# Parameter Estimation and Assessment of Infiltration Models for Madjez Ressoul Catchment, Algeria

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Field Measurements and Measuring Methods

#### 2.3. Parametrization of Infiltration Models for Madjez Ressoul Catchment

^{−1}], ${f}_{c}$ is the final constant infiltration capacity in [LT

^{−1}], ${f}_{0}$ is the initial infiltration capacity at time $t=0$ in [LT

^{−1}], and k in [T

^{−1}] is the decay rate constant.

^{−1}], and $A$ and $B$ are the unknown equation parameters representing soil infiltration characteristics, with A being a measure of the initial rate of infiltration and structural condition of the soil, and B an index of soil structural stability.

^{−1}], $S$ in [LT

^{−0.5}] is the sorptivity parameter reflecting the soil absorption capacity as a function of the soil matric forces during the initial phases of the infiltration process, and $K$ in [LT

^{−1}] is a constant proportional to the hydraulic conductivity.

#### 2.4. Model Calibration and Assessment of Model Parameters

^{2}).

^{−1}), $\overline{{f}_{\mathrm{Obs}}}\left(i,j\right)$ is the mean observed infiltration rate in (LT

^{−1}), ${f}_{sim}\left(i,j\right)$ is the simulated infiltration rates in (LT

^{−1}).

## 3. Results

#### 3.1. Effect of Soil Texture and Soil Moisture on Infiltration Rates

#### 3.2. Performance Evaluation of Infiltration Models for Predicting Infiltration Rates

**B**varies between 0.425 and 0.6 for most sites except site 2, where the maximum value of 0.89 was obtained. Similarly, Philip parameter

**K**varies for most sites between 0.012 and 0.038 cm/h except for sites 5, 11, and 20, which have significantly higher values of 0.99, 0.743, and 0.841 cm/h, respectively. The results obtained for Kostiakov parameters

**A**and

**B**agree with earlier studies despite the arguments of [79] that the range of parameter

**B**can be mathematically higher than one. Higher B values were obtained for steeper slopes and for a more significant rate of decline in soil infiltration, as shown for sites 12, 15, 21, and 24. The other asserted drawback from the results of this study is the weakness of the Kostiakov model for converging toward a final steady infiltration rate (${f}_{c}$).

^{−1}) at site 6 to 6.744 (h

^{−1}) at site 2, and the Kostiakov parameter A ranges from 2.174 at site 2 to 7.29 at site 14. Nonetheless, several sites exhibit similar values. The Philip parameter S (i.e., soil sorptivity) has significantly higher variation, ranging from 4.854 cm/h

^{−0.5}at site 20 to 6.17 cm/h

^{−0.5}at site 6, in contrast to nearly 16 cm/h

^{−0.5}at sites 14, 15, and 25. Nonetheless, 12 out of 25 sites exhibited equivalent sorptivity values ranging between S = 11 cm/h

^{−0.5}and S = 13 cm/h

^{−0.5}. Table 4 summarizes the best-estimated parameters for the three infiltration models at each test location.

**S**of the Philip model reflects approximately the Sorptivity of the soil, parameter

**K**was found as not closely dependent on the infiltration rate [80,81]. The inferior ability of the Philip model to accurately express infiltration rates for Madjez Ressoul Catchment suggests that the soil structure and other hydraulic parameters are crucial factors affecting infiltration. It can be concluded that the applicability of the Philip model for the Madjez Ressoul Catchment requires further site investigations and measurements on small grids to estimate its parameters experimentally, rather than using estimates from the model. It is also clear that site 2 (i.e., a superficial formation within a dry farming zone) and site 7 (i.e., a conglomerate soil) require further site investigations.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Davidsen, S.; Löwe, R.; Ravn, N.H.; Jensen, L.N.; Arnbjerg-Nielsen, K. Initial Conditions of Urban Permeable Surfaces in Rainfall-Runoff Models Using Horton’s Infiltration. Water Sci. Technol.
**2018**, 77, 662–669. [Google Scholar] [CrossRef] [PubMed] - Guellouz, L.; Askri, B.; Jaffré, J.; Bouhlila, R. Estimation of the soil hydraulic properties from field data by solving an inverse problem. Sci. Rep.
**2020**, 10, 9359. [Google Scholar] [CrossRef] [PubMed] - Nartowska, E.; Kozłowski, T.; Gawdzik, J. Assessment of the influence of copper and zinc on the microstructural parameters and hydraulic conductivity of bentonites on the basis of SEM tests. Heliyon
**2019**, 5, e02142. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sakellariou-Makrantonaki, M.; Angelaki, A.; Evangelides, C.; Bota, V.; Tsianou, E.; Floros, N. Experimental Determination of Hydraulic Conductivity at Unsaturated Soil Column. Procedia Eng.
**2016**, 162, 83–90. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Shao, M. Effects of rainfall intensity on rainfall infiltration and redistribution in soil on Loess slope land. Ying Yong Sheng Tai Xue Bao
**2006**, 17, 2271–2276. [Google Scholar] [PubMed] - Tsai, Y.J.; Yeh, H.-f. Effect of variations in rainfall intensity and different return period rainfall events on unsaturated slope stability. J. Taiwan Agric. Eng.
**2019**, 65, 34–50. [Google Scholar] [CrossRef] - Lipiec, J.; Kuś, J.; Słowińska-Jurkiewicz, A.; Nosalewicz, A. Soil porosity and water infiltration as influenced by tillage methods. Soil Tillage Res.
**2006**, 89, 210–220. [Google Scholar] [CrossRef] - Sajjadi, S.-A.-H.; Mirzaei, M.; Nasab, A.F.; Sarkardeh, H. Effect of Soil Physical Properties on Infiltration Rate. Geomech. Eng.
**2016**, 10, 727–736. [Google Scholar] [CrossRef] - Barbosa, L.C.; de Souza, Z.M.; Franco, H.C.J.; Otto, R.; Rossi Neto, J.; Garside, A.L.; Carvalho, J.L.N. Soil texture affects root penetration in oxisols under sugarcane in Brazil. Geoderma Reg.
**2018**, 13, 15–25. [Google Scholar] [CrossRef] - Biswas, A. Joint multifractal analysis for three variables: Characterizing the effect of topography and soil texture on soil water storage. Geoderma
**2019**, 334, 15–23. [Google Scholar] [CrossRef] - Kalhoro, S.A.; Ding, K.; Zhang, B.; Chen, W.; Hua, R.; Hussain Shar, A.; Xu, X. Soil infiltration rate of forestland and grassland over different vegetation restoration periods at Loess Plateau in northern hilly areas of China. Landsc. Ecol. Eng.
**2019**, 15, 91–99. [Google Scholar] [CrossRef] - Hino, M.; Odaka, Y.; Nadaoka, K.; Sato, A. Effect of initial soil moisture content on the vertical infiltration process—A guide to the problem of runoff-ratio and loss. J. Hydrol.
**1988**, 102, 267–284. [Google Scholar] [CrossRef] - Schoener, G.; Stone, M.C. Impact of antecedent soil moisture on runoff from a semiarid catchment. J. Hydrol.
**2019**, 569, 627–636. [Google Scholar] [CrossRef] - Avellaneda, E. Infiltration through Roadside Swales. Master’s Thesis, University of Central Florida, Orlando, FL, USA, 1985. [Google Scholar]
- Neris, J.; Tejedor, M.; Rodríguez, M.; Fuentes, J.; Jiménez, C. Effect of forest floor characteristics on water repellency, infiltration, runoff and soil loss in andisols of Tenerife (Canary Islands, Spain). CATENA
**2013**, 108, 50–57. [Google Scholar] [CrossRef] - Pingping, H.; Xue, S.; Zhanbin, L. Effect of vegetation cover types on soil infiltration under simulating rainfall. Nat. Environ. Pollut. Technol.
**2013**, 12, 193–198. [Google Scholar] - Zhao, C.; Jia, X.; Zhu, Y.; Shao, M.A. Long-term temporal variations of soil water content under different vegetation types in the Loess Plateau, China. CATENA
**2017**, 158, 55–62. [Google Scholar] [CrossRef] - Rahman, M.A.; Moser, A.; Anderson, M.; Zhang, C.; Rötzer, T.; Pauleit, S. Comparing the infiltration potentials of soils beneath the canopies of two contrasting urban tree species. Urban For. Urban Green.
**2019**, 38, 22–32. [Google Scholar] [CrossRef] - Vieux, B.E. Infiltration modeling. In Distributed Hydrologic Modeling Using GIS; Water Science and Technology Library; Springer: Dordrecht, The Netherlands, 2004; Volume 48, pp. 91–113. [Google Scholar] [CrossRef]
- Fox, D.M.; Bryan, R.B.; Price, A.G. The influence of slope angle on final infiltration rate for interrill conditions. Geoderma
**1997**, 80, 181–194. [Google Scholar] [CrossRef] - Chatterjee, D.; Murali Krishna, A. Effect of slope angle on the stability of a slope under rainfall infiltration. Indian Geotech. J.
**2019**, 49, 708–717. [Google Scholar] [CrossRef] - Patle, G.T.; Sikar, T.T.; Rawat, K.S.; Singh, S.K. Estimation of infiltration rate from soil properties using regression model for cultivated land. Geol. Ecol. Landsc.
**2019**, 3, 1–13. [Google Scholar] [CrossRef] - Sihag, P.; Tiwari, N.K.; Ranjan, S. Support vector regression-based modeling of cumulative infiltration of sandy soil. ISH J. Hydraul. Eng.
**2020**, 26, 44–50. [Google Scholar] [CrossRef] - Sihag, P.; Kumar, M.; Sammen, S.S. Predicting the infiltration characteristics for semi-arid regions using regression trees. Water Supply
**2021**, 21, 2583–2595. [Google Scholar] [CrossRef] - Cortes-D, D.L.; Camacho-Tamayo, J.H.; Giraldo, R. Spatial prediction of soil infiltration using functional geostatistics. AUC Geogr.
**2018**, 53, 149–155. [Google Scholar] [CrossRef] [Green Version] - Mishra, S.K.; Tyagi, J.V.; Singh, V.P. Comparison of Infiltration Models. Hydrol. Process.
**2003**, 24, 2629–2652. [Google Scholar] [CrossRef] - Zakwan, M.; Muzzammil, M.; Alam, J. Application of spreadsheet to estimate infiltration parameters. Perspect. Sci.
**2016**, 8, 702–704. [Google Scholar] [CrossRef] [Green Version] - Sihag, P.; Tiwari, N.K.; Ranjan, S. Estimation and intercomparison of infiltration models. Water Sci. Technol.
**2017**, 31, 34–43. [Google Scholar] [CrossRef] [Green Version] - Singh, B.; Sihag, P.; Singh, K. Comparison of infiltration models in NIT. Kurukshetra Campus. Appl. Water Sci.
**2018**, 9, 63. [Google Scholar] [CrossRef] [Green Version] - Vand, A.S.; Sihag, P.; Singh, B.; Zand, M. Comparative evaluation of infiltration models. KSCE J. Civ. Eng.
**2018**, 22, 4173–4184. [Google Scholar] [CrossRef] - Farid, H.U.; Mahmood-Khan, Z.; Ahmad, I.; Shakoor, A.; Anjum, M.N.; Iqbal, M.M.; Mubeen, M.; Asghar, M. Estimation of infiltration models parameters and their comparison to simulate the onsite soil infiltration characteristics. Int. J. Agric. Biol. Eng.
**2019**, 2, 84–91. [Google Scholar] - Ebrahimian, H.; Ghaffari, P.; Ghameshlou, A.N.; Tabatabaei, S.-H.; Alizadeh Dizaj, A.A. Extensive comparison of various infiltration estimation methods for furrow irrigation under different field conditions. Agric. Water Manag.
**2020**, 230, 105960. [Google Scholar] [CrossRef] - Ramesh, V.B.; Bandhyopadhyay, K.K.; Sharma, K.L.; Bhattacharyya, T.; Wani, S.P. Land use and soil management effects on infiltration model parameters in semi-arid tropical alfisols. Ann. Arid. Zone
**2010**, 49, 1–8. [Google Scholar] - Horton, R.E. Analysis of runoff-plat experiments with varying infiltration-capacity. Eos. Trans. Am. Geophys. Union
**1939**, 20, 693–711. [Google Scholar] [CrossRef] - Holtan, H.N. A Concept of Infiltration Estimates in Watershed Engineering; ARS (Series) Agricultural Research Service 41–51; U.S. Department of Agriculture: Washington, DC, USA, 1961; pp. 1–32.
- Bauer, S.W. A modified Horton equation for infiltration during intermittent rainfall. Hydrol. Sci. Bull.
**1974**, 19, 219–225. [Google Scholar] [CrossRef] - Gabellani, S.; Silvestro, F.; Rudari, R.; Boni, G. General calibration methodology for a combined Horton-SCS infiltration scheme in flash flood modeling. Nat. Hazards Earth Syst. Sci.
**2008**, 8, 1317–1327. [Google Scholar] [CrossRef] - Verma, S.C. Modified Horton’s infiltration equation. J. Hydrol.
**1982**, 58, 383–388. [Google Scholar] [CrossRef] - Akan, A.O. Horton Infiltration Equation revisited. J. Irrig. Drain. Eng.
**1992**, 118, 828–830. [Google Scholar] [CrossRef] - Esen, I.I.; Almedeij, J. Generalized Horton Model for Low-Intensity rainfall. Soil Sci.
**2013**, 178, 174–179. [Google Scholar] [CrossRef] - Green, I.R.A. An explicit solution of the modified Horton equation. J. Hydrol.
**1986**, 83, 23–27. [Google Scholar] [CrossRef] - Aron, G. Adaptation of Horton and SCS infiltration equations to complex storms. J. Irrig. Drain. Eng.
**1992**, 118, 275–284. [Google Scholar] [CrossRef] - Arnold, J.G.; Allen, P.M.; Bernhardt, G. A comprehensive surface-groundwater flow model. J. Hydrol.
**1993**, 142, 47–69. [Google Scholar] [CrossRef] - Diskin, M.H.; Nazimov, N. Linear reservoir with feedback regulated inlet as a model for the infiltration process. J. Hydrol.
**1995**, 172, 313–330. [Google Scholar] [CrossRef] - Ottoni Filho, T.B.O.; Ottoni, M.V.; Oliveira, M.B.; Macedo, J.R. Estimation of field capacity from ring infiltrometer-drainage data. Rev. Bras. Ciênc. Solo
**2014**, 38, 1765–1771. [Google Scholar] [CrossRef] [Green Version] - Razzaghi, S.; Khodaverdiloo, H.; Dashtaki, S.G. Effects of long-term wastewater irrigation on soil physical properties and performance of selected infiltration models in a semi-arid region. Hydrol. Sci. J.
**2016**, 61, 1778–1790. [Google Scholar] [CrossRef] - Li, M.; Liu, T.; Duan, L.; Luo, Y.; Ma, L.; Zhang, J.; Zhou, Y.; Chen, Z. The scale effect of double-ring infiltration and soil infiltration zoning in a semi-arid steppe. Water
**2019**, 11, 1457. [Google Scholar] [CrossRef] [Green Version] - Mbagwu, J.S.C. Analysis of Physical Properties Controlling Steady-State Infiltration Rates on Tropical Savannah Soils; IC—93/289; International Atomic Energy Agency: Vienna, Austria, 1993; Volume 25, pp. 1–11. [Google Scholar]
- Askari, M.; Tanaka, T.; Setiawan, B.I.; Saptomo, S.K. Infiltration characteristics of tropical soil based on water retention data. J. Jpn Soc. Hydrol. Water Resour.
**2008**, 21, 215–227. [Google Scholar] [CrossRef] [Green Version] - Suryoputro, N.; Soetopo, W.; Suhartanto, E.S.; Limantara, L.M. Evaluation of infiltration models for mineral soils with different land uses in the tropics. J. Water Land Dev.
**2018**, 37, 153–160. [Google Scholar] [CrossRef] - Bach, L.B.; Wierenga, P.J.; Ward, T.J. Estimation of the Philip Infiltration Parameters from Rainfall Simulation Data. Soil Sci. Soc. Am. J.
**1986**, 50, 1319–1323. [Google Scholar] [CrossRef] - Mahapatra, S.; Jha, M.K.; Biswal, S.; Senapati, D. Assessing variability of infiltration characteristics and reliability of infiltration models in a tropical sub-humid region of India. Sci. Rep.
**2020**, 10, 1515. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Oku, E.; Aiyelari, A. Predictability of Philip and Kostiakov infiltration models under inceptisols in the humid forest zone, Nigeria. Kasetsart J. Nat. Sci.
**2011**, 45, 594–602. [Google Scholar] - Utin, U.E.; Oguike, P.C. Evaluation of Philip’s and Kostiakov’s infiltration models on soils derived from three parent materials in Akwa Ibom state, Nigeria. J. Sci. Eng. Res.
**2018**, 5, 79–87. [Google Scholar] - Zolfaghari, A.A.; Mirzaee, S.; Gorji, M. Comparison of different models for estimating cumulative infiltration. Int. J. Soil Sci.
**2012**, 7, 108–115. [Google Scholar] [CrossRef] [Green Version] - Zakwan, M. Assessment of dimensionless form of Kostiakov model. Aquademia Water Environ. Technol.
**2017**, 1, 1. [Google Scholar] [CrossRef] - Jagani, A.H.; Shrivastava, P.K.; Dwivedi, D.K. Evaluation of Kostiakov’s and Philip’s infiltration models on the soil of Dediapada, India. India J. Appl. Nat. Sci.
**2018**, 10, 1073–1077. [Google Scholar] [CrossRef] - Igboekwe, M.U.; Adindu, R.U. Use of Kostiakov’s infiltration model on Michael Okpara University of Agriculture, Umudike soils, Southeastern, Nigeria. Water Resour. Prot.
**2014**, 6, 888–894. [Google Scholar] [CrossRef] [Green Version] - Lei, G.; Fan, G.; Zeng, W.; Huang, J. Estimating parameters for the Kostiakov-Lewis infiltration model from soil physical properties. J. Soils Sediments
**2020**, 20, 166–180. [Google Scholar] [CrossRef] - Thomas, A.; Ofosu, A.; Emmanuel, A.; De-Graft, A.; Ayine, A.; Asare, A.; Alexander, A. Comparison and Estimation of Four Infiltration Models. Open J. Soil Sci.
**2020**, 10, 45–57. [Google Scholar] [CrossRef] [Green Version] - Ogbe, V.B.; Jayeoba, O.J.; Ode, S.O. Comparison of four soil infiltration models on a sandy soil in Lafia, Southern Guinea Savanna zone of Nigeria. Prod. Agric. Technol.
**2011**, 7, 116–126. [Google Scholar] - Mohamoud, Y.M. Evaluating the green and αMPT infiltration parameter values for tilled and crusted soils. J. Hydrol.
**1991**, 123, 25–38. [Google Scholar] [CrossRef] - Adindu, R.; Igbokwe, K.; Chigbu, T.; Ike-Amadi, C. Application of Kostiakov’s infiltration model on the soils of umudike, Abia state—Nigeria. Am. J. Environ. Eng.
**2014**, 4, 1–6. [Google Scholar] - Rahmati, M.; Weihermüller, L.; Vanderborght, J.; Pachepsky, Y.A.; Mao, L.; Sadeghi, S.H.; Moosavi, N.; Kheirfam, H.; Montzka, C.; Van Looy, K.; et al. Development and analysis of the Soil water Infiltration Global database. PANGAEA
**2018**, 10, 1237–1263. [Google Scholar] [CrossRef] [Green Version] - Zadjaoui, A. Numerical modelling of infiltration profiles in the silt Tlemcen (Algeria). E3S Web Conf.
**2016**, 9, 11015. [Google Scholar] [CrossRef] [Green Version] - Smail, A.S.; Bouheraoua, A.; Abdesselam, M. Caractérisation hydrodynamique des sols de la haute vallée de l’oued Sébaou (Algérie): Étude expérimentale, numérique et analytique. Phys. Géo
**2013**, 7, 261–283. [Google Scholar] [CrossRef] - Boers, T.M.; van Deurzen, F.J.M.P.; Eppink, L.A.A.J.; Ruytenberg, R.E. Comparison of infiltration rates measured with an infiltrometer, a rainulator and a permeameter for erosion research in SE Nigeria. Soil Technol.
**1992**, 5, 13–26. [Google Scholar] [CrossRef] - Akinbile, C. Comparative analysis of infiltration measurements of two irrigated soils in Akure, Nigeria. Adv. Appl. Sci. Res.
**2010**, 1, 49–57. [Google Scholar] - Mavimbela, S.S.W.; van Rensburg, L.D. Characterizing infiltration and internal drainage of South African dryland soils. Earth Surf. Process. Landf.
**2017**, 42, 414–425. [Google Scholar] [CrossRef] - Lasisip, M.O.; Bof, P.; Awe, B.S. Assessment of infiltration capacity of agricultural soil in Ado-Ekiti southwestern Nigeria using selected empirical models. Int. J. Innov. Sci. Eng. Technol.
**2017**, 4, 111–117. [Google Scholar] - Ehiomogue, P.; Ojedele, O.S.; Ikechuchu-Ede, C.E.; Okosa Iorji, F.N.; Ahaneku, I.E. Calibration of existing infiltration models on different amended soils. Am. J. Eng. Res.
**2018**, 7, 242–247. [Google Scholar] - Robinson, A.R.; Rohwer, C. Measurement of canal seepage. Trans. ASCE
**1957**, 122, 347–363. [Google Scholar] - Weiler, M.; Naef, F. An experimental tracer study of the role of macropores in infiltration in grassland soils. Hydrol. Process.
**2003**, 17, 477–493. [Google Scholar] [CrossRef] - Horton, R.E. An approach toward a physical interpretation of infiltration-capacity. Soil Sci. Soc. Am. J.
**1941**, 5, 399–417. [Google Scholar] [CrossRef] - Beven, K.; Robert, E. Horton’s perceptual model of infiltration processes. Hydrol. Process.
**2004**, 18, 3447–3460. [Google Scholar] [CrossRef] - Kostiakov, A.N. The dynamics of the coefficients of water percolation in soils and the necessity for studying it from a dynamic point of view for purpose of amelioration. Soc. Soil Sci.
**1932**, 14, 17–21. [Google Scholar] - Philip, J.R. The theory of infiltration: 1. The infiltration equation and its solutions. Soil Sci.
**1957**, 83, 345–358. [Google Scholar] [CrossRef] - Monroe, J.S.; Wicander, R. The Changing Earth: Exploring Geology and Evolution, 5th ed.; Brooks Cole: Salt Lake City, UT, USA, 2008; p. 735. [Google Scholar]
- Ghosh, R.K. A note on Lewis-Kostiakov’s infiltration equation. Soil Sci.
**1985**, 139, 193–196. [Google Scholar] [CrossRef] - Philip, J.R. Theory of Infiltration. Adv. Hydrosci.
**1969**, 5, 215–296. [Google Scholar] [CrossRef] - Sir, M.; Kutilek, M.; Kuraz, V.; Krejca, M.; Kubik, F. Field estimation of the soil hydraulic characteristics. Soil Technol.
**1988**, 1, 63–75. [Google Scholar] [CrossRef]

**Figure 5.**Inter-comparison of field infiltration rates from different models for Madjez Ressoul catchment.

**Figure 6.**(

**a**) Overall linear dependency of observed versus simulated infiltration rates at all site locations. (

**b**) Overall behavior of the models’ simulations compared to the overall field measurements.

**Figure 8.**Variation of the three models’ parameters and infiltration rates over Medjaz Ressoul catchment.

N° | X (m) | Y (m) | N° | X (m) | Y (m) |
---|---|---|---|---|---|

P1 | 375,425.62 | 4,058,710.17 | P14 | 366,337.18 | 4,054,866.19 |

P2 | 374,496.25 | 4,057,723.53 | P15 | 369,589.50 | 4,051,912.45 |

P3 | 374,533.68 | 4,056,506.43 | P16 | 371,186.40 | 4,052,366.52 |

P4 | 373,893.76 | 4,055,315.90 | P17 | 371,897.50 | 4,049,519.69 |

P5 | 372,720.30 | 4,054,656.09 | P18 | 370,680.00 | 4,047,361.72 |

P6 | 371,720.73 | 4,054,348.72 | P19 | 368,502.03 | 4,047,109.89 |

P7 | 369,870.38 | 4,053,866.53 | P20 | 366,831.31 | 4,048,601.47 |

P8 | 368,255.99 | 4,054,208.03 | P21 | 365,040.89 | 4,048,188.93 |

P9 | 367,492.01 | 4,054,096.72 | P22 | 368,495.87 | 4,050,579.35 |

P10 | 366,726.87 | 4,054,144.07 | P23 | 363,989.19 | 4,050,114.83 |

P11 | 365,854.40 | 4,053,583.85 | P24 | 363,162.02 | 4,051,752.15 |

P12 | 366,080.29 | 4,052,571.78 | P25 | 364,839.14 | 4,050,714.70 |

P13 | 366,465.12 | 4,051,965.49 |

N° | Initial Infiltration Rate f_{0} at t = 2 min [cm/min] | Final Infiltration Rate f _{c} min [cm/min] |
---|---|---|

P1 | 1 | 0.6 |

P2 | 2.5 | 0.1 |

P3 | 1 | 0.2 |

P4 | 1 | 0.1 |

P5 | 0.9 | 0.1 |

P6 | 0.5 | 0.1 |

P7 | 1.1 | 0.1 |

P8 | 1.3 | 0.2 |

P9 | 1.1 | 0.1 |

P10 | 1.2 | 0.1 |

P11 | 1 | 0.2 |

P12 | 1.2 | 0.2 |

P13 | 1 | 0.1 |

P14 | 1.3 | 0.1 |

P15 | 1.5 | 0.1 |

P16 | 1 | 0.1 |

P17 | 1.2 | 0.1 |

P18 | 1 | 0.1 |

P19 | 1.1 | 0.1 |

P20 | 0.5 | 0.1 |

P21 | 1.1 | 0.1 |

P22 | 1 | 0.1 |

P23 | 1 | 0.2 |

P24 | 1.1 | 0.1 |

P25 | 1.5 | 0.1 |

N° | Day | Moisture Content (%) | N° | Day | Moisture Content (%) |
---|---|---|---|---|---|

P1 | 14 April 2019 | 21.21 | P14 | 28 April 2019 | 23.00 |

P2 | 15 April 2019 | 40.06 | P15 | 6 May 2019 | 13.90 |

P3 | 19 April 2019 | 26.58 | P16 | 6 May 2019 | 21.21 |

P4 | 17 April 2019 | 29.03 | P17 | 7 May 2019 | 16.69 |

P5 | 20 April 2019 | 25.79 | P18 | 7 May 2019 | 9.89 |

P6 | 20 April 2019 | 14.81 | P19 | 9 May 2019 | 19.33 |

P7 | 22 April 2019 | 8.58 | P20 | 9 May 2019 | 19.76 |

P8 | 22 April 2019 | 12.11 | P21 | 11 May 2019 | 24.69 |

P9 | 23 April 2019 | 13.77 | P22 | 11 May 2019 | 14.16 |

P10 | 23 April 2019 | 16.82 | P23 | 12 May 2019 | 28.53 |

P11 | 25 April 2019 | 14.81 | P24 | 12 May 2019 | 16.69 |

P12 | 25 April 2019 | 12.11 | P25 | 13 May 2019 | 13.38 |

P13 | 28 April 2019 | 20.77 |

N° | Horton’s Model | Kostiakov’s Model | Philip’s Model | ||
---|---|---|---|---|---|

k (h^{−1})
| A | B | S (cm/h^{0.5})
| $\mathit{K}$(cm/h) | |

P1 | 5.403 | 3.875 | 0.586 | 9.893 | 0.012 |

P2 | 6.744 | 2.174 | 0.890 | 11.688 | 0.014 |

P3 | 2.18 | 6.975 | 0.462 | 12.647 | 0.0379 |

P4 | 2.576 | 5.920 | 0.514 | 12.216 | 0.020 |

P5 | 1.897 | 6.625 | 0.425 | 10.211 | 0.990 |

P6 | 1.795 | 3.182 | 0.483 | 6.070 | 0.012 |

P7 | 3.243 | 5.695 | 0.503 | 11.429 | 0.012 |

P8 | 2.682 | 6.527 | 0.554 | 15.218 | 0.010 |

P9 | 2.643 | 5.334 | 0.542 | 11.885 | 0.010 |

P10 | 3.411 | 6.529 | 0.524 | 13.930 | 0.010 |

P11 | 2.402 | 6.671 | 0.449 | 11.077 | 0.743 |

P12 | 4.774 | 3.529 | 0.687 | 12.218 | 0.010 |

P13 | 2.368 | 5.434 | 0.510 | 11.156 | 0.010 |

P14 | 3.504 | 7.290 | 0.530 | 15.682 | 0.010 |

P15 | 4.080 | 6.403 | 0.586 | 16.078 | 0.020 |

P16 | 2.939 | 5.512 | 0.506 | 11.182 | 0/013 |

P17 | 4.037 | 6.678 | 0.517 | 13.960 | 0.012 |

P18 | 2.786 | 4.747 | 0.689 | 13.748 | 0.010 |

P19 | 5.320 | 3.855 | 0.634 | 11.217 | 0.020 |

P20 | 1.987 | 2.975 | 0.454 | 4.854 | 0.841 |

P21 | 4.611 | 3.420 | 0.671 | 11.003 | 0.010 |

P22 | 3.055 | 5.371 | 0.531 | 11.668 | 0.030 |

P23 | 4.000 | 5.209 | 0.536 | 11.414 | 0.030 |

P24 | 3.517 | 5.110 | 0.579 | 12.553 | 0.012 |

P25 | 4.537 | 6.145 | 0.593 | 15.581 | 0.015 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dahak, A.; Boutaghane, H.; Merabtene, T.
Parameter Estimation and Assessment of Infiltration Models for Madjez Ressoul Catchment, Algeria. *Water* **2022**, *14*, 1185.
https://doi.org/10.3390/w14081185

**AMA Style**

Dahak A, Boutaghane H, Merabtene T.
Parameter Estimation and Assessment of Infiltration Models for Madjez Ressoul Catchment, Algeria. *Water*. 2022; 14(8):1185.
https://doi.org/10.3390/w14081185

**Chicago/Turabian Style**

Dahak, Asma, Hamouda Boutaghane, and Tarek Merabtene.
2022. "Parameter Estimation and Assessment of Infiltration Models for Madjez Ressoul Catchment, Algeria" *Water* 14, no. 8: 1185.
https://doi.org/10.3390/w14081185