Modeling Modern Glacier Response to Climate Changes Along the Andes

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Journal of Advances in Modeling Earth Systems

REVIEW ARTICLE Modeling modern glacier response to climate changes along 10.1002/2015MS000482 the Andes Cordillera: A multiscale review

Key Points: Alfonso Fernandez 1,2,3 and Bryan G. Mark1,2 Models allow process understanding and supplement existing data 1Department of Geography, The Ohio State University, Columbus, Ohio, USA, 2Byrd Polar and Climate Research Center, on Andean glacier changes The Ohio State University, Columbus, Ohio, USA, 3Department of Geography, Universidad de Concepcion, Concepcion, Variety of approaches are identified, but their application does not seem Chile to follow spatial pattern Deficit of continental scale studies precludes global to local linkages Abstract Here we review the literature preferentially concerned with modern glacier-climate modeling of glacier change trends along the Andes. We find a diverse range of modeling approaches, from empirical/statistical models to relatively complex energy balance procedures. We analyzed these models at three different spatial scales. First, Correspondence to: we review global approaches that have included the Andes. Second, we depict and analyze modeling exer- A. Fernandez, [email protected] cises aimed at studying Andean glaciers as a whole. Our revision shows only two studies dealing with glacier modeling at this continental scale. We contend that this regional approach is increasingly necessary

Citation: because it allows for connecting the ‘‘average-out’’ tendency of global studies to local observations or mod- Fernandez, A., and B. G. Mark (2016), els, in order to comprehend scales of variability and heterogeneity. Third, we revise small-scale modeling, Modeling modern glacier response to ﬁnding that the overwhelming number of studies have targeted glaciers in Patagonia. We also ﬁnd that climate changes along the Andes Cordillera: A multiscale review, J. Adv. most studies use temperature-index models and that energy balance models are still not widely utilized. Model. Earth Syst., 8, 467–495, However, there is no clear spatial pattern of model complexity. We conclude with a discussion of both the doi:10.1002/2015MS000482. limitations of certain approaches, as for example the use of short calibration periods for long-term modeling, and also the opportunities for improved understanding afforded by new methods and techniques, Received 20 MAY 2015 such as climatic downscaling. We also propose ways to future developments, in which observations and Accepted 17 JAN 2016 models can be combined to improve current understanding of volumetric glacier changes and their climate Accepted article online 21 JAN 2016 Published online 23 FEB 2016 causes.

1. Introduction Glaciers result from climatic and topographic conditions that define a dynamic equilibrium between accumulation and ablation. Thus, the volume of any given glacier depends on the amount of snow that nour- ishes the accumulation zone, the rate of mass loss due to melting, and the characteristics of the underlying lithology that partially controls the ice flow [Cuffey and Paterson, 2010]. In this context, a detailed understanding of glaciers as indicators of climate changes requires employing a variety of techniques to account for such multifaceted controls, for instance snowpits and stakes to monitor accumulation and ablation rates [Rivera et al., 2005], remote sensing to map changes on glaciers’ shape [Poveda and Pineda, 2009], and numerical models to simulate the behavior of glaciers according to a range of past and future climatic scenarios [Roe and O’Neal, 2009]. Currently available observations of glacier changes show generalized shrinkage that is linked to a global trend of temperature increase [Ohmura, 2011; Marzeion et al., 2014]. However, this global increase in temperature is not positively correlated to glacier volume loss everywhere, which underscores the importance of regional and local factors that may modify the impact of changes detected in the majority of observations. A good example is the positive mass balance that some Norwegian glaciers showed between 1980 VC 2016. The Authors. and 2000, which led to frontal advance [Chinn et al., 2005; Nesje et al., 2008]. Those changes are thought This is an open access article under the terms of the Creative Commons to have resulted from increased precipitation as a consequence of strengthened westerly flow, as well as Attribution-NonCommercial-NoDerivs the onset of a period of lower temperatures [Chinn et al., 2005]. Such apparently anomalous glacier behavior License, which permits use and testifies to the complex relationship between glaciers and climate, whereby global-scale forcing like trends distribution in any medium, provided in temperature and precipitation may be modified by local factors impacting glacier mass balance and the original work is properly cited, the response time to climatic perturbations. This attests to the need for compiling databases that account for use is non-commercial and no modifications or adaptations are local factors, such as topoclimatic conditions, in order to understand the processes leading to glaciers’ volu- made. metric fluctuations, including the temporal scale in which changes in climatic elements (e.g., temperature

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 467 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

and precipitation) occur [Kuhn et al., 1985; Roe, 2011; Pedersen and Egholm, 2013]. Thus, compilation efforts such as the Global Terrestrial Network of Glaciers (GTN-G), established during the 1990s, are invaluable sources of observations of glacier state, including mass balance, outlines, and thickness, among others [Zemp et al., 2009]. Such organized structures for compiling and delivering data (see Haeberli [1998] for a detailed historical description of how these efforts have been organized since 1894) allow scholars to rapidly and accurately evaluate the quality of available records and the need for new ones [e.g., Braithwaite, 2002; Pfeffer et al., 2014]. On the contrary, no similar compilation currently exists to comparatively assess the approaches and results of glacier modeling studies, excluding those in Antarctica and Greenland. In fact, the glacier community has only recently begun to perform intercomparison studies of modeling (GlacierMIP, see http://www.climate- cryosphere.org/activities/targeted/glaciermip). This suggests that we need more progress within the scien- tiﬁc community to produce a uniﬁed source of glacier modeling approaches. In order to contribute to a better assessment of glacier modeling approaches, here we review studies dealing with modeling of glacier mass balance and related indicators such as the equilibrium line altitude (ELA) in the Andes. Outside Antarctica, the Andes concentrate the largest glacier surface area in the Southern Hemisphere [Pfeffer et al., 2014]. Yet among all major glacierized regions, the modern (twentieth century) Andean cryosphere is one of the least comprehensively studied, featuring a low density of observations Zemp et al. [2008], compared to the longer tradition of paleoglacier research in the region, which has con- tributed to understanding the complexity of glacier-climate interactions at millennial scales [Vuille et al., 2008a; Rodbell et al., 2009].

1.1. The Observational Record in the Andes and the Role of Modeling The modeling of glacier surface mass balance and volumetric changes, as consequence of fluctuations in climatic elements, has been facilitated by recent enhances in computing power, process-based studies, and availability of data at the global scale. The latest modeling studies have expanded earlier simple sensitivity analyses to simulations of glacier volumetric changes, assessment of climate drivers, and the consequences of glacier change [e.g., Marzeion et al., 2012]. But glacier models have also been employed to fill gaps in mass balance observations [Vuille et al., 2008b], understand topoclimatic controls responsible for observed trends in glacier parameters such as the equilibrium line altitude (ELA) [Cook et al., 2003] and, in the case of inverse modeling, to reconstruct temperature trends from glacier length records [Leclercq and Oerlemans, 2012]. The best source of information about glacier mass balance is measurements taken in the field. Also known as the glaciological method, this technique utilizes a series of stakes and snowpits to record ice/snow surface lowering, or ablation, and surface thickening, or accumulation, at annual or biannual scales [Cogley et al., 2011]. Further measurement accuracy is achieved when snow density and ice displacement are recorded (more details on the method can be found in Benn and Evans [2010]). Therefore, direct mass balance monitoring programs are key to understanding the relationship between glacier mass balance and climate changes [Braithwaite, 2002]. In the Andes, mass balance programs are scarce, and most of them provide short time series. Figure 1a demonstrates that, of approximately 27,500 glaciers represented in the Randolph Glacier Inventory (RGI) [Pfeffer et al., 2014], only one glacier has been continuously measured for more than 30 years (Echaurren Norte, Chile) while most of the other field programs cover less than 10 years. Over the last decade, newly established programs display a wide regional distribution (Figure 1a), improving the potential to sample glaciers located in different Andean climates. Nevertheless, the main issue is the lack of long-term time series, since most mass balance programs began during the mid-1990s, and some of the earlier ones have gaps and/or were abandoned after a few years of measurement [e.g., Ames and Hastenrath, 1996a]. Remote sensing is another technique with unique advantage to capture several glacier characteristics. The most common application is the use of aerial photographs and multispectral satellite images to delineate glaciers at different dates. Although a complete list of these studies is beyond the scope of this contribution, the reader is directed to recent reviews [Rabatel et al., 2013; Pellicciotti et al., 2014] for details. Remote sensing has also been utilized to build digital elevation models (DEMs). When two or more DEMs of different dates are subtracted, calculated differences represent glacier thickness changes [e.g., Fernandez et al., 2010;

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 468 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

Figure 1. Location maps of studied glaciers along the Andes using relative size of dark gray circles to depict numbers with data from the current version of the WGI. (a) Length of the time series of glaciers currently monitored with the glaciological mass balance method. The Echaur- ren Norte glacier is highlighted with a cross inside its corresponding circle. (b) Glaciers in which length changes have been measured, showing the number of times the length of each glacier has been consigned. Light gray dots are the locations of glaciers from the RGI.

Huh et al., 2012] which can theoretically be interpreted as changes in surface mass balance [Bamber and Riv- era, 2007]. In several regions, DEM subtraction has allowed researchers to determine long-term volume change [Rignot et al., 2003; Soruco et al., 2009]. The state of the use of remote sensing techniques to study Andean glaciers can be contextualized by observing Figure 1b, showing the number of glaciers in which length changes have been mapped, as recorded by the last version of World Glacier Inventory (WGI) [WGMS and NSIDC, 1989, updated in 2012]. Compared against mass balance programs (Figure 1a), the number of glaciers in which length changes have been recorded is far larger (Figure 1b). Nevertheless, highlighted glaciers in Figure 1b account for less than 1% of the glacier inventory. This means there are large areas yet to be studied in detail. In addition, significant uncertainties still exist in available glacier inventories owing to difficulties in defining and quantifying errors in mapping as consequence of the range of methods and data sources employed, as well as the challenges that seasonal snow cover, debris cover, and cloudiness impose [Pfeffer et al., 2014, see the detailed treatment of South America]. In summary, although there has been a combined effort to compile and evaluate the available information on Andean glaciers, in large areas more and better data are still needed. This means that there are several regions in which the paucity and quality of data remain significant obstacles to developing a detailed understanding on the timing and extent of glacier responses to changes in climate at diverse spatial and temporal scales. In our view, this justifies the use of simulations of glacier mass balance and/or glacier volumetric changes as a supplementary source of information, i.e., a way to organize and make sense of existent data. Models that simulate glacier mass balance and volumetric changes according to fluctuations in climate elements can yield spatial and temporal information on past and present trends by assimilating climatological observations and their uncertainties. Such an approach allows glacier models to simulate a range

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 469 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

of plausible scenarios of past and future climate changes that can be employed to understand the topoclimatic factors and feedbacks that lead to observed volumetric changes, which usually correspond to a discontinuous set of observations in time and space. However, the use of models presents important challenges because (a) forcing them with independent observations is difﬁcult and (b) uncertainty analysis of input data is rarely possible. This is especially crucial when surface mass balance simulations are employed as climate proxy.

1.2. Focus and Organization of This Review Our main goal in this paper is to list and review the current state of glacier-climate modeling across the Andes, with a special focus on surface mass balance and ELA. We account for the type of modeling approaches that have been applied and also analyze some of their advantages and limitations according to their (a) usefulness as a supplementary source of information for understanding glacier-climate interactions, (b) the data they use, and (c) their potential as an example for future work. We focus on studies encompass- ing a climatically relevant temporal scale (30 years). Because of our emphasis, we largely avoid glacier melt-only studies, except when those have useful insights for glacier-climate modeling. Additionally, we did not review rock and debris-mantled glaciers since existent literature is not related to glacier-climate modeling [Dornbusch, 2005; Azocar and Brenning, 2010]. We have organized our review into sections divided by scale. We first review global modeling studies that have included Andean glaciers. Next, we analyze ‘‘regional’’ papers, in which the entire Andes were modeled. Finally, we document studies undertaken on specific sectors of the Andes or individual glaciers. From these sections, it will become apparent that, although a number of approaches exist, they can be roughly classified in three main classes: empirical or statistical, semiempirical, and physically based. We summarize with some conclusions and recommendations for future work, in which we discuss the open challenges, such as the diversity of approaches applied to modeling glacier surface mass balance and volume changes, and also propose pathways for future research in this topic.

2. The Andes as Seen by Global Modeling Global glacier modeling exercises are used for three primary purposes (a summary is presented in Table 1): (a) hydrological purposes; (b) the study of sea level changes; and (c) climatic reconstruction/analysis. We have identified two approaches in category (a). In the first, Hirabayashi et al. [2010] utilize a temperature-index (TI) model to calculate glacier mass balance for the period 1948–2006. A TI model is a semiempirical approach that linearly links temperature to melt and accumulation, also known as a Positive Degree-day model [Braithwaite and Zhang, 1999]. Modeled glaciers were represented in a grid of 0.58. Mass balance changes in each grid-cell were converted to volume changes by applying area-volume scaling [Bahr et al., 1997]. A transfer coefficient linking temperature and melt was sought by calibration against observations presented by Dyurgerov and Meier [2005], which only included a handful of Andean glaciers. The glacier database was a combination of the WGI and the Global Hydrographic Database (GGHYDRO) [Cogley and Adams, 1998], the latter being a 18 gridded product that represents glacier area per grid-cell. Most climatic inputs for the simulation were taken from Hirabayashi et al. [2008]. Results showed many grid-cells with negative mass balance as low as 25 m/yr, while the average long-term glacier mass balance calculated across the Andean region was relatively small, attributed to a disproportionate effect of large glaciers with positive mass balance [Hirabayashi et al., 2010]. Another study falling in category (a) is Schaner et al. [2012], who simulated the contribution of glacier melt to river discharge. They employed a more physically based, 27 year simulation at 0.258 spatial resolution. To determine the glacier contribution to runoff, they coupled an energy balance glacier mass balance model to outputs from a global land surface model [Liang et al., 1994]. Thus, the actual estimate was the ratio between the discharge from glaciers and that from the land surface model. For the Andes, the model underestimated the glacier contribution determined from field data. This study does not provide information on the validity of comparing discrete sampling points to model output at such coarse spatial resolution. In addition, it seems that they did not consider that glacier melt has a delayed effect on local discharge, compared to river discharge, since the latter reacts faster to changes in precipitation. The timing in the contribution of melt to local hydrology has been shown to be a significant factor controlling discharge [Kaser et al., 2010].

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 470 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

Table 1. Global Glacier Modeling Studies That Have Included the Andes Representation of/Results Study Major Goal Type of Model for the Andes Meier [1984] Calculation of sea level change contribution. Mass balance amplitude from climatic data. Large contribution of Patagonian glaciers relative to their size. Zuo and Calculation of sea level change Regionally differentiated. Uses previously 12% of modeled glaciarized surface Oerlemans [1997] contribution since 1865. calculated glacier sensitivity to area. Large contribution of precipitation and temperature. Patagonian glaciers relative to their size. Gregory and Calculation of sea level change contribution Same model as above. Represented as in Zuo and Oerlemans Oerlemans [1998] for present and future conditions. [1997]. van de Wal and Wild [2001] Calculation of sea level change contribution. Same model as above but with area-volume Data from WGI as for 1989. The con- scaling [Bahr et al., 1997] to obtain volume tribution of South America glaciers change. Time varying precipitation thereby was more sensitive to changing glacier sensitivity. temperature. Oerlemans [2005] Temperature change from length records. Linear model relating length changes, glacier Six glaciers, from Patagonia. sensitivity and response time. Raper and Braithwaite [2005] Calculation of sea level change contribution. Temperature-index model and area-volume scaling. GGHYDRO database [Cogley, 2003]. Raper and Braithwaite [2006] Calculation of sea level change contribution. Same as above. Same as above. Braithwaite et al. [2006] Accumulation at the ELA. Temperature-index model at the ELA. Data after [Dyurgerov, 2002]. Andean sensitivity did not match other regions. These glaciers were excluded from further analysis. Bahr et al. [2009] Calculation of sea level change contribution. AAR and area-volume scaling. Most data from [Dyurgerov and Meier, 2005]. Validation using Zongo and Antisana 15 glaciers. Hock et al. [2009] Same model as above. Temperature index. GGHYDRO database. Tropical glaciers low sensitivity to temperature. Pat- agonian glaciers high sensitivity. Hirabayashi et al. [2010] Global mass balance for water resources Temperature index in elevation bins. Area-volume Data from WGI and GHYDRO. Rela- assessment (1948–2006). scaling to compute changes. tively small losses in South America. Radic´ and Hock [2011] Calculation of sea level change contribution. Temperature-index run at different elevation bins. Data from WGI. Tropics give almost zero contribution. Southern Andes (308S–558S) give 0.01 m. Leclercq and Oerlemans [2012] Temperature change from length records. Same as [Oerlemans, 2005]. Extended Oerlemans’ [2005] database due to inclusion of more Patago- nian glaciers. Marzeion et al. [2012] Calculation of sea level change contribution. Temperature based for melt. Linear model for From RGI [Pfeffer et al., 2014]. For vali- snow accumulation. Area-volume scaling dation, six glacier from [Cogley and [Bahr et al., 1997]. Accounts for glacier Adams, 1998] database. Errors in adjustment to climate [Johannesson et al., 1989]. volume are large in the Southern Andes. High uncertainty in the Tropics. Giesen and Oerlemans [2012] Calibration of a global model. Simpliﬁed mass and energy balance model. Two Andean glaciers used. Low skill and for tropical glaciers. Schaner et al. [2012] Glacier contribution to river discharge. Variable Inﬁltration Capacity (VIC) land surface Database came from the digital chart hydrological model [Liang et al., 1994]. of the world and GLIMS [Zemp et al., 2014]. Underestimation of glacier contribution compared to observations.

Studies from category (b) have mostly utilized a form of TI model [e.g., Zuo and Oerlemans, 1997] coupled to area-volume scaling [Marzeion et al., 2012] and applied for a variable number of Andean glaciers. For example, Bahr et al., [2009] represented only the small number of currently monitored glaciers, whereas Radic´ and Hock [2011] employed WGI’s descriptors to model more glaciers. Most category (b) studies have found disproportionate contribution of the Southern Andes (south of 308S) to sea level change relative to their area [Meier, 1984; Zuo and Oerlemans, 1997; Hock et al., 2009; Radic´ and Hock, 2011; Marzeion et al., 2012]. Some of these studies have also found a high degree of model uncertainty in tropical areas [e.g., Marzeion et al., 2012]. This suggests that modeled Andean glacier volume ﬂuctua- tion is greatly determined by Patagonian glaciers. A simple calculation exempliﬁes this. We utilized the RGI and the scaling method according to Bahr et al. [1997] to compute the relative contribution of each polygon of that database to a continental change in volume (V) derived from a 5% decrease in glacier surface area (A):

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 471 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

p2 V5p1A (1)

where p1 and p2 are parameters as deﬁned by Bahr et al. [1997]. In our case, since we wanted to compare

the relative contributions, we skipped the more uncertain p1 parameter and we utilized 1.375 for p2. Results indicate that only 18 polygons, all of them located between 458S and 558S, account for 64% of the Andean volume change. This confirms that for continental scale calculations, the actual Andean signal is largely the result of a small number of glaciers. Hence, these few glaciers mask any uncertainty in the calculations for other sectors. Given the goal of the type (b) studies, this masked uncertainty should not impact the calculation of relative regional contribution to sea level. On the other hand, for studies targeting hydrological impacts of volume changes in the Andes, the uncertainty in the Tropics may preclude obtaining accurate estimations. Hence, the research aims of each study ultimately constrain the usefulness of the results. Category (c) studies have modeled glaciers to derive temperature trends [Oerlemans, 2005], sensitivity of glaciers to warming [Braithwaite et al., 2006], and to investigate model performance [Giesen and Oerlemans, 2012]. Oerlemans [2005] and Leclercq and Oerlemans [2012] utilize length records to reconstruct temperature through the inversion of a linear model that calculates length changes from known values of glacier sensitivity to temperature and precipitation, and response time. While Oerlemans [2005] included six Andean glaciers, all from Patagonia, Leclercq and Oerlemans [2012] augmented this to 64 glaciers, 49 of them within the strip 308S–558S and nine from the Tropics. The linear model may not properly represent tropical glaciers, where mass balance gradients are not linear [Kaser, 2001]. In fact, other studies have found problems in using simple models on these glaciers. Braithwaite et al. [2006] initially included Andean glaciers from the Dyurgerov [2002] database, although they were assessed as outliers and later excluded from the analysis. Three out of the five glaciers representing the Andes were tropical glaciers. Giesen and Oerlemans [2012] utilized a simplified energy balance approach and found low model skill in the simulated mass balance in the Tropics during the dry season.

3. Modeling Andean Glaciers at the Continental Scale At the continental scale, we found only two studies. These dealt with linkages between the ELA (or snowline) and variables of temperature and precipitation. Condom et al. [2007] applied a statistical model to determine spatiotemporal changes of the ELA along the Andes. They utilized an equation of the form

y 5 a 1 b*log10(x) 1 c to calculate the ELA from precipitation and temperature data. More speciﬁcally, in that formula ELA (y) was determined by annual precipitation (x), the mean annual 08C isotherm altitude (c), and two regression coefﬁcients (a and b). Utilizing the 10’ climatology from the Center for Climate Research of the University of East Anglia (CRU) [New et al., 2002] as input data, Condom et al. [2007] utilized this logarithmic expression (see equation (2), discussed below) to calculate the average ELA for the period 1961– 1990. In order to obtain a 08C isotherm (Iso08C) for every grid-cell of interest, they extrapolated near-surface temperature from CRU by applying a lapse rate of 278C/km. The main product of the paper was a series of maps showing all Andean areas above the ELA, attributed as glacierized areas in the Andean region. A qualitative validation was employed, in which modeled ELAs were compared against the known latitudinal trend of that variable as presented in the WGI, in which ELAs in excess of 4000 m occur along the tropical and subtropical Andes (128Nto358S), to gradually descend toward sea level along the southern Andes [WGMS and NSIDC, 1989, updated 2012]. An additional comparison included the use of ELA data from three glaciers: Zongo (168S), de los Tres (498S), and Pıo XI (498S). They found good agreement between their model and those observations. A closer inspection to their results, however, suggests that the model missed most of the Cordillera Real in Bolivia and that the region around 308S was not well reproduced. Among other reasons for this disagreement, we can cite uncertainty related to the lapse rate employed and the selection of the statistical model according to each subregion studied [Fox, 1991; A. Fox, Cornell University, unpublished data, 1993]. In the following, we provide further analysis of this model in order to account for these differences. Condom et al. [] based their work on previous research by Fox [1993], who mapped modern and Pleistocene snowline elevations along the region between 58S and 288S. Fox (Cornell University, unpublished data, 1993) established the relationship between precipitation and the normalized snowline altitude (NSA), which is the difference between the regional snowline altitude and the mean annual 08C isotherm altitude. The NSA was deemed a useful index for isolating the effect of temperature and precipitation on the behavior of

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 472 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

modern and Pleistocene snowline. Condom et al. [2007] did not discuss why such model could be applied to the whole Andes. The actual equation they utilized was

ELA5342721148log10ðÞPp 1T=0:0071z (2)

The ﬁrst two terms of the right-hand side represent the relationship between precipitation (Pp) and the NSA, derived by Fox (Cornell University, unpublished data, 1993) for the region between 58S and 208S. The last two terms in equation (2) were used to calculate the 08C isotherm from near-surface temperature (T), elevation (z), and the lapse rate. Condom et al. [2007] offered no explanation for selecting the equation, in a study area (58S and 288S) for which another formulation was also available (Fox, Cornell University, unpublished data, 1993, p. 9). Moreover, Fox (Cornell University, unpublished data, 1993) presented several ver- sions of the NSA formulation, differentiated by subregions. One of those, showing a linear relationship for the Altiplano (Fox, Cornell University, unpublished data, 1993, p. 112,176), was not discussed in Condom et al. [2007]. Yet in an earlier work, Fox [1991] described another, different type of equation to calculate the snowline elevation (SN):

SN50:001ðÞPp 222ðÞPp 232ðÞT 10:2ðÞIso0C (3)

Again, Pp is precipitation, T is near-surface temperature and Iso08C is the 08C isotherm. Regardless of possible inaccuracies in the method employed to determine the snowline, there is an actual empirical and theo- retical basis for the logarithmic relationship found by Fox (Cornell University, unpublished data, 1993). Oerlemans and Fortuin’s [1992] numerical experiments using an energy balance model revealed a logarithmic relationship between mean specific glacier mass balance and precipitation, in which the rate of change of specific mass balance change due to 1 K temperature increase diminishes as precipitation diminishes. This model indicates that the mass balance of glaciers located in wetter climates is more sensitive to changes in temperatures, because it presents high accumulation rates allowing glaciers to extend and remain at relatively low elevations, where temperature can be higher than the melting point. Other studies found second-order polynomials for ablation gradients and precipitation [Carr and Coleman, 2007], and for precipitation and temperature at the ELA [Ohmura et al., 1992], which resemble equation (3). These results attest to the nonlinear nature of the relationship between the ELA and precipitation. Fox’s (Cornell University, unpublished data, 1993) interpretation of the logarithmic models was that, by subtracting the nonlinear relation between NSA and precipitation, any change in the NSA would linearly follow changes in annual 08C isotherm. That reasoning was employed by Condom et al. [2007] to restate the equation as a method to determine the ELA everywhere along the Andes. In practice, however, that NSA calculation gives a wide range of values, with a maximum of approximately |5000| m when precipitation tends to zero. Such maximum elevation may distort the calculation of the ELA in the Altiplano region, where many peaks reach elevations in excess of 6000 m. There, the existence of glaciers is controversial, as local modeling studies have not found the necessary climatic conditions for permanent ice cover [Kull and Grosjean, 2000; Kull et al., 2002]. In zones with low amounts of precipitation, such as the outer Tropics and the Sub- tropics, the dry season is characterized by substantial amounts of ablation, thus leading to large differences between the ELA and the 08C isotherm [Benn et al., 2005]. In that case, other processes such as humidity deficit or wind speed may be more important in the ELA behavior, and temperature (and hence the 08C isotherm) may have minimal impact [Seltzer, 1993, 1994; Rodbell et al., 2009]. Instead, we suggest that Fox’s (Cornell University, unpublished data, 1993) formulation is a first-order appraisal of the ELA sensitivity to changes in the 08C isotherm. Indeed, if we set the NSA to zero we can restate equation (2) to determine the precipitation amount where the influence of the 08C isotherm on the

ELA is greatest (PpSmax): ðÞa PpSmax510 b (4)

where a and b are the coefficients of the logarithmic equation. To a first approximation, we utilize the coeffi-

cients from equation (2). This calculation yields PpSmax equivalent to 966 mm. The validation reported by Condom et al. [2007] was biased to glaciers where the annual precipitation was near (Zongo glacier) or

above (de los Tres, Pıo XI) PpSmax, which may be the cause of the agreement between model and observations. However, we contend that these conditions are not representative of the entire Andes because in

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 473 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

several subregions the precipitation is well below PpSmax. Thus, this validation is not a convincing assessment of the model skill to determine the ELA. A different approach to modeling was presented by Sagredo et al. [2014]. They applied a surface energy and mass balance model [Rupper and Roe, 2008] to study the sensitivity of glacier ELAs to changes in temperature and precipitation. In this model, the surface energy balance is computed from net radiation and turbulent fluxes. To determine melting, the surface energy balance is calculated using an iterative process whereby surface temperature is recalculated to minimize the surface energy balance. Melt occurs when an optimal solution is reached and the calculated surface temperature in above zero. This approach delivers separate estimations of melt, sublimation, and evaporation. The mass balance is calculated by subtracting accumulation, which equals precipitation. The ELA is determined by locating the altitude where ablation and accumulation add to zero, utilizing the climatic lapse rate. Sagredo et al. [2014] forced the model with the 10’ CRU climatology [New et al., 2002] and NCAR/NCEP reanalysis [Kalnay et al., 1996]. The temperature lapse rate for each grid-cell was determined from NCAR/NCEP fields at the geopotential levels closest to the glaciers’ elevations. They evaluated model output against an ELA database produced specifically for this study, utilizing the terminus-to-head altitude ratio (THAR) method. The ratio employed was 0.5, which is equivalent to using the median altitude or Kurowski altitude [Kurowski, 1891], a technique deemed less biased compared to others such as the use of shape changes in contour lines [Cogley and Mclntyre, 2003]. The reason for such an exercise boils down to the disparity of dates of ELA values that are stored in current databases, such as the WGI [WGMS and NSIDC, 1989, updated 2012]. The results repeated previous findings on low sensitivity of dry areas to temperature [Seltzer, 1993, 1994; Klein et al., 1999], although they put them in better regional context. They also found a nearly linear relationship between ELA change and precipitation perturbation, conflicting with the logarithmic model of sensitivity derived from Fox (Cornell University, unpublished data, 1993). In spite of their relatively thorough approach, there are important uncertainties in Sagredo et al.’s [2014] study that have consequences for accurately determining ELA sensitivity. First, the use of the coarse resolution NCAR/NCEP reanalysis (200 km at the equator) implies that important ice-covered mountains are oversimplified in that reanalysis. The regridding that Sagredo et al. [2014] applied to the input data sets from reanalysis in order to obtain a finer spatial resolution to match CRU data (almost 4 times finer), does not solve this resolution issue, because the problem is with solar radiation; at coarse grid scale resolution, topography is necessarily coarse, causing solar radiation to be overestimated. Therefore, the glacier surface energy balance was unrealistically too negative, forcing the ELA to be very high, specifically in areas of more complex topography such as the Cordillera Blanca (98S), represented by one grid-cell (Figure 2). Other cause could also be the CRU database, which provided precipitation and temperature input. These are interpolated fields using data from nearby stations. The lack of observations across the Andes may mean that these variables can be over or underestimated. Thus, overestimation of radiation or air temperature, or underestimation of precipitation can explain why simulated ELAs erred by at least 800 m above observed values. In fact, all simulated ELAs in Ecuador are above the highest mountaintops. Another feature of the model is the use of a single albedo value. In Sagredo et al.’s [2014] sensitivity analysis, the largest uncertainty was produced by modest (610%) changes in albedo, especially along the Andean dry outer Tropics and Subtropics. By utilizing a single albedo, crucial tropical feedbacks are neglected. One difference between Andean tropical glaciers and Central Asia, the area modeled by Rupper and Roe [2008] is that the latter presents seasonal patterns in radiation, temperature, and precipitation [Bohner€ , 2006]. By con- trast, the tropical Andes have weaker seasonality in solar radiation and temperature [Kaser and Osmaston, 2002]. In this context, albedo fluctuations in tropical glaciers exert a different control on the energy budget compared with subtropical glaciers. In the Tropics, the amount of solar energy absorbed will be determined by the albedo [Vuille et al., 2008a] and observations confirm that it varies significantly [Sicart et al., 2008]. On the other hand, in the Subtropics, the solar radiation varies according to the wet-cold (lower radiation) and warm-dry (higher radiation) which in turn is inversely related to albedo [Abermann et al., 2014]. Given the relatively constant incoming solar energy, albedo changes due to sudden snow accumulation [Oke, 1987] as result for instance, from convective storms, can alter significantly the surface energy balance. This limitation of the model is further indicated in the decoupling between simulated accumulation and ablation through changes in albedo. The feedback between accumulation and albedo has been well studied in different envi- ronments [e.g., Oerlemans and Knap, 1998; Gardner and Sharp, 2010; Gurgiser et al., 2013]. A more realistic

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Figure 2. Comparison between topography from (a) NCAR/NCEP reanalysis and (b) SRTM. Both maps are hillshade representations of the northern Andes of Peru. Glaciers are highlighted using white color.

approach would have allowed for a decreased amount of absorbed solar radiation at the surface during the wet season when accumulation predominates. This might have reduced the discrepancy between simulated and observed ELAs.

4. Modeling Andean Glaciers and Climate Changes at Specific Locations See Table 2 and Figure 3 for a summary.

4.1. Venezuela No publications about glacier-climate modeling in the Andes of Venezuela were found in the indexed literature. The current state of Venezuelan glaciers, the country with the smallest ice coverage along South Amer- ica, has recently been reviewed by Braun and Bezada [2013] and Rabatel et al. [2013], indicating fast demise during the last century has been observed. Thus, only qualitative inferences on glaciers and climate changes have been proposed thus far.

4.2. Colombia In this country, only the IDEAM (Spanish acronym of the Colombian Institute for Hydrology, Meteorology, and Environmental Research) has recently released a report about current glacier monitoring [Ceballos et al., 2012]. Therein, a statistical linear model is utilized to assess and project glacier thickness changes in the Conejeras glacier, Santa Isabel volcano (48470N). The glacier is divided into ﬁve elevation bins, where mass balance measurements have been taken since 2005. Each mass balance time series is regressed against time in order to determine a linear model of change. Extrapolation of the linear model until 2030 predicts almost total ice loss.

4.3. Ecuador Currently, Ecuador is one of the few Andean countries with a long-term glacier monitoring program. It started in 1994 on the Antisana 15 glacier [Caceres et al., 2006]. This program has been instrumental for quantifying the impact of El Nino~ Southern Oscillation (ENSO) on glacier surface mass balance in the inner Tropics. Francou et al. [2004] coupled an energy balance study to 8 years of mass balance data, ﬁnding that cloud cover reduction, shift of rainfall toward more snow, and weaker winds, enhance ablation during El Nino~ years.

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Table 2. Regionally Focused Glacier Modeling Studies Along the Andes ID in Figure 3 Location Type of Model Data Sets Main Results Source 1 Conejeras glacier Statistical: linear regression. Field measurements of mass Almost complete glacier demise by Ceballos et al. [2012] balance. 2030. 2 Antisana 15 glacier Same as above. Precipitation and temperatures from Overall negative mass balance since Manciati et al. [2011, 2014] nearby stations. 1891, driven by temperature changes. 3 Cordillera Blanca Hydrological balance reconstruction Runoff and precipitation from 10 High positive between mass balance Vuille et al. [2008b] [Kaser et al., 2003]. watersheds across the region. and: precipitation and relative humidity at 500 mb. 4 Zongo glacier Statistical: linear multiregression Field measurements of mass bal- Solar radiation and length of the Ribstein et al. [1995] between melt and meteorological ance, precipitation, solar radia- diurnal cycle highly correlated to variables. tion, and temperatures. glacier melt when temperature is greater than 38C. 5 Upsala and Perito Temperature-index model. Ablation and temperatures measure- Detected glacier thinning is not Naruse et al. [1997] Moreno glaciers ments in the study area. entirely explained by temperature. 6 Perito Moreno glacier Same as above. Precipitation and temperature from Lack of long-term mass balance Stuefer et al. [2007] nearby stations. trend. 7 Martial Este glacier Temperature-index model plus Field measurements of mass bal- Mass balance is more sensitive to Buttstadt€ et al. [2009] volume-area scaling. ance. Precipitation and tempera- temperature. 93% of the glacier ture from nearby stations. area is lost by 2099. 8Frıas glacier Simplified energy balance plus flow Precipitation and temperature from Temperature is the main driver of Leclercq et al. [2012] line model. ERA Interim reanalysis (for mod- glacier changes. ern conditions) and tree-ring reconstructions (past conditions). 9 Tapado glacier Semiempirical energy balance Field measurements of precipitation, Modern ELAs were well reproduced. Kull and Grosjean [2000] model plus flow model. temperature, wind speed, and and Kull et al. [2002] vapor pressure. 10 Chilean central Andes Statistical model to determine ELA Temperature from radiosonde data Future rise of ELA, due mainly to Carrasco et al. [2005] fluctuation [Condom et al., 2007; and precipitation from stations. temperature. Fox, Cornell University, unpublished data, 1993]. 11 Chile Same as above. Same as above. Significant rise of ELA in north and Carrasco et al. [2008] central sectors after 1978. 12 South central Chile Temperature-index model Radiosonde data from nearby sta- Winter melt events around the ELA Brock et al. [2012] tions, field measurements of tem- occur regularly. perature and precipitation, and NCAR/NCEP synoptic fields (e.g., sea level pressure at 775 hPa). 13 Patagonia Surface energy balance. Precipitation and temperature from Modern ELA more sensitive to tem- Kerr and Sugden [1994] nearby stations. perature in wetter areas. 14 Southern Patagonia Surface energy balance. Precipitation, temperature, solar Ablation correlates to elevation. Cook et al. [2003] Icefield (SPI) radiation, longwave incoming West-east gradient in meteoro- radiation from the MM5 model. logical control on mass balance. MM5 forced by ECMWF global reanalysis. 15 Northern Patagonia Simplified surface energy balance. Precipitation and temperature from An increase of accumulation Schaefer et al. [2013] Icefield (NPI) a dynamical downscaling using between 1990 and 2011 versus the WRF model. WRF forced by 1975 and 1990. Increase in abla- NCAR/NCEP (present conditions) tion from 2050. and ECHAM5 (future scenarios). 16 SPI Same as above. Same as above. Overall positive mass balance Schaefer et al. [2015] between 1975 and 2011. 17 NPI and SPI Surface energy balance. Simulated as a subroutine of the Sharp mass balance gradients. Statis- Lenaerts et al. [2014] RACMO model using ERA Interim tically significant positive mass reanalysis as forcing. balance linear trend (1979–2012). 18 San Rafael glacier Temperature-index plus two calving Precipitation and temperature from Positive mass balance. Koppes et al. [2011] models. NCAR/NCEP and field measurements. 19 SPI Temperature-index and glacier Synthetic time series of precipita- The position of the ELA in the hypso- De Angelis [2014] hypsometry. tion, snow accumulation, and metric curve controls climate temperature, derived from obser- sensitivity. vations at Perito Moreno glacier. 20 Gran Campo Temperature-index plus calibrated Field measurements of precipitation Predicted net volume loss by 2099. Moller€ et al. [2007] and Nevado volume-area scaling. and temperature. Moller€ and Schneider [2008]

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Figure 3. Locations of glacier modeling studies along the Andes. Stars represent single glaciers, while polygons denote approximate boundaries of modeled regions as described in section 4. Numbers correspond to the ID in Table 2. Underlined italic numbers identify the studies performed in regions.

Only short-term and spatially discrete modeling has been performed so far in Ecuador, mostly to simulate hydrological processes in the glacierized catchments [e.g., Wagnon et al., 2009]. Two recent papers by Man- ciati et al. [2011, 2014] reconstructed surface mass balance of the Antisana 15 glacier since 1891 utilizing nearby meteorological records. They regressed time series of temperature and precipitation against mass balance and tested simple and multiregression models. In general, all models explained at least 48% of variance, suggesting a predominance of temperature on mass balance. Model output suggested negative mass balance since 1891.

4.4. Peru The vast majority of tropical glaciers are concentrated in Peru [Vaughan et al., 2013]. Since most of the country’s population inhabits the dry Pacific coast, there is very intensive use of mountain water resources in the agriculture, energy, and mining sectors [Vergara et al., 2007]. This situation strongly influences the scope of glacier studies. In effect, most modeling work has aimed to simulate the fate of meltwater in a changing climate, and consequences for water availability [e.g., Juen et al., 2007; Baraer et al., 2012]. Early attempts to understand climate-glacier relationships were based upon a few years of mass balance measurements during the 1970s to 1980s. A series of papers documented the monitoring of energy fluxes, height changes and velocity measurements in Yanamarey, Uruashraju (both in the Cordillera Blanca, 98300S) and Santa Rosa (Cordillera Raura 108300S) glaciers, and the Quelccaya Ice cap (148S) [e.g., Hastenrath, 1978; Ames and Hastenrath, 1996a]. Simple sensitivity analyses were performed to calculate what changes in energy fluxes would be needed to keep glaciers in equilibrium with respect to calculated negative mass balance [Hastenrath and Ames, 1995; Ames and Hastenrath, 1996a,b]. The main conclusions of these studies were that a one-tenth increase in cloudiness (because of their effect on global radiation), a 1.5–28C decrease

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in temperature (affecting sensible heat) and a 1 g/kg decrease in specific humidity (affecting latent heat), would keep those glaciers in equilibrium. Later studies have shown that the changes in latent and sensible heat may have had a larger role in glacier changes because they control the proportion of sublimation versus melt [Mark and Seltzer, 2005; Winkler et al., 2009]. However, finding the correct combination of parameters that produce the observed changes is difficult because the manifold sources of uncertainty that each parameter adds to the model. As Seltzer [1994] expressed in his work on the sensitivity of the snowline to climatic changes in millennial scales, this analysis requires the knowledge of parameters such as transfer coefficients for turbulent fluxes, lapse rates, and accumulation gradients. In the modeling of these glaciers [e.g., Hastenrath and Ames, 1995], some of these input parameters were derived from about a decade of measurements, a short period that does not warrant that those findings apply at longer time scales. To date, only the study by Vuille et al. [2008b] has compared climate trends and glacier mass balance relationships in Peru. They simulated glacier surface mass balance anomalies along the west side of the Cordil- lera Blanca for the period 1953–1993. Their model outputs were correlated to precipitation and temperature observations, as well as to ENSO time series and descriptors of large-scale climate dynamics. They found significant positive correlation between precipitation trends and mass balance anomalies, a somewhat less significant negative correlation to near-surface temperature, and a negative but barely significant correlation to gridded vapor pressure (CRU TS 2.1). Many negative (positive) surface mass balance anomalies corresponded to El Nino~ (La Nina)~ years, although the relationships seemed to breakdown at times. In terms of large-scale climatic fields, the study documented a significant positive correlation between relative humidity at the 500 mb and surface mass balance. In summary, Vuille et al. [2008b] argued that the surface glacier mass balance of the Cordillera Blanca between 1953 and 1993 was predominantly responding to precipitation variability, climatic conditions in the tropical Pacific, and large-scale climate in a similar manner as suggested for the Altiplano region, in which easterly flow brings wet conditions while westerly flow produces dry conditions [Garreaud et al., 2003]. The cornerstone of this analysis was a hydrology-based reconstruction of glacier surface mass balance anomalies delivered in Kaser et al. [2003]. This reconstruction was based on runoff and precipitation records from 10 watersheds located in the west side of the Cordillera Blanca. They found that the amount of seasonally lagged stream flow was positively correlated to the proportion of glacier coverage in the catchment. With these results, the authors simulated monthly glacier surface mass balance from the difference between precipitation and stream flow, both normalized by the period’s mean stream flow. Some assumptions in this Kaser et al. [2003] model have important implications for interpretations made subsequently by Vuille et al. [2008b]. The most noticeable has to do with precipitation. The model is in fact forced by the same precipitation records in which it was later compared, suggesting that possibly the high correlation between precipitation and mass balance was a spurious self-correlation [Kenney, 1982]. A previous study that measured glacier volume loss since 1962 did not find sufficient changes in precipitation to explain such ice loss [Mark and Seltzer, 2005]. Another critical assumption was the negligible effect of groundwater storage, referred to as swamps. New evidence suggests that groundwater can be a very important contributor to, and delayer of, the catchment stream flow in the Cordillera Blanca [Baraer et al., 2012, 2015]. Indeed, it is now clear that paramos (Andean wetlands) are fundamental for base flow in the tropical Andes [Buytaert et al., 2006]. This suggests that the computed mass balance time series may constitute a mixed signal of several contributors to stream flow that are responsive to precipitation, each one presenting different resi- dence times of water.

4.5. Bolivia A long, uninterrupted glacier monitoring program has been maintained in the Cordillera Real since early 1990s [Rabatel et al., 2013], producing rich data about volumetric changes and hydrology, central to glacier- climate analysis [Rabatel et al., 2006; Soruco et al., 2009]. An early attempt to relate climate ﬂuctuation and glacier variations through modeling was performed by Ribstein et al. [1995]. In that work, the authors analyzed the ﬁrst few years of mass balance data from the Zongo glacier (168150S) and a set of meteorological and hydrological variables to uncover factors controlling meltwater release. They searched for statistical relationships between runoff at the glacier outlet and some of the hydrometeorological variables they measured, by applying a stepwise linear multiregression. They found that solar radiation and the length of the diurnal period explained more than 84% of the variance in runoff, provided that the temperature was greater or equal to 38C at the Zongo station, located at 4770 m and about 1 km downstream of the Zongo

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glacier. In order to reconstruct runoff since 1973, they also utilized the high correlation between their runoff gauge and readings at a nearby hydroelectric plant. That reconstructed glacier runoff (and hence negative glacier mass balance) correlated to El Nino~ years, as for example during 1982–1983. The best positive correlation of monthly runoff and ENSO (using the SOI index) was identified when a 5 month lag was employed (r2 5 0.37%). Another noteworthy result from the study was related to the observation of rainfall gradients. In their 2 year observation, these researchers found a negative gradient of rainfall due to elevation between Zongo station and Botijlaca (3490 m). Conversely, longer records located at lower altitudes did not show such a gradient. In order to explain that discrepancy, Ribstein et al. [1995] suggested that their measurements were unable to accurately record snowfall due to wind. That observation is a note of caution for modeling approaches that rely on precipitation gauges to calculate gradients of rainfall, which in turn are used to simulate snow accumulation. There is potential to utilize a network of observations in which each contains bias, which may deliver inaccurate calculations of gradients and affect simulation outcomes. Most of the subsequent studies after Ribstein et al. [1995] have focused on short-term (mostly seasonal) melt modeling rather than mass balance modeling itself [Caballero et al., 2007; Lejeune et al., 2007; Moya Quiroga et al., 2013]. However, it is worth mentioning Sicart et al.’s [2008] study, in which they correlated temperature with components of the surface energy budget in three glaciers located on low, mid, and high latitudes. Their target for tropical areas was Zongo, utilizing valuable energy flux observations from Novem- ber 1997 to March 1998 and from November to December during 1999. In their results, these authors stated that TI models are not accurate for daily melting calculation, although the factors should perform well on longer scales. They claimed that TI models may be useful on a yearly basis, based on the high correlation between temperature and Zongo’s mass balance. Though the short observed period may not be climatically relevant, their results do provide some clues about processes in the background and their importance in tropical glacier modeling. We detail those clues in the next paragraph. Differences in daily versus yearly scales can result from a combination of several processes at play during the hydrological year that are critical in tropical glacier mass balance (Figure 4). It is well known that most of the annual melting in this tropical region occurs during the wet season (September–April, Figure 4a), coincident with the accumulation season [Kaser, 2001; Francou et al., 2003]. It follows that during the wet season there are more clouds and humidity. Cloudiness may simultaneously dampen the direct component of the incoming solar radiation and enhance incoming longwave energy flux by changing the atmospheric emissivity. This may result in an overall decrease in ablation energy with respect to the dry season, when clear skies dominate, and in turn, an increase in the relative weight of longwave incoming energy and of melting over sublimation. Furthermore, clouds and humidity reduce the difference in vapor pressure between the atmosphere and the ice surface, leading to a preference of melting over sublimation. However, although the proportion of melting versus sublimation would increase, the absolute amount of melting energy would reduce, because longwave incoming energy would be less than the potential amount of solar radiation hitting the surface during a clear-sky day. Finally, seasonal accumulation increases snow albedo, which in turn reduces the amount of absorbed solar energy relative to the dry season. Thus, although ablation energy variations may most likely be controlled by incoming solar energy that reaches the surface, longwave energy, and hence temperature, will control the relative importance of melting in ablation. Sicart et al. [2008] did not find correlation between longwave energy flux and air temperature in their study but did find correlation between mass balance and temperature in the longer term. A previous study identified longwave incoming energy as a key flux controlling seasonal melting energy [Sicart et al., 2005]. Thus, TI models cannot accurately simulate seasonal (short-term) ablation because longwave energy is uncorrelated to temperature at this scale. Better correlation between long-term ablation and temperature is due to its cumulative effect on increasing incoming longwave energy over time, which justifies the use of TI models at this time scale (Figure 4b).

4.6. Argentina Since ice-covered mountains extend from the southern dry Andes to Patagonia, Argentinian glaciers can potentially integrate subtropical and humid midlatitude climate changes. Furthermore, as most glaciers are on the east side of the Andes, they constitute an excellent setting to compare reactions with respect to Chil- ean glaciers, which preferentially face the west slope of the Andes at equivalent latitudes. There has been a recent increase in studies of glacier ﬂuctuations, especially toward the north [Masiokas et al., 2009]. How- ever, the amount of modeling studies has not followed that trend, with the majority targeting the

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Figure 4. Schematic view of the relationship between temperature versus (a) seasonal and (b) multiyear glacier ablation. Vertical arrows represent incoming solar radiation (bold) and longwave energy (segmented). Top rectangles represent the glacier surface, where the seasonal change in albedo is denoted by shades of gray in Figure 4a. Rectangles in the midsection show the relative proportion between melt and sublimation. Scatterplots of the bottom section denote the correlation between temperature and ablation.

Patagonian Andes. That is unfortunate because Central Argentina has a rich database of glacier fluctuations and a long, though discontinuous, mass balance time series [Leiva et al., 2007]. Naruse et al. [1997] studied the Upsala and Perito Moreno glaciers (508S) in the Southern Patagonia Ice- field (SPI). They correlated ablation measured at the Perito Moreno glacier and the cumulative sum of positive degree days obtained from temperature records for the period November 1993 to December 1994. The calculated linear relationship was used to estimate a melt factor of 7.1 mmwe 8C21 d21, which in turn, was utilized to calculate ablation during the period 1964–1994 for both glaciers using a TI model. Results indicated that observed thinning rates were not entirely explained by temperature variations, leading these scholars to infer that winter precipitation and its effect on albedo, or cloud cover in summer, influenced ablation as well. In another study, Stuefer et al. [2007] analyzed long-term mass balance fluctuations and sensitivity to climate factors of the Perito Moreno glacier. The researchers employed a TI model, calibrated with nearby stations for the period 1993–2004. Model output indicates that the glacier is in nearly steady state, since they deemed that the deviation from zero glacier surface mass balance was small, in agreement with the temperature observations at nearby Lago Argentino that did not show a clear trend. This result dif- fers from trends observed in neighboring glaciers. From their model output, the authors interpreted three distinct periods in the mass balance time series: two with positive cumulative mass balance (1974–1989 and 1999–2004) and one with negative (1990–1998). They also found that Perito Moreno glacier is equally sensitive to precipitation and temperature. This study exemplifies the great potential of long-term modeling for the contextualization of short-term observations. In 2009, Buttstadt€ et al. performed a mass balance reconstruction, a climatic sensitivity analysis, and a projection of the glacier surface mass balance of the Martial Este glacier (548460S), a small ice body located in the Argentinian section of Tierra del Fuego. They utilized a TI model, calibrated against 10 days of mass balance measurements between December 2005 and February 2006. For the period between 1960 and 2007, the glacier surface mass balance reconstruction was derived from station data. Buttstadt€ et al. [2009]

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obtained future climatic scenarios until the year 2099 from statistically downscaled outputs from the Third UK Met Office Hadley Centre Coupled Ocean-Atmosphere global climate model (HadCM3). This climate model output represented the worst-case scenario of the IPCC’s fourth assessment on climate change (A2) [IPCC, 2007]. In order to determine mass balance change to volume change, this study utilized volume-area scaling formulations according to Bahr et al. [1997]. The sensitivity analysis suggested that Martial Este glacier reacted more strongly to temperature changes relative to precipitation fluctuations. The simulation of the 21st century behavior indicated a 93% of reduction in surface area by 2099, continuing with the negative trend modeled for the period 1960–2007. The work by Leclercq et al. [2012] is one of the very few examples of coupling glacier mass balance and ice- flow models in the Andes. These authors studied the Frıas glacier on Mount Tronador (418S) by means of a simplified surface energy balance model and a flow line model. This glacier has a long record of glacier length changes based on tree-ring-dated moraines, historical sources, and remote sensing that comprises a good data set for model calibration. A simplified energy balance model computed melting from temperature and precipitation, while accumulation was determined from precipitation and a temperature threshold [Oerlemans, 2010]. The modeled mass balance profile feeds a flow line routine to account for ice flow that solved glacier thickness and length fluctuations in a staggered grid at 2 h time step. Their main results indicated that glacier retreat from 1639 to 2009 was more related to temperature variations than to precipitation. There is some uncertainty with this modeling approach that arises from difficulties in capturing local geometry effects that may distort the simulated climate reaction of a glacier. Nevertheless, as Leclercq et al. [2012] point out, the advantages of Frıas glacier are its currently small area of debris coverage and lack of evidence for any calving or surges. For mass balance modeling over modern time scales, the focus of this review, these features provide the optimal scenario to work with. If historical records and aerial/satellite imagery can help to rule out nonclimatic controls, then glacier changes can be more accurately modeled. At longer time scales, however, this is more difficult. For instance, there is no current proxy by which to distinguish whether or not a glacier had extensive debris coverage in the past. The lower section of the Frıas glacier is oriented to the north and resembles the neighboring Casa Pangue glacier, which currently is a regenerated glacier with a thick debris cover on its ablation zone [Fernandez et al., 2006]. This suggests that Frıas was also likely debris covered in the past, which may distort some climatic conclusions in Leclercq et al. [2012].

4.7. Chile Presently, Chile contains more than 60% of Andean glacier area [Williams and Ferrigno, 1999]. Further- more, the largest number of modeling studies is found here, specifically in Patagonia [Masiokas et al., 2009]. More recent research has begun to study northern parts of the country, motivated by concerns on water resources management [Vicuna~ et al., 2010; Gascoin et al., 2011]. Pellicciotti et al. [2014] reviewed the problem of hydrological impacts and glaciohydrological modeling in Chile, and we refer to that work for details. Here, our glacier-climate emphasis is different from Pellicciotti et al.’s [2014] glaciohydrological focus. We mostly review other studies, though when needed, we recall some of Pellicciotti et al.’s [2014] arguments. The Northern Chilean Andes (178300S–308S) is the least researched area of the country. The few observations on climate patterns and glacier processes during the 1990s [e.g., Vuille and Ammann, 1997] have only been recently supplemented by new data [MacDonell et al., 2013]. Kull and Grosjean [2000] and Kull et al. [2002] are examples of the few modeling efforts undertaken in this region. Both works applied the same model to analyze Pleistocene glacier-climate interactions, and simulate current conditions in order to validate their approach. An empirical-statistical mass balance model was coupled to a simplified ice-flow model. For the validation of modern conditions, the Tapado glacier (308S) and two ice-free valleys (at 188S and 228S) were simulated and compared against field measurements of balance gradients and ELAs. Cli- matic parameters and statistical relationships were derived from observations in the vicinity of the (former) glacier(s) and the glacier itself. The model included a series of regression-derived equations to calculate accumulation, sublimation, and melt. The formulation for accumulation considered one temperature threshold for snowfall (28C) and a range in which a mixture of snow and rain was expected (28C–48C). Melt was calculated using a TI model. A sublimation routine was derived from a linear multiregression between observed values versus wind speed, vapor pressure, and solar radiation.

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Results of the work showed promising model performance, with a number of important caveats. The validation showed that modern ELAs, located above mountaintops, were well reproduced. Model output also indicated that while both sublimation and accumulation had modest altitudinal gradients, melt showed a nonlinear decrease with increasing altitude. However, one important aspect to consider in these studies, and specifically for Kull et al. [2002], is that climatic parameters for modern conditions were mostly derived from in situ observations during the period 1998/1999 in the Cerro Tapado glacier. That means that at least half of the data were captured during one of the strongest El Nino~ events on record, also known as super El Nino~ [Hong et al., 2014]. It is well known that El Nino~ is related to increases in winter (June–August) precipitation around 308S[Montecinos et al., 2000]. This lengthened snowfall season may homogenize seasonal changes in lapse rates by the effect of snow on albedo and hence the surface energy balance. Moreover, Kull et al. [2002] utilized observed lapse rates, which were similar to the environmental lapse rate (26.88C/ km for summer and 27.18C/km for winter). Modern studies have shown that winter (or accumulation season) temperature lapse rates on glaciers are closer to the environmental lapse rate, and that inversions in lapse rates (i.e., increase of temperature from the glacier surface toward the near surface) are frequent in summer [Gardner et al., 2009; Marshall and Losic, 2011]. This implies a likelihood of bias in some of the gradients utilized by Kull et al. [2002]. In the central part of the country (308Sto408S) few studies have dealt with long-term climate changes and glacier responses. Carrasco et al. [2005] followed the approach from Fox (Cornell University, unpublished data, 1993), and by extension Condom et al. [2007], to assess long-term behavior of the ELA as result of fluctuations in temperature and precipitation. Two modifications of these previous works were imple- mented. The first was the use of radiosonde data from coastal stations in order to determine the 08C isotherm. The second was to employ observed ELAs, precipitation and isotherm gradients, to fit Condom et al.’s [2007] logarithmic model to a more suitable set of coefficients for the region. This corrected model detected a 125 m increase in the ELA and projected an increase ranging from 350 to 440 m for the year 2100. The paper also found that ELAs here were mostly sensitive to temperature. In the prior section on regional modeling, we analyzed Fox’s (Cornell University, unpublished data, 1993) model and provided a reinterpretation of it as an index of ELA sensitivity to changes in the 08C isotherm

rather than as a tool to compute ELAs. Using Carrasco et al.’s [2005] coefficients, we calculated PpSmax using equation (4), finding it at 2366 mm. That figure roughly coincides with the threshold at which that study found a change of sign in the relationship between the 08C isotherm and the precipitation. Because it was a necessary condition for the success of the model, we also tried to replicate the latitudinal ELA profile determined in Carrasco et al.’s [2005] study, using the details provided there and in Carrasco et al. [2008]. Although we were able to fit a third-order polynomial expression, we were unable to obtain either the same coefficients or the same signs for them, even when we utilized latitudes in negative form. Carrasco et al. [2008] extended the work of Carrasco et al. [2005] by using the same statistical model to calculate ELA changes along the whole Chilean Andes for the period 1958–2006. These researchers employed all four Chilean radiosonde stations to calculate regional changes in the ELA. Whereas they found no statistically significant trends in ELA fluctuations during 1958–2006, they did find statistically significant changes when the time series in North (178300S–308S) and Central Chile (308Sto388S) were split before and after 1976; negative until 1976 and positive since then. Above we review that there is justification to support a high sensitivity of the ELA to temperature in Central Chile, based on modeling showing that toward the southern limit of Central Chile, ELA behavior is more sensitive to temperature than precipitation [Kerr and Sugden, 1994]. Regarding the use of radiosondes, a recent study found good correlation between radiosondes and mountain climate toward the southern tip of the central Andes of Chile [Brock et al., 2012, discussed below]. Toward the North, however, the relationship between free air temperature sampled by radiosondes and the ELA is more troublesome to reconcile. As described in the regional modeling section, the NSA may reach large values when precipitation tends to zero, which is the case in the North of Chile [Garreaud, 2009]. This may produce a detachment between free air temperatures observed at the coast (the location of the radiosonde measurement) and the climatology of the glacier boundary layer, which is highly complex in terms of temperature inversions and wind regimes [van den Broeke, 1997]. Moreover, there is not unequivocal evidence that radiosondes in the area portray an accurate representation of mountain conditions [Seidel and Free, 2003], and in fact earlier short-term observations suggested that ELAs and 08C iso- therms do not have a close relationship here [Hastenrath, 1971].

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 482 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

The study by Brock et al. [2012] aimed to reconstruct winter melt events between 388S and 428S. Data employed came from meteorological stations on two ice-covered volcanoes in the area, radiosonde data from Puerto Montt (418260S) and synoptic fields from the NCAR/NCEP reanalysis [Kalnay et al., 1996]. Signifi- cant correlations between temperatures on the glaciers and those from the radiosonde allowed them to calculate winter melt between 1958 and 2010 at the regional ELA by applying a TI model. Outputs were compared against ENSO indexes (e.g., Multivariate ENSO Index or MEI) [Wolter and Timlin, 2011] and aver- aged synoptic fields, in order to detect the main controls on melt events. They found that winter melt events at the ELA occurred regularly in the area, although there were not melt measurements to validate the results. The synoptic analysis suggested that midlatitude migratory high-pressure systems crossing Chile and adiabatic compression derived from northwesterly flows were the main causes. These authors also claimed significant relationships between modeled time series (melt day frequency and total winter melt), sea surface temperatures (south of 238S) and bimonthly MEI values from late winter to late spring (August– November). However, those correlations, although statistically significant, were rather low as the maximum explained variance was only 16%. This work suggested a strong relationship between radiosonde temperature data and meteorological measurements on the glaciers, despite the fact that those data spanned a few years. These findings support the use of freezing levels from radiosonde temperatures as a proxy for ELA behavior, as previously done by Carrasco et al. [2005, 2008]. As the authors suggested, the geometry of the glaciers in the area may make them more sensitive to free air temperatures, as the conical shape of the volcanoes would prevent the development of an isolated boundary layer. That relationship may also be enhanced by the straightforward synoptic connection between the coast and mountains, due to the seasonal westerly flow. Such connection involves particular topoclimatic conditions that may prevent such correlation from being extrapolated elsewhere. The majority of published glacier modeling studies in Chile have tried to simulate Patagonian glaciers. This is facilitated because there are a number of studies that provide data to assess interactions between climate and glaciers [e.g., Masiokas et al., 2009]. These data include glacier chronologies [e.g., Harrison et al., 2007], short-term glacioclimatic monitoring [e.g., Takeuchi et al., 1999], and volumetric fluctuations [e.g., Willis et al., 2012b]. Early modeling work was concerned with the onset and timing of Pleistocene glaciations [Hul- ton et al., 1994; Kerr and Sugden, 1994]. Those studies had to include some representation of modern processes in order to reconstruct glacier conditions in the past. In particular, the seminal work by Kerr and Sugden [1994] was instrumental in understanding the climatic sensitivity of the west-east ELA gradient. They adopted a surface energy balance model for melt and a simple accumulation model to simulate mass balance gradients and ELA between 408S and 568S. The energy balance model accounted for solar radiation, longwave energy, and turbulent fluxes. The accumulation model assumed that solid precipitation falls when the temperature was below 28C. The ELA was determined using the AAR method [Benn and Evans, 2010]. The environmental lapse rate (26.58C/km) and linear gradients of precipitation were utilized to redistribute such quantities from low altitude meteorological stations to the ELA. A minor simplification was the exclusion of wind speed in the turbulent fluxes formulae, as the transfer coefficient was not explicitly calculated. As pointed out in the paper, this simplification may have caused some underestimation in sensible heat and sublimation, although the latter is known to be low due to the high, year-round humidity. The main results for modern times showed that ELAs are more sensitive to temperature fluctuations in wetter areas. In their sensitivity analysis, they found that at the San Pedro station, located at 478S in one of the islands facing the Pacific Ocean, a 50% decrease in precipitation lowered the ELA by 95 m while a temperature reduction of 28C lowered ELA by 315 m. This implies that approximately 0.58C temperature shift was equivalent to 50% change in precipitation. This larger sensitivity to temperature is related to the high mass turnover as product the high amounts of precipitation that the westerly flow brings. This allows glaciers to reach elevations far below the snowline and thus they remain more sensitive to changes in temperature [Oerlemans and Fortuin, 1992]. Hulton et al.’s [1994] model also calculated mass balance gradients to force an ice-flow model of Patago- nia at a 20 km spatial resolution. They devised a continentality factor in order to control the steepness and the maximum mass balance values in the model. The results did not match modern glacierized areas. They numbered a series of reasons to explain such a mismatch, mostly related to the manner in which variables at the ELA, and the ELA itself, were represented, together with the coarse resolution of the model.

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More modern studies of Patagonia have utilized climatic downscaling to produce input fields to glacier simulations. Climatic downscaling is a technique whereby output from a Global Climate Model is rescaled to account for local climate [Wilby and Wigley, 1997]. Cook et al. [2003] utilized the Fifth-Generation Penn State/NCAR Mesoscale Model (MM5) [Grell et al., 1995] to drive a surface energy balance model for the SPI. In this paper, a domain at 90 km spatial resolution fed a nest at 30 km. The MM5 model ran climatological simulations for a typical summer (January) and a winter (July) month. Several MM5 output variables such as solar radiation and longwave incoming were used as input to run a glacier surface mass balance model. Conversely, snow accumulation and turbulent fluxes utilized both MM5 output and external parameteriza- tions, such as rain-to-snow fixed thresholds. Noteworthy features of the glacier model were the use of different albedos on glacierized surfaces, an equation to determine heat diffusion in the ice, and mass balance calculation at different pressure levels. Some findings of this work were: (a) the correlation between elevation and annual ablation was higher than for that between elevation and annual accumulation; (b) there was no winter ablation; (c) the modeled ELA was higher than the observations utilized for validation; and (d) there was a clear west-east gradient in the meteorological control of glacier mass balance. Finding (d) is particularly intriguing, since the authors showed that the eastern side was more sensitive to ablation changes than the western side, arguing that eastern facing glaciers, usually in relatively drier areas, were more susceptible to low-level wind speed, humidity, and near-surface temperature. Those results, specifically regarding temperature, contradict findings of Kerr and Sugden [1994]. In the Northern Patagonian Icefield (NPI), Schaefer et al. [2013] reported the application of the Weather Research and Forecast (WRF) model [Skamarock et al., 2008] to produce climatological fields to run a version of a simplified energy balance model [Oerlemans, 2001]. This is a TI model supplemented by the incoming solar radiation model according to Corripio [2003]. Temperature from WRF output was utilized in the melt equation as well as in the accumulation routine. Precipitation was also taken from WRF and corrected by a factor to fix the mismatch between observations and model output along the eastern side of the study area. A 5 km grid-cell WRF domain simulated climate from 2005 to 2011. Precipitation and temperature were further downscaled to 450 m grid-cell spatial resolution by means of statistical techniques. To expand the length of climate fields to 1975, they computed statistical models between observations and fields from NCAR/NCEP reanalysis. For simulating future mass balance, they downscaled ECHAM5 outputs corresponding to a midrange future scenario of greenhouse gases emissions [IPCC, 2000]. In addition to the model, this study assessed the importance of calving processes in the overall change of mass in the icefield. Modeled mass balance output was subtracted from previously known volume changes in San Rafael and San Quintin glaciers, and the residual was attributed to calving. Schaefer et al. [2013] qualitatively validated outputs of the glacier mass balance model order to determine the best parameters to use in the final simulations. Model outputs were ranked according to their performance against previous volume estimations [Willis et al., 2012]. Among other results, the paper reported higher amounts of ablation on the glacier tongues along the eastern side of Patagonia, and accumulation in excess of 20 mwe on the highest sections of the icefield. They also found that 50%–80% of calving fluxes were due to dynamics in the San Rafael glacier, broadly agreeing to previous studies [Koppes et al., 2011]. Schaefer et al. [2015] applied the same approach to study the surface mass balance of the SPI. They found an overall positive surface mass balance between 1975 and 2011. Positive surface mass balance was simulated in many glaciers facing the western slope of the SPI, including some of the largest ice bodies such as the Pio XI glacier (498S). On the contrary, a number small glaciers located around the SPI showed negative modeled surface mass balance. These findings suggest the crucial importance of calving in the behavior of the largest glaciers in both the NPI and SPI, and the need for more extensive study. The use of this simple glacier mass balance model, however, precluded the comparison of these results against other studies [Kerr and Sugden, 1994; Cook et al., 2003; Lenaerts et al., 2014]. This is because these other studies simulated the mass balance accounting for more components of the energy balance, allowing for a better description of the controlling mechanisms. In addition, and as already pointed out in Pellicciotti et al. [2014], the use of only one future scenario/model was a limitation in their forecast. Unlike the previous two applications of dynamical downscaling techniques, the study by Lenaerts et al. [2014] employed the climate model RACMO [Van Meijgaard et al., 2008] to directly simulate glacier surface mass balance in Patagonia. That means that glacier processes were coupled to those from the atmosphere, thus allowing the icefields to feed back their energetics. Not only did the model allow for those interactions,

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 484 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

it also had routines to deal with albedo changes over time and space, as well as snow drift by wind. Another difference between this approach and the other two previously presented was that whereas the models employed by Cook et al. [2003] and Schaefer et al. [2013] were nonhydrostatic, Lenaerts et al.’s [2014] approach was hydrostatic. As far as we know, there are no studies comparing the performance of hydrostatic versus nonhydrostatic models in this region. However, the spatial resolution of Lenaerts et al.’s [2014] work and the little convective activity relative to the frontal activity [Garreaud et al., 2014] may justify the assumption of hydrostatic balance. The study simulated surface glacier mass balance for the period 1979– 2012 at a 5.5 km grid-cell. ERA Interim reanalysis [Dee et al., 2011] was the main source of climatic fields. Results confirmed sharp mass balance gradients between west and east facing glaciers, and found extreme positive mass balance (in excess of 30 mwe/yr) on several sectors of the main plateau. Although linear positive trends in mass balance were found in both icefields, only in the NPI were they identified as statistically significant. Noticeable geographic contrasts in surface melt and runoff were ascribed to precipitation, spatial distribution of shortwave radiation and, albedo. Unlike the previous two studies, Koppes et al. [2011] included a model representation of calving processes while simulating San Rafael glacier’s (468410S) surface mass balance between 1950 and 2005. A novelty of this approach was the application of two models to calculate calving rates. They found an overall positive mass balance, with calving rates having played a fundamental role in the observed frontal retreat. The model had a TI routine for ablation and a temperature threshold for accumulation. A statistical downscaling technique provided the climatic fields to run the simulation. Data output from the NCAR/NCEP reanalysis were correlated to nearby short-term meteorological observations, establishing linear models to compute downscaled long-term climatic time series. Reanalysis and observed temperature correlated better than reanalysis and precipitation. Precipitation correlation improved when wind speed was included. In order to account for vertical variations in accumulation and ablation, they utilized an orographic enhancement factor for precipitation and a calibrated lapse rate for temperature. They found high sensitivity of modeled mass balance to the proximity of maximum snow fall to the ELA, and the influence of glacier geometry of the glacier margin in controlling ice thinning, calving, and frontal retreat. De Angelis [2014] studied the impact of glacier geometry on the climatic sensitivity of Patagonian glaciers. More specifically, the study aimed to determine the impact of glacier hypsometry in the climatic sensitivity of the ELA along the SPI. The modeling framework was a TI model forced by synthetic time series of precipitation and temperature. The author derived ELAs and mapped hypsometry of 139 SPI glaciers using remotely sensed imagery and the SRTM digital elevation model [Rabus et al., 2003]. Results indicated that the position of the ELA with respect to the areal distribution of a glacier controls much of the climatic sensitivity. In effect, the most sensitive glaciers were those having a larger share of their area below the ELA. De Angelis’s [2014] results agree with previous studies that underscored the crucial role of glacier hypsometry in climatic sensitivity and glacier response over diverse spatial and temporal scales [Brocklehurst and Whip- ple, 2004; Pedersen and Egholm, 2013]. This study suggests an inverse relationship between the sensitivity of glaciers’ frontal variation to changes in ELA and that of the mass balance, which implies nonlinear response to climate fluctuations. These results challenge the assumption of a direct relationship between these quantities, utilized in inverse modeling of climate derived from glacier length records and glacier sensitivity to climate variables [e.g., Leclercq and Oerlemans, 2012]. A few modeling studies have been published in the last ten years or so relating to glaciers south of Patago- nia. Moller€ et al. [2007] and Moller€ and Schneider [2008, 2010] model glacier behavior in the Gran Campo Nevado (GCN, 538S) and explore temperature versus precipitation sensitivity. Moller€ et al. [2007] tried to make sense of volume changes calculated through the comparison of DEMs between 1984 and 2000. Their GIS-based assessment showed large thinning within ablation zones and moderate thickening in accumulation zones, leading to an overall ice loss. A TI model was calibrated through meteorological and glaciological observations taken in the vicinity of the GCN, and within the GCN itself. Specific glacier mass balance gradients were derived from the model and then used to investigate the independent and combined impact of temperature and precipitation in the changes observed. The outcomes of this analysis suggested that the observed volume changes could have resulted from a 7% to 8% precipitation decrease or a 0.3 K warming. The use of a TI model here seems well grounded based on observations that account for 54% of the energy balance due to sensible heat transfer [Schneider et al., 2007]. However, it should be noted that reported energy balance measures did not account for a net radiation partition. Besides, they were taken

FERNANDEZ AND MARK MODELING ANDEAN GLACIERS 485 Journal of Advances in Modeling Earth Systems 10.1002/2015MS000482

during summer, when the glacier surface is closest to 08C. That means that the contribution of longwave incoming energy is still uncertain and could also be a good candidate to explain why the TI model worked well here. Subsequent work not only studied climatic sensitivity [Moller€ and Schneider, 2008] but also reported volume change projections utilizing statistical climatic downscaling [Moller€ and Schneider, 2010], as well as the impact of different downscaling techniques [Weidemann et al., 2013]. The main results predicted net volume loss and showed the downscaling method chosen for the analysis had a considerable impact. As in other parts of the Andes, only one climatic projection was downscaled, precluding better evaluation of uncertainties. Additionally, ice ﬂow and the role of calving in glacier changes were not explored.

5. Final Considerations 5.1. Findings and Open Challenges A heterogeneous glacier population characterizes the Andes, intrinsically associated with particular climatic and topographic settings. Andean glaciers take a variety of forms, from small mountain glaciers to large tidewater valley glaciers. Yet all are, in one way or another, an expression of the complex interaction between large-scale atmospheric processes and modifications at the local scale. What makes the Andes important for global change studies is that it transverses almost all climatic regimes of the Southern Hemi- sphere outside Antarctica and extends through the Northern Hemisphere Tropics. This quasi-seamless glacier cover between 138N and 558S bestows unique potential for better understanding the processes that connect global climate changes, such as increases in temperatures, with observations of changes in glacier mass balance and volume at local scales. Despite this extensive potential to be an indicator of climate changes spanning most of the Southern Hemi- sphere, Andean glaciers have been less studied than other glacierized landscapes. In this review, we have shown that there are several regions in which data on glacier mass balance and volumetric fluctuations are still unavailable. However, current efforts on improving that scenario, as for instance from the GTN-G, are providing and will provide more and better data, which will allow more in-depth glacioclimatic knowledge. Here we argue that modeling information is not yet as organized, evaluated, and assessed as the case of observations. In our view, this task is difficult because (a) different types of models have been applied and (b) these are mostly research studies that not always reprocess data according to standardized procedures. Even in each category we have defined here (e.g., TI, statistical modeling, and energy balance for local models) there are important differences in the applications. For example, all TI models we have reviewed present diverse melt (or degree-day) factors, some of them determined from observations, while others according to literature. In Table 3, we provide a summary of the melt factors utilized in the studies revised in section 4. Some authors utilized a unique factor [Naruse et al., 1997], while others have utilized different figures according to the kind of surface (ice or snow) or the season (summer or winter), such as Stuefer et al. [2007]. Other important difference between TI models, but also in the application of energy balance approaches, is the temperature lapse rate; there is a range of figures that have been utilized (Table 3). Lapse rates of about 88C/km [Stuefer et al., 2007] to 5.78C/km [Moller€ and Schneider, 2008] can produce significant differences in amount of simulated melt and in accumulation, the latter due to its effect in the precipitation phase [e.g., De Angelis, 2014]. This diversity makes it difficult to assess the uncertainty of model results according the assumptions utilized in each study. In that regard, we propose that, in the future, model intercomparisons should account for the sensitivity of models to these factors, besides testing the performance of different model setups across the region, according to what available observations show. In her review on glacier modeling, Hock [2005] asserts that TI models will remain the standard for most applications. And this is what has happened since 9 out of 12 analyzed modeling studies published after 2005 correspond to some form of TI model (Table 2). One of the reasons behind this predominance of TI models boils down to the yet inadequate coverage of climatic instruments in high elevation areas. This means that accurate determination of melt factors, lapse rates, and other related parameters will continue to be essential for accurate simulation of the volumetric response of glaciers to climate changes. Another challenge to modeling that we find useful to highlight is the estimation of more accurate precipitation gradients. In our analysis of Bolivian glaciers, we found that gradients derived from stations can have unaccounted uncertainties due to biases in the observations [Ribstein et al., 1995]. Obtaining a better estimation of rainfall gradients could be done by combining data from satellites and models of orographic

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Table 3. Melt (Degree-Day) Factors and Lapse Rates Utilized in Regionally Focused Glacier Modeling Studies Study Location Factor (mmwe 8 C21 d21) Lapse Rate (K/km) Source Ceballos et al. [2012] Rıo Claro, Colombian Not used 5.4 Local climatic observations. Andes Ribstein et al. [1995] Zongo glacier Not used 7.4 Local climatic observations. Naruse et al. [1997] Upsala and Perito 7.1 Not used Observations on the glaciers. Moreno glaciers Stuefer et al. [2007] Perito Moreno glacier 6.1–7.6 (summer) 8 Nearby observations for lapse rate 2.7–4.3 (winter) and on the glacier for the melt factor. Buttstadt€ et al. [2009] Martial Este glacier 4.7 (snow) 6.9 (mean) Nearby observations for lapse rates 9.4 (ice) 7.1 (summer) and on the glacier for the melt factors. 5.7 (winter) Leclercq et al. [2012] Frıas glacier Not used 4.8 Linear fit through pressure levels from ERA interim. Kull and Grosjean [2000] Tapado glacier 4.5 (annual mean) 6.8 6 0.03 Local climatic observations for lapse rate. and Kull et al. [2002] The melt factors vary during the year according to elevation and the day of the year. Brock et al. [2012] South central Chile 3.5 (snow) 6.5 but with several Local climatic observations for lapse rate and the inversions. Not used mean of values presented in in the modeling Braithwaite [2008] for the melt factor. Kerr and Sugden [1994] Patagonia Not used 6.5 Not specified. Schaefer et al. [2013, 2015] NPI and SPI Not used 6.5 Lapse rate used only for redistribution of temperature inside each 5 km gird-cell. Koppes et al. [2011] San Rafael glacier 3.9 (snow) 5.5 6 0.9 Local observations and NCAR-NCEP data for lapse rate. 6.6 (ice) For melt factor, correlation between observed melt and NCAR-NCEP fields and also Hock [2003]. De Angelis [2014] SPI 3.5 (snow) 8 Stuefer et al. [2007] for lapse rate (Hernan De Angelis, 6.5 (ice) email communication) and Hock [2003] for melt factors. Moller€ et al. [2007] and Gran Campo Nevado 3.5 (snow) 6.3 Local climatic observations for lapse rate and Moller€ and Schneider 7 (ice) observations on the GCN for the melt factor. [2008] Mean 5.4 (all) 6.6 (all) 3.8 (snow) 7.4 (ice)

precipitation. For example, data from Tropical Rainfall Measurement Mission (TRMM) can be used to create relatively high resolution estimations of long-term rain rates and frequency, from 0.18 to 0.058 [Nesbitt and Anders, 2009; Biasutti et al., 2012]. Due to its spatial coverage, which extends across the globe between latitudes 508N and 508S, TRMM can potentially be utilized along most of the Andes. These estimations can be supplemented by relatively simple models of orographic precipitation, which have already been utilized in glacier models [Jarosch et al., 2012]. Our review also shows there is room to improve the representation of Andean glaciers in global and regional approaches. In our view, two main features of global approaches are important to keep in mind. The ﬁrst is the overrepresentation of Patagonian glaciers. We have shown that incorporating more Patagonian glaciers to the detriment of ice bodies from other locations is not an issue for eustatic sea level calculation as these glaciers are the largest contributors by several orders of magnitude. We posit that results of linear models utilizing primarily temperature may be biased to these glaciers, precluding a better understanding of climatic processes at play in other areas. Patagonian glaciers are located on a climate characterized by the absence of a dry season and little temperature amplitude, very different from what occurs north of 388S. In effect, subtropical climates present a marked seasonal pattern of temperature and precipitation according to the slope of the Andes, with warm (cold) and dry (wet) summers (winters) toward the west, while precipitation is usually more intense during the warm summer on the eastern slope [Garreaud, 2009]. On the other hand, although the temperature varies little during the year, seasonal maxima in humidity and precipitation occur during the austral summer months in the Tropics [Vuille et al., 2008a; Garreaud et al., 2009]. These climatic differences lead subtropical and tropical glaciers to a different ablation-accumulation pattern compared to Patagonia, which we believe is not yet captured by these global linear models. Accurately simulating tropical glaciers presents an ongoing challenge, as evidenced by the fact that most uncertainties in global modeling were found there. More complex energy balance approaches are needed to truly represent glacier behavior across the Tropics where mass ﬂuxes are predominantly controlled by seasonality in precipitation, but such endeavor has to be tied to more and better observations. In fact, the larger uncertainty in tropical glacier may be related to a bias of observations toward midlatitude glaciers [Braithwaite, 2002, 2009].

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After reviewing global approaches, we examined modeling studies incorporating all Andean glaciers as a regional entity. These studies are important because they allow adequate identification of heterogeneous glacier responses to changes in climate. Such regional modeling efforts are increasingly necessary because they connect the insights retrieved from global studies, which tend to ‘‘average-out’’ uncertainty, to local observations or models, allowing for more comprehensive and multiscale evaluations of variability and heterogeneity. The ‘‘continental scale’’ we advocate focusing on here should not be understood as one of several other aggregations like ‘‘climatic’’ or ‘‘hydrological’’ regions. Such criteria, by definition, do not expose heterogeneity of glacier response; rather, by denoting homogeneity they do not add value to the regional approach. In the Himalayas, this regional analysis has been instrumental in connecting apparently divergent glacier behavior to recent climatic changes [e.g., Yao et al., 2012]. Because of their natural latitudinal extension, the Andes are perhaps the most prominent laboratory on Earth to test hypotheses of glacier sensitivity to changes in climate elements, such temperature, precipitation, and humidity, and how the topographic context, such as the glacier orientation with respect to mesoscale circulation systems, can modify the volumetric change of a glacier. Eventually, the regional approach may allow for a more detailed understanding of how climate changes control glacier fluctuations, compared to the traditional temperature-precipitation dichotomy. At this scale, however, there remain major challenges in adapting modeling approaches to the particular climate setting of each region. We have shown that the statistical model used by Condom et al. [2007] and Carrasco et al. [2008] can be useful to estimate glacier sensitivities, but it still needs to be tested in other areas. On the other hand, more parameterized models such as the one used by Sagredo et al. [2014] have to consider important feedbacks such as albedo. The diversity of modeling research we have found for the Andes makes it difficult to find a clear pattern of complexity in approaches versus spatial or temporal scale. As expressed above, there are relatively complex models aimed at the same spatial scales [Lenaerts et al., 2014] as simpler ones [Schaefer et al., 2015]. Increas- ing the complexity of models will reveal a large number of interactions and feedbacks between topoclimatic variables that determine changes in glacier surface mass balance, but these approaches are limited by data availability. For example, a relatively complex energy balance approach needs to account at least for solar radiation, air temperature, surface temperature, humidity, wind speed, pressure, and precipitation, or 4 times the number variables needed for a common TI model. Thus, finding an adequate trade-off between the complexities wished and the real availability of data may be necessary in many areas, requiring some knowledge of the possible relevant climate elements that explain most of the variance in mass balance. An empirical/statistical approach utilizing regional climatic data sets and other data available (e.g., reanalysis data), such as the one utilized in Manciati et al. [2014], can be useful as a method to determine how strong the correlation between available variables and mass balance is. This type of analysis may lead to determine locations where a semiempirical model can accurately simulate glacier surface mass balance and where a more complex model is required (Figure 5). This is particularly important in the Tropical Andes, since sometimes temperature does not seem to be correlated to ablation, suggesting that its importance may be mediated by other variables such as humidity or cloud cover [Sicart et al., 2008].

5.2. Envisioning Future Developments Given the features of the modeling studies we have reviewed here, we find useful to propose ways in which modeling studies can better represent processes across the Andes. As we have highlighted in section 5.1, it is important to perform intercomparison studies. We recommend these comparisons to be performed using the same data sets on glaciers or regions representing different climates, in which we can also find relatively long time series of volumetric changes and climatic measurements. For tropical areas, we think that Anti- zana and Zongo glaciers can be good targets to represent inner and outer Tropics respectively. Down south, Echaurren Norte (338S) can be considered representative of subtropical glaciers, because it contains the longest mass balance time series, it is instrumented, and its size is in the range of most glaciers located in the region [Escobar et al., 1995; Bown et al., 2008]. For Patagonian latitudes, representing cold and humid climates, the GCN can be a good option, given the fact one of its glaciers was well instrumented and monitored in the past decade [Moller€ and Schneider, 2008]. Here we consider it important to keep in mind that, unless more continuous observations are taken, the Patagonian Icefields will remain poorly represented. The strategy we propose should use ensembles of models, as in mainstream climatology, to run diverse scenarios according to the uncertainty of model parameters and climate change scenarios. The large

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Figure 5. Flowchart describing the steps that can be utilized to connect the modeling approaches identiﬁed in this paper in order to obtain a reasonable trade-off between process representation and data constrains. The sizes of the circles represent the difference in data needed for each approach, i.e., a physically based model needs about 4 times more data than a semiempirical one. Empirical and semiempirical, on the other hand, are less different in the amount of data they need. Inside each circle, an example of each type of model is cited.

computing capacity required to perform these analysis encourages the configuration of large modeling consortia. In this regard, examples like GlacierMIP are efforts to be repeated and expanded. Increasing the number of observations and model studies may help to develop improved applications of energy balance approaches based upon data from the region. Here we argue there are grounds for future studies using energy balance approaches. This is now possible because the climatic data available in mountains can be connected to climatic model outputs by means of dynamical and statistical downscaling, thus shedding light on the mesoscale processes that determine changes in glacier mass balance and how they relate to large-scale systems [Molg€ and Kaser, 2011; Molg€ et al., 2013]. However, we consider that use of downscaling for future projections must be taken with caution. As seen in our analysis of several of the reviewed studies [e.g., Stuefer et al., 2007; Buttstadt€ et al., 2009], short and discontinuous glacier mass balance measurements limit the use of models, specifically empirically based models such as TI, because they have to rely on short-term calibration periods in order to effectively simulate mass balance trends. Short calibration periods may be a double-edged sword. On the one hand, a good calibration ensures that the model reproduces observed trends; on the other hand, such good calibration of model parameters to short- term measurements does not warrant an assumption that the relationship will hold in the future. If scholars do not regularly update those studies, it is impossible to discern whether or not conclusions were under or overstated. One alternative solution to the issue of short calibration periods may be the use of climatic proxy data as done in the Frıas glacier, Argentina [Leclercq et al., 2012]. There are many places in which observed climatic trends can be merged with proxy data, including tree-rings chronologies and sediments cores [Ahmed et al., 2013], in order to provide continuous time series that can be used as input for models that simulated glacier surface mass balance. Further studies using this combination need to examine what is the actual gain in climatic knowledge when a proxy time series (e.g., tree-rings) is used to generate another proxy, such as glacier fluctuations. We also find it important to incorporate data assimilation techniques in glacier-climate simulations. In particular, we propose to assimilate surface mass balance models, glaciologic, geodetic measurements, and

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yearly resolved mass balance or net accumulation from ice cores. As we expressed above, more and continuous mass balance monitoring programs have been established across the Andes since 2000 [e.g., Ceballos et al., 2012; MacDonell et al., 2013]. These data can be supplemented with estimations of ELA using remote sensing, as this index is significantly correlated to mass balance, especially in midlatitudes [Rabatel et al., 2005]. In addition, there are several locations in which ice cores can be utilized to determine accumulation rates at the annual scale covering several centuries [Vimeux et al., 2009; Thompson et al., 2013]. All these data can be assimilated to produce a first approximation of a mathematically robust and regionally representative view of Andean mass balance changes. One task associated with this proposed exercise is the quantification of uncertainties. In its simplest form, the assimilation of model output and observations requires an estimation of uncertainties, which are usually assumed to follow a Gaussian distribution. These uncertainties are utilized in a cost function to determine the optimal trade-off between model output and observations in order to produce the best estimation of the true state of the variable of interest [Reichle, 2008], which in this case is the glacier surface mass balance. Thus, the use of data assimilation requires determining the uncertainties of models and observations. We think that our proposed intercomparison among models can provide the data needed. For observations, Zemp et al. [2013] provide a list with potential sources of error and a method to determine uncertainty. We believe that this proposal supplements the hierarchical strategy of the GTN-G [Haeberli et al., 2007]. In conclusion, the use of glacier modeling as a tool with which to compare volumetric glacier changes and recent climate changes along the Andes has not been hitherto widespread. However, the corollary of this review is that there are plenty of opportunities to increase the number of studies that render concrete interaction between the groups working on this topic, and make such interaction more necessary than ever.

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