Advertisement

KSCE Journal of Civil Engineering

, Volume 10, Issue 1, pp 59–65 | Cite as

Probabilistic solution to soil water evaporated flow equation

  • Sangdan Kim
Water Engineering

Abstract

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.

Keywords

cumulant expansion evaporation soil water upscale 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. 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
  3. 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
  4. 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
  5. Green, W.H. and Ampt, G.A. (1911). “Studies on soil physics”.Journal Agricultural Science, Vol. 4, pp. 1–24.CrossRefGoogle Scholar
  6. 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
  7. 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
  8. 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
  9. 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
  10. Kubo, R. (1963). “Stochastic liouville equations”.Journal Mathematical Physics, Vol. 4, pp. 174–183.MATHCrossRefMathSciNetGoogle Scholar
  11. Mein, R.G. and Larson, C.L. (1973). “Modeling infiltration during a steady rain”.Water Resources Research, Vol. 9, pp. 384–394.CrossRefGoogle Scholar
  12. Van Kampen, N.G. (1981).Stochastic Processes in Physics and Chemistry, Elsevier North-Holland, Amsterdam, Netherland.MATHGoogle Scholar
  13. Yoon, J. and Kavvas, M.L. (2004). “Probabilistic solution to stochastic overland flow equation”.Journal Hydrologic Engineering, Vol 8, pp. 54–63.CrossRefGoogle Scholar

Copyright information

© KSCE and Springer jointly 2006

Authors and Affiliations

  • Sangdan Kim
    • 1
  1. 1.Department of Environmental System EngineeringPukyong National UniversityBusanKorea

Personalised recommendations