Saturday, 15 July 2006
137-13

General Theoretical Framework for Estimating Soil Water Retention from Textural Data.

John R. Nimmo1, William N. Herkelrath1, and Ana M. Laguna Luna2. (1) US Geological Survey, 345 Middlefield Rd., Mail Stop 421, Menlo Park, CA 94025, (2) Univ of Córdoba, Dept of Applied Physics, Córdoba, 14080, Spain

Models used to estimate soil water retention from more easily measured textural data can be derived from a single basic framework. Although most of the models are based on particular geometric relationships between pore and particle shapes and dimensions, the only necessary starting point is the assumption that every particle has a characteristic dimension R associated uniquely with a matric pressure ψ. The ψ(R) function is the defining characteristic of possible specific models. Substituting the inverted function R(ψ) into the mass-based cumulative particle-size distribution, and multiplying by the porosity, gives θ(ψ). Specific models can be derived from the general model by specifying geometric relationships of the pores and particles. We illustrate three examples with the familiar but not essential assumptions that particles are spheres with radius R, that pores are cylinders with volume equal to the associated particle volume times the void ratio, and that the inverse proportionality between capillary radius and matric pressure is valid: (1) A fixed pore shape for a given soil, with cylinder length proportional to cylinder radius (Mualem, 1976). (2) Pores of uniform length, with cylinder radius equal to the value that gives the correct cylinder volume (Arya and Dierolf, 1992). (3) Cylinder radius specified by a formula involving an exponential relation that includes a parameter value determined empirically from a database of relevant properties for a variety of soils (Arya and Paris, 1981). Whereas derivation of the fixed-pore-shape and fixed-pore-length models is straightforward, the Arya-Paris model presents complications stemming from the limitations that its output depends on the size of finite intervals used in calculation (Haverkamp and Parlange, 1982), and that its specified particle-pore size relationship depends on the particle size distribution itself. Formulating this model within the general framework serves to highlight the nature of these limitations and, with additional assumptions, to produce a near-equivalent of the Arya-Paris model without these limitations. The resulting model produces results consistent with the large number of Arya-Paris model calculations of the past, but using a formula that is a continuous function. The new model eliminates dependence on interval size, is calculable by directly applying an algebraic formula rather than manipulating tables of data and intermediate results, and easily combines with other models (for example incorporating structural effects) that are formulated on a continuous basis. The generalized framework is valuable for highlighting the differences and similarities among the specific models. This framework facilitates modifications or development of new, possibly superior models which may or may not rely on sphere/cylinder geometry or capillary theory. This approach also clarifies relationships among models, for example that the fixed-pore-shape model is a special case of the Arya-Paris model, and that the Arya-Dierolf model with a suitable choice for the universal pore length is essentially equivalent to the Arya-Paris model. References: (1) Arya, L.M., and T.S. Dierolf. 1992. Predicting soil moisture characteristics from particle-size distributions--An improved method to calculate pore radii from particle radii. In M. T. van Genuchten, et al. (eds.) Indirect methods for estimating the hydraulic properties of unsaturated soils. University of California, Riverside, CA. P. 115-124. (2) Arya, L.M., and J.F. Paris. 1981. A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data. Soil Science Society of America Journal 45(6):1023-1030. (3)Haverkamp, R., and J.Y. Parlange. 1982. Comments on "A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data". Soil Science Society of America Journal 46(6):1348. (4)Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12(3):513-522.

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