Sensitivity analyses of the theoretical equations used in point velocity probe (PVP) data interpretation

Point velocity probes (PVPs) are dedicated, relatively low-cost instruments for measuring groundwater speed and direction in non-cohesive, unconsolidated porous media aquifers. They have been used to evaluate groundwater velocity in groundwater treatment zones, glacial outwash aquifers, and within streambanks to assist with the assessment of groundwater-surfaced water exchanges. Empirical evidence of acceptable levels of uncertainty for these applications has come from both laboratory and field trials. This work extends previous assessments of the method by examining the inherent uncertainties arising from the equations used to interpret PVP datasets. PVPs operate by sensing tracer movement on the probe surface, producing apparent velocities from two detectors. Sensitivity equations were developed for the estimation of groundwater speed, v∞, and flow direction, α, as a function of the apparent velocities of water on the probe surface and the α angle itself. The resulting estimations of measurement uncertainty, which are inherent limitations of the method, apply to idealized, homogeneous porous media, which on the local scale of a PVP measurement may be approached. This work does not address experimental sources of error that may arise from the presence of cohesive sediments that prevent collapse around the probe, the effects of centimeter-scale aquifer heterogeneities, or other complications related to borehole integrity or operator error, which could greatly exceed the inherent sources of error. However, the findings reported here have been shown to be in agreement with the previous empirical work. On this basis, properly installed and functioning PVPs should be expected to produce estimates of groundwater speed with uncertainties less than ±15%, with the most accurate values of groundwater speed expected when horizontal flow is incident on the probe surface at about 50° from the active injection port. Directions can be measured with uncertainties less than 15° with the most accurate measurements occurring when the flow angles are relatively low - on the order of 20°. At still lower flow angles, quantitation may suffer due to experimental limitations related to tracer delivery. However, useful qualitative assessments of α may still be possible under these conditions.