# Impact of Infiltration Process Modeling on Soil Water Content Simulations for Irrigation Management

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Infiltration Models

#### 2.1.1. The SCS-Curve Number

_{a}is the initial abstraction. S and CN are related by:

_{t}is the degree of saturation of the soil, θ

_{t}is the actual water content at time t [L

^{3}/L

^{3}], θ

_{s}is the saturated water content [L

^{3}/L

^{3}] and θ

_{r}is the residual water content [L

^{3}/L

^{3}].

#### 2.1.2. Philip’s Equation

^{−1}]

#### 2.1.3. Green and Ampt

_{0}) at the soil surface, the value of the suction head occurring at the wetting front is constant in time and depth with a uniform initial water content.

_{f}is the effective suction at the wetting front [L], θ

_{s}is the saturated water content [L

^{3}/L

^{3}], θ

_{i}is the initial water content [L

^{3}/L

^{3}], F is the accumulated infiltration [L] and f is the infiltration rate [L/T]. Several modifications have been suggested to adapt Green and Ampt model to address situations beyond the assumptions of its development. Bouwer [42] extended this model to layered soil and non-uniform antecedent water content. Childs and Bybordi [43] implemented a heterogeneous soil profile with decreasing conductivity and developed a specified infiltration law according to the variability of the conductivity throughout the soil profile. To implement it within hydrological models for long simulation periods, it was required to modify the Green and Ampt for unsteady rainfall conditions. Mein and Larson [44] developed a method to detect the ponding time with infiltration into the soil using the Green and Ampt infiltration. The solution is based on pre-ponding phase during which the rainfall intensity is lower than infiltration capacity, than the ponding occurs when the rainfall rate starts to be equal or higher than the infiltration capacity. At the ponding time (t

_{p}) [T], the cumulative infiltration (F

_{p}) [[L] is equal to

#### 2.1.4. Ross (2003) Solution

^{3}/L

^{3}], h is the pressure head [L], Z is the soil depth [L] positive downward, K is the hydraulic conductivity [L/T] and t is the time [T]. Within the unsaturated regions, the unknown parameter for Ross solution is the degree of saturation of the soil S, while at the saturated regions Kirchhoff potential is considered. Solving the Richards equation requires the determination of the parameters of K(h) and h(θ) curves. Originally, Ross solution was developed using Brooks and Corey model for soil water retention and conductivity functions. Brooks and Corey model [29] for retention function is given by the following formula:

^{3}/L

^{3}], θ

_{r}is the residual water content [L

^{3}/L

^{3}] and θ

_{s}is the saturated water content [L

^{3}/L

^{3}]. K is the hydraulic conductivity [L/T], Ks is the hydraulic conductivity at saturation [L/T], h is the pressure head [L], h

_{e}is the pressure head at saturation or at the air entry [L], and λ and η are shape parameters of water retention and conductivity curves. This model was tested by Varado et al. [23], and has proven to be fast and robust, and provide accurate solution of Richards equation for homogeneous or heterogeneous soils and under saturated or unsaturated conditions.

_{e}value; this assumption leads to poor results in particular for fine textured soils. Later, Van Genuchten [30] modified Brooks and Corey model to get more accurate description of the retention curve near saturation. Then, Crevoisier et al. [24] improved Ross solution by including Van Genuchten model which is given by:

_{S}is the saturated hydraulic conductivity [L T

^{−1}], and α [L

^{−1}], m and n are parameters depending on the pore size distribution.

#### 2.2. Study Site Description

_{FC}the water is content at field capacity [L

^{3}/L

^{3}] and θ

_{WP}is the water content at the wilting point [L

^{3}/L

^{3}]. p is the allowable depletion that depends on the crop was assumed equal to 0.5 for maize crop [50]. The water surplus takes place when the value of the soil moisture exceeds the θ

_{FC}.

#### 2.3. Model Simulations

_{i}is the water content at time t [L

^{3}/L

^{3}], θ

_{FC}is the water content at the field capacity [L

^{3}/L

^{3}] and θ

_{wp}is the water content at the wilting point [L

^{3}/L

^{3}].

_{t}

_{+1}is the water content at the time t + 1 [L

^{3}/L

^{3}], θ

_{t}is the water content at time t [L

^{3}/L

^{3}], I is the infiltration rate [L/T], D is the drainage rate [L/T], ET is the actual evapotranspiration [L/T], Z is the soil depth [L] and Δt is the time step [T].

_{t}is the water content at time t [L

^{3}/L

^{3}], θ

_{r}is the residual water content [L

^{3}/L

^{3}], θ

_{s}is the water content at saturation [L

^{3}/L

^{3}], and λ is the Brooks and Corey parameter.

^{2}and RMSE.

^{2}:

^{2}corresponds to the coefficient of correlation according to Bravais–Pearson.

#### 2.4. Sensitivity Analysis

## 3. Results and Discussions

#### 3.1. Results of the Sensitivity Analysis

#### 3.2. Results of the Sensitivity Analysis

^{2}for the both calibration and validation years. The calculated performance indicators RMSE and R

^{2}confirm the improvement of the simulation after the calibration. Even before calibration, good performances were reached in particular for SCS-CN with RMSE equal to 0.023. After calibration, similar RMSE values were found of about 0.019, 0.020 and 0.019 for SCS-CN, Green and Ampt and Philip models respectively.

^{2}proved this result with 0.74, 0.83, and 0.74 for the calibration year and 0.66, 0.57, and 0.61 for the validation year for Philip, GA and SCS-CN, respectively, consequently with slight advantage to Philip model with RMSE of 0.017 after the calibration.

^{2}for Ross-BC were 0.035 and 0.49 while for the validation year were 0.032 and 0.28, respectively. For Ross-VG, these values were 0.041 and 0.53 for the calibration year and 0.034 and 0.33 for the validation year, respectively. The top soil was subjected to high fluctuations of soil moisture, which caused more soil moisture variability that was observed in the measured water content at 10 cm soil depth. This is also because the top soil is more subjected to the evaporative fluxes as well as to the disturbance of the soil structure during the cropping season. One set of parameters was considered for whole soil profile that is supposed to be homogeneous. Capturing these fluctuations was not possible when the average soil moisture of the 50 cm soil profile was considered.

#### 3.3. Evaluation of Irrigation Scheduling

^{3}/cm

^{3}. The uncertainty of the model, implemented as decision support tool to plan irrigation water applications, is critical. About this issue, we selected SCS-CN and Ross-VG to carry out our analyses. Figure 6 and Figure 7 present the results of simulations based on Ross-VG and SCS-CN respectively. Simulations without irrigation showed that more stress conditions appeared in particular during summer season when the crop was fully developed. The occurrence of surplus conditions could not be avoided and occurred after a heavy rainfall or irrigation. Simulations based on SCS-CN did not allow assessing the water stress presence at different soil depths. The irrigation should be applied when the stress threshold is reached. In terms of evaluation of effectiveness of the irrigation based on the Figure 6, it can be concluded that at irrigation was applied at a good timing when the soil water content reached the stress threshold. This irrigation allowed avoiding stress conditions that were observed for the no-irrigation scenario.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Results of calibration (2012 year) and (

**b**) validation (2014 year) of Curve number, Green and Ampt and Philip equations based soil moisture simulations.

**Figure 3.**Ensemble modeling of soil moisture based on Curve number, Green and Ampt and Philip equations.

**Figure 6.**Soil moisture simulations of 2012 growing season in Livraga using SCS-CN for 40 cm soil profile.

**Figure 7.**Soil moisture simulations of 2012 growing season in Livraga using Ross-VG model at different soil depth.

**Figure 8.**Variation of soil moisture (cm

^{3}/cm

^{3}) within the soil profile measurements and simulations based on Ross model before, during and after an irrigation event on 29 June 2012.

Parameter | Value |
---|---|

Water content at Saturation (m^{3}/m^{3}) | 0.501 |

Residual water content (m^{3}/m^{3}) | 0.015 |

Water content at field capacity (m^{3}/m^{3}) | 0.33 |

Water content at wilting point (m^{3}/m^{3}) | 0.133 |

Saturated hydraulic conductivity (m/s) | 2.36 E^{−7} |

% Sand | 32.73 |

% Silt | 48.08 |

% Clay | 19.19 |

Soil texture | Loamy |

Crop | K_{cini} | K_{cmid} | K_{cend} |
---|---|---|---|

Maize | 0.26 | 1.02 | 0.62 |

Class | Index | Sensitivity |
---|---|---|

Ι | $0.00\le \left|{\rm I}\right|<0.05$ | Small to negligible |

ΙΙ | $0.05\le \left|{\rm I}\right|<0.2$ | Medium |

ΙΙΙ | $0.2\le \left|{\rm I}\right|<1.00$ | High |

ΙV | $\left|{\rm I}\right|\ge 1.00$ | Very high |

**Table 4.**Sensitivity of SCS-CN Philip and Green and Ampt models’ output to soil hydraulic input parameters.

Soil Moisture | Infiltration | Drainage | Evaporation | |
---|---|---|---|---|

SCS-CN | ||||

Saturated hydraulic conductivity | III | II | III | II |

Saturated water content | IV | II | IV | IV |

Residual water content | I | I | I | I |

Field capacity | III | II | IV | IV |

Wilting point | I | I | II | II |

Pore size distribution index | III | II | IV | II |

Curve number | IV | IV | IV | II |

Philip equation | ||||

Saturated hydraulic conductivity | II | III | IV | I |

Saturated water content | IV | III | IV | IV |

Residual water content | I | I | II | I |

Alpha | II | III | IV | I |

Field capacity | III | II | IV | IV |

Wilting point | I | I | III | II |

Pore size distribution index | III | II | IV | III |

Green and Ampt | ||||

Saturated hydraulic conductivity | II | III | IV | II |

Saturated water content | IV | III | IV | IV |

Residual water content | II | I | III | I |

Alpha | I | I | I | I |

Field capacity | II | II | IV | IV |

Wilting point | I | I | III | II |

Pore size distribution index | III | II | IV | III |

Suction | II | III | IV | II |

Soil Moisture | Infiltration | Drainage | Evaporation | |
---|---|---|---|---|

Ross-BC | ||||

Saturated hydraulic conductivity | III | II | II | II |

Saturated water content | IV | II | IV | III |

Residual water content | I | I | I | I |

Alpha | I | I | III | III |

Field capacity | II | I | III | III |

Wilting point | I | I | I | I |

Pore size distribution index | III | II | III | II |

Ross-VG | ||||

Saturated hydraulic conductivity | III | II | III | III |

Saturated water content | IV | II | IV | IV |

Residual water content | I | I | I | I |

Alpha | III | I | III | III |

Field capacity | II | I | III | IV |

Wilting point | I | I | I | I |

n | III | II | II | III |

m | IV | II | III | III |

**Table 6.**Comparison between the performances of the simulation of soil moisture based on different implemented infiltration models before and after calibration for 2012 and 2014 cropping seasons.

Calibration Year 2012 | RMSE (cm^{3}/cm^{3}) | Validation Year 2014 | RMSE (cm^{3}/cm^{3}) | ||||||

Philip | Green and Ampt | SCS-CN | Multimodel | Philip | Green and Ampt | SCS-CN | Multimodel | ||

Before calibration | 0.041 | 0.059 | 0.023 | 0.037 | Before calibration | 0.046 | 0.06 | 0.039 | 0.047 |

After calibration | 0.019 | 0.02 | 0.019 | 0.02 | After calibration | 0.017 | 0.039 | 0.025 | 0.024 |

Calibration Year 2012 | R^{2} | Validation Year 2014 | R^{2} | ||||||

Philip | Green and Ampt | SCS-CN | Multimodel | Philip | Green and Ampt | SCS-CN | Multimodel | ||

After calibration | 0.74 | 0.83 | 0.74 | 0.80 | 0.66 | 0.57 | 0.61 | 0.65 |

**Table 7.**Performances of the simulation of soil moisture based on Ross Model based on Brooks and Corey and Van Genuchten parametric equations before and after calibration for 2012 and 2014 cropping seasons.

Calibration Year 2012 | RMSE | Validation Year 2014 | RMSE | ||||||||||

Ross-BC | Ross-VG | Ross-BC | Ross-VG | ||||||||||

Depth | 10 cm | 30 cm | Average | 10 cm | 30 cm | Average | Depth | 10 cm | 30 cm | Average | 10 cm | 30 cm | Average |

Before calibration | 0.077 | 0.094 | 0.089 | 0.062 | 0.069 | 0.062 | Before calibration | 0.081 | 0.066 | 0.07 | 0.051 | 0.036 | 0.034 |

After calibration | 0.035 | 0.024 | 0.276 | 0.041 | 0.028 | 0.026 | After calibration | 0.032 | 0.032 | 0.023 | 0.034 | 0.031 | 0.021 |

Calibration Year 2012 | R^{2} | Validation Year 2014 | R^{2} | ||||||||||

Ross-BC | Ross-VG | Ross-BC | Ross-VG | ||||||||||

Depth | 10 cm | 30 cm | Average | 10 cm | 30 cm | Average | Depth | 10 cm | 30 cm | Average | 10 cm | 30 cm | Average |

After calibration | 0.49 | 0.48 | 0.56 | 0.53 | 0.50 | 0.54 | 0.28 | 0.56 | 0.55 | 0.33 | 0.46 | 0.57 |

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**MDPI and ACS Style**

Feki, M.; Ravazzani, G.; Ceppi, A.; Milleo, G.; Mancini, M. Impact of Infiltration Process Modeling on Soil Water Content Simulations for Irrigation Management. *Water* **2018**, *10*, 850.
https://doi.org/10.3390/w10070850

**AMA Style**

Feki M, Ravazzani G, Ceppi A, Milleo G, Mancini M. Impact of Infiltration Process Modeling on Soil Water Content Simulations for Irrigation Management. *Water*. 2018; 10(7):850.
https://doi.org/10.3390/w10070850

**Chicago/Turabian Style**

Feki, Mouna, Giovanni Ravazzani, Alessandro Ceppi, Giuseppe Milleo, and Marco Mancini. 2018. "Impact of Infiltration Process Modeling on Soil Water Content Simulations for Irrigation Management" *Water* 10, no. 7: 850.
https://doi.org/10.3390/w10070850