A method for correcting measured coherence spectra for the effect of incoherent instrument noise has been developed and demonstrated. Coherence measurements are widely used in engineering and science to determine the extent to which two signals are alike. The signals may come from two different sources or from the same source at different times. The coherence of time- lagged signals from a single source is an excellent indication of the effective lifetime of the signal components as a function of their frequency. Unfortunately, incoherent instrument noise will bias the measurement to lower values and may lead the user of the data to false conclusions about the longevity of significant features.
The new method may be used whenever both the signal and noise power spectra are known and the noise is incoherent both with the signal and with itself at the applicable time delays. It provides a corrected coherence spectrum given the measured coherence and power spectra. For power-law signal spectra and instrumental white noise, the correction formula takes a particularly simple and explicit form. Since many geophysical signals exhibit power-law behavior and most instrument noise spectra approach white noise, the simplified form should be widely applicable in meteorology, oceanography, geology, and planetary geophysics.
The derivation of the method and the resulting formulas for both the general case and the power-law/white-noise case may be found in the Appendix to "The Coherence Time of Mid-Tropospheric Wind Features as a Function of Vertical Scale From 300 m to 2 Km", Journal of Applied Meteorology, Vol. 39, pp 2409-2420, December 2000.
This work was done by Francis J. Merceret of Kennedy Space Center.
Inquiries concerning rights for the commercial use of this invention should be addressed to the Technology Commercialization Office, Kennedy Space Center, (321) 867-8130. Refer to KSC-12267.