Abstract
The irrigation advance problem in irrigation hydraulics has been spread across the engineering and soil science literature over a number of decades. The Lewis–Milne framework has been used extensively, but one problem has been to find a suitable infiltration equation. The infiltration advance solutions of Philip and Farrell, and Collis-George and Freebairn are compared to a new solution based on the linear soil infiltration equation. It is shown that the linear soil solution is able to give similar results to the Philip and Farrell solution at early stages of infiltration when this is valid, and the Collis-George and Freebairn solution at longer times when this is valid. The linear soil infiltration advance solution presented here is the first using physically meaningful parameters which is able to give adequate infiltration and advance behaviour over all time scales. To further test the linear soil concept, we inversely fit irrigation advance data to get the sorptivity, saturated hydraulic conductivity and infiltration rate behaviour of the soil using all three infiltration equations. The linear soil is shown to give the best fit for the infiltration behaviour to the measured results with an average r 2 of 0.98 compared to 0.84 for Philip and Farrell and 0.77 for Collis-George and Freebairn. The linear soil model was also the best fit using other statistical tests such as RMSE and RSR.
Similar content being viewed by others
References
Bautista E, Clemmens AJ, Strekroff TS (2009) Structured application of the two-point method for the estimation of infiltration parameters in surface irrigation. J Irrig Drain Eng 135(5):566–578
Clothier BE, White I (1981) Measurement of sorptivity and soil water diffusivity in the field. Soil Sci Soc Am J 45(2):241–245
Clothier BE, Scotter DR, Kerr JP (1977) Drainage flux in permeable soil underlain by a coarse-textured layer. Soil Sci Soc Am J 41:671–676
Collis-George N, Freebairn DM (1979) A laboratory and field study of border check irrigation. Aust J Soil Res 17:75–87
Connell LD, Jayatilaka C, Gilfedder M, Mein RG, Vandervaere JP (2001) Modeling flow and transport in irrigation catchments 1. Development and testing of subcatchment model. Water Resour Res 37(4):949–963
Cook FJ, Broeren A (1994) Six methods for determining sorptivity and hydraulic conductivity with disc permeameters. Soil Sci 157(1):2–11
Doble RC, Crosbie RS, Smerdon BD, Peeters L, Cook FJ (2012) Groundwater recharge from overbank floods. Water Resour Res. (Accepted)
Ebrahimian H, Liaghat A, Ghanbarian-Alavijeh B, Abbasi F (2010) Evaluation of various quick methods for estimating furrow and border infiltration parameters. Irrig Sci 28(6):479–488
Finkel HJ, Nir D (1960) Determining infiltration rates in an irrigation border. J Geophysical Res 65(7):2125–2131
Goswami MD (2007) Mathematical model on flow regime and water harvesting in inundation plains. J Am Water Resour Assoc 43(3):588–593
Hamblin AP (1982) Soil water behaviour in response to changes in soil structure. J Soil Sci 33:375–386
Horton RE (1940) Approach toward a physical interpretation of infiltration capacity. Soil Sci Soc Am Proc 5:399–417
Khatri KL, Smith RJ (2005) Evaluation of methods for determining infiltration parameters from irrigation advance data. Irrig Drain 54(4):467–482
Knight JH (1980) An improved solution for the irrigation-advance problem in irrigation hydraulics. In 7th Aust. Hydraulics and fluid mechanics conference, Brisbane, 18–22 August, 1980, pp 258–261
Kostiakov AN (1932) On the dynamics of the coefficients of water percolation in soils and on the necessity of studying it from a dynamic point of view for purpose of amelioration. Transactions of the 6th communication of the international society of soil sciences, Part A:17–21
Lewis MR, Milne WE (1938) Analysis of border irrigation. Agric Eng 19:267–272
Moore ID, Foster GR (1990) Hydraulics and overland flow. In: Anderson MG, Burt TP (eds) Process studies in hillslope hydrology. Wiley, New York, pp 215–254
Moriasi DN, Arnold JG, Van Liew MW, Binger RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900
Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models: part 1. A discussion of principles. J Hydrol 10(3):282–290
Niswonger RG, Prudic DE, Fogg GE, Stonestrom DA, Buckland EM (2008) Method for estimating spatially variable seepage loss and hydraulic conductivity in intermittent and ephemeral streams. Water Resour Res 44(5):W05418, 1–14
Parlange J-Y (1973) Note on infiltration advance front from border irrigation. Water Resour Res 9:1075–1078
Philip JR (1957) The theory of infiltration:4. Sorptivity and algebraic infiltration equations. Soil Sci 83:257–264
Philip JR (1966) A linearization technique for the study of infiltration. UNESCO Symposium, vol 1. Water Unsaturated Zone, Wageningen, pp 471–478
Philip JR (1969) Theory of infiltration. Adv Hydrosci 5:215–296
Philip JR (1987) The infiltration joining problem. Water Resour Res 23(12):2239–2245
Philip JR, Farrell DA (1964) General solution of the infiltration-advance problem in irrigated hydraulics. J Geophysical Res 69(4):621–631
Rasmussen WO (1994a) Infiltration-advance equation for finite linear source. J Irrig Drain Eng 120(4):796–812
Rasmussen WO (1994b) Infiltration-advance equation for radial spreading. Water Resour Res 30(4):929–937
Renault D, Wallender WW (1992) ALIVE (advance linear velocity)–surface irrigation rate balance theory. J Irrig Drain Eng 118(1):138–155
Smiles DE, Knight JH (1976) A note on the use of the Philip infiltration equation. Aust J Soil Res 14:103–108
Su NH (2007) Radial water infiltration-advance-evaporation processes during irrigation using point source emitters in rigid and swelling soils. J Hydrol 344:190–197
Systat Software (2010) SigmaPlot 12 Users Guide. Systat Software Inc., 767p
Talsma T (1969) In situ measurement of sorptivity. Aust J Soil Res 7:269–276
Taylor AR (1981) A method for surface irrigation design based on infiltration using the border strip as an infiltrometer. PhD Thesis, University of Canterbury, Lincoln College, 229p
Valiantzas JD (2000) Surface water storage independent equation for predicting furrow irrigation advance. Irrig Sci 19(3):115–123
Zerihun D, Furman A, Warrick AW, Sanchez CA (2005) Coupled surface-subsurface transport model for irrigation borders and basins. I Model development. J Irrig Drain Eng 131(5):396–406
Acknowledgments
The authors would like to thank Professor Frank Kelliher who provided a copy of Dr Anthony Taylor’s thesis. We would like to thank for a very thorough review of this manuscript Professor Gerard Kluitenberg, and we greatly appreciate his efforts which have improved the manuscript. We would also like to thank the other anonymous reviewer for his suggested changes.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by J. Li.
Appendix
Appendix
Philip and Farrell (1964) propose solving the inverse problem by only considering the first two terms in their Eq. (35) and by plotting x/qt versus t 1/2. The intercept is 1/c, and the slope is −2S/3c 2 (which is incorrectly given as −2S/3c). Similarly, for long time, from their Eq. (42) Philip and Farrell (1964) suggested plotting x/q versus t −1/2, and again only considering the first two terms the intercept is 1/A and the slope is −S/2A 2 (which is incorrectly given as −2S/2A in Philip and Farrell (1964)).
Rights and permissions
About this article
Cite this article
Cook, F.J., Knight, J.H., Doble, R.C. et al. An improved solution for the infiltration advance problem in irrigation hydraulics. Irrig Sci 31, 1113–1123 (2013). https://doi.org/10.1007/s00271-012-0392-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00271-012-0392-7