Determining Near-Surface Soil Heat Flux Density Using the Gradient Method: A Thermal Conductivity Model–Based Approach

Abstract

<p>In the gradient method, soil heat flux density at a known depth <em>G</em> is determined as the product of soil thermal conductivity <em>λ</em> and temperature <em>T</em> gradient. While measuring <em>λ</em> in situ is difficult, many field studies readily support continuous, long-term monitoring of soil <em>T</em> and water content <em>θ</em> in the vadose zone. In this study, the performance of the gradient method is evaluated for estimating near-surface <em>G</em> using modeled <em>λ</em> and measured <em>T</em>. Hourly <em>λ</em> was estimated using a model that related <em>λ</em> to <em>θ</em>, soil bulk density <em>ρ</em>_<em>b</em>, and texture at 2-, 6-, and 10-cm depths. Soil heat flux <em>G</em>_<em>m</em> was estimated from modeled <em>λ</em> and measured <em>T</em> gradient (from thermocouples). The <em>G</em>_<em>m</em> results were evaluated with heat flux data <em>G</em>_HP determined using independent measured <em>λ</em> and <em>T</em> gradient from heat-pulse probes. The <em>λ</em> model performed well at the three depths with 3.3%–7.4% errors. The <em>G</em>_<em>m</em> estimates were similar to <em>G</em>_HP (agreed to within 15.1%), with the poorest agreement at the 2-cm soil depth, which was caused mainly by the relatively greater variability in <em>ρ</em>_<em>b</em>. Accounting for temporal variations in <em>ρ</em>_<em>b</em> (with core method) improved the accuracies of <em>λ</em> and <em>G</em>_<em>m</em> at the 2-cm depth. Automated <em>θ</em> monitoring approaches (e.g., time domain reflectometry), rather than gravimetric sampling, captured the temporal dynamics of near-surface <em>λ</em> and <em>G</em> well. It is concluded that with continuous <em>θ</em> and <em>T</em> measurements, the <em>λ</em> model–based gradient method can provide reliable near-surface <em>G</em>. Under conditions of soil disturbance or deformation, including temporally variable <em>ρ</em>_<em>b</em>, data improves the accuracy of <em>G</em> data.</p>