Free surface oscillations and tides of Lakes Michigan and Superior

From records of water levels at nineteen shoreline stations on Lakes Michigan, Huron and Superior (figure 1), we have prepared power spectra from 95 station-data sets and 128 spectra of interstation coherence and phase difference. Those spectra have been used to (1) identify the first five free gravitational, barotropic modes (surface seiches) of the three basins; (ii) estimate the corresponding seiche frequencies, Lake Huron table 2, Lake Michigan tables 3 and 4, Lake Superior table 7; (iii) determine, for some modes, the phase progression around the basin imposed by the Earth's rotation; and (iv) speculate on the structure of other oscillations, including diurnal and semidiurnal tides. Because the number of recording stations was limited, the phase progression of individual modes could only be determined with confidence for the first and second in Lake Michigan (figure 13), for the first, second, third, and eighth mode in Lake Superior (figures 22 and 32b) and for the semidiurnal tide in both basins (figure 31). Except for the Superior semidiurnal tide, which progresses clockwise, all the modes illustrated in figures 13 and 22 and the Lake Michigan semidiurnal tide conform to a positive amphidromic pattern - counterclockwise progression. Possible reasons for the difference in tidal behaviour in the two basins are discussed in section 4 and by Hamblin (1976). There is very close agreement between the observed frequency and the phase progression of the first three and eighth Superior modes and results from the two dimensional computations of Platzman (1972) and Rao & Schwab (1976). Because some of the level recorders were not protected from local harbour oscillations in the period range below 2 h, and because some of the data sets listed in tables 1 and 6 were available only in the form of hourly readings, spectra from some stations exhibited contamination by aliasing. Section 2 (b) is devoted to a discussion of: (i) the nature of this spectral contamination (see figure 4); (ii) its extent in our examples; and (iii) attempts to minimize its influence through identification of the principal aliases and exploitation of the discovery that useful information can still be extracted from interstation coherence and phase spectra, even if the power spectra from one or both stations of the pair are badly aliased. With aliases identified or absent, the remaining spectral and interstation coherence peaks correspond to free modes (and tides). In Lake Michigan the first three modes are the most strongly excited and are clearly identified as longitudinal seiches (section section 2 (c-f), 2(i)). A transverse (E-W) seiche is also strongly excited, probably in the form of a negative amphidrome, in the south-central reach of the basin (for example T1 in figure 6), but the structure and identity of oscillations corresponding to spectral peaks at higher frequencies cannot yet be resolved. For Green Bay, a 192 km (120 mile) long gulf opening into Lake Michigan, a remarkable double resonance is described in section 2 (g). The Bay responds as a viscously damped system driven by two forcing oscillations - the semidiurnal tide and the first mode of the main Michigan basin - at respective frequencies 1.93 and 2.67 cycles per day (c/d), one on each side of the natural frequency of the Bay-Lake system, 2.2 c/d (figures 9 and 10). In the Superior basin, topographically more complex than Michigan, the first three longitudinal modes are also the most conspicuous, but some modes above the third are also strongly excited. Of these, the fourth, fifth, and eighth modes can be identified through comparison with Rao & Schwab's (1976) numerical determinations. The most striking feature of the eighth mode, often strongly excited, is a transverse (N-S) oscillation of the eastern half of the basin as a negative amphidrome (figure 32b). In spite of prior removal of a linear trend from the input data, the spectra exhibit a steep rise in power as the low-frequency end is approached, where interpretation is therefore difficult. However, examination of the frequency range below 4 c/d, in section section 2 (h) and 3 (e) and in figure 11, establishes the following points: (i) for reasons discussed in the text, the semidiurnal tidal peak covers a narrower frequency range than peaks corresponding to the seiche modes; (ii) there is minor but persistent evidence of a co-oscillation of the main Michigan basin and Green Bay; (iii) diurnal oscillations arising from tidal and meterorological forcing, section 4, are generated more strongly in the Superior than in the Michigan basin; (iv) no spectral peaks are unambiguously identified as surface manifestations of internal waves known to be present, for example in the near-inertial frequency range 1.3-1.4 c/d; and (v) there is a small but significant rise in power near 0.35 c/d in spectra from both basins. Possible but not yet verified explanations of this rise are: meteorological forcing; excitation of a rotational mode (Rao & Schwab 1976); or both. For Lake Michigan a possible further explanation is provided by excitation of the lowest gravitational mode of the combined Michigan-Huron basin, seen in the currents of the connecting straits (figure 12).