Research Project: MANAGING AGRICULTURAL WATER QUALITY IN FIELDS AND WATERSHEDS: NEW PRACTICES AND TECHNOLOGIES

Location: Agroecosystems Management Research

Title: An analytical solution to the one-dimensional heat conduction-convection equation in soil

Author
 Wang, Linlin Zhiqiu, Gao Horton, Robert Lenschow, Donald Meng, Kai Jaynes, Dan Shao, Mingan

 Submitted to: Soil Science Society of America Journal Publication Type: Peer Reviewed Journal Publication Acceptance Date: 7/24/2012 Publication Date: 10/5/2012 Publication URL: http://handle.nal.usda.gov/10113/56437 Citation: Wang, L., Zhiqiu, G., Horton, R., Lenschow, D.H., Meng, K., Jaynes, D.B., Shao, M. 2012. An analytical solution to the one-dimensional heat conduction-convection equation in soil. Soil Science Society of America Journal. 76:1978-1986. DOI:10.2136/sssaj2012.0023N. Interpretive Summary: Infiltration of water from canals, streams, flood-irrigated fields, and recharge basins can be affected by daily temperature fluctuations. These fluctuations can significantly affect delivery rates of water in canals and streams and affect infiltration measurements in flood irrigated fields. This study developed a set of mathematical equations describing the temperature dependence of water infiltration rates and heat loss to soils. The equations were solved analytically and the solution was tested successsfully against field measurements of daily infiltration rates and soil profile temperatures. With the development of this solution, this research is important to scientists and water managers who will be able to make more accurate water and heat loss calculations for flood-irrigated fields and recharge basins. Technical Abstract: Heat transfer in soil occurs by conduction and convection. Infiltrating water affects soil temperature distributions, and measuring soil temperature distributions below infiltrating water can provide a signal for the flux of water. In earlier work a sine wave function (hereinafter referred to as the sine wave model) for diurnal soil water infiltration and diurnal soil surface temperature variations was used to evaluate the impact of conductive and convective heat transfer processes on subsoil temperature variations with depth and time. A previous analysis of field measurements with the sine wave model indicated that convection heat transfer made significant contributions to the subsurface temperature oscillations. In this work we improve the sine wave model by using 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 is solved analytically using a Fourier transformation. Soil temperature values calculated by the single sine wave model and by the Fourier series model are compared with field soil temperature values measured at depths of 0.1 m and 0.3 m below an infiltrating ponded surface during a 5-day period of typical Arizona springtime conditions. The Fourier series model provides better estimates of observed field temperatures than does the sine wave model. The new model provides a general way to describe soil temperature under an infiltrating water source.