Statistical procedures for evaluating group and phase velocities of scalar quantities measured in an array

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Any scalar quantity measured in a two- or three-dimensional array may be visualized as a map of isopleths drifting and changing shape. Appropriate correlation functions may be used to represent the mean slope and orientation of closed isopleths as an ellipsoid in space and time coordinates. The group velocity is evaluated for the velocity of the center of ellipsoidal contours. This is equivalent to determining the displacement vector for two sensors in order to obtain a maximum correlation for a fixed time lag. It is shown that this procedure is preferable to the frequently used method involving the ratio of a fixed sensor separation to the time required for maximum correlation. Also, phase velocities are evaluated from the velocity of the center of ellipsoidal correlation contours obtained from co-spectra and quadrature spectra from selected frequency bands. The power spectra can be partitioned as the sum of spectral estimates arising from a drifting pattern of isopleths and random changes in that pattern. Data obtained from single-component Gill propellor anemometers positioned 2 m above the ground in a jack-pine forest are used to illustrate the procedures. Such information provides a basis for gaining further insight into the mechanisms of transport phenomena within a forest. © 1989.

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Agricultural and Forest Meteorology