water

Article Evaluating Glacier Volume Changes since the Little Ice Age Maximum and Consequences for Stream Flow by Integrating Models of Glacier Flow and Hydrology in the Cordillera Blanca, Peruvian Andes

Kyung In Huh 1,*, Michel Baraër 2, Bryan G. Mark 3 and Yushin Ahn 4

1 Department of Geography and Anthropology, California State Polytechnic University Pomona, Pomona, CA 91768, USA 2 Département de génie de la construction, École de technologie supérieure, Montréal, QC H3C 1K3, Canada; [email protected] 3 Department of Geography, Ohio State University, Columbus, OH 43210, USA; [email protected] 4 Department of Civil & Geomatics Engineering, Fresno State University, Fresno, CA 93740, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-909-869-3591



Received: 25 September 2018; Accepted: 23 November 2018; Published: 26 November 2018


Abstract: Evaluating the historical contribution of the volume loss of ice to stream flow based on reconstructed volume changes through the Little Ice Age (LIA) can be directly related to the understanding of glacier-hydrology in the current epoch of rapid glacier loss that has disquieting implications for a water resource in the Cordillera Blanca in the Peruvian Andes. However, the accurate prediction of the future glacial meltwater availability for the developing regional Andean society needs more extensive quantitative estimation from long-term glacial meltwater of reconstructed glacial volume. Modeling the LIA paleoglaciers through the mid-19th century (with the most extensive recent period of mountain glacier expansion having occurred around 1850 AD) in different catchments of the Cordillera Blanca allows us to reconstruct glacier volume and its change from likely combinations of climatic control variables and time. We computed the rate and magnitude of centennial-scale glacier volume changes for glacier surfaces between the LIA and the modern era, as defined by 2011 Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model Version 2 (GDEM V2) and 2008 Light Detection and Range (LiDAR) data. The model simulation showed good agreement with the observed geomorphic data and the volume and surface area (V-S) scaling remained within the 25% error range in the reconstructed simulation. Also, we employed a recently demonstrated approach (Baraër, M. et al.) to calculate meltwater contribution to glacierized catchment runoff. The results revealed multiple peaks of both mean annual and dry season discharge that have never been shown in previous research on the same mountain range.

Keywords: glacial meltwater; runoff; Cordillera Blanca; Peruvian Andes; ASTER; LiDAR

1. Introduction Glacier meltwater plays a vital role as a water resource for populations situated downstream of glaciated mountain ranges. This valuable natural water storage affects runoff characteristics in glacierized catchments and downstream river flow regimes. However, the decrease in glacier volume due to climate change causes a net loss of water from storage, leading to a significant ephemeral increase in meltwater runoff from high alpine drainages, followed by a decrease in runoff to regional

Water 2018, 10, 1732; doi:10.3390/w10121732 www.mdpi.com/journal/water Water 2018, 10, 1732 2 of 25 stream flows [1–5]. The reduction in glacier size diminishes the amount of glacier melting and is associated with a decrease in direct runoff [6,7]. Hence, the mean annual total discharge may not change very much, but the seasonality is enhanced with more runoff during the wet season and less runoff during the dry season [3,6,7]. Especially in the tropical Andes in South America, the shrinkage of glaciers can cause a substantial seasonal water scarcity. Hence, glacier retreat will disrupt the current water budgets and become a real threat in the future [2,6]. This not only has strong environmental and economic impacts in downstream societies, but national and even continental economies are affected as glacial meltwater supplies freshwater for hydroelectricity production in the Andean region, for irrigation, and for the drinking water supplies of coastal economies and cities [8–10]. For this reason, measurements of glacier volume and melt rates are the most crucial variables needed to estimate the future impacts of glacial retreat on water resources. In this context, airborne ice-penetrating radar is extensively applied over ice sheets, ice caps, and large mountain glaciers [11–14]. However, radar remains a field-based method. When applied to small glaciers in rugged mountain terrain with steep and narrow valleys, these conditions hinder the achievement of clear data results from the airborne radar systems. Even though ground-penetrating radar (GPR) for ice has improved measurements [14–18], field research is still difficult due to environmental hazards and time-consuming work. Glacier changes based on field observation as well as digitized glacier inventories, including airborne and spaceborne imagery and its digital elevation models (DEMs), can be useful for quantitative methods and models. Besides employing all available datasets to update and improve calculations for the current meltwater regime, it is also important to apply a simple model to reconstruct long-term trends for glacier evolution and to predict the trends of such challenging environments if neither detailed subglacial topography from GPR nor ice-depth information from drilling are feasible [19–22]. Many studies have focused on evaluating the current contribution of meltwater to downstream flows, as well as on making predictions for the near future [1,8,23–27]. Yet, very few studies have been performed to estimate the long-term runoff history of glacierized catchments based on reconstructed glacier ice volume as a water resource. Further understanding of glacier meltwater regimes requires an estimation of the current glacier volume and a reconstruction of past glacier volume changes. Here, we reconstruct key glacier volumes through the Little Ice Age (LIA) advance (around 1850 AD) in the Cordillera Blanca, Peru [28]. We approach the solution by using a simple cellular automata model to simulate mass balance and simple flow from the glaciological processes, and constrain it with satellite DEMs, hillshade images, and information of LIA moraine position. Studies have focused on the LIA because it is one of the most recent examples of natural climate variability identifiable using dating methods, which serves as a basis for analyzing the effects of human action on Earth [28–32]. The LIA is also important for analyzing future climate trends, thus the extension of glacier fluctuations due to the variability of the climate during the last few centuries can be a great reference for comparing projections of future evolution of glaciers. Knowledge of modern glacier fluctuations in the Cordillera Blanca is relatively poor, with a lack of both observational and multi-proxy reconstructed data compared to other glaciers in the mid- and high latitudes [28,33,34]. However, efforts to reconstruct the chronology of tropical Andean LIA glaciers using lichenometry show that moraines corresponding to the LIA maximum glacial advance date to the 17th century on the Pacific-draining slopes [31,35–38]. After this period of major glacial advance, glaciers in the Tropics continued to retreat with less extensive and minor advances of the LIA during the early 18th century (1720 AD) through the early to mid-19th century (1800–1870 AD). This trend appeared to be synchronous between the Cordillera Real, Bolivia and the Cordillera Blanca, Peru [28,31,35–38]. The LIA in the Cordillera Blanca was a period that corresponded with a general glacial advance from the late 16th century to the early 19th century, which was observed from a clear decrease in δ18O[39]. After a temporary minimum advance of glaciers around the mid-1920s, a striking retreat took place between 1930 and 1950, after which the retreat became much weaker [34,40]. Water 2018, 10, 1732 3 of 25

To reconstruct paleoglaciers, paleo-Equilibrium Line Altitudes (ELAs) are estimated from the stages of moraines using the Accumulation Area Ratio (AAR) method [41,42], while modern ELAs can be estimated from the median glacier altitude (which is equivalent to the balanced-budget ELA; the ELA where the mean specific balance is equal to zero) [43]. The median altitude is the altitude dividing the glacier area into equal halves, whereas the mean altitude is the area-weighted mean altitude [43–45]. However, if the median altitude is unknown for modern ELAs, the mid-range altitude (the average of the maximum and the minimum glacier altitudes) is a good indicator of ELA [46,47], with a correlation coefficient of 0.99 for the balanced-budget ELA [43,45]. The estimated absolute errors of the balanced-budget ELA from median altitudes were −38 ± 82 m for their 94 glacier samples over at least 5 years of joint record, whereas the corresponding values from mid-range altitudes were −27 ± 125 m [43]. Although there are differences among glaciers, the ELA of the Artesonraju glacier followed the same general trend: for example, its ELA from mass balance calculations was about 5100 ± 50 m for the period of 2000–2005 AD [48], which is almost equivalent to the median altitude. The general trend in the Cordillera Blanca showed an increase in the ELA of about 108 ± 30 m from the LIA maximum glacial extension at the beginning of the 17th century to the beginning of the 20th century [31]. During the 20th century, the ELA increased by about 70 ± 30 m, in some cases more than 150 m, between the 1930s and the end of the 20th century. The general trend of retreating glaciers over the Cordillera Blanca between the mid-17th and late 19th centuries showed a retreat distance of about 1000 m. The connection between climate change and glacier dynamics—the link among climate, glacier volumes, and mountain hydrology—is a critical research topic. Reconstructed former glacier extent defined by landscape changes can explain glacier fluctuation and thus can give clues of historical meltwater runoff characteristics of alpine drainage basins [23,27,49]. Simulating the dynamics of long-term glacier volume fluctuation as a change in water storage and regional water supply with available models is crucial for the assessment of future water balance [6,27,50]. Here, we employ a hydrological model [1] to reconstruct the long-term runoff from the reconstructed glacial mass changes from the LIA in the Cordillera Blanca, to assess the impact of glacial retreat on changes to historical trends in watershed discharge characteristics. The model isolates the impact of glacier retreat on discharge and does not depend on meteorological data availability. Also, this model can be applied for any watershed as long as there are glacier area sequences. Assessing the hydrological response to glacier retreat via a hydrology trend analysis [1] with a combination of available satellite and airborne Light Detection and Ranging (LiDAR) imagery, in addition to the DEMs for the reconstruction of glacier coverage from the cellular automata model, can provide a broader window to examine a slow-responding and long-lasting phenomenon of the glacio-hydrology regime, rather than just using the limited time series of measured discharge from the field. Situating the currently unfolding hydrological transformation in a longer time perspective should facilitate a comparison and enable us to appreciate the relative magnitude of current changes, as well as anticipate the likely amplitude of future changes. Moreover, the concept of a single discharge peak applies to idealized conditions of continuous and accelerating glacier retreat. The same study [1] suggests that, in a context of strongly variable volumetric recession, the long-term hydrological impact of glacier retreat may exhibit a more chaotic pattern and may be made of a succession of shorter peaks rather than single phases of increase and decrease in stream discharge. However, no studies thus far have identified retreat conditions that could produce multiple peaks of hydrological response to glacier retreat over a longer, retrospective time series. This experimental simulation to extend volume changes from the LIA maximum from a hydrological perspective enables us to describe the response of glaciers to recent climatic fluctuations and analyze the hydrological impact of meltwater on stream flow over the evolution of glaciers. Water 2018, 10, x FOR PEER REVIEW 4 of 25 coverage is in Peru [51,52]. It spans 180 km along the South American continent divide between 8° and 10° S latitude, with 27 summits over 6000 m and over 200 peaks over 5000 m in elevation [34,53]. Both the Yanamarey and Queshque main glaciers are the most studied glaciers in terms of hydrology inWater the2018 Cordillera, 10, 1732 Blanca, Peruvian Andes, between 9°39′ S–9°52’30’’ S and 77°15′00’’ W (Figure 1).4 The of 25 study area features an outer tropical climate with low thermal seasonality and highly seasonal precipitation. The daily temperature variation is greater than the average annual temperature and the2. Study monthly Site precipitation and Geographic has a Setting strong seasonality with most precipitation falling between October and AprilThe Cordillera [34,54]. Blanca is the most glacierized range in the tropical region, containing 25% of the world’sMost glacial tropical meltwater glaciers bydrains area. into In addition,the Santa more River, than which 70% flows of the to world’s the Pacific tropical Ocean glacier [1]. areaThe glaciercoverage meltwater is in Peru of [ 51the,52 watershed]. It spans 180in the km Santa along River the South can Americanprovide 10 continent to 20% of divide the total between annual 8◦ discharge,and 10◦ S latitude,possibly with reaching 27 summits as much over as 600040% mof andthe overtotal 200discharge peaks overduring 5000 the m dry in elevation season, despite [34,53]. onlyBoth having the Yanamarey <10% glacier and Queshque coverage in main the glacierswatershed are [3]. the The most meltwater studied glaciers from the in termsYanamarey of hydrology glacier drainsin the Cordillerawithin the 64 Blanca, km2 area Peruvian of the Querococha Andes, between watershed, 9◦390 S–9 which◦52’30” was S~2% and glacierized 77◦15000” in W 2009–2010. (Figure1). Meanwhile,The study area the features meltwater an outerfrom tropicalthe Queshque climate withmain lowglacier thermal drains seasonality into the and277 highlykm2 Yanayacu seasonal watershed,precipitation. which The dailywas 2.62% temperature glacierized variation in 2009–20 is greater10. As than of 2010, the average the Yanamarey annual temperature glacier (YAN) and had the anmonthly area of precipitation 0.32 km2, accounting has a strong for seasonality0.50% of the with Queroccoch most precipitationa watershed, falling while between the Queshque October main and glacierApril [34 (QUE),54]. had an area of 1.37 km2, accounting for 0.49% of the Yanayacu watershed.

Figure 1. Yanamarey and Queshque main glaciers in the study area. The background is a false Figure 1. Yanamarey and Queshque main glaciers in the study area. The background is a false color color composite (Bands 3, 2, and 1) ASTER image (take on 12 August 2005; downloaded from https: composite (Bands 3, 2, and 1) ASTER image (take on 12 August 2005; downloaded from //lpdaac.usgsu.gov). The Querococha flows into the Santa River. https://lpdaac.usgsu.gov). The Querococha flows into the Santa River. Most glacial meltwater drains into the Santa River, which flows to the Pacific Ocean [1]. The glacier 3.meltwater Data and of Method the watershed in the Santa River can provide 10 to 20% of the total annual discharge, possibly reaching as much as 40% of the total discharge during the dry season, despite only having 3.1. Remote Sensing Imagery <10% glacier coverage in the watershed [3]. The meltwater from the Yanamarey glacier drains within the 64We km computed2 area of the the Querococha rate and magnitude watershed, of which centennial-scale was ~2% glacierized glacier volume in 2009–2010. changes Meanwhile, for glacier surfacesthe meltwater between from the the LIA Queshque and the modern main glacier era, defined drains by into 2008 the LiDAR 277 km data,2 Yanayacu as well as watershed, 2011 Advanced which Spacebornewas 2.62% glacierized Thermal Emission in 2009–2010. and Reflection As of 2010, Radi the Yanamareyometer (ASTER) glacier Global (YAN) Digital had an Elevation area of 0.32 Model km2, accounting for 0.50% of the Queroccocha watershed, while the Queshque main glacier (QUE) had an area of 1.37 km2, accounting for 0.49% of the Yanayacu watershed. Water 2018, 10, x FOR PEER REVIEW 5 of 25

VersionWater 22018 (GDEM, 10, 1732 V2) and its imagery. High-resolution airborne LiDAR data were acquired during5 of 25 2–16 July 2008 (Yellow boxes in Figure 2) and ASTER GDEM V2 was released on 17 October 2011 (covering the entire study area depicted in Figure 2). Also, 1962 aerial photo coverage is represented 3. Data and Method in the figure by the blue boxes. 3.1.For Remotecellular Sensing automata Imagery modeling, both ASTER GDEM V2 and LiDAR DEMs were used. The dataset was resampled mainly from LiDAR DEM of 10 m and partially from ASTER GDEM V2 of 30 m to fill Wesurface computed areas thewhere rate LiDAR and magnitude DEM data of centennial-scaledid not cover the glacier glacier volume valley, changes to compute for glacier paleoglaciersurfaces betweenflow. ASTER the LIA satellite and the imagery modern was era, used defined for bythe 2008 recent LiDAR estimates data, asof wellglacier as 2011areas. Advanced The absoluteSpaceborne vertical Thermalaccuracy Emission of ASTER and GDEM Reflection V2 was Radiometer as small as (ASTER) 8 m (generated Global Digitalfrom 10–20 Elevation ASTER Model scenes,Version covering 2 (GDEM most V2)areas and in itsthe imagery. Cordillera High-resolution Blanca) to between airborne 8 and LiDAR 15 m data (produced were acquired using five during scenes2–16 or Julyless 2008over(Yellow the northern boxes inportion Figure of2) andthe Cordillera ASTER GDEM Blanca) V2 was[55]. releasedFor the onmodel 17 October used to 2011 reconstruct(covering the the glacier entire volume study area in this depicted study, in DEMs Figure were2). Also, resampled 1962 aerial to a photoresolution coverage of 100 is representedm to meet in the computationalthe figure by the requirement blue boxes. of cellular automata modeling.

9.02

9

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8.94 8.92 8.9 1.8 2 2.2 2.4 2.6 2.8 5 x 10

Figure 2. Study glaciers (red outline) and dataset used for this study. Left: Mosaicked Advanced Figure 2. Study glaciers (red outline) and dataset used for this study. Left: Mosaicked Advanced SpaceborneSpaceborne Thermal Thermal Emission Emission and Reflection and Reflection Radiometer Radiometer (ASTER) (ASTER) Global Global Digital Digital Elevation Elevation Model Model VersionVersion 2 (GDEM 2 (GDEM V2) with V2) withLight Light Detection Detection and Rang and Rangee (LiDAR) (LiDAR) digital digital elevation elevation models models (DEMs) (DEMs) for for modeling.modeling. Right: Right: The coverage The coverage of 1962 of 1962aerial aerial photos photos (blue (blueoutline) outline) and 2008 and 2008LiDAR LiDAR flights flights (yellow (yellow outline)outline) over overthe Southern the Southern Cordillera Cordillera Blanca, Blanca, Peru. Peru. Background Background is an isASTER an ASTER mosaic mosaic image. image.

3.2. PaleoglacierFor cellular Extent automata modeling, both ASTER GDEM V2 and LiDAR DEMs were used. The dataset wasTo check resampled the outputs mainly of fromthe simulation LiDAR DEM of paleoglacier of 10 m and reconstruction partially from from ASTER the cellular GDEM automata V2 of 30 m to model,fill we surface compared areas wherethe result LiDAR with DEM the LIA data mo didraine not positions cover the and glacier valley valley, morphology to compute determined paleoglacier fromflow. LiDAR ASTER shaded satellite relief imagery images was created used from for the its recent DEMs estimates and 1962 of aerial glacier photographs. areas. The absolute These are vertical valuableaccuracy sources of ASTER of information, GDEM V2 indicating was as small the pr asevious 8 m (generated glacial extent from since 10–20 the ASTER LIA [28,31,33,38]. scenes, covering Also,most the surveyed areas in the data Cordillera information Blanca) of YAN to between [56,57] 8 was and used 15 m to (produced compare using with fivethe model scenes simulation or less over the result.northern We limited portion the of simulation the Cordillera applying Blanca) the [55 cellular]. For the automata model usedmodel to reconstructover the two the glacier glacier sites volume (YANin and this QUE) study, due DEMs to the were visibility resampled of the to aLIA resolution moraines of from 100 m the to cross-section meet the computational of LiDAR DEMs requirement and of its hillshadecellular automataimages over modeling. major glacier valleys for this study. The LIA moraines located down-valley of the target glaciers are readily visible from the cross-section profiles of LiDAR DEMs and 1962 aerial

Water 2018, 10, 1732 6 of 25

3.2. Paleoglacier Extent To check the outputs of the simulation of paleoglacier reconstruction from the cellular automata model, we compared the result with the LIA moraine positions and valley morphology determined from LiDAR shaded relief images created from its DEMs and 1962 aerial photographs. These are valuable sources of information, indicating the previous glacial extent since the LIA [28,31,33,38]. Also, the surveyed data information of YAN [56,57] was used to compare with the model simulation result. We limited the simulation applying the cellular automata model over the two glacier sites (YAN and QUE) due to the visibility of the LIA moraines from the cross-section of LiDAR DEMs and its hillshade images over major glacier valleys for this study. The LIA moraines located down-valley of the target Water 2018, 10, x FOR PEER REVIEW 6 of 25 glaciers are readily visible from the cross-section profiles of LiDAR DEMs and 1962 aerial photographs. From thephotographs. terminus From locations the terminus of the locations LIA paleoglaciers, of the LIA paleoglaciers, it was possible it was topossible estimate to estimate the volume the and surfacevolume area of and the surface paleoglaciers area of the as paleoglaci well as theirers as changeswell as their over changes time. over time.

3.3. Glacier3.3. Glacier Mass Mass Balance Balance Model: Model: Cellular Cellular Automata Automata We modeledWe modeled the glacier the glacier dynamics dynamics 160 160 years years back to to the the LIA LIA across across the landscape the landscape using usinga cellular acellular automata technique in MATLAB version R2016b from MathWorks. The cellular automata model for automata technique in MATLAB version R2016b from MathWorks. The cellular automata model for glacier flow modeling [58] was initially a landscape evolution approach, but a modified version for glacierglacier flow modelingflow was adopted [58] was in this initially study. a A landscape schematic overview evolution of approach,the cellular automata but a modified model and version a for glacierhydrologic flow was water adopted balance in thismodel study. [1] (see A Section schematic 3.6 for overview the hydrology of the model) cellular is shown automata in Figure model 3. and a hydrologic water balance model [1] (see Section 3.6 for the hydrology model) is shown in Figure3.

Figure 3. Schematic overview of cellular automata model [58] with hydro balance model [1] used for Figure 3. Schematic overview of cellular automata model [58] with hydro balance model [1] used for this study. this study.

AccordingAccording to a to previous a previous study study [58 [58],], this this approachapproach can can examine examine how how glacier glacier dynamics dynamics can be can be simulated.simulated. This This model model is simple is simple because because thethe focusfocus is is on on a afirst-order first-order representation representation of climate of climate and and glaciersglaciers at the at scale the scale of theof the mountain mountain valley.valley. For For modeling, modeling, we used we used simple simple input parameters input parameters such as such as DEMDEM model, model, glacier glacier boundary boundary of the initial initial year, year, initial initial year year of ELA, of ELA, initial initial year of year mass of balance mass balance maximummaximum gradient, gradient, time time of simulation, of simulation, and and time time increment with with valley valley topography. topography. The model starts from the ice boundary of 2008 glacier polygons and grows the glaciers inversely The model starts from the ice boundary of 2008 glacier polygons and grows the glaciers inversely based on 2008 and 2011 DEMs. The model mimics the accumulation and ablation of snow and ice, as based onwell 2008 as its and redistribution 2011 DEMs. by glacier The model motion. mimics The model the runs accumulation until the time and of ablationsimulation of with snow the and ice, as wellprescribed as its redistribution climate condition. by glacier To verify motion. the accuracy The model of the runsmodel, until the theresults time of ofthe simulation test run were with the prescribedcompared climate with condition. 1962 glacier polygons To verify over the both accuracy YAN and of QUE. the model,For YAN, the an undated results LIA of the maximum, test run were comparedassumed with to 1962 be around glacier 1850 polygons AD, with over a surveyed both YAN series and of terminus QUE.For position YAN, records an undated (1939, 1948, LIA 1982, maximum, assumed1988) to and be aroundtheir longitudinal 1850 AD, profiles with were a surveyed available to series compare of terminus with the model position performed records [56] (1939, (see 1948, Figure 4). 1982, 1988) and their longitudinal profiles were available to compare with the model performed [56] (see Figure4).

Water 2018, 10, 1732 7 of 25 Water 2018, 10, x FOR PEER REVIEW 7 of 25

(a)

(b)

Figure 4. Surveyed data of the Yanamarey glacier [56]. (a) The ice extent of the Yanamarey glacier over Figure 4. Surveyed data of the Yanamarey glacier [56]. (a) The ice extent of the Yanamarey glacier the time series (1939, 1948, 1962, 1973, 1982, and 1988) to the maximum (undated) inferred from large over the time series (1939, 1948, 1962, 1973, 1982, and 1988) to the maximum (undated) inferred from moraines [56]. (b) The longitudinal profiles of the glacier surface, bed, and width, along the central line large moraines [56]. (b) The longitudinal profiles of the glacier surface, bed, and width, along the showncentral in the line upper shown panel in the (scale upper 1:20,000) panel (scale [56 1:20,000)]. [56]. 3.4. Cellular Automata Model Setup 3.4. Cellular Automata Model Setup TheThe landscape landscape was was discretized discretized into into a a regularregular he hexagonalxagonal lattice lattice computed computed from from 100-m 100-m resolution resolution DEMsDEMs for the for modelthe model requirement. requirement. This This allows allows for six six degrees degrees of of flexibility flexibility for forparticle particle motion motion between between adjacentadjacent cells. cells. The The ELA ELA used used here here as as anan inputinput parameterparameter was was the the median median glacier glacier altitude altitude for each for each glacierglacier model model run, run, since since the the median median glacier glacier altitudealtitude is is an an alternative alternative indirect indirect method method of depicting of depicting the the ELAsELAs of glaciers of glaciers [43 [43].]. Furthermore, Furthermore, the the ELA ELA began began to decrease to decrease 1 m per 1 m year per when year the when model the was model run was run because the ELA increased by about 70 ± 30 m during the 20th century as the glaciers retreated, reaching a 150-m increase in some cases from the 1930s to the end of the 20th century [31]. For a good example, the evolution of the ELA of the Artesonraju over the past centuries shows that the ELA Water 2018, 10, 1732 8 of 25 of the glacier around 1850 AD can be easily interpolated to be around 4870–4880 m, from 4860 m in 1800 AD and 4885 m in 1880 AD [31], further increasing to about 5100 ± 50 m during 2000–2005 AD [48]. Since the trend of the Artesonraju is concordant with the general trend, setting the ELA change to 1 m per year for glaciers within the same mountain range for the model would be justified. Meanwhile, the time steps are made to depict mean annual climate conditions. The simulation glacier particles move within the lattice synchronously, at discrete time steps. The glacier particles representing the water equivalent of snow and ice are added to and removed from the lattice following the rules of precipitation and ablation. The glacial ice motion is considered to be plastic with a yield stress of 1 bar, 100 kPa, including deformation and sliding, which accommodate flux to maintain the basal shear stress, τb, at the yield stress [59,60].

τb = ρgh sinα ≈ 1 bar, (1) where ρ = density, g = acceleration due to gravity, h = ice thickness, and sinα = ice surface slope. Values of τb are normally between 50 and 150 kPa (100 kPa = 1 bar). The flux determines the velocity and geometry of glaciers. Plasticity is a widely applied simplification in glacier flow modeling [60] and holds to the first order provided that along-glacier shear is the dominant mode of deformation. A large body of observational and analytical evidence supports this assumption [20,60], including in situ measurements of the full strain rate tensor in a valley glacier [61]. When the model runs, any ice thickness causing stress exceeding 1 bar will flow to the lower adjacent cell. Although the model does not reconstruct ice flow perfectly, the results predict the general LIA glacier extent [58]. The mass balance was assumed to be constant the accumulation area, while the value was set to decrease at a constant rate of 6 m/year/km of altitude in the ablation area based on the balance gradient [56] and maximum accumulation of 1 m/year. The parameters for the cellular automata model for YAN and QUE are listed in Table1.

Table 1. Input parameters for the cellular automata model employed in this study.

Parameters YAN QUE Median height (m) from DEM 4898 5057 Equilibrium Line Altitude (ELA) for model (m) 4780 4950 Net balance in ablation (103 kg m−2 year−1) 6 6 Max mass balance (103 kg m−2 year−1) 1 1 Total time (year) (test: 2011 to 1962) 49 49 Total time (year) (2011 to 1850) 161 161 YAN: Yanamarey glacier, QUE: Queshque main glacier.

First, the test version of the cellular automata model (almost 50 years; 2011 to 1962) was performed to evaluate the model by comparing 1962 glacier polygons from aerial photographs available for target glacier valleys. After these tests were completed, the LIA paleoglacier modeling was conducted for both the YAN and QUE sites. Then, we performed the modeling of the LIA glaciers retrospect over 161 years (younger and minor advances: 1850 AD) [28,31,38]. To check the ability of the model to accurately simulate paleoglaciers, the simulation results were compared with surveyed records from previous research [57]. The headwall-to-terminus distance, the elevation of the terminus position, the surface area, and the volume of all reconstructed information of the YAN site over different years were compared with the available measurement data [57].

3.5. Volume and Surface Area (V-S) Scaling from the Model After the simulation to reconstruct paleoglaciers through the LIA maximum for YAN and QUE was achieved, the volume and surface (V-S) scaling for individual glaciers was performed. The volume (V) of any individual glacier or ice cap is related to its surface area (S) by a simple power law relationship Water 2018, 10, 1732 9 of 25

expressed with a scaling coefficient (C0) and a scaling exponent (C1) that depends on glacier type, both empirically computed from the measured V and S [19,20] as follows:

C1 V = C0 · S , (2) where the unit of V is 106 m3 and that of S is 106 m2. Observations of a wide range of glaciers mostly located in mid and high latitudes gave values of 28.5 and 1.36 for C0 and C1, respectively [19–21]. This value of C1 agrees with observations from References [20,62,63]. Based on six glaciers, including YAN and QUE, in the Cordillera Blanca [64], Equation (2) becomes:

V = 48.032 · S1.275. (3)

The uncertainty of the V-S scaling of Equation (3) based on the principle of error propagation [64,65] shows that the magnitude of error of V-S scaling is approximately 25% of the computed volume (V). Equation (3) of the V-S scaling from six glaciers in the Cordillera Blanca [64] was compared with the scaling factors from the V-S scaling of YAN and QUE obtained from the reconstructed surface area and volume as well as the change in surface area and volume. Also, the volume difference of YAN between the literature and the results from the cellular automata model presented here was taken as an uncertainty of the reconstruction using the cellular automata model.

3.6. Hydrology Model We also performed an experimental approach to model changes in glacial meltwater using a water balance model to see if the historical mountain glacial hydrology regime could be reconstructed back to the LIA maximum. This enabled us to analyze the long-term trend of glacial meltwater discharge as well as the impact of the recession of glaciers. The schematic overview of the water balance model with the cellular automata model is shown in Figure3. This water balance model is a relatively simple approach [1], which can evaluate both historical and recent time series of the discharge of selective watersheds in the Cordillera Blanca as well as calculate discharge hydrographs based on glacier retreat sequences. The water balance model for the yearly discharge (Qn)[1] can be expressed as follows:

Qn= (∆Vgl + pp·Agl)·dmelt + (AT − Agl) · (pp − etngl) − ETrl, (4) where ∆Vgl is the interannual change in glacier volume in water equivalent, pp is the average depth of precipitation received, etnglis the non-glacierized evapotranspiration per unit area, dmelt is the fraction of annually ablated ice (snow and firn included) that is not lost by sublimation, and finally AT and Agl are the total watershed area and glacierized areas, respectively. The dry season discharge (Qdn) can be expressed as follows:

Qdn = (∆Vgl + pp·Agl)·αd’melt + (AT − Agl) · qngl − ETrl, (5) where α is defined as the fraction of annual ablation that occurs during July and August, d’melt is used instead of dmelt, and qngl is the net slow-flow dry season specific discharge, which accounts for the water released from groundwater minus the specific transpiration. The major input parameters for the model to create synthetic hydrographs are the initial glacierized surface area, the watershed area, and the annual average precipitation. The LIA paleoglacier maximum extent of the mid-19th century (around 1850 AD) was estimated from both the cellular automata model and the LIA moraine positions and was then used as an input parameter to determine the initial glacier surface area. As the model requires a continuous time series of glacier areas over the study period, the outputs of the cellular automata model for YAN were interpolated using pattern assimilation from a published description of regional glacier area fluctuation over the last 150 years [40]; the glacier front position data recorded in 1948 and a time series from 1976 to 2006 by the Autoridad Water 2018, 10, 1732 10 of 25

Nacional del Agua (ANA) del Peru; and the 1962 aerial photo-based estimates [64] with recent estimates of 2001–2008 obtained from ASTER satellite imagery [64]. The model assumes that the path of glacier surface area change was similar to that of glacier front retreat. The retreat sequence pattern implies that glaciers were generally retreating slowly from 1850 to 1920 [40]. This period was followed by a marked advance from 1920 to 1930, leading to glacier surface areas almost equal to those of 1850. The period between 1930 and 1945 was characterized by a strong mass wasting from the glaciers, which slowed after 1945. Both glacier surface area time series were extrapolated until 2050 to provide estimations of how stream discharge may change as the glaciers continue to retreat. The projection of glacier surface area was simply based on a quadratic extrapolation from the glacier surface area of 2001–2009. The times series of change in surface area were substituted for the annual glacier retreat rate of surface area with a linear interpolation in the model. A similar method was used to create the QUE surface area time series using the YAN surface area fluctuation pattern as a model. Precipitation yearly average was kept constant at 1850 mm per year for the entire studied period in the model. This was justified by the absence of a regional trend in precipitation over the period of record [1]. Using a fixed precipitation value for the simulation allowed for the removal of noise of the interannual natural variation, which would have affected the discharge simulation. Therefore, the fixed precipitation parameter allowed the model to produce discharge time series that fluctuate only from glacier retreat. This benefit was obtained at the expense of the year-to-year representative of the model. Consequently, only discharge trends can be interpreted from the model output and the year-to-year variations cannot be considered to match the reality. The value of 1850 mm per year was adjusted from the historical precipitation record from two meteorological stations of 1981–1999 and 2001–2008 located near YAN in the Querococha watershed [66]. Other model parameters were adjusted from those that were applied to the Querococha watershed, which hosts YAN (Figure1), in a previous study [1] based on the yearly and the dry season discharges recorded at a discharge station situated at the outlet of the YAN proglacial lake. This was achieved by targeting a yearly mean discharge difference between the simulated and observed discharges of less than 5% for the data available from 2002 to 2007. Considering QUE, which has the same orientation as YAN and is located within 15 km, we kept the model parameters tuned for YAN since there is no gauge system installed at the Yanayacu watershed, which hosts QUE. The parameterized model result was used to generate time series of the yearly average discharge (Q) and the yearly dry season discharge (Qdry) based on precipitation, the time series of the glacier surface area, and the surface area of the watershed.

4. Results and Discussion

4.1. Cellular Automata Model

4.1.1. Modeling Test: 50 Years Back (2011 through 1962) To evaluate the model, first we performed a test run from the 2008 glacier polygons for YAN and QUE extracted using 2008 ASTER images (almost 50 years; 2011 to 1962) and compared the results with the 1962 glacier polygon extracted from the 1962 aerial photographs (Figure5). All three different polygons of the test results of the modeled glacier boundaries (shown in red) of YAN and QUE, 1962 glacier polygons (shown in green), and 2008 glacier polygons (shown in blue) are displayed in 2D (Figure5). The results in Figure5 show that the modeled glacier terminus positions agree with the positions based on the pictorial representation from 1962 aerial photographs. For QUE, the modeled glacier coverage is wider in the valley than the actual 1962 glacier extent. This may be because the cellular automata model is sensitive to the shape of the glacier valley and topography. If the shape of the valley is wide at the initial stage of the model run, then the output of the model gives a broader surface area, and this may affect the V-S relationship. Through repeated model runs over both glaciers, we confirmed ELAs of 4780 m for YAN, 4950 m for QUE, and a net balance gradient of 6 m/year/1 km. For the comparison with the 1939 AD field Water 2018, 10, 1732 11 of 25 record for YAN [57], we ran the model through 1939 AD. Based on parameters from the illustrated results of the test run, we performed the modeling of the LIA glaciers retrospectively up to 161 years Water 2018, 10, x FOR PEER REVIEW 11 of 25 (younger advance: 1780–1880 AD, LIA maximum in 1850 AD) [28,31,38].

6 x 10

8.9335

8.933

8.9325

8.932

8.9315

8.931

8.9305

2.485 2.49 2.495 2.5 2.505 2.51 2.515 2.52 2.525 2.53 5 x 10 (a) 6 x 10

8.92

8.919

8.918

8.917

8.916

8.915

2.51 2.515 2.52 2.525 2.53 2.535 2.54 2.545 2.55 2.555 5 (b)

Figure 5. The test run result of 1962 from the cellular automata model for both YAN (a) and QUE (b). TheFigure results 5. ofThe the test 1962 runmodel result of run 1962 (red; from 49-year the cellular time simulation) automata model agree for with both the YAN boundary (a) and drawn QUE (b from). theThe 1962 results aerial of photos the 1962 (green). model run The (red; polygon 49-year of thetime 2008 simulation) boundary agree is shown with th ine boundary blue. drawn from the 1962 aerial photos (green). The polygon of the 2008 boundary is shown in blue.

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Water 2018, 10, x FOR PEER REVIEW 12 of 25 4.1.2. Modeling through LIA Maximum (1850 AD) 4.1.2. Modeling through LIA Maximum (1850 AD) Starting from the 2008 terminus achieved from 2008 polygons, the cellular automata model Starting from the 2008 terminus achieved from 2008 polygons, the cellular automata model simulated until the LIA maximum for both YAN and QUE with an ELA decrease of 1 m per year. simulated until the LIA maximum for both YAN and QUE with an ELA decrease of 1 m per year. While the model was simulating, the new ELA was computed from the new glacier boundary and While the model was simulating, the new ELA was computed from the new glacier boundary and the new updated ELA in retrospect to 150 years, indicating an LIA maximum ELA 150 m lower than the new updated ELA in retrospect to 150 years, indicating an LIA maximum ELA 150 m lower than the present ELA. The pictorial result of the simulation shows the evolution of YAN over the period the present ELA. The pictorial result of the simulation shows the evolution of YAN over the period studiedstudied (See (See Figure Figure6a). 6a).

(a)

The Cross-section of LiDAR DEM over YAN

LIA maximum Late 1962

Around 1850 AD 1930s boundary

(b)

FigureFigure 6. ( a6.) ( Thea) The simulation simulation result result of theof the time time series series of theof the modeled modeled glacier glacier terminus terminus positions positions from from the Littlethe Ice Little age Ice (LIA) age maximum(LIA) maximum (1850 AD)(1850 up AD) to up 1988 to AD1988 for AD YAN. for YAN. (b) The (b) cross-sectionThe cross-section of LiDAR of LiDAR DEM usedDEM to verify used to LIA verify moraine LIA moraine positions positions over YAN. over YAN.

TheThe comparison comparison of of the the length, length, surface surface area, area, and and volumevolume of YAN (headwall to to terminus) terminus) between between thethe model model and and that that reported reported inin ReferenceReference [57] [57] is is de describedscribed in inSection Section 4.2. 4.2 Th.e Thesimulation simulation output output and andthe the measurement measurement data data show show good good agreement agreement [57]. [ 57Although]. Although there thereis no isreference no reference for QUE, for QUE,the thesimulation simulation was was performed performed based based on onthe the retrospect retrospect time time series series of 1988–1939, of 1988–1939, the same the same as YAN, as YAN, as

Water 2018, 10, 1732 13 of 25 Water 2018, 10, x FOR PEER REVIEW 13 of 25 as shown in Figure7, and revealed that the modeled glacier terminus positions agree well with the shown in Figure 7, and revealed that the modeled glacier terminus positions agree well with the moraine positions obtained from the cross-section of the LiDAR DEM. Figure8 shows the series of moraine positions obtained from the cross-section of the LiDAR DEM. Figure 8 shows the series of reconstructed paleoglacier boundaries over a 10-year interval. reconstructed paleoglacier boundaries over a 10-year interval.

1988 1982 1973 1962 1948 1939 1850

(a)

Late 1962 LIA maximum

1930s boundary Around 1850 AD

~150 years moraine

The Cross-section of LiDAR DEM over QUE

(b)

Figure 7. (a) The simulation result of the time series of modeled glacier terminus positions from the Figure 7. (a) The simulation result of the time series of modeled glacier terminus positions from the LIA maximum (1850 AD) to 1988 AD for QUE. (b) The cross-section of the LiDAR DEM was employed LIA maximum (1850 AD) to 1988 AD for QUE. (b) The cross-section of the LiDAR DEM was employed to verify the LIA moraine positions over QUE. to verify the LIA moraine positions over QUE.

Water 2018, 10, 1732 14 of 25 Water 2018, 10, x FOR PEER REVIEW 14 of 25

(a)

(b)

Figure 8. The paleoglacier reconstruction of the LIA maximum (1850 AD). The series of reconstructed paleoglacier boundaries inin 10-year10-year intervalsintervals forfor ((aa)) YAN,YAN, ((bb)) QUE.QUE.

Water 2018, 10, 1732 15 of 25

4.2. Model vs. Previous Research on YAN How well does the model reconstruct the glacier? To assess the model’s performance of YAN simulation, the outputs were compared with surveyed data [57]. Although these measurements are short-term and intermittent, they are enough to compare on a year-to-year basis (Table2).

Table 2. The comparison between model outputs and measurement data from previous research [57]. H&A is from the surveyed data from [57].

Distance from Headwall to Terminus Surface Area Volume (106m3) Terminus (m) Elevation (m) (106m2) Year Model H&A Diff. Model H&A Model H&A Model H&A 1988 991.65 1250 258.35 4631.3 4630 0.86 0.8 32.29 25 1982 1098.28 1350 251.72 4625.92 4600 0.91 0.87 35.04 32 1973 1268.88 1500 231.12 4618.86 4595 0.97 0.95 38.43 - 1962 1432.62 1550 117.38 4624.55 4600 1.05 1.02 43.09 - 1948 1695.40 1600 −95.40 4600 4590 1.20 1.0 52.27 54 1939 1855.34 1850 −5.34 4530.34 4520 1.22 1.2 59.99 - 1850 2991.60 2800 −191.60 4348.13 4420 1.73 1.7 88.71 89

Generally, the modeled glacier terminus positions agree with the measured positions [57]. The model output shows that the difference in distance between the model and the reference is about 117 m in 1962 AD, decreasing to 5.34 m in 1939 AD. For 1850 AD, the terminus position from the model simulation is 191.60 m longer than the position of the reference. However, the surface area and volume between the two show results indicating that there are no big differences between the model and reference (Table2). The cellular automata model with simple parameters succeeded in simulating the extent of the LIA maximum paleoglacier over the YAN and QUE valleys, although the model did not mimic the ice flow exactly. The results were based on constant climate parameters except for the ELA setting, while glaciers in the real world exist under variable climate conditions. We presumed that the ELAs were within a few tens of meters of the modeled value, although we do not have any field evidence to back this up. Although setting the ELA to decrease by 1 m per year for the model may not be realistic for the beginning years retrospectively, it may be valid for a long-term model simulation. Therefore, the simulation result should represent conditions averaged over centuries. Also, the length and the width of the simulated glaciers may be sensitive to the complex elevation distribution of both surface area and slope. However, long-term mass balance data do not exist for broader mountain ranges in the Cordillera Blanca and only cumulative values are available for a few glaciers without time series [56,57,67–69]. Also, there are limited numbers of chronology studies for the study area, and those that exist are focused more on millennial scales (Last Glacial Maximum; LGM) [29,30,70–72]. This limits the possibility of comparing our regional, long-term model to ground truth over the entire range. Moreover, the results of the model simulation were based on constant climate parameters, while glaciers in the real world exist under non-stationary climate conditions.

4.3. Volume Reconstruction from the Model vs. V-S Scaling Fit

4.3.1. The V-S Scaling of YAN from the Cellular Automata Model Based on the reconstructed surface area (S) and its volume (V), Equation (2) for YAN can be written as follows and is shown below in Figure8:

V = 40.156 · S1.446. (6)

The V-S scaling over YAN from the simulation shows C0 = 40.156 and C1 = 1.446. Since the V-S scaling relationship over glaciers in the Cordillera Blanca [64], including YAN, shows that Water 2018, 10, 1732 16 of 25

Water 2018, 10, x FOR PEER REVIEW 16 of 25 C0 = 48.043 and C1 = 1.275, the differences in volume between the V-S scaling from six glaciers in the Cordillera Blanca, including YAN, and the V-S scaling generated from the cellular automata model of AD (size of 0.66 km2), while the difference in volume between the V-S scaling of YAN from the cellular YAN were 8.20% in 1850 AD (size of 1.73 km2), 14.33% in 1962 AD (size of 1.16 km2), and 22.15% in automata model and that from Chen and Ohmura (1990) ranged from 26 to 32% (Table 3). 2001 AD (size of 0.66 km2), while the difference in volume between the V-S scaling of YAN from the cellular automata model and that from Chen and Ohmura (1990) ranged from 26 to 32% (Table3). Table 3. Difference in the V-S scaling of YAN between the cellular automata model and six glaciers in the Cordillera Blanca [19,65]. Table 3. Difference in the V-S scaling of YAN between the cellular automata model and six glaciers in the Cordillera Blanca [19,64]. Volume Volume Volume Volume from Volume from from V-S Volume Size Diff. (CA Diff. (CB6 Year VolumeV-S from ScalingVolume V-S from ScalingVolume Scaling from VolumeDiff. Diff.(CB6 Volume Diff. Volume Diff. Size 2 Year (kmV-S) Scaling CA V-S Scaling V-S Scaling (CB6 vs. CA) (CAvs. vs. C&O) C&O) vs.(CB6 C&O) vs. C&O) (km2) CA (106m3) CB6 (106m3) C&O vs. CA) (%) (106m3) CB6 (106m3) C&O (106m3) (%) (%) (%)(%) (106m3) 18501850 1.73 1.73 88.71 88.71 96.64 96.64 60.01 60.01 8.20 8.20 32.35 37.90 37.90 19621962 1.16 1.16 49.46 49.46 57.73 57.73 34.68 34.68 14.33 14.33 29.88 39.93 39.93 2001 0.66 22.02 28.28 16.23 22.15 26.29 42.62 2001 0.66 22.02 28.28 16.23 22.15 26.29 42.62 CA: cellular automata model; CB6: six glaciers in the Cordillera Blanca [64]; C&O: from Reference [19]. CA: cellular automata model; CB6: six glaciers in the Cordillera Blanca [65]; C&O: from Reference [19].

The approachapproach usingusing the the cellular cellular automata automata model model to reconstruct to reconstruct paleoglaciers paleoglaciers and their and V-S their scaling V-S worksscaling wellworks for well YAN for because YAN because the model the showsmodel thatshows the that volume the volume estimation estimation achieves achieves a similar a similar range (8.20%)range (8.20%) when thewhen glacier the glacier reached reached the LIA th maximume LIA maximum in 1850 in AD 1850 (Table AD 3(Table). 3). Also, we we can can verify verify the the error error estima estimationtion of the of the V-S V-S scaling scaling in Figure in Figure 9. Based9. Based on the on 25% the error 25% range error (sixrange glaciers (six glaciers in the in Cordillera the Cordillera Blanca) Blanca) calculated calculated from from the the error error propagation propagation [65] [64 ](black (black dotted dotted line shown in Figure 99),), itit cancan bebe observedobserved thatthat thethe V-SV-S scalingscaling estimatedestimated fromfrom thethe cellularcellular automataautomata modelmodel of YAN it isis veryvery similarsimilar toto thethe V-SV-S scalingscaling calculatedcalculated from the datadata ofof sixsix glaciersglaciers in thethe CordilleraCordillera Blanca. Moreover, Moreover, the the fitting fitting seems seems to be to bein a in good a good range range untiluntil the surface the surface area does area not does exceed notexceed 4 km2. 2 Although4 km . Although the V-S the scaling V-S scaling of the of cellular the cellular automata automata is always is always within within the the 25% 25% error error range range in in the 2 reconstruction simulation, simulation, the the volume volume estimation estimation should should work work for for glaciers glaciers smaller smaller than than 8 km 8 km2 [65].[64 ].

Figure 9. The volume and surface area (V-S) scaling of YAN from the cellular automata (CA) model and its fitting fitting with scaling factors (red) for the co comparisonmparison with the V-S scaling calculated from six individual glaciersglaciers [ 64[65],], including including YAN YAN (green), (green), and and the the V-S V-S scaling scal froming from Chen Chen and Ohmura, and Ohmura, 1990 (blue). 1990 (blue).The black The dotted black linedotted represents line represents the 25% the error 25% estimation error estimation from the V-Sfrom scaling the V-S from scaling six individual from six individualglaciers in theglaciers Cordillera in the Blanca.Cordillera Blanca.

4.3.2. The V-S Scaling of QUE from the Cellular Automata (CA) Model Based on the reconstructed surface area (𝑆) and its volume (V), Equation (2) for QUE can be written as follows and is shown below in Figure 10:

Water 2018, 10, x FOR PEER REVIEW 17 of 25

𝑉 = 19.284 ∙𝑆. (7) Water 2018, 10, 1732 17 of 25 The V-S scaling over QUE from the simulation using the cellular automata (CA) model shows

𝐶 = 19.284 and 𝐶 = 1.793. Since the V-S scaling relationship over the glaciers in the Cordillera 4.3.2. The V-S Scaling of QUE from the Cellular Automata (CA) Model Blanca [65], including YAN, shows that 𝐶 = 48.043 and 𝐶 = 1.275 , the differences in volume betweenBased the on V-S the scaling reconstructed generated surface from the area CA (S )model and its of volumeQUE and (V that), Equation calculated (2) from for QUE the data can beof writtensix glaciers as follows in the Cordillera and is shown Blanca, below including in Figure QUE, 10: were 22.63% in 1850 AD (size of 3.55 km2), 34.82% in 1962 AD (size of 2.55 km2), and 49.29% in 2001 AD (size of 1.57 km2) (Table 4). While the simulation of QUE showed that the glacier surface areaV =grows19.284 unrealistically· S1.793 wide at the initial stage (Figures (7)5b and 7b), the volume estimation of the V-S scaling from the model was 21% lower than that in a previousThe study V-S scaling [19]. This over also QUE confirms from the that simulation the CA model using is thesensitive cellular to automatathe shape of (CA) the modelglacier showsvalley andC0 = its19.284 topography.and C1 = 1.793. Since the V-S scaling relationship over the glaciers in the Cordillera BlancaNevertheless, [64], including from YAN, the showserror estimation that C0 = 48.043 of V-Sand scalingC1 = with1.275 the, the 25% differences error range in volume (black between dotted linethe V-Sshown scaling in Figure generated 9), the from V-S the scaling CA model estimated of QUE from and the that CA calculated model of from QUE the exhibited data of sixfitting glaciers in a 2 goodin the range Cordillera until Blanca,the surface including area (S) QUE, does were not 22.63%exceed in6 km 18502 (Figure AD (size 10). of 3.55 km ), 34.82% in 1962 AD 2 2 (sizeFrom of 2.55 the km results,), and the 49.29% V-S scaling in 2001 using AD (sizethe recons of 1.57truction km ) (Table simulation4). While from the the simulation CA model showed of QUE thatshowed the absolute that the glacier error of surface the volu areame grows estimation unrealistically increases wide with at the the size initial of the stage glacier; (Figures therefore,5b and7 b),the volumethe volume of larger estimation glaciers of should the V-S be scalingindividually from es thetimated. model Again, was 21% the lowershape thanof the that glacier in avalley previous and itsstudy topography [19]. This should also confirms be considered that the for CA the model error propagation is sensitive toof thethe shapeCA model. of the glacier valley and its topography. Table 4. Difference in the V-S scaling of QUE between the CA model and six glaciers in the Cordillera BlancaTable 4. [19,65].Difference in the V-S scaling of QUE between the CA model and six glaciers in the Cordillera Blanca [19,64]. Volume Volume Volume Volume Volume Volume fromfrom V-SVolume from from V-S Volumefrom V-S from Volume Diff. Volume Diff. Volume Diff. Size Size Diff. (CA Diff. (CB6 Year Year2 V-S Scaling CAScalingV-S ScalingScaling V-SScaling Scaling Diff.(CB6 (CB6 vs. CA) (CA vs. C&O) (CB6 vs. C&O) (km ) (km26) 3 6 3 6 3 vs. C&O) vs. C&O) (10 m ) CA CB6 (10 mCB6) C&OC&O (10 m ) vs. CA)(%) (%) (%) (%) (%) (%) 1850 3.55 186.96(106m3) 241.64(106m3) (10 159.176m3) 22.63 14.86 34.13 1962 2.551850 3.55 103.3 186.96 158.47241.64 101.59159.17 22.63 34.82 14.86 1.65 34.13 35.89 2001 1.571962 2.55 43.3 103.3 85.39158.47 101.59 52.61 34.82 49.29 1.65− 21.5035.89 38.39 CA:2001 cellular 1.57 automata model; 43.3 CB6: six 85.39 glaciers in the 52.61 Cordillera Blanca 49.29 [64]; C&O:−21.50 from Reference38.39 [19 ]. CA: cellular automata model; CB6: six glaciers in the Cordillera Blanca [65]; C&O: from Reference [19].

Figure 10. TheThe V-S V-S scaling scaling of of QUE QUE from from the the CA CA model model and and its itsfitting fitting with with scaling scaling factors factors (red) (red) for the for comparisonthe comparison with with the theV-S V-Sscaling scaling from from six individual six individual glaciers glaciers [65], [64 includin], includingg QUE QUE (green), (green), and and the theV- V-S scaling from a previous study [19]. The black dotted line is the 25% error estimation from the V-S scaling from six individual glaciers in the Cordillera Blanca.

Water 2018, 10, 1732 18 of 25

Nevertheless, from the error estimation of V-S scaling with the 25% error range (black dotted line shown in Figure9), the V-S scaling estimated from the CA model of QUE exhibited fitting in a good 2 Waterrange 2018 until, 10, x theFOR surface PEER REVIEW area (S) does not exceed 6 km (Figure 10). 18 of 25 From the results, the V-S scaling using the reconstruction simulation from the CA model showed thatS thescaling absolute from a errorprevious of study the volume [19]. The estimation black dotted increases line is the with 25% theerror size estimation of the from glacier; the V-S therefore, thescaling volume from of largersix individual glaciers glac shouldiers in be the individually Cordillera Blanca. estimated. Again, the shape of the glacier valley and its topography should be considered for the error propagation of the CA model. 4.4. Hydrology Model 4.4. Hydrology Model 4.4.1. The Yanamarey Glacier (YAN) 4.4.1. The Yanamarey Glacier (YAN) YAN showed an average surface area loss of 72.62% with an average loss of 1.58% per year YAN showed an average surface area loss of 72.62% with an average loss of 1.58% per year during during the period of 1962–2008 [65], while the Querococha watershed showed the fastest glacial area reductionthe period with of 1962–2008 an average [64 ],loss while of the1.1% Querococha per year watershedbetween 1953 showed and the 2009 fastest [1]. glacialSince areathere reduction was a temporarywith an average glacier lossadvance of 1.1% during per yearthe 1920s between [40], 1953 we applied and 2009 the [1 glacial]. Since re-advance there was aand temporary the retreat glacier as inputsadvance for duringthe model. the 1920sFrom 1962 [40], weto the applied mid-197 the0s, glacial the model re-advance showed and that the YAN retreat started as inputs a gradual for the retreatmodel. with From a smooth 1962to decline, the mid-1970s, followed theby a model dramat showedic decrease that in YAN surface started areaa from gradual the mid-1970s retreat with to a thesmooth late 1990s. decline, This followed was also by proven a dramatic by YAN decrease leng inth surface data measured area from from the mid-1970s ANA del toPeru the [73] late 1990s.(see FigureThis was11). also proven by YAN length data measured from ANA del Peru [73] (see Figure 11).

Front line observation (ANA) This study

Reconstruction (Interpolation) Extrapolation

Figure 11. The change in surface area of YAN. Data of 1850 AD (blue dot in 1850 AD) are the results Figure 11. The change in surface area of YAN. Data of 1850 AD (blue dot in 1850 AD) are the results from the CA model. The observation (glacier length) data (red dots; 1948 and late 1970s to early 2000s) from the CA model. The observation (glacier length) data (red dots; 1948 and late 1970s to early [73] agree well with the glacier area size measured from aerial photos (12 June 1962) and the series of 2000s) [73] agree well with the glacier area size measured from aerial photos (12 June 1962) and the ASTER imagery for this study (blue dots during 2001–2008 AD) [65]. The thick black line is the series of ASTER imagery for this study (blue dots during 2001–2008 AD) [64]. The thick black line is interpolation of the change in glacier extent. The information of the glacier re-advance (late 1920s to the interpolation of the change in glacier extent. The information of the glacier re-advance (late 1920s early 1930s) is included in the interpolation [65]. to early 1930s) is included in the interpolation [64].

TheThe model model results results for for YAN YAN gave gave two two synthetic synthetic hydrographs hydrographs of of yearly yearly discharge discharge (black) (black) and and dischargedischarge in inthe the dry dry season season (blue), (blue), as aswell well as asthe the chan changege in insurface surface area area of ofthe the glacier glacier (red) (red) (Figure (Figure 12). 12 ). FromFrom the the perspective perspective of of discharge, discharge, the the model model re resultssults showed showed that that there there were were three three major major peaks peaks for both yearly (Q in black) and dry season (Qdry in blue) discharges in the late 1930s, 1980s, and early for both yearly (Q in black) and dry season (Qdry in blue) discharges in the late 1930s, 1980s, and early 2000s,2000s, as as depicted depicted in in Figure Figure 12a. 12a. When When YAN YAN re-a re-advanceddvanced in in the the 1920s, 1920s, the the discharge discharge pattern pattern showed a a downwarddownward trendtrend duedue to to the the extra extra frozen frozen water water storage storage that that did did not not release release water. water. From From the latethe 1970slate 1970sto the to mid-1980s,the mid-1980s, the model the model showed showed a second a second peak peak for both for theboth yearly the yearly discharge discharge (Q) and (Q) the and annual the annual dry season discharge (Qdry) to match the start of the accelerated glacier retreat. This pattern dry season discharge (Qdry) to match the start of the accelerated glacier retreat. This pattern could also couldbe observed also be observed at the watershed at the watershed level, where level, a clear wher acceleratione a clear acceleration in the dry season in the average dry season discharge average was discharge was calculated from daily data in the Querococha watershed from the early 1960s, followed by a dominant decrease after the early 1980s [1]. In the early 2000s, another peak in discharge was observed, lasting for 4–5 years while the glacial retreat was exceptional and ice reservoir decreased. We also marked the yearly averaged measured discharge dataset of YAN (measured during 2002– 2008 AD) to compare the model and the actual dataset (shown in two large empty circles (black and

Water 2018, 10, 1732 19 of 25

calculated from daily data in the Querococha watershed from the early 1960s, followed by a dominant decrease after the early 1980s [1]. In the early 2000s, another peak in discharge was observed, lasting for 4–5 years while the glacial retreat was exceptional and ice reservoir decreased. We also marked the yearly averaged measured discharge dataset of YAN (measured during 2002–2008 AD) to compare the model and the actual dataset (shown in two large empty circles (black and blue) located around the late 2000s), as shown in Figure 12b. Overall, the model results were close to the measured annual and dry season discharge data. During the whole studied time period, from 1850 to 2050 AD, the yearly discharge (Q) did not Waterchange 2018 much, 10, x FOR (around PEER 13.3%REVIEW reduction; 0.15 m3s−1 to 0.13 m3s−1); however, the dry season discharge19 of 25 (Q ) decreased significantly along with the recession of glacier surface area (over 77.8% reduction; blue)dry located around the late 2000s), as shown in Figure 12b. Overall, the model results were close to 0.09 m3 s−1 to 0.02 m3 s−1). Based on the changes in the surface area data [73] and the findings of this the measured annual and dry season discharge data. study, the demise of YAN will be unavoidable after 2040.

(a) 0.25 80

Yanamarey

70 Projec on 0.2

second) 60

watershed)

per 50 0.15

total

of 40

%

0.1

(in 30 (cubicmeter

A

gl dry Q

area 20 x Qn x Qdry 0.05 and 4 points Moving average (Q ) 10 n n

Q

Glacier 4 points Moving average (Qdry) 0 0 1850 1870 1890 1910 1930 1950 1970 1990 2010 2030 2050

(b)

Figure 12. Modeled hydrographs for YAN. The mean yearly (black) and mean dry season (blue) Figuredischarge 12. fromModeled the hydro hydrographs balance modelfor YAN. with The change mean in ye surfacearly (black) area (size)and mean of glacier dry (red)season from (blue) the dischargeinterpolation from for the the hydro model balance input. mo (a)del Three with discharge change in peaks surface can area be observed (size) of inglacier both yearly(red) from and drythe interpolationseason discharge. for the Dots model represent input. ( yearlya) Three individual discharge results peaks andcan be the ob lineserved is a in smoothed both yearly curve and using dry seasona smoothing discharge. spline Dots parameter represent of yearly 0.214. individual (b) Two large results empty and circlesthe line (black is a smoothed and blue) curve of measured using a smoothingdischarge data spline (2002–2008 parameter AD) of show 0.214. that (b) the Two modeled large empty data are circles close to(black the measured and blue) discharge of measured data. discharge data (2002–2008 AD) show that the modeled data are close to the measured discharge data.

During the whole studied time period, from 1850 to 2050 AD, the yearly discharge (Q) did not change much (around 13.3% reduction; 0.15 m3s−1 to 0.13 m3s−1); however, the dry season discharge (Qdry) decreased significantly along with the recession of glacier surface area (over 77.8% reduction; 0.09 m3 s−1 to 0.02 m3 s−1). Based on the changes in the surface area data [73] and the findings of this study, the demise of YAN will be unavoidable after 2040.

4.4.2. The Queshque Glacier (QUE) After the interpolation of glacier surface area available for this study, the pattern showed a change in the surface area of QUE from 1850 AD to the 1980s, which was similar to that of YAN.

Water 2018, 10, 1732 20 of 25

4.4.2. The Queshque Glacier (QUE)

After theWater interpolation 2018, 10, x FOR PEER of REVIEW glacier surface area available for this study, the pattern showed20 of 25 a change in the surface area of QUE from 1850 AD to the 1980s, which was similar to that of YAN. Subsequently, Subsequently, the surface area of QUE decreased in a more gradual fashion through the 2000s (Figure the surface13). area of QUE decreased in a more gradual fashion through the 2000s (Figure 13).

This study

Reconstruction (Interpolation) Extrapolation

Figure 13. TheFigure change 13. The inchange surface in surface area area ofQUE. of QUE. Data Data ofof 1850 AD AD (blue (blue dot in dot 1850 in AD) 1850 are AD) the results are the results of the CA model. The change in glacier surface area was measured from aerial photos (blue dot on 12 of the CA model. The change in glacier surface area was measured from aerial photos (blue dot on June 1962) and the series of ASTER imagery (blue dots during 2001–2008 AD)[65], and the thick black 12 June 1962)line andrepresents the series the interpolation of ASTER ofimagery the change (blue in glacier dots extent. during The 2001–2008 information AD)of the [glacier64], and re- the thick black line representsadvance (late the1920s interpolation to early1930s) is of included the change in the interpolation in glacier extent.[65]. The information of the glacier re-advance (late 1920s to early1930s) is included in the interpolation [64]. The model results of QUE showed that synthetic hydrographs of both yearly and dry season The modeldischarge results have two of QUEdistinct showed peaks, but that the syntheticresponse to hydrographsthe recent retreat of acceleration both yearly of QUE and was dry season different. QUE does not show a clear separation between the two last peaks, where YAN may have discharge haveexperienced two distinctthe most dramatic peaks, glacier but the retreat response impact on to discharge the recent at the retreat beginning acceleration of the 21st century of QUE was different. QUE(Figure does 14). Also, not showwe found a clearthat the separation discharge of between the dry season the (Q twodry) lastis predicted peaks, to where decrease YAN as the may have experiencedsurface the most area of dramatic the glacier glacier becomes retreat smaller. impact Likewise, on dischargefrom YAN, during at the beginningthe whole studied of the time 21st century period from 1850 AD to 2050 AD, the yearly discharge (Q) does not change much (around 16% (Figure 14). Also, we found that the discharge of the dry season (Qdry) is predicted to decrease as the reduction; 0.25 m3 s−1 to 0.21 m3 s−1), while the dry season discharge (Qdry) is decreased significantly surface areaalong of the with glacier the recession becomes of glacier smaller. surface Likewise, area (over from 64.7% YAN, reduction; during 0.17m the3 s−1 wholeto 0.06 m studied3 s−1). time period from 1850 AD to 2050 AD, the yearly discharge (Q) does not change much (around 16% reduction; 3 −1 3 −1 0.25 m s to 0.21 m s ), while the dry season discharge (Qdry) is decreased significantly along with the recession of glacier surface area (over 64.7% reduction; 0.17m3 s−1 to 0.06 m3 s−1). The results of YAN and QUE both showed a dramatic decline in water availability during this century, as small glaciers in the Cordillera Blanca will disappear and precipitation becomes the only water resource [74]. However, the overall annual discharge may not vary much due to possible increased runoff during the wet season. Another study also showed that the annual discharge may not change significantly but seasonality will be greatly intensified in one catchment in the Cordillera Blanca [6]. Climate simulations based on four different Intergovernmental Panel on Climate Change (IPCC) emission climate scenarios show the same prediction over the Llanganuco catchment as is the case of YAN in the Querococha catchment—that total annual runoff remains almost unchanged for all model runs due to much more direct runoff, which compensates for reduced glacier melt under the higher amountFigure 14. of Modeled total precipitation. hydrographs for QUE, However, showing mean future yearly water (black) and management mean dry season will (blue) be challenged by a much greaterdischarge decrease from the ofhydro low balance runoff model. from Dots all repr scenariosesent yearlyof individual model results runs and for the the lines dry are season in the Cordillera Blanca,smoothed Peru using [6]. a smoothing spline parameter of 0.214.

The reconstructed initial glacierized area parameter from the CA model, the surface area information from previous research in the middle of the model period [1], and the glacierized area calculated from ASTER imagery from 2001–2008 help fill in the data gaps and improve the analysis to link glacial retreat and runoff discharge. Observing multiple peaks in mean annual and dry season discharge hydrographs from the results of this study shown in both glacier catchments is the first case Water 2018, 10, x FOR PEER REVIEW 20 of 25

Subsequently, the surface area of QUE decreased in a more gradual fashion through the 2000s (Figure 13).

This study

Reconstruction (Interpolation) Extrapolation

Figure 13. The change in surface area of QUE. Data of 1850 AD (blue dot in 1850 AD) are the results of the CA model. The change in glacier surface area was measured from aerial photos (blue dot on 12 June 1962) and the series of ASTER imagery (blue dots during 2001–2008 AD)[65], and the thick black line represents the interpolation of the change in glacier extent. The information of the glacier re- advance (late 1920s to early1930s) is included in the interpolation [65].

The model results of QUE showed that synthetic hydrographs of both yearly and dry season Water 2018discharge, 10, 1732 have two distinct peaks, but the response to the recent retreat acceleration of QUE was 21 of 25 different. QUE does not show a clear separation between the two last peaks, where YAN may have experienced the most dramatic glacier retreat impact on discharge at the beginning of the 21st century of glacier(Figure meltwater 14). Also, runoff we found models that implementedthe discharge of in the the dry same season mountain (Qdry) is predicted range [75 to]. decrease Moreover, as the this case confirmssurface that area the inclusionof the glacier of morebecomes datasets smaller. of Likewise, glacierized from area YAN, as inputduring parameters the whole studied will improve time the period from 1850 AD to 2050 AD, the yearly discharge (Q) does not change much (around 16% assessment of past and present influences of glaciers on stream discharge, to accurately project future reduction; 0.25 m3 s−1 to 0.21 m3 s−1), while the dry season discharge (Qdry) is decreased significantly hydrologicalalong with regimes. the recession of glacier surface area (over 64.7% reduction; 0.17m3 s−1 to 0.06 m3 s−1).

FigureFigure 14. Modeled 14. Modeled hydrographs hydrographs for for QUE, QUE,showing showing mean mean yearly yearly (black) (black) and andmean mean dry season dry season (blue) (blue) dischargedischarge from from the hydrothe hydro balance balance model. model. DotsDots representrepresent yearly yearly individual individual results results and the and lines the are lines are smoothed using a smoothing spline parameter of 0.214. smoothed using a smoothing spline parameter of 0.214.

Despite the limitation of unavailable data for the Yanayacu watershed, in which QUE is located, the generation of the presented hydrograph series is considered to be adequate for the purpose of this study because the model simulation generated from the reconstructed initial surface areas of glaciers provided a trend analysis. Results obtained from the hydrograph simulation can be compared with the patterns of the dry season daily discharge at the watershed level for the Querococha and averaged measured discharge especially during 2002–2008 over YAN. Results indicate that both glaciers may have exhibited multiple peaks of discharge over the study period. For the model sensitivity in terms of both mean annual and the dry season discharge, the hydrographs visually conformed to the expected hydrologic progression [1]. When the glacierized area decreases continuously, both mean yearly and mean dry season discharge experience a period of increase followed by a period of decrease and then a period of stabilized discharge similar to or below the initial levels. The final dry season discharge was found to be more than 60% lower than the beginning levels for both glacier catchments, while the final mean annual discharges were reduced by no more than 16% of their initial levels. Both yearly and dry season discharge were compatibly sensitive to changes in glacier retreat, in that an overall decreasing trend was observed as the glaciers lose area, although the yearly discharge showed a very limited overall decline with time. The sensitivity analysis [1] showed that while the initial surface area of the glaciers and their rate of loss are both crucial to determine how glaciers influence a watershed’s hydrology, the reconstruction of glaciers based on robust reference, ground truth, and the delineation of glacier surface area for available years with accurate parameters from each individual glacier is essential for a better understanding of the historical impact of glaciers on the hydrological regime. Projections suggest that we are probably witnessing the influence of YAN stream discharge fade away, with the dry season discharge stabilizing at a level more than three times lower than what it was almost 200 years ago. The situation is slightly different for QUE, where the overall negative trend in the dry season discharge is expected to be maintained for the coming decade. Regardless of any circumstance, the complete demise of glaciers will lead to much more vulnerability due to dry season water scarcity.

5. Conclusions We modeled the LIA maximum glaciers (mid-19th century) using a CA model with 2008 LiDAR DEMs and 2011 ASTER GDEM (V2). We employed a recently demonstrated approach [1] to calculate Water 2018, 10, 1732 22 of 25 glacier contribution to meltwater runoff as a function of glacier retreat in the YAN and QUE catchments, and effectively reconstructed long-term glacier significance for stream flow. The simulation results of the CA model and the V-S scaling showed that the approach using this simple model to reconstruct paleoglaciers is very useful and has potential for glaciers smaller than 8 km2. The hydrographs from the water balance model revealed multiple peaks of both mean annual and dry season discharge in both catchments that have never been shown in previous research in the same mountain range. This means that the interpolation of the glacierized area from the reconstructed glacier as an initial size, the frontal change (glacier length) information from other research, and the glacierized area calculated from satellite imagery in recent years helped us to assess past and present influence of glaciers on stream discharge, enabling us to identify and predict past and future long-term hydrological regimes. By combining experimental modeling using the CA technique with the hydrological balance model, it is possible to estimate the contributions of individual glaciers to discharge in glacierized watersheds in the Peruvian Andes and make initial connections among climate, glaciers, and hydrology. These modeling results provide a framework for the better understanding of the LIA maximum glacier volume and its meltwater runoff regime by reconstructing the past, and ultimately for predicting the response of glaciers to future climate change without major investment in infrastructure. Support from further chronological research modeling LIA paleoglaciers in other mountain ranges in the Tropics would be necessary to confirm these estimates and extend the knowledge of history of frozen water storage in tropical glaciers.

Author Contributions: Conceptualization, K.I.H. and B.G.M.; methodology, K.I.H. and M.B.; software, K.I.H., M.B., and Y.A.; formal analysis, K.I.H.; resources, K.I.H. and B.G.M.; writing—original draft preparation, K.I.H.; writing—review and editing, K.I.H., B.G.M., and M.B.; visualization, K.I.H., M.B., and Y.A.; funding acquisition, B.G.M. for this research. Funding: This research was funded by the NASA New Investigator Program (grant number NNX06AF11G). Acknowledgments: This research was carried out as a part of the project, “Glacier volume changes in the Tropical Andes: A multi-scale assessment in the Cordillera Blanca, Peruvian Andes”. We would like to express our gratitude to Jesus Gomez from Parque Nacional Huascaran, SERNANP. Conflicts of Interest: The authors declare no conflict of interest.

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