The spatial variability of water and solute transport properties in unsaturated soil: II. Scaling models of water transport
AuthorsWilliam A. Jury
Authors AffiliationsWilliam A. Jury was Professor of Soil Science and Soil Physicist, Department of Soil and Environmental Sciences, University of California, Riverside; 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; Garrison Sposito was Professor of Soil Science and Soil Chemist, Department of Soil and Environmental Sciences, University of California, Riverside.
Hilgardia 55(4):33-56. DOI:10.3733/hilg.v55n04p025. July 1987.
In this paper, we examine the possibility of introducing a single stochastic scaling factor α, derived from macroscopic Miller similitude, to describe the spatial variability of soil hydraulic properties. Most of the information available allowed only a conventional statistical analysis of the scaling factors derived from different soil properties. The field studies of (Nielsen, Biggar, and Erh (1973)) and (Russo and Bresler (1981)) were suitable also for more detailed structural analyses. Results of these analyses suggested that the spatial structure of the α-set derived from the hydraulic conductivity function K(?) is different from that of the α-set derived from the water retentivity function h(?), reflecting the different spatial structures of the K(?) and the h(?) functions. Consequently, the statistical relationship between the uncorrelated residuals of the two α-sets was rather weak. For the Hamra field of (Russo and Bresler (1981)), the use of relative hydraulic properties to estimate the scaling factor sets considerably improved the correlation between the α-sets, which had essentially the same spatial structure but slightly different variances.
In this study, where the soil hydraulic properties are assumed to be described by the model of (Brooks and Corey (1964)), analytical expressions for the variances of the two different α-sets indicated that (1) both α-sets are dependent on the range of water saturation that is used to estimate them, (2) the correlation between the two sets will improve in media with a wide pore-size distribution, and (3) the two sets will be identical if and only if the relative hydraulic conductivity function Kr(hr) is described by a deterministic function, Kr(hr) = hr-2. This result suggested that, in general, a second scaling factor for Kr is required for media that are not characterized by this single deterministic relationship.
A more general Kr(hr) relation, defined by Kr = hr-?;, was introduced using ?; as a second stochastic variable. In this representation, the α scaling factor for Kr is defined by Kr/Kr* = α?; instead of α2 as in macroscopic Miller similitude. For the Hamra field, the resultant new α-set was identical to the α-set derived from the relative retentivity function. For the Panoche field, using the values of ?; to estimate the scaling factor from the relative hydraulic conductivity function considerably improved the correlation and the similarity between the two α-sets, but did not render them identical. The results of our analysis suggest that, for transient water flow, describing the spatial variability of K(?) and h(?) requires at least three stochastic variates: Ks, α, and ?;.
Aitcheson J., Brown J. A. C. The lognormal distribution. 1976. Cambridge, England: Cambridge University Press.
Averjanov S. F. About permeability of subsurface soils in case of incomplete saturation. Eng. Collect. 1950. p.7.
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. 1983a. 19:421-28.
Bresler E., Dagan G. Unsaturated flow in spatially variable fields. 3. Solute transport models and their application to two fields. Water Resour. Res. 1983b. 19:429-35. DOI: 10.1029/WR019i002p00429 [CrossRef]
Bresler E., Russo D., Miller R. D. Rapid estimate of unsaturated hydraulic conductivity function. Soil Sci. Soc. Am. J. 1978. 42:170-72. DOI: 10.2136/sssaj1978.03615995004200010038x [CrossRef]
Brooks R. H., Corey A. T. Hydraulic properties of porous media. Colo. State Univ. Fort Collins Hydrol. Pap. 1964. p.3.
Burdine N. T. Relative permeability calculation from size distribution data. Trans. Am. Inst. Min. Eng. 1953. 198:71-78.
Childs E. C., Collis-George N. The permeability of porous materials. Proc. R. Soc. London Ser. A. 1950. 201:392-405. DOI: 10.1098/rspa.1950.0068 [CrossRef]
Dagan G., Bresler E. Solute dispersion in unsaturated heterogeneous soil at field scale. 1. 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]
Elrick D. E., Sandrett J. H., Miller E. E. Tests of capillary flow scaling. Soil Sci. Soc. Am. J. 1959. 23:329-32. DOI: 10.2136/sssaj1959.03615995002300050008x [CrossRef]
Hald A. Statistical theory with engineering applications. 1952. New York: Wiley.
Huff D. D., Luxmoore R. J., Mankin J. B., Begovich C. L. TEHM: A terrestrial ecosystem hydrology model. 1976. Rep. ORNL/NSF/EATC-27, Oak Ridge, Tennessee: Oak Ridge Nat. Lab
Jury W. A. Spatial variability of soil physical parameters in solute migration: A critical literature review. EPRI Topical Rep. 1985. Palo Alto: Electric Power Research Institute. EA4228
Jury W. A., Russo D., Sposito G., Elabd H. The spatial variability of water and solute transport properties in unsaturated soil. I. Analysis of property variation and spatial structure with statistical models. Hilgardia. 1987. 55(4): (this issue) DOI: 10.3733/hilg.v55n04p056 [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]
Klute A., Wilkinson G. E. Some tests of the similar media concept of capillary flow. I. Reduced capillary conductivity and moisture characteristic data. Soil Sci. Soc. Am. Proc. 1958. 22:278-81. DOI: 10.2136/sssaj1958.03615995002200040002x [CrossRef]
Luxmoore R. J., Sharma M. L. Runoff response to soil heterogeneity: Experimental and simulation comparisons for two contrasting watersheds. Water Resour. Res. 1980. 16:675-84. DOI: 10.1029/WR016i004p00675 [CrossRef]
Miller E. E., Hillel D. Similitude and scaling of soil water phenomena. Applications of soil physics. 1980. New York: Academic Press. p. 300-318.
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]
Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 1976. 12:513-22. DOI: 10.1029/WR012i003p00513 [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]
Peck A. J., Luxmoore R. J., Stolzy L. J. Effects of spatial variability of soil hydraulic properties in water budget modeling. Water Resour. Res. 1977. 13:348-54. DOI: 10.1029/WR013i002p00348 [CrossRef]
Philip J. R. The theory of infiltration. Adv. Hydrosci. 1969. 5:215-90. DOI: 10.1016/B978-1-4831-9936-8.50010-6 [CrossRef]
Rao P. S. C., Jessup R. E., Hornsby A. C., Cassel D. K., Pollans W. A. Scaling soil microhydrologic properties of Lakeland and Konowa soils using similar media concepts. Agric. Water Manage. 1983. 6:277-90. DOI: 10.1016/0378-3774(83)90015-X [CrossRef]
Reichardt K., Libardi P. L., Nielsen D. R. Unsaturated hydraulic conductivity determination by a scaling technique. Soil Sci. 1975. 120:165-68. DOI: 10.1097/00010694-197509000-00001 [CrossRef]
Reichardt K., Nielsen D. R., Biggar J. W. Scaling of horizontal infiltration into homogeneous soils. Soil Sci. Soc. Am. J. 1972. 36:241-45. DOI: 10.2136/sssaj1972.03615995003600020014x [CrossRef]
Russo D., Bresler E. Scaling soil hydraulic properties of a heterogeneous field. Soil Sci. Soc. Am. J. 1980. 44:681-83. DOI: 10.2136/sssaj1980.03615995004400040003x [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. A univariate versus a multivariate parameter distribution in a stochastic-conceptual analysis of unsaturated flow. Water Resour. Res. 1982. 18:483-88. DOI: 10.1029/WR018i003p00483 [CrossRef]
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., 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]
Sposito G., Jury W. A. Inspectional analysis in the theory of water flow through unsaturated soil. Soil Sci. Soc. Am. J. 1985. 49:791-98. DOI: 10.2136/sssaj1985.03615995004900040001x [CrossRef]
Tillotson P., Nielsen D. R. Scale factors in soil science. Soil Sci. Soc. Am. J. 1984. 48:953-59. DOI: 10.2136/sssaj1984.03615995004800050001x [CrossRef]
Warrick A. W., Amoozegar-Fard A. Infiltration and drainage calculations using spatially scaled hydraulic properties. Water Resour. Res. 1980. 15:1116-20. DOI: 10.1029/WR015i005p01116 [CrossRef]
Warrick A. W., Mullen G. J., Nielsen D. R. Scaling field measured soil hydraulic properties using a similar media concept. Water Resour. Res. 1977. 13:355-62. DOI: 10.1029/WR013i002p00355 [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. 319-344.
Wilkinson G. E., Klute A. Some tests of the similar media concept of capillary flow. II. Flow systems data. Soil Sci. Soc. Am. J. 1959. 23:434-37. DOI: 10.2136/sssaj1959.03615995002300060021x [CrossRef]
Youngs E. G., Price R. I. Scaling of infiltration behavior in dissimilar porous media. Water Resour. Res. 1981. 17:1065-70. DOI: 10.1029/WR017i004p01065 [CrossRef]
Also in this issue:The spatial variability of water and solute transport properties in unsaturated soil: I. Analysis of property variation and spatial structure with statistical models
Research collaboration best defense against Pierce's disease
Scientists, state aggressively pursue Pierce's disease
How to distinguish glassy-winged sharpshooter from its “look-a-likes”
Proximity to citrus influences Pierce's disease in Temecula Valley vineyards
Egg-laying and brochosome production observed in glassy-winged sharpshooter
Insecticides sought to control adult glassy-winged sharpshooter
New closterovirus in ‘Redglobe’ grape causes decline of grafted plants
Survey identifies sediment sources in North Coast rangelands
Alfalfa water use pinpointed in saline, shallow water tables of Imperial Valley
Sudangrass uses water at rates similar to alfalfa, depending on location