# Comparative Evaluation of Five Hydrological Models in a Large-Scale and Tropical River Basin

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. HYMOD Model

#### 2.2. GR4J Model

#### 2.3. SMAP Model

#### 2.4. HBV Model

#### 2.5. MGB-IPH Model

#### 2.6. Performance Metrics

#### 2.7. Statistical Tests

#### 2.8. Bias Correction

## 3. Case Study

#### 3.1. Overview

#### 3.2. Data

#### 3.3. Results Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Schematic diagram of linear reservoirs used by the MGB-IPH model. Adapted from: [55].

**Figure 9.**Boxplots of deterministic metrics for the original and corrected simulated data for the vaildation period.

**Figure 10.**Hydrographs for the validation stage comparing the observed and the simulated streamflows by different hydrological models at the Estreito UHE.

**Figure 11.**Curves describing the duration of daily streamflow in the Tocantins river basin for the validation period (2005–2010).

**Figure 12.**Statistical tests of each hydrological model in the validation stage. The horizontal line indicates the significance level $\alpha =0.05$.

**Figure 13.**Violin plot describing the low, median, and high flows simulated in the Tocantins river basin by multiple hydrological models. Calibration period.

**Figure 14.**Violin plot describing the low, median, and high flows simulated in the Tocantins river basin by multiple hydrological models. Validation period.

Model | Calibrated Parameters | Conceptual Storage | Type of Flows | Input Data | Routing Method |
---|---|---|---|---|---|

GR4J | 4 | Production soil storage | Fast flow | Precipitaiton | Triangular weighting function |

Routing soil storage | Slow flow | PET | |||

HYMOD | 5 | Soil moisture layer | Surface flow | Precipitation | Triangular weighting function |

Quick flow reservoirs | Groundwater flow | PET | |||

Slow Flow Reservoir | |||||

HBV | 11 | Soil moisture layer | Surface flow | Precipitaiton | Triangular weighting function |

Upper zone storage | Base flow | Temperature | |||

Lower zone storage | Long-term monthly temperature | ||||

Long-term monthly PET | |||||

SMAP | 11 | Upper soil reservoir | Surface flow | Precipitation | Triangular weighting function |

Second upper soil reservoir | Base flow | PET | |||

Lower soil reservoir | |||||

Groundwater storage | |||||

MGB-IPH | 27 | Soil layers | Surface runoff | Digital Elevation Model (DEM) | Muskingum-Cunge |

Surface flow reservoir | Subsurface flow | Precipitation | |||

Interflow reservoir | Base flow | Climate variables | |||

Groundwater reservoir | Hydrological response units (GRU) |

Parameter | Units | Limits | Description |
---|---|---|---|

${C}_{max}$ | mm | 50 to 3000 | Maximum moisture (storage in the soil layer) |

${\beta}_{exp}$ | - | 0 to 2 | Distribution of soil moisture store |

$\alpha $ | - | 0.2 to 0.99 | Factor of flow distribution between quick and slow reservoirs |

${K}_{q}$ | day | 0.5 to 1.2 | Quick response reservoir residence time |

${K}_{s}$ | day | 0.001 to 0.5 | Slow response reservoir residence time |

Parameter | Units | Limits | Description |
---|---|---|---|

${X}_{1}$ | mm | 50 to 3000 | Maximum capacity of the production store |

${X}_{2}$ | mm/day | −10 to 10 | Inter-catchment exchange coefficient |

${X}_{3}$ | mm | 10 to 200 | Maximum capacity of the routing store |

${X}_{4}$ | mm | 0.7 to 10 | Base time of the unit hydrograph |

Parameter | Units | Limits | Description |
---|---|---|---|

H | mm | 0 to 500 | Representative height for the overflow in the R${}_{sup}$ reservoir |

$H1$ | mm | 0 to 500 | Representative height for the second flow in the R${}_{sup}$ reservoir |

$Capc$ | % | 0 to 200 | Soil field capacity |

$Crec$ | % | 0 to 50 | Parameter that regulates the underground recharge |

$K1t$ | day | 0 to 10 | Overflow recession coefficient in the R${}_{sup}$ reservoir |

$K2t$ | day | 0 to 10 | First flow recession coefficient in the R${}_{sup}$ reservoir |

$K2t2$ | day | 0 to 10 | Second flow recession coefficient in the R${}_{sup}$ reservoir |

$K3t$ | day | 0 to 10 | Flow recession coefficient in the R${}_{sup2}$ reservoir |

$Kkt$ | day | 0 to 10 | Base streamfow recession coefficient in the R${}_{sub}$ reservoir |

$Str$ | mm | 0 to 500 | Maximum volume stored in the soil reservoir |

$Ecof$ | - | 0 to 1.5 | Adjustment coefficient of potential evapotranspiration |

${P}_{BASMAX}$ | day | 1 to 10 | Routing time |

Parameter | Units | Limits | Description |
---|---|---|---|

$TT$ | °C | 0 | Temperature threshold for snowmelt |

$DD$ | mm°C${}^{-1}$ | 2 to 15 | Degree-day factor |

$FC$ | mm | 100 to 300 | Maximum soil storage capacity |

$\beta $ | - | 0 to 4 | Distribution of soil moisture sotre |

C | °C${}^{-1}$ | 0 to 0.4 | Temperature correction factor |

${K}_{0}$ | day${}^{-1}$ | 0.01 to 0.2 | Quick response coefficient (upper deposit) |

L | mm | 0 to 5 | Quick runoff response threshold |

${K}_{1}$ | day${}^{-1}$ | 0.01 to 0.1 | Slow reponse coefficient (upper deposit) |

${K}_{2}$ | day${}^{-1}$ | 0.01 to 0.1 | Lower deposit response coefficient |

${K}_{p}$ | day${}^{-1}$ | 0.01 to 0.1 | Maximum flow for percolation coefficient |

$PWP$ | mm | 90 to 200 | Soil Permanent Wilting Point |

${P}_{BASMAX}$ | day | 1 to 10 | Routing time |

**Table 6.**Descriptive statistics of observed daily streamflow and precipitation for the period 2010–2019.

UHE | Total Drainage Area (km${}^{2}$) | Incremental Total Area (km${}^{2}$) | Total Annual Rainfall (mm) | Daily Streamflow (m${}^{3}$/s) | ||||
---|---|---|---|---|---|---|---|---|

Mean | SD | CV | Max | Min | ||||

Serra da Mesa | 50,678 | 50,678 | 1324 | 529 | 528 | 99 | 4690 | 53 |

Cana Brava | 57,979 | 7301 | 1454 | 585 | 581 | 99 | 4840 | 70 |

Sao Salvador | 63,695 | 5716 | 1627 | 640 | 635 | 99 | 4970 | 79 |

Peixe Angical | 126,995 | 63,300 | 1137 | 1071 | 1093 | 102 | 8210 | 127 |

Lajeado | 183,608 | 56,613 | 1441 | 1526 | 1567 | 102 | 11,700 | 173 |

Estreito | 285,778 | 102,170 | 1652 | 2750 | 2395 | 87 | 14,600 | 269 |

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**MDPI and ACS Style**

Ávila, L.; Silveira, R.; Campos, A.; Rogiski, N.; Gonçalves, J.; Scortegagna, A.; Freita, C.; Aver, C.; Fan, F.
Comparative Evaluation of Five Hydrological Models in a Large-Scale and Tropical River Basin. *Water* **2022**, *14*, 3013.
https://doi.org/10.3390/w14193013

**AMA Style**

Ávila L, Silveira R, Campos A, Rogiski N, Gonçalves J, Scortegagna A, Freita C, Aver C, Fan F.
Comparative Evaluation of Five Hydrological Models in a Large-Scale and Tropical River Basin. *Water*. 2022; 14(19):3013.
https://doi.org/10.3390/w14193013

**Chicago/Turabian Style**

Ávila, Leandro, Reinaldo Silveira, André Campos, Nathalli Rogiski, José Gonçalves, Arlan Scortegagna, Camila Freita, Cássia Aver, and Fernando Fan.
2022. "Comparative Evaluation of Five Hydrological Models in a Large-Scale and Tropical River Basin" *Water* 14, no. 19: 3013.
https://doi.org/10.3390/w14193013