# Saturated Hydraulic Conductivity Estimation Using Artificial Intelligence Techniques: A Case Study for Calcareous Alluvial Soils in a Semi-Arid Region

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## Abstract

**:**

^{−1}, root means square error (RMSE) of 3.096 mm h

^{−1}, coefficient of determination (R

^{2}) of 0.940, and correlation coefficient (CC) of 0.970. Therefore, the ANN could be suggested among the neural-network-based models. Otherwise, RF could also be used for the estimation of Ks among the tree-based models.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

^{3}cm

^{−3}), Ps is particle density (g cm

^{−3}), Pb is bulk density (g cm

^{−3}), EP is effective porosity (cm

^{3}cm

^{−3}), and FC is field capacity by volume (cm

^{3}cm

^{−3}).

#### 2.2. Machine Learning Methods

#### 2.2.1. Artificial Neural Networks

#### 2.2.2. Deep Learning

#### 2.2.3. Decision Tree

#### 2.2.4. Random Forest

#### 2.3. Selected Inputs and Model Development

#### 2.4. Performance Evaluation

^{2}), and correlation coefficient (CC). The calculations of these metrics are shown below:

_{i}is the observed value. $\overline{Y}$ is the mean value of observed values and $\overline{Z}$ is the mean value of the predicted values. For the evaluation of the model performance, the high model performance can be confirmed when the RMSE and MAE values are low, and ${\mathrm{R}}^{2}$ and CC values are high.

## 3. Results

#### 3.1. Adjustment of Input Variables

^{−1}for silt, field capacity, porosity, and effective porosity, and the positive values of kurtosis were 0.12, 0.08, 0.12 and 3.37 mm h

^{−1}for bulk density, porosity, lime, and organic carbon, respectively. The maximum, minimum, mean, and standard deviation values of Ks were 58.91, 0.88, 16.08, and 11.33 mm h

^{−1}, respectively. The highest value of variation coefficient was observed for Ks values with 0.66 mm h

^{−1}. The highest value of skewness was obtained by Ks value with 0.86 mm h

^{−1}and the lowest value of kurtosis was obtained by an effective porosity value of −0.88.

#### 3.2. Performance of Machine Learning Methods

#### 3.3. Performances of Neural-Network-Based Machine Learning Methods

^{−1}), RMSE (3.096 mm h

^{−1}), ${\mathrm{R}}^{2}$ (0.940), and CC (0.970). However, the ANN2 fed with soil inputs of clay and effective porosity had the poorest performance with MAE of 4.272 mm h

^{−1}, RMSE of 5.603 mm h

^{−1}, ${\mathrm{R}}^{2}$ of 0.806, and CC of 0.897. The scatter plots of estimated Ks values by the ANN model with eight soil input combinations are shown in Figure 5A. The data of the scatter plots are generally close to the reference line (1:1) for all combinations. However, the combinations of 1, 2, and 8 for the ANN model showed more scattered points than combinations of 3, 4, 5, 6, and 7. The residual plots of estimated Ks values by the ANN model with eight soil input combinations are shown in Figure 5B. The residual plot demonstrated that the most errors occurred in combination 8, while the least error occurred in combination 6 for the ANN model.

^{−1}, RMSE of 3.423 mm h

^{−1}, ${\mathrm{R}}^{2}$ of 0.919, and CC of 0.959. The scatter plots of estimated Ks values by the DL model with eight soil input combinations are shown in Figure 6A. From the figure, it can be seen that combinations 2 and 8 had more scattered points than other combinations. The least scattered points were observed for the combination of 7. The residual plots of estimated Ks values by the DL model with eight soil input combinations are shown in Figure 6B. The least residual errors were observed for the combination of 7, while the most residual errors were observed for the combination 8 for the DL model.

#### 3.4. Performances of Tree-Based Machine Learning Methods

^{−1}), RMSE (5.736 mm h

^{−1}), ${\mathrm{R}}^{2}$ (0.887), CC (0.942). The performance metrics improved significantly when adding organic carbon instead of bulk density values from the soil inputs. In that case, the highest performance was observed for the fifth combination with MAE of 2.121 mm h

^{−1}, RMSE of 5.130 mm h

^{−1}, ${\mathrm{R}}^{2}$ of 0.804, and CC of 0.896. Similar performances were obtained for combination 1 and 3 and also for combinations 4 and 7. The scatter plots of estimated Ks values by the DT model with eight soil input combinations are shown in Figure 7A. It can be noticed that the combinations of the DT model were more scattered than the combinations of the ANN, DL, and RF models. The residual plots of estimated Ks values by the DT model with eight soil input combinations are shown in Figure 7B. The highest residual Ks values were observed in combination 6 with the value of 18.60 mm h

^{−1}. The least residual errors occurred in combination 5 for the DT model.

^{−1}, RMSE of 5.736 mm h

^{−1}, ${\mathrm{R}}^{2}$ of 0.755, and CC of 0.869. The performance of the RF model improved when adding organic carbon instead of bulk density from the soil inputs. The performance metrics demonstrated similar performance to the RF model for the third, fourth, and fifth input combinations. The best performance was observed for the RF5 model with soil inputs of sand, clay, effective porosity, and bulk density with MAE of 2.685 mm h

^{−1}, RMSE of 3.936 mm h

^{−1}, ${\mathrm{R}}^{2}$ of 0.887, and CC of 0.942. The scatter plots of estimated Ks values by the RF model with eight soil input combinations are shown in Figure 8A. The most scattered points were obtained from combination 8, while the least scattered points were obtained from combination 7 for the RF model. The residual plots of estimated Ks values by the RF model with eight soil input combinations are shown in Figure 8B. According to the figure, similar residual errors were observed for the combination of 3, 4, and 5. However, among them, the least residual errors occurred in combination 5 for the RF model.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Performance metrics of machine learning models with eight combinations of soil input data.

Parameters | Abbreviations | Units | Methods | References |
---|---|---|---|---|

Soil texture (Clay, Silt, Sand) | - | % | Bouyoucos hydrometer method | [40] |

Bulk density | Pb | g cm^{−3} | Core method (50 * 51 mm core samples) | [41] |

Particle density | Ps | g cm^{−3} | Pycnometer method | [42] |

Field capacity | FC | cm^{3} cm^{−3} | Pressure plate apparatus at 0.33 bars | [43] |

Permanent wilting point | PWP | cm^{3} cm^{−3} | Pressure plate apparatus at 15 bars | |

Available water capacity | AWC | cm^{3} cm^{−3} | ||

Aggregate stability | AS | % | Cornell Sprinkle Infiltrometer | [44] |

Penetration resistance | PR | PSI | Digital penetrometer (Eijkelkamp) | |

Lime content | L | % | Scheibler Calcimeter 1:3 acid/water | [45] |

Organic carbon | OC | % | Dry combustion C and N analyzer | [46] |

Sand | Silt | Clay | Pb | FC | PWP | P | EP | AS | PR | Lime | OC | Ks1 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Silt | −0.288 *** | ||||||||||||

Clay | −0.923 *** | −0.104 ns | |||||||||||

Pb | 0.471 *** | −0.161 *** | −0.424 *** | ||||||||||

FC | −0.809 *** | 0.133 ns | 0.787 *** | −0.504 *** | |||||||||

PWP | −0.772 *** | 0.015 ns | 0.796 *** | −0.496 *** | 0.893 *** | ||||||||

P | −0.487 *** | 0.143 * | 0.448 *** | −0.974 *** | 0.510 *** | 0.496 *** | |||||||

MP | 0.273 *** | −0.001 ns | −0.283 *** | −0.565 *** | −0.414 *** | −0.321 *** | 0.563 *** | ||||||

AS | −0.385 *** | 0.122 * | 0.350 *** | −0.412 *** | 0.211 *** | 0.219 *** | 0.395 *** | 0.212 *** | |||||

PR | 0.335 *** | −0.260 *** | −0.244 *** | 0.464 *** | −0.392 *** | −0.361 *** | −0.459 *** | −0.106 ns | −0.186 *** | ||||

Lime | −0.542 *** | −0.138 * | 0.619 *** | −0.080 ns | 0.263 *** | 0.320 *** | 0.122 * | −0.138 * | 0.206 *** | 0.069 ns | |||

OC | −0.398 *** | −0.059 ns | 0.436 *** | −0.185 *** | 0.253 *** | 0.369 *** | 0.196 *** | −0.034 ns | 0.273 *** | 0.001 ns | 0.341 *** | ||

Ks1 | 0.391 *** | −0.187 *** | −0.331 *** | −0.131 * | −0.313 *** | −0.237 *** | 0.113 ns | 0.430 *** | −0.080 ns | −0.036 ns | −0.302 *** | −0.195 *** | |

Ks2 | 0.548 *** | −0.392 *** | −0.411 *** | −0.255 *** | −0.537 *** | −0.386 *** | 0.226 *** | 0.788 *** | 0.009 ns | 0.059 ns | −0.223 *** | −0.061 ns | 0.559 *** |

Combination Numbers | Machine Learning Models | Input Combinations | |||
---|---|---|---|---|---|

1 | ANN1 | DL1 | DT1 | RF1 | Sand, EP |

2 | ANN2 | DL2 | DT2 | RF2 | Clay, EP |

3 | ANN3 | DL3 | DT3 | RF3 | Sand, Clay, EP |

4 | ANN4 | DL4 | DT4 | RF4 | Sand, Clay, EP, FC |

5 | ANN5 | DL5 | DT5 | RF5 | Sand, Clay, EP, Pb |

6 | ANN6 | DL6 | DT6 | RF6 | Sand, Clay, EP, FC, Pb, PWP, P, Lime |

7 | ANN7 | DL7 | DT7 | RF7 | Sand, Silt, Clay, FC, Pb, PWP |

8 | ANN8 | DL8 | DT8 | RF8 | Sand, Clay, Pb, OC |

Sand (%) | Silt (%) | Clay (%) | Pb (Mg m ^{−3}) | FC (cm ^{3} cm^{−3}) | PWP (cm ^{3} cm^{−3}) | P (cm ^{3} cm^{−3}) | EP (cm ^{3} cm^{−3}) | AS (%) | PR (PSI) | Lime (%) | OC (%) | Ks_{1}(mm h ^{−1}) | Ks_{2}(mm h ^{−1}) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Maximum | 66.40 | 40.00 | 79.57 | 1.75 | 0.42 | 0.29 | 0.59 | 0.31 | 61.01 | 434 | 41.50 | 2.30 | 24.45 | 58.91 |

Minimum | 5.43 | 11.60 | 21.10 | 1.09 | 0.14 | 0.09 | 0.35 | 0.00 | 3.15 | 60 | 6.47 | 0.29 | 0.00 | 0.88 |

Mean | 28.24 | 24.41 | 47.36 | 1.31 | 0.28 | 0.17 | 0.51 | 0.15 | 21.74 | 198 | 15.96 | 0.85 | 5.083 | 17.21 |

Standard deviation | 13.91 | 5.38 | 13.39 | 0.12 | 0.05 | 0.05 | 0.04 | 0.07 | 11.04 | 70.16 | 6.79 | 0.30 | 5.095 | 11.35 |

Variation coefficient | 49.25 | 22.05 | 28.27 | 9.32 | 18.82 | 26.26 | 8.79 | 49.34 | 50.78 | 35.49 | 42.51 | 35.35 | 100.24 | 65.93 |

Skewness | 0.59 | −0.06 | 0.10 | 0.57 | −0.06 | 0.32 | −0.57 | −0.13 | 0.58 | 0.71 | 0.66 | 1.38 | 1.50 | 0.86 |

Kurtosis | −0.52 | −0.23 | −0.66 | 0.12 | −0.57 | −0.63 | 0.08 | −0.88 | −0.05 | 0.12 | 0.12 | 3.37 | 1.94 | 0.68 |

**Table 5.**Performance metrics of neural-network-based models (ANN and DL) for estimation of Ks with eight different soil data.

Method | MAE | RMSE | R^{2} | CC |
---|---|---|---|---|

(mm h^{−1}) | (mm h^{−1}) | |||

ANN1 | 3.617 | 5.230 | 0.838 | 0.915 |

ANN2 | 4.272 | 5.603 | 0.806 | 0.897 |

ANN3 | 2.684 | 3.817 | 0.910 | 0.954 |

ANN4 | 2.512 | 3.411 | 0.920 | 0.959 |

ANN5 | 2.411 | 3.301 | 0.924 | 0.961 |

ANN6 | 2.015 | 3.109 | 0.929 | 0.964 |

ANN7 | 2.407 | 3.096 | 0.940 | 0.970 |

ANN8 | 4.081 | 4.876 | 0.825 | 0.908 |

DL1 | 4.283 | 5.285 | 0.816 | 0.903 |

DL2 | 4.898 | 6.965 | 0.707 | 0.840 |

DL3 | 3.977 | 4.936 | 0.861 | 0.928 |

DL4 | 3.427 | 4.428 | 0.880 | 0.938 |

DL5 | 3.833 | 3.853 | 0.894 | 0.945 |

DL6 | 3.244 | 4.099 | 0.872 | 0.934 |

DL7 | 2.167 | 3.423 | 0.919 | 0.959 |

DL8 | 4.407 | 5.655 | 0.776 | 0.881 |

**Table 6.**Performance metrics of tree-based models (DT and RF) for estimation of Ks with eight different soil data.

Method | MAE | RMSE | R^{2} | CC |
---|---|---|---|---|

(mm h^{−1}) | (mm h^{−1}) | |||

DT1 | 2.508 | 5.586 | 0.769 | 0.876 |

DT2 | 2.860 | 5.905 | 0.744 | 0.862 |

DT3 | 2.193 | 5.459 | 0.774 | 0.879 |

DT4 | 2.223 | 5.333 | 0.785 | 0.886 |

DT5 | 2.121 | 5.130 | 0.804 | 0.896 |

DT6 | 3.074 | 6.163 | 0.729 | 0.852 |

DT7 | 2.410 | 5.358 | 0.791 | 0.889 |

DT8 | 3.179 | 6.886 | 0.661 | 0.811 |

RF1 | 3.072 | 4.290 | 0.860 | 0.927 |

RF2 | 3.229 | 4.912 | 0.820 | 0.906 |

RF3 | 2.760 | 4.099 | 0.874 | 0.935 |

RF4 | 2.789 | 4.178 | 0.869 | 0.932 |

RF5 | 2.685 | 3.936 | 0.887 | 0.942 |

RF6 | 3.626 | 4.998 | 0.822 | 0.906 |

RF7 | 3.104 | 4.663 | 0.844 | 0.919 |

RF8 | 4.106 | 5.736 | 0.755 | 0.869 |

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## Share and Cite

**MDPI and ACS Style**

Yamaç, S.S.; Negiş, H.; Şeker, C.; Memon, A.M.; Kurtuluş, B.; Todorovic, M.; Alomair, G. Saturated Hydraulic Conductivity Estimation Using Artificial Intelligence Techniques: A Case Study for Calcareous Alluvial Soils in a Semi-Arid Region. *Water* **2022**, *14*, 3875.
https://doi.org/10.3390/w14233875

**AMA Style**

Yamaç SS, Negiş H, Şeker C, Memon AM, Kurtuluş B, Todorovic M, Alomair G. Saturated Hydraulic Conductivity Estimation Using Artificial Intelligence Techniques: A Case Study for Calcareous Alluvial Soils in a Semi-Arid Region. *Water*. 2022; 14(23):3875.
https://doi.org/10.3390/w14233875

**Chicago/Turabian Style**

Yamaç, Sevim Seda, Hamza Negiş, Cevdet Şeker, Azhar M. Memon, Bedri Kurtuluş, Mladen Todorovic, and Gadir Alomair. 2022. "Saturated Hydraulic Conductivity Estimation Using Artificial Intelligence Techniques: A Case Study for Calcareous Alluvial Soils in a Semi-Arid Region" *Water* 14, no. 23: 3875.
https://doi.org/10.3390/w14233875