## 3 Materials and Methods
### Geodetic Mass Balance and Volume Changes  
The geodetic mass balance method provides important information on the current status and evolution of many glaciers worldwide [7]. We obtained the geodetic mass balance derived by DEMs differencing for four periods. Table 2 shows the complete dataset of topographic information, comprising topographic maps, Shuttle Radar Topography Mission (SRTM) and LiDAR products. The study site is covered by historical topographic maps at a 1:50,000 scale, published by the Geographic Military Institute of Chile (IGM) in 1975. The topographic mapping was undertaken using the same aerial photographs as the delineated area (HYCON), with levelling based on a terrestrial theodolite survey to provide vertical and horizontal reference. Several point measurements were used as ground control by the IGM to obtain the maps. The 1975 maps were originally produced in PSAD56 datum, UTM projection 19S, and were adjusted to WGS84 Datum. A digital elevation model (DEM) based on the 50 m altitude contour lines from the digitalized IGM map was created and resampled, using the kriging interpolation method (e.g., [46]). In addition, we used SRTM C-band data in this study. The SRTM dataset was comprised of interferometric synthetic aperture radar (InSAR) data that were acquired simultaneously in the C-band and X-band frequencies between the 11 th and 22 nd of February 2000 [47]. The X-band system operated with a swath width of \(\sim\)50 km (C-band \(\sim\)225 km), which does not allow for global data coverage [48]. A 30 m resolution DEM derived from TanDEM-X data was generated in this study. TerraSAR-X and TanDEM-X (TDX) is an ongoing (bi-static) satellite constellation launched and operated jointly by the German Aerospace Center (DLR) and EADS Astrium. We followed the TanDEM-X processing scheme as described in [49; 50] using GAMMA software and own code. The SRTM-C DEM was used as a reference DEM for the InSAR processing. The topographic phase was simulated from the SRTM-C DEM using TanDEM-X interferometric parameter to obtain the double difference interferogram. Noise in the interferogram was suppressed using a Goldstein filter [51]. Areas degraded due to shadow and water bodies (coherence < 0.2) were masked out before unwrapping the differential phase. We unwrapped the phase using a Minimum Cost Flow (MCF) algorithm [52]. It was ensured that no phase jumps (or residual phase) remained before converting the unwrapped phase into differential height; the SRTM-C reference DEM was then re-added to the differential heights. Finally, to mosaic, we applied a sequence of a concatenation of all raw DEM scenes using a stable ground mask derived from optical data and correct all vertical bias applying a polynomial fitting [53]. Additionally, two airborne laser altimetry (LiDAR) campaigns in April 2009 and February 2015 have been sponsored by DGA. The LiDAR points have a vertical accuracy of \(\pm\) 0.3m, calculated from the simultaneous comparison with ground GNSS measurements performed on- and off-gl glacier areas [41; 54]. We generated two DEMs from the LiDAR point cloud data using a Triangulated Irregular Network (TIN) interpolation method in ArcGIS 10.1, achieving 1 m of spatial resolution for each year. In order to keep consistency between the datasets, elevation values were converted to a common vertical reference system in orthometric heights (EGM96 geoid). In order to obtain accurate and reliable values among potentially misaligned DEMs, we extensively reviewed the three-dimensional (3-D) orientation of all DEMs used in this study. Each DEM was horizontally and vertically co-registered following the universal approach by [PERSON] and [PERSON] [55].