# 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 | $\mathrm{NSE}=1-\frac{{\displaystyle \sum _{i=1}^{N}}{\left[{q}_{\mathrm{obs},i}-{q}_{\mathrm{sim},i}\right]}^{2}}{{\displaystyle \sum _{i=1}^{N}}{\left[{q}_{\mathrm{obs},i}-{\overline{q}}_{\mathrm{obs}}\right]}^{2}}$ |

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

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

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

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**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