TC The Cryosphere TC The Cryosphere 1994-0424 Copernicus GmbH Göttingen, Germany 10.5194/tc-9-1663-2015ENSO influence on surface energy and mass balance at Shallap Glacier, Cordillera Blanca, Peru MaussionF. GurgiserW. GroßhauserM. KaserG. MarzeionB. Institute of Meteorology and Geophysics, University of Innsbruck, Innsbruck, Austria F. Maussion ( 9 4 16631683 13April2015 28May2015 24July2015 31July2015 This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit This article is available from The full text article is available as a PDF file from

The El Niño/Southern Oscillation (ENSO) is a major driver of climate variability in the tropical Andes, where recent Niño and Niña events left an observable footprint on glacier mass balance. The nature and strength of the relationship between ENSO and glacier mass balance, however, varies between regions and time periods, leaving several unanswered questions about its exact mechanisms. The starting point of this study is a 4-year long time series of distributed surface energy and mass balance (SEB/SMB) calculated using a process-based model driven by observations at Shallap Glacier (Cordillera Blanca, Peru). These data are used to calibrate a regression-based downscaling model that links the local SEB/SMB fluxes to atmospheric reanalysis variables on a monthly basis, allowing an unprecedented quantification of the ENSO influence on the SEB/SMB at climatological time scales (1980–2013, ERA-Interim period). We find a stronger and steadier anti-correlation between Pacific sea-surface temperature (SST) and glacier mass balance than previously reported. This relationship is most pronounced during the wet season (December–May) and at low altitudes where Niño (Niña) events are accompanied with a snowfall deficit (excess) and a higher (lower) radiation energy input. We detect a weaker but significant ENSO anti-correlation with total precipitation (Niño dry signal) and positive correlation with the sensible heat flux, but find no ENSO influence on sublimation. Sensitivity analyses comparing several downscaling methods and reanalysis data sets resulted in stable mass balance correlations with Pacific SST but also revealed large uncertainties in computing the mass balance trend of the last decades. The newly introduced open-source downscaling tool can be applied easily to other glaciers in the tropics, opening new research possibilities on even longer time scales.


The climate of the Cordillera Blanca in the Peruvian Andes is characterized by a wet season from October to April followed by a dry season with little or no precipitation. These dry and wet periods can be modified during El Niño and La Niña events, the El Niño Southern Oscillation (ENSO) being an important driver of climate variability in the region e.g.. In this particular setting, the glaciers of the Cordillera Blanca are of great economical, environmental and scientific importance. They are not only important suppliers of fresh-water during the dry periods e.g., but they also act as sensitive indicators of climate variability and climate change, as evidenced by the glacier shrinkage observed since the Little Ice Age .

The response of tropical glaciers to climate variations differs from their mid-latitudinal counterparts e.g. and has been studied extensively, in Africa e.g. and in South-America (e.g. and references herein; see and for a review). At low latitudes the annual cycle of temperature is small and humidity becomes an important driver of mass balance seasonality by its control on precipitation, net radiation, and sublimation . By determining the phase of precipitation and thus the surface albedo, changes in temperature can have a significant impact on mass balance inter-annual variability e.g.. The physical basis of tropical glaciers' responses to various atmospheric forcings are therefore best studied with process-based models that aim at the full decomposition of the surface energy and mass balance (SEB/SMB) e.g.. Since SEB/SMB models require high quality, high resolution glacio-meteorological observations for calibration and validation, the available time-series are short and unsuitable for long-term studies of glacier-climate interactions.

The starting point of this study is a 4-year long time series of distributed SEB/SMB fluxes at Shallap Glacier, Cordillera Blanca, obtained using a process-based model . Our first objective is to extend the length of these time series while still preserving the advantages of the decomposition into individual SEB/SMB components. The SEB/SMB variability is tied to large scale driven weather conditions, and we hypothesize that by using atmospheric reanalysis data we can compute (downscale) the energy fluxes with sufficient accuracy to determine the atmospheric drivers of SEB/SMB variability on longer timescales. This hypothesis is the foundation of any empirical statistical retrieval of glacier climatic mass balance (MB), no matter of which complexity.

“Temperature index” or “positive degree day” models e.g. are probably the simplest example of seeking statistical relationships between glacier MB and local climate variables (in this case temperature and precipitation). Extensions of temperature-based models include so-called “semi-empirical” models that incorporate further explanatory variables and/or physical processes while still relying on observational data for calibration e.g.. Another approach is to use observed relations between the MB and atmospheric variables or global circulation indexes in order to build statistical models that predict glacier MB seefor a probably very first attempt in this direction. Several variations of this method have been applied to glaciers in Northern Europe , northern America and in the Tropics . All these studies use the MB as the predicted variable and do not use the terminology of “downscaling”, that is extensively used in climate research. Statistical downscaling studies that target glaciological applications often focus on one or more meteorological variables at the glacier surface for use in a subsequent MB model for example .

Here we follow the general idea that, in principle, any target variable can be downscaled from large-scale atmospheric fields – as long as there is a physical reason for the local- and large-scale variables to be related . We present a new open-source tool (DownGlacier) developed especially to retrieve glacier SEB/SMB fluxes from large-scale atmospheric data. Inspired from existing software packages , it is a semi-automated, regression-based statistical downscaling tool (see Sect. ).

The second and main objective of this study is to quantitatively assess the impact of ENSO on the SEB/SMB of the Shallap Glacier. The influence of ENSO in the tropical and central Andes can be roughly summarized with prevailing warmer and drier conditions during El Niño phases, while colder and wetter conditions prevail during La Niña phases. As a result, studies dealing with ENSO's influence on tropical Andean glaciers reported a significant anti-correlation between Pacific sea-surface temperature anomalies (SSTA) and MB . The extreme 1997/98 Niño year, for example, caused exceptional glacier melt in the outer tropics . advanced that glaciers in the outer and inner tropics react similarly to El Niño events, mainly because of a precipitation deficit in the outer tropics and a temperature increase in the inner tropics, both leading to a rise in snow line altitude.

However, ENSO influences are neither spatially nor temporally coherent, especially in regions of complex terrain between the outer and inner tropics . Several studies in the Zongo valley Bolivia, 16 S; or in the Cordillera Vilcanota 14 S; report less strong or even opposite (“Niño/wet, Niña/dry”) local ENSO effects. The related studies of and are the only reports of ENSO influence in the Cordillera Blanca (9 S) to date. Based on a hydrological reconstruction of glacier MB for the period 1953–1993 , they found a significant anti-correlation between annual MB and October to April Pacific SSTA, supporting the expected “Niño negative MB, Niña positive MB” pattern. This relationship however did not hold true during at least three individual years after the mid-1970s, leading the authors to conclude that ENSO characteristics may have undergone changes in recent decades.

Map of the Cordillera Blanca with glacier outlines from the Randolph Glacier Inventory . The Shallap Glacier is colored in red. Color contours: 1998–2009 annual rainfall climatologies (mm) at 5km resolution provided by (

Here we use DownGlacier to retrieve monthly SEB/SMB fluxes at Shallap Glacier from atmospheric reanalysis data. This allows a first time assessment of the influence of ENSO on the individual components of the SEB/SMB during a longer climatological period (1980–2013). The seasonal variations of the ENSO signal and its varying impact with altitude will be of particular interest. The rest of the paper is organized as follows. In Sect. , we present the study region, describe the DownGlacier tool and the data used. In Sect. , we present the downscaling results for the ablation area of the glacier where the glacio-meteorological measurements took place. In Sect. , we apply the downscaling procedure to the entire glacier area and discuss the strengths and limitations of our method. We assess the robustness of our results in Sect.  by using several sensitivity analyses. The influence of ENSO will be analyzed and discussed for each of these steps before concluding our study in Sect. .

Study region, data and methods Study region and meteorological data

The Shallap Glacier (920 S, 7720 W, cf. Fig. ) spans the altitude range 4700–5800 ma.s.l.. It lies in the Cordillera Blanca, which hosts nearly a quarter of all tropical glaciers by area . Precipitation in the region is essentially of convective nature and is tied to the moisture originating from the Amazonian Basin . The Andes mountain chain (reaching > 6700 ma.s.l. in the Cordillera Blanca) divides the wet Amazonian climate in the east from the dry coastal areas in the west e.g.. The map in Fig.  illustrates the control of topography on triggering precipitation and the pronounced changes occurring within short distances.

The Shallap Glacier has been the subject of an intensive field program in recent years. Two automatic weather stations were operated over two distinct and partly overlapping periods: at the glacier surface (July 2010–September 2012, with several gaps) and on the southern moraine (2002–2009 and July 2011 to February 2012). Here, we used the southern moraine data from October 2005 to September 2009 (longest period with complete data coverage). The Unidad de Glaciología y Recursos Hidricos (UGRH) of the Peruvian Autoridad Nacional de Agua (ANA) started surface height change measurements in the ablation zone of the glacier in 2003. From August 2006 to August 2008 (end of data collection), additional measurement points are available (20 ablation stakes in total) with a reading frequency of 14 to 64 days. The average altitudes of the stake points as measured by the UGRH in August 2006 and August 2009 ranges between 4758 and 4824 ma.s.l. For a geographic overview of the stations and stakes see (their Fig. 1).


DownGlacier is an open-source tool programmed in the Python language. It relies on the statistical libraries Scikit-learn and Statsmodels for the regression models, and adds specific SEB/SMB and uncertainty assessment tools. The project repository ( contains the source code, some usage examples and all data and scripts used to generate the plots presented in this paper.

Surface energy and mass balance

The function of DownGlacier is to compute the glacier SEB equation as resolved by most process-based melt models e.g.: SWin+SWout+LWin+LWout+QS+QL+QC+QPS=F, where SWin and SWout are the incoming and outgoing shortwave radiation, LWin and LWout the incoming and outgoing longwave radiation, QS and QL the turbulent sensible and latent heat fluxes, QC the conductive heat flux inside snow or ice, and QPS the penetrating shortwave radiation. An energy flux (W m-2) has a positive (negative) sign when it induces an energy gain (loss) at the surface. The sum of these fluxes yields a resulting flux F, which represents the available energy for melting QM if the glacier surface temperature is at the melting point (0 C). This energy is then converted to melt and added to the other mass fluxes (kg m-2) to compute the climatic mass balance MB: MB=PRCPSolid-QM/lmeltMMelt-QL/lsubliMSubli+MSubs, where PRCPSolid is solid precipitation, lmelt and lsubli the latent heats of melting and vaporization/sublimation/deposition, and MSubs the subsurface mass fluxes (subsurface melt largely due to QPS and refrozen melt water in snow or at the ice surface).

SWin, SWout, LWin, LWout, QS, QL, QC, QPS, PRCPSolid, MSubs in Eqs. (1) and (2) are the fluxes that are downscaled based on calibration time series provided by the process-based model (see Sect. ). The other variables are called diagnostic variables and are computed from the downscaled fluxes. Note that Eqs. (1) and (2) are valid at any instant, but not for averaged time periods. To compute the SEB/SMB from monthly averaged fluxes we assume that F is always equal to QM and that lsubli is equal to the enthalpy of sublimation (and not vaporization). The effect of these approximations is generally small and depends on temperature and therefore on altitude (see Appendix  for details and Sect.  where we present a method to mitigate the errors related to these assumptions).

Downscaling strategy

The purpose of the downscaling procedure is to find a function f such as the following: Y=f(X)+ε, where Y is the variable to be predicted (predictand), X=X1,X2,,Xp are the explanatory variables (predictors), and ε is a random error term

ε comprises an irreducible error (the part of variability in Y which cannot be explained by X) and a reducible error (originating from the error made when approximating f).

. In principle, the downscaling process is similar to any statistical learning problem . The term downscaling refers to the fact that, in this case, the predictors X are extracted from large-scale atmospheric data (reanalysis data of atmospheric model output, representative of a large space) and the predicted variables Y are the glacier SEB/SMB fluxes, representative of a local state .

DownGlacier proposes several options to define f but for this study we use the so-called Lasso “least absolute shrinkage and selection operator”, which performed best in our cross-validation tests. The Lasso is a shrinkage method developed to overcome some of the problems of least-squares regression such as over-fitting and the high sensitivity to the predictor subset. By penalizing the fitting of the regression coefficients by a factor λ, it shrinks some coefficients and sets others to zero . The resulting model is still a linear combination of multiple predictors (as for stepwise regression), but the chosen coefficients are not the same as with standard least-squares. Lasso is widely used in statistical learning problems across disciplines but it is not (yet) used much in climate downscaling studies despite of encouraging results e.g.. Due to the novelty of this approach in a glaciological context, we provide more elements about Lasso in Appendix .

Calibration SEB/SMB data

The SEB/SMB data used to calibrate and validate the downscaling model was generated using an updated version of the process-based model developed and described by previously applied at Shallap glacier by . Air temperature, humidity, wind speed, global radiation and total precipitation measured at the southern glacier moraine serve as model input for the period October 2005 to September 2009. The model calculates the SEB/SMB as formulated in Eqs. (1) and (2) at hourly time steps and for the entire glacier surface on a 50m×50 m grid.

The distributed SEB/SMB time series are aggregated to monthly values and averaged spatially over altitude slices of 50 m height (the altitude slice at 4750 ma.s.l. for example being the average of the grid points in the 4750–4800 m range). The uncertainty associated with this reference data has to be assessed independently using the measurements at the ablation stakes: the annual RMSE (root mean square error) of the reference MB was estimated to 0.76 m w.e. (water equivalent) for the year 2007 and 0.88 m w.e. for the year 2008. We kept the more conservative estimate of 0.88 m w.e. and scaled it by a factor of 1/12 (following the normality assumption) to obtain a monthly RMSE of 0.25 m w.e. month-1. This value will be taken into account and added to the downscaling error when analyzing our results at 4750 ma.s.l. (where most ablation stakes are located). For other altitudes and for the intermediate SEB variables no uncertainty assessment can be realized: this is discussed in more detail in Sect. .

Atmospheric predictors

The selection of the predictor set is crucial for the accuracy and stability of the downscaled time series e.g.. For this study, we chose to select the predictors out of the nearest grid point of the atmospheric reanalysis data set, which is a common approach in downscaling studies e.g.. It prevents dubious correlations with remote indices and ensures that the local glacier features are indeed related to the local atmospheric state (from the coarse data set perspective). Another more practical advantage of this procedure is its systematic and objective aspect.

In a first step, we chose to use ERA-Interim reanalysis data provided by the European Centre for Medium-range Weather Forecasts (ECMWF), which proved to be most accurate for downscaling purposes in the region . We chose to follow a similar approach as in and previously smoothed the ERA-interim fields using a spatial Gaussian filter with σ=1 (approximately a 3×3 box average), reducing the noise related to the arbitrary choice of the nearest grid-point. The starting predictor set consists of 27 predictors at the surface and at selected pressure levels in the atmosphere (Table ). The sensitivity of our results on the chosen predictor set and the reanalysis data set is assessed in Sects.  and .

The 5-month running average of Niño 3.4 sea surface temperature anomalies (SSTA, base period: 1981–2010) and Niño/Niña classification after . The threshold values (-0.4 and 0.4 K) are indicated by black broken lines. The length of each period (in months) is indicated at the bottom. Note that here and throughout the paper the SSTAa time series have been shifted forward by 3 months to account for the lagged response of the atmospheric conditions at Shallap Glacier.

Selected predictors from the monthly ERA-Interim fields.

Name Description Levels (Surface or hPa) prcp Precipitation sfc ssrd Short-wave downward radiation sfc tcc Total cloud cover sfc t Temperature 650, 550, 450, 350 rh Relative humidity 650, 550, 450, 350 gh Geopotential height 650, 550, 450, 350 u Zonal wind component 650, 550, 450, 350 v Meridional wind component 650, 550, 450, 350 ws Wind speed 650, 550, 450, 350
Uncertainty analysis

The uncertainty associated with our method has two major sources: the calibration of the SEB/SMB time series (see Sect. ) and the downscaling procedure itself. To a certain extent, the later can be assessed using cross-validation e.g.. Here we use a variant of the leave-one-out cross-validation in which a five-elements window is removed iteratively from the calibration set. The model selection and calibration procedure is repeated 48 times (one for each month), providing new “penalized” time series obtained by 48 different models, each of them unaware of the 5 months period surrounding each data point. The period of ±2 months was chosen based on the predictands properties: the lag-3 autocorrelation values of the predictands at 4750 ma.s.l. were all close to 0, the highest being MSubs with an r2 of 0.08. Refer to Appendix  for more details about the cross-validation procedure.

Variables statistics (monthly mean and standard deviation), number of selected predictors and out-of-sample cross-validation scores r2, RMSE, RMSEσ (expressed in % of the standard deviation σ) and Brier skill score (BSS) for the downscaled variables and the diagnostic variable MB at the 4750 ma.s.l. altitude slice. The variables Temp (air temperature), VP (vapor pressure), WS (wind speed) and PRCPTotal (total precipitation) are downscaled and listed here for information, but they are not used to calculate MB.

Units Mean SD Npreds r2 RMSE RMSEσ BSS Temp K 1.58 0.39 14 0.78 0.18 0.47 0.82 VP hPa 4.99 0.71 11 0.93 0.19 0.27 0.78 WS m s-1 2.48 0.63 11 0.83 0.26 0.42 0.59 SWin W m-2 208.21 20.31 12 0.54 13.93 0.69 0.50 SWout W m-2 -112.22 30.65 12 0.58 19.99 0.65 0.47 LWin W m-2 276.84 16.19 8 0.92 4.71 0.29 0.73 LWout W m-2 -309.55 2.39 11 0.74 1.23 0.51 0.63 QS W m-2 13.90 6.27 12 0.78 2.92 0.47 0.46 QL W m-2 -10.65 10.55 8 0.87 3.86 0.37 0.62 QC W m-2 8.90 4.94 7 0.92 1.39 0.28 0.73 QPS W m-2 -24.14 13.12 12 0.74 6.65 0.51 0.67 MSubs kg m-2 month-1 -109.90 81.51 12 0.62 50.74 0.62 0.64 PRCPSolid kg m-2 month-1 96.13 68.34 16 0.73 35.77 0.52 0.42 PRCPTotal kg m-2 month-1 143.37 97.95 17 0.80 43.73 0.45 0.21 MB4750 kg m-2 month-1 -427.51 294.72 0.69 162.97 0.55 0.69

For the evaluation of the model skill we used standard metrics computed from the cross-validation: coefficient of determination r2, root mean square error (RMSE), and the Brier skill score (BSS), defined as follows: BSS=1-MSEdsMSEref, with MSEds and MSEref being the mean square error of the downscaling and of the reference model, respectively. The reference model is the leave-one-out monthly average of the calibration time series (i.e. the value for June 2007 is the average of the June values in 2006, 2008 and 2009). A positive BSS evaluates the capacity of the downscaling model to make better predictions than taking the “climatology” (a perfect model having a BSS of 1).

Time series of the reference data set (black), full downscaling model (dotted blue) and out-of-sample cross-validation (red) during the calibration period. Shown are the variables air temperature, solid precipitation, net shortwave radiation, and MB at 4750 ma.s.l.

ENSO classification

For the ENSO events classification we use the sea surface temperature anomalies (SSTA, relative to the base period 1981–2010) in the Niño 3.4 region obtained from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC). We follow the classification recommended by : El Niño (La Niña) occurs if the 5-month running average of Niño 3.4 SSTA exceeds 0.4 K (falls below -0.4 K) for 6 months or more (Fig. ). This results in 192 neutral (47 %), 95 Niño (23 %) and 121 Niña months (30 %). The same index was also chosen by and for similar purposes. In addition, we shifted the SSTA time series by 3 months (as suggested by and confirmed by our own correlation analyses) to account for the lagged response of the MB anomalies at Shallap glacier. We assess the sensitivity of our results to the choice of other ENSO indexes and lag values in Sect. .

Checking the physical consistency of the downscaled variables. Scatter plots of reference (2005–2009, red) and downscaled (1980–2014, blue) time series at 4750 ma.s.l. (a) and (b): sensible heat flux vs. wind-speed and air temperature. (c) and (d): latent heat flux vs. vapor pressure and wind-speed. (e): albedo vs. solid precipitation. (f) represents the scatter plot of the diagnostic mass balance (computed from the several downscaled variables) vs. the downscaled mass balance (1980–2014).


We first present the results of the downscaling at the 4750–4800 ma.s.l. altitude slice which is located in the ablation area of the glacier. Here we have the highest confidence in the calibration time series and in their uncertainty estimates. From now on we use the term “year” as replacement for “hydrological years” (1998 for example referring to the period October 1997 to September 1998). For simplicity, we refer to the 4750–4800 m a.s.l. altitude slice with the shorter “4750 m a.s.l.” and add a 4750 subscript to the MB variable name wherever judged necessary to avoid ambiguities.

Downscaling results Validation

A summary of the cross-validation results is presented in Table . All downscaled variables have a positive BSS, the highest (0.81) for Temp and the lowest (0.21) for PRCPTotal. The most determinant variables for MB4750 are the short-wave variables SWin and SWout as well as PRCPSolid. Their scores are generally lower than those of other variables but they are satisfying considering the complex nature of the precipitation and surface albedo processes. We discuss the conditions for the successful downscaling of SWout in Sect. .

The example of PRCPTotal illustrates the importance of considering all scores when assessing the model results. RMSEσ of PRCPTotal is lower than that of PRCPSolid, meaning that the model is working satisfyingly. However, the inter-annual variability of PRCPTotal is smaller and results in an efficient reference model that penalizes the BSS. PRCPSolid, in turn, has a higher inter-annual variability (tied to the temperature variations, see Fig. ) better caught by the downscaling model than by the reference climatology.

Figure  shows a comparison between the reference and modeled time series of Temp, SWnet, PRCPSolid and MB4750. As expected, the full-model time series are closer to the reference than the cross-validation time series. However, the differences between the two are small, which indicates that the chosen predictors and their coefficients are stable regardless of the calibration period. The inter-annual variability is well caught by the model: the MB4750 of the two last years is less negative due to lower air temperatures, higher snowfall and lower short-wave radiation input, for both the reference and the downscaled model. This raises a question: are the downscaled variables consistent with the glacier surface processes and can we interpret them in the same way as we would do it with a physical model?

Physical consistency of the downscaled variables

Albedo (ratio SWout/SWin) for example is strongly related to solid precipitation (Fig. e). The downscaled fields reproduce the expected relationship and the spread (related to other factors such as snowfall frequency) but some issues arise: in rare cases (6 %) the downscaled precipitation is slightly negative and for two cases the albedo is close to the high value of 1. This is due to the linear nature of the downscaling algorithm and is a known issue of statistical models, which are not aware of the physical properties of the downscaled variables. In DownGlacier the precipitation values are clipped to zero but we decided to leave the short-wave variables unchanged, since the occurrence of extreme low/high albedo are rare and correspond to a realistic atmospheric forcing (low/high solid precipitation). For other expected relationships such as the relation between the turbulent fluxes QS and QL with wind speed and vapor pressure (Fig. a and c), the downscaling produces realistic fields as well. Since monthly air temperature is always close to 0 and therefore close to the surface temperature, the sensible heat flux is more dependent on wind speed than on air temperature (Fig. d). The latent heat flux is also well correlated with wind speed (Fig. e), but this is also due to the peculiar conditions at Shallap glacier, where wind speed and vapor pressure are well correlated (not shown).

The physical consistency of the MB with the downscaled fluxes is ensured by the computation of the SEB/SMB budget (Eqs. 1 and 2) and is an advantage of DownGlacier over other approaches downscaling the MB only. Interestingly, the direct downscaling of MB4750 is slightly less accurate than the diagnostic method (BSS of 0.65 instead of 0.69) but we obtain a downscaled MBDown extremely close to the diagnostic MBDiag (Fig. f). Two reasons can explain this encouraging result. First, while the SEB/SMB equations are additive in nature, the non-linear processes are resolved beforehand by the process-based model and then mimicked by the downscaling procedure. Second, this result can be seen as an implicit confirmation that the downscaling procedure has “caught” all the SEB/SMB variability that can be explained by the large scale atmospheric fields. The remaining uncertainty is related either to missing information and errors in the large-scale atmospheric data or to the simplifying nature of the downscaling functions. In Appendix , we describe these functions and discuss their interpretation.

Time series of the computed monthly mass balance at 4750 ma.s.l. The grey shading represents ±RMSE (including the RMSE of both the downscaled and the reference data). The calibration period is outlined by the green vertical bars.

Annual cycles of mass balance, air temperature, solid and total precipitation at 4750 ma.s.l. for each Niño (red) and Niña (blue) periods (note that some annual cycles are incomplete). The average of all neutral months is drawn in black (error range omitted for clarity).

Influence of ENSO on the SEB/SMB fluxes

The downscaled monthly MB4750 is mostly negative for the period 1980–2013 and displays a pronounced intra- and inter-annual variability (Fig. ). A few months have a positive MB4750, all of them occurring during Niña periods. Inversely, the most negative events occur during Niño periods. We will now investigate if we can detect a systematic pattern by building composites of the Niño and Niña periods.

Niño/Niña composites

The annual cycles of MB4750, temperature, snowfall and total precipitation for each of the seven Niña and eight Niño periods are shown in Fig. . Despite of a large spread between individual years we distinguish a clear signal with below (above) average MB4750 during Niño (Niña) periods, confirming the findings of previous studies e.g.. The largest differences between Niño and Niña occur between December and May, although the ENSO signal remains visible towards the end of the year for both MB4750 and temperature. Temperature displays a larger spread for Niño than for Niña years, with temperature anomalies up to +2K for extreme months. We also distinguish a Niño  dry/Niña  wet signal in total precipitation during the wet season, but it is less pronounced, with at least 2 wetter than average Niño years. Snowfall displays a clearer tendency, all Niña years being above the average from December to May and several Niño years having almost no snowfall at 4750 m a.s.l. during the same period. Due to this large spread it would be difficult to define a “typical” Niño or Niña period. In fact, our attempts to go beyond the visual interpretation by testing the statistical significance of these differences were unfruitful because of the large standard deviation between years, the small number of composites, and the variables' RMSEs.

Annual cycles of the surface energy (top) and mass (bottom) fluxes at 4750 ma.s.l. Left: 1980–2014 average. Right: average difference between the Niño and Niña composites. The numbers of values for the Niño (red) and Niña (blue) composites are indicated at the bottom of the plots. Note the different y axis ranges and that none of these differences is significant in the statistical sense because of the large standard deviation between years combined with the small number of composites and the variables' RMSE.

As for most glaciers, the energy budget at the ablation area of Shallap is dominated by the radiation fluxes (Fig. ). The annual cycle of the energy budget is rather flat with an average annual energy gain of 60Wm-2. The minimum of SWNet in February/March is combined with a smaller energy loss by LWNet, while during the dry season LWNet and QL inversely compensate the high SWNet. The turbulent fluxes are more important during the dry season, the sensible (latent) flux being constantly positive (negative) throughout the year. The resulting SMB cycle follows a bimodal pattern: the first peak (less negative MB4750) in February is due to a combined effect of a smaller energy gain and a maximum of accumulation, while the second peak in July is related to the stronger energy sink by QL.

The composites presented on the right panel of Fig.  (note the different y axis ranges) provide useful information about the factors that possibly control the differences between Niño and Niña periods. The differences in SEB are overwhelmingly dominated by the short-wave balance, the other fluxes playing a smaller role (higher energy loss by LWNet in January/February of Niño years, smaller energy loss from April to June by QL). The increase in SWNet is directly related to a snowfall deficit, mostly between December and May. At least in the ablation zone of the glacier, the picture seems to unequivocally follow the pattern described for other tropical Andes glaciers e.g..

Annual average of the computed MB4750 and of Niño 3.4 SSTA shifted forward by 3 months (note the inverted right y axis). The shading represents ±RMSE (including the error of both the downscaling and the reference data sets).

Out-of-sample cross-validation scores for selected variables and for each 50 m altitude slice at Shallap Glacier. Left: RMSE expressed in % of the standard deviation σ. Right: Brier skill score (BSS).

Inter-annual variability

The individual Niña and especially Niño years are highly variable regarding their signal on MB4750 since the events differ in strength, but how well is the Pacific SST related to MB4750? Figure  displays the annual averages of MB4750 and of Niño 3.4 SSTA. The relationship is striking throughout most of the period with a coefficient of determination of r2=0.8 (p10-5) which reduces to r2=0.67±0.06 (p10-5) when taking the RMSE into account

Mean and standard deviation of r2 computed from 10 000 random realizations of MB4750±RMSE.

. The latter figure is more realistic because the downscaled MB4750 represents the deterministic part of the “real” MB4750: local and random processes which are not caught by the downscaling procedure are more likely to weaken the relationship than enhance it. We distinguish two periods with a slightly weakened relationship: 1991–1995 and 2002–2005, which are the exact same periods described by (their Fig. 9) or by (their Fig. 9, for 1991–1995).

Distributed SEB/SMB: exploring the potential and limitations of the procedure

In the previous section we limited our analyses to 4750 ma.s.l. where the accuracy of the reference SEB/SMB model could be assessed thoroughly using external data (ablation stakes), leading to a robust error assessment of the entire modeling chain. Using DownGlacier for the entire glacier is straightforward, at least in practice: the distributed SEB/SMB data are averaged over altitude slices of a fixed range (here 50 m, see Sect. ) and each variable/slice is downscaled independently. The cross-validation scores are computed in the same way (Fig. ). The scores of PRCPSolid and LWNet are stable for all altitudes (PRCPSolid is getting closer to PRCPTotal as temperature lowers). The score of SWNet, however, is highly variable and determines the accuracy of MB at lower altitudes where it is the largest energy input. In the 4800–4900 altitude range the capacity to downscale SWNet worsens with a maximum RMSEσ=0.83 (the reasons for this low accuracy are discussed below). After 5000 ma.s.l., SWNet becomes less relevant for the energy budget and has less impact on the model skill. The BSS scores are low at high altitudes due to uncertainties in the estimation of the energy available for melting (QM). To address this issue, we can introduce a correction factor c which guarantees that the average downscaled QM is equal to the average calibration QM. The usage of this factor can also be cross-validated (MBCor in Fig. ): it has a positive impact from 4950 m a.s.l. upwards, and is particularly efficient at high altitudes. However, it has a negative impact at low altitudes where it constrains the variability of the model. Altogether, this correction factor has only a very small impact on our conclusions, and we decided to use the non-corrected time series for further analyses.

Time series of the reference data set (black), full downscaling model (dotted, blue) and out-of-sample cross–validation (red) during the calibration period. Shown are the mass balance time series at the 4850, 5450 and 5700 ma.s.l. altitude slices and averaged over the whole glacier.

Figure  shows that the negative BSS at 5450 ma.s.l. is related to exceptional errors during the dry season where unrealistic negative MB is predicted for a few isolated months, an issue that is strongly reduced when using MBCor (not shown). At 5700 ma.s.l. the problem is weaker and the predictions are satisfying. At 4850ma.s.l., however, we reach the limits of the downscaling procedure: abrupt MB variations from one month to another are not reproduced and the model's attempts to catch those result in bad predictions for the second half of the period. These jumps from positive to highly negative values are directly related to the surface conditions of the glacier; snow cover is a function of previous snowfall and melt (information which is not available in the reanalysis data). Our efforts to account for this monthly persistence by including lagged predictors were unsuccessful: increasing the number of predictors also increased the noise, and it is probable that the linear nature of the Lasso method is not able to cope for these complex effects.

The conditions for the successful downscaling of SWNet are found for example at 4750 ma.s.l. where snowfall and melt occur within days, or at higher altitudes when there is a permanent snow cover. It is therefore probable that the current version of DownGlacier will perform poorly on e.g. mid-latitudes glaciers, where persistent effects can be determinant for the annual MB e.g.who showed that spring snowfall conditions on a Tibetan glacier regulate the entire annual mass balance due to the albedo feedback. In these cases the purely statistical approach used here should be complemented by physical albedo models.

The altitudes between 4850 and 4950 m a.s.l. with the highest RMSE represent approx. 20 % of the glacier area and are responsible for most uncertainties of the MB variability

These errors however have no systematic impact on the average specific MB, thanks to the property of statistical models to preserve the mean.

. Despite of these errors occurring around the location of the equilibrium line, the MB averaged over the entire glacier (specific MB) is well predicted by the model (RMSEσ of 0.5 and BSS of 0.64, time series in Fig. ). The reasons for these good scores are the reliable downscaling in the lower parts of the glacier (which account for the majority of the mass loss) and of the accumulation processes in the upper parts.

These encouraging results call for an analysis of the model's glacier-wide predictions for 1980–2013, presented in Fig. . We arbitrarily multiplied the cross-validation RMSE by a factor 2 to account for unknown errors in the upper parts. We see that the SSTA MB relationship is less strong for the glacier average, with a deterministic correlation of r2=0.51 (p<10-5) diminishing to r2=0.38±0.08 (p<10-3) when taking the RMSE into account. These values are lower than at the 4750 ma.s.l. altitude, and are closer to the correlation values found by . As for most tropical glaciers , Shallap glacier has large accumulation areas where precipitation falls as snow most of the time. Total precipitation is less sensitive to ENSO events than temperature: at 4750 ma.s.l. the deterministic correlation of snowfall with Pacific SSTA is r2=0.75 (p<10-5) while it is 0.39 (p<10-3) for total precipitation.

Results of the sensitivity experiments for MB4750: skill scores RMSE (mm w.e month-1) and BSS, linear trend (m w.e yr-1) and correlation with Pacific SST Anomalies (detrended, without taking RMSE into account). Trends and correlation values adjoined with a * indicate significance at p<0.01.

Notes RMSE BSS Trend SST r2 Reference Ref Reference run 162.97 0.69 0.06 0.81* Algorithm SPcor Stepwise, partial correlation 195.51 0.55 0.10 0.78* SRMSE Stepwise, RMSE 195.18 0.55 0.08 0.83* SPC Stepwise, principle components 234.80 0.35 0.00 0.80* L8fold Lasso: 8-fold crossval 167.78 0.67 0.06 0.81* Predictors Lag1 + Lag 1 predictors 188.34 0.58 0.07 0.81* hPa Levels: 300, 400, 500, 600, 700 186.18 0.59 0.02 0.80* NoTemp No temperature 179.97 0.62 0.05 0.78* NoSfc No surface variables 186.37 0.59 0.04 0.79* NoRH No relative humidity 203.92 0.51 0.02 0.80* Reanalyses ERA Levels: 300, 400, 500, 600, 700 186.18 0.59 0.02 0.79* CFSR Levels: 300, 400, 500, 600, 700 146.86 0.74 -0.18* 0.59* MERRA Levels: 300, 400, 500, 600, 700 183.42 0.60 -0.12* 0.77* NCEP Levels: 300, 400, 500, 600, 700 212.76 0.46 -0.02 0.56*
Sensitivity analyses

We test the robustness of our conclusions by presenting the results of a series of sensitivity experiments grouped in three categories: downscaling method, predictor set and reanalysis data (Table  and Fig. ). In a fourth experiment we analyze the sensitivity of our results to the choice of the ENSO index and lag value.

Sensitivity to the downscaling method

In this study we have used the Lasso, but other traditional regression methods include stepwise regression or principle component regression e.g.. We test several variants:

SPcor: after an iterative selection, all predictors have a partial correlation significant at the p=0.01 value;

SRMSE: predictors are added and removed until the inner cross-validation RMSE reaches a minimum;

SPC: same as SPcor but run with the 11 most important principle components (explaining 98 % of the total variance);

L8fold: same as the standard run (Lasso) but with the λ parameter selection based on 8-fold cross-validation (instead of 4-fold).

All methods have a lower skill than the reference run (Table ), with an increase of the RMSE by about 20 % for SRMSE or SPcor and up to 33 % for SPC. As shown by the correlation values and the time series in Fig. , the sensitivity of the results to the chosen method is marginal with respect to the MB4750 variability (with the exception of the principle components regression which shows a different trend and smaller variability). The Lasso is only weakly sensitive to the method chosen to select the penalization parameter. Stepwise regression methods show a stronger sensitivity to the choice of the stopping rule, such as the significance of the partial correlation (not shown).

Same as Fig.  but for the glacier averaged MB. The shading represents ±2 RMSE. Note that this mass balance does not account for changing glacier geometry.

Computed annual MB4750 for each category of the sensitivity experiments (see Table  for the description of the experiments). The period 2005–2009 is the calibration period and thus with the smallest spread.

Glacier averaged contribution (x axis) and correlation (y axis) between annual Niño 3.4 SSTA and each SEB (left panel) and SMB (right panel) flux for 1980–2013. Note that the error bars are related to the uncertainty of the downscaling only (not of the calibration data) and that these results do not account for changing glacier geometry.

Sensitivity to the predictor choice

We run five experiments with another predictor set. Predictors were either removed (temperature, relative humidity or surface variables), changed (pressure levels) or added (with a lag of 1 month). Here again, all experiments result in lower downscaling skill but lead to similar conclusions. Surprisingly, omitting temperature has the smallest effect on the model skill and has only a relative impact on the correlation with SST. This means that large parts of the temperature signal can be found in the other predictors. This is not the case with relative humidity: omitting this predictor has the strongest negative impact on the prediction skill. Further predictor denial experiments lead to inefficient models and are not shown here.

The Lag1 experiment is particularly instructive with respect to the skill of the downscaling procedure: doubling the number of predictors by adding the lagged ones results in a lower out of sample cross-validation skill by increasing the noise and the chance for Lasso to select false-positive predictors. This is more likely to occur with short calibration periods and might also be one of the reasons for the increase of RMSE of 15 % when changing the predictor pressure levels (hPa experiment). Indeed, it is possible that the MB4750 variability is more related to the levels chosen for the reference run (350, 450, 550 and 650 hPa) than the new ones, but it is more likely that the hPa experiment increased the noise and made the job for the Lasso more difficult.

Sensitivity to the reanalysis choice

Several studies e.g. have discussed the sensitivity of the downscaling results to the choice of the reanalysis products used for calibration. Here we test three additional data sets chosen for their historical significance (NCEP/NCAR R1) or for their relative novelty and sophistication (ERA-Interim, MERRA and CFSR)

Refer to the acknowledgements for data access and acronym description.


NCEP: NCEP/NCAR R1 reanalysis belongs to the most widely used reanalysis data sets. It is of coarser resolution (2.5) and is one of the oldest systems still operating to date.

MERRA: Modern Era Retrospective- Analysis for Research and Applications reanalysis from the NASA is of higher resolution (0.5) and belongs to the so-called “third generation” of reanalysis products (including ERA-Interim and CFSR).

CFSR: NCEP Climate Forecast System Reanalysis , also of higher resolution (0.5).

The sensitivity of the downscaling to the various reanalysis data sets is larger than to the other experiments (Table ). The three most recent reanalyses have comparably higher skills than NCEP, and CFSR shows the highest skill overall (higher than the reference run). Unlike for the other experiments, the differences in skill are accompanied with differences in trends and correlations with Pacific SST. As shown in Fig. , the time series still display a strong covariability but disagree for certain years (e.g. 1985, 2010). The low correlation of NCEP with SST is attributed to a smaller variability and a lower accuracy, while the lower correlation of CFSR is quite unexpected. Overall, the most striking differences concern the trends of the time series, from negative for MERRA and CFSR to statistically insignificant for ERA and NCEP. Looking for the reasons of these disagreements is beyond the scope of this study, but we can learn from this analysis that if the ENSO MB4750 relationship is quite stable regardless of the method and data used, it is less the case for trends or for the predicted absolute MB4750. In Appendix , we use NCEP/NCAR R1 to analyze the relationship for the longer period 1950–2013.

Sensitivity to the ENSO index

In this study we used the Niño 3.4 index which is widely acknowledged as a good indicator for ENSO variations e.g. and was also used by for their study in the Cordillera Blanca. However, other studies found that the Niño 1+2 index had a higher predictive skill for Chacaltaya Glacier's MB in the outer tropics with a lag of 2 and 4 months, respectively. Recently, the Multivariate ENSO Index MEI, was presented as alternative to the purely SST based indices such as Niño 3.4. In Table , we test if our results at 4750 m a.s.l. are sensitive to a change to the Niño 1+2 and MEI indices. It appears that Niño 3.4 and MEI both have very high correlations with MB4750, with a maximum at lag 2 and 3, respectively (which was to expect since both indexes are highly covariable during the study period). The Niño 1+2 however has a lower predictive skill, which maximizes at lag 2. Most of these differences, however, are not significant in comparison to the uncertainty estimates of our computed MB.

Summary and discussion

Based on four years of distributed SEB/SMB at Shallap glacier, we calibrated a statistical model linking each individual SEB/SMB flux to local atmospheric variables extracted from reanalysis data. We presented a new open-source tool developed for this purpose and applied it first to the ablation area and then to the entire glacier surface. The downscaled time series (1980–2013) revealed a strong ENSO footprint on glacier MB, a result consolidated by subsequent sensitivity analyses. If individual Niño and Niña years can vary in intensity, the control of Pacific SSTA on MB appears to be constant throughout the period as shown by the significant anti-correlation between annual MB and Niño 3.4 SSTA. The mechanisms of this control could be quantified thanks to the decomposition of the SEB/SMB into individual fluxes (a summary of the SSTA SEB/SMB correlations is provided in Fig. ). Niño (Niña) events imply an increase (decrease) of air temperature leading to a higher (lower) snowfall altitude and thus to an increase (decrease) of the net short wave radiation supply. This effect is enhanced by a further precipitation deficit (excess) during Niño (Niña) years. The influence of ENSO is therefore stronger at lower altitudes but it remains detectable at higher elevations through changes in total precipitation. We find a small influence of ENSO on the sensible heat flux but no significant influence on net long-wave radiation or sublimation.

Coefficient of determination (r2) between the computed annual MB4750 and various ENSO indices, for lags between 0 and 5 months.

Lag 0 1 2 3 4 5 Niño 1+2 0.44 0.47 0.49 0.47 0.43 0.36 Niño 3.4 0.68 0.76 0.79 0.80 0.79 0.77 MEI 0.71 0.77 0.80 0.79 0.77 0.72

Our results are in accordance with our current understanding of the ENSO/glacier relationship in the Central and Tropical Andes e.g.. However, we find a stronger SSTA MB relationship than described in and cannot confirm their exceptional years (1983 and 1994). This discrepancy could be explained by the different methods used to retrieve the MB, but it is likely that the relationship is also modified by regional and altitudinal differences: analyzed the MB for the sum of several glacierized catchments of the western part of the Cordillera Blanca, while our results are valid for Shallap glacier only. If ENSO's influence on temperature is regionally stable in the Andes, its influence on precipitation is less known and highly variable. A recent study by found a Niño/wet signal in the Cordillera Vilcanota south of the Cordillera Blanca which, if confirmed, could counterbalance the albedo effect described here. A bit further south, reported opposite ENSO effects within short distances, with a Niña/dry signal in the Zongo valley lowlands and a Niña/wet signal on the higher Altiplano. While our study aimed at identifying the ENSO footprint on glacier MB, future studies should focus on the atmospheric mechanisms of this relationship and assess its latitudinal and altitudinal stability.

A major source of uncertainty in our method is the short period available for calibration, preventing us to develop more sophisticated models (for example including distant predictors or seasonally dependant downscaling functions). Fortunately, the four years used here are dynamically variable and contain neutral and Niña periods, as well as a few months with SSTA above the Niño threshold. Our uncertainty estimates computed with cross-validation are robust, but they remain high and prevent more detailed analyses of individual events. In particular, the sensitivity analyses showed that if the MB variability is persistent between the experiments, the absolute values and trends can vary considerably. This is especially the case when changing the reanalysis products, an issue that should be kept in mind when carrying out long-term glacier modeling studies.

Nevertheless, DownGlacier proved to be a versatile and efficient tool to extend existing SEB/SMB series in time, provided that there are no persistence effects or heavy auto-correlation in the calibration time series. These conditions are met for monthly values in the tropics, were we expect DownGlacier to bring helpful insights on decadal to centennial glacier variability. For mid-latitude glaciers covered with seasonal snowpack it will be necessary to include non-linear and persistent effects (for example by adding surface albedo parameterizations). The major obstacle to such enhancements is the lack of long and reliable SEB/SMB time series for calibration: here, combined statistical and dynamical approaches might help to complement the otherwise irreplaceable glacio-meteorological observations.

<sec id="App1.Ch1.S1.SS1"> <title>Solving the SEB/SMB equations on monthly averages

On monthly averages, the ice surface is practically never at the melting point and the equality F=QM does not hold true. DownGlacier implements a simple test to assess this error: in a “perfect downscaling” experiment, the downscaled variables (bold in Eqs. 1 and 2) are set to their calibration values and the skill of the diagnostic variables is assessed using the usual statistical scores that show the error related to the averaging only. Figure  displays the RMSEσ of the perfect downscaling experiment for all altitude slices of the glacier along with monthly air temperature. For most parts of the glacier the error is close to 1 %, but reaches 14 % at the 5000 ma.s.l. altitude slice where the air temperature is closest to 0 C. For conditions close to the melting point a substantial part of the energy residual F will not be converted to melt but will heat the ice. At colder temperatures, F will be close to 0 and less relevant. This error is small in comparison to the other uncertainties of the method (see Sect. ) and is negligible at the altitude of 4750 ma.s.l.

The Lasso

Extensive treatment of the Lasso method can be found in and in statistical textbooks e.g.. Here we provide some elements about basic principles of the method. First, we recall that for a multiple linear regression problem with p predictors the objective is to find the parameters β0βp such as Y=β0+β1X1+β2X2++βpXp, where Y is the variable to predict (vector of n observations y1yn) and X1Xp are the predictor vectors (also of length n). The free parameters β0βp are usually fitted by minimizing the residual sum of squares RSS: RSS=i=1nyi-β0-j=1pβkxij2. This method becomes unstable when the predictors are collinear (anti-correlated predictors will lead to very high parameter estimates) and is subject to over-fitting when p becomes large. The role of stepwise regression algorithms is to select meaningful predictors in order to keep p small and prevent these problems. The Lasso, in turn, can fit a model containing all original p predictors (thus generalizing the predictor selection problem) using a technique that constrains the coefficient estimates by minimizing the quantity i=1nyi-β0-j=1pβkxij2+λj=1p|βj|=RSS+λj=1p|βj|, where λ0 is a penalization coefficient which has to be determined separately. This penalization has the advantage to prevent over-fitting by shrinking the coefficients and to force some of the coefficients to be equal to zero (predictor selection) when λ is large. λ is usually chosen among an ensemble of predefined values which are tested one by one: the value leading to the smallest cross-validation RMSE is selected

DownGlacier uses the coordinate-descent algorithm implemented by Scikit-learn, with a 4-fold cross-validation.


Results of the “perfect downscaling” experiment (see Appendix ): RMSEσ and Temp for each 50 m altitude slice at Shallap Glacier.

Box plots of the Brier skill score (BSS) of each validation step for the Lasso and the stepwise downscaling algorithms. Each box represents a population of 14 scores (one for each downscaled variable listed in Table ).

The advantage of Lasso over stepwise regression is shown by our sensitivity analyses (Sect. ) and is also illustrated in Fig.  (see next Appendix for details). The improvements over the other methods is not overwhelming in this case but Lasso proved to be much more stable (and fast) in the early exploration stages of this study, when we considered many different predictor combinations. With very large p, stepwise regression showed high variance and high sensitivity to the predictor set (low out-of-sample cross-validation scores) while Lasso remained robust.


The principle of cross-validation it to hide information to the statistical model by calibrating it with a smaller subset of the data and testing its predictions against the remaining (unseen) subset. DownGlacier realizes two automatic steps to choose the downscaling function f: selection (s) and calibration (c). In the case of Lasso, (s) consists of choosing the penalization parameter λ using in-sample cross-validation and (c) consists of fitting the penalized coefficients. In the case of stepwise regression, (s) consists of choosing a subset of the predictors and (c) consists of fitting the least-square coefficients. As discussed early by e.g. , it is crucial to evaluate both steps (s) and (c) in the cross-validation procedure.

The need for out-of-sample cross-validation is not always obvious (when model selection is based on partial-correlation for example) even if all automated predictor selection methods should be cross-validated. The following way to select the predictors is more obvious: the predictors might be added and removed iteratively for their capacity to reduce the cross-validation RMSE. We provide an example of using this stepwise algorithm in Fig. , which displays the scores of three different validation steps: full model (selection s and fit f based on all available data), cross-validation (selected only once based on all available data but fitted 48 times using cross-validation) and out-of-sample cross-validation (selected and fitted 48 times using cross-validation). We see that the algorithm is able to reach “better” cross-validation scores than the Lasso. However, several of the predictors chosen by the algorithm are very likely to be added by chance rather than for their real predictive skill, as shown by the out-of-sample cross-validation scores.

Interpretation of the downscaling functions

The number of predictors selected by the Lasso varies between 7 and 17 (Table ), which is larger than the number of predictors we would obtain with stepwise regression algorithms. Indeed, the Lasso might choose a linear combination of correlated predictors instead of a single predictor with less predictive skill, by shrinking less significant coefficients to values close to zero. Table  presents the six most important predictors and their coefficients (normalized in %) for each downscaled variable. Some of the functions allow a direct and meaningful interpretation: LWin for example is strongly related to relative humidity. It is also coherent that higher temperatures imply a more negative LWout. Similarly, the first two predictors of QS are wind components, and QL is controlled by relative humidity to a large extent. PRCPTotal is a function of relative humidity and total cloud cover and is also inversely proportional to the zonal wind flow at 650 hPa, which is consistent with the assumption that most of the moisture in the Cordillera Blanca originates from the Amazon Basin. We should however not over-interpret these functions, as shown by some unexpected results (e.g. prcpsfc positively correlated to SWin). Covariability (positive and negative) between predictors confuses the interpretation, and choosing another predictor set can produce very similar predictions despite of distinct downscaling functions (see Sect. ).

Relationship between SSTA and MB for 1951–2013

The NCEP/NCAR R1 products are available from 1948 onwards and the SSTA data from 1950 onwards, allowing us to analyze the SSTA  MB4750 relationship for the period 1951–2013 (Fig. ). In general, the downscaled MB4750 does not correlate as well with NCEP/NCAR R1 as it does with other reanalysis products (Table ). The relation is clear throughout the 60 years but with lower correlations values for the 1951–1980 period (“deterministic” r2, i.e. without RMSE and without detrending)

1951–2013: r2=0.45 (p<10-5)

1981–2013: r2=0.56 (p<10-5)

1951–1980: r2=0.42 (p<10-3).

The lower pre-1980 correlations are mostly due to several exceptionally low MB4750 values during La Niña and Neutral events during that period. The reasons for these differences are speculative but some discrepancies are likely to be explained by deficiencies in the reanalysis products before the introduction of satellite data in 1979. This effect is particularly strong in the Southern Hemisphere, where observational data are sparse e.g..

Same as Fig.  but using NCEP/NCAR R1 reanalysis and for the period 1951–2013.

The six most important predictors and their coefficients (normalized in %) for each downscaled variable at 4750 m a.s.l.

1 2 3 4 5 6 Temp +20t650 -13rh450 +12rh650 +12t450 -8rh350 +7gh450 VP +67rh550 +9t550 +6gh350 -6ws550 +5v550 +4v350 WS -25u550 -19v450 -13rh450 -12u650 +9gh650 +8v650 SWin -29rh450 +20prcpsfc +20ssrdsfc -7v350 -7u650 -6ws650 SWout -25rh450 +21t450 -11v650 +10ws650 -9rh650 +9gh350 LWin +60rh550 +12v450 +7rh450 +7t450 +7t650 -4u350 LWout -33rh550 -18t450 -14t650 +10v650 -9v450 -5gh450 QS -22u550 -18v450 -13rh550 -8ssrdsfc -8rh450 +8v650 QL +42rh550 +21u550 +15v450 -11ws650 +4ssrdsfc +3t550 QC -72rh550 -16v550 -4rh450 -2v450 +2ws550 -2t550 QPS +35rh450 -19prcpsfc +10rh650 -8ssrdsfc +6v350 -6gh350 MSubs +31rh450 -18prcpsfc -12t450 -10ssrdsfc -7t650 +6v350 PRCPSolid +14rh350 +13tccsfc -13u650 -11t450 +9rh450 -6ws650 PRCPTotal +14rh350 -14u650 +11tccsfc -8ws650 -7t450 +7u450

F. Maussion developed DownGlacier, analyzed the results and wrote the paper, based on an original idea by M. Großhauser. W. Gurgiser did the SEB/SMB model runs and prepared the calibration data. W. Gurgiser, M. Großhauser, G. Kaser, and B. Marzeion participated in field work. All authors continuously discussed the results and developed the analysis further.


This study was funded by the Austrian Science Fund (FWF), projects P22443-N21 and I900-N21. ERA-interim data were obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) at MERRA data were obtained from the Goddard Earth Sciences Data and Information Services Center at NASA ( CFSR data were obtained at the Research Data Archive at the National Center for Atmospheric Research, Computational and Information Systems Laboratory ( NCEP Reanalysis R1 data were obtained at the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, ( We used B. Bookhagen's TRMM 3B31 rainfall climatologies available at We are grateful to the developers and providers of the open-source tools ConfigObj, IPython, Matplotlib, NetCDF4, Numpy, Pandas, Python, Scipy, Scikit-learn, Seaborn and Statsmodels. We wish to thank two anonymous referees and the editor T. Bolch for their detailed and helpful comments. Edited by: T. Bolch

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