"The World Is Our Laboratory"
The data presented here are preliminary. Technical problems have prevented achieving the full accuracy possible with phase-sensitive detection. These problems are associated with "phase slips" of one cycle of the 200 kHz carrier and may be associated wi th surface reflections. Comparison with measurements over the same path using a commercially available ultrasonic velocity meter agree rather well with our measurements, though there is an indication of a systematic offset in our data. However, the pres ent results at reduced resolution still indicate a number of interesting features.
The variation of the current speed over a tidal cycle shows a peculiar "flat-top" structure during maximum flow in one direction, but not the other. This may indicate non-linearity of the flow through the Slough due to the onset of turbulence. Turbulenc e increasing with increasing current velocity is clearly visible in our data.
On the most rapid time scale, sampling three times per second, we observe the effect of wakes from passing boats in the time series. We are exploring recognition of these signals using wavelet transforms.
We would like to acknowledge the support and advice of Dean James Kelley, College of Science, SFSU; Professor Gerald Fisher, chair of the Physics and Astronomy Dept., SFSU; Tim Hollibaugh, Director, Romberg Tiburon Center; and Derek Sciable, Brad Mellema, Deirdre Patterson, Ralph Larson, and Robert Johnson
Our method is based upon determining the travel time of an acoustic signal over the known distance between a transmitting and a receiving transducer. The transmissions are bi-directional, so that the current velocity can be determined by calculating the r elative speed of sound in opposite directions.
The signal (see FIGURE 4) consists of an ultrasonic sinusoidal carrier which is digitally phase-shift modulated. The modulation consists of a pseudo-random binary sequence. Highly accurate relative travel time measurements are accomplished by performing a cross-correlation between the received signals for the two opposite directions. The cross-correlation calculation produces a result that varies from -1 to 1 as a function of the difference in travel time between the two directions (we call this the offse t time). In principle, finding the offset time that corresponds to the maximum value of the cross-correlation leads directly to the relative speed of sound in the two directions, and hence, to the line velocity (the component of current velocity along the line of direction between the two transducers).
A sample output of the cross-correlation is shown in FIGURE 5. Note the sinusoidal structure within a Gaussian envelope centered on the offset time corresponding to the correct relative speed of sound (shown in detail in the enlarged view).
We apply a curve-fitting algorithm that finds the offset time corresponding to the maximum of the Gaussian envelope. This is the time that leads to the value of relative speed of sound, and hence to the line velocity.
In FIGURE 6 we show all of our usable current data since our measurements began in November of 1995. The gaps in the data are due to various glitches in the data collection, as well as hurricane-strength winds which led to parting of a signal cable. In F IGURE 6A, we show a close up of several days worth of continuous data.
An existing UVM (Ultrasonic Velocity Meter) has obtained measurements of the current speed at Three-Mile Slough. Our data are still preliminary and of reduced precision and reliability, due to some unresolved technical signal-processing problems. Howeve r, we have compared the USGS data with this preliminary data, averaged over intervals of about 15 minutes. The USGS data also represent 15 minute averages. The agreement is good in most respects (see FIGURE 7). One rather surprising feature of the diurn al tide cycle is the "flat-top" during the stronger of the two daily tidal flows in the direction from the San Joaquin River towards the Sacramento River.
Our data show a systematic offset towards negative values compared with the USGS data (see FIGURE 8). Such a shift affects the net flow integrated over a tidal cycle, which is perhaps the most important result to be obtained from these measurements, and the most difficult to determine reliably. However, we have not yet carried out careful determinations of important factors such as a possible difference in the south-to-north and north-to-south path lengths. We do not consider this difference significan t at present.
Rapid sampling of the current velocity reveals structure on every time scale that we have investigated. Wakes from boats make a major contribution at frequencies above about 0.1 Hz. We hope to develop techniques for isolating, classifying and quantifyin g these signals.
One of the characteristics of these signals is the part of the frequency spectrum which they occupy. However, Fourier analysis of the signal only identifies the frequency components at the price of losing all information about the time at which the signa l was detected. The technique of wavelet analysis aims at optimally extracting the time of occurrence of a signal of a definite shape.
The wavelet technique represents a signal as a linear combination of orthogonal packet-like functions (the wavelets). There are many different sets of orthogonal wavelets to choose from. The coefficients of the terms in the expansion are determined as in Fourier analysis, using the orthogonality property of the wavelets. Various kinds of filtering can then be carried out by modifying the coefficients, then inverting the transformation.
In analyzing our data we have used the WaveLab( toolbox for Matlab, provided by the Donoho group at Stanford University. We used wavelets called coiflets, shown in FIGURE 10. We show the first three scalings of the wavelet. Scale 0 consists of a single function covering the entire range of the signal, scale 1 consists of two functions, each covering 1/2 the range, scale 3 consists of four functions covering 1/4 the range, and so on.