Root-Water Uptake Model at Heterogeneous Soil Fields
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Volume 10, Issue 2
Abstract
A new stochastic model for one-dimensional root-water uptake is developed with main emphasis on its probabilistic structure from random variations in saturated hydraulic conductivity. The resulting model has the form of a two-dimensional Fokker-Planck equation, and its applicability as a model for the probabilistic evolution of the nonlinear stochastic root-water uptake process is explored with the saturated hydraulic conductivity taken as stochastic random field. In order to perform this exploration, the generalization of a one-dimensional numerical scheme for the numerical solution of a two-dimensional Fokker-Planck equation is attempted. The proposed model has the advantage of providing a probabilistic solution to soil-water flow under root-water uptake, from which one can obtain the ensemble average behavior of the soil-water system at the scale of a heterogeneous field soil.
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References
Allen, R. G., Pereira, L. S., Raes, D., and Smith, M. (1998). “Crop evapotranspiration—guidelines for computing crop water requirements.” FAO Irrigation and Drainage Paper No. 56, Food and Agriculture Organization of the United Nations, Rome.
Chang, J. S., and Cooper, G. (1970). “A practical difference scheme for Fokker-Planck equations.” J. Comput. Phys., 6, 1–16.
Chen, Z.-Q., Govindaraju, R. S., and Kavvas, M. L. (1994). “Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Development of models.” Water Resour. Res., 30, 523–533.
Clausnitzer, V., and Hopmans, J. W. (1994). “Simultaneous modeling of transient three-dimensional root growth and soil water flow.” Plant Soil, 164, 299–314.
Dunne, T. (1978). “Field studies of hillslope flow processes.” Hillslope hydrology, M. J. Kirkby, ed., Wiley-Interscience, New York, 227–293.
Feddes, R. A., Kowalik, P., Malinka, K. K., and Zarandy, H. (1976). “Simulation of field water uptake by plants using a soil water dependent root extraction function.” J. Hydrol., 31, 13–26.
Govindaraju, R. S., Morbidelli, R., and Corradini, C. (2001). “Areal infiltration modeling over soils with spatially correlated hydraulic conductivities.” J. Hydrologic Eng., 6(2), 150–158.
Grayson, R. B., Bloschl, G., and Moore, I. D. (1995). “Distributed parameter hydrologic modeling using vector elevation data: Thales and TAPES-C.” Computer models of watershed hydrology, V. P. Singh, ed., Water Resources Publications, Highlands Ranch, Colo, 669–695.
Kavvas, M. L. (2003). “Nonlinear hydrologic processes: Conservation equations for determining their means and probability distributions” J. Hydrologic Eng., 8(2), 44–53.
Kavvas, M. L., and Karakas, A. (1996). “On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers.” J. Hydrol., 179, 321–351.
Kim, S., Kavvas, M. L., and Yoon, J. (2005). “Upscaling of vertical unsaturated flow model under infiltration condition.” J. Hydrologic Eng., 10(2), 151–159.
Kubo, R. (1963). “Stochastic Liouville equations.” J. Math. Phys., 4, 174–183.
Lai, C. T., and Katul, G. (2000). “The dynamic role of root-water uptake in coupling potential to actual transpiration.” Adv. Water Resour., 23, 427–439.
Noilhan, J., and Planton, S. (1989). “A simple parameterization of land processes for meteorological models.” Mon. Weather Rev., 117, 536–549.
Ogata, G., Richards, L. A., and Gardner, W. R. (1959). “Transpiration of alfalfa determined from soil water content changes.” Soil Sci., 89, 179–182.
Perrochet, P. (1987). “Water uptake by plant roots—a simulation model, I. Conceptual model.” J. Hydrol., 95, 55–61.
Philip, J. R. (1957). “The physical principles of soil water movement during the irrigation cycle.” Proc., 3rd Congress, Int. Comm. Irrig. Drain., Quest. 8, 8.125–8.154.
Somma, F., Hopmans, J. W., and Clausnitzer, V. (1998). “Transient three-dimensional modeling of soil water and solute transport with simultaneous root growth, root water and nutrient uptake.” Plant Soil, 202, 281–293.
Stephenson, G. R., and Freeze, R. A. (1974). “Mathematical simulation of subsurface flow contributions to snowmelt and runoff, Reynolds Ck., Watershed, Idaho.” Water Resour. Res., 10, 284–294.
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Published In
Journal of Hydrologic Engineering
Volume 10 • Issue 2 • March 2005
Pages: 160 - 167
Copyright
© 2005 ASCE.
History
Received: Nov 7, 2003
Accepted: Jun 3, 2004
Published online: Mar 1, 2005
Published in print: Mar 2005
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