SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION doi: 10.1038/ngeo1122 Global sea-level contribution from the Patagonian Icefields since the Little Ice Age maximum Methods Error Assessment Supplementary Figures 1 and 2 Supplementary References Methods The outlines of the contemporary major outlet glaciers of the SPI and NPI were digitised as polygons at 1:50,000 scale on recent Landsat and Terra ASTER satellite images (2002 or more recent). LIA glacier extent was digitised for 270 major outlet glaciers of the two icefields (220 from the SPI and 50 from the NPI), based on the distribution of trimlines and terminal moraines formed at the time of this maximum advance. All mapping and analysis was performed in ESRI ARCMap. The inferred LIA glacier extents were checked against known LIA positions from our own previous dendrochronolgical and lichenometric dating studies 1, and published literature 2-5. In situations where the LIA extent was unknown or where multiple trimlines or moraines existed, we digitised the LIA limit along the trimline / moraine with the shortest horizontal distance from the glacier in order to produce a minimum estimate of ice-volume loss. The ASTER Global Digital Elevation Model (ASTER GDEM; http://www.gdem.aster.ersdac.or.jp/) was used to generate a digital elevation model (DEM) of the topography of the area around the NPI and SPI. Shuttle Radar Topographic Mission (SRTM; http://srtm.csi.cgiar.org/) data were used to fill gaps (e.g. errors created by cloud cover) in the ASTER GDEM. Ice-volume changes were then calculated by differencing the two shapefiles (the LIA glacier extent and the contemporary topography using the DEM). The method employed generates a surface from the LIA trimline polygon across individual valleys. We converted this surface from a TIN to a raster file and found the volumetric difference between this and the ASTER DEM dataset. Changes in volume were calculated for vertical columns with a cell size of the projected ASTER raster of 18 m. GIS Shapefiles (in ESRI ARCMap) of digitised contemporary glacier extent and mapped moraines and trimlines used to identify the former LIA glacier extent for the 270 outlet glaciers of the SPI and NPI can be supplied on request from N.F. Glasser (nfg@aber.ac.uk). Supplementary Figure 1 illustrates the conceptual framework for these calculations of ice-loss in the terminal zones of the glaciers since their LIA maximum. The horizontal extent of individual glaciers at their LIA maximum is clearly identifiable on satellite images in the form of moraines and trimlines (Supplementary Figure 1a). When draped on the ASTER GDEM, the shapefiles of glacier extent (based on mapped lateral moraines and trimlines) indicate that the majority of ice loss is at the former glacier snout, and that ice loss volumes decrease up-ice (Supplementary Figure 1b). The main assumption in our nature geoscience www.nature.com/naturegeoscience 1

calculations is that the volume lost in the terminal zones of these glaciers can therefore be approximated by a wedge of ice that is thickest at the former snout and thinnest some distance up-glacier (Supplementary Figure 1b). Example of method used: calculating ice-loss volume from the North and South Patagonian Icefields We used an eight-step process to determine the volumetric change between the Little Ice Age (LIA) and the present day. These steps are outlined below, using the North Patagonian Icefield (NPI) and South Patagonian Icefields as examples. The description of the method used is provided to aid reproduction of the results, and we acknowledge that there are a number of other methods and sequences that could be employed in other Geographical Information Systems (GIS) to arrive at estimates for ice-volume losses. 1. DELINEATE GLACIAL EXTENT DURING LIA USING TRIMLINES AND MORAINES The outlines of the contemporary major outlet glaciers of the SPI and NPI were digitised as polygons at 1:50,000 scale on recent Landsat and Terra ASTER satellite images (2002 or more recent). LIA glacier extent was digitised for 270 major outlet glaciers of the two icefields (220 from the SPI and 50 from the NPI), based on the distribution of trimlines and terminal moraines formed at the time of this maximum advance (Supplementary Figure 2). This produced a glacial extent LIA shapefile for use in the subsequent processing stages. 2. CONSTRUCT REGIONAL DEMs FOR THE NPI & SPI We downloaded the minimum number of ASTER tiles needed to cover the area of the Patagonian Icefields (NPI and SPI). ASTER data were provided in WGS-84 format. Data layers were imported to ESRI ARCMap. Tiles were displayed as regional mosaic for the whole of the SPI and NPI. It was then necessary to clip these to smaller regional extents (separate NPI and SPI subsets). This was performed using ARCMap s buffering tool, whereby a 100 m buffer around the LIA NPI and SPI extent was determined. Next, we used ARCMap s spatial analyst tool to clip the grid using these two buffered polygons according to the clearly defined method explained in (http://www.gps.caltech.edu/gislab/howto/docs/clipgrids.pdf). Finally, we transformed the new NPI and SPI clipped ASTER datasets to a projected coordinate system (WGS_1984_UTM_Zone_18S). The result of this stage was two (NPI and SPI) projected DEM layers for use in the subsequent stages. 3. DEFINING THE ELA

Because we are only concerned with ice-volume loss below the Equilibrium Line Altitude (ELA), it is necessary to define an ELA for the LIA. Since the LIA was about 0.6 o C cooler in the Southern Hemisphere and around 1 o C cooler in central and southern Chile than the late 20th century 6,7 this implies a reduction of the ELA of c. 200m based on a saturated adiabatic lapse rate of c. 5 o C per km and contemporary ELAs in the range 900 to 1300m in Patagonia 8-10. 4. CONTOURING THE DEM TO RETRIEVE GLACIAL ARMS A contour dataset was then created using the data from stage 2. This was contoured at 50 m intervals, beginning at sea level (0 m). The resulting contour dataset was used to subset the LIA glacial extent (from stage 1) using ARCMap s Xtools add-on. This was performed using the 900 m ELA to produce a series of glaciers which were used in the subsequent analysis. This was repeated for both the NPI and SPI datasets described in stage 2. Polygons above the 900 m ELA were discarded from subsequent analysis. The product of this stage was therefore a polygon layer showing the location and extent of glacial arms feeding off the NPI and SPI regions in the LIA. 5. DETERMINE LIA GLACIAL EXTENT ELEVATION USING DEM The data from stage 4 comprises a series of x,y attributed polygons which needed referencing to an elevation. This was performed using ARCMap s 3D Analyst toolbox, to attribute the z elevation position from the ASTER DEM (stage 2), to the x,y positions extracted from the glacial arm polygons (stage 4). 6. CREATING GLACIAL SURFACES USING TINs The next stage was to create a surface for each glacier, using the polygons from stage 5. Firstly an empty triangular irregular network (TIN) was created and the polygons from stage 5 were added using ARCMap s 3D Analyst Tool as a soft-clip feature. 7. GLACIAL SNOUT MODEL FOR SAN QUINTIN AND SAN RAFAEL GLACIERS For the San Quintin and San Rafael glaciers, which are largely unconstrained by valley walls, the snouts were modelled as having a 70 degree angle to the surface normal, with a glacial thickness of 70 m. This was performed using ARCMap s buffering functionality and was necessary because these two glaciers were unique in the way that they drain to lakes at sea level. The resultant data were added to the TIN from stage 6 using a hard-edge feature.

8. DETERMINING THE DIFFERENCE BETWEEN LIA GLACIAL SURFACE AND CURRENT GLACIER SURFACE Using ARCMap s 3D Analyst toolbar we converted the LIA TIN (from stage 6 +7) into a raster layer, using the options: elevation (Z) factor = 1, cell size = 20. Then, using the Cut/Fill tool, we calculated the volumetric change between the LIA TIN and the ASTER DEM. The attribute table of the resulting dataset was exported to a text file and opened in Microsoft Excel. We obtained the overall volume change by summing the volume column. Using this technique, we calculated the volume change between the LIA position and the contemporary position of the snouts of the 270 largest individual outlet glaciers of the SPI and NPI. We then summed the total volume loss for all individual glaciers from the LIA to present and converted this into a sea level equivalent. Ice-volume changes were converted into sea level contribution in two steps, assuming glacier ice has a density of 0.9 11 and an area of ocean of 362 million km 2 (www.worldatlas.com). The two steps are as follows: 1. Convert ice volume into water equivalent volume (weqv): weqv (km 3 ) = ice volume (km 3 ) x ice density 2. Convert weqv into sea level equivalent (sle): sle = weqv (km 3 ) / total area of ocean (km 2 ) Error Assessment It is important to acknowledge the possible errors in our ice-volume loss calculations and subsequent global sea level contribution estimate. Possible sources of errors are: 1. Errors in the geomorphological mapping of LIA extent. These are considered unlikely because the moraines and trimlines formed by glaciers at the LIA maximum are large features, picked out by clear and sharp vegetation boundaries (Figure 2 and Supplementary Figure 2). We have also been able to compare our geomorphological mapping of LIA extent with other, independent published studies 5. A possible source of error occurs in situations where the LIA extent is unknown or where multiple trimlines or moraines exist in front of the glacier. In these situations, we chose to draw the LIA limit at the trimline or moraine closest to the glacier terminus in order to produce a minimum estimate of icevolume loss.

2. The assumption that glacier downwasting occurs only below the ELA (i.e. below the equilibrium line altitude in the terminal zone). Our calculations include only ice-volume loss in the glacier terminal zones below the LIA ELA (900 m.a.s.l.). Recent ice-volume loss from Patagonian glaciers has been greatest near the glacier snouts 12, and is negligible at higher elevations above the ELA (see discussion in paper). We cannot be certain that this peripheral thinning is not balanced by ice thickening in the accumulation zones of the glaciers. This is an uncertainty inherent to all glacier-volume change estimates. 3. The method used to make volume calculations in the GIS. To make the calculations we have used representations of the contemporary and LIA glacier snouts draped in three-dimensions on a DEM of the surrounding topography (see above). The ASTER DEM has pre-production estimated accuracies of 20 meters at 95% confidence for vertical data and 30 meters at 95% confidence for horizontal data. SRTM was used to correct for small areas of cloud observed in the ASTER DEM for the SPI. However, since our method involves draping glacier extent shapefiles onto the same topographic DEM (and does not involve DEM-differencing of different glacier elevations) there are no cross-dem errors associated with this method. Thus our method is actually an improvement on previous icevolume calculation methods, which rely on glacier DEM-differencing with the attendant uncertainty errors in DEM accuracy. 4. The method used to represent the cross-valley surfaces of the reconstructed glaciers. Our volumetric calculations for the reconstructed glacier snouts are calculated using a method based on reconstruction of the LIA glacier snouts with an assumed convex cross-valley profile i.e. that the reconstructed ice surfaces rise from the lateral margins towards a maximum height at the glacier centre-line. This was achieved using the buffer command in ARCMap to create convex cross-valley profiles with the height at the glacier centre-line rising to a maximum value of 50 m above the height at the glacier margin. Sensitivity analysis of this method shows that the calculated ice-volume loss for individual glaciers varies ~20% depending on the exact shape of the glacier cross-valley profile chosen and the topographic context. The calculations are relatively insensitive to the shape of the cross-profile as long as a convex glacier profile is maintained. We therefore used this percentage (+/- 20%) to provide error estimates for our calculated ice-volume losses. 5. The method used to calculate potential sea level contribution from the calculated ice-volume changes. We have used the same method for this conversion as previous studies in Patagonia and globally. Our results are therefore directly comparable to previous estimates of the glacier contribution to sea level rise elsewhere.

Supplementary Figures Supplementary Figure 1. Conceptual framework illustrating the method used to make calculations of ice loss in the terminal zones of the Patagonian glaciers since their LIA maximum. Panel (a) shows how lateral moraines and trimlines on the valley side and terminal moraines (green dots) can be used to define the former LIA glacier extent (red line, indicating the polygon defined in the GIS). Panel (b) shows how these 2-d polygons (red lines) can be draped over a DEM to create a 3-d model in order to calculate ice-volume loss since the LIA (shaded blue areas). Supplementary Figure 2. Subscene from Landsat satellite image illustrating prominent LIA trimlines and moraines on Bravo Glacier and two adjacent glaciers on the Southern Patagonian Icefield. Strong contrasts in vegetation above and below the trimlines mean that we can confidently delimit former LIA glacier snout extent.

Supplementary References 1. Harrison, S. Winchester, V. & Glasser, N.F. The timing and nature of recession of outlet glaciers of Hielo Patagónico Norte, Chile, from their Neoglacial IV (Little Ice Age) maximum positions. Glob. Plan. Change 59, 67-78 (2007). 2. Koch, J. & Kilian, R. Little Ice Age glacier fluctuations, Gran Campo Nevado, southernmost Chile. The Holocene 15, 20-28 (2005). 3. Villalba, R. Tree-ring and glacial evidence for the Medieval Warm Epoch and the Little Ice Age in southern South America. Clim. Change 26, 183-197 (1994). 4. Aniya, M. Holocene glacial chronology in Patagonia: Tyndall and Upsala Glacier. Arct. Alp. Res. 27, 311-322 (1995). 5. Masiokas, M.H. et al. Glacier fluctuations in extratropical South America during the past 1000 years. Palaeogeog., Palaeoclim., Palaeoecol. 281, 242-268 (2009). 6. Mann, M.E. and Jones, P.D. Global surface temperatures over the past two millennia. Geophysical Research Letters 30, 1-4 (2003). 7. von Gunten, L. et al. A quantitative high-resolution summer temperature reconstruction based on sedimentary pigments from Laguna Aculeo, central Chile, back to AD 850. The Holocene 19, 873-881 (2009). 8. Aniya, M. Glacier inventory for the Northern Patagonian Icefield, Chile, and variations 1944/5 to 1985/86. Arct. Alp. Res. 18, 307-316 (1988). 9. Aniya, M. et al. The use of satellite and airborne imagery to inventory outlet glaciers of the Southern Patagonia Icefield, South America. Photogram. Eng. Rem. Sens. 62, 1361-1369 (1996). 10. Rivera, A. & Casassa, G. Volume changes on Glacier Pio XI, Patagonia: 1975-1995. Global Planet. Change 22, 233-244 (1999). 11. W.S.B. Paterson, The Physics of Glaciers 3 rd Edition (Butterworth- Heinemann, Oxford 1994). 12. Aniya, M. & Enomoto, H. Glacier variations and their causes in the Northern Patagonian Icefield, Chile, since 1944. Arct. Alp. Res. 18, 307-316 (1986).