# What Can We Learn from Comparing Glacio-Hydrological Models?

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Catchment

#### 2.2. Meteorological and Hydrological Data

#### 2.3. Glacier Information Data

#### 2.4. Climate Simulations

#### 2.5. Downscaling/Bias Correction of the Climate Simulations

## 3. Glacio-Hydrological Models

#### 3.1. Overview of the Two Independent Glacio-Hydrological Models

#### 3.2. HQsim-GEM Model Coupling

#### 3.2.1. Model Coupling Strategy

**First (‘static’) model run of HQsim:**Input data include daily minimum, maximum and mean air temperature as well as precipitation from either measured meteorological data or downscaled EURO-CORDEX climate data referred to the closest station, and the AGI information data to initialize the model in 1969, for a constant glacier simulation run.- Air temperature and precipitation data are adjusted to account for altitudinal differences between the station and the locations of the glaciers.
- HQsim converts daily air temperature and precipitation for each glacier to monthly values. These time series are used to force GEM in a subsequent step.

**Coupling with the GEM:**Running the GEM with input data delivered from the first HQsim run. Characteristics such as glacier area and terminus height are calculated for each year and transferred back to HQsim to account for glacier changes.**Second (‘dynamic’) model run of HQsim**: In a second HQsim run, dynamical glacier changes data provided by the GEM are updated each glaciological year (in September). Glacierized Hydrological Response Units (Section 3.2.2) are updated in terms of spatial extent and mean elevation (through updated terminus height). This way, updated calculations of hydrological quantities (like total runoff and glacier melt, etc.) are considered in this second iteration, complementing the model coupling scheme.

#### 3.2.2. Model Description of HQsim

#### 3.2.3. Model Description of GEM

#### 3.2.4. Setup of the Coupled Model for the Rofenache Catchment

#### 3.3. AMUNDSEN

## 4. Results

#### 4.1. Downscaling/Bias Correction of Climate Simulations

#### 4.2. Comparison of Model Results

#### 4.2.1. Glacierization

#### 4.2.2. Runoff Regimes

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AMUNDSEN | Alpine Multiscale Numerical Distributed Simulation Engine |

BE | Benchmark efficiency |

CRU | Climate Research Unit |

GCM | General Circulation Model |

GEM | Glacier Evolution Model |

GIS | Geographic Information System |

HQsim | HQ (high flow Q) simulation |

HRU | Hydrological Response Unit |

LAI | Leaf Area Index |

MELODIST | MEteoroLOgical observation time series DISaggregation Tool |

NSE | Nash–Sutcliffe efficiency |

OGGM | Open Global Glacier Model |

PBIAS | Percent bias |

RCM | Regional Climate Model |

RCP | Representative Concentration Pathway |

RMSE | Root Mean Square Error |

## Appendix A. Definitions and Parameters

**Table A1.**Skill measures used throughout the manuscript. Time series of observed ${q}_{\mathrm{obs}}$ and modeled ${q}_{\mathrm{sim}}$ quantities, each consisting of N values, are considered for all time steps t, whereby ${\overline{q}}_{\mathrm{obs}}$ represents the mean observed values and ${q}_{\mathrm{bench}}$ is a long-term average computed for the day of the year corresponding to time step i, respectively.

Skill Measure | Formula |
---|---|

Nash–Sutcliffe model efficiency | $\mathrm{NSE}=1-\frac{{\displaystyle \sum _{i=1}^{N}}{\left(\right)}^{{q}_{\mathrm{obs},i}}2}{}{\displaystyle \sum _{i=1}^{N}}{\left(\right)}^{{q}_{\mathrm{obs},i}}2$ |

Benchmark Nash–Sutcliffe model efficiency [68] | $\mathrm{BE}=1-\frac{{\displaystyle \sum _{i=1}^{N}}{\left(\right)}^{{q}_{\mathrm{obs},i}}2}{}{\displaystyle \sum _{i=1}^{N}}{\left(\right)}^{{q}_{\mathrm{obs},i}}2$ |

Percent Bias | $\mathrm{PBIAS}=100\%\xb7\frac{{\displaystyle \sum _{i=1}^{N}}\left(\right)open="["\; close="]">{q}_{\mathrm{sim},i}-{q}_{\mathrm{obs},i}}{}{\displaystyle \sum _{i=1}^{N}}{q}_{\mathrm{obs},i}$ |

Root Mean Square Error | $\mathrm{RMSE}=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{({q}_{\mathrm{sim},i}-{q}_{\mathrm{obs},i})}^{2}}$ |

## References

- Radić, V.; Hock, R. Glaciers in the Earth’s hydrological cycle: Assessments of glacier mass and runoff changes on global and regional scales. Surv. Geophys.
**2014**, 35, 813–837. [Google Scholar] [CrossRef] - Schaefli, B.; Hingray, B.; Niggli, M.; Musy, A. A conceptual glacio-hydrological model for high mountainous catchments. Hydrol. Earth Syst. Sci.
**2005**, 9, 95–109. [Google Scholar] [CrossRef] [Green Version] - Huss, M.; Farinotti, D.; Bauder, A.; Funk, M. Modelling runoff from highly glacierized alpine drainage basins in a changing climate. Hydrol. Process.
**2008**, 22, 3888–3902. [Google Scholar] [CrossRef] - Finger, D.; Heinrich, G.; Gobiet, A.; Bauder, A. Projections of future water resources and their uncertainty in a glacierized catchment in the Swiss Alps and the subsequent effects on hydropower production during the 21st century. Water Resour. Res.
**2012**, 48. [Google Scholar] [CrossRef] [Green Version] - Farinotti, D.; Usselmann, S.; Huss, M.; Bauder, A.; Funk, M. Runoff evolution in the Swiss Alps: Projections for selected high-alpine catchments based on ENSEMBLES scenarios. Hydrol. Process.
**2012**, 26, 1909–1924. [Google Scholar] [CrossRef] - Addor, N.; Rössler, O.; Köplin, N.; Huss, M.; Weingartner, R.; Seibert, J. Robust changes and sources of uncertainty in the projected hydrological regimes of Swiss catchments. Water Resour. Res.
**2014**, 50, 7541–7562. [Google Scholar] [CrossRef] [Green Version] - Hanzer, F.; Förster, K.; Nemec, J.; Strasser, U. Projected cryospheric and hydrological impacts of 21st century climate change in the Ötztal Alps (Austria) simulated using a physically based approach. Hydrol. Earth Syst. Sci.
**2018**, 22, 1593–1614. [Google Scholar] [CrossRef] [Green Version] - Farinotti, D.; Huss, M.; Bauder, A.; Funk, M. An estimate of the glacier ice volume in the Swiss Alps. Glob. Planet. Chang.
**2009**, 68, 225–231. [Google Scholar] [CrossRef] - Bahr, D.B. Global distributions of glacier properties: A stochastic scaling paradigm. Water Resour. Res.
**1997**, 33, 1669–1679. [Google Scholar] [CrossRef] - Huss, M.; Jouvet, G.; Farinotti, D.; Bauder, A. Future high-mountain hydrology: A new parameterization of glacier retreat. Hydrol. Earth Syst. Sci.
**2010**, 14, 815. [Google Scholar] [CrossRef] [Green Version] - Maussion, F.; Butenko, A.; Champollion, N.; Dusch, M.; Eis, J.; Fourteau, K.; Gregor, P.; Jarosch, A.H.; Landmann, J.; Oesterle, F.; et al. The Open Global Glacier Model (OGGM) v1.1. Geosci. Model Dev.
**2019**, 12, 909–931. [Google Scholar] [CrossRef] [Green Version] - Huss, M.; Zemp, M.; Joerg, P.C.; Salzmann, N. High uncertainty in 21st century runoff projections from glacierized basins. J. Hydrol.
**2014**, 510, 35–48. [Google Scholar] [CrossRef] [Green Version] - Uhlmann, B.; Jordan, F.; Beniston, M. Modelling runoff in a Swiss glacierized catchment-Part II: Daily discharge and glacier evolution in the Findelen basin in a progressively warmer climate. Int. J. Climatol.
**2013**, 33, 1301–1307. [Google Scholar] [CrossRef] [Green Version] - Förster, K.; Oesterle, F.; Hanzer, F.; Huttenlau, M.; Strasser, U. Bestimmung der Auswirkungen des Klimawandels auf die Gletscherdynamik und das Abflussregime im Rofental unter Verwendung eines gekoppelten glazio-hydrologischen Modells. In Innsbrucker Jahresberichte 2014–2015; Institut für Geographie der Universität Innsbruck in Zusammenarbeit mit der Innsbrucker Geographischen Gesellschaft: Innsbruck, Austria, 2015; pp. 23–40. [Google Scholar]
- Huss, M.; Hock, R. Global-scale hydrological response to future glacier mass loss. Nat. Clim. Chang.
**2018**, 8, 135–140. [Google Scholar] [CrossRef] [Green Version] - Wijngaard, R.R.; Helfricht, K.; Schneeberger, K.; Huttenlau, M.; Schneider, K.; Bierkens, M.F. Hydrological response of the Ötztal glacierized catchments to climate change. Hydrol. Res.
**2016**, 47, 979–995. [Google Scholar] [CrossRef] - Takala, M.; Pulliainen, J.; Metsamaki, S.J.; Koskinen, J.T. Detection of snowmelt using spaceborne microwave radiometer data in Eurasia from 1979 to 2007. IEEE Trans. Geosci. Remote Sens.
**2009**, 47, 2996–3007. [Google Scholar] [CrossRef] - Barnett, T.P.; Adam, J.C.; Lettenmaier, D.P. Potential impacts of a warming climate on water availability in snow-dominated regions. Nature
**2005**, 438, 303–309. [Google Scholar] [CrossRef] - Stone, R.S.; Dutton, E.G.; Harris, J.M.; Longenecker, D. Earlier spring snowmelt in northern Alaska as an indicator of climate change. J. Geophys. Res. Atmos.
**2002**, 107, ACL 10-1–ACL 10-13. [Google Scholar] [CrossRef] - IPCC. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change; Cambridge University Press: Cambridge, UK, 2013. [Google Scholar]
- Horton, P.; Schaefli, B.; Mezghani, A.; Hingray, B.; Musy, A. Assessment of Climate-Change Impacts on Alpine Discharge Regimes with Climate Model Uncertainty. Hydrol. Process.
**2006**, 20, 2091–2109. [Google Scholar] [CrossRef] - Fatichi, S.; Rimkus, S.; Burlando, P.; Bordoy, R.; Molnar, P. High-Resolution Distributed Analysis of Climate and Anthropogenic Changes on the Hydrology of an Alpine Catchment. J. Hydrol.
**2015**, 525, 362–382. [Google Scholar] [CrossRef] - Kobierska, F.; Jonas, T.; Zappa, M.; Bavay, M.; Magnusson, J.; Bernasconi, S.M. Future Runoff from a Partly Glacierized Watershed in Central Switzerland: A Two-Model Approach. Adv. Water Resour.
**2013**, 55, 204–214. [Google Scholar] [CrossRef] - Bergström, S. The HBV Model: Its Structure and Applications; Swedish Meteorological and Hydrological Institute: Norrköping, Sweden, 1992. [Google Scholar]
- Bergström, S. Development and Application of a Conceptual Runoff Model for Scandinavian Catchments. Ph.D. Thesis, Swedish Meteorological and Hydrological Institute, Norrköping, Sweden, 1976. [Google Scholar]
- Kleindienst, H. Erweiterung und Erprobung Eines Anwendungsorientierten Hydrologischen Modells zur Gangliniensimulation in Kleinen Wildbacheinzugsgebieten. Unpublished Diploma Thesis, Ludwig Maximilians Universität München, Munich, Germany, 1996. [Google Scholar]
- Winter, B.; Schneeberger, K.; Förster, K.; Vorogushyn, S. Event generation for probabilistic flood risk modelling: Multi-site peak flow dependence model vs. weather generator based approach. Nat. Hazards Earth Syst. Sci.
**2020**, 20, 1689–1703. [Google Scholar] [CrossRef] - Mackay, J.D.; Barrand, N.E.; Hannah, D.M.; Krause, S.; Jackson, C.R.; Everest, J.; Aðalgeirsdóttir, G. Glacio-hydrological melt and run-off modelling: Application of a limits of acceptability framework for model comparison and selection. Cryosphere
**2018**, 12, 2175–2210. [Google Scholar] [CrossRef] [Green Version] - Clark, M.P.; Kavetski, D.; Fenicia, F. Pursuing the method of multiple working hypotheses for hydrological modeling. Water Resour. Res.
**2011**, 47, W09301. [Google Scholar] [CrossRef] [Green Version] - Marzeion, B.; Jarosch, A.H.; Hofer, M. Past and future sea-level change from the surface mass balance of glaciers. Cryosphere
**2012**, 6, 1295–1322. [Google Scholar] [CrossRef] [Green Version] - Strasser, U. Die Modellierung der Gebirgsschneedecke im Nationalpark Berchtesgaden; Berchtesgaden National Park Research Report; Nationalparkverwaltung Berchtesgaden: Berchtesgaden, Germany, 2008; Volume 55. [Google Scholar]
- Hanzer, F.; Helfricht, K.; Marke, T.; Strasser, U. Multilevel spatiotemporal validation of snow/ice mass balance and runoff modeling in glacierized catchments. Cryosphere
**2016**, 10, 1859–1881. [Google Scholar] [CrossRef] [Green Version] - Strasser, U.; Marke, T.; Braun, L.; Escher-Vetter, H.; Juen, I.; Kuhn, M.; Maussion, F.; Mayer, C.; Nicholson, L.; Niedertscheider, K.; et al. The Rofental: A High Alpine Research Basin (1890–3770 m a.s.l.) in the Ötztal Alps (Austria) with over 150 Years of Hydrometeorological and Glaciological Observations. Earth Syst. Sci. Data
**2018**, 10, 151–171. [Google Scholar] [CrossRef] [Green Version] - Institute of Meteorology and Geophysics. Climate Data Vent, Ötztal Alps, 1935–2011; University of Innsbruck: Innsbruck, Austria, 2013. [Google Scholar] [CrossRef]
- Kuhn, M.; Helfricht, K.; Ortner, M.; Landmann, J.; Gurgiser, W. Liquid water storage in snow and ice in 86 Eastern Alpine basins and its changes from 1970–97 to 1998–2006. Ann. Glaciol.
**2016**, 57, 11–18. [Google Scholar] [CrossRef] [Green Version] - Schöber, J.; Schneider, K.; Helfricht, K.; Schattan, P.; Achleitner, S.; Schöberl, F.; Kirnbauer, R. Snow cover characteristics in a glacierized catchment in the Tyrolean Alps-Improved spatially distributed modelling by usage of Lidar data. J. Hydrol.
**2014**. [Google Scholar] [CrossRef] - Fischer, A.; Olefs, M.; Abermann, J. Glaciers, snow and ski tourism in Austria’s changing climate. Ann. Glaciol.
**2011**, 52, 89–96. [Google Scholar] [CrossRef] [Green Version] - Zemp, M.; Paul, F.; Hoelze, M.; Haeberli, W. Glacier fluctuations in the European Alps, 1850–2000. Darkening Peaks Glacier Retreat Sci. Soc.
**2008**. [Google Scholar] [CrossRef] - Abermann, J.; Lambrecht, A.; Fischer, A.; Kuhn, M. Quantifying changes and trends in glacier area and volume in the Austrian Ötztal Alps (1969-1997-2006). Cryosphere
**2009**, 3, 205. [Google Scholar] [CrossRef] [Green Version] - Lambrecht, A.; Kuhn, M. Glacier changes in the Austrian Alps during the last three decades, derived from the new Austrian glacier inventory. Ann. Glaciol.
**2007**, 46, 177–184. [Google Scholar] [CrossRef] [Green Version] - Gross, G. Der Flachenverlust der Gletscher in Osterreich 1850-1920-1969. Z. Gletscherkunde Glazialgeol.
**1987**, 23, 131–141. [Google Scholar] - Paul, F.; Rastner, P.; Azzoni, R.S.; Diolaiuti, G.; Fugazza, D.; Le Bris, R.; Nemec, J.; Rabatel, A.; Ramusovic, M.; Schwaizer, G.; et al. Glacier shrinkage in the Alps continues unabated as revealed by a new glacier inventory from Sentinel-2. Earth Syst. Sci. Data
**2020**, 12, 1805–1821. [Google Scholar] [CrossRef] - Jacob, D.; Petersen, J.; Eggert, B.; Alias, A.; Christensen, O.B.; Bouwer, L.M.; Braun, A.; Colette, A.; Déqué, M.; Georgievski, G.; et al. EURO-CORDEX: New high-resolution climate change projections for European impact research. Reg. Environ. Chang.
**2014**, 14, 563–578. [Google Scholar] [CrossRef] - Giorgi, F.; Jones, C.; Asrar, G.R. Addressing climate information needs at the regional level: The CORDEX framework. World Meteorol. Organ. (WMO) Bull.
**2009**, 58, 175. [Google Scholar] - Gudmundsson, L.; Bremnes, J.B.; Haugen, J.E.; Engen-Skaugen, T. Technical Note: Downscaling RCM precipitation to the station scale using statistical transformations—A comparison of methods. Hydrol. Earth Syst. Sci.
**2012**, 16, 3383–3390. [Google Scholar] [CrossRef] [Green Version] - Thrasher, B.; Maurer, E.P.; McKellar, C.; Duffy, P. Bias correcting climate model simulated daily temperature extremes with quantile mapping. Hydrol. Earth Syst. Sci.
**2012**, 16, 3309. [Google Scholar] [CrossRef] [Green Version] - Hofer, M.; Nemec, J.; Cullen, N.J.; Weber, M. Evaluating predictor strategies for regression-based downscaling with a focus on glacierized mountain environments. J. Appl. Meteorol. Climatol.
**2017**, 56, 1707–1729. [Google Scholar] [CrossRef] - Förster, K.; Hanzer, F.; Winter, B.; Marke, T.; Strasser, U. An open-source MEteoroLOgical observation time series DISaggregation Tool (MELODIST v0.1.1). Geosci. Model Dev.
**2016**, 9, 2315–2333. [Google Scholar] [CrossRef] [Green Version] - Bahr, D.B.; Meier, M.F.; Peckham, S.D. The physical basis of glacier volume-area scaling. J. Geophys. Res. Solid Earth
**1997**, 102, 20355–20362. [Google Scholar] [CrossRef] - Federer, C.A.; Lash, D. BROOK: A Hydrologic Simulation Model for Eastern Forests; Water Resources Center, University of New Hampshire: Durham, NH, USA, 1978. [Google Scholar]
- Achleitner, S.; Rinderer, M.; Kirnbauer, R. Hydrological modeling in alpine catchments: Sensing the critical parameters towards an efficient model calibration. Water Sci. Technol. J. Int. Assoc. Water Pollut. Res.
**2009**, 60, 1507–1514. [Google Scholar] [CrossRef] [PubMed] - Achleitner, S.; Schöber, J.; Rinderer, M.; Leonhardt, G.; Schöberl, F.; Kirnbauer, R.; Schönlaub, H. Analyzing the operational performance of the hydrological models in an alpine flood forecasting system. J. Hydrol.
**2012**, 412, 90–100. [Google Scholar] [CrossRef] [Green Version] - Priestley, C.H.; Taylor, R.J. On the Assessment of Surface Heat Flux and Evaporation Using Large-Scale Parameters. Mon. Weather Rev.
**1972**, 100, 81–92. [Google Scholar] [CrossRef] - Archibald, J.A.; Walter, M.T. Do Energy-Based PET Models Require More Input Data than Temperature-Based Models?—An Evaluation at Four Humid FluxNet Sites. J. Am. Water Resour. Assoc.
**2014**, 50, 497–508. [Google Scholar] [CrossRef] - Bristow, K.L.; Campbell, G.S. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agric. Forest Meteorol.
**1984**, 31, 159–166. [Google Scholar] [CrossRef] - Walter, M.T.; Brooks, E.S.; McCool, D.K.; King, L.G.; Molnau, M.; Boll, J. Process-based snowmelt modeling: Does it require more input data than temperature-index modeling? J. Hydrol.
**2005**, 300, 65–75. [Google Scholar] [CrossRef] [Green Version] - Förster, K.; Meon, G.; Marke, T.; Strasser, U. Effect of meteorological forcing and snow model complexity on hydrological simulations in the Sieber catchment (Harz Mountains, Germany). Hydrol. Earth Syst. Sci.
**2014**, 18, 4703–4720. [Google Scholar] [CrossRef] [Green Version] - Strasser, U.; Marke, T. ESCIMO.spread—A spreadsheet-based point snow surface energy balance model to calculate hourly snow water equivalent and melt rates for historical and changing climate conditions. Geosci. Model Dev.
**2010**, 3, 643–652. [Google Scholar] [CrossRef] [Green Version] - Marke, T.; Mair, E.; Förster, K.; Hanzer, F.; Garvelmann, J.; Pohl, S.; Warscher, M.; Strasser, U. ESCIMO.spread (v2): Parameterization of a spreadsheet-based energy balance snow model for inside-canopy conditions. Geosci. Model Dev.
**2016**, 9, 633–646. [Google Scholar] [CrossRef] [Green Version] - Tarboton, D.G.; Luce, C. Utah Energy Balance Snow Accumulation and Melt Model (UEB): Computer Model Technical Description and Users Guide; Utah Water Research Laboratory and USDA Forest Service Intermountain Research Station: Ogden, UT, USA, 1996.
- Förster, K.; Gelleszun, M.; Meon, G. A weather dependent approach to estimate the annual course of vegetation parameters for water balance simulations on the meso- and macroscale. Adv. Geosci.
**2012**, 32, 15–21. [Google Scholar] [CrossRef] [Green Version] - Rutter, A.; Kershaw, K.; Robins, P.; Morton, A. A predictive model of rainfall interception in forests, 1. Derivation of the model from observations in a plantation of Corsican pine. Agric. Meteorol.
**1971**, 9, 367–384. [Google Scholar] [CrossRef] - Van Genuchten, M.T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J.
**1980**, 44, 892–898. [Google Scholar] [CrossRef] [Green Version] - Rickenmann, D. Fliessgeschwindigkeit in Wildbächen und Gebirgsflüssen. Wasser Energie Luft
**1996**, 88, 298–304. [Google Scholar] - New, M.; Lister, D.; Hulme, M.; Makin, I. A high-resolution data set of surface climate over global land areas. Clim. Res.
**2002**, 21, 1–25. [Google Scholar] [CrossRef] [Green Version] - Bellinger, J.; Achleitner, S.; Schöber, J.; Schöberl, F.; Kirnbauer, R.; Schneider, K. The impact of different elevation steps on simulation of snow covered area and the resulting runoff variance. Adv. Geosci.
**2012**, 32, 69–76. [Google Scholar] [CrossRef] [Green Version] - Klemeš, V. Operational testing of hydrological simulation models. Hydrol. Sci. J.
**1986**, 31, 13–24. [Google Scholar] [CrossRef] - Schaefli, B.; Gupta, H.V. Do Nash values have value? Hydrol. Process.
**2007**, 21, 2075–2080. [Google Scholar] [CrossRef] [Green Version] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. Asabe
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Huss, M.; Farinotti, D. Distributed ice thickness and volume of all glaciers around the globe. J. Geophys. Res. Earth Surf.
**2012**, 117. [Google Scholar] [CrossRef] - Marzeion, B.; Cogley, J.G.; Richter, K.; Parkes, D. Attribution of global glacier mass loss to anthropogenic and natural causes. Science
**2014**, 345, 919–921. [Google Scholar] [CrossRef] [PubMed] - Braun, L.; Weber, M.; Schulz, M. Consequences of climate change for runoff from Alpine regions. Ann. Glaciol.
**2000**, 31, 19–25. [Google Scholar] [CrossRef] [Green Version] - Beniston, M.; Farinotti, D.; Stoffel, M.; Andreassen, L.M.; Coppola, E.; Eckert, N.; Fantini, A.; Giacona, F.; Hauck, C.; Huss, M.; et al. The European mountain cryosphere: A review of its current state, trends, and future challenges. Cryosphere
**2018**, 12, 759–794. [Google Scholar] [CrossRef] [Green Version] - Baraer, M.; Mark, B.G.; McKenzie, J.M.; Condom, T.; Bury, J.; Huh, K.I.; Portocarrero, C.; Gómez, J.; Rathay, S. Glacier recession and water resources in Peru’s Cordillera Blanca. J. Glaciol.
**2012**, 58, 134–150. [Google Scholar] [CrossRef] [Green Version] - Stahl, K.; Moore, R. Influence of watershed glacier coverage on summer streamflow in British Columbia, Canada. Water Resour. Res.
**2006**, 42. [Google Scholar] [CrossRef] - Eis, J.; Maussion, F.; Marzeion, B. Initialization of a global glacier model based on present-day glacier geometry and past climate information: An ensemble approach. Cryosphere
**2019**, 13, 3317–3335. [Google Scholar] [CrossRef] [Green Version] - Stahl, K.; Weiler, M.; Kohn, I.; Freudiger, D.; Seibert, J.; Vis, M.; Gerlinger, K.; Bohm, M. The Snow and Glacier Melt Components of Streamflow of the River Rhine and Its Tributaries Considering the Influence of Climate Change; Technical Report; International Commision for the Hydrology of the Rhine Basin: Lelystad, The Netherlands, 2016. [Google Scholar]
- Braun, L.; Escher-Vetter, H. Glacial discharge as affected by climate change. In Proceedings of the Interpraevent 1996: Protection of Habitat against Floods, Debris Flows and Avalanches, Garmisch-Partenkirchen, Germany, 24–28 June 1996. [Google Scholar]
- Marzeion, B.; Jarosch, A.H.; Gregory, J.M. Feedbacks and Mechanisms Affecting the Global Sensitivity of Glaciers to Climate Change. Cryosphere
**2014**, 8, 59–71. [Google Scholar] [CrossRef] [Green Version] - Zekollari, H.; Huss, M.; Farinotti, D. Modelling the Future Evolution of Glaciers in the European Alps under the EURO-CORDEX RCM Ensemble. Cryosphere
**2019**, 13, 1125–1146. [Google Scholar] [CrossRef] [Green Version] - Schulla, J. Model Description WaSiM (Water Balance Simulation Model)-Completely Revised Version of 2012 with 2013 to 2015 Extensions; Hydrology Software Consulting J. Schulla: Zurich, Switzerland, 2015. [Google Scholar]
- Förster, K.; Garvelmann, J.; Meißl, G.; Strasser, U. Modelling forest snow processes with a new version of WaSiM. Hydrol. Sci. J.
**2018**, 63, 1540–1557. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Map of the Rofenache catchment including glacierized areas and the locations of the runoff gauge and the meteorological station in Vent.

**Figure 3.**Future multi-model ensemble mean projections of (i) annual mean air temperature and (ii) annual sum of precipitation by using a centered 11-year moving average (both parameters refer to the entire catchment area of the upper Ötztal). Shadows display the full range of the ensembles within the 95% confidence interval.

**Figure 4.**Results for the catchment glacierization from the two glacio-hydrological models HQsim-GEM (

**left**sub-figures) and AMUNDSEN (

**right**sub-figures). The top row shows only the three GCM-RCM combinations which are available for all three RCPs, the middle row all GCM-RCM combinations (i.e., three for RCP 2.6 and 14 each for RCP 4.5 and 8.5), and the bottom row the same but with the uncertainty (95% confidence interval) shown as shaded bands instead of the individual model realizations.

**Figure 5.**Simulated runoff for HQsim-GEM (

**left**) and AMUNDSEN (

**right**) under the different emission scenarios RCP 2.6 (

**top**), RCP 4.5 (

**middle**) and RCP 8.5 (

**bottom**). Lines represent monthly multi-model ensemble means for total runoff (solid lines) and ice melt (dashed lines) for three different future climate periods (colored lines). Grey and black lines correspond to observed runoff during the period 1998–2011 (grey) and the corresponding simulation results (black).

HQsim-GEM | AMUNDSEN | |
---|---|---|

Time resolution | daily (HQsim), monthly (GEM) | 3 h |

Spatial resolution | HRU (≈1.4 km${}^{2}$) | 100 m |

Input variables | minimum air temperature, maximum air temperature, precipitation (Vent meteo station only) | mean air temperature, precipitation, relative humidity, global radiation, wind speed |

Glacier model | GEM [30] | $\Delta h$ [10] |

Glacier representation | 0-D | 2-D |

Glacier initialization | area, height of the glacier tongue | distributed ice thickness |

Glacier initialization time | 1969 | 1997 |

Glacier geometry update | Volume-area-time scale | elevation-dependent surface elevation change |

Snow and ice melt | simplified energy balance | full energy balance |

Calibration period | 1971–1990 (HQsim) | 1998–2006 |

Validation period | 1991–2010 (HQsim) | 2007–2013 |

Key advantages | low data requirement, efficient computational time, allows glacier advances | explicit ice thickness representation |

Key limitations | neglects actual glacier extent (in terms of shape) | cannot account for glacier expansion |

**Table 2.**Skill scores (Nash–Sutcliffe efficiency NSE, benchmark efficiency BE, percent bias PBIAS and root mean square error RMSE, see Table A1) of the calibration and validation of the Rofenache catchment, based on daily runoff data. Calibration and validation periods for the HQsim-GEM model are 1971–1990 and 1991–2010 (note that the first year of each period is the model warm-up) and for the AMUNDSEN model 1998–2006 and 2007–2013.

Model | NSE $[-]$ | BE $[-]$ | PBIAS $[\%]$ | RMSE $[{\mathbf{m}}^{3}/\mathbf{s}]$ | |
---|---|---|---|---|---|

HQsim-GEM | Calibration | 0.86 | 0.48 | 3.38 | 2.14 |

Validation | 0.90 | 0.60 | 1.64 | 2.03 | |

AMUNDSEN | Calibration | 0.93 | 0.70 | 8.27 | 1.78 |

(original) | Validation | 0.87 | 0.42 | 19.24 | 2.42 |

AMUNDSEN | Calibration | 0.78 | 0.12 | 23.54 | 3.05 |

(disaggregated) | Validation | 0.72 | −0.21 | 28.04 | 3.49 |

**Table 3.**Specific model parameters of both glacio-hydrological models HQsim and AMUNDSEN. Calibrated parameters are italic and bold. Model parameters for the glacier model GEM are identical to those in Marzeion et al. [30].

Parameter | HQsim | AMUNDSEN | |
---|---|---|---|

Temperature gradient | [K/m] | 0.0065 | 0.0038–0.0068 |

Lower temperature threshold | (snow/rain) | 0.0 | 2 |

Upper temperature threshold | (snow/rain) | 2.0 | 2 |

Precipitation gradient | [L/m] | 0.00043 | 0.0005–0.001 |

Snow albedo | 0.9 | 0.55–0.85 | |

Firn albedo | 0.6 | 0.4 | |

Ice albedo | 0.2 | 0.2 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Stoll, E.; Hanzer, F.; Oesterle, F.; Nemec, J.; Schöber, J.; Huttenlau, M.; Förster, K.
What Can We Learn from Comparing Glacio-Hydrological Models? *Atmosphere* **2020**, *11*, 981.
https://doi.org/10.3390/atmos11090981

**AMA Style**

Stoll E, Hanzer F, Oesterle F, Nemec J, Schöber J, Huttenlau M, Förster K.
What Can We Learn from Comparing Glacio-Hydrological Models? *Atmosphere*. 2020; 11(9):981.
https://doi.org/10.3390/atmos11090981

**Chicago/Turabian Style**

Stoll, Elena, Florian Hanzer, Felix Oesterle, Johanna Nemec, Johannes Schöber, Matthias Huttenlau, and Kristian Förster.
2020. "What Can We Learn from Comparing Glacio-Hydrological Models?" *Atmosphere* 11, no. 9: 981.
https://doi.org/10.3390/atmos11090981