Scaling to generalize a single solution of Richards' equation for soil water redistribution

Morteza Sadeghi, Bijan Ghahraman, Kamran Davary, Seyed Majid Hasheminia, Klaus Reichardt

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Using scaling methods, a single solution of Richards' equation (RE) will suffice for numerous specific cases of water flow in unsaturated soils. In this study, a new method is developed to scale RE for the soil water redistribution process. Two similarity conditions are required: similarity in the shape of the soil water content profiles as well as of the water flux density curves. An advantage of this method is that it is not restricted to a specific soil hydraulic model - hence, all such models can be applied to RE. To evaluate the proposed method, various soil textures and initial conditions were considered. After the RE was solved numerically using the HYDRUS-1D model, the solutions were scaled. The scaled soil water content profiles were nearly invariant for medium- and fine-textured soils when the soil profile was not deeply wetted. The textural range of the soils in which the similarity conditions are held decreases as the initial conditions deal with a deeply wetted profile. Thus, the scaling performance was poor in such a condition. This limitation was more pronounced in the coarse-textured soils. Based on the scaling method, a procedure is suggested by which the solution of RE for a specific case can be used to approximate solutions for many other cases. Such a procedure reduces complicated numerical calculations and provides additional opportunities for solving the highly nonlinear RE as in the case of unsaturated water flow in soils.

Original languageEnglish (US)
Pages (from-to)582-591
Number of pages10
JournalScientia Agricola
Issue number5
StatePublished - 2011
Externally publishedYes


  • Invariant solutions
  • Nielsen-similarity
  • Spatial variability


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