Any method of measuring soil water fluxes implicitly assumes that the flux is spatially uniform over some soil volume around the measuring instrument. When the flux may not be uniform it is important to know what is the "volume of influence" of the instrument. In a typical heat pulse method for measuring soil water flux, a pulse of heat is emitted by a thin wire and temperature signals are received by detectors upstream and downstream of the emitter. We analyse the sensitivity of the method to small spatial variations in soil water content, thermal conductivity and water flux. We assume that each of these quantities is approximately uniform, with departures from uniformity being expressed as small perturbations. We then perform a rigorous perturbation expansion on the advection diffusion equation to derive an exact analytical expression for the spatial sensitivity of the method to variations in each of the above three parameters.
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