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The spatial variability of water and solute transport properties in unsaturated soil: I. Analysis of property variation and spatial structure with statistical models
Authors
David RussoHesham Elabd
William A. Jury
Garrison Sposito
Authors Affiliations
David Russo was Visiting Scientist in the Department of Soil and Environmental Sciences, University of California, Riverside, from 1984 to 1986. He has since returned to his position as Soil Physicist at the Volcani Center, Agricultural Research Organization, Bet-Dagan, Israel; Hesham Elabd was former Graduate Research Assistant in the Department of Soil and Environmental Sciences, University of California, Riverside, is now Postdoctoral Researcher at New Mexico State University, Las Cruces; William A. Jury was Professor of Soil Science and Soil Physicist, Department of Soil and Environmental Sciences, University of California, Riverside; Garrison Sposito was Professor of Soil Science and Soil Chemist, Department of Soil and Environmental Sciences, University of California, Riverside.Publication Information
Hilgardia 55(4):1-32. DOI:10.3733/hilg.v55n04p056. July 1987.
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Abstract
This review presents and examines relevant information from existing spatial variability studies of soil water and solute transport properties. Although most of the information available allowed only a conventional statistical analysis (mean and variance) of the pertinent properties, the field studies of (Nielsen, Biggar, and Erh (1973)) and (Russo and Bresler (1981)) were also suitable for spatial structure analysis. Detailed structural analysis of the saturated hydraulic conductivity (Ks) of these two fields demonstrated how this type of analysis may reveal field characteristics that are not apparent from conventional statistical analysis.
Using the Akaike Information Criterion for model discrimination, the three-dimensional spatial distributions of lnKs of both fields were shown to be described best by a spherical covariance function and a linear drift function. The Hamra field of (Russo and Bresler (1981)) had a much larger deterministic drift component and a smaller stochastic component than the Panoche field of (Nielsen, Biggar, and Erh (1973)). The stochastic component of lnKs in the Bet-Dagan field possessed a large nugget variance (40 percent of total) and was characterized by an integral scale of J = 14.5 m, as compared with J = 8.1 m and a small nugget variance (13 percent of total) in the Panoche field.
Literature Cited
Aitcheson J., Brown J. A. C. The lognormal distribution. 1976. Cambridge, England: Cambridge University Press.
Amoozegar-Fard A., Nielsen D. R., Warrick A. W. Soil solute concentration distributions for spatially varying pore water velocities and apparent diffusion coefficients. Soil Sci. Soc. Am. J. 1982. 46:3-8. DOI: 10.2136/sssaj1982.03615995004600010001x [CrossRef]
Babalola O. Spatial variability of soil water properties in tropical soils of Nigeria. Soil Sci. 1978. 126:269-79. DOI: 10.1097/00010694-197811000-00003 [CrossRef]
Bakr A. A., Gelhar L. W., Gutjahr A. L., MacMillan J. R. Stochastic analysis of spatial variability in subsurface flows. 1. Comparison of one- and three-dimensional flows. Water Resour. Res. 1978. 14:263-71. DOI: 10.1029/WR014i002p00263 [CrossRef]
Bear J. Dynamics of fluids in porous media. 1972. New York: American Elsevier.
Beckett P. H. T., Webster R. Soil variability: A review. Soils Fert. 1971. 34:1-15.
Biggar J. W., Nielsen D. R. Spatial variability of the leaching characteristics of a field soil. Water Resour. Res. 1976. 12:78-84. DOI: 10.1029/WR012i001p00078 [CrossRef]
Bouwer H. Rapid field measurement of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resour. Res. 1966. 2:729-38. DOI: 10.1029/WR002i004p00729 [CrossRef]
Bresler E., Dagan G. Solute dispersion in unsaturated heterogeneous soil at field scale. 2. Applications. Soil Sci. Soc. Am. J. 1979. 43:467-72. DOI: 10.2136/sssaj1979.03615995004300030009x [CrossRef]
Bresler E., Dagan G. Convective and pore scale dispersive solute transport in unsaturated heterogeneous fields. Water Resour. Res. 1981. 17:1683-93. DOI: 10.1029/WR017i006p01683 [CrossRef]
Bresler E., Dagan G. Unsaturated flow in spatially variable fields. 2. Application of water flow models to various fields. Water Resour. Res. 1983. 19:421-28. DOI: 10.1029/WR019i002p00421 [CrossRef]
Bresler E., Green R. E. Soil parameters and sampling scheme for characterizing soil hydraulic properties of a watershed 1982. p.148. Univ. Hawaii Tech. Rep
Cameron D. R. Variability of soil water retention curves and predicted hydraulic conductivities. Soil Sci. 1978. 126:364-71. DOI: 10.1097/00010694-197812000-00009 [CrossRef]
Cassel D. K. Spatial and temporal variability of soil physical properties following tillage of Norfolk loamy sand. Soil Sci. Soc. Am. J. 1983. 47:196-201. DOI: 10.2136/sssaj1983.03615995004700020004x [CrossRef]
Cressie N., Verly . Towards resistant geostatistics. NATO ASI Series, Series C, Mathematical and Physical Sciences. 1984. Dordrecht, The Netherlands: D. Reidel Publishing. In Geostatistics for natural resources characterization, I. Proceedings of the NATO Advanced Study Institute, eds. et al
Cressie N., Hawkins D. M. Robust estimation of the variogram, I. J. Int. Assoc. Math. Geol. 1980. 12:115-25. DOI: 10.1007/BF01035243 [CrossRef]
Dagan G. Stochastic modelling of groundwater flow by unconditional and conditional probabilities. 2. The solute transport. Water Resour. Res. 1982. 18:835-48. DOI: 10.1029/WR018i004p00835 [CrossRef]
Dagan G. Solute transport in heterogeneous porous formations. J. Fluid Mech. 1984. 145:151-77. DOI: 10.1017/S0022112084002858 [CrossRef]
Dagan G., Bresler E. Solute dispersion in unsaturated heterogeneous soil at field scale. I. Theory. Soil Sci. Soc. Am. J. 1979. 43:461-67. DOI: 10.2136/sssaj1979.03615995004300030008x [CrossRef]
Dagan G., Bresler E. Unsaturated flow in spatially variable fields. 1. Derivation of models of infiltration and redistribution. Water Resour. Res. 1983. 19:413-20. DOI: 10.1029/WR019i002p00413 [CrossRef]
Delfiner P., Guarasco M. Linear estimation of non-stationary spatial phenomena. Advanced geostatistics in the mining industry. 1976. Dordrecht, The Netherlands: D. Reidel Publishing. p. 49-68. DOI: 10.1007/978-94-010-1470-0_4 [CrossRef]
Delhomme J. P. Kriging in the hydrosciences. Adv. Water Resour. 1978. 1:251-66. DOI: 10.1016/0309-1708(78)90039-8 [CrossRef]
Delhomme J. P. Spatial variability and uncertainty in ground-water flow parameters: A geostatistical approach. Water Resour. Res. 1979. 15:269-80. DOI: 10.1029/WR015i002p00269 [CrossRef]
Doob J. L. Stochastic processes. 1953. New York: John Wiley.
Dowd P. A., Verly . The variogram and kriging: Robust and resistant estimators, In Geostatistics for natural resources characterization, I. Proceedings of the NATO Advanced Study Institute. NATO ASI Series, Series C, Mathematical and Physical Sciences. 1984. Dordrecht, The Netherlands: D. Reidel Publishing.
Duffy C., Wierenga P. J., Kselik R. A. Variations in infiltration rate based on soil survey information and field measurements 1981. N. M. Agric. Exp. Stn. Bull. 60
Freeze R. A. A stochastic conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media. Water Resour. Res. 1975. 11:725-41. DOI: 10.1029/WR011i005p00725 [CrossRef]
Gambolati G., Volpi G. Groundwater contour mapping in Venice by stochastic interpolators. 1. Theory. Water Resour. Res. 1979. 15:281-90. DOI: 10.1029/WR015i002p00281 [CrossRef]
Gelhar L. W. Stochastic subsurface hydrology from theory to applications. Water Resour. Res. 1986. 22:135S-45S. DOI: 10.1029/WR022i09Sp0135S [CrossRef]
Gelhar L. W., Axness C. Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 1983. 19:161-80. DOI: 10.1029/WR019i001p00161 [CrossRef]
Gelhar L. W., Gutjahr A. L., Naff R. L. Stochastic analysis of macrodispersion in a stratified aquifer. Water Resour. Res. 1979. 15:1387-97. DOI: 10.1029/WR015i006p01387 [CrossRef]
Greminger P. J., Sud Y. Y., Nielsen D. R. Spatial variability of field-measured soil-water characteristics. Soil Sci. Soc. Am. J. 1985. 49:1075-82. DOI: 10.2136/sssaj1985.03615995004900050001x [CrossRef]
Gumaa G. A. Spatial variability of in situ available water 1978. Ph.D. dissertation. Univ. of Arizona, Tucson
Haan C. T. Statistical methods in hydrology. 1977. Ames: The Iowa State University Press.
Hald A. Statistical theory with engineering applications. 1952. New York: Wiley.
Hippel K. W. Geophysical model discrimination using the Akaike Information Criterion. IEEE Trans. Autom. Control. 1981. AC-26(2):358-78. DOI: 10.1109/TAC.1981.1102597 [CrossRef]
Hoeksema R. J., Kitanidis P. K. Analysis of the spatial structure of properties of selected aquifers. Water Resour. Res. 1985. 21:563-72. DOI: 10.1029/WR021i004p00563 [CrossRef]
Jones A. J., Wagenet R. J. In situ estimation of hydraulic conductivity using simplified methods. Water Resour. Res. 1984. 20:1620-26. DOI: 10.1029/WR020i011p01620 [CrossRef]
Journel A. G., Huijbregts Ch. J. Mining geostatistics. 1978. London: Academic Press.
Jury W. A. Simulation of solute transport with a transfer function model. Water Resour. Res. 1982. 18:363-68. DOI: 10.1029/WR018i002p00363 [CrossRef]
Jury W. A. Chemical transport modeling: Current research and unresolved problems. Chemical mobility and reactivity in soil systems. 1983. Soil Sci. Soc. Am. Special Publ. II.
Jury W. A. Spatial variability of soil physical parameters insolute migration: A critical literature review 1985. EPRI Topical Rep. EA4228. Palo Alto: Electric Power Research Institute
Jury W. A., Elabd H., Collins T. J. Field scale movement of adsorbing and nonadsorbing chemicals applied to the soil surface 1983. In Proc. Symp. Characterization and Monitoring of the Vadose Zone, 203-22. Worthington, Ohio: National Water Well Assn
Jury W. A., Sposito G., White R. E. A transfer function model of solute transport through soil. 1. Fundamental concepts. Water Resour. Res. 1986. 22:243-47. DOI: 10.1029/WR022i002p00243 [CrossRef]
Jury W. A., Stolzy L. H., Shouse P. A field test of the transfer function model for predicting solute transport. Water Resour. Res. 1982. 18:369-75. DOI: 10.1029/WR018i002p00369 [CrossRef]
Keisling T. C., Davidson J. M., Weeks D. L., Morrison R. D. Precision with which selected soil physical parameters can be estimated. Soil Sci. 1977. 124:241-48. DOI: 10.1097/00010694-197710000-00008 [CrossRef]
Kendall M., Stuart A. The advanced theory of statistics. 1979. 2: London: Charles Griffin &; Co.
Kitanidis P. K. Statistical estimation of polynomial generalized covariance functions and hydrologic applications. Water Resour. Res. 1983. 19:909-21. DOI: 10.1029/WR019i004p00909 [CrossRef]
Kitanidis P. K. Minimum-variance unbiased quadratic estimation of covariances of regionalized variables. J. Int. Assoc. Math. Geol. 1985. 17:195-208. DOI: 10.1007/BF01033154 [CrossRef]
Kitanidis P. K., Lane R. W. Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss-Newton method. J. Hydrol. 1985. 79:53-71. DOI: 10.1016/0022-1694(85)90181-7 [CrossRef]
Kitanidis P. K., Vomvoris E. G. A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations. Water Resour. Res. 1983. 19:677-90. DOI: 10.1029/WR019i003p00677 [CrossRef]
Libardi P. L., Reichardt K., Nielsen D. R., Biggar J. W. Simple field methods for estimating soil hydraulic conductivity. Soil Sci. Soc. Am. J. 1980. 44:3-6. DOI: 10.2136/sssaj1980.03615995004400010001x [CrossRef]
Lumley J. L., Panofsky A. The structure of atmospheric turbulence. 1964. New York: John Wiley &; Sons.
Matheron G. The theory of regionalized variables and its applications. Cah. Cent. Morphol. Math. 1971. 5:211
Matheron G., deMarsily G. Is transport in porous media always diffusive? A counterexample. Water Resour. Res. 1980. 16:901-7. DOI: 10.1029/WR016i005p00901 [CrossRef]
Miller E. E., Miller R. D. Physical theory for capillary flow phenomena. J. Appl. Phys. 1956. 27:324-32. DOI: 10.1063/1.1722370 [CrossRef]
Miller R. J., Biggar J. W., Nielsen D. R. Chloride displacement in Panoche clay loam in relation to water movementand distribution. Water Resour. Res. 1965. 1:63-73. DOI: 10.1029/WR001i001p00063 [CrossRef]
Nielsen D. R., Biggar J. W., Erh K. T. Spatial variability of field-measured soil-water properties. Hilgardia. 1973. 42(7):215-59. DOI: 10.3733/hilg.v42n07p215 [CrossRef]
Panchev S. Random functions and turbulence. 1971. Oxford: Pergamon Press.
Richter G. Microlysimeter and field study of water and chemical movement through soil 1984. M. S. thesis. University of California, Riverside
Rogowski A. S. Watershed physics: Soil variability criteria. Water Resour. Res. 1972. 8:1015-23. DOI: 10.1029/WR008i004p01015 [CrossRef]
Rose C. W., Stern W. R., Drummand J. E. Determination of hydraulic conductivity as a function of depth and water content for soil in situ. Aust. J. Soil Res. 1965. 3:1-9. DOI: 10.1071/SR9650001 [CrossRef]
Russo D. Design of an optimal sampling network for estimating the variogram. Soil Sci. Soc. Am. J. 1984a. 48:708-16. DOI: 10.2136/sssaj1984.03615995004800040003x [CrossRef]
Russo D. A geostatistical approach to solute transport in heterogeneous fields and its applications to salinity management. Water Resour. Res. 1984b. 20:1260-70. DOI: 10.1029/WR020i009p01260 [CrossRef]
Russo D., Bresler E. Soil hydraulic properties as stochastic processes. I. An analysis of field spatial variability. Soil Sci. Soc. Am. J. 1981. 45:682-87. DOI: 10.2136/sssaj1981.03615995004500040002x [CrossRef]
Russo D., Bresler E. Soil hydraulic properties as stochastic processes. II. Errors of estimates in a heterogeneous field. Soil Sci. Soc. Am. J. 1982. 46:20-6. DOI: 10.2136/sssaj1982.03615995004600010004x [CrossRef]
Russo D., Jury W. A. A theoretical study of the estimation of the correlation scale in spatially variable fields. I. Stationary fields 1987a. Water Resour. Res. (in press)
Russo D., Jury W. A. A theoretical study of the estimation of the correlation scale in spatially variable fields. II. Nonstationary fields. Water Resour. Res. 1987b. (in press)
Schweppe F. C. Uncertain dynamic systems. 1973. Englewood Cliffs: Prentice-Hall.
Sharma M. L., Gander G. A., Hunt C. G. Spatial variability of infiltration in a watershed. J. Hydrol. 1980. 45:101-22. DOI: 10.1016/0022-1694(80)90008-6 [CrossRef]
Simmons C. S. A stochastic convective transport representation of dispersion in one-dimensional porous media systems. Water Resour. Res. 1982. 18:1193-1214. DOI: 10.1029/WR018i004p01193 [CrossRef]
Simmons C. S., Nielsen D. R., Biggar J. W. Scaling of field-measured soil-water properties. Hilgardia. 1979. 47(4):77-174. DOI: 10.3733/hilg.v47n04p075 [CrossRef]
Sisson J. B., Wierenga P. J. Spatial variability of steady state infiltration rates as a stochastic process. Soil Sci. Soc. Am. J. 1981. 45:699-704. DOI: 10.2136/sssaj1981.03615995004500040005x [CrossRef]
Smith L., Schwartz F. W. Mass transport. 1. Stochastic analysis of macrodispersion. Water Resour. Res. 1980. 16:303-13. DOI: 10.1029/WR016i002p00303 [CrossRef]
Sposito G., Jury W. A., Gupta V. K. Fundamental problems in the stochastic convection-dispersion model of solute transport in aquifers and field soils. Water Resour. Res. 1986. 22:77-88. DOI: 10.1029/WR022i001p00077 [CrossRef]
Starr J. L., de Roo H. C., Frink C. R., Parlange J. Y. Leaching characteristics of layered field soil. Soil Sci. Soc. Am. J. 1978. 42:386-91. DOI: 10.2136/sssaj1978.03615995004200030002x [CrossRef]
Van De Pol R. M., Wierenga P. J., Nielsen D. R. Solute movement in a field soil. Soil Sci. Soc. Am. J. 1977. 41:10-13. DOI: 10.2136/sssaj1977.03615995004100010008x [CrossRef]
Vieira S. R., Nielsen D. R., Biggar J. W. Spatial variability of field-measured infiltration rate. Soil Sci. Soc. Am. J. 1981. pp.1040-48. DOI: 10.2136/sssaj1981.03615995004500060007x [CrossRef]
Wagenet R. J., Nielsen D. R., Bouma J. Measurement and interpretation of spatially variable leaching processes. Proc. of Workshop of ISSS and Soil Sci. Soc. Am. 1985. Wageningen, Netherlands: Pudoc. In Soil spatial variability, eds
Wagenet R. J., Rao B. K. Description of nitrogen movement in the presence of spatially variable soil hydraulic properties. Agric. Water Manage. 1983. 6:227-43. DOI: 10.1016/0378-3774(83)90011-2 [CrossRef]
Warrick A. W., Biggar J. W., Nielsen D. R. Simultaneous solute and water transfer for an unsaturated soil. Water Resour. Res. 1971. 7:1216-25. DOI: 10.1029/WR007i005p01216 [CrossRef]
Warrick A. W., Nielsen D. R., Hillel D. Spatial variability of soil physical properties in the field. Applications of soil physics. 1980. New York: Academic Press. p. 319-44.
Wild A., Babiker I. A. The aysmmetric leaching pattern of NO3 and Cl in a loamy sand under field conditions. J. Soil Sci. 1976. 27:460-66. DOI: 10.1111/j.1365-2389.1976.tb02015.x [CrossRef]
Willardson L. S., Hurst R. L. Sample size estimates in permeability studies. J. Irrig. Drain. Div. ASCE. 1965. 91:1-9.
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