Interactive comment on “ Estimating glacier and snowmelt contributions to stream flow in a Central Andes catchment in Chile using natural tracers ”

Samples were taken manually and automatically. Manual samples were filtrated in field and stored in insulated bags to keep a low temperature in the samples during fieldwork. In the lab, samples were stored at 5◦C. Samples recorded for cation analysis were dropped with nitric acid (10ml acid/1lt sample) to lower pH and ensure a complete dilution thus avoiding possible precipitation of minerals. Automatic samples were filtered in the lab. The automatic samples were collected each 15 days, which sets the upper limit on the time any sample remained unfiltered. Bicarbonate analyses were not carried out in the automatic samples due to the long time between the collection and the filtration. However bicarbonate was measured in manual samples; likewise, charge balances were made in manual samples to ensure the quality of data. The charge balances in automatic samples were estimated using the bicarbonate present in manual samples made in the same day of automatic collector sampling. Our analysis shows that charge balances remain acceptable even if samples were not filtered the same day of collection. Two principal reasons explain this: first, the storage box for the automatic collector was located in a shaded and well ventilated zone in order to avoid heating of the water samples; second, all sample bottles were treated with a small quantity of mineral oil, which avoids any contact between the water and air inside the bottle. In the reviewed manuscript we will further discuss the charge balances and tritation process applied to our samples.


Introduction
Like many semi-arid regions in the world, the extra-tropical region of South America 20 depends on snow and glacier melt from a nearby mountain ridge (in this case the Andes Cordillera) for its water supply. Although it has been well established that under future climate scenarios Andean watersheds should experience significant changes in the amount and timing of seasonal runoff (Casassa et al., 1998;Marengo et al., 2011;Vicuña et al., 2010), the precise nature of these possible changes is still difficult to 25 describe because of large uncertainties pertaining, among other things, the relative 8950 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | time-varying contribution of snow and glacier melt as well as subsurface sources to river flow (Ragettli et al., 2013). Without this knowledge, most hydrologic modelseven those that are physically based -suffer from over-parameterization and can be subject to large predictive errors. In this work, we combine hydrochemical and isotopic information about hydrologic components in a semi-arid, high-elevation, moderately 5 glaciarized Andean watershed in order to discriminate the most likely sources to the observed river hydrograph at different times during a season; our ultimate goal is to inform future modeling exercises in order to better constrain hydrologic predictions under global change scenarios.
Hydrograph separation (HS) using natural tracers can be a useful tool to quantify and describe source evolution in order to enhance hydrological conceptual and numerical models. Many hydrograph separations studies have considered chemical tracers (Heppell and Chapman, 2006;Mul et al., 2008), natural isotopes (Liu et al., 2008) or a combination of both (Merot et al., 1995;Meriano et al., 2011;Ladouche et al., 2001). A review of isotopic hydrograph separation was performed by Klaus and McDonnell 15 (2013) wherein they remark on the spatial variability of isotopic signals as well as on the potential for using both stable water isotopes, and not only one, in order to glean deeper insights on the hydrological function of a basin. Many studies have shown the importance of soil water as a source of runoff during a rainfall event (Laudon and Slaymaker, 1997;Ogunkoya and Jenkins, 1993;Tan et al., 2008;Soulsby and Dunn, 2003). 20 Other HS-studies carried out in mountainous sites have noticed the importance of snow and glacier as primary sources generating runoff (Liu et al., 2004;Cable et al., 2011;Hirose and Marshall, 2013). Notwithstanding these advances, significant uncertainty remains associated to most methods of hydrograph separation, which can be separated in "statistical" and "model" 25 uncertainty. In this case the first can be due by inadequate sampling in remote areas and fractionation for automatic, un-attended sampling during long periods while the model uncertainty stems from the different options of conceptual hydrologic model applied (Moore and Semmens, 2008;Joerin et al., 2002).

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Some effort has been made in the last few years in order to describe better the contribution from snow-and glacier melt to streamflow in Andean basins (Gascoin et al., 2011;Pellicciotti et al., 2008;Ragettli and Pellicciotti, 2012;Peña and Nazarala, 1987). These works show variable glacier contribution depending on climatic factors, with glacier contribution being more relevant in dry years than in wet years due to the 5 diminished influence of the seasonal snowpack on the former. Other studies on source contribution have been carried out in alpine environments (Martinec et al., 1982;Liu et al., 2004) showing the importance of glacier-and snow-melt in runoff generation and the evolution of stream flow. Glacier ice comprise one of the most important water reservoirs in semi-arid regions, and in dry water years it can supply a high per- 10 centage of summer runoff. A description of glacier discharge and its importance as a water reservoir can be found in Jansson et al. (2003) and more recently in Baraer et al. (2012). Glacier melt contribution has been studied using different approaches. Hydrologic models have enhanced the understanding of glacier melt and the evolution of its contribution (Hannah and Gurnell, 2001;Verbunt et al., 2003). Usually, studies of 15 glacier mass balance show meteorological and stream flow data (Kaser et al., 2003;Hirabayashi et al., 2010;Yu et al., 2013;Wagnon et al., 1999), information used to describe the glacier evolution during different season and under different climatic patterns. Other studies have directly measured river flow in alpine regions where water is generated primary due to glacier melt (Singh et al., 2006;Mingjie et al., 2013;Hodgkins, 20 1998).
Despite these efforts, large uncertainties remain with respect to the hydrologic role of glaciers in remote regions, in no small part due to the inadequate observational networks monitoring this specific aspect of the hydrologic cycle (Pellicciotti et al., 2013). Therefore, novel data collection techniques and improved interpretation tools for infor-25 mation of different origin/type can provide useful insights toward process understanding and improved modeling. In this study we aim at discriminating between glacier and seasonal snowpack melt contributions to streamflow in a high elevation semi-arid Andean watershed. Our analysis improves the understanding of the isotopic and chemical evolution of a typical Andean headwater catchment, and builds upon the work by Ohlanders et al. (2013), who document the contribution of different sources to river flow using isotopic data measured in different sections of the river, in the snowpack, and rainfall. Now we complement that study by incorporating solute data recorded during the same period and applying multiple models to analyze their performance for hy-5 drograph separation. Specifically, we aim at: (i) comparing the information provided by a long-term water solute dataset, obtained at quarterly intervals and a one-year, high resolution dataset obtained specifically for purposes of this research; (ii) develop a methodology for hydrograph separation in Andean watersheds with emphasis on identifying glacier-related hydrologic sources to flow; and (iii) estimating the glacier-10 related contributions to annual and seasonal flow in a representative Andean catchment, during a dry year.
In this work, we propose three models to analyze the contribution of different sources to river flow. First, hydrograph separation is performed using the basic end-member mixing analysis (EMMA), with a previous step of Principal Component Analysis (PCA) 15 for reducing data dimensionality. This model is named Mixing PCA model (MPCA). Because extreme component sources are successfully identified, this analysis is able to reproduce the stream water chemistry variability (Christophersen and Hooper, 1992) and hydrograph separation is therefore feasible. A sub-model performed using the same principles that MPCA was built only upon stable water isotope data, and here 20 is called Isotopic Model (IM  Parnell et al., 2010), but for hydrological applications fewer examples exist; Cable et al. (2011) documented source contributions on a glacierized basin using a non-informative hierarchical Bayesian model. Our approach incorporates the knowledge acquired in past studies to the model, and updates the probability density functions (pdf) of relative contributions as new data becomes available. 10 The MPCA and IBM models cannot be applied continuously along the water year because of two factors: precipitation of ionic tracers and ephemeral presence of snow as a source throughout the catchment. Conversely, the Isotopic Model can be applied continuously, and at a lower cost thanks to the decreasing expense of stable isotope laboratory analysis. 15 2 Study area and available data

Study area
The Juncal at Juncal River basin is a 256.2 km 2 catchment within the Valparaiso region, located in the Andes of central Chile 60 km northeast from Santiago, Chile's capital city. The climate is semi-arid with cold winters and warm, dry summers. The mean annual 20 temperature in 2011 at the outlet of the catchment was 9.9 • C. Annual precipitation is about 600 mm at an elevation of approx. 3000 m a.s.l. (Dirección Meteorológica de Chile, 2001) and it occurs mainly in solid phase. The geology of the basin in the eastern site is dominated by limestone, calcite, and calcareous sandstone, which are easily weathered, influencing the chemistry of the river and resulting in high concentrations 25 of sulphate and calcium ions. Volcano-sedimentary strata dominate the local lithology 8954 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | in the central and western site of the basin, with an important presence of dacitic, pyroclastic and basaltic rocks. Older sedimentary strata compose the eastern portion of the basin, and in some areas on the northeastern reaches, natural gypsum deposits have been identified and exploited commercially.

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Streamflow data are available for the "Juncal at Juncal" stream gauge, which is operated by the Chilean Water Agency (Dirección General de Aguas, DGA). This station defines our study catchment outlet, and has been active since 1970. Rating curves are updated regularly, and historical monthly flows range between 1.0 and 30.0 m 3 s −1 .
Air temperature, radiation and precipitation are measured at two meteorological sta- 10 tions in the vicinity of the basin, namely "Hornitos" and "Riecillos". The former is operated by the Department of Civil Engineering at U. de Chile, and is located in the outlet of the catchment; the latter is operated by DGA and is located approximately 20 km west from the catchment outlet. The latter station is the nearest precipitation station of the Chilean water agency and has a longer period of record of precipitation and air 15 temperature.

Water isotope and chemical data
DGA has recorded river flow chemical data at the catchment outlet since 1996, reporting instantaneous concentrations of major metals (Cu, Ag, Al, Mg, Ca, etc.), nonmetals (Cl, inorganic N and P, etc.) and some water quality properties like temperature and 20 pH, every three or four months approximately. Between 2011 and 2012, we obtained a series of ad-hoc measurements of water chemical properties including major natural tracers and isotopic composition, aimed specifically at researching the origins of river flow. River water samples were collected at the basin outlet using an automatic water sampler; the sampling frequency varied from two (early spring) to one day (on late 25 spring and early summer), and water samples were analyzed for sulphate, chlorate,

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | calcium, potassium, magnesium, sodium, silica, delta value of deuterium and oxygen 18 (Barthold et al., 2010). Isotopic data was obtained following the methodology documented by Ohlanders et al. (2013). Several fieldwork campaigns were carried out in order to sample water characteristics in various-sized streams within the basin, as well as in rain and the seasonal snowpack between January 2011 and April 2012 ( Fig. 1).

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Two rain collectors were set up on the Juncal basin (The first at the Juncal River Outlet and the second near Juncal Norte glacier) while a third was located in a location outside the Juncal catchment, at an elevation of 2099 m a.s.l. These rain collectors were in place at intervals between September 2011 and April 2012, and as such sampled mostly spring and summer precipitation. Snow samples were collected along a nearby 10 mountain road, in order to study the altitudinal gradient in snow isotopic composition in the range 2200-3000 m a.s.l., as reported by Ohlanders et al. (2013). Also, several snow samples were collected at the Juncal River outlet (2200 m a.s.l.) during the winter season of 2011. 15 All water samples were filtered on site at the time of collection (except samples from the automatic collector which were filtered at the moment of sample retrieval, approximately every two weeks) using a 0.45 µm nitrocellulose filter (Type HAWP04700). After filtration, water for cation analysis was acidified with nitric acid at 4N to avoid mineral precipitation and was stored in high-density plastic bottles to ensure complete dilution. 20 Samples for anion analysis were preserved at 5 • C in the laboratory. Titration was conducted at the Water Quality Lab at the Civil Engineering Department and at the Geochemistry Lab of the Geology Department, both at the University of Chile. Major cations as well as Si were measured by an Inductively Coupled Plasma-Optical Emission Spectrometer (ICP-OES, Optima 7300V, HF version) at the Geochemistry Lab at the Geol- 25 ogy Department at University of Chile and by an Inductively Coupled Plasma Atomic Absorption Spectrometer (ICP-AES, Perkin Elmer Optima 3000) at the Research Analytical Laboratory at University of Minnesota. Both results were compared to ensure 8956 data reliability. Anion concentrations were measured by an ion chromatographer (IC, 861 advanced compact) at the University of Chile and by an ion chromatographer (IC, Dionex model DX-120) at the University of Minnesota. Samples from the automatic collector and manual campaigns were compared to ensure accuracy between on-site, filtered and non-filtered samples. Ionic charge balances were generally less than ±5 %, 5 although for some samples we did observe differences between ±5 and ±10 %. The largest errors were observed for samples from streams with high solute concentrations.

Methodology
As described in the previous section, two different sets of solute data are available. One, here named "DGA", contains long-term (since 1996) data obtained quarterly on solutes only at the basin outlet; the other, available only for water year 2011/12, was recorded at the same site but at a much higher temporal resolution, includes stable isotope information and is complemented with spatially distributed observations of water chemical and isotopical properties. We evaluate the usefulness of these two datasets for hydrograph separation purposes by assessing the fit of the observed data projected 15 onto two different 2-D spaces, constructed with the principal component decomposition of each data set. Subsequently, we estimate the relative source contribution to the daily hydrograph by three alternative models, hereby referred to as: (i) Isotopic model, (ii) Mixing-PCA model and (iii) Informative-Bayesian model. We used principal component analysis in order to reduce the dimensionality of the problem preserving most of 20 the observed variability.

Data comparison and sources
We compared daily data (UChile) against quarterly data (DGA). In this context, data comparison means that we aim to evaluate the information content in each dataset for the purpose of hydrograph separation. In order to achieve this, a Principal Component 25 8957 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Analysis (PCA) was applied on each data set using the same subset of solute concentrations available both in the UChile and DGA data. The data sets were projected onto two 2-D spaces obtained with the dominant eigenvectors from each PCA in order to compare the mixing spaces determined with each data set, using the root mean square error (R RRMSE ) and relative bias (B RB ) as fit metrics. It was accepted that the 5 best data for hydrograph separation was that for which the fit metrics were minimal. The fit metrics were computed as: Where, x i j = raw data in milligrams per liter,x j = mean of each solute,x i j = solute projection in the U space (space constructed with eigenvectors from PCA) and n = number of samples recorded. The subscript "i " and "j " represent the samples and solutes respectively.

Mixing-PCA models
Hydrograph separation was performed using a deterministic method based on solute mass and water volume conservation. The first model is MPCA. All samples were projected onto the orthogonal space defined by the eigenvectors from PCA (U space) and possible sources were identified among glacier, snow and soil, thereby determining 20 end-member sources to be applied in hydrograph separation. Juncal River outlet and end-members were projected onto the U space and the Euclidean distance between the U and S spaces (the space defined by tracer data) was computed in order to evaluate the data fit onto the former. 8958 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | In a three-component model, the hydrograph separation equations are expressed as: (3) Where Q i = flow from source i , Q T = streamflow in the outlet of the basin; numerals indicate sources {1, 2, 3}; superscripts A and B represent generic solutes and f i is the fraction of discharge coming from source i . 10 Moreover, by preserving the information provided by δD and δ 18 O we are able to develop another HS methodology, here referred to as the Isotopic Model. The model still corresponds to a simple mixing equation on two dimensions given by the isotopiconly tracers, but in contrast to other studies, we recognize that both isotopic tracers provide non-redundant information about the evolution of water sources to river flow. 15 By rotating the coordinate system using PCA we are able to infer important hydrologic properties of the system in question; here the dimensionality of the problem is preserved (two tracers), but the rotation clarifies the dynamic behavior of this hydrologic system. 20 The Bayesian framework was established in order to explicitly account for the uncertainty due to measurement errors, model misrepresentation, and parameter estimation by estimating the probability density function of each source's contribution to flow. The aim of the framework is to combine information gathered in previous studies with new data as it becomes available in order to continually update and improve the hydro-25 graph separation model. Compared with the deterministic models described above, the Bayesian approach also enables us to estimate uncertainty bounds on the percentage 8959 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | contribution of each source, and as such provides information useful for characterizing possible weaknesses as well as for guiding data collection strategies for improving the mixing model. The Bayesian model can be described by Eq. (7).

Informative-Bayesian model
5 The vector f q contains the source contribution in each component. The subscript q indicates that q proposed vectors must be generated. The probability p(f q ) represents the prior distribution and p(D Data |f q ) is the likelihood function of observed data given a state of nature (f q ). The denominator is a numerical approximation of the marginal 10 probability, necessary for normalizing the posterior probability p(f s |D Data ). A Dirichlet prior distribution, which is a generalization of the Beta distribution (Parnell et al., 2010), was used in order to satisfy mass balance constraints. The parameters of the prior distribution were calculated using the algorithm presented by Minka (2009) after creating a random one-dimensional normal distribution, representing prior knowledge about 15 each source.
The likelihood was assigned as a multivariate normal distribution, whose dimension 20 depends on the number of tracers selected. The proposed mean and variance were established from random values of f q , considering the mean and variances of the sources (Eqs. 10 and 11) since in this study we apply a simple Bayesian model, as opposed to a more complex model such a Hierarchical Bayesian model (see Cable et al., 2011). We used a simple Bayesian model because given the origin of the available data it is variance of each source in our analysis was directly set from the values measured. We looked for the simplest Bayes approximation in order to make our result as clear and easily reproducible as possible. Fractionation processes were not considered in the analysis, because our data is insufficient to determine the statistical properties of the fractionation of each isotope in all the sources. Fractionation in river water occurs due 5 to contact between the water, atmosphere and soil. The contact between water and the atmosphere generates a continuous isotopic exchange along the river. Moreover, the contact between water and soil is another interface where isotopic fractionation can occur. These processes cannot be studied with our data, and a more detailed sampling should be performed along the river in order to address this issue.
Where m i j is the mean of the j th isotope on the i th source. Because of the complexity of the analytical solution of Eq. (7), we applied a Markov 15 Chain Monte Carlo (MCMC) algorithm in order to find a solution to the Bayesian model. A block wise updating procedure was used in order to find a solution to the Bayesian problem, a generalized multivariate approach of the Metropolis-Hastings Sampling (Steyvers, 2011). The mathematical approach is detailed in Fig. 2 where p is the target density. θ values will form the probability distribution that must be normalized (in 20 our case θ represents the vector containing the fraction of each source, the asterisk designates the proposal and t the step in Fig. 2) and q is the proposal probability. To discriminate if a θ value is selected or not, a comparison between the "α" value and a random "u" value is made.

Temporal covariation of available data
Juncal at Juncal watershed outlet data is shown in Fig. 3 in order to illustrate the evolution of all natural tracers together. In order to better visualize the variations of anions, cations and discharge, data was centered and scaled. We split the data from the au-5 tomatic sample collector in three periods according to streamflow evolution. The first period spans from April to October 2011, when flow is stable in time. The second period is from October to December 2011, when spring melt onset occurs and flow increases rapidly. The last period spans from December 2011 to April 2012, after flow has peaked, and decreases towards fall (April) minima. Figure 3 shows stable, high ion 10 concentrations during fall and winter, changing to lower concentrations during summer and spring. Isotopic behavior is more variable in each season, although relatively constant values can be observed in fall and winter. The highest value is rapidly reached in the middle of October, decreasing to a minimum in mid December. After this, a rapidly variable isotopic signal is observed. More details of this behavior can be found in Oh-

Stream water chemistry
The piper diagram in Fig. 4 shows the chemical composition of samples taken at different sites in the Juncal River valley. Juncal outlet stream samples (Junc-R1) are similar to Navarro Creek (Nava-R1) and Monos de Agua (Mono-R1), which are streams 20 coming from sulphate-calcium facies with high soil influence. Glaciated flow samples (Glac-R1) are less sulfated and more carbonated due to the minimal contact of this water with east-basin type soils. Samples from the western slopes of the valley (West-R1 and R2) are more similar to glacier samples which both are bicarbonate-calcium faces.
High sulphate and calcium concentrations originate mainly by interaction between recorded historically by DGA are located in the same area on the piper diagram, so additional analysis are shown in order to assess the information content of each dataset for HS purposes.

Isotopic characterization of water samples
Data is located in different zones in a δD-δ 18 O plot depending on the season (Fig. 5).

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The displacement between data and the Global and Chilean meteoric water line is due to the high altitude of the source areas (above 3000 m a.s.l. in the Andean Ridgefor further details the reader is referred to Ohlanders et al. (2013). In fall (April-June) and winter (July-September) data is located over the first eigenvector (enriched in Deuterium and slightly depleted in Oxygen 18 delta values). In spring (October-December), 10 data moves "across" the first eigenvector and concentrates toward more enriched values in both isotopes. In summer (January-March), data is depleted in δ 2 H and δ 18 O values, although it is less organized in the δ 2 H-δ 18 O plot. Clark and Fritz (1997)  the measurements lie near the detection limit; the sample cannot be said to be random from a direct inspection of Fig. 5, thus we propose that a seasonal pattern can be discerned.

Dataset information content, number of sources and hydrochemical data
DGA and UChile data sets were compared in order to determine which was more 25 suitable for hydrograph separation. This analysis only included chemical data because 8963 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | DGA does not record water isotopic characteristics. First, two different U Spaces were built by performing PCA on the DGA historical data and on our one-year high-resolution data. Then, we projected both the raw DGA and UChile data onto each of the generated U spaces, and calculated the Relative Root Mean Square Error (R RRMSE ) and Relative Bias (B RB ) for each of the four cases. Our analysis shows that the R RRMSE and B RB 5 are lower or relatively constant when projecting both sets of raw data onto the UChilebased U space Fig. 6. The number of sources needed for reliable hydrograph separation is studied with all the information collected at the Juncal catchment outlet for the water year 2011-2012. Isotope and chemical data is used to perform the analysis, but we neglected 10 solutes that could precipitate, retaining only Cl, SO 4 , Na, K, δ 18 O and δD. However, two difficulties arise in the mixing problem when several tracers are available and the HS is attempted for the entire year. As more solutes are incorporated into the analysis, more end-members will be necessary to characterize the variations in water characteristics (Barthold et al., 2011), and the mathematical solution for the mixing problem will be 15 more complex. The second issue is that an annual analysis of all data recorded is complicated by the fact that several sources are activated at different times during a hydrologic year, a feature not easily incorporated into a mixing-type analysis. In order to simplify the analysis we split the hydrologic year in three parts (Fig. 6). During the fall and winter seasons (April to October 2011) saturation index analysis strongly indicates 20 the potential for solute precipitation, so no hydrograph separation was attempted in this period. Summer (December to April 2012) is characterized by minimal presence of snow over the catchment and some rainfall events that fail to be recorded by the observational network but that leave a trace in the isotopic composition of river water (Ohlanders et al., 2013). It is possible for snowfall to occur above 4000 m a.s.l., melting in a few hours or days. Because of the above, a "pure" snow signal is problematic for endmember mixing analysis. Moreover, although snowmelt could remain in the soil through summer and contribute later to river flow, our data is insufficient to explain fractionation processes in the snowpack, subsurface or on groundwater throughout the season.
PCA was performed on Juncal River outlet data for the spring (SON) and summer (DJF) seasons. In addition, we applied the Hooper approach (Hooper, 2003) in order to identify the number of sources required for hydrograph separation and to evaluate 5 the quality of the mixing space obtained. The eigenvectors and eigenvalues generated by PCA are depicted on Table 1. 2-D residuals plots for potassium, δ 18 O and δD show as light, non-conclusive trend (Fig. 7) suggesting the need for incorporating a new eigenvector. In general, 2-D Residual plots are very well behaved. The 2-D U space explains 78 % of the observed variability, which means that three sources are required 10 to explain river solute variability. By the "rule of 1" (Hooper, 2003), this space is well constructed because the next eigenvector (third) explains only 12 % of the observed variability: a threshold of 16.7 % should be reached for an eigenvector to be included in the reduced space. Samples were projected on a 3-D mixing U space built upon the first three eigen- 15 vectors. Juncal River outlet samples did not show a strong variation along the U1 and U3 axes, whereas possible end-members can be seen from glacier melt, east and west creek, snow and rain (Fig. 8). From Fig. 8 it is possible to identify a pattern in snow, rain and glacier snout river samples on the U1-U3 plane, all with high U2 values. The highest U3 rain values were sampled in summer (highly isotopically enriched as stated by 20 Ohlanders et al., 2013), but other rainfall events recorded in spring are located closer to the origin in the U1-U3 plane, near some of the most enriched snow samples from our dataset. The same altitudinal snow gradient shown by Ohlanders et al. (2013) is seen again in the form of U vectors.

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Mixing-PCA model
Snow covered area is negligible throughout the basin during the summer season, and therefore "direct snowmelt" cannot be a source to flow in this period. In order to differentiate between sources with none or substantial soil contact, we assume here that 5 water coming from the western part of the basin is representative of a "snow" (as opposed to glacierized) end-member. In the western part of the catchment the glacier cover is restricted to small shaded locations and snowmelt is arguably the most important water input. Steep slopes allow only small and restricted aquifers in small, elevated valley floors above 3500 m a.s.l., but their effect on the hydrology of this zone can not 10 be assessed with our current database. Soils are also relatively less weatherable in the western portion, because basaltic, dacitic and pyroclastic rocks are predominant in this area. Therefore, we assume that water coming from the western portion of the Juncal River catchment is a mix of shallow subsurface flow, and direct snow melt. Based on these considerations, we performed EMMA on spring season Juncal outlet data 15 (Fig. 9). The results show that glacierized, snow and east-basin samples surround the Juncal outlet data. The hydrograph separation can be seen in Fig. 10. For summer data we switch to a geographically based hydrograph separation considering east and west soil water from creeks and springs, and glacierized headwater flow. 20 A simple Bayesian model was implemented for spring and summer season data (Fig. 10). Prior information was included from the study of Ragettli and Pellicciotti (2012) and Liu et al. (2004). The former considers discharge as a mix of rainfall, glacier melt and snowmelt, but does not evaluate the influence of soil water. Liu et al. (2004) studied high-elevation basins in the US, using chemical tracers, carrying out separa-reacted and unreacted water. In an attempt to adopt a prior distribution coherent with the sources of the current study we split glacier and snowmelt sources into surface and baseflow components. Since we performed our analysis on spring and summer, both time windows are of interest. In spring the catchment is dominated by direct flow from glacier and snowmelt, as 5 well as reacted water. Liu et al. (2004) estimated that reacted water contributed with 61 and 44 % of streamflow of flow for each of their study basins respectively. We take the ratio of the results from Ragettli and Pellicciotti (2012) and the average of these values (53 %) to create our own prior information.

Informative-Bayesian model
For summer season data, we changed the end-member sources because snow 10 cover is negligible throughout the basin. This led us to assume that soil water should replace the snow signal (i.e. a conceptual model assumption) if we accept that snowmelt should reach the river primarily in the form of subsurface flow.

Isotopic model
Isotopic samples show a characteristic pattern due to activation of different runoff 15 sources throughout the season (Fig. 5). Winter and autumn samples are enriched in δD and depleted in δ 18 O, and are located above the first eigenvector. In spring (and sometimes in summer), samples move below the first eigenvector. We relate snowmelt and the interaction between water and soil matrix with the aforementioned behaviors in Sect. 4.3. In early autumn the basin is free of snow, therefore, discharge at the Juncal 20 River outlet must be from glacier melt or soil water. However, in the fall season, energy inputs are not high enough for us to expect significant ice melt rates. Based on these observations, we associate glacier-snow contribution to the first eigenvector, while the second eigenvector provides information about water with low and high soil interaction. We did not include the last eigenvector in the HS exercise because of a lack of adequate information to define the amount of poorly and highly soil interacted flows when the sample values in the second eigenvector are highest and 5 lowest, respectively. However, the first eigenvector was used to separate the HS in two sources of interest (glacierized and snow sources in Fig. 11).

Final results
The relative contributions to streamflow estimated with the Mixing-PCA and Informative-Bayesian models are shown on Table 2. In spring, glacierized areas are the most important sources, with a contribution of over 50 % of Juncal River outlet discharge. Snowmelt contributes with nearly 20 % and the remaining 30 % can be described as soil water. In summer, glacier contribution increases, surpassing 60 % of the seasonal volume. Water inputs from snowmelt are not important and soil water remains constant in its contribution. The results of the isotopic model indicate that the annual 15 contribution of glacierized and snow sources approximate 62 % and 38 % respectively. The relative contribution of snow and glacier melt to soil water cannot be quantified with the data available for this study. 20 In tracer-based hydrograph separation studies it is very important to verify that solutes used as tracers are conservative. We used saturation indexes (SI) to identify non-conservative solutes and to evaluate minerals precipitation in the river. Using the Phreecq computer package (Parkhurst and Appelo, 2013), we studied solute precipitation over anhydrite, calcite, dolomite and gypsum minerals as a function of water 25 8968 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | temperature and pH at different locations within the studied catchment. Based on the observed water temperatures, we assumed a constant temperature of 10 • C in the Juncal River outlet, 8 • C for higher elevation sub-catchments and 2 • C for the glacieroriginating river. Usually in our data, precipitation of calcite and dolomite occurs during low discharge periods over Junc-R1. Conservative mixing is not guaranteed in the Juncal River throughout the study period. We detected non-conservative behavior in the concentration of calcium, sulphate, carbonate and magnesium, expressed as precipitation of anhydrite and gypsum. Therefore, care must be exercised when performing HS, and we chose to apply this method only during spring and summer seasons, when samples have negative or near zero saturation index values. Given the objective of this research, namely estimating glacier contributions to flow during spring and summer, this decision seems justified 15 and assures a small effect of mineral precipitation on the overall conclusions stemming from our work.

Selection of space dimension
Samples in Fig. 8 show different U value composition for the same source in different seasons. The pattern suggests that as snow is deposited higher in the basin, its 20 U3 values are lower and become more similar to the characteristic of glacier-snout samples. On the other hand, rainfall, which in this basin occurs mostly during summer months, has high U3 values. Therefore, U3 allows us to infer that precipitation (solid or liquid) coming from summer storms is more enriched and is situated above basin outlet samples in the U3 direction. Conversely, wintertime rain/snow show lower val-25 ues in the U3 direction. The importance of this lies in that a more complex HS can be performed. The analysis by Hooper (2003) notes some difficulties in 2-D hydrograph separations. Candidate end-members do not fit the base of the data because all end 8969 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | members have similar U3 base values, but it can be seen that high altitude snow shows lower U3 values. Nonetheless, when plotting all the potential end-members in the 3-D space together with the Juncal outlet data, we observe that it is not possible to explain the entire range of variability based on the available end-members. Therefore, we attempt to perform a hydrograph separation by retaining only three end-members, in 5 a two-dimensional U space.

General discussion on the mixing models
The Mixing-PCA model allows us to visualize trends in the data, but also to distinguish sources. Understanding the relative contribution of sources to river flow, it is possible to enhance conceptual models and better describe factors determining river flow variabil-10 ity. If many end-members have been identified and more than one group can be used to carry out a hydrograph separation, the selection of the best group will depend on the sources that need to be identified, on the Euclidean distance from the raw samples to the projection in the U space (Christophersen and Hooper, 1992) and on how the end members surround the cloud of observed river flow composition points. Since only 15 a limited number of sources were identified in this study, we did not perform any particular method to select them. Nava-R1 were selected over Mono-R1 samples as base flow because it was seen in an autumn field trip that most river water was originating from soils at this time of the year (springs, moraine, etc.). We solve our model using six tracers, eliminating non-conservatives ones based on the previously described SI 20 analysis. With a PCA we performed a 3-source hydrograph separation using all tracers.
The Informative-Bayesian model was applied on the same period as the Mixing-PCA model after performing a principal component analysis. Its main advantage is that it can provide uncertainty estimates on the relative contribution to streamflow from hydrologic sources, as well as an indication on how different data can contribute to diminish this uncertainty. On a practical level, the IB Model, unlike the MPCA model, can find a solution to the mixing problem even if there are streamflow samples lying outside the space defined by the end-members: the Monte Carlo sampling algorithm is able to approximate these samples, but the modeled values will always lay within the end-member region. The acceptance of these solutions will depend on parameters "u" and "α" (see Fig. 2). Figure 12 depicts a typical 2-dimensional space in a hydrograph separation model. In a Mixing-PCA model, point B will have a higher contribution from source 3 and 5 a lower contribution from the other sources. But point A cannot be described for a set of f i , and must therefore be projected onto the line that links sources 2 and 3. The Bayesian model searches the solution for f i in a different fashion. Point A does not need to be projected to the edge of the cloud of points. The governing equations in the Bayesian approach are the same as for the Mixing-PCA model (Eqs. 3, 4 and 5), 10 so the search for the solution will be carried out inside the triangle defined by the endmembers. However, the solution won't be exact, since a set of f i capable of reproducing the value A in terms of the three end members does not exist. Accordingly, probabilistic estimates of source contribution approaching zero must be studied carefully, because of the possibility of obtaining a feasible but biased solution due to the impossibility of 15 representing the river sample by the candidate set of weights or fractions.
The Bayesian model is capable of finding a solution for multiple sources (f i , i = {1, 2, . . . , n}) in a reduced space. The points around "D" in Fig. 12 indicate the sampling using MCMC. This sample can be obtained with many sources maintaining the constraints given by Eqs. (8) and (9). The acceptance of the candidate solution will be 20 determined by a probabilistic parameter. In the case of the Mixing-PCA model, this cannot be achieved because the problem is under-determined, and many solutions are feasible. On the other hand, if the problem is over-determined with many tracers, the Bayesian approach is capable to find an approximation, unlike the Mixing-PCA model. However, a Bayesian approach is capable of finding an approximation. The error will 25 be given by the distance between the river outlet sample in the tracer space (S space) and the geometrical space constructed with the end-members. It is probable that many feasible solutions will be rejected in the latter case, and the solution will be biased. Rather than running the model without any consideration about the cloud of points and 8971 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the geometrical space constructed with end-members, it is appropriate to visualize the problem in order to avoid a biased and out-of-bounds solution.
The isotopic model only uses δD and δ 18 O as tracers, which allows us to use this model throughout the hydrologic year. The model is based on the assumption that water is affected by isotopic fractionation produced by two factors: (i) interaction with 5 rock at low temperatures and (ii) between liquid and solid water phase.
The first idea stems from the notion that "fractionation between rock and water results in an enrichment of δ 2 H and a depletion of δ 18 O" (Clark and Fritz, 1997). However, two conditions are necessary to observe such fractionation, (i) an important rock reservoir with very low water-rock ratios and (ii) geological time scales, because of very low 10 rates of exchange between water and rock. Enrichment factors of ε 18 O of 27 ‰ and ε 2 H of −60 ‰ have been reported by Clark and Fritz (1997). Variations over isotopic concentration in our data are very low between seasons in comparison to those values. Many springs in the basin are present during the entire dry season, and it is therefore probable that water interacts with soil for some months. However, the changes account 15 for only 5 ‰ in δ 2 H and for 1.5 ‰ in δ 18 O. The standard error of the analysis accounts for 1.3 and 0.2 ‰ in δ 2 H and δ 18 O respectively. Hence Juncal River outlet isotopic change between seasons is near the error margin. Our assumption is that water interacts with rock for a short period, sufficient to be modified by fractionation. However, this assumption must be verified with further research. 20 The second idea that justifies our model is supported by findings by Liu et al. (2004), who recognized that snowmelt changes its isotopic composition during the season resulting in an enrichment of δ 18 O due to a depletion of δ 18 O in the liquid water because of fractionation between liquid and solid phases. DeWalle and Rango (2008) show δ 18 O value increases in all cases during the melt season. A similar behavior has been 25 observed in the stream flow in Alaska during snowmelt (Cooper, 1998). We associate the first eigenvector with variation between glacier and low altitude snow because "glacier" samples (this is, water samples obtained in the river at the glacier snout) turned out to be the most depleted and show the lowest U1 (first eigenvector) values, whereas snow samples were more enriched respect to the basin outlet data, and showed the highest U1 values. The second eigenvector, which may be interpreted to describe reacted water, also displays interesting feature variations in time. In fall and winter, samples are depleted in δ 18 O and relatively enriched in δD, just as happens when water interacts with the soil matrix and fractionation is the main 5 isotopic process. Spring samples show the opposite pattern, associated mainly to enriched snowmelt due to isotopic fractionation within the snowpack produced by high melt rates. However, the information available isn't sufficient to perform hydrograph separation in the second eigenvector due to the fact that extreme values in the second eigenvector don't represent absolute values in the amount of reacted and unreacted 10 water.

Conclusions
This study documents a hydrograph separation exercise aimed at estimating the hydrological role of glaciers in a high elevation, Andean watershed in Central Chile during a dry water year (2011/12). Water isotopic and chemical characteristics were sampled 15 at high temporal resolution at the basin outlet, and these observations were complemented with information from several locations within the basin, each representing a distinct hydrological feature. Long-term water quality data recorded by the Chilean Water Directorate were assessed in terms of its potential to inform tracer-based hydrograph separation studies. This first analysis showed that water quality data recorded in 20 a short-term experimental design is richer, if not overwhelmingly so, than long-term information, providing a better base from which extract end-member sources in a rapidly changing hydrologic system. Although not evaluated here, the relatively modest discrepancies in fit statistics between reduced spaces obtained with short and long-term data suggest that small adjustments in the experimental design of operational water 25 quality data retrievals could increase their value for hydrologic research objectives. This research also demonstrated the capability of combined isotopic and solute information for informing mixing models for hydrologic research in mountain environments. Because of the temporal variability of snow cover, we propose different models for different times of the year, with emphasis on spring and summer months, when the watershed is highly "active", hydrologically speaking. We were successful in reducing the 5 dimensionality of the problem by rotating the system of reference and reducing the variation space to at most three directions, using principal component analysis. A Bayesian version of a mixing model provided uncertainty bounds on the relative importance of each source, and it was found that collected data from the 2011/12 water year narrowed the expected error of our estimates from that expected from the prior estimates 10 based on recent literature. Based on our end-member source analysis, we were able to identify different sources for spring and summer seasons: direct-snow, soil-influenced and glaciarized (i.e., associated with a highly glaciated subcatchment) sources could be identified during spring (September-December), whereas glaciarized and east/west soil sources were identified for summer, when snow has disappeared from the basin. 15 During 2011/12, the Juncal river watershed experienced very dry conditions, with annual flow on the 8th decile and with winter precipitation having a probability of exceedance of 83 % measured at the Riecillos rain gage. For these conditions, both the EMMA and the Bayesian models yield very similar estimates of source contribution, with glaciarized sources contributing as much as 51-55 % of the seasonal flow in 20 spring. Snow direct runoff accounted for 19-25 % of seasonal flow during the same season, and subsurface sources contributed 20-30 % to spring flow. During summer, the contribution from glaciarized sources increased to 58-66 % of seasonal flow, with the remaining runoff coming from subsurface sources. At the annual level, the isotopic model estimation was that 62 and 38 % of flow could be associated with glacial 25 and snow sources, respectively. This result must be interpreted with care, because the available data is insufficient for estimating the interaction of glacier and snow melt with subsurface reservoirs at an annual aggregation level.
Further research is required to refine this methodology and to incorporate results such as those presented here in hydrologic modeling exercises. Here, were use the term "glaciarized" to refer to water coming from the outlet of a small sub-basin covered by glaciers in more that 60 % of its surface area. However, this term does contain the signal of snow accumulated over the glacier and in the adjacent slopes. Future field 5 designs should sample directly the ice surface, in order to obtain isotopic characteristics associated with superficial ice-cores. Also, the altitudinal variation in isotopic snow properties was sampled at a rather limited range, and higher elevation snow properties may suggest different interpretation of isotopic flow characteristics. Finally, we were unable to obtain direct samples of subsurface water. Future experiments should consider 10 wells dug in valley bottoms, which would allow for an integrated view of the subsurface behavior of relevant aquifer systems in mountain catchments, in terms of isotopic, chemical and hydrologic variables. Hydrol. Process., 17, 403-416, doi:10.1002/hyp.1132, 2003 Wagnon, P., Ribstein, P., Kaser, G., and Berton, P.: Energy balance and runoff seasonality of 10 a Bolivian glacier, Global Planet. Change, 22, 49-58, doi:10.1016Change, 22, 49-58, doi:10. /S0921-8181(99)00025-9, 1999.

If u≤α
Proposal accepted