A new stochastic model for one-dimensional evaporated soil water flow is proposed with major focus on its probabilistic structure. The newly developed model has the form of the Fokker-Planck equation, and its validity as a model for the probabilistic evolution of the nonlinear stochastic unsaturated flow process is investigated under a stochastic soil-related parameter (i.e., saturated hydraulic conductivity). This model is based on a parabolic type of stochastic partial differential equation, and has the advantage of providing the probabilistic solution in the form of a probability distribution function, from which one can obtain the ensemble average behavior of the flow system. The comparison results with Monte Carlo simulations show that the proposed model can reproduce well the vertically varying soil water wetting front depth. Overall, the ensemble averaging approach using the cumulant expansion method shows good promise for the stochastic modeling of nonlinear hydrologic processes.
cumulant expansion evaporation soil water upscale
This is a preview of subscription content, log in to check access.
Brooks, R.H. and Corey A.T. (1964). Hydraulic Properties of Porous. Media. Hydrol. Pap. 3, 27 pp., Colorado State University, Fort Collins.Google Scholar
Chang, J.S. and Cooper G. (1970). “A practical difference scheme for Fokker-Planck equations”.Journal Computational Physics, Vol. 6, pp. 1–16.MATHCrossRefGoogle Scholar
Chen, Z.-Q., Govindraju, R.S., and Kavvas, M.L. (1994a). “Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Development of medels.”Water Resources Research, Vol. 30, pp. 523–533.CrossRefGoogle Scholar
Chen, Z-Q., Govindraju, R.S., and Kavvas, M.L. (1994b). “Spatial averageing of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Numerical simulations”.Water Resources Research, Vol. 30, pp. 535–548.CrossRefGoogle Scholar
Green, W.H. and Ampt, G.A. (1911). “Studies on soil physics”.Journal Agricultural Science, Vol. 4, pp. 1–24.CrossRefGoogle Scholar
Dagan, G. and Bresler, E. (1983). “Unsaturated flow in spatially variable fields, 1, derivation of models of infiltration and redistribution”.Water Resources Research, Vol. 19, pp. 413–420.CrossRefGoogle Scholar
Kavvas, M.L. (2003). “Nonlinear hydrologic processes: conservation equations for their ensemble averages and probability distributions”.Journal of Hydrologic Engineering, Vol. 8, pp. 44–53.CrossRefGoogle Scholar
Kavvas, M.L. and Karakas, A. (1996). “On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers”.Journal of Hydrologic Engineering, Vol. 179, pp. 321–351.Google Scholar
Kim, S., Jang, S.H., Yoon, Y.N. and Yoon, J. (2004). “Probabilistic solution to infiltrated flow equation”. KSCEJournal of Civil Engineering, Vol. 8, pp. 651–662.Google Scholar