Sensitivity of the Dual-Probe Heat-Pulse Method to Spatial Variations in Heat Capacity and Water Content
2007
Knight, John H. | Jin, Wei | Kluitenberg, Gerard J.
Dual-probe heat-pulse (DPHP) sensors are useful for measuring soil heat capacity (C) and water content (θ), yet little is known about their effective measurement volume. We have adapted previous work on well testing to investigate the spatial sensitivity of the DPHP method for measuring both C and θ. Spatial sensitivity functions were derived by using a perturbation expansion approach in which C and θ vary with position, but differ only slightly from their uniform values C ₀ and θ₀, respectively. Because the dimensionless forms of these spatial sensitivity functions are identical, the spatial sensitivity of the DPHP method is the same for both C and θ measurements. The spatial sensitivity function is not radially symmetric about the heater probe. Instead, the locations of the temperature and heater probes are of equal importance in defining the spatial sensitivity. The spatial sensitivity is greatest in small areas immediately outside of the heater and temperature probes. Far from the sensor, contours of equal spatial sensitivity approach the shapes of a family of ellipses. For a sensor with a probe spacing of 6 mm, the boundary containing 99% of the total spatial sensitivity is closely approximated by an ellipse with area 168 mm² and a major axis 15.6 mm in length. The spatial sensitivity for C is unaffected by the magnitude of the soil thermal properties near the sensor, as long as the thermal properties are uniform. Likewise, for θ measurements, the spatial sensitivity is independent of the value of θ near the sensor, as long as θ is uniform.
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