Lettershttps://doi.org/10.1038/s41558-018-0375-7

1Institut für Geographie, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany. 2Centro de Investigación Gaia Antártica, Universidad de Magallanes, Punta Arenas, Chile. 3Dirección General de Aguas, Ministerio de Obras Públicas, Santiago, Chile. 4Instituto de Investigaciones Geológicas y del Medio Ambiente, Universidad Mayor de San Andrés, La Paz, Bolivia. 5Glaciarium, Centro de Interpretación de Glaciares, El Calafate, Argentina. *e-mail: matthias.h.braun@fau.de

Excluding the large ice sheets of Greenland and Antarctica, glaciers in South America are large contributors to sea-level rise1. Their rates of mass loss, however, are poorly known. Here, using repeat bi-static synthetic aperture radar inter-ferometry over the years 2000 to 2011/2015, we compute continent-wide, glacier-specific elevation and mass changes for 85% of the glacierized area of South America. Mass loss rate is calculated to be 19.43 ± 0.60 Gt a−1 from elevation changes above ground, sea or lake level, with an additional 3.06 ± 1.24 Gt a−1 from subaqueous ice mass loss not con-tributing to sea-level rise. The largest contributions come from the Patagonian icefields, where 83% mass loss occurs, largely from dynamic adjustments of large glaciers. These changes contribute 0.054 ± 0.002 mm a−1 to sea-level rise. In comparison with previous studies2, tropical and out-tropical glaciers — as well as those in Tierra del Fuego — show consid-erably less ice loss. These results provide basic information to calibrate and validate glacier-climate models and also for decision-makers in water resource management3.

Recent estimates of glacier contributions to sea-level rise and their future evolution under different climate scenarios highlight the need for improved regional mass balance assessments for calibration and validation of glacier models1,3,4. They show that Patagonian glaciers are amongst the largest contributors in terms of mass loss1. In the Andes and many coastal plains, glacier melt water is a major source for irrigation, hydro power and drinking water supply, in particular during the dry season and drought periods, as well as for wetland ecology5,6.

Previous estimates of glacier mass changes throughout South America were based on either the glaciological method using in situ observations or gravimetric measurements from satellites with respective large uncertainties2,7–9. Both approaches have limita-tions in South America: the classic glaciological method based on stake measurements is restricted to a limited number of accessible glaciers and requires substantial extrapolation for regional assess-ments. The spaceborne gravimetry mission Gravity Recovery and Climate Experiment (GRACE) measures mass change, indepen-dently of its source, over large regions. It is hampered by other sig-nal components that range in the same magnitude. The signal from the glacier areas in the tropics is very small and thus difficult to assess precisely by GRACE. It also does not resolve individual gla-ciers10. Laser altimetry requires interpolation between tracks and is often limited by clouds. Radar altimeters with novel interferomet-ric swath mode processing are only suited for the larger icefields11.

Only photogrammetric time series techniques and radar interfer-ometry are able to resolve individual glaciers, cope with frequent cloud cover and efficiently cover large regions.

In this study, we provide regionally aggregated values of eleva-tion and mass changes for all glacier areas in South America based on glacier-specific measurements. Our observations span from the inner tropics in Venezuela to the sub-Antarctic climatic zone in Tierra del Fuego. We use digital elevation models (DEM) from two bi-static radar interferometry missions. The high-resolution data (30 m) cover 85% of the glacierized area in South America, provid-ing new insights into the regional patterns of glacier changes.

We apply differential synthetic aperture radar (SAR) interferom-etry using data from the Shuttle Radar Topography Mission (SRTM) from 11 to 22 February 200012 and the German TerraSAR-X-Add-on for Digital Elevation Measurements mission (TanDEM-X)13 com-prising more than 500 data frames acquired between 2011 and 2015 (Fig. 1). Previous successful processing approaches were further developed and automated14 (Methods). A strength of this method is that radar signals are not influenced by pervasive cloud cover, which is particularly attractive considering the weather patterns in Fuego-Patagonia or in the tropical Andes. Two density scenarios for volume-to-mass conversion are applied (850 and 900 kg m−3). Our error assessment includes uncertainties resulting from co-registration, glacier outlines, radar penetration, volume-to-mass conversions and spatial interpolation within measurement voids. We compare our volume and mass change estimates against a comprehensive collection of published values at regional and gla-cier-specific levels. Our glacier-specific measurements have been aggregated over 11 regions (regions 01–11), defined according to prevailing climatic conditions and based on previous regional sub-divisions (Fig. 1, Methods).

Our results show a strong latitudinal variability of the surface elevation change rates (Fig. 1). The largest thickness changes are observed in Patagonia South (region 09) followed by Patagonia North (region 08), with the large Northern and Southern Patagonian icefields (NPI and SPI; subregions 081 and 091) contributing the overall highest values (Table 1). The ice masses south of SPI (regions 10 and 11) reveal comparable change rates to glaciers outside the two Patagonian icefields (subregions 082 and 092). Those rates are even smaller than the observed thickness changes in the wet outer tropics of Peru-Bolivia (region 03). The inner tropics show volume loss in the observation period with values slightly smaller than in the southern, wet outer tropics (region 03). The balanced conditions in the northern wet outer tropics in Peru (region 02) are remarkable.

Constraining glacier elevation and mass changes in South AmericaMatthias H. Braun   1*, Philipp Malz   1, Christian Sommer1, David Farías-Barahona1, Tobias Sauter1, Gino Casassa2,3, Alvaro Soruco4, Pedro Skvarca5 and Thorsten C. Seehaus   1

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Values for those regions are subject to higher interpolation errors, mainly due to voids in the SRTM reference DEM. Hence, for both wet outer tropical regions (regions 02 and 03), the lowest percent-ages of glacierized area were measured (Table 1). Glaciers in the Desert Andes (region 05) were mapped to within 96% and show a slight positive elevation change rate, but with large uncertainties. For the Central Andes (region 06) and the Lake District (region 07), we reveal, on average, only small changes in elevation.

The altitudinal distribution of the surface elevation changes for all regions is shown in Fig. 2 in detail and summarized in supple-mentary Fig. 1. The elevation bins where a change from negative to positive conditions occurs (equilibrium line altitude, ELA) are relevant for glacier mass balance considerations. In the majority of regions, glaciers show balanced conditions and even elevation increase at higher elevations, while for low elevations the pattern is spatially more variable. The high altitudinal variability for the inner tropics (region 01) is caused by the recession of some small ice

masses in northern Ecuador and Colombia within the observation period. For the wet outer tropics of Peru and Peru-Bolivia (regions 02 and 03), a mass loss at lower elevations and a mass gain in the upper reaches are observed. The mean equilibrium line altitude is located around 5600 m and 5800 m, respectively. Marked positive elevation changes are also seen in the Central Andes (region 06) at elevations higher than 5000 m a.s.l., while thickness loss is observed for elevations below this. Glaciers in the Lake District (region 07) show approximately balanced conditions over the entire elevation range apart from the lowest elevations. For Patagonia (regions 08 and 09), we observe an overall volume loss at lower elevations, and only for the large icefields (subregions 081 and 091) do we measure positive elevation gains in the highest reaches. It has to be noted that those areas with positive balance cover only a very small frac-tion of the entire glacierized area (Fig. 2). The small ice masses of Gran Campo Nevado and Isla Riesco (region 10) are all at elevations below the ELA. In Tierra del Fuego (region 11) we observe balanced

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Fig. 1 | Glacierized areas, TanDeM-X coverage and elevation change rates in different regions of South America. a. Red polygons indicate the TanDEM-X scenes and black lines the divisions between glacier regions. b. The inner circles display the mean elevation change rate in a region, while the outer circle depicts the glacierized area as well as the area percentage of different glacier types in a region (tide water, lake calving and land terminating). The region subdivisions as well as the absolute elevation change rates are given. IT: Inner tropics; OT: Outer tropics; DA: Desert Andes; CA: Central Andes; LD: Lake District; PN: Patagonia North; PS: Patagonia South; GCN-IR: Gran Campo Nevado and Isla Riesco; TF: Tierra del Fuego.

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to positive elevation change rates above approximately 900 m a.s.l., while in areas below this, mass loss occurs. The regional balance is negative. This is consistent with the known situation that some tide-water glaciers in Cordillera Darwin of Tierra del Fuego are advanc-ing while the majority of glaciers exhibit retreat.

We compute a total mass loss rate of 19.43 Gt a−1 ± 0.60 Gt a−1 for glaciers in South America from surface elevation changes in the period 2000 to 2011–15 using an ice density scenario of 900 kg m−3. The main contributors are both Patagonian icefields (subregions 081&091) (Table 1). Together they constitute about 83% of the ice mass loss occurring in South America. This number results from the large glacierized area (56% of the studied area) combined with the large specific mass loss rates. The ice masses in Tierra del Fuego (region 11) contribute approximately 5% to the overall mass loss. The total glacier mass change of the tropical Andes (inner and outer tropics, regions 01–04) amounts to 3%. The main contributors for the tropical Andes are the glaciers of the southern wet outer tropics in Peru-Bolivia (region 03).

These estimates are lower bounds since they do not contain contributions below lake or sea level. In Fuego-Patagonia (regions 08–11), the retreating sections of glaciers are often located in over-deepened valleys below sea level in near-buoyant conditions15. Subaqueous melt and calved-off ice additionally contribute to mass loss, which needs to be combined with mass losses from subaerial ice elevation changes measured by satellite interferometry. Those amounts can be substantial, since the submerged valleys are known to be several hundreds of metres deep16,17. We estimate those losses to be about 3.06 ± 1.24 Gt a−1 using the rate of glacier area retreat18 and an estimated thickness of 250 m (Methods, supplementary Tables 2 and 3). These mass losses below sea or lake level do not contribute to sea-level rise.

We compare our results with previous regional and local gla-cier elevation and mass change estimates for different regions (supplementary Figs. 2–8). A continent-wide assessment using gra-vimetry2 reported − 29 ± 10 Gt a−1 for the southern Andes in the period 2003–2009 and − 4 ± 1 Gt a−1 for the low latitudes, based on

Table 1 | elevation, volume and mass change rates as well as mass balance rates for the different subregions derived from the elevation change measurements

iD region name

Median date of TanDeM-X data and observation period

Glacier area (km²)

Area measured (%)

Mean elevation change rate (m a−1)

Volume change rate (km³ a−1)

Mass change rate (Gt a−1)a

Mass change rate (Gt a−1) b

Mass balance rate (mwe a−1)a

Mass balance rate (m w.e. a−1)b

01 Inner tropics 12 August 2013 (2000–2012/2014)

187 74.9 − 0.20 ±  0.10 − 0.04 ±  0.02 − 0.03 ±  0.02 − 0.03 ±  0.02 − 0.17 ±  0.11 − 0.18 ±  0.12

02 Outer tropics (Peru)

17 February 2012 (2000–2012)

698 42.4 − 0.01 ±  0.13 − 0.01 ±  0.11 − 0.01 ±  0.10 − 0.01 ±  0.10 − 0.01 ±  0.14 − 0.01 ±  0.15

03 Outer tropics (Peru-Bolivia)

16 March 2013 (2000–2013)

1,280 62.2 − 0.40 ±  0.08 − 0.52 ±  0.12 − 0.44 ±  0.11 − 0.47 ±  0.11 − 0.34 ±  0.08 − 0.36 ±  0.09

04 Outer tropics (Peru-Bolivia)

23 March 2013 (2000–2013/2014)

164 91.3 − 0.24 ±  0.09 − 0.04 ±  0.01 − 0.03 ±  0.01 − 0.04 ±  0.01 − 0.20 ±  0.08 − 0.22 ±  0.08

05 Desert Andes

13 March 2012 (2000–2012/2014)

409 96.0 0.03 ±  0.17 0.01 ±  0.07 0.01 ±  0.06 0.01 ±  0.07 0.02 ±  0.15 0.02 ±  0.16

06 Central Andes

22 February 2013 (2000–2011/2014)

1,660 86.8 − 0.10 ±  0.10 − 0.17 ±  0.21 − 0.14 ±  0.19 − 0.15 ±  0.20 − 0.09 ±  0.11 − 0.09 ±  0.12

07 Lake District 12 February 2013 (2000–2011/2014)

478 95.4 − 0.05 ±  0.08 − 0.03 ±  0.05 − 0.02 ±  0.04 − 0.02 ±  0.05 − 0.05 ±  0.09 − 0.05 ±  0.10

08 Patagonia Northc

23 February 2014 (2000–2012/2015)

6,977 79.2 − 0.76 ±  0.04 − 5.29 ±  0.39 − 4.50 ±  0.46 − 4.77 ±  0.48 − 0.65 ±  0.07 − 0.68 ±  0.07

081 NPIc 23 February 2014 (2000–2012/2015)

4,653 85.1 − 1.00 ±  0.01 − 4.65 ±  0.17 − 3.96 ±  0.32 − 4.19 ±  0.32 − 0.85 ±  0.07 − 0.90 ±  0.07

082 Outside NPIc 6 March 2013 (2000–2012/2015)

2,324 67.3 − 0.33 ±  0.11 − 0.77 ±  0.35 − 0.66 ±  0.31 − 0.70 ±  0.32 − 0.28 ±  0.13 − 0.30 ±  0.14

09 Patagonia Southc

3 March 2012 (2000–2012/2014)

15,101 92.1 − 0.93 ±  0.01 − 14.04 ±  0.56 − 11.93 ±  0.97 − 12.64 ±  0.98 − 0.79 ±  0.06 − 0.84 ±  0.07

091 SPIc 3 March 2012 (2000–2012/2014)

13,231 93.7 − 1.01 ±  0.00 − 13.35 ±  0.79 − 11.35 ±  1.05 − 12.02 ±  1.07 − 0.86 ±  0.08 − 0.91 ±  0.08

092 Outside SPIc 3 March 2012 (2000–2012/2014)

1,869 80.5 − 0.32 ±  0.09 − 0.60 ±  0.18 − 0.51 ±  0.16 − 0.54 ±  0.17 − 0.28 ±  0.09 − 0.29 ±  0.09

10 Gran Campo Nevado and Isla Riescoc

14 February 2013 (2000–2012/2014)

1,254 88.6 − 0.27 ±  0.05 − 0.34 ±  0.06 − 0.29 ±  0.06 − 0.31 ±  0.06 − 0.23 ±  0.05 − 0.25 ±  0.05

11 Tierra del Fuegoc

2 March 2013 (2000–2011/2014)

3,545 81.8 − 0.32 ±  0.02 − 1.13 ±  0.10 − 0.96 ±  0.11 − 1.02 ±  0.11 − 0.27 ±  0.03 − 0.29 ±  0.03

Sum/area weighted average

31,751 85.4 − 0.68 ±  0.04 − 21.60 ±  0.38 − 18.35 ±  0.59 − 19.43 ±  0.60 − 0.58 ±  0.07 − 0.61 ±  0.07

acomputed with 850 ±  60 kg m−3 density scenario, bcomputed with 900 ±  60 kg m−3 density scenario. Mass balance rate unit (m we a−1): meter water equivalent per year. cSubaqueous ice loss (Supplementary Table 2) is not included in those values.

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glaciological in situ measurements and upscaling. An earlier study7 revealed − 6 ± 12 Gt a−1 for South America excluding Patagonia and − 23 ± 9 Gt a−1 for Fuego-Patagonia using GRACE data over the

period 2003–2010. Our values are smaller for the tropics; however, the error bars of the previous studies were large and hence overlap with ours. These differences may come from working with small ice

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Fig. 2 | Glacier hypsometry and elevation change distribution versus altitude per region. Glacier hypsometry of the entire glacier area (grey bars) and measured area (red bars). The measured elevation changes (blue dots) and the respective normalized median absolute deviation per elevation bin (blue error bars) are plotted for each region.

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masses in large mountainous regions with GRACE and hence the difficulties in detecting a very small signal7. The values from a local geodetic mass balance study at Antisana 15α in Ecuador19 measured similar rates to ours (region 01) in a comparable observation period (supplementary Fig. 2). Different measurement techniques in the Cordillera Real (supplementary Fig. 3) revealed much higher mass change rates than ours (region 03). This might be related to upscal-ing from a few reference glaciers in previous studies6 or to the fairly low coverage of the region by our measurements.

The few glaciological observations available from the Central Andes (region 06) of Argentina and Chile (supplementary Fig. 4) show several strongly positive mass balance years in the beginning of the millennium and subsequently strongly negative conditions until the end of our observation period. Our measurements reflect the multi-annual average of this variability. In the Lake District (region 07) (supplementary Fig. 5), our regionally averaged value indicates almost balanced conditions, while values reported by other studies show a mixed pattern. This highlights the importance of regional assessments, since extrapolations based on single gla-ciers might be biased. On the other hand, such detailed local studies are relevant for water resource management of a specific catchment.

For Patagonia (regions 08 and 09) and in particular the Patagonian icefields (subregions 081 and 091), our elevation and mass change rates agree well with most other geodetic studies in the same observation period (supplementary Figs. 6–7). Some of the slightly higher mass change rates14,20–23 can be attributed to their different methodology and time frames as well as the assumption of 2 m Shuttle Radar Topography Mission (SRTM) radar penetra-tion21,22, which was best practice at that time, but now proven to

be erroneous for the NPI23. For Tierra del Fuego (region 11), our values reveal only about one quarter of the mass change stated in the previous analysis of time series from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) (2000–2011)24. Their 2 m radar penetration assumption alone cannot explain those differences. None of these previous glacier-specific geodetic mass change estimates accounted for subaqueous ice mass loss in Fuego-Patagonia.

For the comparison with GRACE (2003–2009), we integrate over the whole of Patagonia (regions 08 and 09). The resulting value of − 17.4 ± 0.8 Gt a−1 (2000 to 2011/2015) is smaller than previous gravimetric measurements2,7; for example, − 29 ± 10 Gt a−1 and − 23 ± 9 Gt a−1 (supplementary Fig. 9). Using an improved solid earth glacio-isostatic adjustment model, a loss of 26 ± 6 Gt a−1 was revealed between 2003 and 200925. The error bars of most studies overlap, although the measurement techniques and the observation intervals differ (supplementary Fig. 8).

Glacier surface mass balance depends on accumulation and various factors affecting melt, such as temperature and the radia-tion balance. The observed climatic changes in South America are regionally very different. We derive decadal trends of skin tem-perature and vertically integrated water vapour over the continent (1979–2017, derived from ERA-Interim reanalysis fields, Fig. 3) as proxies. The skin temperatures show significant increases in the high Andes, in particular in the outer tropics and Desert Andes (regions 01–05). This agrees with previous studies26,27. In the inner tropics (region 01), the rise in temperature is less pronounced. Throughout the tropical region, there is a significant increase in water vapour in the Amazon basin close to the Andes of more than 5% dec−1. While

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Fig. 3 | Decadal trends of skin temperature and vertically integrated water vapour across South America. a. Skin temperature trend derived from ERA-interim data (ERA: European Reanalysis) over the period 1979–2017. The dotted areas mark cells with significant trends(P <  0.05). The glacier regions are indicated by the numbers (Table 1) and magenta circles denote cells with glacier cover. b. Same as a, but for water vapour. The arrows indicate the direction and magnitude of the mean water vapour flux over the period 1979–2017.

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the enhanced moisture explains the observed mass gain in gla-ciers at higher elevations in the northern, wet outer tropics of Peru (region 02), the rise in skin temperatures leads to higher ablation rates and retreat at the glacier tongues at lower elevations (Fig. 2). A similar pattern exists for the cold, dry outer tropics of Peru-Bolivia (region 04), where a small but significant increase in vertically inte-grated water vapour is obtained. The southern, wet outer tropics of Peru-Bolivia (region 03) benefit less from the increased moisture from the Amazonian basin towards the Andes compared with the northern, wet outer tropics (region 02). This decline is related to the strengthening of the subtropical high-pressure system over the Pacific Ocean. The strengthening system causes an enhanced trans-port of cool and dry air masses over the Altiplano. These air masses suppress the convection of the humid Amazonian air masses on the eastern slope to the Bolivian mountain ranges and the nearby east-ern Altiplano and are thus partially decoupled from the moisture changes in the Amazon basin. The strongest positive skin tempera-ture trends (~1 K dec−1) can be found in the Desert Andes (region 05), while the moisture trends are slightly negative for this region. Our elevation change measurements indicate balanced conditions. At those high elevations, the temperature increase is not sufficient to enhance melt to such a degree that it has an impact on the gla-cier mass balance, while the decrease in moisture is not sufficient to reduce the ice volume to a detectable degree.

For Fuego-Patagonia (regions 08–11), the water vapour shows no significant trend, while the skin temperature trend is positive, indicating enhanced melt conditions. When we compare the spe-cific mass balance rates of the different regions (Fig. 4), the NPI and SPI (subregions 081 and 091) show the largest specific contri-butions. The areas outside of the large icefields (subregions 082 and 092) comprise smaller glaciers and have lower change rates, similar to Gran Campo Nevado (region 10) or Tierra del Fuego (region 11) glaciers. This strongly supports the assumption that the mass loss of the Patagonian icefields is mainly driven by dynamic adjustments of the tidewater and lake calving glaciers28.

Our regionally aggregated assessment reveals robust patterns of large spatial variability of glacier elevation changes between 2000 and 2011/2015 in South America. The glacier mass loss

corresponds to a sea-level rise of 0.054 ± 0.002 mm a−1. However, the actual amount of sea-level rise is unknown, since discharge and the continental storage are not addressed in this study. Our values are smaller than previous estimates based on satellite gravimetry and extrapolated glaciological field measurements. The results of this study are relevant for calibrating and validating glacier mass balance models and as input to ice dynamic flow models or physi-cally based ice thickness reconstruction approaches29. Some regions are measured for the first time on a regional scale. Our values for the tropical Andes are considerably lower than previous estimates. The glacier mass changes in the tropical Andes, as well as in the Desert and Central Andes (regions 01–06), are of importance for water resource management. In those regions, glacier melt can con-tribute up to 15% of the annual and 27% of the dry season runoff30. Meltwater is used for irrigation in agriculture, drinking water, min-ing and hydro power. The region between ~18°S and ~42°S (regions 05–07) shows comparable small elevation change rates, while the two Patagonian icefields (regions 08 and 09) are the largest contrib-utors due to dynamic adjustments of the outlet glaciers.

Online contentAny methods, additional references, Nature Research reporting summaries, source data, statements of data availability and asso-ciated accession codes are available at https://doi.org/10.1038/s41558-018-0375-7.

Received: 17 July 2018; Accepted: 22 November 2018; Published: xx xx xxxx

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01 Inner Tropics

a b

02 OT (Peru)

03 OT (Peru–Bolivia)

04 OT (Peru–Bolivia)

05 Desert Andes

06 Central Andes

07 Lake District

08 Patagonia North

081 NPI

082 Outside NPI

09 Patagonia South

091 SPI

092 Outside SPI

10 GCN-IR

11 Tierra del Fuego

Subaqueous ice loss

0.2 –0.2 –0.4

(m.w.e yr–1) (Gt yr–1)

–0.6 –0.8 –10 0 –2 –4 –6 –8 –10 –12 –14

Fig. 4 | Glacier mass balance rates per area unit (specific mass balance) and absolute mass changes for the different regions. OT: Outer Tropics; GCN +  IR: Gran Campo Nevado and Isla Riesco; SPI: Southern Patagonian Icefield; NPI: Northern Patagonian Icefield. Light colour bars and grey text indicate the values measured for the Patagonian subregions, error ranges covering uncertainties from DEM differencing, glacier outlines, volume-to-mass conversion, radar signal penetration and hypsometric gap filling. The value for subaqueous ice loss was normalized using the entire glazierized area of regions 08–11.

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5. Garreaud, R. D. et al. The 2010–2015 megadrought in central Chile: impacts on regional hydroclimate and vegetation. Hydrol. Earth Syst. Sci. 21, 6307–6327 (2017).

6. Mark, B. G. et al. Glacier loss and hydro-social risks in the Peruvian Andes. Glob. Planet. Change 159, 61–76 (2017).

7. Jacob, T., Wahr, J., Pfeffer, W. T. & Swenson, S. Recent contributions of glaciers and ice caps to sea level rise. Nature 482, 514–518 (2012).

8. Mernild, S. H. et al. Mass loss and imbalance of glaciers along the Andes Cordillera to the sub-Antarctic islands. Glob. Planet. Change 133, 109–119 (2015).

9. Rabatel, A. et al. Current state of glaciers in the tropical Andes: a multi-century perspective on glacier evolution and climate change. Cryosphere 7, 81–102 (2013).

10. Dietrich, R. et al. Rapid crustal uplift in Patagonia due to enhanced ice loss. Earth. Planet. Sci. Lett. 289, 22–29 (2010).

11. Foresta, L. et al. Heterogeneous and rapid ice loss over the Patagonian Ice Fields revealed by CryoSat-2 swath radar altimetry. Remote Sens. Environ. 211, 441–455 (2018).

12. Farr, T. G. et al. The Shuttle Radar Topography Mission. Rev. Geophys. 45, RG2004 (2007).

13. Krieger, G. et al. TanDEM-X: a satellite formation for high-resolution SAR interferometry. IEEE. Trans. Geosci. Remote Sens. 45, 3317–3341 (2007).

14. Malz, P. et al. Elevation and mass changes of the Southern Patagonia icefield derived from TanDEM-X and SRTM data. Remote Sens. 10, 188 (2018).

15. Warren, C., Benn, D., Winchester, V. & Harrison, S. Buoyancy-driven lacustrine calving, Glaciar Nef, Chilean Patagonia. J. Glaciol. 47, 135–146 (2001).

16. Gourlet, P., Rignot, E., Rivera, A. & Casassa, G. Ice thickness of the northern half of the Patagonia Icefields of South America from high-resolution airborne gravity surveys: ICE THICKNESS PATAGONIA. Geophys. Res. Lett. 43, 241–249 (2016).

17. Carrivick, J. L., Davies, B. J., James, W. H. M., Quincey, D. J. & Glasser, N. F. Distributed ice thickness and glacier volume in southern South America. Glob. Planet. Change 146, 122–132 (2016).

18. Meier, W. J.-H., Grießinger, J., Hochreuther, P. & Braun, M. H. An updated multi-temporal glacier inventory for the Patagonian Andes with changes between the Little Ice Age and 2016. Front. Earth Sci. https://doi.org/10.3389/feart.2018.00062 (2018).

19. Basantes-Serrano, R. et al. Slight mass loss revealed by reanalyzing glacier mass-balance observations on Glaciar Antisana 15α (inner tropics) during the 1995–2012 period. J. Glaciol. 62, 124–136 (2016).

20. Abdel Jaber, W. Derivation of Mass Balance and Surface Velocity of Glaciers by Means of High Resolution Synthetic Aperture Radar: Application to the Patagonian Icefields and Antarctica. PhD thesis, TU Munich (2016).

21. Willis, M. J., Melkonian, A. K., Pritchard, M. E. & Ramage, J. M. Ice loss rates at the Northern Patagonian Icefield derived using a decade of satellite remote sensing. Remote Sens. Environ. 117, 184–198 (2012).

22. Willis, M. J., Melkonian, A. K., Pritchard, M. E. & Rivera, A. Ice loss from the Southern Patagonian Ice Field, South America, between 2000 and 2012. Geophys. Res. Lett. 39, L17501 (2012).

23. Dussaillant, I., Berthier, E. & Brun, F. Geodetic mass balance of the Northern Patagonian Icefield from 2000 to 2012 using two independent methods. Front. Earth Sci. https://doi.org/10.3389/feart.2018.00008 (2018).

24. Melkonian, A. K. et al. Satellite-derived volume loss rates and glacier speeds for the Cordillera Darwin Icefield, Chile. Cryosphere 7, 823–839 (2013).

25. Ivins, E. R. et al. On-land ice loss and glacial isostatic adjustment at the Drake Passage: 2003–2009. J. Geophys. Res. Solid Earth. 116, B02403 (2011).

26. Vuille, M. et al. Rapid decline of snow and ice in the tropical Andes – Impacts, uncertainties and challenges ahead. Earth Sci. Rev. 176, 195–213 (2018).

27. Vuille, M. et al. Climate change and tropical Andean glaciers: Past, present and future. Earth Sci. Rev. 89, 79–96 (2008).

28. Sakakibara, D. & Sugiyama, S. Ice-front variations and speed changes of calving glaciers in the Southern Patagonia Icefield from 1984 to 2011. J. Geophys. Res. F Earth Surf. 119, 2541–2554 (2014).

29. Fürst, J. J. et al. Application of a two-step approach for mapping ice thickness to various glacier types on Svalbard. Cryosphere 11, 2003–2032 (2017).

30. Soruco, A. et al. Contribution of glacier runoff to water resources of La Paz city, Bolivia (16° S). Ann. Glaciol. 56, 147–154 (2015).

AcknowledgementsThis study was financially supported with the grant BR2105/14-1 within the DFG Priority Program 'Regional Sea Level Change and Society’ and by grant SA2339/3-1, the BMBF-CONICYT project GABY-VASA (01DN15020, BMBF20140052), the DLR/BMWi grant GEKKO (50EE1544) as well as the HGF Alliance Remote Sensing & Earth System Dynamics and FONDECYT 1161130. D.F.B. was funded under a BECAS-Chile scholarship.

Author contributionsM.H.B. initiated and led the study and wrote the manuscript, P.M., T.C.S. and C.S. wrote the analysis code; P.M. processed all data from the SPI, T.C.S. processed all data from Peru and Bolivia, C.S. processed the inner tropics, northern Chile and Patagonia outside SPI and NPI, computed the subaqueous mass loss and generated the graphs, D.F.B. processed the data for the central Andes, Lake District and NPI and compiled the supplemental data on glacier elevation and mass changes. T.S. provided the climate data analysis and interpretation of results; A.S., G.C. and P.S. contributed to the interpretation of the data. All authors revised the manuscript.

Competing interestsThe authors declare no competing interests.

Additional informationSupplementary information is available for this paper at https://doi.org/10.1038/s41558-018-0375-7.

Reprints and permissions information is available at www.nature.com/reprints.

Correspondence and requests for materials should be addressed to M.H.B.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© The Author(s), under exclusive licence to Springer Nature Limited 2019

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MethodsRegional glacier subdivision. We adapted previous subdivisions of glaciers31–33 (Fig. 1). For the Southern Andes and Fuego-Patagonia, we provide more subdivisions to enable a better comparison with previous studies and a better separability of previously unmeasured areas. In particular, we separate the two large Patagonian icefields from the surrounding glaciers for improved process understanding of mass changes by enabling a comparison between glaciers and the large icefields in the same latitude and climate conditions. Glaciers in the inner tropics (region 01, Venezuela, Colombia and Ecuador) are characterized by ablation and accumulation throughout the year and by slight extra precipitation during the crossing of the inner tropical convergence zone (ITCZ)34. Glaciers are located above 4500 to 5000 m, mainly on top of large volcanoes. The outer tropics are located between the inner tropics and the subtropics and are characterized by accumulation occurring only during the wet season. Glaciers in the outer tropics are subdivided into three main classes: the northern wet outer tropics of Peru (region 02; uniform temperature seasonality close to 0 K and high relative humidity of 71%; precipitation is mainly controlled by ITCZ, corresponding to monsoon (Am) and tropical savanna (Aw) climate after Köppen-Geiger’s climate classification35) covering the western Peruvian cordillera north of 13°S, including Cordillera Blanca; the southern wet outer tropics of Peru-Bolivia (region 03; annual temperature variability of up to or more than 4 K and lower relative humidity of 60%; precipitation is controlled by ITCZ and South American summer monsoon, humid subtropical/oceanic subtropical highland climate after Köppen-Geiger, Cwb), covering the southeastern Peruvian and eastern Bolivian cordillera south of 13°S, including Cordillera Real, and the cold dry outer tropics of Peru-Bolivia (region 04, cold semi-arid climate after Köppen-Geiger, BSk) including southern Peru and the western cordilleras of northern Chile and Bolivia. Glaciers in the dry outer tropics are located in high altitudes on top of volcanoes, whereas in the wet outer tropics, valley glaciers dominate. South of this region, we identified the Desert Andes (region 05, cold desert after Köppen-Geiger, Bwk) comprising small glaciers at very high elevations under a dry and cold climate. The Central Andes (region 06, cold desert to temperate Mediterranean climate after Köppen-Geiger, Bwk–Csb) are separated from the Desert Andes due to their more extensive glacier coverage and stronger westerly influence. A marked gap in the glacier coverage separates the Central Andes from the Lake District (region 07, temperate Mediterranean to temperate oceanic climate, Csb–Cfb). The glacier cover here is dominated by glaciers on top of active, dormant or extinct volcanoes (< 4000 m a.s.l.) and the climate shows considerably more winter precipitation due to its location within the southern hemisphere westerlies. Region 08 (Patagonia North) comprises all glaciers south of Puerto Montt to Río Baker and includes the NPI and smaller glaciers in its vicinity. Similarly, south of the Río Baker, we distinguish the SPI and surrounding glaciers in the region 09 Patagonia South. South of the SPI, the Andes on the main continent have lower elevation and are only covered by a few mountain glaciers, summarized in the region 10 of Gran Campo Nevado (GCN) and Isla Riesco (IR). All Patagonian regions are located in the Köppen-Geiger cool oceanic climate zone (Cfc). In Tierra del Fuego we integrate all glacierized areas including the Cordillera Darwin in region 11 (oceanic subpolar climate to tundra climate after Köppen-Geiger, Cwc–ET).

TanDEM-X data processing and DEM differencing. We use data from the SRTM of the National Aeronautics and Space Administration (NASA) and of the TerraSAR-X add-on for Digital Elevation Measurement mission (TanDEM-X) operated jointly by the German Aerospace Center (DLR) and Astrium Defense and Space. The SRTM mission acquired globally bi-static C-band interferometric synthetic aperture radar (InSAR) data of landmasses between 60°N and 54°S from 11 to 22 February 200012. The data were processed to a global, high-resolution digital elevation model (DEM). Subsequently, several related DEM products were derived from these SRTM data. We use the void-filled LP DAAC NASA Version 3 SRTM DEM (1 arcsec ground resolution)36, reprojected to UTM projection (Univerial Transverse Mercator). The TanDEM-X mission has been acquiring bi-static X-band InSAR data since 201013,37 with a complete global coverage for its DEM core product. In order to minimize effects of radar penetration into snow and firn, we use whenever possible only TanDEM-X data from the same season as the SRTM mission. The TanDEM-X coverage is shown in Fig. 1. It comprises data between 2011 and 2015 with about 80% from the global DEM phase in 2012 and 2013. Each TanDEM-X scene has a specific acquisition date, and this is used as the end point of our bi-temporal DEM differencing.

The TanDEM-X scenes are processed using differential SAR interferometry14. The individual scenes cover an area of 30 × 60 km²; however, scenes along one track from the same acquisition date are concatenated before processing. Using the void-filled SRTM DEM as reference, a differential interferogram is formed. Subsequently, the differential interferogram is filtered, unwrapped applying either a branch cut or a minimum cost flow algorithm (the best results of both algorithms are selected manually) and converted to differential elevation values. The reference DEM heights are then added and the resulting new raw TanDEM-X DEM is geocoded.

For the height change measurements, we apply DEM differencing. In order to achieve optimal results, the TanDEM-X DEMs are bi-linearly co-registered vertically to the SRTM DEM on stable ground. Stable points are selected in areas

outside the glaciers (Randolph Glacier Inventroy, RGI 6.038) with less than 15° surface slope (using the SRTM DEM) and by masking out vegetation (Normalized Differential Vegetation Index thresholds between < 0.3 and < 0.4) as well as water (Normalized Differential Water Index mask). The latter masks are generated based on cloud-free Landsat data sets. Subsequently, the TanDEM-X DEMs are horizontally coregistered to the SRTM DEM using an iterative approach39. To remove any remaining vertical offsets, the TanDEM-X DEMs are again bi-linearly vertically adjusted to the SRTM elevations. We finally mosaic DEMs of adjacent tracks to one single DEM for a region. In this process, we label each pixel of the new adjusted TanDEM-X DEM with a defined time stamp. Nevertheless, it has to be noted that slightly different observation periods exist within and between regions due to the TanDEM-X coverage from different years and seasons. This might lead to some additional uncertainty, which cannot be directly quantified, but is considered small for the observation period of ~13 years.

For the subsequent DEM differencing, we use the TanDEM-X time stamp of each pixel to compute elevation change rates (Δ h/Δ t) for the respective periods. Since the SRTM DEM is a blended product from various acquisitions during the mission period, we use the mean date of 2000-FEB-16 as the reference date. In the void-filled SRTM DEM, gaps were filled with elevation information from different sources without providing an exact reference or label of the respective pixel. Therefore, we apply a void mask to exclude filled pixels in the SRTM DEM for the DEM differencing. Those pixels are subsequently filled using an elevation change versus altitude function. To determine this function, we use glacier outlines close to the starting year (RGI 6.038) and measure the elevation change rate (Δ h/Δ t function) on the glacier area. We apply an additional cutoff for steep slopes (> 50°) where the DEMs are less reliable40 and almost no accumulation occurs (avalanche slopes). For each region we generate a Δ h/Δ t function using 100 m height bins. For each elevation band the Δ h/Δ t values are filtered by applying three times the normalized median absolute deviation (NMAD)41, and the resulting mean Δ h/Δ t values of the individual elevation bands are calculated. The void-filled SRTM DEM is used as elevation reference for the hypsometric computations and respective interpolation of data gaps in the TanDEM-X DEM, where mean values are applied according to reference elevation class.

The elevation change measurements are converted to mass budgets following the UNESCO definition42. We first integrate the elevation change rates over the glacier area and apply a conversion factor (density) to obtain geodetic mass balance rates (Δ M/Δ t). We use two density scenarios (ρ), one recommended43 based on a study of alpine glaciers (850 ± 60 kg m−3) and an approximation of the density of ice corresponding to 900 ± 60 kg m−3. While the lower density scenario refers more to alpine-type glaciers responding to climate variations, the higher density scenario is closer to pure ice and hence better reflects the melt out of ice masses or surface elevation changes due to dynamic adjustments. Since by far the largest ice losses are observed at the Patagonian ice fields and are attributed to dynamic adjustments, the higher density scenario is used to report the total observed mass change in our study region. Depending on the observation interval, the volume change rate and the mass balance gradient, the conversion factor can vary strongly43. Our observation periods are sufficiently long, and no strong changes of the mass balance gradients are assumed to occur in the regions. Thus, in order to account for the larger uncertainty of the conversion factor in regions with mass balance rates smaller than ± 200 kg m−2 a−1, we applied a higher error of 300 kg m−3 for the conversion factor.

We use the RGI 6.0 as baseline for our glacier areas due to the lack of a second inventory coincident with the TanDEM-X acquisitions. This implies that advancing areas are not represented in this data set; however, their portion is marginal in regard to the overall glacierized areas. In Fuego-Patagonia, 13 out of 11,209 glaciers showed advance between 2006 and 201618. For area-specific elevation and mass change estimates, we also refer to the RGI 6.0 area as reference and not a temporal mean as suggested by the UNESCO definition42. This affects areas of large relative area change more strongly (for example, region 03, outer tropics). Our elevation and mass balance rates in those regions are smaller than they would be following the UNESCO definition using a mean glacier area. Additional uncertainties may result when the dates of RGI 6.0 and SRTM do not coincide. This effect cannot be quantified without respective outlines.

Uncertainty analysis and error budget. In our error budget we consider the following terms:• error from the DEM differencing (considering spatial auto-correlation) (δΔh/Δt)• error from the glacier outlines (δS)• uncertainty from the volume-to-mass conversion using a fixed density (δρ)• uncertainty from radar signal penetration (Vpen/Δ t)• uncertainty by hypsometric gap filling (included in δΔh/Δt)

The uncertainty of the mass balance estimates (δΔM/dt) is calculated according to equation(1):

δ Δ

Δδ δ δρ

ρ Δρ= + + +Δ Δ

Δ ΔΔΔ

∕∕M

t SVpen

t* (1)M t

h tht

S2

22 2 2

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where Δ M/Δ t denotes the mass balance estimate, Δ h/Δ t the extrapolated average elevation change, S the glacier area and ρ the density for the volume-to-mass conversion.

We calculate δΔh/Δt by analysing Δ h/Δ t on stable areas (ice-free plus masking out water bodies and vegetation) and used a 2–98% quantile filter to remove strongly deviating values caused by processing relicts that would contribute disproportionately highly to the result. Since the accuracy of Δ h/Δ t depends on the surface slope, we use standard deviations (σΔh/Δt) derived on 5° slope bins on stable ground and calculated the slope-based area weighted standard deviation (σΔh/Δt AW) on glaciated areas14,41,44–46. Similarly to the gap filling approach, we applied a three time NMAD filter in each slope bin before calculating σΔh/Δt AW. In order to account for spatial auto-correlation in the error budget44, we generate semivariograms of the elevation change values on stable ground, and calculate a mean lag distance (dc) of 375 m. Since we are calculating region-wide average glacier changes, we follow an approved analysis41,44, which is appropriate when integrating elevation changes over a large region:

δ σ

δ σ

= >

= <

Δ Δ Δ Δ

Δ Δ Δ Δ

∕ ∕

∕ ∕

SS

for S S

for S S5 (2)h t

C

Gh tAW G C

h t h tAW G C

where SG is the glacier area and Sc = dc²*π the correlation area. SG is multiplied by a factor of 5 in equation (2). This weighting factor for the observation area to the correlated area is an empirically determined approximation44. Equation 2 is applied for each continuous ice-covered area. By using an area weighting over the individual glaciated areas, the region-wide values of δΔh/Δt are computed. To account for the error due to the hypsometric extrapolation, we follow the approach from literature41 and multiply δΔh/Δt by a constant factor of 2 for the fraction of glacier area not covered by elevation change measurements.

For the uncertainty resulting from the glacier area determination (δS), we refer to a previous detailed analysis47 that revealed an error of 3% for alpine catchments. However, the authors found a perimeter to area ratio (rP/S) of 5.03 km−1, whereas ours revealed rP/S values of the individual regions ranging from 0.67 to 10.81 km−1. Thus, we apply a scaling to the error reported to render a larger area determination error in tropical mountain and valley glaciers in contrast to the minor error in the more compact icefields of Patagonia:

δ = ⋅∕

∕ .S

rr

*0 03 (3)P S

P S Pauletal

The error of signal penetration is strongly dependent on the prevailing surface conditions (frozen/melting) during the respective image acquisition of SRTM and TanDEM-X. During melting conditions and when liquid water is present, the microwave signal at X- and C-band frequencies shows almost no signal penetration, while during frozen conditions a penetration of several metres might occur. As such, we cannot give a specific value for each scene, but provide an upper bound to account for this uncertainty.

Therefore, the uncertainty due to the different SAR signal penetration between SRTM C-band and TanDEM-X X-band is estimated according to a previous study14. Differences in radar penetration between X- and C-band below the equilibrium line altitude (ELA) are neglected. We used published ELA values individually for each region to estimate the mean ELAs (Supplementary Table 1), since a consistent analysis of the late summer snow line was beyond the scope of this paper and for several regions, the database of optical imagery did not allow for this. Above the ELA, we assume a linear increase of radar signal penetration difference from 0 m up to 5 m at the maximum elevation of the study region, which is integrated over the area above the ELA to obtain Vpen. In the supplementary material (supplementary Fig. 9), we provide a sensitivity analysis of the error contribution of the radar penetration shifting our ELA values by a multiple of 100 m.

A previous study23 showed that SAR signal penetration was minimal on the Patagonian icefields during SRTM acquisition, and intensity image inspection revealed primarily melting conditions for most of the icefields during the austral summer acquisitions of TanDEM-X and SRTM20. However, in order to use a consistent methodology throughout the study, we apply the same penetration depth correction for all regions. Since the largest mass loss results from the Patagonian icefields, our error estimate for radar penetration can be seen as an upper bound.

Subaqueous volume and mass loss estimate for Fuego-Patagonia. To estimate the ice volume and mass calved off below sea or lake level, we use the RGI Vers. 6.038 inventory to identify lake and ocean calving glaciers and the outlines from 2000 to 2003 and 2016 to 201718 in order to determine the area lost at the glacier front of ocean and lake calving glaciers (Supplementary Table 2). From those, we

compute mean annual change rates, assuming a linear retreat of the glacier fronts. A review of publications in regard to lake and ocean bathymetry close to the glacier front (Supplementary Table 3) revealed that a region-wide glacier-specific analysis is very difficult due to the availability of data and heterogeneous conditions. Maximum water depths range between 100 and 600 m. Most lake bottom/ocean floors appear to show a clear U-shape. Considering also lower depths at the margins and that no other retreating glacier system has the dimension of Upsala Glacier, we estimate a mean depth in the retreated areas of 250 ± 100 m. We use this mean depth as ice thickness of the ice lost below sea/lake level to compute the ice volume. For volume-to-mass conversion, we apply a density of 900 kg m−3. No uncertainty is associated with this density due to the calving glacier tongues consisting of ice. This ice volume does not contribute to sea-level change.

Climate data analysis. The decadal temperature and moisture flux changes have been calculated from ERA-Interim reanalysis data for the period 1979–2017. This enables a comparison with the observed elevation changes and allows a certain lag time of glacier adjustment to climate perturbations and changes. The significance of the linear trends was determined by the F-test at a 95% confidence level.

Data availabilityElevation change fields are available via the World Data Center PANGAEA operated by AWI Bremerhaven under https://doi.org/10.1594/PANGAEA.893612. Glacier-specific results can be generated from those fields, but will also be made available through submission to the World Glacier Monitoring Service.

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