Thermocouple frequency response compensation leads to convergence of the surface renewal alpha calibration

Ramp-like shapes in the turbulent scalar trace are the signature of coherent structures, and their characteristics (i.e., amplitude and duration) are resolved via a structure-function model for use in the surface renewal flux calculation. The potential for surface renewal to provide inexpensive sensible heat flux measurements has not been fully realized because this method has required calibration against eddy covariance or other more expensive flux measurement techniques. The calibration factor alpha is ideally 0.5, but a broad range of values have been reported in the surface renewal literature. Although it has been hypothesized that the sensor size, and hence sensor frequency response characteristics, influence alpha, no effort has been previously made to compensate the thermocouple signal in surface renewal measurements. We evaluate methods for compensating the frequency response of a thermocouple in the time domain and the frequency domain, and we present a novel method for compensation in the lag domain (i.e., compensating the structure function directly). We evaluated the compensation procedure as it affects the resolution of ramp characteristics at both the smallest and the second smallest scales of ramp-like turbulent shapes. The surface renewal sensible heat flux estimates from the compensated robust thermocouples (76 μm diameter wire) agree well with the estimates from the compensated fragile thermocouples (13 μm diameter). Using both the data collected for the present experiment and a meta-analysis of data in the surface renewal literature, we correct the surface renewal estimates for thermocouple frequency response characteristics to obtain alpha calibrations that converge to close to the predicted value of 0.5. We conclude that the frequency response characteristics of the thermocouple are the prevailing influence on the alpha calibrations reported in the literature.