### Abstract

Known integrable models for ID flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C - 1)/(C - Θ) ^{2}, where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant-concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C-1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C - 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.

Original language | English |
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Article number | W03526 |

Journal | Water Resources Research |

Volume | 46 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 1 2010 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Water Science and Technology

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## Cite this

*Water Resources Research*,

*46*(3), [W03526]. https://doi.org/10.1029/2009WR008181