Two versions of the band-pass covariance technique were applied to the turbulence data collected during daytime with a simple and portable measurement system over the sparse grasslands of the Tibetan Plateau. The coherency spectra between the temperature and the specific humidity, which is a spectral counterpart of the correlation coefficient, were used as a dynamic indicator of the energy-containing ranges as well as that of the sensor attenuation at higher frequencies. The comparison with independent measurements by the eddy covariance method showed that the original version of the band-pass covariance technique occasionally fails. This indicates breakdowns of the similarity between the temperature and the water vapor, especially in the lowest-frequency regions. On the other hand, the latent heat flux computed with the advanced version exhibited adequate agreement with the eddy covariance method. This paper demonstrates that the current implementation of the advanced version with the embedded self-calibration procedure provides a robust method of frequency extrapolation in scalar flux measurements under unstable conditions.