# Evaluation and Development of Pedotransfer Functions and Artificial Neural Networks to Saturation Moisture Content Estimation

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Soil Textures

#### 2.3. Statistical Analysis

#### 2.4. Development of the PTFs and the ANNs

## 3. Results

#### 3.1. PTFs

#### 3.2. ANN

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematic representation of principal types ANNs. Recovered from [43].

**Figure 3.**Distribution of soil textures for calibration (450 points) and validation (450 points) data. Abbrevations are as follows: clay (Cl), sand (Sa), silt (Si), loam (Lo), sandy clay (SaCl), silty clay (SiCl), sandy clay loam (SaClLo), clay loam (ClLo), silty clay loam (SiClLo), sandy loam (SaLo), silty loam (SiLo) and loamy sand (LoSa).

**Figure 4.**Comparison between the measured ${\theta}_{\mathrm{s}}$ and the estimated one by the PTF. The PTF equations are at the top left, and the values for each constant are below that. In addition, the ${R}^{2}$ value and a residual histogram are available.

**Figure 5.**Results for the 81 ANN configurations. (

**Top**) The RMSE variations for each ANN configuration. (

**Bottom**) Statistical analysis (RMSE and R${}^{2}$) for each ANN configuration; 2L4I means two layers and four input parameters, while 2L5I is two layers and five input data points.

**Figure 6.**Results for the 4-9-10-1 (

**left**) and 5-10-10-1 (

**right**) configuration predictions applied in the validation data.

PTF | Formula | Source |
---|---|---|

PTF1 | ${\theta}_{\mathrm{s}}=0.81799+9.9\times {10}^{-4}\xb7\mathrm{Cl}-0.3142\xb7\mathrm{BD}+1.8\times {10}^{-4}\xb7\mathrm{CEC}+0.00451\xb7\mathrm{pH}-5\times {10}^{-6}\xb7\mathrm{Sa}\xb7\mathrm{Cl}$ | [2] |

PTF2 | ${\theta}_{\mathrm{s}}=0.81-0.283\xb7\mathrm{BD}+0.001\xb7\mathrm{Cl}$ | [36] |

PTF3 | ${\theta}_{\mathrm{s}}=0.7019+0.001691\xb7\mathrm{Cl}-0.29619\xb7\mathrm{BD}-1.491\times {10}^{-6}\xb7{\mathrm{Si}}^{2}+8.21\times {10}^{-5}\xb7{\mathrm{OM}}^{2}+0.02427\xb7{\mathrm{Cl}}^{-1}+0.01113\xb7\phantom{\rule{0ex}{0ex}}{\mathrm{Si}}^{-1}+0.01472ln\left(\mathrm{Si}\right)-7.33\times {10}^{-5}\xb7\mathrm{OM}\xb7\mathrm{Cl}-6.19\times {10}^{-4}\xb7\mathrm{BD}\xb7\mathrm{Cl}-0.001183\xb7\mathrm{BD}\xb7\mathrm{OM}-1.664\times {10}^{-4}\xb7\mathrm{Si}\xb7\mathrm{tps}$ | [37] |

^{3}); OC = Organic Carbon (% by weight); OM = Organic Matter (% by weight); CEC = Cation Exchange Capacity (cmol/kg soil); pH (dimensionless); tps is the topsoil and is a qualitative variable having the value of 1.

PTF | Formula | R${}^{2}$ |
---|---|---|

PTF-1 | ${\theta}_{\mathrm{s}}=a\xb7{\mathrm{Cl}}^{2}+b\xb7\mathrm{Cl}+c$ | 0.9046 |

PTF-2 | ${\theta}_{\mathrm{s}}=a\xb7{\mathrm{Cl}}^{2}+b\xb7\mathrm{Cl}+c+d\xb7\mathrm{Sa}$ | 0.9705 |

PTF-3 | ${\theta}_{\mathrm{s}}=a\xb7{\mathit{K}}_{\mathrm{s}}^{2}+b\xb7{\mathit{K}}_{\mathrm{s}}+c+d\xb7\mathrm{Sa}$ | 0.9445 |

PTF-4 | ${\theta}_{\mathrm{s}}=a\xb7{\mathit{K}}_{\mathrm{s}}^{2}+b\xb7{\mathit{K}}_{\mathrm{s}}+c+d\xb7\mathrm{Sa}+e\xb7{\mathrm{Cl}}^{2}+f\xb7\mathrm{Cl}$ | 0.9877 |

PTF-5 | ${\theta}_{\mathrm{s}}=a\xb7exp(b\xb7\mathrm{Cl})$ | 0.9328 |

PTF-6 | ${\theta}_{\mathrm{s}}=a+b\xb7ln\left(\mathrm{Cl}\right)+c\xb7\mathrm{BD}$ | 0.9469 |

PTF-7 | ${\theta}_{\mathrm{s}}=a+b\xb7{\mathrm{Cl}}^{2}+c\xb7\mathrm{Cl}+d\xb7\mathrm{BD}$ | 0.9542 |

PTF-8 | ${\theta}_{\mathrm{s}}=a+b\xb7{\mathrm{Cl}}^{2}+c\xb7\mathrm{Cl}+d\xb7\mathrm{BD}+e\xb7\mathrm{Sa}$ | 0.9783 |

^{3}); Ks (cm/h) and the coefficients from a to f are obtained by fitting the model to the experimental data.

ANN | RMSE | R${}^{2}$ | ME |
---|---|---|---|

4-9-10-1 | 0.0182 | 0.9891 | 0.0091 |

5-10-10-1 | 0.0195 | 0.9903 | 0.0095 |

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**MDPI and ACS Style**

Trejo-Alonso, J.; Fuentes, S.; Morales-Durán, N.; Chávez, C. Evaluation and Development of Pedotransfer Functions and Artificial Neural Networks to Saturation Moisture Content Estimation. *Water* **2023**, *15*, 220.
https://doi.org/10.3390/w15020220

**AMA Style**

Trejo-Alonso J, Fuentes S, Morales-Durán N, Chávez C. Evaluation and Development of Pedotransfer Functions and Artificial Neural Networks to Saturation Moisture Content Estimation. *Water*. 2023; 15(2):220.
https://doi.org/10.3390/w15020220

**Chicago/Turabian Style**

Trejo-Alonso, Josué, Sebastián Fuentes, Nami Morales-Durán, and Carlos Chávez. 2023. "Evaluation and Development of Pedotransfer Functions and Artificial Neural Networks to Saturation Moisture Content Estimation" *Water* 15, no. 2: 220.
https://doi.org/10.3390/w15020220