Exact Solutions of the Richards Equation With Nonlinear Plant-Root Extraction

Philip Broadbridge, Edoardo Daly, Joanna Goard

Research output: Contribution to journalArticleResearchpeer-review

47 Citations (Scopus)


The Richards equation, commonly used to model water flow in unsaturated soils, is highly nonlinear, thus making it very challenging to solve analytically for situations meaningful in practical applications. The inclusion of realistic forms of root-water uptake rates in this equation adds complications in deriving exact solutions. This study provides for the first time analytical solutions of the Richards equation with a sink term nonlinearly dependent on soil water content. These solutions are applied to irrigation furrows, using Cartesian coordinates, and irrigation from a circular plate, in cylindrical coordinates.

Original languageEnglish
Pages (from-to)9679-9691
Number of pages13
JournalWater Resources Research
Issue number11
Publication statusPublished - 1 Nov 2017


  • exact solutions
  • nonlinear model
  • plant root extraction
  • Richards equation

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