# Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}wide basin located in the Eastern Italian Alps, over the 1992–2019 period. The study area was selected due to the dense network of meteorological stations used to provide input to a snowpack model and to validate the ERA-5 performance. The TOPMELT model [14] is used for seasonal snowpack dynamics and SWE simulation. TOPMELT is a semi-distributed snowpack model based on an extended temperature index approach capable of estimating the full spatial distribution of the SWE at each time step. TOPMELT exploits a statistical representation of the distribution of clear-sky potential solar radiation to drive the snowpack model, which drastically reduces the computational costs associated with the fully spatially distributed simulation of SWE over vast areas and an extended period of time while preserving simulation accuracy [14]. The good accuracy of TOPMELT SWE and SC simulations over the study area has been tested with respect to available in situ data and MODIS observations by [15,16].

## 2. Materials and Methods

#### 2.1. Study Area and In Situ Data

^{2}. The elevation ranges from about 200 m a.s.l. in the southern valley bottoms to around 3900 m a.s.l. in the western upper ranges, with a mean elevation of 1800 m a.s.l.

^{2}) and 124 temperature gauges (1 per 55 km

^{2}) covering the study region. The Hydrographic Office of Bozen, Bolzano, has made hourly temperature, precipitation, and runoff data available from 1991 until 2019. To assess the performance of the model at varying basin sizes, sixteen sub-catchments within the study basin were selected for the analysis. The drainage areas of the study basins range from 49 km

^{2}to 6924 km

^{2}(Figure 1, Table 1). These watersheds were chosen for analysis due to the relatively minor impact of operations from artificial reservoirs, which allowed for the use of a hydrological model and ensuing comparison of simulated versus observed discharges.

#### 2.2. ERA5 Reanalysis

#### 2.3. The Snowpack Model: TOPMELT

_{b}elevation bands, and the full spatial distribution of clear-sky potential solar radiation is discretized into a number of radiation classes for each elevation band. This is achieved by dividing each elevation band into n

_{c}equally distributed radiation classes, where the i

^{th}class contains the band sub-area corresponding to the i

^{th}percentile of the incident radiation energy. TOPMELT accounts separately for snow and glacier melt; to account for the presence of a glacier area associated with an energy class, each one of the n

_{b}× n

_{c}model cells is characterized by the corresponding fraction of glacier area.

_{c}, which identifies solid precipitation. Lastly, the basin precipitation, p

_{basin}, is obtained by applying a precipitation correction factor (PCF), which is a non-dimensional constant used to take into account the poor spatial coverage of the rain gauge stations. For a given i

^{th}elevation band, the model computes the precipitation p

_{i}(t) (mm h

^{−1}) at time t by applying a vertical precipitation gradient G (km

^{−1}), which considers increased precipitation over elevation as given in Equation (1):

^{th}elevation band and of the basin, respectively. For the temperature, T

_{i}(°C) is provided as input for each time step and elevation band. The use of a vertical temperature lapse rate helps to obtain the mean air temperature over the i

^{th}elevation. The estimation of the precipitation phase (solid or liquid) is performed using the threshold temperature T

_{c}, thus obtaining the snow water equivalent of the precipitation at time t, snow

_{i}(t).

^{th}elevation band and j

^{th}radiation class, the snowmelt rate ${F}_{i,j}\left(t\right)\left[\mathrm{m}\mathrm{m}{\mathrm{h}}^{-1}\right]$ at time t is calculated as in Equation (2):

^{th}elevation band at time t, while ${T}_{b}$ = 0 °C is the temperature threshold above which snowmelt is assumed to occur, both in [°C]. The snow albedo at each elevation band is computed using the method described by [20] as given in Equation (3):

_{2}is a dimensionless parameter, and ${\sum}_{k}{T}_{i}\left({t}_{k}\right)(\xb0\mathrm{C})$ is the summation of the positive hourly temperatures that are above the threshold base temperature (T

_{b}) from the last snowfall until the current time t. The model accounts for rain-on-snow and melting during the night employing a temperature index approach through two additional parameters: the rain melt factor (RMF) and the night melt factor (NMF).

_{i,j}, mm) for each model cell is updated considering the snow water equivalent of the precipitation and melt, as given in Equation (4):

_{i,j}(t) = we

_{i,j}(t − 1) + snow

_{i}(t) − F

_{i,j}(t)

_{i,j}is less than a threshold (WETH), ice melt begins. The glacier melt is computed as given in Equation (2), but the snow albedo is replaced with a constant glacier albedo (ALBG).

#### 2.4. The Hydrological Model: ICHYMOD

#### 2.5. ERA5 Bias Adjustment Method

#### 2.6. Reference Precipitation at ERA5 Spatial Resolution

#### 2.7. Comparison Statistics

## 3. Results

^{2}, the KGE is close to one, whereas it decreases markedly for basins smaller than 1000 km

^{2}and even more remarkably for basins less than 100 km

^{2}, with values around 0.6 for the smallest basin.

^{2}, the impact of basin-scale errors may be in the same range as ERA5-only errors.

## 4. Discussion and Conclusions

^{2}, with a distinct effect observed for basins with an area less than 100 km

^{2}.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The upper Adige River basin closed at Bronzolo. The red triangles indicate the stream gauges, which are listed in Table 1.

**Figure 3.**KGE of precipitation: (

**a**) ERA5-calibration, (

**b**) PC-ERA5-calibration, (

**c**) ERA5-validation, (

**d**) PC-ERA5-validation.

**Figure 6.**SWE simulation performances over the validation period: mean bias ratio for (

**a**) ERA5, (

**b**) PC-ERA5, (

**c**) TC-ERA5, (

**d**) PTC-ERA5, (

**e**) PTC-cali-ERA5; and KGE for (

**f**) ERA5, (

**g**) PC-ERA5, (

**h**) TC-ERA5, (

**i**) PTC-ERA5, (

**j**) PTC-cali-ERA5.

**Figure 7.**SWE simulation performances obtained by using SIER input over the validation period: (

**a**) mean bias ratio and (

**b**) KGE.

Sn | Name | Elevation Range (m) | Mean Elevation (m) | Area (km^{2}) |
---|---|---|---|---|

1 | Rio Plan at Plan | 1561–3445 | 2387 | 49 |

2 | Rio Riva at Seghe | 1523–3421 | 2386 | 76 |

3 | Rio Anterselva at Bagni | 1092–3421 | 2026 | 82 |

4 | Rio Braies at Braies | 1124–3074 | 1911 | 93 |

5 | Rio Riva at Caminata | 855–3421 | 2278 | 115 |

6 | Rio Casies at Colle | 1196–2815 | 1961 | 117 |

7 | Rio Gadera at Pedraces | 1318–3111 | 2027 | 125 |

8 | Aurino at Cadipietra | 811–3111 | 2162 | 150 |

9 | Rio Ridanna at Vipiteno | 1046–3417 | 1933 | 210 |

10 | Gadera at Mantana | 944–3441 | 1855 | 397 |

11 | Rio Passirio at Merano | 336–3445 | 1851 | 414 |

12 | Aurino at Caminata | 844–3421 | 2117 | 420 |

13 | Aurino at S.Giorgio | 817–3421 | 2036 | 608 |

14 | Rienza at Vandoies | 732–3421 | 1859 | 1919 |

15 | Adige at Ponte Adige | 236–3889 | 1895 | 2732 |

16 | Adige at Bronzolo | 236–3889 | 1805 | 6924 |

ERA5 | PTC-ERA5 | |||
---|---|---|---|---|

Statistics | Braies | Bronzolo | Braies | Bronzolo |

Precipitation MBR | 1.31 | 1.36 | 0.96 | 0.95 |

Mean temperature difference (°C) | −0.56 | −0.57 | 0.02 | 0.02 |

SWE MBR | 2.10 | 1.44 | 1.06 | 0.75 |

SWE KGE | −0.35 | 0.47 | 0.91 | 0.62 |

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## Share and Cite

**MDPI and ACS Style**

Shrestha, S.; Zaramella, M.; Callegari, M.; Greifeneder, F.; Borga, M.
Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins. *Climate* **2023**, *11*, 154.
https://doi.org/10.3390/cli11070154

**AMA Style**

Shrestha S, Zaramella M, Callegari M, Greifeneder F, Borga M.
Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins. *Climate*. 2023; 11(7):154.
https://doi.org/10.3390/cli11070154

**Chicago/Turabian Style**

Shrestha, Susen, Mattia Zaramella, Mattia Callegari, Felix Greifeneder, and Marco Borga.
2023. "Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins" *Climate* 11, no. 7: 154.
https://doi.org/10.3390/cli11070154