The Spatial Sensitivity of Heat Pulse Methods for Measuring Soil Water Fluxes.

The heat pulse method for measuring soil water flux uses a short pulse of heat emitted by a thin wire transverse to the flow. Temperature signals are measured by detectors upstream and downstream of the emitter and compared to the source signal. Analytical solutions for a medium with spatially uniform thermal properties and soil water velocity are used to infer the velocity from either differences or ratios between upstream and downstream measured temperatures. It is important to know what is the "volume of influence" of the measurement, and how this depends on soil water velocity and thermal properties. We investigate this by analyzing the sensitivity of the method to small spatial variations in these quantities, using a similar perturbation method to that previously used to analyze the heat pulse method for measuring soil water content. We derive an explicit mathematical expression for the spatial weighting function for the heat pulse method of measuring soil water flux, and explain its physical significance.