Spatial Heterogeneity and Scale in the Infiltration Response of Catchments

  • M. Sivapalan
  • E. F. Wood
Part of the Water Science and Technology Library book series (WSTL, volume 6)


The effect of spatial heterogeneity in soil and rainfall characteristics on the infiltration response of catchments is studied. Quasi-analytical expressions are derived for the statistics of the ponding time and the infiltration rate for two cases: (i) spatially variable soils and uniform rainfall, and (ii) constant soil properties and spatially variable rainfall. The derivations show that the cumulative ponding time distribution is a critical variable which governs the mean and covariance of the infiltration process. This distribution determines the proportion of the catchment which is soil controlled and the proportion which is rainfall controlled. The heterogeneity of the infiltration response, part being rainfall controlled and part soil controlled, causes a temporal variation in the correlograms. Over time, the correlation of the infiltration goes from the correlogram of the rainfall (at initial time) to that of the soil properties (at large time).


Rainfall Intensity Infiltration Rate Scale Problem Variable Soil Water Resource Research 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Benjamin, J.R., and C.A. Cornell, 1970, Probability, Statistics, and Decision for Civil Engineers, McGraw-Hill, New York.Google Scholar
  2. Bresler, E.; and G. Dagan, 1983, “Unsaturated Flow in Spatially Variable Fields, 2. Application of Water Flow Models to Various Fields”, Water Resources Research, Vol. 19, No. 2, pp. 421–428.CrossRefGoogle Scholar
  3. Brutsaert, W. 1976, “The Concise Formulation of Diffusive Sorption of Water in Dry Soil”, Water Resources Research, Vol. 12, No. 6, pp. 1118–1124.CrossRefGoogle Scholar
  4. Dagan, G., and E. Bresler, 1983, “Unsaturated Flow in Spatially Variable Fields, 1. Derivation of Models of Infiltration and Redistribution”, Water Resources Research, Vol. 19, No. 2, pp. 413–420.CrossRefGoogle Scholar
  5. Dooge, J.C.I., 1981, “Parameterization of Hydrologic Processes”, paper presented at the JSC Study Conference on Land Surface Processes in Atmospheric General Circulation Models, Greenbelt, USA, January, pp. 243–284.Google Scholar
  6. Ibrahim, H.A. and W. Brutsaert, 1968, “Intermittent Infiltration into Soils with Hysteresis”, ASCE, Journal of Hydrology, HY1, pp. 113–137.Google Scholar
  7. Journel, A.G., and Ch. J. Huijbregts, 1978, Mining Geostatistics, Academic Press, 600 pp.Google Scholar
  8. Mailer, R.A., and M.L. Sharma, 1981, “An Analysis of Areal Infiltration Considering Spatial Variability”, Journal of Hydrology, Vol. 52, pp. 25–37.CrossRefGoogle Scholar
  9. Mailer, R.A. and M.L. Sharma, 1984, “Aspects of Rainfall Excess from Spatially Varying Hydrological Parameters”, Journal of Hydrology, Vol. 67, pp. 115–127.CrossRefGoogle Scholar
  10. Mijia, J.M., and I. Rodríguez-Iturbe, 1974, “Correlation Links Between Normal and Lognormal Processes”, Water Resources Research, Vol. 10, No. 4, pp. 689–690.CrossRefGoogle Scholar
  11. Milly, P.C.D. and P.S. Eagleson, 1982, “Infiltration and Evaporation at Inhomogeneous Land Surfaces”, MIT Ralph M. Parsons Laboratory Report No. 278, 180 pp.Google Scholar
  12. Mood, A.M., F.A. Graybill, and D.C. Boes, 1974, Introduction to the Theory of Statistics, McGraw-Hill, Third Edition, 564 pp.Google Scholar
  13. Nagao, M., and M. Kadoya, 1971, “Two Variate Exponential Distribution and its Numerical Table for Engineering Application”, Bull. Disas. Prev. Res. Inst., Kyoto University, Vol. 20, Part 3, No. 178, pp. 183–197.Google Scholar
  14. Philip, J.R., 1957, “The Theory of Infiltration”, Soil Science, Vols. 83, 84 and 85.Google Scholar
  15. Reeves, M. and E.E. Miller, 1975, “Estimating Infiltration for Erratic Rainfall”, Water Resources Research, Vol. 11, No. 1, pp. 102–110.CrossRefGoogle Scholar
  16. Rodríguez-Iturbe, I., and J.M. Mejia, 1974, “On the Transformation from Point Rainfall to Areal Rainfall”, Water Resources Research, Vol. 10, No. 4, pp. 729–735.CrossRefGoogle Scholar
  17. Sharma, M.L., and E. Seely, 1979, “Spatial Variability and its Effects on Areal Infiltration”, Proceedings Hydrology and Water Resources Symposium, Inst. Eng., Australia, Perth, W.A., pp. 69–73.Google Scholar
  18. Sherman, L.K., 1943, “Comparison of F-curves Derived by the Methods Sharp and Holtan and of Sherman and Mayer”, Trans. Am. Geophys. Un., Vol. 24, pp. 465–467.Google Scholar
  19. Smith, R.E., and R.H.P. Hebbert, 1979, “A Monte Carlo Analysis of the Hydrologic Effects of Spatial Variability of Infiltration”, Water Resources Research, Vol. 15, No. 3, pp. 419–429.CrossRefGoogle Scholar
  20. Valdes, J.B., I. Rodríguez-Iturbe, and V.K. Gupta, 1985, “Approximations of Temporal Rainfall from a Multidimensional Model”, Water Resources Research, Vol. 21, No. 8, pp. 1259–1270.CrossRefGoogle Scholar
  21. Whittle, P., 1954, “On Stationary Processes in the Plane”, Biometrika, Vol. 41, pp. 434–449.Google Scholar
  22. Wood, E.F., M. Sivapalan, and K. Beven, 1986, “Scale Effects in Infiltration and Runoff Production”, Paper to be presented at the 2nd Scientific Assembly of the IAHS, Budapest Hungary, July 2–10, 1986.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • M. Sivapalan
  • E. F. Wood

There are no affiliations available

Personalised recommendations