Solution to Green–Ampt infiltration model using a two-step curve-fitting approach

  • Shakir Ali
  • Adlul Islam
Original Article


Infiltration is an important hydrological process affecting the runoff, groundwater recharge and solute transport process. The Green–Ampt (GA) model, describing one-dimensional infiltration process, yields an implicit equation for estimation of cumulative infiltration with time. In this paper, an explicit approximation to the GA model is derived using two-step curve-fitting technique. The Marquardt’s algorithm is employed for least-squares estimation of nonlinear parameters. Performance of the proposed model is compared with the implicit GA model using numerical and published field experimental data. The quantitative statistical indicators namely, percent relative error (RE), maximum absolute percent relative error (MARE), percent bias (PB), and Nash–Sutcliffe modeling efficiency (E), are used to assess the performance of the proposed model. The solution of the proposed model matched very well with that of the implicit GA model with MARE ≤ 0.146%, PB ≤ 0.070%, and E value approximately equal to 1 for both the dimensionless numerical and dimensional field experimental infiltration estimates. Simulation results of the proposed model demonstrated the capability of the derived model in estimating infiltration rate and cumulative infiltration accurately and can be applied to solve variety of real-life hydrological problems.


Green–Ampt Explicit model Infiltration Marquardt’s algorithm 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ICAR-Indian Institute of Soil and Water Conservation (IISWC), Research CentreKotaIndia
  2. 2.Natural Resource Management DivisionIndian Council of Agricultural Research (ICAR)New DelhiIndia

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