# The Modelling of the Evapotranspiration Portion of the Water Footprint: A Global Sensitivity Analysis in the Brazilian Serra Gaúcha

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## Abstract

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## 1. Introduction

#### 1.1. Previous Studies

#### 1.2. Proposed Current Study

## 2. Materials and Methods

#### 2.1. Modelling

#### 2.1.1. The Reference Evapotranspiration Model

#### 2.1.2. Crop Evapotranspiration Model

#### 2.1.3. Water Footprint Model

#### 2.2. Brazilian Serra Gaúcha

#### 2.3. Global Sensitivity Analysis Techniques

#### 2.3.1. Sampling Strategy

#### 2.3.2. Analysis of Elementary Effects (EEs)

#### 2.3.3. Fourier Amplitude Sensitivity Testing—FAST

#### 2.4. Assumptions of This Study

- The analysis considers only latitude, altitude, the fraction of mulch covering the soil, and the temperatures during three months (October, November, and December) in the water footprint for the wine production;
- The water footprint only considers the evapotranspiration portion of the viticulture of wine production;
- Temperatures, relative humidities, and wind speeds are considered to be the same for the different latitudes and altitudes (this assumption may be reasonable considering the small size of the region under consideration; on the other hand, new studies can be conducted considering the uncertainties in temperatures and wind speeds, for instance). Additionally, as already evidenced, the range of variation in the maximum temperatures is higher than the real differences in the regions under study.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

EE | elementary effects. |

FAO | Food and Agriculture Organization. |

FAST | Fourier Amplitude Sensitivity Test. |

LHS | Latin Hypercube Sampling. |

VBSA | Variance-Based Sensitivity Analysis. |

WF | water footprint. |

## Appendix A. Evapotranspiration Model

## References

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**Figure 2.**Maximum temperatures for the months of October, November, and December in the Serra Gaúcha (2013–2023).

**Figure 3.**Scatterplots (inputs–output) for the water footprint (L/bottle of wine) considering the uncertainties in the soil-covered fraction (dimensionless), altitude (m), and latitude. $N=3000$.

**Figure 5.**Elementary effects (EEs) for the water footprint (L/bottle of wine) with $r=500$ and ${N}_{boot}=100$.

Morris EE (${\mathit{\mu}}^{*}$) | FAST Index | |
---|---|---|

Covered fraction | 34.2017 | 7.1938 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-1}$ |

Altitude | 15.2832 | 1.4891 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-1}$ |

Latitude | 2.9088 | 6.5333 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-3}$ |

${T}_{max,oct}$ | 7.6636 | 4.0507 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ |

${T}_{max,nov}$ | 8.3152 | 4.7451 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ |

${T}_{max,dec}$ | 5.9991 | 2.2368 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ |

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## Share and Cite

**MDPI and ACS Style**

Platt, G.M.; Nunes, V.K.; Martins, P.R.; Corrêa, R.G.d.F.; Oliveira, F.B.S.
The Modelling of the Evapotranspiration Portion of the Water Footprint: A Global Sensitivity Analysis in the Brazilian Serra Gaúcha. *Earth* **2024**, *5*, 133-148.
https://doi.org/10.3390/earth5020007

**AMA Style**

Platt GM, Nunes VK, Martins PR, Corrêa RGdF, Oliveira FBS.
The Modelling of the Evapotranspiration Portion of the Water Footprint: A Global Sensitivity Analysis in the Brazilian Serra Gaúcha. *Earth*. 2024; 5(2):133-148.
https://doi.org/10.3390/earth5020007

**Chicago/Turabian Style**

Platt, Gustavo Mendes, Vinícius Kuczynski Nunes, Paulo Roberto Martins, Ricardo Gonçalves de Faria Corrêa, and Francisco Bruno Souza Oliveira.
2024. "The Modelling of the Evapotranspiration Portion of the Water Footprint: A Global Sensitivity Analysis in the Brazilian Serra Gaúcha" *Earth* 5, no. 2: 133-148.
https://doi.org/10.3390/earth5020007