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Developing a novel method for estimating parameters of Kostiakov–Lewis infiltration equation

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Abstract

In this study, the volume balance equation and Elliott and Walker’s two-point method were employed to estimate the Kostiakov–Lewis (KL) infiltration equation parameters. The volume balance equation has a maximum point, whose location (distance) is a function of two parameters, r (constant parameter in advance equation) and fo. (final infiltration rate). If the length of the field is less than the distance of maximum point, then parameters of the infiltration equation obtained by the two-point method will have appropriate values. Otherwise, the values of infiltration parameters would depend on the values of r and fo, and there would be a possibility of their values being inappropriate. In this method, the soil texture of the field is assumed to be homogeneous; so, the relationship between r and fo is ignored, which may render the two-point method unsuitable in heterogeneous soils. By investigating the effect of soil heterogeneity on the values of r and fo, it was found that in the two-point method, point information is used for the estimation of parameters of the KL infiltration and that there is no clear relationship between these two points. As a result, a novel method was developed in this study to estimate the KL infiltration equation parameters and applied in three irrigation fields. The infiltration parameters obtained by the proposed method had appropriate values. The infiltration depth computed with the use of parameters so obtained was in close agreement with observed infiltration depth. Thus, the proposed method is potentially useful for estimating the KL infiltration equation parameters.

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Abbreviations

\(a\) :

The exponent factor in the infiltration equation

\(A\) :

Water flow cross-section at the beginning of the field

\(f_{o}\) :

Final infiltration rate

\(f_{1}\) :

Final infiltration rate at the beginning of the field

\(i\) :

Cumulative infiltration

\(I_{x}\) :

The average depth infiltrated along x from the beginning of the field by the exponential part of the infiltration equation

\(i_{\text{Advance}}\) :

Average infiltration depth in the advance phase

\(i_{\text{Total}}\) :

Average infiltration depth in the entire phase of irrigation time

\(I_{L}\) and \(V_{L}\) :

The average depth infiltrated along L by the exponential part of the infiltration equation

\(I_{{\frac{L}{2}}}\) and \(V_{{\frac{L}{2}}}\) :

Average depth infiltrated along L/2 by exponential part of the infiltration equation

I max :

The maximum depth infiltrated through the exponential aspect of the Kostiakov–Lewis equation

\(k\) :

Constant parameter in the infiltration equation

\(L\) :

Field length

\(p\) :

Constant parameter in advance equation

\(Q_{o}\) :

Inflow rate to the field

\(Q_{\text{out}}\) :

Outflow rate of the Field

\(r\) :

Constant parameter in advance equation

\(t\) :

Time of infiltration of water in soil

\(t_{{\frac{{I_{L} }}{2}}}\) :

Time to advance to the point where it is \(I_{x} = \frac{{I_{L} }}{2}\)

\(t_{L}\) :

The time for water advance to L

\(t_{{\frac{L}{2}}}\) :

The time for water advance to L/2

\(t_{x}\) :

The time for water advance to x

\(x\) :

The length of the water advance in the field based on the beginning of the field

\(\beta \left( {r,a + 1} \right)\) :

Beta function

\(\varGamma\) :

Gamma function

\(\lambda\) :

Ratio the first half permeability of the field to the permeability of the total e field

\(\sigma_{y}\) :

The conversion parameter of the initial cross-sectional water flow to the average cross-sectional flow along the field

\(\sigma^{\prime}_{z}\) and \(\sigma_{z}\) :

Subsurface shape factors

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Authors and Affiliations

  1. Department of Irrigation and Reclamation Engineering, University of Tehran, Tehran, Iran

    Amin Seyedzadeh & Amir Panahi

  2. Department of Water Engineering, Faculty of Agriculture, University of Kurdistan, Sanandaj, Iran

    Eisa Maroufpoor

  3. Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A&M University, 2117 TAMU, College Station, Texas, TX 77843‑2117, USA

    Vijay P. Singh

  4. School of Science, Western Sydney University, Locked Bag 1797, Penrith, NSW, 2751, Australia

    Basant Maheshwari

Authors
  1. Amin Seyedzadeh
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  2. Amir Panahi
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  3. Eisa Maroufpoor
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  4. Vijay P. Singh
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  5. Basant Maheshwari
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Correspondence to Eisa Maroufpoor.

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Seyedzadeh, A., Panahi, A., Maroufpoor, E. et al. Developing a novel method for estimating parameters of Kostiakov–Lewis infiltration equation. Irrig Sci 38, 189–198 (2020). https://doi.org/10.1007/s00271-019-00660-4

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  • DOI: https://doi.org/10.1007/s00271-019-00660-4

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