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DIVISION S-1—SOIL PHYSICS

Predicting Temperature and Heat Flow in a Sandy Soil by Electrical Modeling

^a CONICET, Dep. de Hidráulica, Facultad de Ingeniería, UNLP, La Plata, Argentina
^b CONICET, Lab. de Oceanografía Costera, Facultad de Ciencias Naturales y Museo, UNLP, Casilla de Correo 45, (1900) La Plata, Argentina
^c CNR, Istituto per lo Studio della Dinamica delle Grandi Masse, Venezia, Italia

* Corresponding author (dguaragl{at}volta.ing.unlp.edu.ar)

A model based on an electrical analogy between a soil column and an electrical transmission line was developed to predict temperature and heat flow as functions of depth and time in a sandy soil, taking into account changes in soil thermal conductivity and volumetric heat capacity due to variations in water content. The model was excited alternatively by both measured soil temperature at the 1-cm depth and solar radiation [S_r(t)], and solved with available electrical analysis software. The results were compared with field data collected during a 35-d field experiment carried out in the Lido beach, Venice, Italy. A very simple transfer function was identified for using measured S_r(t) as the input signal. This transfer function turned out to vary inversely with S_r(t). When the model is excited by temperature, and soil water content corrected every 5 d, the root mean square error (RMSE) for the calculated temperature at the 5-cm depth is less than 1°C. When it is excited by S_r(t), the RMSE at the 1-cm depth is less than 2°C. Hourly temperatures at different depths were found to depend strongly on surface phenomena, and to a lesser extent on other factors like soil water content below the top layers.

Abbreviations: c, specific heat (J kg^-1 °C^-1) • C_e, electrical capacitance (F) • C_t, heat capacity per unit area of a soil layer (J °C^-1 m^-2) • f, frequency (Hz) • G, electrical conductance (^-1) • G_T(t), function equivalent to an electrical conductance (W m^-2 °C^-1) • I₁(t), heat flow at the surface and within the top centimeter of soil (W m^-2) • I₂(t), heat flow transmitted below the 1-cm depth (W m^-2) • L, electrical inductance (H) • R-C, ladder of resistances and capacitances for modeling soil below the 1-cm depth • r, correlation coefficient • R_e, electrical resistance () • R_t, thermal resistance per unit area of a soil layer (°C m² W^-1) • R_T(t), time dependent transfer function for the surface and top centimeter of soil (W^-1 m² °C) • RMSE, root mean square error • S_r(t), solar radiation (W m^-2) • t, time (s) • T₁(t), soil temperature at depth of 1 cm (°C) • Z, electrical impedance () • T, temperature difference across a soil layer (°C) • z, thickness of a surface-parallel soil layer (m) • , soil water content (m³ m^-3) • , thermal diffusivity (m² s^-1) • , thermal conductivity (W m^-1 °C^-1) • , density (kg m^-3) • c, volumetric heat capacity (J m^-3 °C^-1) • , heat flux density (W m^-2)