Standard Article

77 Inverse Modeling of Soil Hydraulic Properties

Part 6. Soils

  1. Jasper A Vrugt1,2,
  2. Jacob H Dane3

Published Online: 15 APR 2006

DOI: 10.1002/0470848944.hsa079

Encyclopedia of Hydrological Sciences

Encyclopedia of Hydrological Sciences

How to Cite

Vrugt, J. A. and Dane, J. H. 2006. Inverse Modeling of Soil Hydraulic Properties. Encyclopedia of Hydrological Sciences. 6:77.

Author Information

  1. 1

    Institute for Biodiversity and Ecosystem Dynamics – Physical Geography, University of Amsterdam, Amsterdam, The Netherlands

  2. 2

    Earth and Environmental Sciences Division, Los Alamos National Laboratory, Alamos, NM, US

  3. 3

    Auburn University, Department of Agronomy and Soils, Auburn, AL, US

Publication History

  1. Published Online: 15 APR 2006


Numerical-simulation models of water flow and solute transport in the vadose zone are important tools in environmental research. The accuracy of predictions with these models heavily relies on accurate estimates of the unsaturated soil hydraulic parameters. Initial attempts on the estimation of the soil hydraulic parameters mainly focused on the use of relatively simple static or steady-state flow experiments. While these laboratory methods have the advantage of being relatively simple to implement, they are typically time consuming and require restrictive initial and boundary conditions to satisfy the assumptions of the corresponding analytical solutions. Significant advances in computational capabilities in the 1980s have stimulated research on the use of Inverse Modelling (IM) for the estimation of soil hydraulic properties. Parameter estimation using IM accommodates much more flexible experimental conditions than required for the static or steady-state flow methods, thereby enabling a rapid characterization of the hydraulic properties of the considered soil domain. This article explores the historical development of current perspectives on the identification of a single “best” set of soil hydraulic parameters using IM (thereby effectively neglecting the influence of possible sources of uncertainty on the final parameter estimates), and discusses alternative (Bayesian and multiple-criteria) parameter estimation strategies which can be used to quantify the uncertainty (probabilistic and multiobjective) associated with the inversely estimated soil hydraulic properties. Throughout this article, we use a classical transient laboratory outflow experiment to further illustrate the various aspects of the IM procedure for estimating the soil hydraulic parameters.


  • vadose zone;
  • unsaturated water flow;
  • Richards' equation;
  • soil hydraulic properties;
  • global optimization;
  • Markov Chain Monte Carlo;
  • parameter uncertainty;
  • Bayesian