3.2 Tidal constituents

The observed tide is represented as a sum of harmonic constituents, each with its own amplitude and phase. The number of constituents, and their corresponding amplitudes and phases, are specific to a given location. The primary tidal constituents fall into three categories: semidiurnal, with periods of approximately half a day; diurnal, with periods of approximately a day; and long-period, with periods of two weeks, to years. The tidal analyses for Monterey Bay and ES are based on record lengths of a year or less. Consequently, it is not yet possible to resolve the longer period constituents. The M2, K1, O1, S2, P1, and N2 constituents (amplitudes in descending order), are the six most important constituents for Monterey Bay. In addition to these, at least 15 other constituents have been identified in tidal records collected in Monterey Bay by the National Ocean Service and recorded in the Tide Tables they have produced.

To obtain data suitable for predicting tidal height and phase, water levels in ES were measured from June 2002 to August 2003. Our 120-day records for three stations in ES were of sufficient length to separate most of the constituents listed in Table A1, which is included in the Appendix A, following the references. However, the tidal amplitudes obtained from these analyses were not directly comparable to those obtained earlier by the National Ocean Service from year-long observations in 1976, because the variability was distributed among slightly different constituents and because the record lengths were different. The data acquired by NOS is included in Table A2 of the Appendix A. Our record lengths varied from 1 to 14 months (Table A1). Although the constituent amplitudes around the diurnal (1 cycle per day [cpd]) and semidiurnal (2 cpd) frequencies for the MB and ES

## A 30-Year History of the Tides and Currents in Elkhorn Slough, California DOI: http://dx.doi.org/10.5772/intechopen.88671

stations are similar, the appearance of the higher frequency constituents between 2.8 and 3.9 cpd inside ES clearly distinguishes its tidal response from that of Monterey Bay. In addition, overtides were found with periods of 8.3, 6.2, and 4.1 h that correspond to the M3, M4, and M6 constituents, respectively. The 8.3-h M3 constituent represents one of the lunar terdiurnal components. Because its period is close to the period of the terdiurnal SO3 compound tide (8.19 vs. 8.28 h), the SO3 constituent could not be clearly separated from the M3 tide.

A comparison of the tidal constituents determined from our water level measurements at six locations is shown in Figure 5 and illustrates the differing character of the tide from MB to the head of ES: Monterey Harbor (a), representative of Monterey Bay, Moss Landing Harbor (b), the H1B (c), the entrance to Parsons Slough (d), Kirby Park (e), and Hudson's Landing (f). Log10 of the amplitude in mm is plotted vs. each constituent frequency in cpd. A similar constituent analysis for Monterey Bay was performed 25 years earlier by the National Ocean Service

#### Figure 5.

Log10 tidal constituent amplitude vs. frequency for five locations in Elkhorn Slough (Figure 1): (a) Monterey Bay (NOS, 1 year); (b) Moss Landing Harbor at MLML Small Boat Dock; (c) Lower Elkhorn Slough 200 m east of Highway 1 Bridge; (d) Railroad Trestle at the entrance to Parsons Slough; (e) Kirby Park; (f) and Hudson Landing.

(NOS) from a 1-year record acquired in 1976 in Monterey Harbor and comparisons with our analysis are constructive.

Our least squares regression results which are summarized in Table A1 of the Appendix A show large amplitudes for the dominant tidal constituents (M2, K1, O1, S2, P1, and N2) at the ES stations indicated above similar to those obtained earlier by NOS (Table A2). Our results in Moss Landing Harbor show insignificant values for the overtides (M3, M4, and M6) and the compound tides (MK3, 2MK3, MN4, and MS4). The amplitudes of these constituents increase significantly as we move landward, consistent with similar increases in these constituents obtained by NOS, and consistent with the increasing influence of frictional effects as the bottom depth decreases moving inland. Of particular note, we find a �25% increase in the 2002 data compared to the 1976 data, suggesting that morphological changes in ES have modified its tidal response noticeably over a period as short as 25 years! In addition, we now include the set of tidal constituents inside the ESNERR South Marsh restoration area in Table A1. They demonstrate that South Marsh is not tidally choked (i.e., providing insufficient time for the unrestricted inflow and outflow of the tidal transport over a complete tidal cycle) despite being limited by the 50-m-wide, 4–6-m-deep entrance under the Southern Pacific Railroad Trestle.

Tidal phase differences in ES were estimated by Wong [13] by comparing the times of high and low water at several locations consistent with tidal propagation up the Slough. Between a point 200 m east of the H1B, and 5 km up the Slough near the Parsons Slough entrance, Wong found, on average, that high water occurred 48 min later at Parsons Slough but low water occurred only 18 min later. The large difference between the HHW and LLW phases at these two locations, emphasizes the tidal asymmetry in ES. Wong also compared these values with the NOS tide predictions from 1976 and found that the time for the tide to propagate over this portion of the Slough had increased significantly.

Based on shallow water wave theory, the expected phase speed, c(x,t), for the incoming tide where tidal elevation and water depth are of the same order, is

$$\mathcal{L}(\mathbf{x},t) = \left[\mathbf{g}(h(\mathbf{x}) + \eta(\mathbf{x},t))\right]^{\natural\_2},\tag{1}$$

where h is the water depth, η is the tidal elevation, and g is the acceleration of gravity. The tide propagates at 6.3 m/s for a water depth of 4 m with a free surface elevation η(x,t) of zero. Integrating c(x,t), the travel times along the Slough from the H1B to Hudson's Landing using channel depths for the diurnal mean tide (high = 1.7 m, low = 0.0 m) are 24 and 31 min. These times change to 23 and 37 min for the greatest observed tidal range (2.0 to �0.6 m).

#### 3.3 Tidal currents

The first measurements of the tidal currents were made in 1970 by Clark [14] in the main channel on the harbor side of the Highway 1 Bridge. We note that since this record was not referenced to a standard tidal datum, the exact depth of these observations is not known but they were acquired at "mid-depth," clearly well above the bottom boundary layer. Clark made a total of five time series measurements with durations of one to two tidal days using a mechanical current meter. A 2-day sample is shown in the first (i.e., top) panel of Figure 6, where maximum currents of almost 40 cm/s were observed during the 0.75 m flood tide and 60 cm/s on the following 1.75 m ebb tide. Ebb domination is apparent as the flood tide lasted almost twice as long as the ebb. Clark observed that the tidal currents in ES were approximately standing wave in character because the tidal heights and currents were approximately 90° out of phase.
