# Artificial Neural Networks for Predicting the Water Retention Curve of Sicilian Agricultural Soils

^{1}

^{2}

^{*}

## Abstract

**:**

_{b}), and soil organic carbon content (OC). In this study, application of PTFs was carried out for 359 Sicilian soils by implementing five different artificial neural networks (ANNs) to estimate the parameter of the van Genuchten (vG) model for water retention curves. The raw data used to train the ANNs were soil texture, ρ

_{b}, OC, and porosity. The ANNs were evaluated in their ability to predict both the vG parameters, on the basis of the normalized root-mean-square errors (NRMSE) and normalized mean absolute errors (NMAE), and the water retention data. The Akaike’s information criterion (AIC) test was also used to assess the most efficient network. Results confirmed the high predictive performance of ANNs with four input parameters (clay, sand, and silt fractions, and OC) in simulating soil water retention data, with a prediction accuracy characterized by MAE = 0.026 and RMSE = 0.069. The AIC efficiency criterion indicated that the most efficient ANN model was trained with a relatively low number of input nodes.

## 1. Introduction

_{s}have been made in respect to different data sets used, different mathematical procedures (regression versus artificial neural network models), and different input parameters.

## 2. Materials and Methods

#### 2.1. Soil Samples

_{b}), geometric mean particle diameter (d

_{g}), organic carbon content (OC), porosity (φ), and volumetric soil water content (θ), determined during a drying sequence of at least eleven matric heads (h) in the range from −0.01 to 150 m. Fractions of Cl, Si, and Sa were determined according to the United States Department of Agriculture (USDA) standard for particle size distribution conducted using the hydrometer method for particles having diameters d < 74 mm and by sieving for particles with 74 ≤ d ≤ 2000 [25]. The texture triangle in Figure 1 shows that all USDA classes were included in the considered database. For each investigated site, Table 1 summarizes the descriptive statistics of the selected soil physical properties.

_{g}(mm) was calculated according to Reference [26]:

^{−1}), respectively, and M

_{cl}, M

_{si}, and M

_{sa}are the mean diameters of clay, silt, and sand, respectively (M

_{cl}= 0.001 mm; M

_{si}= 0.026 mm; M

_{sa}= 1.025 mm).

_{b}, Mg·m

^{−3}), and porosity (φ) was calculated assuming a value of the soil particle density equal to 2.65 Mg·m

^{−3}.

^{3}·cm

^{−3}) is the water content at matric potential h (cm), θ

_{s}and θ

_{r}are the saturated and residual water contents (cm

^{3}·cm

^{−3}), respectively, n (-) is the curve shape factor which controls the steepness of the S-shaped retention curve, m (-) is an empirical shape factor related to n by m = 1 − (1/n), and α (cm

^{−1}) is an empirical scale parameter related to the inverse of the air entry suction. Fitting of Equation (2) to experimental data was carried out using the RETC software [28]. Figure 2 shows, for each site, the mean fitted water retention curve. The mean value of root-mean-square error (RMSE) ranged from 0.005 to 0.047, with an average value for Sicily equal to 0.014.

#### 2.2. Artificial Neural Networks (ANNs)

_{s}, θ

_{r}, α, and n. The transfer function was the hyperbolic tangent for all the layers.

_{s}, θ

_{r}, α, and n were also calculated for each ANN, in order to compare the overall performance of each ANN in the simulation of the vG parameters. Estimated θ(h) values were calculated at the selected eleven matric potentials from Equation (2) with parameters θ

_{s}, θ

_{r}, α, and n obtained by the ANNs. The performance in simulating water retention was evaluated by means of MAE, RMSE, and determination coefficient (r

^{2}).

^{2}).

_{s}, θ

_{r}, α, and n values or the difference between measured and estimated θ(h) values.

## 3. Results

_{s}, with NRMSE values of 0.11–0.12 and NMAE values of 0.088–0.096, and for n, with NRMSE values of 0.1264–0.1339 and NMAE values of 0.093–0.097. The lowest performance was obtained for θ

_{r}with NRMSE and NMAE values in the range 0.24–0.27 and 0.20–0.23, respectively.

_{s}and n, and the lowest values (r = 0.16–0.50) for θ

_{r}and α. In this regard, it can be shown that r is oversensitive to extreme values (outliers), which characterized θ

_{r}and α much more than θ

_{s}and n, both having a narrower range of variation. As an example, the trends of the observed and simulated vG parameters are reported in Figure 4 for ANN1 and in Figure 5 for ANN4. Mean values of NRMSE and NMAE obtained for θ

_{r}, θ

_{s}, α, and n were also calculated for each ANN in order to compare the overall performance in the simulation of the vG parameters. Although the results were very similar, it can be noted that the lowest values were achieved by ANN4 (NRMSE = 0.1412 and NMAE = 0.1077), while the highest ones were obtained by ANN3 (NRMSE = 0.1467 and NMAE = 0.1150). Intermediate values were obtained by ANN5 (NRMSE = 0.1436 and NMAE = 0.1123), ANN2 (NRMSE = 0.1457 and NMAE = 0.1148) and ANN1 (NRMSE = 0.1464 and NMAE = 0.1150).

## 4. Discussion

_{s}, was the best simulated parameter. It is worth noting that these results are in agreement with those found by Reference [35], who implemented different models of ANNs, and obtained RMSE values ranging from 0.053 to 0.085 with three inputs (textural data) and from 0.048 to 0.08 with four inputs (textural data and bulk density). Also interesting is the comparison with the statistical values obtained by Reference [18], who used a feed-forward ANN with various combinations of input parameters, including textural data alone or together with bulk density and organic matter. Specifically, RMSE values reported in Table 6 were higher than those obtained by Reference [18], ranging from 0.039 to 0.047. Also, r

^{2}values were sensibly higher, given they were in the range 0.65−0.79 for the present study (Table 5) as compared to those found by Reference [18], which were between 0.12 and 0.34. The results obtained in terms of MAE, ranging from 0.016 and 0.032 (Table 6), were also in agreement with values obtained by Reference [18]. In this study, comparisons of estimated mean RSS values and AIC indicators were in good agreement for all ANNs, showing that all the developed models are able to reproduce the central tendency of the observed data.

_{b}. Similar results were obtained by Reference [36] using RSS as a selector criterion.

_{s}and n. In their work, the authors of Reference [37] instead suggested that the ANN approach results better in point predictions than in predicting vG parameters, based on r

^{2}and RMSE, due to over-parameterization problems. The results of this study evidenced that, in the ANN approach, all dependent soil hydraulic parameters were predicted from independent variables simultaneously. This saves time and energy, and might probably lead to better results in case of using better algorithms in the ANN. Therefore, the results of the study indicate that studies on ANN should continue relating soil hydraulic parameters to basic soil properties as an alternative to regression, which is commonly used.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**United States Department of Agriculture (USDA) texture classification for the investigated Sicilian soils (n = 359).

**Figure 2.**Mean soil water retention curve according to the van Genuchten (vG) model (Equation (2)) at each investigated Sicilian site; n is the number of sampled soils at each site.

**Table 1.**Mean values and standard deviations of the fractions of clay (Cl), silt (Si), and sand (Sa), geometric mean particle diameter (d

_{g}), dry soil bulk density (ρ

_{b}), organic carbon content (OC), and porosity (φ) for the investigated Sicilian soils; n is the number of sampled soils at each site.

Site | n | Clay (%) | Silt (%) | Sand (%) | d_{g} (mm) | OC (g·kg^{−1}) | ρ_{b} (Mg·m^{−3}) | φ |
---|---|---|---|---|---|---|---|---|

Palermo | 3 | 18.0 (±1.7) | 28.6 (±2.5) | 53.4 (±3.5) | 0.10 (±0.02) | 3.4 (±1.19) | 1.1.2 (±0.04) | 0.58 (±0.01) |

Bulgherano | 32 | 16.4 (±3.8) | 27.1 (±3.9) | 56.5 (±4.1) | 0.13 (±0.03) | 2.1 (±0.52) | 1.25 (±0.10) | 0.53 (±0.04) |

Caccamo | 1 | 7.4 | 18.0 | 74.6 | 0.02 | 1.51 | 1.25 | 0.53 |

Castelvetrano | 5 | 35.3 (±7.9) | 24.0 (±4.6) | 40.7 (±4.0) | 0.04 (±0.02) | 2.0 (±0.50) | 1.31 (±0.07) | 0.51 (±0.03) |

Comiso | 1 | 28.2 | 46.5 | 25.3 | 0.03 | 2.8 | 1.09 | 0.59 |

Corleone | 6 | 41.2 (±19.1) | 32.4 (±2.5) | 26.4 (±21.1) | 0.04 (±0.06) | 2.2 (±0.67) | 1.07 (±0.17) | 0.60 (±0.06) |

Etna | 1 | 0.5 | 9.7 | 89.9 | 0.70 | 1.86 | 1.37 | 0.48 |

Dirillo | 85 | 20.6 (±11.1) | 33.6 (±15.9) | 45.7 (±25.7) | 0.15 (±0.17) | 1.1 (±0.73) | 1.40 (±0.16) | 0.47 (±0.06) |

Menfi | 82 | (±11.4) | (±10.1) | 47.0 (±18.4) | 0.12 (±0.10) | 1.5 (±0.21) | 1.26 (±0.14) | 0.52 (±0.05) |

Mineo | 2 | 21.8 | (±2.3) | 32.5 (±6.6) | 0.04 (±0.02) | 1.5 (±0.66) | 1.26 (±0.03) | 0.52 (±0.01) |

Monreale | 1 | 5.4 | 22.7 | 71.9 | 0.31 | 0.3 | 1.26 | 0.53 |

Palazzelli | 32 | 10.5 (±3.8) | (±5.8) | 69.7 (±7.6) | 0.26 (±0.09) | 1.2 (±0.27) | 1.25 (±0.08) | 0.53 (±0.03) |

Pettineo | 1 | 24.9 | 34.2 | 40.9 | 0.05 | 4.6 | 1.14 | 0.57 |

Pollina | 2 | 24.8 (±4.17) | (±8.9) | 33.8 (±13.1) | 0.04 (±0.03) | 3.6 (±0.18) | 1.15 (±0.02) | 0.57 (±0.01) |

Ramacca | 2 | 29.7 (±4.4) | (±2.7) | 35.5 (±7.1) | 0.04 (±0.01) | 0.7 (±0.46) | 1.32 (±0.00) | 0.50 (±0.00) |

Rapitalà | 2 | 28.3 (±11.7) | (±11.4) | 34.8 (±23.1) | 0.05 (±0.05) | 1.6 (±0.22) | 1.30 (±0.10) | 0.51 (±0.04) |

Resuttano | 6 | 51.1 (±17.5) | (±13.1) | 7.1 (±5.9) | 0.01 (±0.01) | 1.6 (±1.17) | 1.30 (±0.15) | 0.51 (±0.06) |

Santa Ninfa | 52 | 20.5 (±18.4) | (±16.0) | 21.6 (±9.9) | 0.04 (±0.02) | 3.4 (±1.38) | 1.13 (±0.09) | 0.57 (±0.03) |

San Michele | 40 | 46.7 (±6.6) | (±6.2) | 36.3 (±9.0) | 0.02 (±0.01) | 2.5 (±0.49) | 1.27 (±0.08) | 0.52 (±0.03) |

Sparacia | 2 | 17.2 (±7.8) | (±2.0) | 62.3 (±5.7) | 0.15 (±0.07) | 0.5 (±0.0) | 1.40 (±0.11) | 0.47 (±0.04) |

Ventimiglia | 1 | 36.3 | 29.8 | 33.9 | 0.03 | 1.3 | 1.25 | 0.53 |

All | 359 | 23.9 | 31.3 | 44.8 | 0.11 | 2 | 1.25 | 0.53 |

Network | Input Data ^{1} |
---|---|

ANN1 | Cl, Si, d_{g}, φ |

ANN2 | Cl, Sa, ρ_{b} |

ANN3 | Cl, Sa, OC |

ANN4 | Cl, Sa, Si, OC |

ANN5 | Cl, Sa, OC, ρ_{b} |

^{1}Clay (Cl), silt (Si), sand (Sa) percentages; geometric mean particle diameter (d

_{g}), dry soil bulk density (ρ

_{b}), organic carbon content (OC), and porosity (φ).

**Table 3.**Statistical indicators used to evaluate reliability of ANN modeling. MAE—mean absolute error; NMAE—normalized MAE; RMSE—root-mean-square error; NRMSE—normalized RMSE.

$MAE=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left|{y}_{i}-{x}_{i}\right|}{n}$ |

$NMAE=\frac{MAE}{\overline{y}}$ |

$RMSE=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({y}_{i}-{x}_{i}\right)}^{2}}{n}}$ |

$NRMSE=\frac{RMSE}{\overline{y}}$ |

$r=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({x}_{i}-\overline{x}\right)\left({y}_{i}-\overline{y}\right)}{\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{2}\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{\left({y}_{i}-\overline{y}\right)}^{2}}}}$ |

$\overline{x}=\frac{{{\displaystyle \sum}}_{i=1}^{n}{x}_{i}}{n}\overline{y}=\frac{{{\displaystyle \sum}}_{i=1}^{n}{y}_{i}}{n}$ |

_{i}is the observed value, x

_{i}is the predicted value.

ANNs | Performance | θ_{r} | θ_{s} | α | N |
---|---|---|---|---|---|

ANN1 | RMSE | 0.0679 | 0.0660 | 0.0973 | 0.2135 |

NRMSE | 0.2751 | 0.1135 | 0.0692 | 0.1277 | |

MAE | 0.0571 | 0.0523 | 0.0596 | 0.1607 | |

NMAE | 0.2314 | 0.0899 | 0.0424 | 0.0962 | |

Min AE | 0.0039 | 0.0030 | 0.0021 | 0.0012 | |

Max AE | 0.1710 | 0.1984 | 0.4797 | 0.7833 | |

r | 0.2762 | 0.6612 | 0.2926 | 0.6944 | |

ANN2 | RMSE | 0.0671 | 0.0677 | 0.0957 | 0.2113 |

NRMSE | 0.2718 | 0.1164 | 0.0681 | 0.1264 | |

MAE | 0.0571 | 0.0533 | 0.0582 | 0.1581 | |

NMAE | 0.2314 | 0.0917 | 0.0414 | 0.0946 | |

Min AE | 0.0047 | 0.0004 | 0.0007 | 0.0016 | |

Max AE | 0.1673 | 0.1953 | 0.4817 | 0.7828 | |

r | 0.2927 | 0.6402 | 0.2766 | 0.7003 | |

ANN3 | RMSE | 0.0650 | 0.0701 | 0.0967 | 0.2238 |

NRMSE | 0.2635 | 0.1206 | 0.0688 | 0.1339 | |

MAE | 0.0555 | 0.0562 | 0.0574 | 0.1634 | |

NMAE | 0.2248 | 0.0966 | 0.0408 | 0.0978 | |

Min AE | 0.0024 | 10^{−5} | 0.0015 | 0.0019 | |

Max AE | 0.1845 | 0.2339 | 0.4873 | 0.8500 | |

r | 0.3789 | 0.6109 | 0.1586 | 0.6574 | |

ANN4 | RMSE | 0.0610 | 0.0681 | 0.0972 | 0.2197 |

NRMSE | 0.2470 | 0.1172 | 0.0691 | 0.1315 | |

MAE | 0.0500 | 0.0554 | 0.0556 | 0.1560 | |

NMAE | 0.2025 | 0.0952 | 0.0396 | 0.0933 | |

Min AE | 0.0018 | 0.0011 | 0.0003 | 0.0029 | |

Max AE | 0.1764 | 0.2149 | 0.4908 | 0.8782 | |

r | 0.5004 | 0.6400 | 0.1673 | 0.6734 | |

ANN5 | RMSE | 0.0657 | 0.0641 | 0.1001 | 0.2120 |

NRMSE | 0.2663 | 0.1102 | 0.0712 | 0.1268 | |

MAE | 0.0552 | 0.0515 | 0.0611 | 0.1567 | |

NMAE | 0.2236 | 0.0885 | 0.0434 | 0.0937 | |

Min AE | 0.0013 | 0.0013 | 0.0003 | 0.0004 | |

Max AE | 0.1788 | 0.1856 | 0.4666 | 0.7842 | |

r | 0.3764 | 0.6887 | 0.2318 | 0.6992 |

Network | MAE | RMSE | r^{2} |
---|---|---|---|

ANN1 | 0.030 | 0.074 | 0.75 |

ANN2 | 0.032 | 0.076 | 0.74 |

ANN3 | 0.032 | 0.089 | 0.65 |

ANN4 | 0.026 | 0.069 | 0.79 |

ANN5 | 0.016 | 0.074 | 0.72 |

**Table 6.**Akaike’s information criterion (AIC) test of efficiency of ANNs in modeling van Genuchten (vG) parameters and water retention curve values. RSS—residual sum of square.

Network | vG Parameters | Water Retention Curve | ||
---|---|---|---|---|

RSS | AIC | RSS | AIC | |

ANN1 | 5.75 | −468.3 | 5.14 | −2887.8 |

ANN2 | 5.74 | −472.4 | 5.48 | −3095.5 |

ANN3 | 6.23 | −464.9 | 7.43 | −2811.6 |

ANN4 | 5.88 | −466.4 | 4.56 | −2999.4 |

ANN5 | 5.63 | −470.2 | 5.23 | −2871.8 |

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**MDPI and ACS Style**

D’Emilio, A.; Aiello, R.; Consoli, S.; Vanella, D.; Iovino, M.
Artificial Neural Networks for Predicting the Water Retention Curve of Sicilian Agricultural Soils. *Water* **2018**, *10*, 1431.
https://doi.org/10.3390/w10101431

**AMA Style**

D’Emilio A, Aiello R, Consoli S, Vanella D, Iovino M.
Artificial Neural Networks for Predicting the Water Retention Curve of Sicilian Agricultural Soils. *Water*. 2018; 10(10):1431.
https://doi.org/10.3390/w10101431

**Chicago/Turabian Style**

D’Emilio, Alessandro, Rosa Aiello, Simona Consoli, Daniela Vanella, and Massimo Iovino.
2018. "Artificial Neural Networks for Predicting the Water Retention Curve of Sicilian Agricultural Soils" *Water* 10, no. 10: 1431.
https://doi.org/10.3390/w10101431