)C in winter, but rise well above freezing point during spring and summer months.  
In the following we outline some major facts about Columbia Glacier. The retreat and speedup of Columbia Glacier started in the 1980s and it is still ongoing. Although the glacier is grounded on its bed, part of its terminus might become afloat for brief periods. For instance, its terminus partially  
Figure 1: Overview map of Columbia Glacier showing front positions in 2011 and the catchments areas in 2016. Prior to 1980, the glacier extended to the north edge of Heather Island. The flux gate at the main branch is shown as AB through which mass flux was computed. The colored dots denote the subset areas of \(\sim\)25 \(\times\) 25 pixels (255 m \(\times\) 255 m on ground) at different elevations (ref. 06/18/2011 TDX DEM) used to compute averaged values of surface velocity and vertical change in phase center (PC). These subsets are abbreviated as M\({}_{100}\), M\({}_{150}\), M\({}_{225}\), M\({}_{350}\), M\({}_{650}\), M\({}_{1000}\), M\({}_{1200}\) and M\({}_{1600}\) for the main branch and W\({}_{50}\), W\({}_{150}\), W\({}_{200}\), W\({}_{300}\), W\({}_{400}\), W\({}_{500}\), W\({}_{800}\) for the west branch. The distances of these observed subsets at the main branch from its front position (06/18/2011) are 0.75 km, 3 km, 5.25 km, 10 km, 14 km, 18.2 km, 25 km, 33 km respectively. The distances of these observed subsets at the west branch from its front position (06/18/2011) are 0.65 km, 2 km, 4 km, 5.25 km, 7 km, 9.5 km and 12.5 km respectively. The meteorological variables were obtained from the weather station (GHCND:USC00501240), indicated as Cannery Creek.  
ungrounded in mid 2007 as it passed through an over-deepening region between Great Nunatak Peak and Kadin Peak (Figure 1) [15].  
In 2010, the glacier split into two branches--the main and the west branch. As previous studies have revealed [13; 16], the main branch comprises the main glacier flow and ice mass contribution. The catchment area of the main branch covers 752.9 km\({}^{2}\) while the west branch covers only 109.4 km\({}^{2}\) (May 2016). This reveals a loss in area of approximately 21.6% compared to \(\sim\)1100 km\({}^{2}\) in the early 1980s published by [PERSON] et al. (2001) [4]. From 1957 to 2007, the mean thickness changed from 281 to 143 m with maximum thinning rates of 10 m yr\({}^{-1}\)[13]. The modeled mean glacier-wide surface mass balance (SMB) was estimated to be \(-\)0.86 m w.e. yr\({}^{-1}\) during 1995\(-\)2007 [17] and approximately \(-\)2.25 m w.e. yr\({}^{-1}\) in 2010 [16]. These numbers show the large changes that occurred over the last 30 years at Columbia Glacier, but also indicate annual to multi-year differences of main glaciological observables (e.g., frontal change, mass balance, etc.).