Introduction

Mountain water resources in the tropical Andes sustain both rural and urban water supplies, irrigated agriculture, hydropower generation and fragile high-elevation ecosystems1,2,3. Most precipitation falls in the wet season between December and March, with glacier meltwater an important water source during the dry season (May to September), and especially during droughts2,3. Seventy percent of the world’s tropical glaciers are in the Peruvian Andes, with most Peruvian glaciers concentrated in the Cordillera Blanca in northern Peru and the Cordilleras Vilcanota-Urubamba in southern Peru4. Both regions have undergone considerable glacier recession in recent decades5,6,7, exacerbating water scarcity and conflicts around water allocation1,8. Rising temperatures have driven increases in freezing level height and snowline altitude9,10,11,12, but the climate that is driving these dramatic changes remains poorly understood. Precipitation patterns in time and space remain uncertain, with some indication of increasing precipitation in the Cordillera Blanca, but not in the Cordillera Vilcanota-Urubamba9,11,13,14.

Future projections based on global CMIP5 (Coupled Model Intercomparison Project version 5) models15 suggest substantial temperature rises over the tropical Andes (of +1 °C to +5 °C) by 210016, and warming of +4.3 °C in the Vilcanota-Urubamba17, and over +5 °C for the Quelccaya Ice Cap18 under the highest emissions scenario, representative concentration pathway (RCP) 8.5 by 2100. These increases would likely lead to the disappearance of a large proportion of the region’s glaciers19. Large-scale studies over South America suggest an increase in future precipitation in the wet season in the Peruvian Andes, based on CMIP6 models20. Few studies have investigated future precipitation in these two regions in detail, and none goes beyond 2030 for the Cordillera Blanca21. Notably, the few works in the Vilcanota-Urubamba region do not agree on the sign of precipitation change, with projections of both increases and decreases22,23,24.

Populations in the Peruvian Andes are highly vulnerable to extreme weather events25,26 and are at risk from both water scarcity and flooding2,3. Extremes such as heat waves and heavy precipitation are expected to increase in North-Western South America, based on global analysis using CMIP6 models27. To the best of our knowledge, there is no research on future heavy precipitation extremes directly in these two regions, and preliminary evidence from southern Peru suggests strong spatial variability in extreme climate indices in the recent past13. In a small region of the northern Andes, long-term extreme wet periods have increased more than meteorological droughts recently26, but large-scale global climate model projections suggest most of the west coast of South America will experience an increase in droughts driven by evapotranspiration28.

To determine precipitation and temperature in the recent past we run the Weather Research and Forecasting (WRF) model over the upper Rio Santa basin (in the Cordillera Blanca, hereafter referred to as Rio Santa), and the Vilcanota-Urubamba basin (Fig. 1a) from 1980 to 2018 at high spatial resolution (4 km). We correct the output for systematic biases in precipitation and temperature using weather station data. To determine future changes in temperature and precipitation, we statistically downscale precipitation and temperature from an ensemble of 30 CMIP5 models29,30, with the bias-corrected WRF dataset used as the historical truth. To date, there have been no attempts to downscale a large ensemble of global climate models for either the Rio Santa or the Vilcanota-Urubamba basins. We use these datasets to analyse past (1980–2018) and future (2019–2100) trends in temperature and precipitation. Future changes to daily extremes are analysed using six Expert Team on Climate Change Detection and Indices (ETCCDI) and future changes in meteorological droughts are determined using the Standardized Precipitation and Standardized Precipitation-Evapotranspiration Indices (SPI and SPEI) for both the high (RCP8.5) and stabilization (RCP4.5) greenhouse gas emissions scenarios. All future changes are determined using the 30 statistically downscaled CMIP5 models, and compared to the control period 1980–2018 from the WRF hindcast.

Fig. 1: Past and future trends in temperature and precipitation in the Rio Santa and Vilcanota-Urubamba basins.
figure 1

a The three WRF model domains (D1-D3) used for the 1980 to 2018 hindcast. The outer domain, D1, covers all of Peru at 12 km resolution. D2 and D3 show the inner domains at 4 km resolution, covering the Rio Santa basin and the Vilcanota-Urubamba basin, respectively. The two river basins are outlined in black, with the upper Rio Santa and 30 km boundary from which station data were used are outlined in blue. The terrain height is shown as filled contours, the ocean and other water bodies are shown in blue, and all stations used in the bias-correction are shown as blue dots. b The 1980-2018 annual trends in temperature (top; °C year−1) and precipitation (bottom; mm year−1) from the bias-corrected WRF hindcast, shown spatially for the upper Rio Santa (referred to as ‘Rio Santa’ in the text and hereafter) (left) and Vilcanota-Urubamba (right), with stippling indicating areas of significant trend and black contours showing elevation in 500 m intervals. The location of the Cordillera Blanca is shown with brown arrows, and the Cordilleras Urubamba and Vilcanota are marked by brown boxes. The outlines of the glaciers are shown in blue. c Timeseries of the basin-averaged recent past (1980-2018) and future (2019–2100) annual-averaged minimum and maximum daily temperature (top; °C) and precipitation (bottom; mm) are shown for the Rio Santa (left) and Vilcanota-Urubamba (right). Black lines show the basin-averaged values from the bias-corrected WRF hindcast. Blue lines show the mean of all statistically downscaled CMIP5 models for the RCP8.5 scenario, and green lines show the RCP4.5 scenario. Shading indicates one standard deviation from the mean (across the 30 statistically downscaled CMIP5 models).

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Results and discussion

A complex picture of past climate trends

From 1980 to 2018, 2 m air temperature from the bias-corrected WRF data shows a basin-averaged increase of 0.016 °C year−1 in the Rio Santa and 0.018 °C year−1 in the Vilcanota-Urubamba (Fig. 1b), with statistical significance over most areas. These values are in-line with recent trends over Peru10. The high-resolution WRF data, however, allows us to determine spatial trends in new detail, and we find that over the higher elevation areas of the Rio Santa, the temperature rise has been smaller than in the lower areas, and is not statistically significant (Fig. 1b). In the Vilcanota-Urubamba, there is ubiquitous and statistically significant warming (Fig. 1b). From September to February, the Urubamba region in the north has warmed at a faster rate than the Vilcanota region in the south-east (Supplementary discussion section 1.1 and Supplementary Fig. 1). This is likely to have contributed to the increased glacier decline in the Urubamba region compared to the Vilcanota in recent decades31.

Precipitation increased over the Rio Santa by an average of 3.1 mm year−1 between 1980 and 2018 according to the bias-corrected WRF data, but the increases are only statistically significant over the south-west of the region (Fig. 1b). In the Vilcanota-Urubamba, precipitation has increased in the north of the basin, around the Cordillera Urubamba, and decreased in the south, but with no statistically significant trends when considered annually (Fig. 1b). In September-October-November (SON) there is statistically significant drying over some glacierised regions of both the Rio Santa and the Cordillera Urubamba, as well as in the south of the Vilcanota-Urubamba Basin (Supplementary discussion section 1.1 and Supplementary Fig. 1). The combination of a particularly large increase in temperature and a reduction in precipitation in September-October-November, which is the end of the dry season (Supplementary discussion section 1.1 and Supplementary Fig. 1), is likely to have been particularly damaging to the glaciers, which have the lowest snow cover and therefore lower albedos at this time. A drying trend during the start of the wet season may also lead to agricultural changes, as September rainfall is important for crop sowing32.

There is good confidence in the past changes presented, as the correlation coefficients between the WRF data and the observations are high. They average 0.83 for the stations around the Rio Santa and 0.85 for the Vilcanota-Urubamba for monthly precipitation, and 0.78 (0.69) for the Rio Santa and 0.92 (0.74) for the Vilcanota-Urubamba for minimum (maximum) daily temperature, averaged monthly. The bias-correction substantially reduces the average root mean square error between the WRF data and the observations. This comparison, and a comparison with other gridded temperature and precipitation products, is shown in Supplementary methods section 2.1.1 and Supplementary Fig. 3.

A warmer, wetter future with increasing glacier melt

Both the Rio Santa and the Vilcanota-Urubamba regions will experience substantial warming until 2100 under both the RCP8.5 and RCP4.5 emissions scenarios based on the output from the statistically downscaled CMIP5 models, but with a clear divergence in trajectories between scenarios (Fig. 1c). By the late 21st century (2062-2100), maximum daily temperature increases of 3.6 °C and 4.1 °C in the Rio Santa and Vilcanota-Urubamba are projected under RCP8.5, compared to the recent past control period (1980–2018) (increases are of 1.9 °C and 2.2 °C under RCP4.5 (Table 1)). The rises in the minimum daily temperature are similar to those in the maximum daily temperature. The maximum and minimum daily temperature increases are statistically significant across all statistically downscaled CIMP5 models in both time periods and RCP scenarios (Table 1).

Table 1 Statistically downscaled CMIP5 multi-model average mean (and standard deviation, in brackets) projected increases in maximum and minimum temperature (°C) and annual precipitation (%) in the mid- (2022–2060) and late- (2062–2100) 21st century for the Rio Santa and Vilcanota-Urubamba regions, compared to the control period (1980–2018).
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Annual precipitation will increase by 12.1% (123 mm year−1) in the Rio Santa and 12.2% (118 mm year−1) in the Vilcanota-Urubamba by the late 21st century under RCP8.5, and 5.8% (59 mm year−1) in the Rio Santa and 5.3% (52 mm year−1) in the Vilcanota-Urubamba by the late 21st century under RCP4.5 (Table 1, Fig. 1c). There is variation between the statistically downscaled CMIP5 models, with a standard deviation of 11% in the Rio Santa and 9.3% in the Vilcanota-Urubamba, under RCP8.5 by the late 21st century.

Importantly, the increasing precipitation shown here for the Vilcanota-Urubamba is in contrast to ref. 24, who suggested that increasing westerly winds at 200 hPa are likely to cause a reduction in precipitation over the Central Andes (including the Vilcanota-Urubamba region). While the correlation between high-altitude westerly winds and precipitation is well established for the present24,33,34, regional climate models over South America suggest mixed trends over the Peruvian Andes in the future, with a rise in precipitation over most of the country35, but with insufficient spatial resolution to determine trends for these two regions. Here we show that almost all the statistically downscaled CMIP5 models project an increase in precipitation in both regions by the late 21st century, with over half showing a statistically significant increase (Table 1, Supplementary Tables 8, 9).

The projected changes in temperature and precipitation will have important consequences for glaciers and water resources. Using the future precipitation and temperature changes from the statistically downscaled CMIP5 models, we determine the potential effect on the glacier mass balance at the five on-glacier weather station sites (located in the Rio Santa and Vilcanota-Urubamba) studied in36. Under RCP8.5 by the late 21st century, the rate of mass loss more than doubles at all five sites, with the current accumulation found at the summit of Quelccaya Ice Cap in the Vilcanota-Urubamba, the highest site, changing to substantial mass loss (from +0.925 m we year−1 (metres water equivalent per year) to −1.875 m we year−1) (Fig. 2). Under RCP4.5, the increase in mass loss is smaller at all glaciers, but in no future time period or RCP scenario are the increases in precipitation sufficient to prevent an increase in the rate of glacier mass loss (Supplementary discussion section 1.2, Supplementary Fig. 2 and ref. 36 for details). Increased glacier shrinkage can heighten the risk of GLOFs (glacier lake outburst floods), and will reduce runoff in the dry season, exacerbating current water scarcity8,17.

Fig. 2: Future glacier mass balance change.
figure 2

Change in mass balance rate (in metres water equivalent per year) due to the climatic changes projected in this manuscript at five on-glacier weather station sites in the two regions: the (a) Shallap (4790 m asl), (b) Artesonraju (4797 m asl), and (c) Cuchillacocha (4821 m asl) Glaciers in the Rio Santa region, and the (d) Quisoquipina Glacier (5180 m asl) and (e) Quelccaya Ice Cap (5650 m asl) in the Vilcanota-Urubamba region. Changes are shown for the mid- (2022–2060) and end- (2062–2100) 21st century for the RCP4.5 and RCP8.5 emissions scenarios, with the mass balance rate for the control period for each station (see ref. 36) above each box. Note that the negative mass balances in the control period for Shallap, Artesonraju, Cuchillacocha and Quisoquipina imply that these stations are located in the ablation zone of the glaciers. These outputs are calculated in the same way as the sensitivity test method used in ref. 36.

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The greatest uncertainty in the future projections is in the different trends from the CMIP5 models themselves, and arises from a combination of model uncertainty, emissions scenario uncertainty and internal variability37. However, the robustness in the sign of the change from the large ensemble of model projections used here indicates the consistency of these results. The statistical downscaling method used here, quantile delta mapping, is designed to preserve the original trends in the CMIP5 models at all quantiles29, but correct the magnitude of temperature and precipitation, and the number of wet days, based on the bias-corrected WRF data. The choice of control period influences the magnitude of the future changes, but the increasing temperature and precipitation trends are consistent across all control periods tested (starting from 1950), see Supplementary methods section 2.2.1.

Amplified heavy precipitation and warm spells

A key finding of this work is that heavy precipitation will increase at a much higher rate than total precipitation (Fig. 3a–c). Average precipitation on wet days (calculated using the simple precipitation intensity index (SDII, see methods) and spatially averaged over the domains) shows a statistically significant increase in 23 of the 30 statistically downscaled CMIP5 models by the late 21st century under RCP8.5, with the median year in each period (averaged over all the statistically downscaled CMIP5 models) increasing from 6.3 mm day−1 in the control period to 7.1 mm day−1 between 2062 and 2100 in the Rio Santa annually, an increase of 12.7% (Fig. 3a). In the Vilcanota-Urubamba, 27 of the 30 statistically downscaled CMIP5 models show a statistically significant increase from 6.2 mm day−1 to 7.0 mm day−1, an increase of 13.0% (Fig. 3a). No models show a statistically significant decrease in simple precipitation index in either region. Importantly, however, total precipitation falling on heavy precipitation days (95th percentile from the control period, (R95pTOT, see methods)) is projected to increase substantially more than average precipitation (Fig. 3c). These increases are largest under RCP8.5 in both regions, with precipitation under this scenario from very wet days in the median year by the late 21st century (276.0 and 262.7 mm in the Rio Santa and Vilcanota-Urubamba, respectively) about 75% higher than the median year amounts for the control period (158.4 and 149.0 mm). Under RCP4.5, these increases are about 30% by the late 21st century. The number of dry days in the year (and seasonally) does not show any substantial change in either region or scenario, with a maximum of 4 out of 30 models showing a statistically significant increase (Fig. 3b), indicating that these changes are due to increasing precipitation on wet days, rather than an increase in the number of wet days. All the precipitation indices show substantial interannual variability, with overlap between the two scenarios.

Fig. 3: Future change in temperature and precipitation climate indices.
figure 3

Box and whisker plots of basin-averaged precipitation and temperature ETCCDI (Expert Team on Climate Change Detection and Indices) for the Rio Santa (top in each pair) and Vilcanota-Urubamba (bottom of each pair) regions for the control period (1980–2018; black boxes), as well as the mid- (2022–2060; hatching) and end of- (2062–2100; dots) 21st century for RCP4.5 (green boxes) and RCP8.5 (blue boxes) emissions scenarios. Results are shown annually, as well as for wet (November to April) and dry (May to October) seasons. For the control period, the middle of the box shows median year from the bias-corrected WRF hindcast, the top (bottom) of the box shows the 75th (25th) quantiles, and the top (bottom) of the whisker shows the maximum (minimum) year. For the future period boxes, the multi-model mean is taken for each quantile from the statistically downscaled CMIP5 models. Panel (a) shows the average precipitation on wet days (SDII), (b) shows the number of dry days, (c) shows the total precipitation falling on days above the 95th quantile of the control period (R95pTOT), (d) shows the monthly maximum of daily maximum temperature (TXx), (e) shows the warm spell duration index (i.e., days where at least six consecutive days fall above the 90th percentile of the control period) (WSDI), (f) shows the number of frost days (FD).

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The monthly maximum temperatures (TXx) will rise substantially, slightly over the average temperature increases (Table 1), from a median of 15.3 °C in the control period to 19.1 °C under RCP8.5 by the late 21st century in the Rio Santa, and from 15.6 °C to 19.8 °C in the Vilcanota-Urubamba (Fig. 3d). Rising temperatures lead to a large increase in warm days (calculated using the warm spell duration index (WSDI, see methods)), and a decrease in the number of frost days per year (Fig. 3e, f). The number of days per year within warm spells increases from 10.9 (5.7) in the Rio Santa (Vilcanota-Urubamba) in the control period to 171.0 (172.8) by the late 21st century under RCP4.5, and 287.8 (306.8) under RCP8.5, meaning that almost every day of the year is projected to be in the top 10% of 1980–2018 days, with consistency in sign across models. The median number of frost days per year (FD) is projected to reduce by around half, from 115.7 and 131.0 days (1980–2018) to 73.5 and 88.7 (64.0 and 79.4) days, under RCP4.5 (8.5) by mid-century (2022–2060), in the Rio Santa and Vilcanota-Urubamba, respectively (Fig. 3f). By the late 21st century, under RCP8.5, there will only be a handful of frost days per year, with a statistically significant decrease in all statistically downscaled CMIP5 models.

The increase in extreme precipitation is likely due to a shift in the distribution of precipitation intensity, such that a greater proportion of days are above the 95th quantile of the control period. In addition, although the Clausius-Clapeyron equation suggests an increase of approximately 7% in atmospheric water vapour for every 1 K of warming, precipitation has been shown to increase at a much smaller rate38. This is consistent with our results, which show precipitation increases of 12% for around 4 K of warming. However, extreme precipitation events, which are typically short-lived, are able to follow Clausius-Clapeyron scaling to its maximum extent. This implies, as is shown in these results, increases in heavy precipitation many times larger than the average precipitation increases.

Extreme rainfall is the most frequent cause of climatic natural hazards such as floods and landslides39,40,41. Andean farming communities also report an agricultural risk from heavy rains, which can wash away soil and destroy crops32. In addition to the effects of heavy precipitation, the decrease in frost days and increase in warm spells found in this study are likely to influence agricultural practices in these regions in the future. While the decrease in frost days may be beneficial to some crops grown in the Andes, others will either have to be sown at a different time of year, or replaced with different varieties32,42,43,44.

Future droughts projected to increase due to evapotranspiration

Meteorological droughts in the two study regions are expected to increase in the future based on the Standardised Precipitation-Evapotranspiration Index (SPEI, see methods), i.e., when potential evapotranspiration is accounted for45. SPEI is projected to decrease (indicating a long-term drying trend) over both regions and both RCP scenarios (Fig. 4c, d). The rising future temperatures discussed above (Fig. 1, Table 1) are reflected in a considerable increase in the number of drought months, by over 50% from 110.2 out of 457 months in the control period 1980–2018 to 172.3 out of 457 months by the late 21st century 2062-2100, in the Vilcanota-Urubamba under RCP4.5. In the Rio Santa, the increase is just under 50%, from 96.1 to 134.6 months (Table 2). Under RCP8.5, the average number of drought months will almost double in both regions, to 174.0 in the Rio Santa and 211.3 in the Vilcanota-Urubamba by the late 21st century. These changes are seen across most of the statistically downscaled CMIP5 models, with around two-thirds or more of the models projecting increases in drought months under both RCP scenarios in both regions by the late 21st century (Table 2).

Fig. 4: Past and future drought indices.
figure 4

Timeseries of the basin-averaged recent past (1980–2018) and future (2019–2100) Standardised Precipitation Index (SPI; a and b) and Standardised Precipitation-Evapotranspiration Index (SPEI; c and d) for the Rio Santa (a and c) and Vilcanota-Urubamba (b and d) regions. The black lines show the values from the bias-corrected WRF hindcast. The blue lines show the mean of all statistically downscaled CMIP5 models for the RCP8.5 scenario, and the green lines show the RCP4.5 scenario. Shading indicates one standard deviation from the mean (across the 30 statistically downscaled CMIP5 models).

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Table 2 Basin-averaged number of drought months for the Rio Santa and Vilcanota-Urubamba regions for the control period (1980–2018) and mid- (2022–2060) and late- (2062–2100) 21st century, based on values of the Standardised Precipitation Index (SPI) and Standardised Precipitation-Evapotranspiration Index (SPEI).
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Importantly, this increase in droughts is not apparent when analysing droughts from precipitation only using the Standardised Precipitation Index (SPI, see methods)46, which shows increases in both regions and for both RCPs (Fig. 4a, b), i.e. reduced meteorological drought events, reflecting the increasing trends in average precipitation (Fig. 1). Accordingly, the spatially-averaged number of drought months calculated using SPI is predicted to decrease considerably in both regions, with most statistically downscaled CMIP5 models showing a decrease in both regions by the late 21st century under RCP8.5 (Table 2). While using potential evapotranspiration can lead to an overestimation of future drought compared to actual evapotranspiration47,48, these contrasting results highlight that evapotranspiration plays a particularly important role in this part of the Andes and is essential in projections of future drought.

Meteorological drought is considered the leading cause of drought26, and water scarcity is already reported by local populations in both the Rio Santa and Vilcanota-Urubamba basins49. There is an increase in the inter-annual variability of precipitation in 22 of the statistically downscaled CMIP5 models for the Rio Santa and 25 statistically downscaled CMIP5 models for the Vilcanota-Urubamba, by the late 21st century under RCP8.5 (Supplementary tables 8 and 9). The greater variation in precipitation, along with intensifying evapotranspiration, is likely to increase both very wet and very dry months, and may be caused by increases in El Niño-Southern Oscillation (ENSO) variability50.

It should be noted that here potential evapotranspiration is estimated using a relatively simple formula, and that estimated potential evapotranspiration can be greater than actual evapotranspiration during periods of low precipitation. A full hydrological model would be needed to project future hydrological droughts.

Which future for the Andes?

Here we find a complex picture of past and future changes in the Andes of Peru, with the projected joint occurrence of both increased droughts and extreme precipitation. Further work is now needed for hydrological and societal modelling to determine the impact of meteorological droughts on hydrological changes, livelihoods, agriculture and hydroelectric power, and to provide scenarios of changes in the combined physical and socio-economic systems that are able to account for the very high variability in climatic changes identified in this study.

Given the likely glacier mass loss driven by these climate changes, the importance of glacier melt for dry season runoff3 and our predicted increase in drought conditions, these two Andean regions are likely to see enhanced dry season water stress in the future. This would have impacts on agriculture, including the irrigated export agriculture schemes on the Pacific coast fed by runoff from the Rio Santa2 and the farmers in the Andean highlands44,51, as well as ecological impacts (e.g. on wetland habitats52). Increased extreme precipitation may partly replenish groundwater supplies, which are crucial for maintaining river discharge in the dry season, but it would likely also lead to an increase in flooding, with associated economic and human consequences53.

The clear divergence between the two RCP scenarios reiterates the necessity of reducing global emissions. In addition, these results point to the need for urgent action to mitigate the future effects of climate change53. Early warning systems have proved effective for mitigating against the impacts of floods and landslides54,55. Diversifying water sources and improving both infrastructure and water governance can increase water access in the dry season56, and crop diversification may improve farming yields with climate change57,58. These adaptations have been shown to have much higher success when planned and developed with local populations, integrating indigenous knowledge into the adaptation process59,60. This work provides the first evidence base to inform novel adaptation and mitigation measures and inspire a new generation of land surface modelling to disentangle the consequences of the complex climatic changes we have identified.

Methods

Historical regional climate model

The WRF model version 3.8.161 is run with an outer domain of 12 km resolution covering Peru, and two 4 km inner domains; D2 over the Rio Santa and D3 over the Vilcanota-Urubamba (Fig. 1), with hourly temporal output (details of the WRF setup in Supplementary Table 1 and ref. 36). The model is driven with data from ERA5 at the boundaries62. Regional climate models have been found to accurately represent the spatio-temporal patterns in precipitaotn and temperature in the Andes63,64, and the WRF output is bias-corrected using present-day observations to reduce systematic biases.

Total daily precipitation and minimum and maximum daily air temperature at 2 m were compared to and bias-corrected against observations, from 35 (35) precipitation and 26 (34) temperature stations around the Rio Santa (Vilcanota-Urubamba). Station data originates from Servicio Nacional de Meteorología e Hidrología del Perú (SENAMHI)65, CIAD de la Universidad Nacional Santiago Antunez de Mayolo (UNASAM), Área de Evaluación de Glaciares y Lagunas de la Autoridad Nacional del Agua (ANA), Universidad Nacional de San Antonio Abad del Cusco (UNSAAC), and Compañia Minera Antamina S.A., de Perú. All stations have some data in the years between 1980 and 2018, and the data were cleaned before use (see ref. 36 for details). Locations of the observational stations are shown in Fig. 1a D2 and D3. Full details of the in-situ weather stations can be found in Supplementary Tables 2 and 3. The precipitation and temperature observations were used to correct the magnitude of the daily temperature output, and the number of wet days and magnitude of the precipitation output (see Supplementary methods, section 2.1).

Statistical downscaling of CMIP5 models

To determine regional changes in the Rio Santa and Vilcanota basins over the 21st century, 30 CMIP5 model projections were statistically downscaled using the bias-corrected WRF dataset in place of observations (Supplementary Table 7 gives details of the CMIP5 models used). The statistical downscaling was carried out for RCP4.5 and RCP8.5, based on the quantile delta mapping method described by Cannon et al. 29. This method preserves the large-scale trends from the CMIP5 models at each quantile (i.e. the trends in both the median and the extremes are preserved), while adjusting the number of wet days and the magnitude of precipitation and temperature based on the values from 1980 to 2018. Further details are available in Supplementary methods section 2.2. Statistical significance for the changes shown in Table 1 was assessed using a bootstrap method66.

Climate change indices

Six of the Expert Team on Climate Change Detection and Indicies (ETCCDI) climate indices67 were calculated in this study: the simple precipitation intensity index describing the total annual precipitation on wet days; the annual total precipitation falling on days where precipitation is above the 95th percentile of the 1980-2018 period; the number of dry days (precipitation under 1 mm) in a year (a variation on ‘continuous dry days’ given in67); the annual average monthly maximum temperature; the warm spell duration index describing the annual count of days with at least 6 consecutive days above the 90th percentile of daily maximum temperature from 1980-2018; and the number of frost days (minimum daily temperature below 0 °C). Indices were calculated based on the python package xclim,68, and statistical significance was assessed using a bootstrap method66.

Drought indices

The standard precipitation index (SPI) transforms the probability density function of precipitation to a standardised normal distribution, such that a value of −1 represents one standard deviation below (drier than) the mean46. To calculate the Standard Precipitation-Evapotranspiration Index (SPEI), potential evapotranspiration is estimated using the Hargreaves equation69, estimating the extra-terrestrial solar radiation from the latitude and day of year (calculated using the python software package Pyeto). The values of precipitation minus potential evapotranspiration are then transformed to a standardized normal distribution. The SPI and SPEI indices are calculated per month, rolling over the previous 12 months (SPI-12 and SPEI-12)45. Note that as the SPI and SPEI indices for a month are based on the previous 12 months, the first control period value is for December 1980. December is taken as the starting month for the mid-century and end-century in the drought calculations to keep the time periods consistent in length. We characterise a drought event as one where the index falls below one negative standard deviation for two consecutive months, which ends when the index turns positive28,70. Note that here we use 1980-2018 as the reference period, rather than the entire timeseries used by28, in order to determine the impact of droughts without adaptation. Further information is given in Supplementary methods section 2.3.

Glacier change

The changes in future precipitation and temperature were calculated at each of five on-glacier weather stations sites in the two regions, to project the change in the mass balance of the glaciers at these sites. At each site we ran the energy-balance melt model component of Tethys-Chloris at the point scale (using the same set-up as in ref. 36 for the climate sensitivity experiments), both with no change (control) and applying the average modelled changes in air temperature and precipitation under RCP scenarios 4.5 and 8.5, and for the mid- and end-of century projections detailed in this manuscript at each station. The vapour pressure and dew point temperature were recalculated based on the changes to the air temperature, but no other changes were made to other input variables.

Inclusion and ethics statement

This research was funded jointly between Peruvian and UK funding agencies, and roles and responsibilities were agreed amongst collaborators before the start of the project. This manuscript is a collaboration between Peruvian and UK researchers, as well as international partners, and all authors were involved throughout the manuscript process. Peruvian research and reports have been cited where appropriate for this study.