International Scientific Journal


To improve the precision of parameters' estimation in Philip infiltration model, chaos gray-coded genetic algorithm was introduced. The optimization algorithm made it possible to change from the discrete form of time perturbation function to a more flexible continuous form. The software RETC and Hydrus-1D were applied to estimate the soil physical parameters and referenced cumulative infiltration for seven different soils in the USDA soil texture triangle. The comparisons among Philip infiltration model with different numerical calculation methods showed that using optimization technique can increase the Nash and Sutcliffe efficiency from 0.82 to 0.97, and decrease the percent bias from 14% to 2%. The results indicated that using the discrete relationship of time perturbation function in Philip infiltration model's numerical calculation underestimated model's parameters, but this problem can be corrected a lot by using optimization algorithm. We acknowledge that in this study the fitting of time perturbation function, Chebyshev polynomial with order 20, did not perform perfectly near saturated and residue water content. So exploring a more appropriate function for representing time perturbation function is valuable in the future.
PAPER REVISED: 2017-12-12
PAPER ACCEPTED: 2017-12-13
CITATION EXPORT: view in browser or download as text file
  1. Green, W. H., et al., Studies on Soils Physics: The Flow of Air and Water Through Soils, J. Agric. Sci., 4 (1911), 1, pp. 1-24
  2. Yang, X. H., et al., Vulnerability of Assessing Water Resources Based on the Improved Set Pair Analy-sis, Thermal Science, 18 (2014), 5, pp. 1531-1535
  3. Horton, R. E., Analysis of Runoff Plat Experiments with Varying Infiltration Capacity, Trans. Am. Ge-ophys. Union, 20 (1939), 4, pp. 693-711
  4. Yang, X. H., et al., Improved Gray-Encoded Evolution Algorithm Based on Chaos Cluster for Parameter Optimization of Moisture Movement, Thermal Science, 21 (2017), 4, pp. 1581-1585
  5. Philip, J. R., The Theory of Infiltration, Adv. Hydrosci., 5 (1969), pp. 215-296
  6. Parlange, J. Y., et al., The Three-Parameter Infiltration Equation, Soil Sci., 133 (1982), 6, pp. 337-341
  7. Parlange, J. Y., et al., Infiltration Under Ponded Conditions: 1. Optimal Analytical Solution and Com-parison with Experimental Observations, Soil Sci., 139 (1985), 4, pp. 305-311
  8. Smith, R. E., et al., Infiltration Theory for Hydrologic Applications, Water Resour. Monogr., AGU, Washington, D. C., 2002
  9. Serrano, S. E., Modeling Infiltration with Approximate Solutions to Richard's Equation, J. Hydrol. Eng., 9 (2004), 5, pp. 421-432
  10. Basha, H. A., Infiltration Models for Semi-Infinite Soil Profiles, Water Resour. Res., 47 (2011), 8, pp. 192-198
  11. Richards, L. A., Capillary Conduction of Liquids in Porous Mediums, Physics, 1 (1931), 5, pp. 318-333
  12. Philip, J. R., The Theory of Infiltration: 1. The Infiltration Equation and its Solution, Soil Sci., 83 (1957a), pp. 345-357
  13. Philip, J. R., The Theory of Infiltration: 2. The Profile of Infinity, Soil Sci., 83 (1957b), pp. 435-448
  14. Philip, J. R., The Theory of Infiltration: 4. Sorptivity and Algebraic Infiltration Equation, Soil Sci., 84 (1957c), pp. 257-264
  15. Philip, J. R. Numerical Solution of Equations of the Diffusion Type with Diffusivity Concentration De-pendent, II. Aust. J. Pyhs., 10 (1957d), pp. 29-42
  16. Brutsaert, W., Hydrology : An Introduction, Cambridge Univ. Press, Cambridge, UK, 2005
  17. Horne, A., et al., Optimization Tools for Environmental Water Decisions: A Review of Strengths, Weaknesses, and Opportunities to Improve Adoption, Environmental Modelling & Software, 84 (2016), Oct., pp. 326-338
  18. Yang, X. H., et al., GHHAGA for Environmental Systems Optimization, Journal of Environmental In-formatics, 5 (2005), 1, pp. 36-41
  19. Yang, X. H., et al., Hierarchy Evaluation of Water Resources Vulnerability under Climate Change in Beijing, Natural Hazards, 84 (2016), Suppl. 1, pp. S63-S76
  20. Yang, X. H., et al., Chaos Gray-Coded Genetic Algorithm and its Application for Pollution Source Iden-tifications in Convection-Diffusion Equation, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), 8, pp. 1676-1688
  21. Buckingham, E., Studies on the Movement of Soil Moisture, US Department of Agriculture, Bureau of Soils, Bull. No. 38, Washington, D. C., 1907
  22. Van Genuchten, M. T., A Closed-Form Equation for Predicting the Hydraulic Conductivity of Unsatu-rated Soils, Soil Sci. Soc. Am. J., 44 (1980), 5, pp. 892-898
  23. Mualem, Y., A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media, Water Resour. Res., 12 (1976), 3, pp. 513-522
  24. Philip, J. R., Numerical Solution of Equations of the Diffusion Type with Diffusivity Concentration De-pendent, Faraday Soc. Trans., 51 (1955), pp. 885-892
  25. Van Genuchten, M. T., et al., The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils, Rep. EPA 600/2-91/065, 85, U. S. Environ. Prot. Agency, Washington, D. C., 1991
  26. Simunek, J., et al., The HYDRUS-1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-saturated Media-Version 4.08, Dep. of Environ. Sci., University of California, Riverside, Cal., USA, 2009
  27. Nash, J. E., et al., River Flow Forecasting through Conceptual Models Part I - A Discussion of Princi-ples, J. Hydrol., 10 (1970), pp. 282-290
  28. Ogden, F. L., et al., Validation of Finite Water-Content Vadose Zone Dynamics Method Using Column Experiments with a Moving Water Table and Applied Surface Flux, Water Resour. Res., 51 (2015), 5, pp. 3108-3125

© 2018 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence