Harmonic and nonlinear function analysis of tree response to meteorological forcings

In 2004 a team of eight students made a suite of circumference measurements for six sweetgum trees at an Atlanta field site. Environmental observations were made at two locations and included tree circumference, cloud cover, air temperature, relative humidity, soil moisture, insolation, rainfall rate, soil moisture and temperature profiles to 0.4 m, and occasional radiative ground and tree temperatures. High soil moisture conditions existed for the three trees near the stream location during much of the five-week measurement period due to the rainfall surplus experienced in the first half of this period. Five weeks of data was measured in three shifts per day, with two observers working per shift and the supervisors working their shift plus extra hours in the daytime. Automated measurements were made for the first two weeks at an hourly interval, and afterwards at a one-minute interval. In the absence of interferences, a tree is expected to expand and contract very precisely at the diurnal rate (i.e., 24-hour period). The goal of the study was to verify this expected 24-hour cycle of tree expansion at night and contraction during the daytime as a result of transpiration of water from the trees. Since the most logical technique to identify cycles in time series data is harmonic analysis, Fourier analysis was applied to the tree circumference data to find the 24-hour period. Since a diurnal signal was not very evident in the first attempts at harmonic analysis, it was clear that some environmental interference was manifesting itself in the data. It was decided that a systematic application of the analysis would need to be devised. Fast Fourier transform decompositions (FFTs) with periods of 64, 128, and 256 hours were run in adjacent blocks from the beginning to end of the time series for each tree in attempt to find the 24-hour cycles in the data. Some of the 64-hour FFTs crossed precipitation events, some of them were between precipitation events, and others were from data far away from precipitation events. Most of the 128-hour FFTs crossed one or more precipitation events. The 256-hour FFTs crossed multiple precipitation events. Significant rainfall events which occurred at peak contraction time (between 1600-1900 hr in the summer) produced spectra with a strong signal at 2.3E-5 Hz. Some of these spectra also contain a strong signal at 1.16E-5 Hz. In the time domain these signals correspond to 12- and 24-hour periods of oscillation, respectively. Since there was such a strong 12-hour signature in many of the resulting spectra, the time series data were searched for an explanation. When the time series data were very carefully examined, it became clear that there was interference in the form of either a smaller than expected contraction during the afternoon rainfall events or even a minor expansion within a contraction interval for some of the trees during the larger rainfall events. Interference due to rainfall events is postulated to explain the strong 12-hour signature seen in the spectra for FFTs that include the significant rainfall events. In addition to the spectral results, mean values of tree circumference were found to decay in a manner similar to the decrease in observed subsurface soil moisture for periods up to about 48 hours after each of the stronger rainfall events. These relaxation phenomena will be discussed in the poster. Hopefully by the time of the conference, the poster will include the application of discrete Fourier transforms to the raw data and use of running averages to identify the range of amplitude swings in the circumference measurements.