# Evaluation of Snowmelt Estimation Techniques for Enhanced Spring Peak Flow Prediction

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials

^{2}including the diverted basins and is primarily covered by forests (97%) and secondarily by water bodies (3%) [28]. According to the Canadian Climate Normals (1981–2010) at La-Grande River (53°38’N, 77°42’W), the mean annual precipitation is 697 mm out of which more than one-third is snowfall. Thus, peak runoff due to spring snowmelt is evident in the basin hydrology. The average temperature ranges between −28 °C to −8 °C in winter (Jan–Mar) and −10 °C to 17 °C in spring (Apr–Jun).

^{2}(Figure 1b). The majority of this watershed lies in the prairie pothole region of the Canadian Prairies [29]. For a detailed understanding of the complex hydrology of the prairie pothole region, the interested reader is referred to [10,29,30]. Based on 1981–2010 data, air temperature varies seasonally between −22 °C to −1.4 °C in winter (Jan-Mar) and −2.6 °C to +21.8 °C in spring (Apr–Jun), with about 511 mm of mean annual precipitation. UASR was selected for the experiment as it is a snow-dominated watershed with more than 80% of the total annual flow occurring during the spring snowmelt season [30,31]. The observed daily precipitation and temperature data were obtained from Environment Canada for the 23 years (1994–2015) period, while streamflow and reservoir inflow time series for the same period was provided by the Hydrologic Forecast Centre, Manitoba Infrastructure (MI). Calibration was conducted at Shellmouth reservoir inflow and one of the major gauging stations feeding the reservoir, the Assiniboine river at Kamsack station.

## 3. Methods

#### 3.1. Hydrological Models

#### 3.1.1. MAC-HBV Model

#### 3.1.2. SAC-SMA Model

#### 3.2. Snowmelt Estimation Methods

#### 3.2.1. Degree-Day Method

_{m}) (usually 0 °C) with degree-day factor (DDF). The melt equation is given by:

_{s}is snowfall (mm/day), P

_{m}is rainfall (mm/day) and ∆t is time-step of a day. Rainfall and snowfall amounts are determined by upper and lower threshold temperatures distinguishing rain, snow and mix of snow and rain. Melt rate along with precipitation as rain is provided to hydrological model to obtain estimates of reservoir inflow.

#### 3.2.2. SNOW-17 Model

_{nr}) is governed by melt factor and is described by:

_{f}= seasonally varying melt factor, MBASE = Base temperature, f

_{r}= Fraction of precipitation in form of rain, Tr = Rain Temperature, Ta = Air temperature, P = Precipitation

#### 3.3. Model Optimization

_{obs}and Q

_{sim}are the observed and simulated streamflow values, respectively, $\overline{{Q}_{obs}}$ is the average of observed streamflow values and N is the total number of data points. Equations (8) and (9) are similar to Equation (6) but they account for log-transformed flows and square-transformed flows and thus emphasize low flows and high flows, respectively. NSE spans between -∞ to 1 with 1 showing optimal performance for NSE and NVE. Inversely, VE ranges from 0 to ∞ and values closer to zero reveals better model performance. Using Equation (5), a single objective calibration approach can be used as a multi-objective approach. We repeated the calibration with objective function NVE (Equation (5)) to put more emphasis on high flows (NSEsqr). The recalibration was carried out for model combinations with the least performing sub-watersheds to check for improvement in performance, but we found that results did not improve peak flow statistics and hydrograph significantly. Henceforth, we include results obtained by training the models with the above objective function Equation (5).

#### 3.4. Model Performance Criteria

## 4. Results

#### 4.1. Evaluation of Snowmelt Estimation Methods: DDM and SNOW-17 Model

#### 4.2. Results of Annually and Seasonally Calibrated Models

#### 4.3. Comparison between Hydrological Models: MAC-HBV and SAC-SMA

#### 4.4. Visual Inspection of Model Performance

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) La-Grande River Basin (LGRB), Quebec, Canada (Left) and (

**b**) Upper Assiniboine River at Shellmouth Reservoir (UASR), Manitoba, Canada (Right).

**Figure 3.**Model Improvement (defined by % reduction in RMSE) obtained by using the SNOW-17 model instead of DDM for LGRB. Positive values mean model improvement when coupled with the SNOW-17 model, while negative values mean model deterioration due to implementation of the SNOW-17 model (with DDM taken as a base model for evaluation). Boxes are delimited by the 25th and 75th percentiles, the median value is printed in the boxes, and the whiskers are delimited by 10th and 90th percentiles.

**Figure 4.**Model Improvement (defined by % reduction in RMSE) obtained by using the SNOW-17 model than DDM for UASR. The description is the same as in Figure 3, and as the model was calibrated at two stations, boxes here represent statistics for both the locations considered.

**Figure 5.**NSE statistics for MAC-HBV-DDM, MAC-HBV-SNOW-17, SAC-SMA-DDM, SAC-SMA-SNOW-17 model structures for annual and seasonal models of LGRB. Boxplot description same as Figure 3, except the median is marked with a thick black line inside boxes.

**Figure 6.**NSE statistics for MAC-HBV-DDM, MAC-HBV-SNOW-17, SAC-SMA-DDM, SAC-SMA-SNOW-17 model structures for annual and seasonal models of UASR. See Figure 4 for a description of the boxplots, and the median is marked with a thick black line inside boxes.

**Figure 7.**NRMSE statistics for MAC-HBV-DDM, MAC-HBV-SNOW-17, SAC-SMA-DDM, SAC-SMA-SNOW-17 model combinations for annual and seasonal models of LGRB. NRMSE is computed for spring season flows above 75 percentile. See Figure 5 for box plot description.

**Figure 8.**NRMSE statistics for MAC-HBV-DDM, MAC-HBV-SNOW-17, SAC-SMA-DDM, SAC-SMA-SNOW-17 model combinations for annual and seasonal models of UASR. See Figure 6 for box plot description.

Parameter Code | Description | Unit | Ranges |
---|---|---|---|

SAC-SMA | |||

UZTWM | Upper-zone tension water maximum storage | mm | 1–150 |

UZFWM | Upper-zone free water maximum storage | mm | 1–150 |

UZK | Upper-zone free water lateral depletion rate | day^{−1} | 0.1–0.5 |

PCTIM | Impervious fraction of the watershed area | - | 0–0.1 |

ADIMP | Additional impervious area | - | 0–0.4 |

ZPERC | Maximum percolation rate | - | 1–250 |

REXP | Exponent of the percolation equation | - | 1–5 |

LZTWM | Lower-zone tension water maximum storage | mm | 1–500 |

LZFSM | Lower-zone free water supplemental maximum storage | mm | 1–1000 |

LZFPM | Lower-zone free water primary maximum storage | mm | 1–1000 |

LZSK | Lower-zone supplemental free water lateral depletion rate | day^{−1} | 0.01–0.25 |

LZPK | Lower-zone primary free water lateral depletion rate | day^{−1} | 0.0001–0.025 |

PFREE | Fraction percolating from upper to lower zone free water storage | - | 0–0.6 |

Rq | Routing coefficient | - | 0.5–1.5 |

MAC-HBV | |||

athorn | Constant for Thornthwaite’s equation | - | 0.1–0.3 |

fc | Maximum soil box water content | mm | 50–800 |

lp | Limit for potential evaporation | mm/mm | 0.1*fc–0.9*fc |

beta | Non-linear parameter controlling runoff generation | - | 0–10 |

k0 | Flow recession coefficient in an upper soil reservoir | days | 1–30 |

lsuz | A threshold value used to control response routing on an upper soil reservoir | mm | 1–100 |

k1 | Flow recession coefficient in an upper soil reservoir | days | 30–100 |

cperc | A constant percolation rate parameter | mm/day | 0.01–6 |

k2 | Flow recession coefficient in a lower soil reservoir | days | 100–500 |

alpha1 | An exponent in relation between outflow and storage representing non-linearity of storage – discharge relationship of lower reservoir | - | 0.5–1.25 |

maxbas | A triangle weighting function for modelling a channel routing routine | days | 1–20 |

DDM | |||

tr | Upper threshold temperature to distinguish between rainfall and snowfall | °C | 0–2.5 |

scf | Snowfall correction factor | - | 0.4–1.6 |

ddf | Degree day factor | mm/day°C | 0–5.0 |

rcr | Rainfall correction factor | - | 0.5–1.5 |

SNOW17 | |||

scf | Snowfall correction factor | - | 0.7–1.6 |

uadj | Average wind function during rain-on-snow events | mm/mb/6 h | 0.03–0.19 |

mbase | Base temperature for non-rain melt factor | °C | 0–1.0 |

mfmax | Maximum melt factor considered to occur on Jun 21 | mm/6 h/°C | 0.5–2.0 |

mfmin | Minimum melt factor considered to occur on Dec 21 | mm/6 h/°C | 0.05–0.49 |

tipm | Antecedent snow temperature index | - | 0.01–1.0 |

nmf | Maximum negative melt factor | mm/6 h/°C | 0.05–0.50 |

plwhc | Percent liquid-water holding capacity | - | 0.02–0.3 |

pxtemp1 | Lower limit temperature dividing transition from snow | °C | −2–0 |

pxtemp2 | Upper limit temperature dividing rain from transition | °C | 1–3 |

Model Calibration Mean | Model Validation Mean | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Models | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) |

MAC DDM | 0.76 | 0.83 | 1.49 | 0.40 | 1.13 | 0.56 | 0.68 | 1.83 | 0.46 | -4.21 |

MAC SNOW-17 | 0.75 | 0.84 | 1.37 | 0.40 | 0.53 | 0.65 | 1.85 | 0.45 | ||

SAC DDM | 0.82 | 0.87 | 1.24 | 0.35 | 0.83 | 0.66 | 0.72 | 1.54 | 0.42 | 4.27 |

SAC SNOW-17 | 0.82 | 0.88 | 1.20 | 0.37 | 0.70 | 0.77 | 1.45 | 0.39 |

Model Calibration Mean | Model Validation Mean | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Models | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) |

MAC DDM | 0.75 | 0.83 | 1.45 | 0.39 | 6.10 | 0.58 | 0.65 | 1.80 | 0.42 | 1.76 |

MAC SNOW-17 | 0.78 | 0.85 | 1.28 | 0.35 | 0.55 | 0.66 | 1.78 | 0.45 | ||

SAC DDM | 0.82 | 0.85 | 1.25 | 0.35 | 1.71 | 0.66 | 0.71 | 1.60 | 0.42 | 2.90 |

SAC SNOW-17 | 0.82 | 0.87 | 1.19 | 0.32 | 0.66 | 0.75 | 1.54 | 0.43 |

Calibration | Validation | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Model | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) |

MAC DDM | 0.48 | 0.74 | 0.32 | 0.47 | 3.07 | 0.56 | 0.57 | 0.54 | 0.53 | -39.17 |

MAC SNOW-17 | 0.51 | 0.73 | 0.34 | 0.48 | 0.19 | 0.23 | 0.79 | 0.62 | ||

SAC DDM | 0.7 | 0.82 | 0.28 | 0.43 | -4.14 | 0.49 | 0.52 | 0.59 | 0.57 | -4.89 |

SAC SNOW-17 | 0.67 | 0.80 | 0.22 | 0.38 | 0.44 | 0.49 | 0.63 | 0.6 |

Calibration | Validation | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Model | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) | NSE | KGE | NRMSE (mm/d) | PFC | Model Improvement (%) |

MAC DDM | 0.42 | 0.72 | 0.36 | 0.49 | 17.67 | 0.52 | 0.6 | 0.54 | 0.52 | -22.28 |

MAC SNOW-17 | 0.61 | 0.78 | 0.31 | 0.45 | 0.28 | 0.35 | 0.72 | 0.61 | ||

SAC DDM | 0.66 | 0.73 | 0.28 | 0.44 | 2.44 | 0.58 | 0.5 | 0.55 | 0.55 | -13.20 |

SAC SNOW-17 | 0.68 | 0.73 | 0.28 | 0.46 | 0.46 | 0.48 | 0.65 | 0.59 |

**Table 6.**Percentage of sub-basins performing better/competitive with a) DDM than SNOW-17 b) Seasonal than Annual model calibration and c) SAC-SMA than MAC-HBV model.

Percentage of Sub-Basins Performing Better/Comparable with DDM Than SNOW-17 Model | Percentage of Sub-Basins Performing Better/Comparable with SEASONAL Models than ANNUAL Models | Percentage of Sub-Basins Performing Better/Comparable with SAC-SMA Than MAC-HBV Hydrologic Model | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

LGRB | NSE | PFC | MI | NSE | KGE | PFC | NRMSE | NSE | KGE | PFC | NRMSE |

Entire Study Period | 51 | 56 | 46 | 54 | 51 | 51 | 53 | 92 | 79 | 74 | 86 |

UASR | NSE | PFC | MI | NSE | KGE | PFC | NRMSE | NSE | KGE | PFC | NRMSE |

Entire Study Period | 56 | 62 | 56 | 62 | 38 | 62 | 75 | 94 | 69 | 75 | 87 |

Sum (LGRB+UASR) | 52 | 57 | 48 | 55 | 49 | 53 | 57 | 93 | 77 | 74 | 86 |

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Agnihotri, J.; Coulibaly, P. Evaluation of Snowmelt Estimation Techniques for Enhanced Spring Peak Flow Prediction. *Water* **2020**, *12*, 1290.
https://doi.org/10.3390/w12051290

**AMA Style**

Agnihotri J, Coulibaly P. Evaluation of Snowmelt Estimation Techniques for Enhanced Spring Peak Flow Prediction. *Water*. 2020; 12(5):1290.
https://doi.org/10.3390/w12051290

**Chicago/Turabian Style**

Agnihotri, Jetal, and Paulin Coulibaly. 2020. "Evaluation of Snowmelt Estimation Techniques for Enhanced Spring Peak Flow Prediction" *Water* 12, no. 5: 1290.
https://doi.org/10.3390/w12051290