10.2: Characteristics of Tides
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Tides are measured by a variety of gauges that continuously monitor the sea surface height. The tide is described by a plot of the water surface height as a function of time, called a “tidal curve” (Fig. 10-6). The tidal curves in Figure 10-6 show that tidal motions are similar to the progressive waves described in Chapter 9. In some locations, the tidal curve resembles a simple progressive wave. In other locations, it resembles the complex waveforms produced when waves of different wave periods and wave heights interfere. Tidal curves are, in fact, the net result of several tide waves of different periods, as explained in the next section.
The most important characteristics of a tidal curve are the times and relative elevations of high tide and low tide, and the tidal range, which is the difference between the height of the high tide and that of the low tide (Fig. 10-6). Because the tide is a wave, the tidal range is an expression of the tide wave height.
Diurnal, Semidiurnal, and Mixed Tides
Tides are classified into three general types based on the number and relative heights of the tides each day at a given location along a coast. Diurnal tides (or daily tides) have one high tide and one low tide in each tidal day, which equals approximately 24 h 49 min (Fig. 10-6a). The next section explains why the tidal day is 49 min longer than the solar day. Semidiurnal tides (or semidaily tides) have two high and two low tides each tidal day, and thus a period of 12 h 24½ min. For pure semidiurnal tides, the two high tides (and the two low tides) each day are equal in height (Fig. 10-6b).
Mixed tides also have two high tides and two low tides each tidal day, but the heights of the two high tides (and/or of the two low tides) in each tidal day are different (Fig. 10-6c). Mixed tides have a higher high water (HHW) and a lower high water (LHW), as well as a higher low water (HLW) and a lower low water (LLW), each day. Figure 10-6c shows that the relationship of these four daily extreme levels varies greatly among different locations.
Mixed tides are the most common. On the North American continent, tides are mixed along the entire Pacific Coast, on the Atlantic Coast of Canada north of Nova Scotia, in the Caribbean Sea, and in parts of the Gulf of America (Golfo de México) (Fig. 10-7). Tides are primarily semidiurnal (or mixed) along the Atlantic Coast of the U.S. and southern Canada, and are diurnal only in certain parts of the Gulf (Fig. 10-7). However, pure semidiurnal and diurnal tides are rare. All tides have some mixed characteristics, but the classifications are useful to mariners and to illustrate the complex tidal motions. In some locations, tides may change in character during the tidal month. For example, they may be semidiurnal for one part of the month and mixed for another part.
Spring and Neap Tides
If we look at tide records for various locations over a period of a month, we see that the daily tidal range varies during the month (Fig. 10-8). This variation occurs at all locations, regardless of whether tides are diurnal, semidiurnal, or mixed. Although the variations are often complex, the daily tidal range generally reaches a maximum twice during each lunar month (29½ days). The tidal range thus oscillates back and forth twice each lunar month. Tides with the largest tidal range during the month are spring tides. Tides with the smallest tidal range are neap tides. Two sets of spring tides and two sets of neap tides occur each lunar month.
If we look at tide records for an entire year or for several years, we find that the tidal range varies during the year and between years. However, these variations are much less than the variation between spring and neap tidal ranges during the lunar month.






