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This article in SSSAJ

  1. Vol. 76 No. 6, p. 1978-1986
     
    Received: Jan 13, 2012
    Published: October 5, 2012


    * Corresponding author(s): rhorton@iastate.edu
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doi:10.2136/sssaj2012.0023N

An Analytical Solution to the One-Dimensional Heat Conduction–Convection Equation in Soil

  1. Linlin Wanga,
  2. Zhiqiu Gaob,
  3. Robert Horton *c,
  4. Donald H. Lenschowd,
  5. Kai Menge and
  6. Dan B. Jaynesf
  1. a State Key Lab. of Atmospheric Boundary Layer Physics and Atmospheric Chemistry Institute of Atmospheric Physics Chinese Academy of Sciences Beijing, China
    b State Key Lab. of Atmospheric Boundary Layer Physics and Atmospheric Chemistry Institute of Atmospheric Physics Chinese Academy of Sciences Beijing, China and Jiangsu Key Lab. of Agric.Meteorology School of Applied Meteorology Nanjing Univ. of Information Sciend and Technology Nanjing, China
    c Dep. of Agronomy Iowa State Univ. Ames, IA 50011
    d National Center for Atmospheric Research Boulder CO 80307-3000
    e Hebei Provincial Meteorological Observatory Hebei, China
    f USDA-ARS National Lab. of Agriculture and Environment Ames, IA 50011-3120

Abstract

Soil heat transfer occurs by conduction and convection. Soil temperatures below infiltrating water can provide a signal for water flux. In earlier work, analysis of field measurements with a sine wave model indicated that convection heat transfer made significant contributions to the subsurface temperature oscillations. In this work, we used a Fourier series to describe soil surface temperature variations with time. The conduction and convection heat transfer equation with a multi-sinusoidal wave boundary condition was solved analytically using a Fourier transformation. Soil temperature values calculated by the single sine wave model and by the Fourier series model were compared with field soil temperature values measured at depths of 0.1 and 0.3 m below an infiltrating ponded surface. The Fourier series model provided better estimates of observed field temperatures than the sine wave model. The new model provides a general way to describe soil temperature under an infiltrating water source.

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Copyright © 2012. Copyright © by the Soil Science Society of America, Inc.