Analytical Model to Predict Annual Soil Surface Temperature Variation

Abstract

An analytical model is developed to predict the annual variation of soil surface temperature from readily available weather data and soil thermal properties. The time variation is approximated by a first harmonic function characterized by an average, an amplitude, and a phase lag. A parametric analysis is presented to determine the effect of various factors such as evaporation, soil absorptivity, and soil convective properties on soil surface temperature. A comparison of the model predictions with experimental data is presented. The comparative analysis indicates that the simplified model predicts soil surface temperatures within ten percent of measured data for five locations.

Undisturbed Ground Temperature—Different Methods of Determination

“…The ambient temperature T a , the temperature of the surface of the ground T s , and the solar radiation flux absorbed by the ground S change periodically in the yearly cycle, according to the following dependencies [12,13]:…”

“…where A = 0.0168 K/Pa [13]. The p i quantity is the saturated vapour pressure at a temperature of the surface of the ground (=P sat,s ), and p = RH·P sat,a .…”

“…It is assumed in the approximate calculations that the average long-wave radiation flux amounts to 63 W/m 2 (in the direction from the surface of the ground) [13,24].…”

“…The heat flux resulting from an algebraic summation of the listed fluxes qcond is transported into the ground (mainly by conduction) or in the opposite direction, depending on its minus/plus sign. The heat balance on the surface of the ground taking into account convection, radiation, and moisture evaporation has the following form [13][14][15][16][17][18][19][20][21]:…”

“…The saturated vapour pressure is a non-linear function of temperature. In paper [13], a linear form of this relation was adopted: P sat = a 1 T + b 1 . Therefore:…”