The Effect of Nonlinear Dynamic Sensor Response on Measured Means

Abstract

Few sensors have perfectly linear dynamic response. Because the atmosphere is inherently turbulent, nonlinear sensor response can lead to errors in measured means. We discuss a technique for estimating this error for both first- and second-order systems involving only a single input and output. We find that the error has two distinct sources: one due to nonlinearity of the response, the other due to nonlinearity of the calibration. We then apply the technique developed here to three examples: a Pilot tube, which we approximate by a first-order dynamic equation, and a thrust anemometer and the CSIRO liquid water probe, which are both considered to be second-order systems. The Pilot tube, and to some extent, the thrust anemometer overestimate the mean in a way similar to a cup anemometer, which has been discussed previously. In particular, the square of the relative turbulence intensity determines the upper limit of this positive bias. We also show that the CSIRO probe may, in some situations, have a significant negative bias.