Feasibility study of a Bottom-mounted Sonic Probe Used to Determine Water Wave Amplitude and Frequency Spectrum
Authors: Johnson K.R. , Weingarten Wayne E. , Oswald James A. 
Published: October 2008

ABSTRACT
The purpose of this research is to determine whether a sonic probe can be used to sample the height of a wave in a large body of water to reconstruct its profile and obtain its frequency spectrum. Knowledge of the characteristics of such waves can be helpful in the study of shoreline erosion and. the design of docks, breakwaters, and other coastal structures. Field tests were conducted in the Portage Waterway on the Upper Peninsula of Michigan. The project was supported by the U.S. Army Corps of Engineers, Lake Survey, Detroit, Michigan.
Unfortunately, actual water waves do not behave or look like the classical trochoid shaped wave. However, since a two-dimensional profile can be mathematically described as a nonperiodic, real-valued function of time, a useful mathematical model of an actual wave is in terms of its frequency spectrum. Thus, using sampling techniques and the magnitude of the wave train at predetermined instants of time, the frequency spectrum F(w) can be constructed.
The impedance discontinuity at a water-air interface yields a very large theoretical reflection coefficient indicating that a strong, sharply defined echo from a water-air interface would make the use of a bottom-mounted sonic probe possible. Several problems, however, arise. First, in a bottom-mounted system, reflection will be strong at the water surface but, except for small scattering surface irregularities, the reflected energy will be directed back to the point of origin only for brief instants at the crest and trough of each wave. The strength of the scattered return depends on surface conditions and the illuminated spot size; conflictingly, a larger spot size implies poorer resolution.
Second, the major "noise" component is introduced by signal reflection from suspended solids and entrained air in the water. In general, the shorter the wavelength, the smaller the particle size that will cause scatter. However, the attenuation of the water also increases rapidly with frequency. In addition, the rep rate must be high enough to provide the redundancy to compensate for missing echo pulses. A compromise of these factors is required in selecting the operating frequency.
Third, pulse duration is also a critical factor. An illuminating pulse may have a minimal reflection during the first part of the pulse duration and a much larger reflection during the later part of the pulse due to a change in the surface configuration during the pulse duration.
The 5-degree transducer used in this investigation Performed very well and, for the water depth and wave sizes encountered during the tests, represented a satisfactory compromise between a desirable directivity end a minimum loss of information on data retrieval. It appears, by comparison with the information currently being obtained-using a bellows wave gage, that the sonic probe should produce more detailed information relative to wave profile. In addition, no calibration is necessary for a sonic probe. Operating voltages and power consumption are such that the system can operate on one or possibly two 12 volt storage batteries and not draw more than 250 ma.